--- /srv/rebuilderd/tmp/rebuilderdOjsLbX/inputs/spooles-doc_2.2-16_all.deb +++ /srv/rebuilderd/tmp/rebuilderdOjsLbX/out/spooles-doc_2.2-16_all.deb ├── file list │ @@ -1,3 +1,3 @@ │ -rw-r--r-- 0 0 0 4 2026-01-06 20:05:00.000000 debian-binary │ --rw-r--r-- 0 0 0 1956 2026-01-06 20:05:00.000000 control.tar.xz │ --rw-r--r-- 0 0 0 8071052 2026-01-06 20:05:00.000000 data.tar.xz │ +-rw-r--r-- 0 0 0 1960 2026-01-06 20:05:00.000000 control.tar.xz │ +-rw-r--r-- 0 0 0 8097208 2026-01-06 20:05:00.000000 data.tar.xz ├── control.tar.xz │ ├── control.tar │ │ ├── ./control │ │ │ @@ -1,13 +1,13 @@ │ │ │ Package: spooles-doc │ │ │ Source: spooles │ │ │ Version: 2.2-16 │ │ │ Architecture: all │ │ │ Maintainer: Debian Science Maintainers │ │ │ -Installed-Size: 8167 │ │ │ +Installed-Size: 8184 │ │ │ Suggests: libspooles2.2-dev │ │ │ Section: doc │ │ │ Priority: optional │ │ │ Multi-Arch: foreign │ │ │ Homepage: https://www.netlib.org/linalg/spooles/ │ │ │ Description: SPOOLES numerical simulation pre- and post-processor documentation │ │ │ SPOOLES is a library for solving sparse real and complex linear systems of │ │ ├── ./md5sums │ │ │ ├── ./md5sums │ │ │ │┄ Files differ ├── data.tar.xz │ ├── data.tar │ │ ├── file list │ │ │ @@ -1,56 +1,56 @@ │ │ │ drwxr-xr-x 0 root (0) root (0) 0 2026-01-06 20:05:00.000000 ./ │ │ │ drwxr-xr-x 0 root (0) root (0) 0 2026-01-06 20:05:00.000000 ./usr/ │ │ │ drwxr-xr-x 0 root (0) root (0) 0 2026-01-06 20:05:00.000000 ./usr/share/ │ │ │ drwxr-xr-x 0 root (0) root (0) 0 2026-01-06 20:05:00.000000 ./usr/share/doc/ │ │ │ drwxr-xr-x 0 root (0) root (0) 0 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/ │ │ │ --rw-r--r-- 0 root (0) root (0) 151661 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/A2.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 151985 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/A2.ps.gz │ │ │ -rw-r--r-- 0 root (0) root (0) 596035 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/ASHCRAFC.ps.gz │ │ │ --rw-r--r-- 0 root 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20:05:00.000000 ./usr/share/doc/spooles-doc/DenseMtx.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 107546 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/Drand.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 121595 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/EGraph.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 221002 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/ETree.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 254527 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/Eigen.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 179635 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/FrontMtx.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 275652 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/FrontTrees.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 184544 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/GPart.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root (0) 190155 2026-01-06 20:05:00.000000 ./usr/share/doc/spooles-doc/Graph.ps.gz │ │ │ +-rw-r--r-- 0 root (0) root 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Fl(double)f(*)i(A2_row)e(\()i │ │ │ │ (A2)g(*mtx,)e(int)i(irow)f(\))h(;)208 541 y Fm(This)27 │ │ │ │ b(metho)r(d)h(returns)f(a)g(p)r(oin)n(ter)g(to)h(the)g(leading)f │ │ │ │ (elemen)n(t)h(of)f(ro)n(w)g Fl(irow)p Fm(.)208 691 y │ │ │ │ Fh(Err)l(or)k(che)l(cking:)41 b Fm(If)29 b Fl(mtx)f Fm(or)g │ │ │ │ Fl(entries)e Fm(is)j Fl(NULL)p Fm(,)e(or)h(if)i Fl(irow)d │ │ │ │ Fm(is)i(not)f(in)i Fl([0,n1-1])p Fm(,)c(an)i(error)f(message)g(is)i │ │ │ │ (prin)n(ted)208 791 y(and)e(the)h(program)e(exits.)101 │ │ │ │ @@ -4902,17 +4913,17 @@ │ │ │ │ Fm(,)e Fl(ppReal)f Fm(or)i Fl(ppImag)e Fm(is)i Fl(NULL)p │ │ │ │ Fm(,)f(or)h(if)g(the)h(matrix)f(is)g(not)h(complex,)f(or)f(if)i │ │ │ │ Fl(irow)e Fm(is)h(not)h(in)208 5407 y Fl([0,n1-1])p Fm(,)c(or)j(if)h │ │ │ │ Fl(jcol)e Fm(is)h(not)h(in)g Fl([0,n2-1])p Fm(,)c(an)j(error)f(message) │ │ │ │ g(is)i(prin)n(ted)f(and)h(the)g(program)d(exits.)p eop │ │ │ │ end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fm(4)p 125 100 1266 4 v │ │ │ │ -1431 w 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+2656 100 V 101 390 a Fm(9.)42 b Fl(double)f(A2_twoNormOfRow)c(\()43 │ │ │ │ b(A2)g(*mtx,)e(int)i(irow)f(\))h(;)208 521 y Fm(This)27 │ │ │ │ b(metho)r(d)h(returns)f(the)h(t)n(w)n(o-norm)e(of)h(ro)n(w)g │ │ │ │ Fl(irow)f Fm(of)h(the)h(matrix.)208 652 y Fh(Err)l(or)d(che)l(cking:)36 │ │ │ │ b Fm(If)22 b Fl(mtx)f Fm(is)h Fl(NULL)p Fm(,)e(or)i Fl(irow)e │ │ │ │ Fm(is)i(not)g(in)g Fl([0,n1-1])p Fm(,)e(an)i(error)e(message)h(is)h │ │ │ │ (prin)n(ted)g(and)g(the)g(program)208 751 y(exits.)60 │ │ │ │ 914 y(10.)41 b Fl(double)g(A2_infinityNorm)o(OfR)o(ow)c(\()43 │ │ │ │ @@ -5157,17 +5168,17 @@ │ │ │ │ (coloff)f(\))i(;)208 5218 y Fm(This)27 b(metho)r(d)h(is)g(used)f(to)h │ │ │ │ (shift)g(the)g(base)f(of)h(the)f(en)n(tries)g(and)h(adjust)g │ │ │ │ (dimensions)f(of)g(the)h Fl(A2)f Fm(ob)5 b(ject.)208 │ │ │ │ 5407 y Fl(mtx\(0:n1-rowoff)o(-1,)o(0:)o(n2)o(-co)o(lo)o(ff-)o(1\))37 │ │ │ │ b(:=)43 b(mtx\(rowoff:n1-1)o(,co)o(lo)o(ff:)o(n2)o(-1)o(\))p │ │ │ │ eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict 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Fh(DRAFT)111 b Ff(Jan)n(uary)25 b(17,)i(2026)p │ │ │ │ +2616 100 V 1245 w Fm(9)60 390 y(23.)41 b Fl(void)g(A2_sub)h(\()h(A2)g │ │ │ │ (*mtxA,)e(A2)h(*mtxB)g(\))h(;)208 523 y Fm(This)27 b(metho)r(d)h │ │ │ │ (subtracts)e(en)n(tries)h(in)h(matrix)e Fl(mtxB)g Fm(from)h(en)n(tries) │ │ │ │ g(in)g(matrix)g Fl(mtxA)p Fm(.)f(Note,)h Fl(mtxA)f Fm(and)h │ │ │ │ Fl(mtxB)f Fm(need)208 622 y(not)34 b(b)r(e)h(of)g(the)f(same)g(size,)i │ │ │ │ (the)f(leading)f Fl(min\(mtxA->n1,mtxB)o(->)o(n1\))28 │ │ │ │ b Fm(ro)n(ws)33 b(and)h Fl(min\(mtxA->n2,mtx)o(B->)o(n2)o(\))208 │ │ │ │ 722 y Fm(columns)27 b(are)f(subtracted.)208 855 y Fh(Err)l(or)k(che)l │ │ │ │ @@ -5423,17 +5434,17 @@ │ │ │ │ (in)i(reading)208 5275 y(the)i(data,)f(the)h(v)-5 b(alue)27 │ │ │ │ b Fl(1)g Fm(is)h(returned.)36 b(If)28 b(an)g(IO)f(error)f(is)h(encoun)n │ │ │ │ (tered)g(from)g Fl(fread)p Fm(,)f(zero)g(is)i(returned.)208 │ │ │ │ 5407 y Fh(Err)l(or)i(che)l(cking:)38 b Fm(If)28 b Fl(mtx)f │ │ │ │ Fm(or)g Fl(fp)f Fm(are)h Fl(NULL)p 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Fm(,)d(closes)j(the)i(\014le)g(and)f(returns)g(the)h(v)-5 │ │ │ │ @@ -5510,17 +5521,17 @@ │ │ │ │ Fm(parameter)g(is)h(the)h(n)n(um)n(b)r(er)g(of)f(ro)n(ws.)307 │ │ │ │ 5144 y Fi(\210)42 b Fm(The)28 b Fl(ncol)e Fm(parameter)g(is)h(the)h(n)n │ │ │ │ (um)n(b)r(er)g(of)f(ro)n(ws.)307 5275 y Fi(\210)42 b │ │ │ │ Fm(The)28 b Fl(inc1)e Fm(parameter)g(is)h(the)h(ro)n(w)f(incremen)n(t.) │ │ │ │ 307 5407 y Fi(\210)42 b Fm(The)28 b Fl(inc2)e Fm(parameter)g(is)h(the)h │ │ │ │ (column)g(incremen)n(t.)p eop end │ │ │ │ %%Page: 11 11 │ │ │ │ -TeXDict begin 11 10 bop 83 100 1245 4 v 1411 100 a Fl(A2)26 │ │ │ │ -b Ff(:)37 b Fh(DRAFT)111 b Ff(Jan)n(uary)25 b(6,)i(2026)p │ │ │ │ -2574 100 V 1245 w Fm(11)307 390 y Fi(\210)42 b Fm(The)28 │ │ │ │ +TeXDict begin 11 10 bop 83 100 1224 4 v 1390 100 a Fl(A2)27 │ │ │ │ +b Ff(:)37 b Fh(DRAFT)110 b Ff(Jan)n(uary)25 b(17,)i(2026)p │ │ │ │ +2595 100 V 1224 w Fm(11)307 390 y Fi(\210)42 b Fm(The)28 │ │ │ │ b Fl(seed)e Fm(parameter)g(is)h(a)h(random)e(n)n(um)n(b)r(er)i(seed.) │ │ │ │ 101 573 y(2.)42 b Fl(test_QR)e(msglvl)h(msgFile)g(type)h(nrow)g(ncol)g │ │ │ │ (inc1)g(inc2)g(seed)208 706 y Fm(This)22 b(driv)n(er)g(program)e(tests) │ │ │ │ j(the)g Fl(A2)p 1376 706 27 4 v 30 w(QRreduce\(\))c Fm(and)k │ │ │ │ Fl(A2)p 2110 706 V 30 w(QRreduce2\(\))18 b Fm(metho)r(ds)23 │ │ │ │ b(whic)n(h)g(reduce)f Fk(A)h Fm(to)g Fk(QR)g Fm(via)208 │ │ │ │ 805 y(rank-1)g(and)i(rank-2)f(up)r(dates.)36 b(Use)25 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -20,15 +20,15 @@ │ │ │ │ │ • A2 IS REAL(mtx) is 1 if mtx has real entries and 0 otherwise. │ │ │ │ │ • A2 IS COMPLEX(mtx) is 1 if mtx has complex entries and 0 otherwise. │ │ │ │ │ TheA2 copyEntriesToVector()methodusesthefollowingconstants: A2 STRICT LOWER,A2 LOWER,A2 DIAGONAL, │ │ │ │ │ A2 UPPER, A2 STRICT UPPER, A2 ALL ENTRIES, A2 BY ROWS and A2 BY COLUMNS. │ │ │ │ │ 1.2 Prototypes and descriptions of A2 methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the A2 object. │ │ │ │ │ 1 │ │ │ │ │ - 2 A2 : DRAFT January 6, 2026 │ │ │ │ │ + 2 A2 : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ Asusual, there are four basic methods to support object creation, setting default fields, clearing any allocated │ │ │ │ │ data, and free’ing the object. │ │ │ │ │ 1. A2 * A2_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the A2 structure and then sets the default fields by a call to │ │ │ │ │ A2 setDefaultFields(). │ │ │ │ │ 2. void A2_setDefaultFields ( A2 *mtx ) ; │ │ │ │ │ @@ -56,15 +56,15 @@ │ │ │ │ │ 4. int A2_inc2 ( A2 *mtx ) ; │ │ │ │ │ This method returns the secondary increment, the stride in memory (with respect to real or complex │ │ │ │ │ entries) between adjacent entries in the same row. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 5. double * A2_entries ( A2 *mtx ) ; │ │ │ │ │ This method returns a pointer to the base address of the entries. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ - A2 : DRAFT January 6, 2026 3 │ │ │ │ │ + A2 : DRAFT January 17, 2026 3 │ │ │ │ │ 6. double * A2_row ( A2 *mtx, int irow ) ; │ │ │ │ │ This method returns a pointer to the leading element of row irow. │ │ │ │ │ Error checking: If mtx or entries is NULL, or if irow is not in [0,n1-1], an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ 7. double * A2_column ( A2 *mtx, int jcol ) ; │ │ │ │ │ This method returns a pointer to the leading element of column jcol. │ │ │ │ │ Error checking: If mtx or entries is NULL, or if jcol is not in [0,n2-1], an error message is printed │ │ │ │ │ @@ -93,15 +93,15 @@ │ │ │ │ │ or if jcol is not in [0,n2-1], an error message is printed and the program exits. │ │ │ │ │ 13. void A2_pointerToComplexEntry ( A2 *mtx, int irow, int jcol, │ │ │ │ │ double **ppReal, double **ppImag ) ; │ │ │ │ │ This method sets *ppReal to the pointer to the real part of the (irow,jcol) entry, and sets *ppImag │ │ │ │ │ to the pointer to the imaginary part of the (irow,jcol) entry. │ │ │ │ │ Error checking: If mtx, ppReal or ppImag is NULL, or if the matrix is not complex, or if irow is not in │ │ │ │ │ [0,n1-1], or if jcol is not in [0,n2-1], an error message is printed and the program exits. │ │ │ │ │ - 4 A2 : DRAFT January 6, 2026 │ │ │ │ │ + 4 A2 : DRAFT January 17, 2026 │ │ │ │ │ 1.2.3 Initialize methods │ │ │ │ │ 1. void A2_init ( A2 *mtx, int type, int n1, int n2, int inc1, int inc2, │ │ │ │ │ double *entries ) ; │ │ │ │ │ This is the basic initializer method. We require that mtx not be NULL, type be either SPOOLES REAL │ │ │ │ │ or SPOOLES COMPLEX, n1 and n2 both be positive, and both inc1 and inc2 both be positive and that │ │ │ │ │ one of them be equal to one. Also, we only initialize a full matrix, i.e., one of inc1 = 1 and inc2 = │ │ │ │ │ nrow or inc1 = ncol and inc2 = 1 must hold. │ │ │ │ │ @@ -134,15 +134,15 @@ │ │ │ │ │ Error checking: If A or workDV is NULL, or if msglvl > 0 and msgFile if NULL, an error message is │ │ │ │ │ printed and the program exits. │ │ │ │ │ 3. void A2_computeQ ( A2 *Q, A2 *A, DV *workDV, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method computes Q from the A = QR factorization computed in A2 QRreduce(). Note: A and Q │ │ │ │ │ must be column major. │ │ │ │ │ Error checking: If Q, A or workDV is NULL, or if msglvl > 0 and msgFile if NULL, an error message is │ │ │ │ │ printed and the program exits. │ │ │ │ │ - A2 : DRAFT January 6, 2026 5 │ │ │ │ │ + A2 : DRAFT January 17, 2026 5 │ │ │ │ │ 4. void A2_applyQT ( A2 *Y, A2 *A, A2 *X, DV *workDV, int msglvl, FILE *msgFile ) ; │ │ │ │ │ T H │ │ │ │ │ This method computes Y = Q X (if real) or Y = Q X (if complex), where Q is stored in Householder │ │ │ │ │ vectors inside A. We assume that A2 reduce() has been previously called with A as an argument. Since │ │ │ │ │ Y is computed column-by-column, X and Y can be the same A2 object. The workDV object is resized │ │ │ │ │ as necessary. Note: Y, A and X must be column major. │ │ │ │ │ Error checking: If Y, A, X or workDV is NULL, or if msglvl > 0 and msgFile if NULL, or if Y, A or X is │ │ │ │ │ @@ -174,15 +174,15 @@ │ │ │ │ │ This method returns the infinity-norm of column jcol of the matrix. │ │ │ │ │ Error checking: If mtx is NULL, or jcol is not in [0,n2-1], an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 8. double A2_oneNormOfRow ( A2 *mtx, int irow ) ; │ │ │ │ │ This method returns the one-norm of row irow of the matrix. │ │ │ │ │ Error checking: If mtx is NULL, or irow is not in [0,n1-1], an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - 6 A2 : DRAFT January 6, 2026 │ │ │ │ │ + 6 A2 : DRAFT January 17, 2026 │ │ │ │ │ 9. double A2_twoNormOfRow ( A2 *mtx, int irow ) ; │ │ │ │ │ This method returns the two-norm of row irow of the matrix. │ │ │ │ │ Error checking: If mtx is NULL, or irow is not in [0,n1-1], an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 10. double A2_infinityNormOfRow ( A2 *mtx, int irow ) ; │ │ │ │ │ This method returns the infinity-norm of row irow of the matrix. │ │ │ │ │ Error checking: If mtx is NULL, or irow is not in [0,n1-1], an error message is printed and the program │ │ │ │ │ @@ -213,15 +213,15 @@ │ │ │ │ │ 1.2.7 Utility methods │ │ │ │ │ 1. int A2_sizeOf ( A2 *mtx ) ; │ │ │ │ │ This method returns the number of bytes owned by this object. │ │ │ │ │ Error checking: If mtx is NULL an error message is printed and the program exits. │ │ │ │ │ 2. void A2_shiftBase ( A2 *mtx, int rowoff, int coloff ) ; │ │ │ │ │ This method is used to shift the base of the entries and adjust dimensions of the A2 object. │ │ │ │ │ mtx(0:n1-rowoff-1,0:n2-coloff-1) := mtx(rowoff:n1-1,coloff:n2-1) │ │ │ │ │ - A2 : DRAFT January 6, 2026 7 │ │ │ │ │ + A2 : DRAFT January 17, 2026 7 │ │ │ │ │ Error checking: If mtx is NULL an error message is printed and the program exits. │ │ │ │ │ 3. int A2_rowMajor ( A2 *mtx ) ; │ │ │ │ │ This method returns 1 if the storage is row major, otherwise it returns zero. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. int A2_columnMajor ( A2 *mtx ) ; │ │ │ │ │ This method returns 1 if the storage is column major, otherwise it returns zero. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ @@ -253,15 +253,15 @@ │ │ │ │ │ This method fills the colZV object with column jcol of the matrix. │ │ │ │ │ Error checking: If mtx or colZV are NULL, or if the matrix is not complex, or if jcol is not in [0,n2-1], │ │ │ │ │ an error message is printed and the program exits. │ │ │ │ │ 12. void A2_setRow ( A2 *mtx, double row[], int irow ) ; │ │ │ │ │ This method fills row irow of the matrix with the entries in the row[] vector. │ │ │ │ │ Error checking: If mtx, entries or row[] are NULL, or if irow is not in [0,n1-1], an error message is │ │ │ │ │ printed and the program exits. │ │ │ │ │ - 8 A2 : DRAFT January 6, 2026 │ │ │ │ │ + 8 A2 : DRAFT January 17, 2026 │ │ │ │ │ 13. void A2_setRowDV ( A2 *mtx, DV rowDV, int irow ) ; │ │ │ │ │ This method fills row irow of the matrix with the entries in the rowDV object. │ │ │ │ │ Error checking: If mtx or rowDV are NULL, or if the matrix is not real, or if irow is not in [0,n1-1], │ │ │ │ │ an error message is printed and the program exits. │ │ │ │ │ 14. void A2_setRowZV ( A2 *mtx, ZV rowZV, int irow ) ; │ │ │ │ │ This method fills row irow of the matrix with the entries in the rowZV object. │ │ │ │ │ Error checking: If mtx or rowZV are NULL, or if the matrix is not complex, or if irow is not in [0,n1-1], │ │ │ │ │ @@ -294,15 +294,15 @@ │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 22. void A2_copy ( A2 *mtxA, A2 *mtxB ) ; │ │ │ │ │ This method copies entries from matrix mtxB into matrix mtxA. Note, mtxA and mtxB need not be of │ │ │ │ │ the same size, the leading min(mtxA->n1,mtxB->n1)rows and min(mtxA->n2,mtxB->n2)columns are │ │ │ │ │ copied. │ │ │ │ │ Error checking: If mtxA or mtxB is NULL, or if the matrices are not of the same type, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ - A2 : DRAFT January 6, 2026 9 │ │ │ │ │ + A2 : DRAFT January 17, 2026 9 │ │ │ │ │ 23. void A2_sub ( A2 *mtxA, A2 *mtxB ) ; │ │ │ │ │ This method subtracts entries in matrix mtxB from entries in matrix mtxA. Note, mtxA and mtxB need │ │ │ │ │ not be of the same size, the leading min(mtxA->n1,mtxB->n1) rows and min(mtxA->n2,mtxB->n2) │ │ │ │ │ columns are subtracted. │ │ │ │ │ Error checking: If mtxA or mtxB is NULL, or if the matrices are not of the same type, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 24. void A2_swapRows ( A2 *mtx, int irow1, int irow2 ) ; │ │ │ │ │ @@ -335,15 +335,15 @@ │ │ │ │ │ This method reads a A2 object from a formatted file whose pointer is fp. If there are no errors in │ │ │ │ │ reading the data, the value 1 is returned. If an IO error is encountered from fscanf, zero is returned. │ │ │ │ │ Error checking: If mtx or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 3. int A2_readFromBinaryFile ( A2 *mtx, FILE *fp ) ; │ │ │ │ │ This method reads a A2 object from a binary file whose pointer is fp. If there are no errors in reading │ │ │ │ │ the data, the value 1 is returned. If an IO error is encountered from fread, zero is returned. │ │ │ │ │ Error checking: If mtx or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ - 10 A2 : DRAFT January 6, 2026 │ │ │ │ │ + 10 A2 : DRAFT January 17, 2026 │ │ │ │ │ 4. int A2_writeToFile ( A2 *mtx, char *fn ) ; │ │ │ │ │ This method writes a A2 object to a file. It tries to open the file and if it is successful, it then calls │ │ │ │ │ A2 writeFromFormattedFile() or A2 writeFromBinaryFile(), closes the file and returns the value │ │ │ │ │ returned from the called routine. │ │ │ │ │ Error checking: If mtx or fn are NULL, or if fn is not of the form *.a2f (for a formatted file) or *.a2b │ │ │ │ │ (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 5. int A2_writeToFormattedFile ( A2 *mtx, FILE *fp ) ; │ │ │ │ │ @@ -374,15 +374,15 @@ │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ • The nrow parameter is the number of rows. │ │ │ │ │ • The ncol parameter is the number of rows. │ │ │ │ │ • The inc1 parameter is the row increment. │ │ │ │ │ • The inc2 parameter is the column increment. │ │ │ │ │ - A2 : DRAFT January 6, 2026 11 │ │ │ │ │ + A2 : DRAFT January 17, 2026 11 │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ 2. test_QR msglvl msgFile type nrow ncol inc1 inc2 seed │ │ │ │ │ This driver program tests the A2 QRreduce()and A2 QRreduce2()methods which reduce A to QR via │ │ │ │ │ rank-1 and rank-2 updates. Use the script file do QR for testing. When msglvl > 1, the matrix A and │ │ │ │ │ matrices R1 and R2 (computed from A2 QRreduce()and A2 QRreduce2(),respectively) are printed to │ │ │ │ │ T T T T │ │ │ │ │ the message file. When the output file is loaded into matlab, the errors A A−R R and A A−R R │ │ ├── ./usr/share/doc/spooles-doc/AllInOne.ps.gz │ │ │ ├── AllInOne.ps │ │ │ │ @@ -12,15 +12,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o AllInOne.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2033 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -2704,16 +2704,18 @@ │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 46 /period put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 61 /equal put │ │ │ │ dup 65 /A put │ │ │ │ dup 66 /B put │ │ │ │ dup 67 /C put │ │ │ │ dup 68 /D put │ │ │ │ dup 71 /G put │ │ │ │ dup 74 /J put │ │ │ │ @@ -2921,199 +2923,207 @@ │ │ │ │ 66D4EBC86C0DF27B789D5597FE88BCDAD2925CFF60F5A8EA618FE867857D585A │ │ │ │ CE25A158AED63B8FE391030C518693AEC75AC0AADD0C11B0065E2ABCF51132F3 │ │ │ │ 82E3718B9A9FAAF727F2D8286177EE27BAD040C66D0D2D7C092B45D9330265B5 │ │ │ │ 6B5C8E29F71C9EF548BFA4BAFAB242B26455E4B7FC1882D68E408D25E6F58EC3 │ │ │ │ 046AAFC52C182BDCD36034FD58E8B379C9F2BD16FA6FBB8C455E36A1BEA8F803 │ │ │ │ 2AC069379392D74A6E8DD64AAC6FB5E7EE151EE99AF33B1D9E55C5C8D601EEB7 │ │ │ │ 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│ │ dup 74 /J put │ │ │ │ dup 76 /L put │ │ │ │ dup 83 /S put │ │ │ │ dup 97 /a put │ │ │ │ dup 101 /e put │ │ │ │ dup 103 /g put │ │ │ │ dup 105 /i put │ │ │ │ @@ -6087,147 +6099,157 @@ │ │ │ │ AEA5E1ACCDA7FB2DF05E9480936281484BC329F0B771775E73F7FD72FE3F45F0 │ │ │ │ 50ADBD03932B38F37A8F0A66B2F739EA3AC8811C8F514E68C5643E4AFF485C81 │ │ │ │ 88475A523D7FCCA5C8809BD49846C77795A38DC6406082000236A4D2628B5932 │ │ │ │ AB7916D44EC2210CB941B4C12515E844F0D26CDF0AEAD63BF1491BB50ED4D6D2 │ │ │ │ 739930E80E26E9B425C25033121899AD22102AE6868648BABB7D5985611C95E3 │ │ │ │ 5B8D365C7D034BA22E904A0ADB0132CE38288C127BBEA0825E600D18383A6854 │ │ │ │ EE28FD1B2F57AF704854AEECF985EEFAE0521DB38B0A7511C803CE8AE0D0BC02 │ │ │ │ -50744F806B8D771AEA2192F982AF1314015F8028B1AB87EE2246CC867DFC7133 │ │ │ │ -E569299A834A73B829CDFF321ADFD514B23ACD54308766504362A049DB8F6F39 │ │ │ │ -5B96266B00C684371EBCE56FAF7551D8630BF65E301408C0AE51D3F002F9E129 │ │ │ │ -10A59085B565C859EB1BC0746ED2B34BF09A2F9FBF45C3AC3146A0983092F578 │ │ │ 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(Linear)g(Systems)327 b Fu(3)0 390 y Ft(C)56 b Fp(allInOne.c)27 │ │ │ │ b Ft({)32 b(A)g(Serial)f Fq(LU)40 b Ft(Driv)m(er)33 b(Program)1941 │ │ │ │ b(39)0 598 y(D)52 b Fp(allInOne.c)27 b Ft({)32 b(A)g(Serial)f │ │ │ │ Fq(QR)h Ft(Driv)m(er)h(Program)1934 b(49)p eop end │ │ │ │ %%Page: 4 4 │ │ │ │ TeXDict begin 4 3 bop 0 100 a Fu(4)327 b Ft(SPOOLES)32 │ │ │ │ b(2.2)27 b Fs(|)g(Solving)g(Linear)g(Systems)p 2053 100 │ │ │ │ -1186 4 v 1379 w(Jan)n(uary)f(6,)h(2026)0 390 y Fr(1)135 │ │ │ │ +1145 4 v 1338 w(Jan)n(uary)e(17,)i(2026)0 390 y Fr(1)135 │ │ │ │ b(Ov)l(erview)0 598 y Fu(The)34 b Ft(SPOOLES)h Fu(soft)n(w)n(are)d │ │ │ │ (library)h(is)h(designed)g(to)g(solv)n(e)f(sparse)g(systems)h(of)g │ │ │ │ (linear)f(equations)h Fq(AX)40 b Fu(=)34 b Fq(Y)53 b │ │ │ │ Fu(for)34 b Fq(X)7 b Fu(,)0 698 y(where)20 b Fq(A)h Fu(is)f(full)h │ │ │ │ (rank)f(and)g Fq(X)27 b Fu(and)20 b Fq(Y)40 b Fu(are)19 │ │ │ │ b(dense)h(matrices.)34 b(The)21 b(matrix)f Fq(A)g Fu(can)g(b)r(e)h │ │ │ │ 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b(L)2629 373 y Fm(A)2666 │ │ │ │ 390 y Fu(T)2712 408 y(E)2758 390 y(X)h(do)r(cumen)n(tation)f(\014les)g │ │ │ │ (are)f(found)0 490 y(in)g(the)h Fp(DenseMtx/doc)15 b │ │ │ │ Fu(directory)-7 b(.)34 b(The)20 b(\014les)g(can)g(b)r(e)g(used)g(to)g │ │ │ │ (create)g(the)g Fp(DenseMtx)d Fu(ob)5 b(ject's)20 b(c)n(hapter)f(in)i │ │ │ │ @@ -8914,15 +8936,15 @@ │ │ │ │ Fq(LU)34 b Fu(and)24 b Fq(QR)h Fu(driv)n(er)0 1013 y(programs.)58 │ │ │ │ b(The)36 b Fp(MT/drivers)31 b Fu(and)k Fp(MPI/drivers)c │ │ │ │ Fu(directories)j(con)n(tain)h(the)h(m)n(ultithreaded)f(and)h(MPI)f │ │ │ │ Fq(LU)43 b Fu(driv)n(er)0 1112 y(programs.)p eop end │ │ │ │ %%Page: 6 6 │ │ │ │ TeXDict begin 6 5 bop 0 100 a Fu(6)327 b Ft(SPOOLES)32 │ │ │ │ b(2.2)27 b Fs(|)g(Solving)g(Linear)g(Systems)p 2053 100 │ │ │ │ -1186 4 v 1379 w(Jan)n(uary)f(6,)h(2026)0 390 y Fr(2)135 │ │ │ │ +1145 4 v 1338 w(Jan)n(uary)e(17,)i(2026)0 390 y Fr(2)135 │ │ │ │ b(Serial)46 b(Solution)f(of)g Fj(AX)e Fi(=)33 b Fj(Y)71 │ │ │ │ b Fr(using)45 b(an)g Fj(LU)56 b Fr(factorization)0 599 │ │ │ │ y Fu(The)27 b(user)g(has)g(some)g(represen)n(tation)f(of)h(the)h(data)f │ │ │ │ (whic)n(h)g(represen)n(ts)f(the)i(linear)f(system,)g │ │ │ │ Fq(AX)j Fu(=)22 b Fq(Y)d Fu(.)37 b(The)27 b(user)g(w)n(an)n(ts)0 │ │ │ │ 699 y(the)h(solution)f Fq(X)7 b Fu(.)36 b(The)28 b Ft(SPOOLES)g │ │ │ │ Fu(library)e(will)i(use)f Fq(A)h Fu(and)g Fq(Y)46 b Fu(and)27 │ │ │ │ @@ -9018,16 +9040,16 @@ │ │ │ │ b Fu(or)23 b Fp(InpMtx)p 3048 5253 V 29 w(inputComplexEntr)o(y\()o(\))p │ │ │ │ 0 5330 1560 4 v 92 5384 a Fg(1)127 5407 y Ff(InpMtx)i │ │ │ │ Fv(stands)g(for)d Ff(Inp)p Fv(ut)j Ff(M)p Fv(a)p Ff(t)p │ │ │ │ Fv(ri)p Ff(x)p Fv(,)f(for)f(it)g(is)g(the)i(ob)t(ject)f(in)n(to)h(whic) │ │ │ │ n(h)e(the)i(user)e(inputs)h(the)h(matrix)e(en)n(tries.)p │ │ │ │ eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 0 100 a Fs(Jan)n(uary)26 b(6,)h(2026)p │ │ │ │ -661 100 1214 4 v 1377 w Ft(SPOOLES)32 b(2.2)27 b Fs(|)g(Solving)g │ │ │ │ +TeXDict begin 7 6 bop 0 100 a Fs(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +702 100 1172 4 v 1336 w Ft(SPOOLES)32 b(2.2)27 b Fs(|)g(Solving)g │ │ │ │ (Linear)g(Systems)327 b Fu(7)0 390 y(to)30 b(place)g(that)g(en)n(try)g │ │ │ │ (in)n(to)g(the)g Fp(InpMtx)e Fu(ob)5 b(ject.)44 b(Finally)30 │ │ │ │ b(this)g(co)r(de)g(segmen)n(t)g(closes)f(the)i(\014le.)44 │ │ │ │ b(\014nalizes)30 b(the)g(input)h(to)0 490 y Fp(InpMtx)23 │ │ │ │ b Fu(b)n(y)j(con)n(v)n(erting)e(the)i(in)n(ternal)f(storage)e(of)j(the) │ │ │ │ g(matrix)f(en)n(tries)g(to)h(a)f(v)n(ector)f(form.)36 │ │ │ │ b(\(This)26 b(is)g(necessary)e(for)h(later)0 589 y(steps.\))0 │ │ │ │ @@ -9099,15 +9121,15 @@ │ │ │ │ (they)h(apply)f(to,)h(or)e(the)i(library)e(name,)h(e.g.,)g │ │ │ │ Ff(SPOOLES)p 3716 5328 V 27 w(REAL)p Fv(.)0 5407 y(They)e(are)g │ │ │ │ (describ)r(ed)g(in)f(the)i(reference)f(man)n(ual)g(in)f(the)i(section)g │ │ │ │ (for)d(the)j(particular)e(ob)t(ject.)p eop end │ │ │ │ %%Page: 8 8 │ │ │ │ TeXDict begin 8 7 bop 0 100 a Fu(8)327 b Ft(SPOOLES)32 │ │ │ │ b(2.2)27 b Fs(|)g(Solving)g(Linear)g(Systems)p 2053 100 │ │ │ │ -1186 4 v 1379 w(Jan)n(uary)f(6,)h(2026)125 390 y Fu(Ev)n(ery)e(ob)5 │ │ │ │ +1145 4 v 1338 w(Jan)n(uary)e(17,)i(2026)125 390 y Fu(Ev)n(ery)e(ob)5 │ │ │ │ b(ject)27 b(in)g Ft(SPOOLES)g Fu(has)g(prin)n(t)g(metho)r(ds)g(to)g │ │ │ │ (output)h(the)f(con)n(ten)n(ts)f(of)h(that)h(ob)5 b(ject.)36 │ │ │ │ b(This)27 b(is)g(illustrated)0 490 y(in)h(this)g(co)r(de)g(segmen)n(t)f │ │ │ │ (b)n(y)h(prin)n(ting)f(the)h(input)h(matrix)e(as)g(con)n(tained)g(in)i │ │ │ │ (the)f Fp(InpMtx)d Fu(ob)5 b(ject,)28 b Fp(mtxA)p Fu(.)e(T)-7 │ │ │ │ b(o)28 b(shorten)f(this)0 589 y(c)n(hapter)g(w)n(e)g(will)g(from)g(no)n │ │ │ │ (w)g(on)g(omit)h(the)g(part)f(of)g(the)h(co)r(de)f(that)h(prin)n(ts)f │ │ │ │ @@ -9179,16 +9201,16 @@ │ │ │ │ 5308 y(The)j(righ)n(t)f(hand)h(side)g(en)n(tries)f(are)g(then)h(in,)h │ │ │ │ (ro)n(w)e(b)n(y)h(ro)n(w,)f(and)h(placed)g(in)n(to)g(their)g(lo)r │ │ │ │ (cations)f(via)g(one)h(of)g(the)g(t)n(w)n(o)0 5407 y(\\set)c(en)n │ │ │ │ (tries")g(metho)r(ds.)37 b(Note,)27 b(the)h(nonzero)f(ro)n(ws)f(can)h │ │ │ │ (b)r(e)h(read)f(from)g(the)h(\014le)g(in)g(an)n(y)e(order.)p │ │ │ │ eop end │ │ │ │ %%Page: 9 9 │ │ │ │ -TeXDict begin 9 8 bop 0 100 a Fs(Jan)n(uary)26 b(6,)h(2026)p │ │ │ │ -661 100 1214 4 v 1377 w Ft(SPOOLES)32 b(2.2)27 b Fs(|)g(Solving)g │ │ │ │ +TeXDict begin 9 8 bop 0 100 a Fs(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +702 100 1172 4 v 1336 w Ft(SPOOLES)32 b(2.2)27 b Fs(|)g(Solving)g │ │ │ │ (Linear)g(Systems)327 b Fu(9)0 390 y Fh(2.3)112 b(Reordering)38 │ │ │ │ b(the)f(linear)h(system)0 564 y Fu(The)30 b(\014rst)g(step)h(is)f(to)g │ │ │ │ (\014nd)h(the)g(p)r(erm)n(utation)f(matrix)f Fq(P)12 │ │ │ │ b Fu(,)31 b(and)g(then)f(p)r(erm)n(ute)h Fq(AX)j Fu(=)27 │ │ │ │ b Fq(Y)49 b Fu(in)n(to)30 b(\()p Fq(P)12 b(AP)3336 534 │ │ │ │ y Fl(T)3389 564 y Fu(\)\()p Fq(P)g(X)7 b Fu(\))27 b(=)g │ │ │ │ Fq(P)12 b(Y)19 b Fu(.)0 664 y(The)32 b(result)g(of)g(the)h │ │ │ │ @@ -9275,16 +9297,16 @@ │ │ │ │ b(ject.)p 0 5330 1560 4 v 92 5384 a Fg(3)127 5407 y Ff(IVL)24 │ │ │ │ b Fv(stands)h(for)e Ff(I)p Fv(n)n(teger)i Ff(V)p Fv(ector)f │ │ │ │ Ff(L)p Fv(ist,)g(i.e.,)e(a)i(list)f(of)g(in)n(teger)h(v)n(ectors.)p │ │ │ │ eop end │ │ │ │ %%Page: 10 10 │ │ │ │ TeXDict begin 10 9 bop 0 100 a Fu(10)327 b Ft(SPOOLES)31 │ │ │ │ b(2.2)c Fs(|)h(Solving)f(Linear)f(Systems)p 2095 100 │ │ │ │ -1145 4 v 1338 w(Jan)n(uary)g(6,)h(2026)125 390 y Fu(Once)i(w)n(e)h(ha)n │ │ │ │ -(v)n(e)f(the)i(p)r(erm)n(utation)f(v)n(ector,)f(w)n(e)h(apply)g(it)g │ │ │ │ +1103 4 v 1297 w(Jan)n(uary)f(17,)i(2026)125 390 y Fu(Once)i(w)n(e)h(ha) │ │ │ │ +n(v)n(e)f(the)i(p)r(erm)n(utation)f(v)n(ector,)f(w)n(e)h(apply)g(it)g │ │ │ │ (to)g(the)h(fron)n(t)f(tree,)g(b)n(y)g(the)h Fp(ETree)p │ │ │ │ 3135 390 27 4 v 29 w(permuteVertices\()o(\))0 490 y Fu(metho)r(d,)41 │ │ │ │ b(and)c(then)h(to)g(the)g(matrix)f(with)h(the)g Fp(InpMtx)p │ │ │ │ 1874 490 V 29 w(permute\(\))c Fu(metho)r(d.)67 b(If)38 │ │ │ │ b(the)g(matrix)f Fq(A)h 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b(ChvManager_new\()o(\))38 b(;)0 490 y(ChvManager_init\()o(chv)o │ │ │ │ (ma)o(na)o(ger)o(,)f(NO_LOCK,)k(1\))h(;)0 589 y(DVfill\(10,)d(cpus,)j │ │ │ │ (0.0\))g(;)0 689 y(IVfill\(20,)d(stats,)j(0\))g(;)0 789 │ │ │ │ y(rootchv)f(=)i(FrontMtx_factorI)o(np)o(Mtx)o(\(f)o(ron)o(tm)o(tx)o(,) │ │ │ │ 38 b(mtxA,)j(tau,)h(droptol,)567 888 y(chvmanager,)d(&error,)h(cpus,)i │ │ │ │ (stats,)f(msglvl,)g(msgFile\))f(;)0 988 y(ChvManager_free\()o(chv)o(ma) │ │ │ │ @@ -9465,15 +9487,15 @@ │ │ │ │ b(for)g(w)n(orking)f(storage.)34 b(The)25 b(last)f(step)h(is)f(to)h(p)r │ │ │ │ (erm)n(ute)g(the)g(ro)n(ws)e(of)h(the)h Fp(DenseMtx)d │ │ │ │ Fu(from)i(the)h(new)f(ordering)f(in)n(to)0 5407 y(the)28 │ │ │ │ b(old)f(ordering.)p eop end │ │ │ │ %%Page: 12 12 │ │ │ │ TeXDict begin 12 11 bop 0 100 a Fu(12)327 b Ft(SPOOLES)31 │ │ │ │ b(2.2)c Fs(|)h(Solving)f(Linear)f(Systems)p 2095 100 │ │ │ │ -1145 4 v 1338 w(Jan)n(uary)g(6,)h(2026)0 390 y Fh(2.7)112 │ │ │ │ +1103 4 v 1297 w(Jan)n(uary)f(17,)i(2026)0 390 y Fh(2.7)112 │ │ │ │ b(Sample)39 b(Matrix)f(and)h(Righ)m(t)d(Hand)i(Side)h(Files)0 │ │ │ │ 568 y Fu(Immediately)34 b(b)r(elo)n(w)g(are)f(t)n(w)n(o)g(sample)h │ │ │ │ (\014les:)50 b Fp(matrix.input)29 b Fu(holds)34 b(the)g(matrix)g(input) │ │ │ │ h(and)f Fp(rhs.input)c Fu(holds)k(the)0 668 y(righ)n(t)20 │ │ │ │ b(hand)h(side.)35 b(This)21 b(example)g(is)g(for)f(a)h(symmetric)g │ │ │ │ (Laplacian)f(op)r(erator)f(on)i(a)f(3)5 b Fb(\002)g Fu(3)21 │ │ │ │ b(grid.)34 b(Only)21 b(en)n(tries)f(in)h(the)h(upp)r(er)0 │ │ │ │ @@ -9502,16 +9524,16 @@ │ │ │ │ (0.0)h(0.0)f(0.0)1533 2351 y(5)h(0.0)g(0.0)f(0.0)g(0.0)h(0.0)f(1.0)g │ │ │ │ (0.0)h(0.0)f(0.0)1533 2451 y(6)h(0.0)g(0.0)f(0.0)g(0.0)h(0.0)f(0.0)g │ │ │ │ (1.0)h(0.0)f(0.0)1533 2550 y(7)h(0.0)g(0.0)f(0.0)g(0.0)h(0.0)f(0.0)g │ │ │ │ (0.0)h(1.0)f(0.0)1533 2650 y(8)h(0.0)g(0.0)f(0.0)g(0.0)h(0.0)f(0.0)g │ │ │ │ (0.0)h(0.0)f(1.0)p 3231 2650 V 1483 2653 1750 4 v eop │ │ │ │ end │ │ │ │ %%Page: 13 13 │ │ │ │ -TeXDict begin 13 12 bop 0 100 a Fs(Jan)n(uary)26 b(6,)h(2026)p │ │ │ │ -661 100 1172 4 v 1336 w Ft(SPOOLES)32 b(2.2)26 b Fs(|)i(Solving)f │ │ │ │ +TeXDict begin 13 12 bop 0 100 a Fs(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +702 100 1131 4 v 1295 w Ft(SPOOLES)32 b(2.2)26 b Fs(|)i(Solving)f │ │ │ │ (Linear)f(Systems)328 b Fu(13)0 390 y Fr(3)135 b(Multithreaded)45 │ │ │ │ b(Solution)h(of)f Fj(AX)e Fi(=)33 b Fj(Y)71 b Fr(using)45 │ │ │ │ b(an)f Fj(LU)57 b Fr(factorization)0 599 y Fu(The)26 │ │ │ │ b(only)f(computations)g(that)h(are)f(m)n(ultithreaded)g(are)g(the)h │ │ │ │ (factorization)e(and)i(forw)n(ard)e(and)h(bac)n(ksolv)n(es.)34 │ │ │ │ b(Therefore,)0 699 y(this)c(section)g(will)g(describ)r(e)g(only)g(the)g │ │ │ │ (di\013erences)g(b)r(et)n(w)n(een)g(the)h(serial)e(driv)n(er)g(in)h │ │ │ │ @@ -9590,18 +9612,18 @@ │ │ │ │ 5308 y(DV_init\(cumopsDV)o(,)d(nthread,)i(NULL\))h(;)0 │ │ │ │ 5407 y(ownersIV)f(=)j(ETree_ddMap\(front)o(ETr)o(ee)o(,)38 │ │ │ │ b(type,)j(symmetryflag,)d(cumopsDV,)i(1./\(2.*nthread\)\))d(;)p │ │ │ │ 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b(whose)f(length)h(is)g │ │ │ │ (the)h(n)n(um)n(b)r(er)f(of)g(threads.)41 b(On)29 b(return)f(from)h │ │ │ │ (the)h(map)f(call,)g(it)h(con)n(tains)e(the)h(n)n(um)n(b)r(er)0 │ │ │ │ 689 y(of)f(factor)e(op)r(erations)h(that)g(will)h(b)r(e)g(p)r(erformed) │ │ │ │ f(b)n(y)h(eac)n(h)f(thread)g(when)g(piv)n(oting)g(for)g(stabilit)n(y)h │ │ │ │ @@ -9679,16 +9701,16 @@ │ │ │ │ b(Mo)r(derate)33 b(sp)r(eedups)g(in)g(the)g(factorization)f(ha)n(v)n(e) │ │ │ │ g(b)r(een)h(for)g(v)-5 b(alues)32 b(of)h Fp(lookahead)d │ │ │ │ Fu(up)j(to)g(the)g(n)n(um)n(b)r(er)208 5308 y(of)i(threads.)58 │ │ │ │ b(F)-7 b(or)35 b(nonzero)f Fp(lookahead)d Fu(v)-5 b(alues,)37 │ │ │ │ b(the)f(amoun)n(t)e(of)h(w)n(orking)f(storage)f(can)i(increase,)g │ │ │ │ (sometimes)208 5407 y(appreciably)-7 b(.)p eop end │ │ │ │ %%Page: 15 15 │ │ │ │ -TeXDict begin 15 14 bop 0 100 a Fs(Jan)n(uary)26 b(6,)h(2026)p │ │ │ │ -661 100 1172 4 v 1336 w Ft(SPOOLES)32 b(2.2)26 b Fs(|)i(Solving)f │ │ │ │ +TeXDict begin 15 14 bop 0 100 a Fs(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +702 100 1131 4 v 1295 w Ft(SPOOLES)32 b(2.2)26 b Fs(|)i(Solving)f │ │ │ │ (Linear)f(Systems)328 b Fu(15)0 390 y(The)22 b(p)r(ost-pro)r(cessing)f │ │ │ │ (of)h(the)g(factorization)f(is)h(exactly)g(the)g(same)g(as)g(the)g │ │ │ │ (serial)f(co)r(de.)35 b(Note,)24 b(this)e(step)g(can)g(b)r(e)h │ │ │ │ (trivially)0 490 y(parallelized,)j(but)j(is)e(not)h(done)f(at)h(presen) │ │ │ │ n(t.)125 614 y(After)d(the)g(p)r(ost-pro)r(cessing)e(step,)j(the)f │ │ │ │ Fp(FrontMtx)d Fu(ob)5 b(ject)24 b(con)n(tains)g(the)i │ │ │ │ Fq(L)2539 626 y Fl(J)n(;I)2631 614 y Fu(,)g Fq(D)2749 │ │ │ │ @@ -9724,15 +9746,15 @@ │ │ │ │ b(in)h(the)g(latter.)0 3167 y Fh(3.7)112 b(Sample)39 │ │ │ │ b(Matrix)f(and)h(Righ)m(t)d(Hand)i(Side)h(Files)0 3345 │ │ │ │ y Fu(The)28 b(m)n(ultithreaded)f(driv)n(er)g(uses)g(the)h(same)f(input) │ │ │ │ h(\014les)g(as)f(found)g(in)h(Section)g(2.7.)p eop end │ │ │ │ %%Page: 16 16 │ │ │ │ TeXDict begin 16 15 bop 0 100 a Fu(16)327 b Ft(SPOOLES)31 │ 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b(;)0 589 y(SubMtxManager_in)o(it\()o │ │ │ │ (mt)o(xm)o(ana)o(ge)o(r,)g(NO_LOCK,)j(0\))j(;)0 689 y(if)g(\()g(type)f │ │ │ │ (==)h(SPOOLES_REAL)38 b(\))43 b({)131 789 y(FrontMtx_init\(fr)o(on)o │ │ │ │ (tm)o(tx,)37 b(frontETree,)i(symbfacIVL,)g(type,)741 │ │ │ │ 888 y(SPOOLES_SYMMETRI)o(C,)e(FRONTMTX_DENSE_F)o(RON)o(TS)o(,)741 │ │ │ │ @@ -11798,15 +11820,15 @@ │ │ │ │ y(/*)131 5073 y(----------------)o(--)o(--)o(---)o(--)o(---)o(--)o(-) │ │ │ │ 131 5172 y(STEP)42 b(8:)g(solve)g(the)g(linear)f(system)131 │ │ │ │ 5272 y(----------------)o(--)o(--)o(---)o(--)o(---)o(--)o(-)0 │ │ │ │ 5372 y(*/)p eop end │ │ │ │ %%Page: 54 54 │ │ │ │ TeXDict begin 54 53 bop 0 100 a Fu(54)327 b Ft(SPOOLES)31 │ │ │ │ b(2.2)c Fs(|)h(Solving)f(Linear)f(Systems)p 2095 100 │ │ │ │ -1145 4 v 1338 w(Jan)n(uary)g(6,)h(2026)0 390 y Fp(mtxX)42 │ │ │ │ +1103 4 v 1297 w(Jan)n(uary)f(17,)i(2026)0 390 y Fp(mtxX)42 │ │ │ │ b(=)h(DenseMtx_new\(\))38 b(;)0 490 y(DenseMtx_init\(mt)o(xX,)f(type,)k │ │ │ │ (0,)i(0,)g(neqns,)e(nrhs,)g(1,)i(neqns\))e(;)0 589 y(FrontMtx_QR_solv)o │ │ │ │ (e\(f)o(ro)o(nt)o(mtx)o(,)c(mtxA,)42 b(mtxX,)f(mtxB,)h(mtxmanager,)785 │ │ │ │ 689 y(cpus,)f(msglvl,)g(msgFile\))f(;)0 789 y(if)j(\()g(msglvl)e(>)i(1) │ │ │ │ g(\))h({)131 888 y(fprintf\(msgFile,)37 b("\\n\\n)k(solution)g(matrix)g │ │ │ │ (in)h(new)h(ordering"\))c(;)131 988 y(DenseMtx_writeFo)o(rH)o(um)o(anE) │ │ │ │ o(ye)o(\(mt)o(xX)o(,)f(msgFile\))i(;)131 1088 y(fflush\(msgFile\))d(;)0 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -1,16 +1,16 @@ │ │ │ │ │ Solving Linear Systems using SPOOLES 2.2 │ │ │ │ │ C. C. Ashcraft, R. G. Grimes, D. J. Pierce, D. K. Wah │ │ │ │ │ Boeing Phantom Works∗ │ │ │ │ │ - January 6, 2026 │ │ │ │ │ + January 17, 2026 │ │ │ │ │ ∗P. O. Box 24346, Mail Stop 7L-22, Seattle, Washington 98124. This research was supported in part by the DARPA │ │ │ │ │ Contract DABT63-95-C-0122 and the DoD High Performance Computing Modernization Program Common HPC Software │ │ │ │ │ Support Initiative. │ │ │ │ │ 1 │ │ │ │ │ - 2 SPOOLES 2.2 — Solving Linear Systems January 6, 2026 │ │ │ │ │ + 2 SPOOLES 2.2 — Solving Linear Systems January 17, 2026 │ │ │ │ │ Contents │ │ │ │ │ 1 Overview 4 │ │ │ │ │ 2 Serial Solution of AX = Y using an LU factorization 6 │ │ │ │ │ 2.1 Reading the input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 │ │ │ │ │ 2.2 Communicating the data for the problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 │ │ │ │ │ 2.3 Reordering the linear system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 │ │ │ │ │ 2.4 Non-numeric work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 │ │ │ │ │ @@ -39,18 +39,18 @@ │ │ │ │ │ 5.3 Reordering the linear system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 │ │ │ │ │ 5.4 Non-numeric work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 │ │ │ │ │ 5.5 The Matrix Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 │ │ │ │ │ 5.6 Solving the linear system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 │ │ │ │ │ 5.7 Sample Matrix and Right Hand Side Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 │ │ │ │ │ A allInOne.c – A Serial LU Driver Program 24 │ │ │ │ │ B allInOne.c – A Serial LU Driver Program 31 │ │ │ │ │ - January 6, 2026 SPOOLES 2.2 — Solving Linear Systems 3 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2 — Solving Linear Systems 3 │ │ │ │ │ C allInOne.c – A Serial LU Driver Program 39 │ │ │ │ │ D allInOne.c – A Serial QR Driver Program 49 │ │ │ │ │ - 4 SPOOLES 2.2 — Solving Linear Systems January 6, 2026 │ │ │ │ │ + 4 SPOOLES 2.2 — Solving Linear Systems January 17, 2026 │ │ │ │ │ 1 Overview │ │ │ │ │ The SPOOLES software library is designed to solve sparse systems of linear equations AX = Y for X, │ │ │ │ │ whereAisfullrankandX andY aredensematrices. ThematrixAcanbeeitherrealorcomplex,symmetric, │ │ │ │ │ Hermitian, square nonsymmetric, or overdetermined. When A is square, there are four steps in the process │ │ │ │ │ of solving AX = Y. │ │ │ │ │ • communicate the data for the problem as A, X and Y. │ │ │ │ │ ee e e T e e │ │ │ │ │ @@ -94,26 +94,26 @@ │ │ │ │ │ The SPOOLES library is based on an object oriented design philosophy. There are several data struc- │ │ │ │ │ tures or objects that the user must interact with. These interactions are performed with a set of methods │ │ │ │ │ for each object. Every object has some standard methods, such as initializing the object, placing data into │ │ │ │ │ the object, extracting data out of the object, writing and reading the object to a input/output file, printing │ │ │ │ │ the contents of the object to a specified file, and freeing the object. │ │ │ │ │ For example, consider the DenseMtx object that models a dense matrix. The DenseMtx/DenseMtx.h │ │ │ │ │ header file defines the object’s C struct and has prototypes (with extensive comments) of the object’s │ │ │ │ │ - January 6, 2026 SPOOLES 2.2 — Solving Linear Systems 5 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2 — Solving Linear Systems 5 │ │ │ │ │ A │ │ │ │ │ methods. Thesourcefiles arefound in the DenseMtx/srcdirectory. The LT X documentation files are found │ │ │ │ │ E │ │ │ │ │ in the DenseMtx/docdirectory. The files can be used to create the DenseMtxobject’s chapter in the Reference │ │ │ │ │ Manual,orinastandalonemannertogeneratetheobject’sdocumentation. TheDenseMtx/driversdirectory │ │ │ │ │ contains driver programs that exercise and validate the object’s functionality. │ │ │ │ │ Almost all the methods in the library are associated with a particular object. There are some exceptions, │ │ │ │ │ mostly found in the misc/src directory. The misc/drivers directory contains the serial LU and QR driver │ │ │ │ │ programs. The MT/drivers and MPI/drivers directories contain the multithreaded and MPI LU driver │ │ │ │ │ programs. │ │ │ │ │ - 6 SPOOLES 2.2 — Solving Linear Systems January 6, 2026 │ │ │ │ │ + 6 SPOOLES 2.2 — Solving Linear Systems January 17, 2026 │ │ │ │ │ 2 Serial Solution of AX = Y using an LU factorization │ │ │ │ │ The user has some representation of the data which represents the linear system, AX = Y . The user wants │ │ │ │ │ the solution X. The SPOOLES library will use A and Y and provide X back to the user. │ │ │ │ │ The SPOOLESlibrary is based on an object oriented design philosophy. The first object that the user │ │ │ │ │ mustinteract with is InpMtx1. The InpMtx object is where the SPOOLES representation of A is assembled. │ │ │ │ │ The user can input the representation of A into the InpMtx object with methods for single matrix entry │ │ │ │ │ (consisting of the row index, the column index, and the value), for an array of entries, for a set of entries in │ │ │ │ │ @@ -145,15 +145,15 @@ │ │ │ │ │ nrhs floating point numbers if the system is real, or 2*nrhs numbers if the system is complex. │ │ │ │ │ • The seed parameter is a random number seed used in the ordering process. │ │ │ │ │ 2.2 Communicating the data for the problem │ │ │ │ │ The following code segment from the full sample program opens the file matrixFileName, reads the first │ │ │ │ │ line of the file, and then initializes the InpMtx object. The program continues by reading each line of the │ │ │ │ │ input matrix data and uses either the method InpMtx inputRealEntry()or InpMtx inputComplexEntry() │ │ │ │ │ 1InpMtx stands for Input Matrix, for it is the object into which the user inputs the matrix entries. │ │ │ │ │ - January 6, 2026 SPOOLES 2.2 — Solving Linear Systems 7 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2 — Solving Linear Systems 7 │ │ │ │ │ to place that entry into the InpMtx object. Finally this code segment closes the file. finalizes the input to │ │ │ │ │ InpMtx by converting the internal storage of the matrix entries to a vector form. (This is necessary for later │ │ │ │ │ steps.) │ │ │ │ │ inputFile = fopen(matrixFileName, "r") ; │ │ │ │ │ fscanf(inputFile, "%d %d %d", &nrow, &ncol, &nent) ; │ │ │ │ │ neqns = nrow ; │ │ │ │ │ mtxA = InpMtx_new() ; │ │ │ │ │ @@ -192,15 +192,15 @@ │ │ │ │ │ • The fifth argument maxnvector is an estimate of the number of number of vectors that will be used, │ │ │ │ │ e.g., number of rows or numbers of columns. │ │ │ │ │ The maxnent and maxnvector arguments only have to be estimates as they are used in the initial sizing of │ │ │ │ │ the object. Either can be 0. The InpMtx object resizes itself as required to handle the linear system. │ │ │ │ │ 2Note that SPOOLES has some pre-defined parameters such as INPMTX BY ROWS for some objects. These parameters are │ │ │ │ │ always uppercase and either begin with the name of the object which they apply to, or the library name, e.g., SPOOLES REAL. │ │ │ │ │ They are described in the reference manual in the section for the particular object. │ │ │ │ │ - 8 SPOOLES 2.2 — Solving Linear Systems January 6, 2026 │ │ │ │ │ + 8 SPOOLES 2.2 — Solving Linear Systems January 17, 2026 │ │ │ │ │ Every object in SPOOLES has print methods to output the contents of that object. This is illustrated │ │ │ │ │ in this code segment by printing the input matrix as contained in the InpMtx object, mtxA. To shorten this │ │ │ │ │ chapter we will from now on omit the part of the code that prints debug output to msgFile for the various │ │ │ │ │ code segments. The complete sample program in Section A contains all of the debug print statements. │ │ │ │ │ After the matrix A has been read in from the file and placed in an InpMtx object, the right hand matrix │ │ │ │ │ Y is read in from a file and placed in a DenseMtx object. The following code fragment does this operation. │ │ │ │ │ inputFile = fopen(rhsFileName, "r") ; │ │ │ │ │ @@ -240,15 +240,15 @@ │ │ │ │ │ number of rows, or neqns. │ │ │ │ │ Theinitialization step allocates storage for the matrix entries, but it does not fill them with any values. This │ │ │ │ │ is done explicitly via the DenseMtx zero() method, which places zeroes in all the entries. This is necessary │ │ │ │ │ since the right hand side matrix Y may be sparse, and so the number of rows in the file may not equal the │ │ │ │ │ number of equations. │ │ │ │ │ The right hand side entries are then in, row by row, and placed into their locations via one of the two │ │ │ │ │ “set entries” methods. Note, the nonzero rows can be read from the file in any order. │ │ │ │ │ - January 6, 2026 SPOOLES 2.2 — Solving Linear Systems 9 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2 — Solving Linear Systems 9 │ │ │ │ │ 2.3 Reordering the linear system │ │ │ │ │ The first step is to find the permutation matrix P, and then permute AX = Y into (PAPT)(PX) = PY. │ │ │ │ │ The result of the SPOOLES ordering step is not just P or its permutation vector, it is a front tree that │ │ │ │ │ defines not just the permutation, but the blocking of the factor matrices, which in turn specifies the data │ │ │ │ │ structures and the computations that are performed during the factor and solves. To determine this ETree │ │ │ │ │ front tree object takes three step, as seen in the code fragment below. │ │ │ │ │ adjIVL = InpMtx_fullAdjacency(mtxA) ; │ │ │ │ │ @@ -287,15 +287,15 @@ │ │ │ │ │ InpMtx_changeCoordType(mtxA, INPMTX_BY_CHEVRONS) ; │ │ │ │ │ InpMtx_changeStorageMode(mtxA, INPMTX_BY_VECTORS) ; │ │ │ │ │ DenseMtx_permuteRows(mtxB, oldToNewIV) ; │ │ │ │ │ The oldToNewIV and newToOldIV variables are IV objects that represent an integer vector. The oldToNew │ │ │ │ │ and newToOld variables are pointers to int, which point to the base address of the int vector in an IV │ │ │ │ │ object. │ │ │ │ │ 3IVL stands for Integer Vector List, i.e., a list of integer vectors. │ │ │ │ │ - 10 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 10 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ Once we have the permutation vector, we apply it to the front tree, by the ETree permuteVertices() │ │ │ │ │ method, and then to the matrix with the InpMtx permute() method. If the matrix A is symmetric or │ │ │ │ │ Hermitian, we expect all nonzero entries to be in the upper triangle. Permuting the matrix yields PAPT, │ │ │ │ │ which may not have all of its entries in the upper triangle. If A is symmetric or Hermitian, the call to │ │ │ │ │ InpMtx mapToUpperTriangle() ensures that all entries of PAPT are in its upper triangle. Permuting the │ │ │ │ │ matrix destroys the internal vector structure, which has to be restored. But first we need to change the │ │ │ │ │ 4 │ │ │ │ │ @@ -330,15 +330,15 @@ │ │ │ │ │ little internal code differences, and it is the hook we have left in the library to extend its capabilities │ │ │ │ │ to out-of-core factors and solves. │ │ │ │ │ • The twelveth and thirteenth parameters define the message level and message file for the factorization. │ │ │ │ │ The numeric factorization is performed by the FrontMtx factorInpMtx() method. The code segment │ │ │ │ │ from the sample program for the numerical factorization step is found below. │ │ │ │ │ 4The i-th chevron of A consists of the diagonal entry Ai,i, the i-th row of the upper triangle of A, and the i-th column of │ │ │ │ │ the lower triangle of A. │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 11 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 11 │ │ │ │ │ chvmanager = ChvManager_new() ; │ │ │ │ │ ChvManager_init(chvmanager, NO_LOCK, 1) ; │ │ │ │ │ DVfill(10, cpus, 0.0) ; │ │ │ │ │ IVfill(20, stats, 0) ; │ │ │ │ │ rootchv = FrontMtx_factorInpMtx(frontmtx, mtxA, tau, droptol, │ │ │ │ │ chvmanager, &error, cpus, stats, msglvl, msgFile) ; │ │ │ │ │ ChvManager_free(chvmanager) ; │ │ │ │ │ @@ -373,15 +373,15 @@ │ │ │ │ │ First we initialize a new DenseMtx object to hold X (and also PX). (Note, in all cases but a nonsymmetric │ │ │ │ │ matrix with pivoting enabled in an MPI environment, X may overwrite Y, and so we can use the same │ │ │ │ │ DenseMtx object for X and Y.) We then solve the linear system with a call to FrontMtx solve(). Note │ │ │ │ │ that one of the arguments is the mtxmanager object, first created for the numerical factorization. The solve │ │ │ │ │ requires working submatrices, and so we continue the convention of having the FrontMtx ask the manager │ │ │ │ │ object for working storage. The last step is to permute the rows of the DenseMtx from the new ordering into │ │ │ │ │ the old ordering. │ │ │ │ │ - 12 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 12 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ 2.7 Sample Matrix and Right Hand Side Files │ │ │ │ │ Immediately below are two sample files: matrix.input holds the matrix input and rhs.input holds the │ │ │ │ │ right hand side. This example is for a symmetric Laplacian operator on a 3×3 grid. Only entries in the upper │ │ │ │ │ triangle are stored. The right hand side is the 9×9 identity matrix. Note how the indices are zero-based as │ │ │ │ │ for C, instead of one-based as for Fortran. │ │ │ │ │ matrix.input │ │ │ │ │ 9 9 21 │ │ │ │ │ @@ -402,15 +402,15 @@ │ │ │ │ │ 7 8 -1.0 8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 │ │ │ │ │ 0 3 -1.0 │ │ │ │ │ 1 4 -1.0 │ │ │ │ │ 2 5 -1.0 │ │ │ │ │ 3 6 -1.0 │ │ │ │ │ 4 7 -1.0 │ │ │ │ │ 5 8 -1.0 │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 13 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 13 │ │ │ │ │ 3 Multithreaded Solution of AX = Y using an LU factorization │ │ │ │ │ The only computations that are multithreaded are the factorization and forward and backsolves. Therefore, │ │ │ │ │ this section will describe only the differences between the serial driver in Section A and the multithreaded │ │ │ │ │ driver whose complete listing is found in Section B. This section will refer the reader to subsections in │ │ │ │ │ Section 2 for the parts of the code where the two drivers are identical. │ │ │ │ │ The shared memory parallel version of SPOOLES is implemented using thread based parallelism. The │ │ │ │ │ multi-threaded code uses much of the serial code — the basic steps are the same and use the serial methods. │ │ │ │ │ @@ -443,15 +443,15 @@ │ │ │ │ │ over a range of orderings, and this is what we recommend, as we see in the code fragment below. │ │ │ │ │ if ( nthread > (nfront = FrontMtx_nfront(frontmtx)) ) { │ │ │ │ │ nthread = nfront ; │ │ │ │ │ } │ │ │ │ │ cumopsDV = DV_new() ; │ │ │ │ │ DV_init(cumopsDV, nthread, NULL) ; │ │ │ │ │ ownersIV = ETree_ddMap(frontETree, type, symmetryflag, cumopsDV, 1./(2.*nthread)) ; │ │ │ │ │ - 14 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 14 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ The first step is to ensure that each thread has a front to own, decreasing the number of threads if necessary. │ │ │ │ │ We then construct the owners map using the front tree object. The cumopsDV object is a double precision │ │ │ │ │ vector object whose length is the number of threads. On return from the map call, it contains the number │ │ │ │ │ of factor operations that will be performed by each thread when pivoting for stability is not enabled. │ │ │ │ │ 3.5 The Matrix Factorization │ │ │ │ │ During the factorization and solves, the threads access data and modify the state of the FrontMtx and │ │ │ │ │ SubMtxManagerobjects in a concurrent fashion, so there must be some way to control this access for critical │ │ │ │ │ @@ -487,15 +487,15 @@ │ │ │ │ │ workcooperativelyto compute the factor matrices, there is idle time while one thread waits on another. │ │ │ │ │ The lookahead parameter controls the ability of the thread to look past the present idle point and │ │ │ │ │ performworkthatisnotsoimmediate. Unfortunately, whileathreadisoffdoingthiswork,itmayblock │ │ │ │ │ a thread at a more crucial point. When lookahead = 0, each processor tries to do only “immediate” │ │ │ │ │ work. Moderate speedups in the factorization have been for values of lookahead up to the number │ │ │ │ │ of threads. For nonzero lookahead values, the amount of working storage can increase, sometimes │ │ │ │ │ appreciably. │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 15 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 15 │ │ │ │ │ Thepost-processing of the factorization is exactly the same as the serial code. Note, this step can be trivially │ │ │ │ │ parallelized, but is not done at present. │ │ │ │ │ After the post-processing step, the FrontMtx object contains the L , D and U submatrices. What │ │ │ │ │ J,I I,I I,J │ │ │ │ │ remains to be done is to specify which threads own which submatrices, and thus perform computations with │ │ │ │ │ them. This is done by constructing a “solve–map” object, as we see below. │ │ │ │ │ solvemap = SolveMap_new() ; │ │ │ │ │ @@ -511,15 +511,15 @@ │ │ │ │ │ DenseMtx_zero(mtxX) ; │ │ │ │ │ FrontMtx_MT_solve(frontmtx, mtxX, mtxY, mtxmanager, solvemap, cpus, msglvl, msgFile) ; │ │ │ │ │ DenseMtx_permuteRows(mtxX, newToOldIV) ; │ │ │ │ │ The only difference between the serial and multithreaded solve methods is the presence of the solve–map │ │ │ │ │ object in the latter. │ │ │ │ │ 3.7 Sample Matrix and Right Hand Side Files │ │ │ │ │ The multithreaded driver uses the same input files as found in Section 2.7. │ │ │ │ │ - 16 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 16 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ 4 MPISolution of AX =Y using an LU factorization │ │ │ │ │ Unlike the serial and multithreaded environments where the data structures are global, existing under one │ │ │ │ │ address space, in the MPI environment, data is local, each process or processor has its own distinct address │ │ │ │ │ space. The MPI step-by-step process to solve a linear system is exactly the same as the multithreaded case, │ │ │ │ │ with the additional trouble that the data structures are distributed and need to be re-distributed as needed. │ │ │ │ │ The ownership of the factor matrices during the factorization and solves is exactly the same as for the │ │ │ │ │ multithreaded case – the map from fronts to processors and map from submatrices to processors are identical │ │ │ │ │ @@ -552,15 +552,15 @@ │ │ │ │ │ adjIVL = InpMtx_MPI_fullAdjacency(mtxA, stats, msglvl, msgFile, MPI_COMM_WORLD) ; │ │ │ │ │ nedges = IVL_tsize(adjIVL) ; │ │ │ │ │ Graph_init2(graph, 0, neqns, 0, nedges, neqns, nedges, adjIVL, NULL, NULL) ; │ │ │ │ │ frontETree = orderViaMMD(graph, seed + myid, msglvl, msgFile) ; │ │ │ │ │ Whilethedataandcomputationsaredistributedacrosstheprocessors,the orderingprocessis not. Therefore │ │ │ │ │ we need a global graph on each processor. Since the matrix A is distributed across the processors, we use │ │ │ │ │ the distributed InpMtx MPI fullAdjacency() method to construct the IVL object of the graph of A+AT. │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 17 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 17 │ │ │ │ │ At this point, each processor has computed its own minimum degree ordering and created a front tree │ │ │ │ │ object. The orderings will likely be different, because each processors input a different random number seed │ │ │ │ │ to the ordering method. Only one ordering can be used for the factorization, so the processors collectively │ │ │ │ │ determine which of the orderings is best, which is then broadcast to all the processors, as the code fragment │ │ │ │ │ below illustrates. │ │ │ │ │ opcounts = DVinit(nproc, 0.0) ; │ │ │ │ │ opcounts[myid] = ETree_nFactorOps(frontETree, type, symmetryflag) ; │ │ │ │ │ @@ -597,15 +597,15 @@ │ │ │ │ │ IV_init(vtxmapIV, neqns, NULL) ; │ │ │ │ │ IVgather(neqns, IV_entries(vtxmapIV), IV_entries(ownersIV), ETree_vtxToFront(frontETree)) ; │ │ │ │ │ At this point we are ready to assemble and distribute the entries of A and Y . │ │ │ │ │ firsttag = 0 ; │ │ │ │ │ newA = InpMtx_MPI_split(mtxA, vtxmapIV, stats, msglvl, msgFile, firsttag, │ │ │ │ │ MPI_COMM_WORLD) ; │ │ │ │ │ InpMtx_free(mtxA) ; │ │ │ │ │ - 18 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 18 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ mtxA = newA ; │ │ │ │ │ InpMtx_changeStorageMode(mtxA, INPMTX_BY_VECTORS) ; │ │ │ │ │ newY = DenseMtx_MPI_splitByRows(mtxY, vtxmapIV, stats, msglvl, │ │ │ │ │ msgFile, firsttag, MPI_COMM_WORLD) ; │ │ │ │ │ DenseMtx_free(mtxY) ; │ │ │ │ │ mtxY = newY ; │ │ │ │ │ The InpMtx MPI split() method assembles and redistributes the matrix entries by the vectors of the local │ │ │ │ │ @@ -640,15 +640,15 @@ │ │ │ │ │ chvmanager, ownersIV, lookahead, &error, cpus, │ │ │ │ │ stats, msglvl, msgFile, firsttag, MPI_COMM_WORLD) ; │ │ │ │ │ ChvManager_free(chvmanager) ; │ │ │ │ │ Note that the ChvManager is not locked. The calling sequence is identical to that of the multithreaded │ │ │ │ │ factorization except for the addition of the firsttag and MPI communicator at the end. │ │ │ │ │ The post-processing of the factorization is the same in principle as in the serial code but differs in that │ │ │ │ │ is uses the distributed data structures. │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 19 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 19 │ │ │ │ │ FrontMtx_MPI_postProcess(frontmtx, ownersIV, stats, msglvl, │ │ │ │ │ msgFile, firsttag, MPI_COMM_WORLD) ; │ │ │ │ │ After the post-processing step, each local FrontMtx object contains the L , D and U submatrices │ │ │ │ │ J,I I,I I,J │ │ │ │ │ for the fronts that were owned by the particular processor. However, the parallel solve is based on the │ │ │ │ │ submatrices being distributed across the processors, not just the fronts. │ │ │ │ │ We must specify which threads own which submatrices, and so perform computations with them. This │ │ │ │ │ @@ -683,15 +683,15 @@ │ │ │ │ │ mtxY = newY ; │ │ │ │ │ IV_free(rowmapIV) ; │ │ │ │ │ } │ │ │ │ │ Each processor now must create a local DenseMtx object to hold the rows of PX that it owns. │ │ │ │ │ ownedColumnsIV = FrontMtx_ownedColumnsIV(frontmtx, myid, ownersIV, │ │ │ │ │ msglvl, msgFile) ; │ │ │ │ │ nmycol = IV_size(ownedColumnsIV) ; │ │ │ │ │ - 20 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 20 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ mtxX = DenseMtx_new() ; │ │ │ │ │ if ( nmycol > 0 ) { │ │ │ │ │ DenseMtx_init(mtxX, type, 0, 0, nmycol, nrhs, 1, nmycol) ; │ │ │ │ │ DenseMtx_rowIndices(mtxX, &nrow, &rowind) ; │ │ │ │ │ IVcopy(nmycol, rowind, IV_entries(ownedColumnsIV)) ; │ │ │ │ │ } │ │ │ │ │ If A is symmetric, or if pivoting for stability was not used, then mtxX can just be a pointer to mtxY, i.e., PX │ │ │ │ │ @@ -722,15 +722,15 @@ │ │ │ │ │ 1 4 -1.0 6 6 4.0 │ │ │ │ │ 6 7 -1.0 │ │ │ │ │ rhs.0.input rhs.1.input rhs.2.input rhs.3.input │ │ │ │ │ 2 1 2 1 2 1 3 1 │ │ │ │ │ 0 0.0 2 0.0 4 1.0 6 0.0 │ │ │ │ │ 1 0.0 3 0.0 5 0.0 7 0.0 │ │ │ │ │ 8 0.0 │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 21 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 21 │ │ │ │ │ 5 Serial Solution of AX = Y using an QR factorization │ │ │ │ │ Let us review the steps is solving AX = Y using a QR factorization. │ │ │ │ │ • communicate the data for the problem as A, X and Y. │ │ │ │ │ ee e T e │ │ │ │ │ • reorder as AX = Y, where A = AP and X =PX. and P is a permutation matrix. │ │ │ │ │ e │ │ │ │ │ • factor A = QR, where Q is orthogonal and R is upper triangular. │ │ │ │ │ @@ -762,15 +762,15 @@ │ │ │ │ │ apply it to the matrix A. This is done by the following code fragment. │ │ │ │ │ oldToNewIV = ETree_oldToNewVtxPerm(frontETree) ; │ │ │ │ │ oldToNew = IV_entries(oldToNewIV) ; │ │ │ │ │ newToOldIV = ETree_newToOldVtxPerm(frontETree) ; │ │ │ │ │ newToOld = IV_entries(newToOldIV) ; │ │ │ │ │ InpMtx_permute(mtxA, NULL, oldToNew)) ; │ │ │ │ │ InpMtx_changeStorageMode(mtxA, INPMTX_BY_VECTORS) ; │ │ │ │ │ - 22 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 22 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ The oldToNewIV and newToOldIV variables are IV objects that represent an integer vector. The oldToNew │ │ │ │ │ andnewToOldvariablesarepointers to int, which point to the base address of the int vector in an IV object. │ │ │ │ │ Once we have the permutation vector, we apply it to the front tree, by the ETree permuteVertices() │ │ │ │ │ method. We need APT, so we permute the InpMtx object using a NULL pointer for the row permutation │ │ │ │ │ (which means do not permute the rows) and the oldToNew vector for the column permutation. At this point │ │ │ │ │ the InpMtx object holds APT in the form required by the factorization. │ │ │ │ │ The final steps are to compute the symbolic factorization, which is stored in an IVL object, and to │ │ │ │ │ @@ -808,15 +808,15 @@ │ │ │ │ │ the sample program for the numerical factorization step is found below. │ │ │ │ │ chvmanager = ChvManager_new() ; │ │ │ │ │ ChvManager_init(chvmanager, NO_LOCK, 1) ; │ │ │ │ │ DVzero(10, cpus) ; │ │ │ │ │ facops = 0.0 ; │ │ │ │ │ FrontMtx_QR_factor(frontmtx, mtxA, chvmanager, cpus, &facops, msglvl, msgFile) ; │ │ │ │ │ ChvManager_free(chvmanager) ; │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 23 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 23 │ │ │ │ │ Working storage used during the factorization is found in the form of block chevrons, in a Chv object, │ │ │ │ │ which hold the partial frontal matrix for a front. Much as with the SubMtx object, the FrontMtx object │ │ │ │ │ does not concern itself with managing working storage, instead it relies on a ChvManager object to manage │ │ │ │ │ the Chv objects. On return facops contains the number of floating point operations performed during the │ │ │ │ │ factorization. │ │ │ │ │ The factorization is performed using a one-dimensional decomposition of the factor matrices. Keeping │ │ │ │ │ the factor matrices in this form severely limits the amount of parallelism for the forward and backsolves. │ │ │ │ │ @@ -853,15 +853,15 @@ │ │ │ │ │ 5 1 2.0 6 5.0 │ │ │ │ │ 5 4 3.0 7 4.0 │ │ │ │ │ 5 5 1.0 │ │ │ │ │ 6 0 2.0 │ │ │ │ │ 6 3 3.0 │ │ │ │ │ 7 1 1.0 │ │ │ │ │ 7 4 3.0 │ │ │ │ │ - 24 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 24 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ A allInOne.c – A Serial LU Driver Program │ │ │ │ │ /* allInOne.c */ │ │ │ │ │ #include "../../misc.h" │ │ │ │ │ #include "../../FrontMtx.h" │ │ │ │ │ #include "../../SymbFac.h" │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ int │ │ │ │ │ @@ -900,15 +900,15 @@ │ │ │ │ │ symmetryflag, type ; │ │ │ │ │ int *newToOld, *oldToNew ; │ │ │ │ │ int stats[20] ; │ │ │ │ │ IV *newToOldIV, *oldToNewIV ; │ │ │ │ │ IVL *adjIVL, *symbfacIVL ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 25 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 25 │ │ │ │ │ -------------------- │ │ │ │ │ get input parameters │ │ │ │ │ -------------------- │ │ │ │ │ */ │ │ │ │ │ if ( argc != 9 ) { │ │ │ │ │ fprintf(stdout, "\n" │ │ │ │ │ "\n usage: %s msglvl msgFile type symmetryflag pivotingflag" │ │ │ │ │ @@ -952,15 +952,15 @@ │ │ │ │ │ symmetryflag = atoi(argv[4]) ; │ │ │ │ │ pivotingflag = atoi(argv[5]) ; │ │ │ │ │ matrixFileName = argv[6] ; │ │ │ │ │ rhsFileName = argv[7] ; │ │ │ │ │ seed = atoi(argv[8]) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ - 26 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 26 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ -------------------------------------------- │ │ │ │ │ STEP 1: read the entries from the input file │ │ │ │ │ and create the InpMtx object │ │ │ │ │ -------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ inputFile = fopen(matrixFileName, "r") ; │ │ │ │ │ fscanf(inputFile, "%d %d %d", &nrow, &ncol, &nent) ; │ │ │ │ │ @@ -1004,15 +1004,15 @@ │ │ │ │ │ fscanf(inputFile, "%d", &jrow) ; │ │ │ │ │ for ( jrhs = 0 ; jrhs < nrhs ; jrhs++ ) { │ │ │ │ │ fscanf(inputFile, "%le", &value) ; │ │ │ │ │ DenseMtx_setRealEntry(mtxY, jrow, jrhs, value) ; │ │ │ │ │ } │ │ │ │ │ } │ │ │ │ │ } else { │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 27 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 27 │ │ │ │ │ double imag, real ; │ │ │ │ │ for ( irow = 0 ; irow < nrow ; irow++ ) { │ │ │ │ │ fscanf(inputFile, "%d", &jrow) ; │ │ │ │ │ for ( jrhs = 0 ; jrhs < nrhs ; jrhs++ ) { │ │ │ │ │ fscanf(inputFile, "%le %le", &real, &imag) ; │ │ │ │ │ DenseMtx_setComplexEntry(mtxY, jrow, jrhs, real, imag) ; │ │ │ │ │ } │ │ │ │ │ @@ -1056,15 +1056,15 @@ │ │ │ │ │ get the symbolic factorization │ │ │ │ │ ---------------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ oldToNewIV = ETree_oldToNewVtxPerm(frontETree) ; │ │ │ │ │ oldToNew = IV_entries(oldToNewIV) ; │ │ │ │ │ newToOldIV = ETree_newToOldVtxPerm(frontETree) ; │ │ │ │ │ newToOld = IV_entries(newToOldIV) ; │ │ │ │ │ - 28 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 28 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ ETree_permuteVertices(frontETree, oldToNewIV) ; │ │ │ │ │ InpMtx_permute(mtxA, oldToNew, oldToNew) ; │ │ │ │ │ if ( symmetryflag == SPOOLES_SYMMETRIC │ │ │ │ │ || symmetryflag == SPOOLES_HERMITIAN ) { │ │ │ │ │ InpMtx_mapToUpperTriangle(mtxA) ; │ │ │ │ │ } │ │ │ │ │ InpMtx_changeCoordType(mtxA, INPMTX_BY_CHEVRONS) ; │ │ │ │ │ @@ -1108,15 +1108,15 @@ │ │ │ │ │ ChvManager_init(chvmanager, NO_LOCK, 1) ; │ │ │ │ │ DVfill(10, cpus, 0.0) ; │ │ │ │ │ IVfill(20, stats, 0) ; │ │ │ │ │ rootchv = FrontMtx_factorInpMtx(frontmtx, mtxA, tau, droptol, │ │ │ │ │ chvmanager, &error, cpus, stats, msglvl, msgFile) ; │ │ │ │ │ ChvManager_free(chvmanager) ; │ │ │ │ │ if ( msglvl > 2 ) { │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 29 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 29 │ │ │ │ │ fprintf(msgFile, "\n\n factor matrix") ; │ │ │ │ │ FrontMtx_writeForHumanEye(frontmtx, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ if ( rootchv != NULL ) { │ │ │ │ │ fprintf(msgFile, "\n\n matrix found to be singular\n") ; │ │ │ │ │ exit(-1) ; │ │ │ │ │ @@ -1160,15 +1160,15 @@ │ │ │ │ │ ------------------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ DenseMtx_permuteRows(mtxX, newToOldIV) ; │ │ │ │ │ if ( msglvl > 0 ) { │ │ │ │ │ fprintf(msgFile, "\n\n solution matrix in original ordering") ; │ │ │ │ │ DenseMtx_writeForHumanEye(mtxX, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ - 30 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 30 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ----------- │ │ │ │ │ free memory │ │ │ │ │ ----------- │ │ │ │ │ */ │ │ │ │ │ @@ -1181,15 +1181,15 @@ │ │ │ │ │ ETree_free(frontETree) ; │ │ │ │ │ IVL_free(symbfacIVL) ; │ │ │ │ │ SubMtxManager_free(mtxmanager) ; │ │ │ │ │ Graph_free(graph) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ return(1) ; } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 31 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 31 │ │ │ │ │ B allInOne.c – A Serial LU Driver Program │ │ │ │ │ /* allInOneMT.c */ │ │ │ │ │ #include "../spoolesMT.h" │ │ │ │ │ #include "../../misc.h" │ │ │ │ │ #include "../../FrontMtx.h" │ │ │ │ │ #include "../../SymbFac.h" │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ @@ -1228,15 +1228,15 @@ │ │ │ │ │ Graph *graph ; │ │ │ │ │ InpMtx *mtxA ; │ │ │ │ │ int error, ient, irow, jcol, jrhs, jrow, lookahead, msglvl, │ │ │ │ │ ncol, nedges, nent, neqns, nfront, nrhs, nrow, │ │ │ │ │ nthread, pivotingflag, seed, symmetryflag, type ; │ │ │ │ │ int *newToOld, *oldToNew ; │ │ │ │ │ int stats[20] ; │ │ │ │ │ - 32 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 32 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ IV *newToOldIV, *oldToNewIV, *ownersIV ; │ │ │ │ │ IVL *adjIVL, *symbfacIVL ; │ │ │ │ │ SolveMap *solvemap ; │ │ │ │ │ SubMtxManager *mtxmanager ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ -------------------- │ │ │ │ │ @@ -1280,15 +1280,15 @@ │ │ │ │ │ } else if ( (msgFile = fopen(argv[2], "a")) == NULL ) { │ │ │ │ │ fprintf(stderr, "\n fatal error in %s" │ │ │ │ │ "\n unable to open file %s\n", │ │ │ │ │ argv[0], argv[2]) ; │ │ │ │ │ return(-1) ; │ │ │ │ │ } │ │ │ │ │ type = atoi(argv[3]) ; │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 33 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 33 │ │ │ │ │ symmetryflag = atoi(argv[4]) ; │ │ │ │ │ pivotingflag = atoi(argv[5]) ; │ │ │ │ │ matrixFileName = argv[6] ; │ │ │ │ │ rhsFileName = argv[7] ; │ │ │ │ │ seed = atoi(argv[8]) ; │ │ │ │ │ nthread = atoi(argv[9]) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ @@ -1332,15 +1332,15 @@ │ │ │ │ │ inputFile = fopen(rhsFileName, "r") ; │ │ │ │ │ fscanf(inputFile, "%d %d", &nrow, &nrhs) ; │ │ │ │ │ mtxY = DenseMtx_new() ; │ │ │ │ │ DenseMtx_init(mtxY, type, 0, 0, neqns, nrhs, 1, neqns) ; │ │ │ │ │ DenseMtx_zero(mtxY) ; │ │ │ │ │ if ( type == SPOOLES_REAL ) { │ │ │ │ │ double value ; │ │ │ │ │ - 34 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 34 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ for ( irow = 0 ; irow < nrow ; irow++ ) { │ │ │ │ │ fscanf(inputFile, "%d", &jrow) ; │ │ │ │ │ for ( jrhs = 0 ; jrhs < nrhs ; jrhs++ ) { │ │ │ │ │ fscanf(inputFile, "%le", &value) ; │ │ │ │ │ DenseMtx_setRealEntry(mtxY, jrow, jrhs, value) ; │ │ │ │ │ } │ │ │ │ │ } │ │ │ │ │ @@ -1384,15 +1384,15 @@ │ │ │ │ │ ETree_writeForHumanEye(frontETree, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ---------------------------------------------------- │ │ │ │ │ STEP 4: get the permutation, permute the front tree, │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 35 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 35 │ │ │ │ │ permute the matrix and right hand side, and │ │ │ │ │ get the symbolic factorization │ │ │ │ │ ---------------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ oldToNewIV = ETree_oldToNewVtxPerm(frontETree) ; │ │ │ │ │ oldToNew = IV_entries(oldToNewIV) ; │ │ │ │ │ newToOldIV = ETree_newToOldVtxPerm(frontETree) ; │ │ │ │ │ @@ -1436,15 +1436,15 @@ │ │ │ │ │ ownersIV = ETree_ddMap(frontETree, type, symmetryflag, │ │ │ │ │ cumopsDV, 1./(2.*nthread)) ; │ │ │ │ │ if ( msglvl > 1 ) { │ │ │ │ │ fprintf(msgFile, "\n\n map from fronts to threads") ; │ │ │ │ │ IV_writeForHumanEye(ownersIV, msgFile) ; │ │ │ │ │ fprintf(msgFile, "\n\n factor operations for each front") ; │ │ │ │ │ DV_writeForHumanEye(cumopsDV, msgFile) ; │ │ │ │ │ - 36 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 36 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ DV_free(cumopsDV) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------------------------ │ │ │ │ │ STEP 6: initialize the front matrix object │ │ │ │ │ @@ -1488,15 +1488,15 @@ │ │ │ │ │ -------------------------------------- │ │ │ │ │ STEP 8: post-process the factorization │ │ │ │ │ -------------------------------------- │ │ │ │ │ */ │ │ │ │ │ FrontMtx_postProcess(frontmtx, msglvl, msgFile) ; │ │ │ │ │ if ( msglvl > 1 ) { │ │ │ │ │ fprintf(msgFile, "\n\n factor matrix after post-processing") ; │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 37 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 37 │ │ │ │ │ FrontMtx_writeForHumanEye(frontmtx, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------------------------------------- │ │ │ │ │ STEP 9: get the solve map object for the parallel solve │ │ │ │ │ @@ -1540,27 +1540,27 @@ │ │ │ │ │ free memory │ │ │ │ │ ----------- │ │ │ │ │ */ │ │ │ │ │ FrontMtx_free(frontmtx) ; │ │ │ │ │ DenseMtx_free(mtxX) ; │ │ │ │ │ DenseMtx_free(mtxY) ; │ │ │ │ │ IV_free(newToOldIV) ; │ │ │ │ │ - 38 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 38 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ IV_free(oldToNewIV) ; │ │ │ │ │ InpMtx_free(mtxA) ; │ │ │ │ │ ETree_free(frontETree) ; │ │ │ │ │ IVL_free(symbfacIVL) ; │ │ │ │ │ SubMtxManager_free(mtxmanager) ; │ │ │ │ │ Graph_free(graph) ; │ │ │ │ │ SolveMap_free(solvemap) ; │ │ │ │ │ IV_free(ownersIV) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ return(1) ; } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 39 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 39 │ │ │ │ │ C allInOne.c – A Serial LU Driver Program │ │ │ │ │ /* allInOneMPI.c */ │ │ │ │ │ #include "../spoolesMPI.h" │ │ │ │ │ #include "../../timings.h" │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ int │ │ │ │ │ main ( int argc, char *argv[] ) { │ │ │ │ │ @@ -1598,15 +1598,15 @@ │ │ │ │ │ double *opcounts ; │ │ │ │ │ DV *cumopsDV ; │ │ │ │ │ ETree *frontETree ; │ │ │ │ │ FILE *inputFile, *msgFile ; │ │ │ │ │ Graph *graph ; │ │ │ │ │ int error, firsttag, ient, irow, jcol, lookahead = 0, │ │ │ │ │ msglvl, myid, nedges, nent, neqns, nmycol, nproc, nrhs, │ │ │ │ │ - 40 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 40 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ nrow, pivotingflag, root, seed, symmetryflag, type ; │ │ │ │ │ int stats[20] ; │ │ │ │ │ int *rowind ; │ │ │ │ │ IV *oldToNewIV, *ownedColumnsIV, *ownersIV, │ │ │ │ │ *newToOldIV, *vtxmapIV ; │ │ │ │ │ IVL *adjIVL, *symbfacIVL ; │ │ │ │ │ SolveMap *solvemap ; │ │ │ │ │ @@ -1650,15 +1650,15 @@ │ │ │ │ │ return(0) ; │ │ │ │ │ } │ │ │ │ │ msglvl = atoi(argv[1]) ; │ │ │ │ │ if ( strcmp(argv[2], "stdout") == 0 ) { │ │ │ │ │ msgFile = stdout ; │ │ │ │ │ } else { │ │ │ │ │ sprintf(buffer, "res.%d", myid) ; │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 41 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 41 │ │ │ │ │ if ( (msgFile = fopen(buffer, "w")) == NULL ) { │ │ │ │ │ fprintf(stderr, "\n fatal error in %s" │ │ │ │ │ "\n unable to open file %s\n", │ │ │ │ │ argv[0], buffer) ; │ │ │ │ │ return(-1) ; │ │ │ │ │ } │ │ │ │ │ } │ │ │ │ │ @@ -1702,15 +1702,15 @@ │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ---------------------------------------------------- │ │ │ │ │ STEP 2: read the rhs entries from the rhs input file │ │ │ │ │ and create the DenseMtx object for Y │ │ │ │ │ - 42 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 42 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ ---------------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ sprintf(buffer, "rhs.%d.input", myid) ; │ │ │ │ │ inputFile = fopen(buffer, "r") ; │ │ │ │ │ fscanf(inputFile, "%d %d", &nrow, &nrhs) ; │ │ │ │ │ mtxY = DenseMtx_new() ; │ │ │ │ │ DenseMtx_init(mtxY, type, 0, 0, nrow, nrhs, 1, nrow) ; │ │ │ │ │ @@ -1754,15 +1754,15 @@ │ │ │ │ │ adjIVL = InpMtx_MPI_fullAdjacency(mtxA, stats, │ │ │ │ │ msglvl, msgFile, MPI_COMM_WORLD) ; │ │ │ │ │ nedges = IVL_tsize(adjIVL) ; │ │ │ │ │ Graph_init2(graph, 0, neqns, 0, nedges, neqns, nedges, adjIVL, │ │ │ │ │ NULL, NULL) ; │ │ │ │ │ if ( msglvl > 2 ) { │ │ │ │ │ fprintf(msgFile, "\n\n graph of the input matrix") ; │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 43 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 43 │ │ │ │ │ Graph_writeForHumanEye(graph, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ frontETree = orderViaMMD(graph, seed + myid, msglvl, msgFile) ; │ │ │ │ │ Graph_free(graph) ; │ │ │ │ │ if ( msglvl > 2 ) { │ │ │ │ │ fprintf(msgFile, "\n\n front tree from ordering") ; │ │ │ │ │ @@ -1806,15 +1806,15 @@ │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------------------------- │ │ │ │ │ STEP 4: generate the owners map IV object │ │ │ │ │ and the map from vertices to owners │ │ │ │ │ - 44 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 44 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ ------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ cutoff = 1./(2*nproc) ; │ │ │ │ │ cumopsDV = DV_new() ; │ │ │ │ │ DV_init(cumopsDV, nproc, NULL) ; │ │ │ │ │ ownersIV = ETree_ddMap(frontETree, │ │ │ │ │ type, symmetryflag, cumopsDV, cutoff) ; │ │ │ │ │ @@ -1858,15 +1858,15 @@ │ │ │ │ │ DenseMtx_writeForHumanEye(mtxY, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------------------------ │ │ │ │ │ STEP 6: compute the symbolic factorization │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 45 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 45 │ │ │ │ │ ------------------------------------------ │ │ │ │ │ */ │ │ │ │ │ symbfacIVL = SymbFac_MPI_initFromInpMtx(frontETree, ownersIV, mtxA, │ │ │ │ │ stats, msglvl, msgFile, firsttag, MPI_COMM_WORLD) ; │ │ │ │ │ firsttag += frontETree->nfront ; │ │ │ │ │ if ( msglvl > 2 ) { │ │ │ │ │ fprintf(msgFile, "\n\n local symbolic factorization") ; │ │ │ │ │ @@ -1910,15 +1910,15 @@ │ │ │ │ │ exit(-1) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------------------------------ │ │ │ │ │ STEP 9: post-process the factorization and split │ │ │ │ │ the factor matrices into submatrices │ │ │ │ │ - 46 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 46 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ ------------------------------------------------ │ │ │ │ │ */ │ │ │ │ │ FrontMtx_MPI_postProcess(frontmtx, ownersIV, stats, msglvl, │ │ │ │ │ msgFile, firsttag, MPI_COMM_WORLD) ; │ │ │ │ │ firsttag += 5*nproc ; │ │ │ │ │ if ( msglvl > 2 ) { │ │ │ │ │ fprintf(msgFile, "\n\n numeric factorization after post-processing"); │ │ │ │ │ @@ -1962,15 +1962,15 @@ │ │ │ │ │ */ │ │ │ │ │ if ( FRONTMTX_IS_PIVOTING(frontmtx) ) { │ │ │ │ │ IV *rowmapIV ; │ │ │ │ │ /* │ │ │ │ │ ---------------------------------------------------------- │ │ │ │ │ pivoting has taken place, redistribute the right hand side │ │ │ │ │ to match the final rows and columns in the fronts │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 47 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 47 │ │ │ │ │ ---------------------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ rowmapIV = FrontMtx_MPI_rowmapIV(frontmtx, ownersIV, msglvl, │ │ │ │ │ msgFile, MPI_COMM_WORLD) ; │ │ │ │ │ newY = DenseMtx_MPI_splitByRows(mtxY, rowmapIV, stats, msglvl, │ │ │ │ │ msgFile, firsttag, MPI_COMM_WORLD) ; │ │ │ │ │ DenseMtx_free(mtxY) ; │ │ │ │ │ @@ -2014,15 +2014,15 @@ │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ -------------------------------------------------------- │ │ │ │ │ STEP 15: permute the solution into the original ordering │ │ │ │ │ and assemble the solution onto processor zero │ │ │ │ │ -------------------------------------------------------- │ │ │ │ │ - 48 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 48 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ */ │ │ │ │ │ DenseMtx_permuteRows(mtxX, newToOldIV) ; │ │ │ │ │ if ( msglvl > 2 ) { │ │ │ │ │ fprintf(msgFile, "\n\n solution in old ordering") ; │ │ │ │ │ DenseMtx_writeForHumanEye(mtxX, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ @@ -2035,15 +2035,15 @@ │ │ │ │ │ DenseMtx_writeForHumanEye(mtxX, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ MPI_Finalize() ; │ │ │ │ │ return(1) ; } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 49 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 49 │ │ │ │ │ D allInOne.c – A Serial QR Driver Program │ │ │ │ │ /* QRallInOne.c */ │ │ │ │ │ #include "../../misc.h" │ │ │ │ │ #include "../../FrontMtx.h" │ │ │ │ │ #include "../../SymbFac.h" │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ int │ │ │ │ │ @@ -2083,15 +2083,15 @@ │ │ │ │ │ /* │ │ │ │ │ -------------------- │ │ │ │ │ get input parameters │ │ │ │ │ -------------------- │ │ │ │ │ */ │ │ │ │ │ if ( argc != 7 ) { │ │ │ │ │ fprintf(stdout, │ │ │ │ │ - 50 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 50 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ "\n usage: %s msglvl msgFile type matrixFileName rhsFileName seed" │ │ │ │ │ "\n msglvl -- message level" │ │ │ │ │ "\n msgFile -- message file" │ │ │ │ │ "\n type -- type of entries" │ │ │ │ │ "\n 1 (SPOOLES_REAL) -- real entries" │ │ │ │ │ "\n 2 (SPOOLES_COMPLEX) -- complex entries" │ │ │ │ │ "\n matrixFileName -- matrix file name, format" │ │ │ │ │ @@ -2135,15 +2135,15 @@ │ │ │ │ │ if ( type == SPOOLES_REAL ) { │ │ │ │ │ for ( ient = 0 ; ient < nent ; ient++ ) { │ │ │ │ │ fscanf(inputFile, "%d %d %le", &irow, &jcol, &value) ; │ │ │ │ │ InpMtx_inputRealEntry(mtxA, irow, jcol, value) ; │ │ │ │ │ } │ │ │ │ │ } else { │ │ │ │ │ for ( ient = 0 ; ient < nent ; ient++ ) { │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 51 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 51 │ │ │ │ │ fscanf(inputFile, "%d %d %le %le", &irow, &jcol, &real, &imag) ; │ │ │ │ │ InpMtx_inputComplexEntry(mtxA, irow, jcol, real, imag) ; │ │ │ │ │ } │ │ │ │ │ } │ │ │ │ │ fclose(inputFile) ; │ │ │ │ │ if ( msglvl > 1 ) { │ │ │ │ │ fprintf(msgFile, "\n\n input matrix") ; │ │ │ │ │ @@ -2187,15 +2187,15 @@ │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------------------------------- │ │ │ │ │ STEP 3 : find a low-fill ordering │ │ │ │ │ (1) create the Graph object for A^TA or A^HA │ │ │ │ │ (2) order the graph using multiple minimum degree │ │ │ │ │ ------------------------------------------------- │ │ │ │ │ - 52 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 52 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ */ │ │ │ │ │ graph = Graph_new() ; │ │ │ │ │ adjIVL = InpMtx_adjForATA(mtxA) ; │ │ │ │ │ nedges = IVL_tsize(adjIVL) ; │ │ │ │ │ Graph_init2(graph, 0, neqns, 0, nedges, neqns, nedges, adjIVL, │ │ │ │ │ NULL, NULL) ; │ │ │ │ │ if ( msglvl > 1 ) { │ │ │ │ │ @@ -2239,15 +2239,15 @@ │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------------------------ │ │ │ │ │ STEP 5: initialize the front matrix object │ │ │ │ │ ------------------------------------------ │ │ │ │ │ */ │ │ │ │ │ - January 6, 2026 SPOOLES 2.2—Solving Linear Systems 53 │ │ │ │ │ + January 17, 2026 SPOOLES 2.2—Solving Linear Systems 53 │ │ │ │ │ frontmtx = FrontMtx_new() ; │ │ │ │ │ mtxmanager = SubMtxManager_new() ; │ │ │ │ │ SubMtxManager_init(mtxmanager, NO_LOCK, 0) ; │ │ │ │ │ if ( type == SPOOLES_REAL ) { │ │ │ │ │ FrontMtx_init(frontmtx, frontETree, symbfacIVL, type, │ │ │ │ │ SPOOLES_SYMMETRIC, FRONTMTX_DENSE_FRONTS, │ │ │ │ │ SPOOLES_NO_PIVOTING, NO_LOCK, 0, NULL, │ │ │ │ │ @@ -2291,15 +2291,15 @@ │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------------- │ │ │ │ │ STEP 8: solve the linear system │ │ │ │ │ ------------------------------- │ │ │ │ │ */ │ │ │ │ │ - 54 SPOOLES2.2—SolvingLinearSystems January 6, 2026 │ │ │ │ │ + 54 SPOOLES2.2—SolvingLinearSystems January 17, 2026 │ │ │ │ │ mtxX = DenseMtx_new() ; │ │ │ │ │ DenseMtx_init(mtxX, type, 0, 0, neqns, nrhs, 1, neqns) ; │ │ │ │ │ FrontMtx_QR_solve(frontmtx, mtxA, mtxX, mtxB, mtxmanager, │ │ │ │ │ cpus, msglvl, msgFile) ; │ │ │ │ │ if ( msglvl > 1 ) { │ │ │ │ │ fprintf(msgFile, "\n\n solution matrix in new ordering") ; │ │ │ │ │ DenseMtx_writeForHumanEye(mtxX, msgFile) ; │ │ ├── ./usr/share/doc/spooles-doc/BKL.ps.gz │ │ │ ├── BKL.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o BKL.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2033 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -2553,16 +2553,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -2750,79 +2752,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 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│ │ │ │ %%Page: 2 2 │ │ │ │ -TeXDict begin 2 1 bop 0 100 a Fl(2)p 136 100 1182 4 v │ │ │ │ -1364 w Fk(BKL)29 b Fh(:)i Fg(DRAFT)f Fh(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2719 100 V 137 399 a Fi(\210)45 b Fk(int)i(*regwghts)39 │ │ │ │ +TeXDict begin 2 1 bop 0 100 a Fl(2)p 136 100 1159 4 v │ │ │ │ +1341 w Fk(BKL)29 b Fh(:)i Fg(DRAFT)f Fh(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2741 100 V 137 399 a Fi(\210)45 b Fk(int)i(*regwghts)39 │ │ │ │ b Fl(:)62 b(p)s(oin)m(ter)41 b(to)h(an)f Fk(int)f Fl(v)m(ector)j(of)e │ │ │ │ (size)h Fk(nreg)p Fl(,)h(used)d(to)i(store)g(the)f(w)m(eigh)m(ts)h(of)g │ │ │ │ (the)227 511 y(domains)30 b(and)g(segmen)m(ts)137 738 │ │ │ │ y Fi(\210)45 b Fk(float)i(alpha)41 b Fl(:)65 b(n)m(um)m(b)s(er)41 │ │ │ │ b(used)g(to)j(store)f(the)f(partition)i(ev)-5 b(aluation)44 │ │ │ │ b(parameter,)i(the)d(cost)g(of)g(the)227 851 y(partition)31 │ │ │ │ b(is)227 1124 y Fk(balance)46 b(=)i(max\(cweights[1],)43 │ │ │ │ @@ -4285,17 +4296,17 @@ │ │ │ │ (call)h(to)f Fk(BKL)p 2265 5125 V 34 w(clearData\(\))c │ │ │ │ Fl(then)j(free's)h(the)f(storage)i(for)227 5238 y(the)31 │ │ │ │ b(structure)f(with)g(a)h(call)g(to)g Fk(free\(\))p Fl(.)227 │ │ │ │ 5407 y Fg(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fl(If)30 │ │ │ │ b Fk(bkl)g Fl(is)g Fk(NULL)p Fl(,)g(an)g(error)g(message)h(is)g(prin)m │ │ │ │ (ted)f(and)g(the)g(program)g(exits.)p eop end │ │ │ │ %%Page: 3 3 │ │ │ │ -TeXDict begin 3 2 bop 91 100 1182 4 v 1363 100 a Fk(BKL)30 │ │ │ │ -b Fh(:)g Fg(DRAFT)121 b Fh(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2671 100 V 1182 w Fl(3)0 399 y Fe(1.3.1)112 b(Initializer)38 │ │ │ │ +TeXDict begin 3 2 bop 91 100 1159 4 v 1340 100 a Fk(BKL)30 │ │ │ │ +b Fh(:)g Fg(DRAFT)122 b Fh(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2694 100 V 1159 w Fl(3)0 399 y Fe(1.3.1)112 b(Initializer)38 │ │ │ │ b(metho)s(ds)111 590 y Fl(1.)46 b Fk(void)h(BKL_init)e(\()j(BKL)f │ │ │ │ (*bkl,)f(BPG)h(*bpg,)f(float)h(alpha)f(\))i(;)227 736 │ │ │ │ y Fl(This)34 b(metho)s(d)g(initializes)j(the)d Fk(BKL)g │ │ │ │ Fl(ob)5 b(ject)35 b(giv)m(en)h(a)f(bipartite)g(graph)f(ob)5 │ │ │ │ b(ject)35 b(and)f(cost)i(function)e(pa-)227 849 y(rameter)g(as)f │ │ │ │ (input.)48 b(An)m(y)33 b(previous)g(data)h(is)f(cleared)h(with)f(a)h │ │ │ │ (call)g(to)g Fk(BKL)p 2868 849 29 4 v 33 w(clearData\(\))p │ │ │ │ @@ -4359,17 +4370,17 @@ │ │ │ │ y(6.)46 b Fk(float)h(BKL_setInitPart)c(\()48 b(BKL)f(*bkl,)f(int)h │ │ │ │ (flag,)f(int)h(seed,)g(int)f(domcolors[])f(\))j(;)227 │ │ │ │ 5294 y Fl(This)43 b(metho)s(d)g(sets)h(the)f(initial)i(partition)f(b)m │ │ │ │ (y)f(coloring)i(the)e(domains)h(and)e(segmen)m(ts.)81 │ │ │ │ b(The)43 b Fk(flag)227 5407 y Fl(parameter)31 b(has)f(the)h(follo)m │ │ │ │ (wing)h(v)-5 b(alues.)p eop end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fl(4)p 136 100 1182 4 v │ │ │ │ -1364 w Fk(BKL)29 b Fh(:)i Fg(DRAFT)f Fh(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2719 100 V 337 399 a Fi(\210)45 b Fk(flag)i(=)g(1)30 │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fl(4)p 136 100 1159 4 v │ │ │ │ +1341 w Fk(BKL)29 b Fh(:)i Fg(DRAFT)f Fh(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2741 100 V 337 399 a Fi(\210)45 b Fk(flag)i(=)g(1)30 │ │ │ │ b Fd(\000)-15 b(!)30 b Fl(random)g(coloring)h(of)g(the)g(domains)337 │ │ │ │ 558 y Fi(\210)45 b Fk(flag)i(=)g(2)30 b Fd(\000)-15 b(!)30 │ │ │ │ b Fl(one)h(blac)m(k)g(domain,)g(\()p Fk(seed)e Fl(\045)h │ │ │ │ Fk(ndom)p Fl(\),)g(rest)h(are)f(white)337 717 y Fi(\210)45 │ │ │ │ b Fk(flag)i(=)g(3)32 b Fd(\000)-15 b(!)32 b Fl(one)g(blac)m(k)i │ │ │ │ (pseudop)s(eripheral)c(domain,)j(found)e(using)g(domain)h(\()p │ │ │ │ Fk(seed)g Fl(\045)g Fk(ndom)p Fl(\))427 830 y(as)f(ro)s(ot,)g(rest)f │ │ │ │ @@ -4437,17 +4448,17 @@ │ │ │ │ b(it)g(returns)e(\()p Fd(j)p Fc(S)5 b Fd(j)21 b Fl(+)f │ │ │ │ Fd(j)p Fc(B)5 b Fd(j)20 b Fl(+)g Fd(j)p Fc(W)13 b Fd(j)p │ │ │ │ Fl(\))1714 5211 y Fa(2)1754 5244 y Fl(.)227 5407 y Fg(Err)-5 │ │ │ │ b(or)34 b(che)-5 b(cking:)40 b Fl(If)30 b Fk(bkl)g Fl(is)g │ │ │ │ Fk(NULL)p Fl(,)g(an)g(error)g(message)h(is)g(prin)m(ted)f(and)g(the)g │ │ │ │ (program)g(exits.)p eop end │ │ │ │ %%Page: 5 5 │ │ │ │ -TeXDict begin 5 4 bop 91 100 1182 4 v 1363 100 a Fk(BKL)30 │ │ │ │ -b Fh(:)g Fg(DRAFT)121 b Fh(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2671 100 V 1182 w Fl(5)111 399 y(3.)46 b Fk(float)h(BKL_eval)e(\()j │ │ │ │ +TeXDict begin 5 4 bop 91 100 1159 4 v 1340 100 a Fk(BKL)30 │ │ │ │ +b Fh(:)g Fg(DRAFT)122 b Fh(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2694 100 V 1159 w Fl(5)111 399 y(3.)46 b Fk(float)h(BKL_eval)e(\()j │ │ │ │ (BKL)f(*bkl,)f(int)h(Sweight,)e(int)i(Bweight,)f(int)h(Wweight)f(\))h │ │ │ │ (;)227 549 y Fl(The)31 b Fd(j)p Fc(S)5 b Fd(j)p Fl(,)31 │ │ │ │ b Fd(j)p Fc(B)5 b Fd(j)31 b Fl(and)f Fd(j)p Fc(W)13 b │ │ │ │ Fd(j)31 b Fl(v)-5 b(alues)31 b(are)g(tak)m(en)h(from)e(the)h │ │ │ │ Fk(Sweight)p Fl(,)f Fk(Bweight)e Fl(and)j Fk(Wweight)d │ │ │ │ Fl(parameters.)227 662 y(If)i(min\()p Fd(j)p Fc(B)5 b │ │ │ │ Fd(j)p Fc(;)15 b Fd(j)p Fc(W)e Fd(j)p Fl(\))26 b Fc(>)f │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -18,15 +18,15 @@ │ │ │ │ │ • int ngaineval : number of gain evaluations, roughly equivalent to the number of degree │ │ │ │ │ evaluations in the minimum degree algorithm │ │ │ │ │ • int *colors : pointer to an int vector of size nreg, colors[idom] is 1 or 2 for domain │ │ │ │ │ idom, colors[iseg] is 0, 1 or 2 for segment iseg. │ │ │ │ │ • int *cweights : pointer to an int vector of size 3, cweights[0] contains the weight of the │ │ │ │ │ separator, cweights[1] and cweights[2] contains the weights of the two components │ │ │ │ │ 1 │ │ │ │ │ - 2 BKL : DRAFT January 6, 2026 │ │ │ │ │ + 2 BKL : DRAFT January 17, 2026 │ │ │ │ │ • int *regwghts : pointer to an int vector of size nreg, used to store the weights of the │ │ │ │ │ domains and segments │ │ │ │ │ • float alpha : number used to store the partition evaluation parameter, the cost of the │ │ │ │ │ partition is │ │ │ │ │ balance = max(cweights[1], cweights[2])/min(cweights[1], cweights[2]) ; │ │ │ │ │ cost = cweights[0]*(1. + alpha*balance) ; │ │ │ │ │ 1.2 Prototypes and descriptions of BKL methods │ │ │ │ │ @@ -47,15 +47,15 @@ │ │ │ │ │ This method clears any data allocated by the object, namely the colors and regwghts vec- │ │ │ │ │ tors. It then fills the structure’s fields with default values with a call to BKL setDefaultFields(). │ │ │ │ │ Error checking: If bkl is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void BKL_free ( BKL *bkl ) ; │ │ │ │ │ This method releases any storage by a call to BKL clearData() then free’s the storage for │ │ │ │ │ the structure with a call to free(). │ │ │ │ │ Error checking: If bkl is NULL, an error message is printed and the program exits. │ │ │ │ │ - BKL : DRAFT January 6, 2026 3 │ │ │ │ │ + BKL : DRAFT January 17, 2026 3 │ │ │ │ │ 1.3.1 Initializer methods │ │ │ │ │ 1. void BKL_init ( BKL *bkl, BPG *bpg, float alpha ) ; │ │ │ │ │ This method initializes the BKL object given a bipartite graph object and cost function pa- │ │ │ │ │ rameter as input. Any previous data is cleared with a call to BKL clearData(). The ndom, │ │ │ │ │ nseg and nreg scalars are set, the regwghts[] vector allocated and filled, and the colors[] │ │ │ │ │ vector allocated and filled with zeros. │ │ │ │ │ Error checking: If bkl or bpg is NULL, an error message is printed and the program exits. │ │ │ │ │ @@ -84,15 +84,15 @@ │ │ │ │ │ This method returns the next domain id in a grey code sequence, used to exhaustively search │ │ │ │ │ of a subspace of partitions defined by set of candidate domains to flip. The value count │ │ │ │ │ ranges from 1 to 2ndom. │ │ │ │ │ Error checking: If bkl is NULL, an error message is printed and the program exits. │ │ │ │ │ 6. float BKL_setInitPart ( BKL *bkl, int flag, int seed, int domcolors[] ) ; │ │ │ │ │ This method sets the initial partition by coloring the domains and segments. The flag │ │ │ │ │ parameter has the following values. │ │ │ │ │ - 4 BKL : DRAFT January 6, 2026 │ │ │ │ │ + 4 BKL : DRAFT January 17, 2026 │ │ │ │ │ • flag = 1 −→ random coloring of the domains │ │ │ │ │ • flag = 2 −→ one black domain, (seed % ndom), rest are white │ │ │ │ │ • flag = 3 −→ one black pseudoperipheral domain, found using domain (seed % ndom) │ │ │ │ │ as root, rest are white │ │ │ │ │ • flag = 4 −→ roughly half-half split, breadth first search of domains, (seed % ndom) as │ │ │ │ │ root │ │ │ │ │ • flag = 5 −→ roughly half-half split, breadth first search of domains, (seed % ndom) as │ │ │ │ │ @@ -119,15 +119,15 @@ │ │ │ │ │ The |S|, |B| and |W| values are taken from the cweights[] vector. If min(|B|,|W|) > 0, this │ │ │ │ │ function returns   │ │ │ │ │ |S| 1+α∗max(|B|,|W|) , │ │ │ │ │ min(|B|,|W|) │ │ │ │ │ 2 │ │ │ │ │ otherwise it returns (|S| + |B| + |W|) . │ │ │ │ │ Error checking: If bkl is NULL, an error message is printed and the program exits. │ │ │ │ │ - BKL : DRAFT January 6, 2026 5 │ │ │ │ │ + BKL : DRAFT January 17, 2026 5 │ │ │ │ │ 3. float BKL_eval ( BKL *bkl, int Sweight, int Bweight, int Wweight ) ; │ │ │ │ │ The |S|, |B| and |W| values are taken from the Sweight, Bweight and Wweight parameters. │ │ │ │ │ If min(|B|,|W|) > 0, this function returns │ │ │ │ │ |S|1+α∗ max(|B|,|W|), │ │ │ │ │ min(|B|,|W|) │ │ │ │ │ 2 │ │ │ │ │ otherwise it returns (|S| + |B| + |W|) . The method checks that bkl is not NULL. │ │ ├── ./usr/share/doc/spooles-doc/BPG.ps.gz │ │ │ ├── BPG.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o BPG.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2033 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1425,16 +1425,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1622,79 +1624,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ B7D99CD533EC5F931B18E6B39BECF67FA2D6DD1AEC76772B068BE06335A94C05 │ │ │ │ 7A4DDEE77B66101DA855C17AC312600370B34E31F5EC3A01300A8EB60B4C9767 │ │ │ │ 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Fk(Err)l(or)j(che)l(cking:)38 b Fm(If)28 b Fl(bpg)f │ │ │ │ @@ -5389,17 +5400,17 @@ │ │ │ │ (the)h(input)g(\014le)f(for)g(the)h Fl(BPG)e Fm(ob)5 │ │ │ │ b(ject.)60 b(It)35 b(m)n(ust)h(b)r(e)f(of)h(the)f(form)g │ │ │ │ Fl(*.bpgf)e Fm(or)390 5407 y Fl(*.bpgb)p Fm(.)i(The)27 │ │ │ │ b Fl(BPG)g Fm(ob)5 b(ject)27 b(is)h(read)e(from)i(the)g(\014le)f(via)g │ │ │ │ (the)h Fl(BPG)p 2449 5407 V 31 w(readFromFile\(\))21 │ │ │ │ b Fm(metho)r(d.)p eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 83 100 1249 4 v 1414 100 a Fl(BPG)27 │ │ │ │ -b Fe(:)g Fk(DRAFT)111 b Fe(Jan)n(uary)25 b(6,)i(2026)p │ │ │ │ -2612 100 V 1249 w Fm(7)307 390 y Fh(\210)42 b Fm(The)33 │ │ │ │ +TeXDict begin 7 6 bop 83 100 1228 4 v 1393 100 a Fl(BPG)27 │ │ │ │ +b Fe(:)h Fk(DRAFT)110 b Fe(Jan)n(uary)25 b(17,)i(2026)p │ │ │ │ +2633 100 V 1228 w Fm(7)307 390 y Fh(\210)42 b Fm(The)33 │ │ │ │ b Fl(outFile)d Fm(parameter)i(is)g(the)i(output)f(\014le)g(for)g(the)g │ │ │ │ Fl(BPG)f Fm(ob)5 b(ject.)52 b(If)33 b Fl(outFile)d Fm(is)j │ │ │ │ Fl(none)f Fm(then)h(the)g Fl(BPG)390 490 y Fm(ob)5 b(ject)30 │ │ │ │ b(is)f(not)h(written)f(to)h(a)f(\014le.)43 b(Otherwise,)30 │ │ │ │ b(the)g Fl(BPG)p 2219 490 27 4 v 30 w(writeToFile\(\))24 │ │ │ │ b Fm(metho)r(d)30 b(is)g(called)f(to)g(write)h(the)390 │ │ │ │ 589 y(graph)c(to)g(a)h(formatted)f(\014le)h(\(if)g Fl(outFile)d │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -29,15 +29,15 @@ │ │ │ │ │ code for the process outweighed (outline’d?) the BPG code for the data. Now if someone wants to modify │ │ │ │ │ (and hopefully improve) the Kernighan-Lin process, they won’t alter the behavior of the bipartite graph │ │ │ │ │ object. │ │ │ │ │ Finding the Dulmage-Mendelsohn decomposition of a bipartite graph is a little less clear cut. When the │ │ │ │ │ vertices in the bipartite graph have unit weight, the process is straightforward. │ │ │ │ │ • Find a maximum matching. │ │ │ │ │ 1 │ │ │ │ │ - 2 BPG : DRAFT January 6, 2026 │ │ │ │ │ + 2 BPG : DRAFT January 17, 2026 │ │ │ │ │ • Drop an alternating level structure from exposed nodes in X. │ │ │ │ │ • Drop an alternating level structure from exposed nodes in Y . │ │ │ │ │ • Based on the two previous steps, partition X into three pieces and Y into three pieces and form a new │ │ │ │ │ separator from the pieces. │ │ │ │ │ (If these terms are not familiar, see [?]; our present purpose is a discussion of software design, not algorithms.) │ │ │ │ │ Amatching is a very common operation on a bipartite graph, so it is not unreasonable to expand the data │ │ │ │ │ object to include some mechanism for matching, e.g., a mate[] vector. Finding a maximum matching is │ │ │ │ │ @@ -78,15 +78,15 @@ │ │ │ │ │ b │ │ │ │ │ separator size. But, if we consider S ∪ (Adj(S) ∩ B) to be a wide separator, the resulting separator S need │ │ │ │ │ not be a separator with minimal weight that is found within the wide separator. The trick is that some │ │ │ │ │ nodes in Adj(S)∩B might be absorbed into W. │ │ │ │ │ Onecanfindaseparatorwith minimal weight from the wide separator S∪(Adj(S)∩B), in fact from any │ │ │ │ │ wide separator that contains S, by solving a max flow problem. The drawback is that the network induced │ │ │ │ │ by S∪(Adj(S)∩B) need not be bipartite. In other words, a bipartite induced graph necessarily implies two │ │ │ │ │ - BPG : DRAFT January 6, 2026 3 │ │ │ │ │ + BPG : DRAFT January 17, 2026 3 │ │ │ │ │ layers to the wide separator, but the converse does not hold. We were then free to examine wide separators │ │ │ │ │ that had more than two layers from which to find a minimal weight separator. It turns out that three layers │ │ │ │ │ is better than two, in practice. │ │ │ │ │ We did write a separate object to solve our max flow problem; see the Network object. To smooth a │ │ │ │ │ separator, i.e., to improve a 2-set partition, we no longer have need of the bipartite graph object. We leave │ │ │ │ │ the two Dulmage-Mendelsohn methods in the BPG object for historical and sentimental reasons. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ @@ -110,15 +110,15 @@ │ │ │ │ │ This method releases the storage for graph via a call to Graph clearData(), and then the structure’s │ │ │ │ │ fields are then set to their default values with a call to BPG setDefaultFields(). │ │ │ │ │ Error checking: If bpg is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void BPG_free ( BPG *bpg ) ; │ │ │ │ │ This method releases any storage by a call to BPG clearData()then free’s the storage for the structure │ │ │ │ │ with a call to free(). │ │ │ │ │ Error checking: If bpg is NULL, an error message is printed and the program exits. │ │ │ │ │ - 4 BPG : DRAFT January 6, 2026 │ │ │ │ │ + 4 BPG : DRAFT January 17, 2026 │ │ │ │ │ 1.2.2 Initializer methods │ │ │ │ │ There are two initializer methods. │ │ │ │ │ 1. void BPG_init ( BPG *bpg, int nX, int nY, Graph *graph ) ; │ │ │ │ │ This method initializes the BPG object when all three of its fields are given in the calling sequence. The │ │ │ │ │ Graphobject has nX + nY vertices. Note, the BPG object now “owns” the Graph object and so will free │ │ │ │ │ the Graph object when it is free’d. The Graph object may contains edges between nodes in X and Y, │ │ │ │ │ but these edges are swapped to the end of each adjacency list and the size of each list is then set. │ │ │ │ │ @@ -151,15 +151,15 @@ │ │ │ │ │ int mark[], int tag ) ; │ │ │ │ │ This method drops a level structure from vertex root, fills the dist[] vector with the distances from │ │ │ │ │ root, and returns the number of levels created. The mark[] vector is used to mark nodes with the tag │ │ │ │ │ value as they are placed in the level structure. The list[] vector is used to accumulate the nodes as │ │ │ │ │ they are placed in the level structure. │ │ │ │ │ Error checking: If bpg, list, dist or mark is NULL, or if root is not in [0, nX+nY), an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ - BPG : DRAFT January 6, 2026 5 │ │ │ │ │ + BPG : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.5 Dulmage-Mendelsohn decomposition method │ │ │ │ │ There is one method to find the Dulmage-Mendelsohn decomposition that uses matching when the graph │ │ │ │ │ is unit weight and a generalized matching technique otherwise. There is a second method to find the │ │ │ │ │ decomposition using a Ford-Fulkerson algorithm to find a max flow and a min-cut on a bipartite network. │ │ │ │ │ This has largely been superceded by the Network object. │ │ │ │ │ 1. void BPG_DMdecomposition ( BPG *bpg, int dmflags[], int stats[], │ │ │ │ │ int msglvl, FILE *msgFile ) │ │ │ │ │ @@ -204,15 +204,15 @@ │ │ │ │ │ the value returned from the called routine. │ │ │ │ │ Error checking: If bpg or fn is NULL, or if fn is not of the form *.bpgf (for a formatted file) or *.bpgb │ │ │ │ │ (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 2. int BPG_readFromFormattedFile ( BPG *bpg, FILE *fp ) ; │ │ │ │ │ This method reads a BPG object from a formatted file. If there are no errors in reading the data, the │ │ │ │ │ value 1 is returned. If an IO error is encountered from fscanf, zero is returned. │ │ │ │ │ Error checking: If bpg or fp is NULL an error message is printed and zero is returned. │ │ │ │ │ - 6 BPG : DRAFT January 6, 2026 │ │ │ │ │ + 6 BPG : DRAFT January 17, 2026 │ │ │ │ │ 3. int BPG_readFromBinaryFile ( BPG *bpg, FILE *fp ) ; │ │ │ │ │ This method reads a BPG object from a binary file. If there are no errors in reading the data, the value │ │ │ │ │ 1 is returned. If an IO error is encountered from fread, zero is returned. │ │ │ │ │ Error checking: If bpg or fp is NULL an error message is printed and zero is returned. │ │ │ │ │ 4. int BPG_writeToFile ( BPG *bpg, char *fn ) ; │ │ │ │ │ ThismethodwritesaBPGobjecttoafile. Themethodtriestoopenthefileandifitissuccessful,it then │ │ │ │ │ calls BPG writeFromFormattedFile()or BPG writeFromBinaryFile(),closes the file and returns the │ │ │ │ │ @@ -243,15 +243,15 @@ │ │ │ │ │ BPG writeStats() method). │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means the BPG │ │ │ │ │ object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • The inFile parameter is the input file for the BPG object. It must be of the form *.bpgf or │ │ │ │ │ *.bpgb. The BPG object is read from the file via the BPG readFromFile() method. │ │ │ │ │ - BPG : DRAFT January 6, 2026 7 │ │ │ │ │ + BPG : DRAFT January 17, 2026 7 │ │ │ │ │ • The outFile parameter is the output file for the BPG object. If outFile is none then the BPG │ │ │ │ │ object is not written to a file. Otherwise, the BPG writeToFile() method is called to write the │ │ │ │ │ graph to a formatted file (if outFile is of the form *.bpgf), or a binary file (if outFile is of the │ │ │ │ │ form *.bpgb). │ │ │ │ │ 2. extractBPG msglvl msgFile inGraphFile inCompidsIVfile │ │ │ │ │ icomp outMapFile outBPGfile │ │ │ │ │ This driver program reads in a Graph object and an IV object that contains the component ids. (A │ │ ├── ./usr/share/doc/spooles-doc/Chv.ps.gz │ │ │ ├── Chv.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Chv.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2033 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -2516,16 +2516,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -2713,79 +2715,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ B7D99CD533EC5F931B18E6B39BECF67FA2D6DD1AEC76772B068BE06335A94C05 │ │ │ │ 7A4DDEE77B66101DA855C17AC312600370B34E31F5EC3A01300A8EB60B4C9767 │ │ │ │ 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b(is)g(the)g(latter)227 737 y(c)m(hevron)31 b(that)g(is)f │ │ │ │ @@ -6884,17 +6896,17 @@ │ │ │ │ y(12.)46 b Fm(void)h(Chv_zero)e(\()j(Chv)f(*chv)f(\))i(;)227 │ │ │ │ 5234 y Fn(This)30 b(metho)s(d)g(zero)s(es)h(the)f(en)m(tries)h(in)f │ │ │ │ (the)h(c)m(hevron.)227 5407 y Fl(Err)-5 b(or)34 b(che)-5 │ │ │ │ b(cking:)40 b Fn(If)30 b Fm(chv)g Fn(is)g Fm(NULL)p Fn(,)g(an)g(error)g │ │ │ │ (message)h(is)g(prin)m(ted)f(and)g(the)g(program)g(exits.)p │ │ │ │ eop end │ │ │ │ %%Page: 17 17 │ │ │ │ -TeXDict begin 17 16 bop 91 100 1154 4 v 1335 100 a Fm(Chv)30 │ │ │ │ -b Fi(:)41 b Fl(DRAFT)121 b Fi(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2654 100 V 1154 w Fn(17)0 399 y Fc(1.2.12)113 b(IO)37 │ │ │ │ +TeXDict begin 17 16 bop 91 100 1131 4 v 1313 100 a Fm(Chv)29 │ │ │ │ +b Fi(:)41 b Fl(DRAFT)121 b Fi(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2676 100 V 1131 w Fn(17)0 399 y Fc(1.2.12)113 b(IO)37 │ │ │ │ b(metho)s(ds)111 592 y Fn(1.)46 b Fm(void)h(Chv_writeForHumanEye)42 │ │ │ │ b(\()48 b(Chv)f(*chv,)f(FILE)h(*fp)f(\))i(;)227 739 y │ │ │ │ Fn(This)30 b(metho)s(d)g(writes)g(a)h Fm(Chv)e Fn(ob)5 │ │ │ │ b(ject)32 b(to)f(a)f(\014le)h(in)f(an)g(easily)i(readable)f(format.)227 │ │ │ │ 887 y Fl(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fn(If)30 │ │ │ │ b Fm(chv)g Fn(or)g Fm(fp)g Fn(are)h Fm(NULL)p Fn(,)e(an)h(error)g │ │ │ │ (message)i(is)e(prin)m(ted)g(and)g(zero)h(is)g(returned.)111 │ │ │ │ @@ -6954,17 +6966,17 @@ │ │ │ │ Fn(is)h(\(1.0,0.0\),)j(when)c(w)m(e)h(are)g(just)g(loading)g(matrix)g │ │ │ │ (en)m(tries)h(in)m(to)g(a)427 5294 y(fron)m(t.)41 b(Ho)m(w)m(ev)m(er,) │ │ │ │ 33 b(when)c(w)m(e)i(factor)g Fb(A)20 b Fn(+)g Fb(\013B)5 │ │ │ │ b Fn(,)31 b(the)f(en)m(tries)h(of)g Fb(B)j Fn(will)d(b)s(e)f(loaded)h │ │ │ │ (with)f Fm(alpha)e Fn(set)427 5407 y(equal)j(to)g Fb(\013)p │ │ │ │ Fn([0)c(:)e(1].)p eop end │ │ │ │ %%Page: 18 18 │ │ │ │ -TeXDict begin 18 17 bop 0 100 a Fn(18)p 182 100 1154 │ │ │ │ -4 v 1336 w Fm(Chv)30 b Fi(:)40 b Fl(DRAFT)31 b Fi(Jan)m(uary)f(6,)h │ │ │ │ -(2026)p 2746 100 V 111 399 a Fn(2.)46 b Fm(test_assmbChv)e(msglvl)j │ │ │ │ +TeXDict begin 18 17 bop 0 100 a Fn(18)p 182 100 1131 │ │ │ │ +4 v 1314 w Fm(Chv)29 b Fi(:)41 b Fl(DRAFT)30 b Fi(Jan)m(uary)g(17,)h │ │ │ │ +(2026)p 2769 100 V 111 399 a Fn(2.)46 b Fm(test_assmbChv)e(msglvl)j │ │ │ │ (msgFile)e(nDJ)i(nUJ)g(nDI)g(nUI)g(type)g(symflag)e(seed)227 │ │ │ │ 553 y Fn(This)30 b(driv)m(er)h(program)g(tests)g(the)h │ │ │ │ Fm(Chv)p 1585 553 29 4 v 33 w(assembleChv)c Fn(metho)s(d.)42 │ │ │ │ b(It)31 b(assem)m(bles)g(a)h(c)m(hevron)f Fb(T)3517 567 │ │ │ │ y Fa(I)3588 553 y Fn(in)m(to)h Fb(T)3826 567 y Fa(J)3875 │ │ │ │ 553 y Fn(,)227 666 y(as)c(is)f(done)h(during)e(the)h(assem)m(bly)h(of)g │ │ │ │ (p)s(ostp)s(oned)e(ro)m(ws)h(and)g(columns)g(during)f(the)i │ │ │ │ @@ -7041,17 +7053,17 @@ │ │ │ │ 881 5144 V 32 w(NONSYMMETRIC)p Fn(.)337 5294 y Fe(\210)45 │ │ │ │ b Fn(The)32 b Fm(pivotingflag)d Fn(parameter)k(is)g(the)g(piv)m(oting)g │ │ │ │ (\015ag)g(|)g Fm(SPOOLES)p 2906 5294 V 32 w(NO)p 3034 │ │ │ │ 5294 V 34 w(PIVOTING)d Fn(for)j(no)f(piv-)427 5407 y(oting,)g │ │ │ │ Fm(SPOOLES)p 1027 5407 V 32 w(PIVOTING)c Fn(for)j(piv)m(oting.)p │ │ │ │ eop end │ │ │ │ %%Page: 19 19 │ │ │ │ -TeXDict begin 19 18 bop 91 100 1154 4 v 1335 100 a Fm(Chv)30 │ │ │ │ -b Fi(:)41 b Fl(DRAFT)121 b Fi(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2654 100 V 1154 w Fn(19)337 399 y Fe(\210)45 b Fn(The)35 │ │ │ │ +TeXDict begin 19 18 bop 91 100 1131 4 v 1313 100 a Fm(Chv)29 │ │ │ │ +b Fi(:)41 b Fl(DRAFT)121 b Fi(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2676 100 V 1131 w Fn(19)337 399 y Fe(\210)45 b Fn(The)35 │ │ │ │ b Fm(storeflag)e Fn(parameter)j(is)g(the)g(storage)h(\015ag,)g(to)g │ │ │ │ (store)f(b)m(y)f(ro)m(ws,)i(use)f Fm(SPOOLES)p 3528 399 │ │ │ │ 29 4 v 32 w(BY)p 3656 399 V 34 w(ROWS)p Fn(,)427 511 │ │ │ │ y(to)31 b(store)g(b)m(y)g(columns,)f(use)g Fm(SPOOLES)p │ │ │ │ 1766 511 V 32 w(BY)p 1894 511 V 34 w(COLUMNS)p Fn(.)337 │ │ │ │ 651 y Fe(\210)45 b Fn(The)30 b Fm(seed)f Fn(parameter)i(is)g(a)f │ │ │ │ (random)g(n)m(um)m(b)s(er)f(seed.)111 853 y(4.)46 b Fm │ │ │ │ @@ -7127,17 +7139,17 @@ │ │ │ │ Fn(parameter)j(determines)f(the)h(message)g(\014le)f(|)h(if)f │ │ │ │ Fm(msgFile)e Fn(is)i Fm(stdout)p Fn(,)g(then)g(the)427 │ │ │ │ 5294 y(message)27 b(\014le)f(is)g Fl(stdout)p Fn(,)i(otherwise)e(a)h │ │ │ │ (\014le)f(is)f(op)s(ened)g(with)h Fl(app)-5 b(end)28 │ │ │ │ b Fn(status)e(to)g(receiv)m(e)i(an)m(y)e(output)427 5407 │ │ │ │ y(data.)p eop end │ │ │ │ %%Page: 20 20 │ │ │ │ -TeXDict begin 20 19 bop 0 100 a Fn(20)p 182 100 1154 │ │ │ │ -4 v 1336 w Fm(Chv)30 b Fi(:)40 b Fl(DRAFT)31 b Fi(Jan)m(uary)f(6,)h │ │ │ │ -(2026)p 2746 100 V 337 399 a Fe(\210)45 b Fn(The)30 b │ │ │ │ +TeXDict begin 20 19 bop 0 100 a Fn(20)p 182 100 1131 │ │ │ │ +4 v 1314 w Fm(Chv)29 b Fi(:)41 b Fl(DRAFT)30 b Fi(Jan)m(uary)g(17,)h │ │ │ │ +(2026)p 2769 100 V 337 399 a Fe(\210)45 b Fn(The)30 b │ │ │ │ Fm(nD)g Fn(parameter)h(is)f(the)h(n)m(um)m(b)s(er)e(of)h(ro)m(ws)h(and) │ │ │ │ e(columns)h(in)h(the)f(\(1,1\))i(blo)s(c)m(k.)337 551 │ │ │ │ y Fe(\210)45 b Fn(The)30 b Fm(nU)g Fn(parameter)h(is)f(the)h(n)m(um)m │ │ │ │ (b)s(er)e(of)h(columns)g(in)g(the)h(\(1,2\))h(blo)s(c)m(k.)337 │ │ │ │ 703 y Fe(\210)45 b Fn(The)30 b Fm(type)f Fn(parameter)i(denotes)g(the)g │ │ │ │ (t)m(yp)s(e)f(of)h(en)m(tries)g(|)f Fm(SPOOLES)p 2818 │ │ │ │ 703 29 4 v 32 w(REAL)g Fn(or)g Fm(SPOOLES)p 3519 703 │ │ │ │ @@ -7209,17 +7221,17 @@ │ │ │ │ b Fm(rowerror)p Fn(,)f Fm(colerror)p Fn(,)h Fm(rowerror11)p │ │ │ │ Fn(,)e Fm(colerror11)f Fn(and)h Fm(diag11error)p Fn(.)59 │ │ │ │ b(All)38 b(should)f(b)s(e)227 5067 y(zero.)337 5294 y │ │ │ │ Fe(\210)45 b Fn(The)f Fm(msglvl)e Fn(parameter)j(determines)f(the)g │ │ │ │ (amoun)m(t)h(of)f(output.)82 b(Use)44 b Fm(msglvl)i(=)i(1)c │ │ │ │ Fn(for)g(just)427 5407 y(timing)31 b(output.)p eop end │ │ │ │ %%Page: 21 21 │ │ │ │ -TeXDict begin 21 20 bop 91 100 1154 4 v 1335 100 a Fm(Chv)30 │ │ │ │ -b Fi(:)41 b Fl(DRAFT)121 b Fi(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2654 100 V 1154 w Fn(21)337 399 y Fe(\210)45 b Fn(The)33 │ │ │ │ +TeXDict begin 21 20 bop 91 100 1131 4 v 1313 100 a Fm(Chv)29 │ │ │ │ +b Fi(:)41 b Fl(DRAFT)121 b Fi(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2676 100 V 1131 w Fn(21)337 399 y Fe(\210)45 b Fn(The)33 │ │ │ │ b Fm(msgFile)e Fn(parameter)j(determines)f(the)h(message)g(\014le)f(|)h │ │ │ │ (if)f Fm(msgFile)e Fn(is)i Fm(stdout)p Fn(,)g(then)g(the)427 │ │ │ │ 511 y(message)27 b(\014le)f(is)g Fl(stdout)p Fn(,)i(otherwise)e(a)h │ │ │ │ (\014le)f(is)f(op)s(ened)g(with)h Fl(app)-5 b(end)28 │ │ │ │ b Fn(status)e(to)g(receiv)m(e)i(an)m(y)e(output)427 624 │ │ │ │ y(data.)337 772 y Fe(\210)45 b Fn(The)30 b Fm(nD)g Fn(parameter)h(is)f │ │ │ │ (the)h(n)m(um)m(b)s(er)e(of)h(ro)m(ws)h(and)e(columns)h(in)h(the)f │ │ │ │ @@ -7289,17 +7301,17 @@ │ │ │ │ (\(1,1\))i(blo)s(c)m(k.)337 5259 y Fe(\210)45 b Fn(The)30 │ │ │ │ b Fm(nU)g Fn(parameter)h(is)f(the)h(n)m(um)m(b)s(er)e(of)h(columns)g │ │ │ │ (in)g(the)h(\(1,2\))h(blo)s(c)m(k.)337 5407 y Fe(\210)45 │ │ │ │ b Fn(The)30 b Fm(type)f Fn(parameter)i(denotes)g(the)g(t)m(yp)s(e)f(of) │ │ │ │ h(en)m(tries)g(|)f Fm(SPOOLES)p 2818 5407 V 32 w(REAL)g │ │ │ │ Fn(or)g Fm(SPOOLES)p 3519 5407 V 32 w(COMPLEX)p eop end │ │ │ │ %%Page: 22 22 │ │ │ │ -TeXDict begin 22 21 bop 0 100 a Fn(22)p 182 100 1154 │ │ │ │ -4 v 1336 w Fm(Chv)30 b Fi(:)40 b Fl(DRAFT)31 b Fi(Jan)m(uary)f(6,)h │ │ │ │ -(2026)p 2746 100 V 337 399 a Fe(\210)45 b Fn(The)20 b │ │ │ │ +TeXDict begin 22 21 bop 0 100 a Fn(22)p 182 100 1131 │ │ │ │ +4 v 1314 w Fm(Chv)29 b Fi(:)41 b Fl(DRAFT)30 b Fi(Jan)m(uary)g(17,)h │ │ │ │ +(2026)p 2769 100 V 337 399 a Fe(\210)45 b Fn(The)20 b │ │ │ │ Fm(symflag)e Fn(parameter)j(is)f(the)h(symmetry)f(\015ag)g(|)g │ │ │ │ Fm(SPOOLES)p 2640 399 29 4 v 33 w(SYMMETRIC)p Fn(,)e │ │ │ │ Fm(SPOOLES)p 3484 399 V 32 w(HERMITIAN)427 511 y Fn(or)31 │ │ │ │ b Fm(SPOOLES)p 881 511 V 32 w(NONSYMMETRIC)p Fn(.)337 │ │ │ │ 659 y Fe(\210)45 b Fn(The)30 b Fm(seed)f Fn(parameter)i(is)g(a)f │ │ │ │ (random)g(n)m(um)m(b)s(er)f(seed.)66 876 y(10.)46 b Fm(test_swap)g │ │ │ │ (msglvl)g(msgFile)f(nD)j(nU)f(type)f(symflag)g(seed)227 │ │ │ │ @@ -7375,17 +7387,17 @@ │ │ │ │ 5260 y Fe(\210)k Fn(The)30 b Fm(ncolT)f Fn(parameter)i(is)f(the)h(n)m │ │ │ │ (um)m(b)s(er)e(of)i(columns)f(in)g(the)g(\(1,1\))i(and)e(\(1,2\))i(blo) │ │ │ │ s(c)m(ks)f(of)g Fb(T)13 b Fn(.)337 5407 y Fe(\210)45 │ │ │ │ b Fn(The)30 b Fm(nDT)g Fn(parameter)g(is)h(the)f(n)m(um)m(b)s(er)g(of)g │ │ │ │ (ro)m(ws)g(and)g(columns)g(in)g(the)h(\(1,1\))h(blo)s(c)m(k)f(of)f │ │ │ │ Fb(T)13 b Fn(.)p eop end │ │ │ │ %%Page: 23 23 │ │ │ │ -TeXDict begin 23 22 bop 91 100 1154 4 v 1335 100 a Fm(Chv)30 │ │ │ │ -b Fi(:)41 b Fl(DRAFT)121 b Fi(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2654 100 V 1154 w Fn(23)337 399 y Fe(\210)45 b Fn(The)30 │ │ │ │ +TeXDict begin 23 22 bop 91 100 1131 4 v 1313 100 a Fm(Chv)29 │ │ │ │ +b Fi(:)41 b Fl(DRAFT)121 b Fi(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2676 100 V 1131 w Fn(23)337 399 y Fe(\210)45 b Fn(The)30 │ │ │ │ b Fm(ncolU)f Fn(parameter)i(is)f(the)h(n)m(um)m(b)s(er)e(of)i(columns)f │ │ │ │ (in)g Fb(U)10 b Fn(.)337 545 y Fe(\210)45 b Fn(The)30 │ │ │ │ b Fm(nrowD)f Fn(parameter)i(is)f(the)h(n)m(um)m(b)s(er)e(of)i(ro)m(ws)f │ │ │ │ (and)g(columns)g(in)g Fb(D)s Fn(.)337 691 y Fe(\210)45 │ │ │ │ b Fn(The)30 b Fm(nentU)f Fn(parameter)i(is)f(the)h(n)m(um)m(b)s(er)e │ │ │ │ (en)m(tries)i(in)f Fb(U)10 b Fn(,)31 b(ignored)f(if)h │ │ │ │ Fm(sparsityflag)44 b(=)j(0)p Fn(.)337 837 y Fe(\210)e │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -23,15 +23,15 @@ │ │ │ │ │ unnecessary, that we put on the Chv object — the number of rows in the (2,1) block and number of │ │ │ │ │ columns in the (1,2) block are equal. The Chv object is used within the context of a factorization of │ │ │ │ │ a sparse matrix that is assumed to have symmetric structure. If we ever extend the code to handle │ │ │ │ │ a true nonsymmetric structure factorization (e.g., umfpack and superlu), then we can modify │ │ │ │ │ the Chv object to handle unequal rows and columns. │ │ │ │ │ During a factorization, a front has to take part in four distinct operations. │ │ │ │ │ 1 │ │ │ │ │ - 2 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 2 Chv : DRAFT January 17, 2026 │ │ │ │ │ 1. Assemble entries from the original matrix (or matrix pencil). (See the Chv addChevron() │ │ │ │ │ method.) │ │ │ │ │ 2. Accumulate updates from descendant fronts. (See the Chv update{S,H,N}() methods.) │ │ │ │ │ 3. Assembleanypostponeddatafromitschildrenfronts. (SeetheChv assemblePostponedData() │ │ │ │ │ method.) │ │ │ │ │ 4. Computethefactorization ofthecompletely assembledfront. (SeetheChv factor()method.) │ │ │ │ │ The implementor of a front object has a great deal of freedom to design the underlying data │ │ │ │ │ @@ -65,15 +65,15 @@ │ │ │ │ │ defineitsrowsandcolumns. ForasymmetricorHermitianmatrix, weonlystorethecolumnindices. │ │ │ │ │ For a nonsymmetric matrix, we store the both the row and column indices. This second case may │ │ │ │ │ seem unnecessary, since we assume that the larger global matrix has symmetric structure. However, │ │ │ │ │ during a factorization with pivoting enabled, a pivot element may be chosen from anywhere in the │ │ │ │ │ (1,1) block, so the row indices and column indices may no longer be identical. │ │ │ │ │ AChv object is inherently a serial, single threaded object, meaning it is designed so that only │ │ │ │ │ one thread or process “owns” or operates on a particular Chv object. A Chv object is an “atom” │ │ │ │ │ - Chv : DRAFT January 6, 2026 3 │ │ │ │ │ + Chv : DRAFT January 17, 2026 3 │ │ │ │ │ of communication. It stores postponed rows and columns to be assembled in a parent front. It │ │ │ │ │ might have to be written to and read from a file in an out-of-core implementation. In a distributed │ │ │ │ │ environment, it is communicated between processes. For these reasons, we designed the object so │ │ │ │ │ that its data (the scalars that describe its dimensions, id and type, the row and column indices, │ │ │ │ │ and its entries) are found in contiguous storage managed by a DV object. A file operation can be │ │ │ │ │ done with a single read or write, a message can be sent without packing and unpacking data, or │ │ │ │ │ defining a new datatype. Managing working storage for a number of Chv objects is now simpler. │ │ │ │ │ @@ -100,15 +100,15 @@ │ │ │ │ │ • int symflag : symmetry flag │ │ │ │ │ – SPOOLES SYMMETRIC =⇒ symmetric entries │ │ │ │ │ – SPOOLES HERMITIAN =⇒ Hermitian entries │ │ │ │ │ – SPOOLES NONSYMMETRIC =⇒ nonsymmetric entries │ │ │ │ │ • int *rowind : pointer to the base address of the int vector that contains row indices. │ │ │ │ │ • int *colind : pointer to the base address of the int vector that contains column indices. │ │ │ │ │ • double *entries: pointer to the base address of the double vector that contains the entries. │ │ │ │ │ - 4 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 4 Chv : DRAFT January 17, 2026 │ │ │ │ │ • DV wrkDV : object that manages the owned working storage. │ │ │ │ │ • Chv *next : link to a next object in a singly linked list. │ │ │ │ │ One can query the type and symmetry of the object using these simple macros. │ │ │ │ │ • CHV IS REAL(chv) is 1 if chv has real entries and 0 otherwise. │ │ │ │ │ • CHV IS COMPLEX(chv) is 1 if chv has complex entries and 0 otherwise. │ │ │ │ │ • CHV IS SYMMETRIC(chv) is 1 if chv is symmetric and 0 otherwise. │ │ │ │ │ • CHV IS HERMITIAN(chv) is 1 if chv is Hermitian and 0 otherwise. │ │ │ │ │ @@ -131,15 +131,15 @@ │ │ │ │ │ This method clears the object and free’s any owned data by invoking the clearData() │ │ │ │ │ methods for its internal DV object. There is a concluding call to Chv setDefaultFields(). │ │ │ │ │ Error checking: If chv is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void Chv_free ( Chv *chv ) ; │ │ │ │ │ This method releases any storage by a call to Chv clearData() and then free the space for │ │ │ │ │ chv. │ │ │ │ │ Error checking: If chv is NULL, an error message is printed and the program exits. │ │ │ │ │ - Chv : DRAFT January 6, 2026 5 │ │ │ │ │ + Chv : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ 1. int Chv_id ( Chv *chv ) ; │ │ │ │ │ This method returns the id of the object. │ │ │ │ │ Error checking: If chv is NULL, an error message is printed and zero is returned. │ │ │ │ │ 2. int Chv_type ( Chv *chv ) ; │ │ │ │ │ This method returns the type of the object. │ │ │ │ │ • SPOOLES REAL =⇒ real entries │ │ │ │ │ @@ -167,15 +167,15 @@ │ │ │ │ │ Error checking: If chv, pncol or pcolind is NULL, an error message is printed and zero is │ │ │ │ │ returned. │ │ │ │ │ 7. int Chv_nent ( Chv *chv ) ; │ │ │ │ │ This method returns number of matrix entries that the object contains. Note, for a complex │ │ │ │ │ chevron, this is the number of double precision complex entries, equal to one half the number │ │ │ │ │ of double precision entries that are stored. │ │ │ │ │ Error checking: If chv is NULL, an error message is printed and zero is returned. │ │ │ │ │ - 6 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 6 Chv : DRAFT January 17, 2026 │ │ │ │ │ 8. double * Chv_entries ( Chv *chv ) ; │ │ │ │ │ This method returns the entries field of the object, a pointer to the base location of the │ │ │ │ │ double precision array that stores the complex data. │ │ │ │ │ Error checking: If chv is NULL, an error message is printed and zero is returned. │ │ │ │ │ 9. double * Chv_diagLocation ( Chv *chv, int ichv ) ; │ │ │ │ │ This method returns a pointer to the address of the entry in the ichv’th diagonal location. │ │ │ │ │ For a real chevron, to find the entry k places to the right of the diagonal entry, add k to the │ │ │ │ │ @@ -205,15 +205,15 @@ │ │ │ │ │ 14. void Chv_complexEntry ( Chv *chv, int irow, int jcol, │ │ │ │ │ double *pReal, double *pImag ) ; │ │ │ │ │ This method fills *pReal with the real part and *pImag with the imaginary part of the the │ │ │ │ │ entry in row irow and column jcol. Note, irow and jcol are local indices, i.e., 0 ≤ irow < │ │ │ │ │ nD+nLand0≤jcolentries[2*kk:2*kk+1]. │ │ │ │ │ @@ -281,15 +281,15 @@ │ │ │ │ │ in *pmaxval. Note, if the chevron is complex, the location is in terms of the complex entries, │ │ │ │ │ not in the real entries, i.e., if k = Chv maxabsRow(chv,...), then the complex entry is found │ │ │ │ │ in chv->entries[2*kk:2*kk+1]. │ │ │ │ │ Error checking: If chv is NULL or irow is not in [0,n1-1], an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 5. int Chv_maxabsInColumn ( Chv *chv, int jcol, int rowmark[], │ │ │ │ │ int tag, double *pmaxval ) ; │ │ │ │ │ - Chv : DRAFT January 6, 2026 9 │ │ │ │ │ + Chv : DRAFT January 17, 2026 9 │ │ │ │ │ This method returns the location of the first element with the largest magnitude in column │ │ │ │ │ jcol. Element jj must have rowmark[jj] = tag to be eligible. Its magnitude is returned │ │ │ │ │ in *pmaxval. Note, if the chevron is complex, the location is in terms of the complex entries, │ │ │ │ │ not in the real entries, i.e., if k = Chv maxabsColumn11(chv,...), then the complex entry │ │ │ │ │ is found in chv->entries[2*kk:2*kk+1]. │ │ │ │ │ Error checking: If chv is NULL or irow is not in [0,n1-1], an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ @@ -322,15 +322,15 @@ │ │ │ │ │ number of leading rows and columns to ignore, useful when delayed rows and columns have │ │ │ │ │ been placed in the leading portion of the chevron. The pirow, pjcol and pntest addresses │ │ │ │ │ are filled with the pivot row, pivot column, and number of pivot tests performed to find the │ │ │ │ │ pivot. If no pivot was found, pirow and pjcol are filled with -1. The return value is the size │ │ │ │ │ of the pivot. If the chevron is symmetric, we can find a 1 × 1 or 2 × 2 pivot. If the chevron │ │ │ │ │ is nonsymmetric, we only find a 1×1 pivot. A return value of zero means that no pivot was │ │ │ │ │ found. │ │ │ │ │ - 10 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 10 Chv : DRAFT January 17, 2026 │ │ │ │ │ Error checking: If chv, workDV, pirow, pjcol or pntest is NULL, or if tau < 1.0, or if │ │ │ │ │ ndelay < 0, an error message is printed and the program exits. │ │ │ │ │ 1.2.6 Update methods │ │ │ │ │ 1. void Chv_updateS ( Chv *chv, SubMtx *mtxD, SubMtx *mtxU, DV *tempDV ) ; │ │ │ │ │ void Chv_updateH ( Chv *chv, SubMtx *mtxD, SubMtx *mtxU, DV *tempDV ) ; │ │ │ │ │ void Chv_updateN ( Chv *chv, SubMtx *mtxL, SubMtx *mtxD, SubMtx *mtxU, │ │ │ │ │ DV *tempDV ) ; │ │ │ │ │ @@ -364,15 +364,15 @@ │ │ │ │ │ This method is used to assemble entries from the matrix pencil A+σB into the block chevron │ │ │ │ │ object. Typically the entries from A or B will come from a InpMtx object, one of whose modes │ │ │ │ │ of storage is by single chevrons. The value ichvis the row and column location of the diagonal │ │ │ │ │ entry. The indices found in chvind[] are offsets. Let off = chvind[ii] be the offset for one │ │ │ │ │ of the chevron’s entries. If off ≥ 0, then the entry is found in location (ichv, ichv+off) of │ │ │ │ │ the matrix. If off < 0, then the entry is found in location (ichv-off, ichv) of the matrix. │ │ │ │ │ The value(s) in alpha[] form a scalar used to scale the entire chevron for its assembly. A │ │ │ │ │ - Chv : DRAFT January 6, 2026 11 │ │ │ │ │ + Chv : DRAFT January 17, 2026 11 │ │ │ │ │ call to assemble entries in A (from the pencil A+σB) would have alpha[] = (1.0,0.0); to │ │ │ │ │ assemble entries in B (from the pencil A+σB) would have alpha[] = (Real(σ),Imag(σ)). │ │ │ │ │ Error checking: If chv, chvind, chvent or alpha is NULL, or if ichv or chvsize are less than │ │ │ │ │ zero, an error message is printed and the program exits. │ │ │ │ │ 2. void Chv_assembleChv ( Chv *chvJ, Chv *chvI ) ; │ │ │ │ │ This method is used to assemble entries from one Chv object into another. The application │ │ │ │ │ is during a factorization with pivoting, postponed entries from the children are stored in the │ │ │ │ │ @@ -386,15 +386,15 @@ │ │ │ │ │ data from the children (objects are held in a list where firstchild is the head) into a Chv │ │ │ │ │ object newchv. The return value is the number of delayed rows and columns from the children │ │ │ │ │ fronts which are found in the leading rows and columns of the chevron. │ │ │ │ │ Error checking: If newchv, oldchv or firstchild is NULL, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 1.2.8 Factorization methods │ │ │ │ │ 1. int Chv_factorWithPivoting ( Chv *chv, int ndelay, int pivotflag, │ │ │ │ │ - IV *pivotsizesIV, DV *workDV, double tau, int *pntest ) ; │ │ │ │ │ + IV *pivotsizesIV, DV *workDV, double tau, int *pntest ) ; │ │ │ │ │ This method factors a front using pivoting for numerical stability. The number of rows and │ │ │ │ │ columns that have been delayed (assembled from the children) is given by ndelay, this allows │ │ │ │ │ the method that finds the pivots to skip over these rows and columns since no pivot can be │ │ │ │ │ found there. When pivoting is enabled (pivotflag is SPOOLES PIVOTING), the workDV object │ │ │ │ │ used during the search process for pivots must be non-NULL, tau is the upper bound on factor │ │ │ │ │ entries, and pivotsizesIV must be non-NULL when the front is symmetric or Hermitian. │ │ │ │ │ The address pntest is incremented with the number of pivot tests by the Chv findPivot() │ │ │ │ │ @@ -404,15 +404,15 @@ │ │ │ │ │ chevron is symmetric or Hermitian, pivotflag == SPOOLES PIVOTING and pivotsizesIV is │ │ │ │ │ NULL, an error message is printed and the program exits. │ │ │ │ │ 2. int Chv_factorWithNoPivoting ( Chv *chv, PatchAndGoInfo *info ) ; │ │ │ │ │ This method factors a front without using pivoting for numerical stability. It does support │ │ │ │ │ “patch-and-go” functionality, where if a small or zero entry is found in the diagonal element │ │ │ │ │ that is to be eliminated, some action can be taken. The return value is the number of │ │ │ │ │ eliminated rows and columns. │ │ │ │ │ - 12 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 12 Chv : DRAFT January 17, 2026 │ │ │ │ │ Error checking: If chv is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. int Chv_r1upd ( Chv *chv ) ; │ │ │ │ │ This method is used during the factorization of a front, performing a rank-one update of the │ │ │ │ │ chevron. The return value is 1 if the pivot is nonzero, 0 otherwise. │ │ │ │ │ Error checking: If chv is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. int Chv_r2upd ( Chv *chv ) ; │ │ │ │ │ This method is used during the factorization of a front, performing a rank-two update of the │ │ │ │ │ @@ -440,15 +440,15 @@ │ │ │ │ │ • CHV STRICT LOWER =⇒ count strict lower entries │ │ │ │ │ • CHV DIAGONAL =⇒ count diagonal entries │ │ │ │ │ • CHV STRICT UPPER =⇒ count strict upper entries │ │ │ │ │ • CHV STRICT LOWER 11 =⇒ count strict lower entries in the (1,1) block │ │ │ │ │ • CHV LOWER 21 =⇒ count lower entries in the (2,1) block │ │ │ │ │ • CHV STRICT UPPER 11 =⇒ count strict upper entries in the (1,1) block │ │ │ │ │ • CHV UPPER 12 =⇒ count upper entries in the (1,2) block │ │ │ │ │ - Chv : DRAFT January 6, 2026 13 │ │ │ │ │ + Chv : DRAFT January 17, 2026 13 │ │ │ │ │ This method is used to compute the necessary storage to store a chevron as a dense front. │ │ │ │ │ Error checking: If chv is NULL or if countflag is not valid, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 2. int Chv_countBigEntries ( Chv *chv, int npivot, int pivotsizes[], │ │ │ │ │ int countflag, double droptol ) ; │ │ │ │ │ This method counts the number of entries in the chevron that are larger in magnitude than │ │ │ │ │ droptol. countflag has the following meaning. │ │ │ │ │ @@ -458,15 +458,15 @@ │ │ │ │ │ • CHV LOWER 21 =⇒ count lower entries in the (2,1) block │ │ │ │ │ • CHV STRICT UPPER 11 =⇒ count strict upper entries in the (1,1) block │ │ │ │ │ • CHV UPPER 12 =⇒ count upper entries in the (1,2) block │ │ │ │ │ This method is used to compute the necessary storage to store a chevron as a sparse front. │ │ │ │ │ Error checking: If chv is NULL or if countflag is not valid, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 3. int Chv_copyEntriesToVector ( Chv *chv, int npivot, int pivotsizes[], │ │ │ │ │ - int length, double dvec[], int copyflag, int storeflag) ; │ │ │ │ │ + int length, double dvec[], int copyflag, int storeflag) ; │ │ │ │ │ This method copies some entries the chevron object into a double precision vector. This │ │ │ │ │ method is called after a front has been factored and is used to store the factor entries into │ │ │ │ │ the storage for the factor matrix. If the front is nonsymmetric, the front contains entries of │ │ │ │ │ L, D and U, where D is diagonal. If the front is symmetric or Hermitian, the front contains │ │ │ │ │ entries of D and U, and D is diagonal if pivotsizesIV is NULL or may contain a mixture of │ │ │ │ │ 1×1and2×2pivots otherwise. copyflag has the following meaning. │ │ │ │ │ • CHV STRICT LOWER =⇒ copy strict lower entries │ │ │ │ │ @@ -477,15 +477,15 @@ │ │ │ │ │ • CHV STRICT UPPER 11 =⇒ copy strict upper entries in the (1,1) block │ │ │ │ │ • CHV UPPER 12 =⇒ copy upper entries in the (1,2) block │ │ │ │ │ If storeflagisCHV BY ROWS,theentriesarestoredbyrowsandifstoreflagisCHV BY COLUMNS, │ │ │ │ │ the entries are stored by columns. │ │ │ │ │ Error checking: If chv or dvec is NULL or if length is less than the number of entries to be │ │ │ │ │ copied, or if copyflag or storeflag is valid, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - 14 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 14 Chv : DRAFT January 17, 2026 │ │ │ │ │ 4. int Chv_copyBigEntriesToVector ( Chv *chv, int npivot, int pivotsizes[], │ │ │ │ │ int sizes[], int ivec[], double dvec[], │ │ │ │ │ int copyflag, int storeflag, double droptol ) ; │ │ │ │ │ This method also copies some entries the chevron object into a double precision vector, but │ │ │ │ │ only those entries whose magnitude is greater than or equal to droptol are copied. This │ │ │ │ │ method is called after a front has been factored and is used to store the factor entries of large │ │ │ │ │ magnitude into the storage for the factor matrix. If the front is nonsymmetric, the front │ │ │ │ │ @@ -517,15 +517,15 @@ │ │ │ │ │ Error checking: If chvI or chvJ is NULL, or if offset < 0 or offset is greater than the │ │ │ │ │ number of chevrons in chvJ, an error message is printed and the program exits. │ │ │ │ │ 1.2.10 Swap methods │ │ │ │ │ 1. void Chv_swapRows ( Chv *chv, int irow, int jrow ) ; │ │ │ │ │ This method swaps rows irow and jrow of the chevron. Both rows must be less than the │ │ │ │ │ width nD of the chevron. The row ids of the two rows are also swapped. If the chevron is │ │ │ │ │ symmetric, then the method Chv swapRowsAndColumns() is called. │ │ │ │ │ - Chv : DRAFT January 6, 2026 15 │ │ │ │ │ + Chv : DRAFT January 17, 2026 15 │ │ │ │ │ Error checking: If chv is NULL or if irow or jrow are less than 0 or greater than or equal to │ │ │ │ │ nD, an error message is printed and the program exits. │ │ │ │ │ 2. void Chv_swapColumns ( Chv *chv, int icol, int jcol ) ; │ │ │ │ │ This method swaps columns icol and jcol of the chevron. Both columns must be less than │ │ │ │ │ the width nD of the chevron. The column ids of the two columns are also swapped. If the │ │ │ │ │ chevron is symmetric, then the method Chv swapRowsAndColumns() is called. │ │ │ │ │ Error checking: If chv is NULL or if icol or jcol are less than 0 or greater than or equal to │ │ │ │ │ @@ -553,15 +553,15 @@ │ │ │ │ │ This method sets the scalar fields and rowind, colind and entries pointers. │ │ │ │ │ Error checking: If chv is NULL, or if nD ≤ 0, or if nL or nU are less than zero, or if type or │ │ │ │ │ symflag are not valid, an error message is printed and the program exits. │ │ │ │ │ 5. void Chv_shift ( Chv *chv, int shift ) ; │ │ │ │ │ This method is used to shift the base of the entries and adjust dimensions of the Chv object. │ │ │ │ │ If shift is positive, the first shift chevrons are removed from the chevron. If shift is │ │ │ │ │ negative, the shift previous chevrons are prepended to the chevron. This is a dangerous │ │ │ │ │ - 16 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 16 Chv : DRAFT January 17, 2026 │ │ │ │ │ method as it changes the state of the object. We use it during the factorization of a front, │ │ │ │ │ where one Chv object points to the entire chevron in order to swap rows and columns, while │ │ │ │ │ another chevron points to the uneliminated rows and columns of the front. It is the latter │ │ │ │ │ chevron that is shifted during the factorization. │ │ │ │ │ Error checking: If chv is NULL an error message is printed and the program exits. │ │ │ │ │ 6. void Chv_fill11block ( Chv *chv, A2 *mtx ) ; │ │ │ │ │ This method is used to fill a A2 dense matrix object with the entries in the (1,1) block of the │ │ │ │ │ @@ -584,15 +584,15 @@ │ │ │ │ │ 11. void Chv_sub ( Chv *chvJ, Chv *chvI ) ; │ │ │ │ │ This method subtracts chvI from chvJ. │ │ │ │ │ Error checking: If chvJ or chvI is NULL, or if their dimensions are not the same, or if either │ │ │ │ │ of their entries fields are NULL, an error message is printed and the program exits. │ │ │ │ │ 12. void Chv_zero ( Chv *chv ) ; │ │ │ │ │ This method zeroes the entries in the chevron. │ │ │ │ │ Error checking: If chv is NULL, an error message is printed and the program exits. │ │ │ │ │ - Chv : DRAFT January 6, 2026 17 │ │ │ │ │ + Chv : DRAFT January 17, 2026 17 │ │ │ │ │ 1.2.12 IO methods │ │ │ │ │ 1. void Chv_writeForHumanEye ( Chv *chv, FILE *fp ) ; │ │ │ │ │ This method writes a Chv object to a file in an easily readable format. │ │ │ │ │ Error checking: If chv or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 2. void Chv_writeForMatlab ( Chv *chv, char *chvname, FILE *fp ) ; │ │ │ │ │ This method writes a Chv object to a file in a matlab format. For a real chevron, a sample │ │ │ │ │ line is │ │ │ │ │ @@ -605,29 +605,29 @@ │ │ │ │ │ returned. │ │ │ │ │ 1.3 Driver programs for the Chv object │ │ │ │ │ 1. test_addChevron msglvl msgFile nD nU type symflag seed alphareal alphaimag │ │ │ │ │ This driver program tests the Chv addChevron method. Use the script file do addChevron │ │ │ │ │ for testing. When the output file is loaded into matlab, the last line to the screen is the error │ │ │ │ │ of the assembly. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ - timing output. │ │ │ │ │ + timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ - message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ - data. │ │ │ │ │ + message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ + data. │ │ │ │ │ • The nD parameter is the number of rows and columns in the (1,1) block. │ │ │ │ │ • The nU parameter is the number of columns in the (1,2) block. │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ • Thesymflagparameteristhesymmetryflag—SPOOLES SYMMETRIC,SPOOLES HERMITIAN │ │ │ │ │ - or SPOOLES NONSYMMETRIC. │ │ │ │ │ + or SPOOLES NONSYMMETRIC. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The alphareal and alphaimag parameters form a complex number that is a scaling │ │ │ │ │ - parameter. Normally alpha is (1.0,0.0), when we are just loading matrix entries into a │ │ │ │ │ - front. However, when we factor A+αB, the entries of B will be loaded with alpha set │ │ │ │ │ - equal to α[0 : 1]. │ │ │ │ │ - 18 Chv : DRAFT January 6, 2026 │ │ │ │ │ + parameter. Normally alpha is (1.0,0.0), when we are just loading matrix entries into a │ │ │ │ │ + front. However, when we factor A+αB, the entries of B will be loaded with alpha set │ │ │ │ │ + equal to α[0 : 1]. │ │ │ │ │ + 18 Chv : DRAFT January 17, 2026 │ │ │ │ │ 2. test_assmbChv msglvl msgFile nDJ nUJ nDI nUI type symflag seed │ │ │ │ │ This driver program tests the Chv assembleChv method. It assembles a chevron T into T , │ │ │ │ │ I J │ │ │ │ │ as is done during the assembly of postponed rows and columns during the factorization when │ │ │ │ │ pivoting is enabled. Use the script file do assmbChv for testing. When the output file is │ │ │ │ │ loaded into matlab, the last line to the screen is the error of the assembly. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ @@ -658,55 +658,55 @@ │ │ │ │ │ • The nD parameter is the number of rows and columns in the (1,1) block. │ │ │ │ │ • The nU parameter is the number of columns in the (1,2) block. │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ • Thesymflagparameteristhesymmetryflag—SPOOLES SYMMETRIC,SPOOLES HERMITIAN │ │ │ │ │ or SPOOLES NONSYMMETRIC. │ │ │ │ │ • The pivotingflag parameter is the pivoting flag — SPOOLES NO PIVOTING for no piv- │ │ │ │ │ oting, SPOOLES PIVOTING for pivoting. │ │ │ │ │ - Chv : DRAFT January 6, 2026 19 │ │ │ │ │ + Chv : DRAFT January 17, 2026 19 │ │ │ │ │ • The storeflag parameter is the storage flag, to store by rows, use SPOOLES BY ROWS, │ │ │ │ │ - to store by columns, use SPOOLES BY COLUMNS. │ │ │ │ │ + to store by columns, use SPOOLES BY COLUMNS. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ 4. test_copyBigEntriesToVector msglvl msgFile nD nU type symflag │ │ │ │ │ pivotingflag storeflag seed droptol │ │ │ │ │ This driver program tests the Chv copyBigEntriesToVector method which is used when │ │ │ │ │ after a front has been factored to store the entries into sparse L and U submatrices. Use │ │ │ │ │ the script file do copyBigEntriesToVector for testing. When the output file is loaded into │ │ │ │ │ matlab, the last line to the screen is a matrix that contains three entries. The first two are │ │ │ │ │ the maximum magnitudes of the entries that were not copied (two different ways), and the │ │ │ │ │ third is the drop tolerance. If the program executes correctly, the third term is larger than │ │ │ │ │ the first two. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ - timing output. │ │ │ │ │ + timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ - message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ - data. │ │ │ │ │ + message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ + data. │ │ │ │ │ • The nD parameter is the number of rows and columns in the (1,1) block. │ │ │ │ │ • The nU parameter is the number of columns in the (1,2) block. │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ • Thesymflagparameteristhesymmetryflag—SPOOLES SYMMETRIC,SPOOLES HERMITIAN │ │ │ │ │ - or SPOOLES NONSYMMETRIC. │ │ │ │ │ + or SPOOLES NONSYMMETRIC. │ │ │ │ │ • The pivotingflag parameter is the pivoting flag — SPOOLES NO PIVOTING for no piv- │ │ │ │ │ - oting, SPOOLES PIVOTING for pivoting. │ │ │ │ │ + oting, SPOOLES PIVOTING for pivoting. │ │ │ │ │ • The storeflag parameter is the storage flag, to store by rows, use SPOOLES BY ROWS, │ │ │ │ │ - to store by columns, use SPOOLES BY COLUMNS. │ │ │ │ │ + to store by columns, use SPOOLES BY COLUMNS. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The droptol parameter is a drop tolerance parameters, entries whose magnitude is │ │ │ │ │ - smaller than droptol are not copied. │ │ │ │ │ + smaller than droptol are not copied. │ │ │ │ │ 5. test_factor msglvl msgFile nD nU type symflag pivotingflag seed tau │ │ │ │ │ This driver program tests the Chv factor method. Use the script file do factor for testing. │ │ │ │ │ Whentheoutputfileisloadedinto matlab, the last line to the screen is a matrix that contains │ │ │ │ │ three entries. The first entry is the error in the factorization. The second and third entries │ │ │ │ │ are the maximum magnitudes of the entries in L and U, respectively. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ - timing output. │ │ │ │ │ + timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ - message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ - data. │ │ │ │ │ - 20 Chv : DRAFT January 6, 2026 │ │ │ │ │ + message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ + data. │ │ │ │ │ + 20 Chv : DRAFT January 17, 2026 │ │ │ │ │ • The nD parameter is the number of rows and columns in the (1,1) block. │ │ │ │ │ • The nU parameter is the number of columns in the (1,2) block. │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ • Thesymflagparameteristhesymmetryflag—SPOOLES SYMMETRIC,SPOOLES HERMITIAN │ │ │ │ │ or SPOOLES NONSYMMETRIC. │ │ │ │ │ • The pivotingflag parameter is the pivoting flag — SPOOLES NO PIVOTING for no piv- │ │ │ │ │ oting, SPOOLES PIVOTING for pivoting. │ │ │ │ │ @@ -735,52 +735,52 @@ │ │ │ │ │ ThisdriverprogramteststheChv maxabsInRow(),Chv maxabsInRow11(),Chv maxabsInColumn(), │ │ │ │ │ Chv maxabsInColumn11() and Chv maxabsInDiagonal11() methods. Use the script file │ │ │ │ │ do maxabs for testing. When the output file is loaded into matlab, look on the screen for the │ │ │ │ │ variables rowerror, colerror, rowerror11, colerror11 and diag11error. All should be │ │ │ │ │ zero. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ timing output. │ │ │ │ │ - Chv : DRAFT January 6, 2026 21 │ │ │ │ │ + Chv : DRAFT January 17, 2026 21 │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ - message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ - data. │ │ │ │ │ + message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ + data. │ │ │ │ │ • The nD parameter is the number of rows and columns in the (1,1) block. │ │ │ │ │ • The nU parameter is the number of columns in the (1,2) block. │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ • Thesymflagparameteristhesymmetryflag—SPOOLES SYMMETRIC,SPOOLES HERMITIAN │ │ │ │ │ - or SPOOLES NONSYMMETRIC. │ │ │ │ │ + or SPOOLES NONSYMMETRIC. │ │ │ │ │ • The pivotingflag parameter is the pivoting flag — SPOOLES NO PIVOTING for no piv- │ │ │ │ │ - oting, SPOOLES PIVOTING for pivoting. │ │ │ │ │ + oting, SPOOLES PIVOTING for pivoting. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ 8. test_r1upd msglvl msgFile nD nU type symflag seed │ │ │ │ │ This driver program tests the Chv r1upd() method. Use the script file do r1upd for testing. │ │ │ │ │ When the output file is loaded into matlab, the last line is the error of the update. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ - timing output. │ │ │ │ │ + timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ - message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ - data. │ │ │ │ │ + message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ + data. │ │ │ │ │ • The nD parameter is the number of rows and columns in the (1,1) block. │ │ │ │ │ • The nU parameter is the number of columns in the (1,2) block. │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ • Thesymflagparameteristhesymmetryflag—SPOOLES SYMMETRIC,SPOOLES HERMITIAN │ │ │ │ │ - or SPOOLES NONSYMMETRIC. │ │ │ │ │ + or SPOOLES NONSYMMETRIC. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ 9. test_r2upd msglvl msgFile nD nU type symflag seed │ │ │ │ │ This driver program tests the Chv r2upd() method. Use the script file do r2upd for testing. │ │ │ │ │ When the output file is loaded into matlab, the last line is the error of the update. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ - timing output. │ │ │ │ │ + timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ - message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ - data. │ │ │ │ │ + message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ + data. │ │ │ │ │ • The nD parameter is the number of rows and columns in the (1,1) block. │ │ │ │ │ • The nU parameter is the number of columns in the (1,2) block. │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ - 22 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 22 Chv : DRAFT January 17, 2026 │ │ │ │ │ • Thesymflagparameteristhesymmetryflag—SPOOLES SYMMETRIC,SPOOLES HERMITIAN │ │ │ │ │ or SPOOLES NONSYMMETRIC. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ 10. test_swap msglvl msgFile nD nU type symflag seed │ │ │ │ │ This driver program tests three methods: Chv swapRowsAndColumns(), Chv swapRows() and │ │ │ │ │ Chv swapColumns(). Use the script file do swap for testing. When the output file is loaded │ │ │ │ │ into matlab, look for the maxerrrowswap1, maxerrcolswap1, maxerrswap, maxerrsymswap1 │ │ │ │ │ @@ -810,15 +810,15 @@ │ │ │ │ │ • The type parameter denotes the type of entries — SPOOLES REAL or SPOOLES COMPLEX │ │ │ │ │ • Thesymflagparameteristhesymmetryflag—SPOOLES SYMMETRIC,SPOOLES HERMITIAN │ │ │ │ │ or SPOOLES NONSYMMETRIC. │ │ │ │ │ • The sparsityflag parameter should be zero for dense U and L, or 1 for sparse U and │ │ │ │ │ L. │ │ │ │ │ • The ncolT parameter is the number of columns in the (1,1) and (1,2) blocks of T. │ │ │ │ │ • The nDT parameter is the number of rows and columns in the (1,1) block of T. │ │ │ │ │ - Chv : DRAFT January 6, 2026 23 │ │ │ │ │ + Chv : DRAFT January 17, 2026 23 │ │ │ │ │ • The ncolU parameter is the number of columns in U. │ │ │ │ │ • The nrowD parameter is the number of rows and columns in D. │ │ │ │ │ • The nentU parameter is the number entries in U, ignored if sparsityflag = 0. │ │ │ │ │ • The offset parameter is the offset of first index in T from the last index in D. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ Index │ │ │ │ │ Chv addChevron(), 10 Chv new(), 4 │ │ ├── ./usr/share/doc/spooles-doc/ChvList.ps.gz │ │ │ ├── ChvList.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o ChvList.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1760,16 +1760,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1957,79 +1959,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ 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/Dotaccent/cedilla/ogonek/quotesinglbase.ts1 4{/.notdef}repeat │ │ │ │ /quotedblbase.ts1/.notdef/.notdef/twelveudash/threequartersemdash │ │ │ │ /afii61664.cap/arrowleft/arrowright/tieaccentlowercase/tieaccentcapital │ │ │ │ /tieaccentlowercase.new/tieaccentcapital.new/.notdef/afii61664.asc/uni2422 3 │ │ │ │ {/.notdef}repeat/dollar/.notdef/.notdef/quotesingle/.notdef/.notdef │ │ │ │ @@ -3415,17 +3427,17 @@ │ │ │ │ (not)h(y)m(et)h(zero.)141 5294 y(Ha)m(ving)27 b(a)g(lo)s(c)m(k)g(asso)s │ │ │ │ (ciated)g(with)f(a)h Fh(ChvList)d Fi(ob)5 b(ject)27 b(is)f(optional,)i │ │ │ │ (for)e(example,)i(it)e(is)g(not)g(needed)g(during)0 5407 │ │ │ │ y(a)31 b(serial)h(factorization)i(nor)c(a)i(MPI)f(factorization.)45 │ │ │ │ b(In)31 b(the)g(latter)h(case)g(there)g(is)f(one)g Fh(ChvList)e │ │ │ │ Fi(p)s(er)h(pro)s(cess.)1927 5656 y(1)p eop end │ │ │ │ %%Page: 2 2 │ │ │ │ -TeXDict begin 2 1 bop 0 100 a Fi(2)p 136 100 1081 4 v │ │ │ │ -1263 w Fh(ChvList)29 b Ff(:)40 b Fe(DRAFT)30 b Ff(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2819 100 V 0 399 a Fi(F)-8 b(or)35 b(a)g(m)m(ultithreaded)g │ │ │ │ +TeXDict begin 2 1 bop 0 100 a Fi(2)p 136 100 1059 4 v │ │ │ │ +1240 w Fh(ChvList)29 b Ff(:)40 b Fe(DRAFT)31 b Ff(Jan)m(uary)f(17,)h │ │ │ │ +(2026)p 2842 100 V 0 399 a Fi(F)-8 b(or)35 b(a)g(m)m(ultithreaded)g │ │ │ │ (factorization)i(there)d(is)h(one)f Fh(ChvList)f Fi(ob)5 │ │ │ │ b(ject)35 b(that)g(is)g(shared)e(b)m(y)i(all)g(threads.)52 │ │ │ │ b(The)0 511 y(m)m(utual)22 b(exclusion)h(lo)s(c)m(k)g(that)f(is)g │ │ │ │ (\(optionally\))i(em)m(b)s(edded)d(in)h(the)g Fh(ChvList)e │ │ │ │ Fi(ob)5 b(ject)23 b(is)f(a)g Fh(Lock)f Fi(ob)5 b(ject)23 │ │ │ │ b(from)e(this)0 624 y(library)-8 b(.)39 b(It)27 b(is)f(inside)g(the)g │ │ │ │ Fh(Lock)f Fi(ob)5 b(ject)27 b(that)g(w)m(e)f(ha)m(v)m(e)i(a)e(m)m │ │ │ │ @@ -3478,17 +3490,17 @@ │ │ │ │ (and)d Fh(heads)p Fi(,)227 5251 y Fh(counts)p Fi(,)29 │ │ │ │ b Fh(lock)g Fi(and)h Fh(flags)f Fi(are)i(set)g(to)g Fh(NULL)e │ │ │ │ Fi(.)227 5407 y Fe(Err)-5 b(or)34 b(che)-5 b(cking:)40 │ │ │ │ b Fi(If)30 b Fh(list)g Fi(is)g Fh(NULL)p Fi(,)f(an)i(error)f(message)h │ │ │ │ (is)g(prin)m(ted)f(and)f(the)i(program)f(exits.)p eop │ │ │ │ end │ │ │ │ %%Page: 3 3 │ │ │ │ -TeXDict begin 3 2 bop 91 100 1081 4 v 1263 100 a Fh(ChvList)28 │ │ │ │ -b Ff(:)41 b Fe(DRAFT)121 b Ff(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2772 100 V 1081 w Fi(3)111 399 y(3.)46 b Fh(void)h(ChvList_clearData)c │ │ │ │ +TeXDict begin 3 2 bop 91 100 1059 4 v 1240 100 a Fh(ChvList)28 │ │ │ │ +b Ff(:)41 b Fe(DRAFT)121 b Ff(Jan)m(uary)30 b(17,)i(2026)p │ │ │ │ +2795 100 V 1059 w Fi(3)111 399 y(3.)46 b Fh(void)h(ChvList_clearData)c │ │ │ │ (\()k(ChvList)f(*list)h(\))g(;)227 555 y Fi(This)41 b(metho)s(d)g │ │ │ │ (clears)h(the)g(ob)5 b(ject)42 b(and)f(free's)h(an)m(y)g(o)m(wned)f │ │ │ │ (data)i(b)m(y)e(calling)i Fh(Chv)p 3220 555 29 4 v 34 │ │ │ │ w(free\(\))c Fi(for)j(eac)m(h)227 668 y(ob)5 b(ject)36 │ │ │ │ b(on)f(the)h(free)f(list.)56 b(If)35 b Fh(heads)f Fi(is)h(not)g │ │ │ │ Fh(NULL)p Fi(,)g(it)g(is)h(free'd.)55 b(If)35 b Fh(counts)e │ │ │ │ Fi(is)i(not)h Fh(NULL)p Fi(,)e(it)i(is)f(free'd)227 781 │ │ │ │ @@ -3551,17 +3563,17 @@ │ │ │ │ 5138 y(metho)s(d)e(returns)f(0.)227 5294 y Fe(Err)-5 │ │ │ │ b(or)34 b(che)-5 b(cking:)40 b Fi(If)29 b Fh(list)g Fi(is)h │ │ │ │ Fh(NULL)p Fi(,)f(or)h(if)g Fh(ilist)e Fi(is)i(not)h(in)e(the)h(range)h │ │ │ │ Fh([0,nlist\))p Fi(,)c(an)j(error)g(message)227 5407 │ │ │ │ y(is)h(prin)m(ted)f(and)f(zero)j(is)e(returned.)p eop │ │ │ │ end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fi(4)p 136 100 1081 4 v │ │ │ │ -1263 w Fh(ChvList)29 b Ff(:)40 b Fe(DRAFT)30 b Ff(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2819 100 V 111 399 a Fi(3.)46 b Fh(Chv)h(*)h(ChvList_getList)43 │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fi(4)p 136 100 1059 4 v │ │ │ │ +1240 w Fh(ChvList)29 b Ff(:)40 b Fe(DRAFT)31 b Ff(Jan)m(uary)f(17,)h │ │ │ │ +(2026)p 2842 100 V 111 399 a Fi(3.)46 b Fh(Chv)h(*)h(ChvList_getList)43 │ │ │ │ b(\()48 b(ChvList)e(*list,)g(int)h(ilist)f(\))h(;)227 │ │ │ │ 549 y Fi(If)28 b(list)h Fh(ilist)e Fi(is)h(empt)m(y)-8 │ │ │ │ b(,)30 b(the)f(metho)s(d)f(returns)f Fh(NULL)p Fi(.)g(Otherwise,)i(if)f │ │ │ │ (the)h(list)g(needs)f(to)h(b)s(e)e(lo)s(c)m(k)m(ed,)k(the)227 │ │ │ │ 662 y(lo)s(c)m(k)37 b(is)e(lo)s(c)m(k)m(ed.)57 b(The)34 │ │ │ │ b(head)h(of)h(the)f(list)h(is)f(sa)m(v)m(ed)i(to)f(a)f(p)s(oin)m(ter)h │ │ │ │ (and)e(then)h(the)h(head)f(is)g(set)h(to)g Fh(NULL)p │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -22,15 +22,15 @@ │ │ │ │ │ The first two operations are queries, and can be done without locking the list. The third operation │ │ │ │ │ needs a lock only when two or more threads will be inserting objects into the list. The fourth │ │ │ │ │ operation requires a lock only when one thread will add an object while another thread removes │ │ │ │ │ the object and the incoming count is not yet zero. │ │ │ │ │ Having a lock associated with a ChvList object is optional, for example, it is not needed during │ │ │ │ │ a serial factorization nor a MPI factorization. In the latter case there is one ChvList per process. │ │ │ │ │ 1 │ │ │ │ │ - 2 ChvList : DRAFT January 6, 2026 │ │ │ │ │ + 2 ChvList : DRAFT January 17, 2026 │ │ │ │ │ For a multithreaded factorization there is one ChvList object that is shared by all threads. The │ │ │ │ │ mutualexclusion lock that is (optionally) embedded in the ChvListobject is a Lock object from this │ │ │ │ │ library. It is inside the Lock object that we have a mutual exclusion lock. Presently we support the │ │ │ │ │ Solaris and POSIX thread packages. Porting the multithreaded codes to another platform should │ │ │ │ │ be simple if the POSIX thread package is present. Another type of thread package will require │ │ │ │ │ some modifications to the Lock object, but none to the ChvList objects. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ @@ -52,15 +52,15 @@ │ │ │ │ │ 1. ChvList * ChvList_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the ChvList structure and then sets the default │ │ │ │ │ fields by a call to ChvList setDefaultFields(). │ │ │ │ │ 2. void ChvList_setDefaultFields ( ChvList *list ) ; │ │ │ │ │ The structure’s fields are set to default values: nlist and nlocks set to zero, and heads, │ │ │ │ │ counts, lock and flags are set to NULL . │ │ │ │ │ Error checking: If list is NULL, an error message is printed and the program exits. │ │ │ │ │ - ChvList : DRAFT January 6, 2026 3 │ │ │ │ │ + ChvList : DRAFT January 17, 2026 3 │ │ │ │ │ 3. void ChvList_clearData ( ChvList *list ) ; │ │ │ │ │ This method clears the object and free’s any owned data by calling Chv free() for each │ │ │ │ │ object on the free list. If heads is not NULL, it is free’d. If counts is not NULL, it is free’d │ │ │ │ │ via a call to IVfree(). If flags is not NULL, it is free’d via a call to CVfree(). If the │ │ │ │ │ lock is not NULL, it is destroyed via a call to Lock free(). There is a concluding call to │ │ │ │ │ ChvList setDefaultFields(). │ │ │ │ │ Error checking: If list is NULL, an error message is printed and the program exits. │ │ │ │ │ @@ -87,15 +87,15 @@ │ │ │ │ │ Error checking: If list is NULL, or if ilist is not in the range [0,nlist), an error message │ │ │ │ │ is printed and zero is returned. │ │ │ │ │ 2. int ChvList_isCountZero ( ChvList *list, int ilist ) ; │ │ │ │ │ If counts is NULL, or if counts[ilist] equal to zero, the method returns 1. Otherwise, the │ │ │ │ │ method returns 0. │ │ │ │ │ Error checking: If list is NULL, or if ilist is not in the range [0,nlist), an error message │ │ │ │ │ is printed and zero is returned. │ │ │ │ │ - 4 ChvList : DRAFT January 6, 2026 │ │ │ │ │ + 4 ChvList : DRAFT January 17, 2026 │ │ │ │ │ 3. Chv * ChvList_getList ( ChvList *list, int ilist ) ; │ │ │ │ │ If list ilist is empty, the method returns NULL. Otherwise, if the list needs to be locked, the │ │ │ │ │ lock is locked. The head of the list is saved to a pointer and then the head is set to NULL. │ │ │ │ │ If the list was locked, the number of locks is incremented and the lock unlocked. The saved │ │ │ │ │ pointer is returned. │ │ │ │ │ Error checking: If list is NULL, or if ilist is not in the range [0,nlist), an error message │ │ │ │ │ is printed and zero is returned. │ │ ├── ./usr/share/doc/spooles-doc/ChvManager.ps.gz │ │ │ ├── ChvManager.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o ChvManager.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ 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│ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fh(4)p 136 100 1057 4 v │ │ │ │ -1239 w Fg(DChvList)28 b Fd(:)41 b Fe(DRAFT)30 b Fd(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2843 100 V 0 399 a Fa(1.2.4)112 b(IO)38 b(metho)s(ds)111 │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fh(4)p 136 100 1035 4 v │ │ │ │ +1217 w Fg(DChvList)28 b Fd(:)40 b Fe(DRAFT)31 b Fd(Jan)m(uary)f(17,)h │ │ │ │ +(2026)p 2866 100 V 0 399 a Fa(1.2.4)112 b(IO)38 b(metho)s(ds)111 │ │ │ │ 595 y Fh(1.)46 b Fg(void)h(ChvManager_writeForHuman)o(Eye)41 │ │ │ │ b(\()48 b(ChvManager)d(*manager,)g(FILE)i(*fp)g(\))g(;)227 │ │ │ │ 745 y Fh(This)30 b(metho)s(d)g(writes)g(the)h(statistics)h(to)f(a)g │ │ │ │ (\014le)f(in)g(user)g(readable)h(form.)227 896 y Fe(Err)-5 │ │ │ │ b(or)34 b(che)-5 b(cking:)40 b Fh(If)30 b Fg(manager)f │ │ │ │ Fh(or)h Fg(fp)g Fh(are)h Fg(NULL)p Fh(,)e(an)h(error)g(message)i(is)e │ │ │ │ (prin)m(ted)g(and)g(zero)h(is)g(returned.)p eop end │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -23,15 +23,15 @@ │ │ │ │ │ finds a smallest object of that size or larger.) If there is no object on the free pool of sufficient │ │ │ │ │ size, one is created and returned. When the user releases an object to the manager, the object │ │ │ │ │ is placed on the free pool. │ │ │ │ │ For the factorization, serial, multithreaded or MPI, we recommend using the recycling mode. │ │ │ │ │ A multithreaded environment creates some difficulties. Should there be one manager object │ │ │ │ │ per thread, or should all the threads share one object? We have chosen the latter course, but this │ │ │ │ │ 1 │ │ │ │ │ - 2 DChvList : DRAFT January 6, 2026 │ │ │ │ │ + 2 DChvList : DRAFT January 17, 2026 │ │ │ │ │ requires that a lock be present to guard the critical section of code where one searches or adds an │ │ │ │ │ object to the list. The lock we use is a Lock object, and so the ChvManager code is completely │ │ │ │ │ independent of the thread package. Porting to a new system might require some modification to │ │ │ │ │ the Lock, but none to the manager object. │ │ │ │ │ Each manager object keeps track of certain statistics, bytes in their workspaces, the total │ │ │ │ │ number of bytes requested, the number of requests for a Chv objects, the number of releases, and │ │ │ │ │ the number of locks and unlocks. │ │ │ │ │ @@ -54,15 +54,15 @@ │ │ │ │ │ ChvManager object. │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. ChvManager * ChvManager_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the ChvManager structure and then sets the default │ │ │ │ │ fields by a call to ChvManager setDefaultFields(). │ │ │ │ │ - DChvList : DRAFT January 6, 2026 3 │ │ │ │ │ + DChvList : DRAFT January 17, 2026 3 │ │ │ │ │ 2. void ChvManager_setDefaultFields ( ChvManager *manager ) ; │ │ │ │ │ Thestructure’sfieldsaresettodefaultvalues: mode,nactive,nbytesactive,nbytesrequested, │ │ │ │ │ nbytesalloc, nrequests, nreleases, nlocks and nunlocks set to zero, and head and lock │ │ │ │ │ are set to NULL . │ │ │ │ │ Error checking: If manager is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. void ChvManager_clearData ( ChvManager *manager ) ; │ │ │ │ │ This method clears the object and free’s any owned data by calling Chv free() for each │ │ │ │ │ @@ -89,15 +89,15 @@ │ │ │ │ │ 2. void ChvManager_releaseObject ( ChvManager *manager, Chv *chv ) ; │ │ │ │ │ This method releases the chv instance into the free pool of objects. │ │ │ │ │ Error checking: If manager is NULL, an error message is printed and zero is returned. │ │ │ │ │ 3. void ChvManager_releaseListOfObjects ( ChvManager *manager, Chv *chv ) ; │ │ │ │ │ This method releases a list of Chv objects into the free pool of objects. The head of the list │ │ │ │ │ is the chv instance. │ │ │ │ │ Error checking: If manager is NULL, an error message is printed and zero is returned. │ │ │ │ │ - 4 DChvList : DRAFT January 6, 2026 │ │ │ │ │ + 4 DChvList : DRAFT January 17, 2026 │ │ │ │ │ 1.2.4 IO methods │ │ │ │ │ 1. void ChvManager_writeForHumanEye ( ChvManager *manager, FILE *fp ) ; │ │ │ │ │ This method writes the statistics to a file in user readable form. │ │ │ │ │ Error checking: If manager or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ Index │ │ │ │ │ ChvManager clearData(), 3 │ │ │ │ │ ChvManager free(), 3 │ │ ├── ./usr/share/doc/spooles-doc/Coords.ps.gz │ │ │ ├── Coords.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Coords.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ 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w(writeStats\(\))24 b Fk(is)k(called)h(to)f(write)g │ │ │ │ (out)g(the)g(header)g(and)f(statistics.)42 b(The)27 b │ │ │ │ Fj(coors[])f Fk(v)m(ector)j(is)227 780 y(then)h(prin)m(ted)g(out.)41 │ │ │ │ @@ -4331,17 +4342,17 @@ │ │ │ │ 5181 y Fg(\210)45 b Fk(The)33 b Fj(msgFile)e Fk(parameter)j(determines) │ │ │ │ f(the)h(message)g(\014le)f(|)h(if)f Fj(msgFile)e Fk(is)i │ │ │ │ Fj(stdout)p Fk(,)g(then)g(the)427 5294 y(message)24 b(\014le)e(is)h │ │ │ │ Fb(stdout)p Fk(,)i(otherwise)e(a)f(\014le)h(is)f(op)s(ened)g(with)g │ │ │ │ Fb(app)-5 b(end)24 b Fk(status)f(to)g(receiv)m(e)h(an)m(y)f(message)427 │ │ │ │ 5407 y(data.)p eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fk(6)p 136 100 1105 4 v │ │ │ │ -1287 w Fj(Coords)29 b Fc(:)40 b Fb(DRAFT)31 b Fc(Jan)m(uary)f(6,)h │ │ │ │ -(2026)p 2795 100 V 337 399 a Fg(\210)45 b Fk(The)20 b │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fk(6)p 136 100 1082 4 v │ │ │ │ +1264 w Fj(Coords)29 b Fc(:)41 b Fb(DRAFT)30 b Fc(Jan)m(uary)g(17,)h │ │ │ │ +(2026)p 2818 100 V 337 399 a Fg(\210)45 b Fk(The)20 b │ │ │ │ Fj(outCoordsFile)d Fk(parameter)j(is)h(the)f(output)g(\014le)g(for)h │ │ │ │ (the)f Fj(Coords)f Fk(ob)5 b(ject.)38 b(If)20 b Fj(outCoordsFile)427 │ │ │ │ 511 y Fk(is)h Fj(none)e Fk(then)h(the)g Fj(Coords)f Fk(ob)5 │ │ │ │ b(ject)21 b(is)f(not)h(written)f(to)h(a)g(\014le.)37 │ │ │ │ b(Otherwise,)22 b(the)f Fj(Coords)p 3409 511 29 4 v 33 │ │ │ │ w(writeToFile\(\))427 624 y Fk(metho)s(d)27 b(is)h(called)h(to)f(write) │ │ │ │ g(the)g(ob)5 b(ject)29 b(to)f(a)g(formatted)g(\014le)g(\(if)g │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -18,15 +18,15 @@ │ │ │ │ │ 1.2 Prototypes and descriptions of Coords methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ Coords object. │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1 │ │ │ │ │ - 2 Coords : DRAFT January 6, 2026 │ │ │ │ │ + 2 Coords : DRAFT January 17, 2026 │ │ │ │ │ 1. Coords * Coords_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Coords structure and then sets the default fields │ │ │ │ │ by a call to Coords setDefaultFields(). │ │ │ │ │ 2. void Coords_setDefaultFields ( Coords *coords ) ; │ │ │ │ │ This method sets the structure’s fields are set to default values: type = COORDS BY TUPLE, │ │ │ │ │ ndim = ncoor = 0 and coors = NULL. │ │ │ │ │ Error checking: If coords is NULL, an error message is printed and the program exits. │ │ │ │ │ @@ -54,15 +54,15 @@ │ │ │ │ │ point, bbox[2] = x-coordinate of the northeast point, and bbox[3] = y-coordinate of the │ │ │ │ │ northeast point. │ │ │ │ │ Error checking: If coordsbboxisNULL,oriftypeisnotCOORDS BY TUPLEorCOORDS BY COORD, │ │ │ │ │ or if any of n1, n2 or ncomp are nonpositive, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 3. void Coords_init27P ( Coords *coords, float bbox[], int type, │ │ │ │ │ int n1, int n2, int n3, int ncomp ) ; │ │ │ │ │ - Coords : DRAFT January 6, 2026 3 │ │ │ │ │ + Coords : DRAFT January 17, 2026 3 │ │ │ │ │ This method initializes a Coords object for a 27-point operator on a n1 ×n2 ×n3 grid with │ │ │ │ │ ncomp degrees of freedom at a grid point. The grid’s location is given by the bounding │ │ │ │ │ box vector, bbox[0] = x-coordinate of the southwest point, bbox[1] = y-coordinate of the │ │ │ │ │ southwest point, bbox[2] = z-coordinate of the southwest point, bbox[3] = x-coordinate │ │ │ │ │ of the northeast point, bbox[4] = y-coordinate of the northeast point, and bbox[5] = z- │ │ │ │ │ coordinate of the northeast point. │ │ │ │ │ Error checking: If coordsbboxisNULL,oriftypeisnotCOORDS BY TUPLEorCOORDS BY COORD, │ │ │ │ │ @@ -94,15 +94,15 @@ │ │ │ │ │ does not lie in the range [0,ncoor), an error message is printed and the program exits. │ │ │ │ │ 5. void Coords_setValue ( Coords *coords, int idim, int icoor, float val ) ; │ │ │ │ │ Thismethodsetsthefloatvalueoftheidim-thcoordinateoftheicoor-thgridpoint. Forex- │ │ │ │ │ ample, Coords setValue(coords, 1, 27, 1.2) sets x =1.2, Coords setValue(coords, │ │ │ │ │ 27 │ │ │ │ │ 2, 16, 3.3) sets y =3.3, and Coords setValue(coords, 3, 118, 0) sets z =0. │ │ │ │ │ 16 118 │ │ │ │ │ - 4 Coords : DRAFT January 6, 2026 │ │ │ │ │ + 4 Coords : DRAFT January 17, 2026 │ │ │ │ │ Error checking: If coords is NULL, or if idim does not lie in the range [1,ndim], or if icoor │ │ │ │ │ does not lie in the range [0,ncoor), an error message is printed and the program exits. │ │ │ │ │ 1.2.4 IO methods │ │ │ │ │ There are the usual eight IO routines. The file structure of a Coords object is simple: type, ndim, │ │ │ │ │ ncoor followed by the coors[] vector. │ │ │ │ │ 1. int Coords_readFromFile ( Coords *coords, char *filename ) ; │ │ │ │ │ This method read a Coords object from a file. It tries to open the file and if it is successful, it │ │ │ │ │ @@ -129,15 +129,15 @@ │ │ │ │ │ This method writes a Coords object to a formatted file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fprintf, zero is returned. │ │ │ │ │ Error checking: If coords or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 6. int Coords_writeToBinaryFile ( Coords *coords, FILE *fp ) ; │ │ │ │ │ This method writes a Coords object to a binary file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ Error checking: If coords or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ - Coords : DRAFT January 6, 2026 5 │ │ │ │ │ + Coords : DRAFT January 17, 2026 5 │ │ │ │ │ 7. int Coords_writeForHumanEye ( Coords *coords, FILE *fp ) ; │ │ │ │ │ This method write the Coords object to a file in an easy to read fashion. The method │ │ │ │ │ Coords writeStats() is called to write out the header and statistics. The coors[] vector is │ │ │ │ │ then printed out. The value 1 is returned. │ │ │ │ │ Error checking: If coords or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 8. int Coords_writeStats ( Coords *coords, FILE *fp ) ; │ │ │ │ │ The header and statistics are written. The value 1 is returned. │ │ │ │ │ @@ -164,15 +164,15 @@ │ │ │ │ │ This driver program creates a Coords object for 9-point finite difference operator on a n1×n2 │ │ │ │ │ grid and optionally writes it to a file. │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ that all objects are written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any message │ │ │ │ │ data. │ │ │ │ │ - 6 Coords : DRAFT January 6, 2026 │ │ │ │ │ + 6 Coords : DRAFT January 17, 2026 │ │ │ │ │ • TheoutCoordsFileparameteristheoutputfilefortheCoordsobject. IfoutCoordsFile │ │ │ │ │ is nonethentheCoordsobjectisnotwrittentoafile. Otherwise,theCoords writeToFile() │ │ │ │ │ method is called to write the object to a formatted file (if outCoordsFile is of the form │ │ │ │ │ *.coordsf), or a binary file (if outCoordsFile is of the form *.coordsb). │ │ │ │ │ Index │ │ │ │ │ Coords clearData(), 2 │ │ │ │ │ Coords free(), 2 │ │ ├── ./usr/share/doc/spooles-doc/DSTree.ps.gz │ │ │ ├── DSTree.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o DSTree.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1406,16 +1406,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1603,79 +1605,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 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Fi(stagesIV)227 779 y(IV)40 b Fj(ob)5 │ │ │ │ b(ject)41 b(is)f(created)h(of)f(size)h Fi(nvtx)47 b(=)g(mapIV->size)p │ │ │ │ @@ -3997,17 +4010,17 @@ │ │ │ │ (in)h(the)f(tree)h(via)g(a)g(p)s(ost-order)f(tra)m(v)m(ersal.)227 │ │ │ │ 5294 y Fh(Err)-5 b(or)34 b(che)-5 b(cking:)41 b Fj(If)29 │ │ │ │ b Fi(dstree)g Fj(is)i Fi(NULL)p Fj(,)e(or)h(if)h(the)f(ob)5 │ │ │ │ b(ject)32 b(has)e(not)g(b)s(een)g(initialized,)j(an)d(error)g(message) │ │ │ │ 227 5407 y(is)h(prin)m(ted)f(and)f(the)i(program)f(exits.)p │ │ │ │ eop end │ │ │ │ %%Page: 5 5 │ │ │ │ -TeXDict begin 5 4 bop 91 100 1153 4 v 1334 100 a Fi(Tree)29 │ │ │ │ -b Fd(:)41 b Fh(DRAFT)121 b Fd(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2700 100 V 1153 w Fj(5)111 399 y(3.)46 b Fi(int)h(DSTree_domainWeight)c │ │ │ │ +TeXDict begin 5 4 bop 91 100 1130 4 v 1312 100 a Fi(Tree)29 │ │ │ │ +b Fd(:)40 b Fh(DRAFT)122 b Fd(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2723 100 V 1130 w Fj(5)111 399 y(3.)46 b Fi(int)h(DSTree_domainWeight)c │ │ │ │ (\()k(DSTree)f(*dstree,)g(int)h(vwghts[])e(\))j(;)227 │ │ │ │ 560 y Fj(This)25 b(metho)s(d)g(returns)g(the)h(w)m(eigh)m(t)h(of)f(the) │ │ │ │ g(v)m(ertices)h(in)f(the)g(domains.)38 b(If)26 b Fi(vwghts)e │ │ │ │ Fj(is)i Fi(NULL)p Fj(,)e(the)i(v)m(ertices)227 673 y(ha)m(v)m(e)32 │ │ │ │ b(unit)e(w)m(eigh)m(t.)227 834 y Fh(Err)-5 b(or)34 b(che)-5 │ │ │ │ b(cking:)40 b Fj(If)30 b Fi(dstree)f Fj(is)h Fi(NULL)p │ │ │ │ Fj(,)g(an)g(error)g(message)i(is)e(prin)m(ted)g(and)g(the)g(program)g │ │ │ │ @@ -4074,17 +4087,17 @@ │ │ │ │ b Fi(dstree)e Fj(or)h Fi(fn)g Fj(are)i Fi(NULL)p Fj(,)d(or)i(if)g │ │ │ │ Fi(fn)f Fj(is)h(not)g(of)f(the)h(form)g Fi(*.dstreef)d │ │ │ │ Fj(\(for)j(a)227 5294 y(formatted)32 b(\014le\))g(or)f │ │ │ │ Fi(*.dstreeb)e Fj(\(for)j(a)f(binary)g(\014le\),)h(an)f(error)g │ │ │ │ (message)i(is)e(prin)m(ted)g(and)g(the)g(metho)s(d)227 │ │ │ │ 5407 y(returns)e(zero.)p eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fj(6)p 136 100 1153 4 v │ │ │ │ -1335 w Fi(Tree)29 b Fd(:)41 b Fh(DRAFT)30 b Fd(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2748 100 V 111 399 a Fj(5.)46 b Fi(int)h(DSTree_writeToFormattedFi)o │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fj(6)p 136 100 1130 4 v │ │ │ │ +1312 w Fi(Tree)29 b Fd(:)41 b Fh(DRAFT)30 b Fd(Jan)m(uary)g(17,)i(2026) │ │ │ │ +p 2770 100 V 111 399 a Fj(5.)46 b Fi(int)h(DSTree_writeToFormattedFi)o │ │ │ │ (le)42 b(\()47 b(DSTree)f(*dstree,)g(FILE)g(*fp)h(\))h(;)227 │ │ │ │ 548 y Fj(This)30 b(metho)s(d)g(writes)g(a)h Fi(DSTree)e │ │ │ │ Fj(ob)5 b(ject)31 b(to)g(a)g(formatted)g(\014le.)41 b(If)30 │ │ │ │ b(there)h(are)g(no)f(errors)g(in)g(writing)h(the)227 │ │ │ │ 661 y(data,)h(the)e(v)-5 b(alue)31 b Fi(1)f Fj(is)g(returned.)40 │ │ │ │ b(If)30 b(an)g(IO)g(error)g(is)g(encoun)m(tered)h(from)f │ │ │ │ Fi(fprintf)p Fj(,)f(zero)i(is)f(returned.)227 810 y Fh(Err)-5 │ │ │ │ @@ -4158,17 +4171,17 @@ │ │ │ │ 5181 V 33 w(writeToFile\(\))17 b Fj(metho)s(d)427 5294 │ │ │ │ y(is)31 b(called)h(to)f(write)g(the)g(ob)5 b(ject)32 │ │ │ │ b(to)f(a)g(formatted)h(\014le)f(\(if)g Fi(outFile)d Fj(is)j(of)g(the)g │ │ │ │ (form)f Fi(*.dinpmtxf)p Fj(\),)427 5407 y(or)h(a)f(binary)g(\014le)g │ │ │ │ (\(if)h Fi(outFile)e Fj(is)h(of)g(the)h(form)f Fi(*.dinpmtxb)p │ │ │ │ Fj(\).)p eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 91 100 1153 4 v 1334 100 a Fi(Tree)29 │ │ │ │ -b Fd(:)41 b Fh(DRAFT)121 b Fd(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2700 100 V 1153 w Fj(7)111 399 y(2.)46 b Fi(writeStagesIV)e(msglvl)j │ │ │ │ +TeXDict begin 7 6 bop 91 100 1130 4 v 1312 100 a Fi(Tree)29 │ │ │ │ +b Fd(:)40 b Fh(DRAFT)122 b Fd(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2723 100 V 1130 w Fj(7)111 399 y(2.)46 b Fi(writeStagesIV)e(msglvl)j │ │ │ │ (msgFile)e(inFile)h(type)h(outFile)227 543 y Fj(This)28 │ │ │ │ b(driv)m(er)h(program)g(reads)f(in)h(a)g Fi(DSTree)e │ │ │ │ Fj(from)h(a)i(\014le,)f(creates)h(a)g(stages)g Fi(IV)e │ │ │ │ Fj(ob)5 b(ject)30 b(and)e(writes)h(it)g(to)227 656 y(a)i(\014le.)337 │ │ │ │ 853 y Fe(\210)45 b Fj(The)28 b Fi(msglvl)f Fj(parameter)i(determines)g │ │ │ │ (the)g(amoun)m(t)g(of)f(output)h(|)f(taking)i Fi(msglvl)46 │ │ │ │ b(>=)h(3)28 b Fj(means)427 965 y(the)j Fi(DSTree)e Fj(ob)5 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -21,15 +21,15 @@ │ │ │ │ │ The DSTree object has a very simple data structure. It contains a Tree object to represent the │ │ │ │ │ tree fields of the domains and separators, and an IV object to hold the map from the vertices to │ │ │ │ │ the domains and separators. │ │ │ │ │ • Tree *tree : pointer to the Tree object │ │ │ │ │ • IV *mapIV : pointer to the IV object that holds the map from vertices to domains and │ │ │ │ │ separators. │ │ │ │ │ 1 │ │ │ │ │ - 2 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 2 Tree : DRAFT January 17, 2026 │ │ │ │ │ 1.2 Prototypes and descriptions of DSTree methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ DSTree object. │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. DSTree * DSTree_new ( void ) ; │ │ │ │ │ @@ -52,15 +52,15 @@ │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ 1. Tree * DSTree_tree ( DSTree *dstree ) ; │ │ │ │ │ This method returns a pointer to its Tree object. │ │ │ │ │ Error checking: If dstree is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. IV * DSTree_mapIV ( DSTree *dstree ) ; │ │ │ │ │ This method returns a pointer to its IV object that maps vertices to domains and separators. │ │ │ │ │ Error checking: If dstree is NULL, an error message is printed and the program exits. │ │ │ │ │ - Tree : DRAFT January 6, 2026 3 │ │ │ │ │ + Tree : DRAFT January 17, 2026 3 │ │ │ │ │ 1.2.3 Initializer methods │ │ │ │ │ There are three initializers and two helper functions to set the dimensions of the dstree, allocate │ │ │ │ │ the three vectors, and fill the information. │ │ │ │ │ 1. void DSTree_init1 ( DSTree *dstree, int ndomsep, int nvtx ) ; │ │ │ │ │ This method initializes an object given the number of vertices, (the dimension of mapIV) and │ │ │ │ │ domains and separators (the number of nodes in tree). It then clears any previous data │ │ │ │ │ with a call to DSTree clearData(). The tree field is created and initialized via a call to │ │ │ │ │ @@ -88,15 +88,15 @@ │ │ │ │ │ This method returns the stages for a nested dissection variant, separators on two adjacent │ │ │ │ │ levels are put into the same stage. The levels of the domains and separators are obtained │ │ │ │ │ via a call to Tree setHeightImetric(). A stagesIV IV object is created of size nvtx = │ │ │ │ │ mapIV->size, filled and then returned. If a vertex is found in a domain, its stage is zero. If │ │ │ │ │ a vertex is found in a separator at level k, its stage is ⌈k/2⌉. │ │ │ │ │ Error checking: If dstree is NULL, or if the object has not been initialized, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ - 4 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 4 Tree : DRAFT January 17, 2026 │ │ │ │ │ 3. IV * DSTree_MS2stages ( DSTree *dstree ) ; │ │ │ │ │ This method returns the stages for the standard multisection ordering. The levels of the │ │ │ │ │ domains and separators are obtained via a call to Tree setHeightImetric(). A stagesIV │ │ │ │ │ IV object is created of size nvtx = mapIV->size, filled and then returned. If a vertex is │ │ │ │ │ found in a domain, its stage is zero. If a vertex is found in a separator, its stage is one. │ │ │ │ │ Error checking: If dstree is NULL, or if the object has not been initialized, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ @@ -125,49 +125,49 @@ │ │ │ │ │ If dstree is NULL, an error message is printed and the program exits. Otherwise, the number │ │ │ │ │ of bytes taken by this object is returned. │ │ │ │ │ Error checking: If dstree is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. void DSTree_renumberViaPostOT ( DSTree *dstree ) ; │ │ │ │ │ This method renumbers the fronts in the tree via a post-order traversal. │ │ │ │ │ Error checking: If dstree is NULL, or if the object has not been initialized, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ - Tree : DRAFT January 6, 2026 5 │ │ │ │ │ - 3. int DSTree_domainWeight ( DSTree *dstree, int vwghts[] ) ; │ │ │ │ │ + Tree : DRAFT January 17, 2026 5 │ │ │ │ │ + 3. int DSTree_domainWeight ( DSTree *dstree, int vwghts[] ) ; │ │ │ │ │ This method returns the weight of the vertices in the domains. If vwghts is NULL, the vertices │ │ │ │ │ have unit weight. │ │ │ │ │ Error checking: If dstree is NULL, an error message is printed and the program exits. │ │ │ │ │ - 4. int DSTree_separatorWeight ( DSTree *dstree, int vwghts[] ) ; │ │ │ │ │ + 4. int DSTree_separatorWeight ( DSTree *dstree, int vwghts[] ) ; │ │ │ │ │ This method returns the weight of the vertices in the separators. If vwghts is NULL, the │ │ │ │ │ vertices have unit weight. │ │ │ │ │ Error checking: If dstree is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.6 IO methods │ │ │ │ │ There are the usual eight IO routines. The file structure of a dstree object is simple: the structure │ │ │ │ │ for a Tree object followed by the structure for an IV object. │ │ │ │ │ - 1. int DSTree_readFromFile ( DSTree *dstree, char *fn ) ; │ │ │ │ │ + 1. int DSTree_readFromFile ( DSTree *dstree, char *fn ) ; │ │ │ │ │ This method reads a DSTree object from a file. It tries to open the file and if it is successful, │ │ │ │ │ it then calls DSTree readFromFormattedFile() or DSTree readFromBinaryFile(), closes │ │ │ │ │ the file and returns the value returned from the called routine. │ │ │ │ │ Error checking: If dstree or fn are NULL, or if fn is not of the form *.dstreef (for a │ │ │ │ │ formatted file) or *.dstreeb (for a binary file), an error message is printed and the method │ │ │ │ │ returns zero. │ │ │ │ │ - 2. int DSTree_readFromFormattedFile ( DSTree *dstree, FILE *fp ) ; │ │ │ │ │ + 2. int DSTree_readFromFormattedFile ( DSTree *dstree, FILE *fp ) ; │ │ │ │ │ This method reads in a DSTree object from a formatted file. If there are no errors in reading │ │ │ │ │ the data, the value 1 is returned. If an IO error is encountered from fscanf, zero is returned. │ │ │ │ │ Error checking: If dstree or fp is NULL, an error message is printed and zero is returned. │ │ │ │ │ - 3. int DSTree_readFromBinaryFile ( DSTree *dstree, FILE *fp ) ; │ │ │ │ │ + 3. int DSTree_readFromBinaryFile ( DSTree *dstree, FILE *fp ) ; │ │ │ │ │ This method reads in a DSTree object from a binary file. If there are no errors in reading the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fread, zero is returned. │ │ │ │ │ Error checking: If dstree or fp is NULL, an error message is printed and zero is returned. │ │ │ │ │ - 4. int DSTree_writeToFile ( DSTree *dstree, char *fn ) ; │ │ │ │ │ + 4. int DSTree_writeToFile ( DSTree *dstree, char *fn ) ; │ │ │ │ │ This method writes a DSTree object to a file. It tries to open the file and if it is successful, │ │ │ │ │ it then calls DSTree writeFromFormattedFile()or DSTree writeFromBinaryFile(),closes │ │ │ │ │ the file and returns the value returned from the called routine. │ │ │ │ │ Error checking: If dstree or fn are NULL, or if fn is not of the form *.dstreef (for a │ │ │ │ │ formatted file) or *.dstreeb (for a binary file), an error message is printed and the method │ │ │ │ │ returns zero. │ │ │ │ │ - 6 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 6 Tree : DRAFT January 17, 2026 │ │ │ │ │ 5. int DSTree_writeToFormattedFile ( DSTree *dstree, FILE *fp ) ; │ │ │ │ │ This method writes a DSTree object to a formatted file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fprintf, zero is returned. │ │ │ │ │ Error checking: If dstree or fp is NULL, an error message is printed and zero is returned. │ │ │ │ │ 6. int DSTree_writeToBinaryFile ( DSTree *dstree, FILE *fp ) ; │ │ │ │ │ This method writes a DSTree object to a binary file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ @@ -195,16 +195,16 @@ │ │ │ │ │ • The inFile parameter is the input file for the DSTree object. It must be of the │ │ │ │ │ form *.dinpmtxf or *.dinpmtxb. The DSTree object is read from the file via the │ │ │ │ │ DSTree readFromFile() method. │ │ │ │ │ • The outFileparameter is the output file for the DSTree object. If outFile is none then │ │ │ │ │ the DSTreeobject is not written to a file. Otherwise, the DSTree writeToFile()method │ │ │ │ │ is called to write the object to a formatted file (if outFile is of the form *.dinpmtxf), │ │ │ │ │ or a binary file (if outFile is of the form *.dinpmtxb). │ │ │ │ │ - Tree : DRAFT January 6, 2026 7 │ │ │ │ │ - 2. writeStagesIV msglvl msgFile inFile type outFile │ │ │ │ │ + Tree : DRAFT January 17, 2026 7 │ │ │ │ │ + 2. writeStagesIV msglvl msgFile inFile type outFile │ │ │ │ │ This driver program reads in a DSTree from a file, creates a stages IV object and writes it to │ │ │ │ │ a file. │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the DSTree object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ @@ -213,16 +213,16 @@ │ │ │ │ │ method. │ │ │ │ │ • The type parameter specifies which type of stages vector to create. There are presently │ │ │ │ │ four supported types : ND, ND2, MS2 and ND3. See the stage methods in Section 1.2.4. │ │ │ │ │ • The outFile parameter is the output file for the stages IV object. If outFile is none │ │ │ │ │ then the IV object is not written to a file. Otherwise, the IV writeToFile() method │ │ │ │ │ is called to write the object to a formatted file (if outFile is of the form *.ivf), or a │ │ │ │ │ binary file (if outFile is of the form *.ivb). │ │ │ │ │ - 3. testDomWeightStages msglvl msgFile │ │ │ │ │ - inDSTreeFile inGraphFile inCutoffDVfile outFile │ │ │ │ │ + 3. testDomWeightStages msglvl msgFile │ │ │ │ │ + inDSTreeFile inGraphFile inCutoffDVfile outFile │ │ │ │ │ This driver program is used to create a stages vector based on subtree weight. It reads in │ │ │ │ │ three objects from files: a DSTree object, a Graph object and a DV object that contains the │ │ │ │ │ cutoff vector, then creates a stages IV object and writes it to a file. │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the DSTree object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ ├── ./usr/share/doc/spooles-doc/DV.ps.gz │ │ │ ├── DV.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o DV.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 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b(ject)38 b(giv)m(en)f(a)g(size)h(for)e(the)h │ │ │ │ (v)m(ector)h(and)e(a)h(p)s(ossible)f(p)s(oin)m(ter)g(to)i(the)227 │ │ │ │ 1066 y(v)m(ectors')30 b(storage.)42 b(An)m(y)28 b(previous)g(data)h(is) │ │ │ │ g(cleared)g(with)f(a)h(call)h(to)f Fk(DV)p 2716 1066 │ │ │ │ @@ -4534,17 +4545,17 @@ │ │ │ │ (offset)f(\))h(;)227 5294 y Fl(This)32 b(metho)s(d)h(shifts)f(the)i │ │ │ │ (base)f(en)m(tries)g(of)h(the)f(v)m(ector)h(and)f(decremen)m(ts)g(the)g │ │ │ │ (presen)m(t)g(size)h(and)f(max-)227 5407 y(im)m(um)g(size)g(of)g(the)f │ │ │ │ (v)m(ector)j(b)m(y)d Fk(offset)p Fl(.)46 b(This)31 b(is)i(a)g │ │ │ │ (dangerous)f(metho)s(d)g(to)h(use)g(b)s(ecause)f(the)h(state)h(of)p │ │ │ │ eop end │ │ │ │ %%Page: 5 5 │ │ │ │ -TeXDict begin 5 4 bop 91 100 1206 4 v 1387 100 a Fk(DV)30 │ │ │ │ -b Fg(:)g Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2647 100 V 1206 w Fl(5)227 399 y(the)37 b(v)m(ector)h(is)e(lost,)j │ │ │ │ +TeXDict begin 5 4 bop 91 100 1183 4 v 1364 100 a Fk(DV)30 │ │ │ │ +b 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Fl(an)h(error)g(message)h(is)g(prin)m(ted)f │ │ │ │ (and)g(the)g(program)g(exits.)p eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fl(6)p 136 100 1206 4 v │ │ │ │ -1388 w Fk(DV)29 b Fg(:)i Ff(DRAFT)f Fg(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2695 100 V 111 399 a Fl(8.)46 b Fk(double)g(*)i(DV_first)d(\()j(DV)f │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fl(6)p 136 100 1183 4 v │ │ │ │ +1365 w Fk(DV)30 b Fg(:)g Ff(DRAFT)g Fg(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2717 100 V 111 399 a Fl(8.)46 b Fk(double)g(*)i(DV_first)d(\()j(DV)f │ │ │ │ (*dv)g(\))g(;)227 511 y(double)f(*)i(DV_next)e(\()h(DV)g(*dv,)g(int)g │ │ │ │ (*pd)g(\))g(;)227 671 y Fl(These)30 b(t)m(w)m(o)i(metho)s(ds)e(are)h │ │ │ │ (used)e(as)i(iterators,)h(e.g.,)227 921 y Fk(for)47 b(\()h(pd)f(=)g │ │ │ │ (DV_first\(dv\))e(;)i(pd)g(!=)h(NULL)e(;)i(pd)f(=)g(DV_next\(dv,)e │ │ │ │ (pd\))i(\))g({)370 1033 y(do)h(something)d(with)i(entry)f(*pd)227 │ │ │ │ 1146 y(})227 1396 y Fl(Eac)m(h)41 b(metho)s(d)f(c)m(hec)m(ks)i(to)f │ │ │ │ (see)g(if)f Fk(dv)g Fl(or)g Fk(pd)g Fl(is)g Fk(NULL)p │ │ │ │ @@ -4673,17 +4684,17 @@ │ │ │ │ b(are)i(the)f(usual)f(eigh)m(t)i(IO)f(routines.)40 b(The)30 │ │ │ │ b(\014le)f(structure)h(of)g(a)g Fk(DV)f Fl(ob)5 b(ject)31 │ │ │ │ b(is)f(simple:)41 b(the)30 b(\014rst)f(en)m(try)h(is)0 │ │ │ │ 5407 y Fk(size)p Fl(,)f(follo)m(w)m(ed)j(b)m(y)f(the)f │ │ │ │ Fk(size)g Fl(en)m(tries)h(found)e(in)h Fk(vec[])p Fl(.)p │ │ │ │ eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 91 100 1206 4 v 1387 100 a Fk(DV)30 │ │ │ │ -b Fg(:)g Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2647 100 V 1206 w Fl(7)111 399 y(1.)46 b Fk(int)h(DV_readFromFile)d(\() │ │ │ │ +TeXDict begin 7 6 bop 91 100 1183 4 v 1364 100 a Fk(DV)30 │ │ │ │ +b Fg(:)h Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2670 100 V 1183 w Fl(7)111 399 y(1.)46 b Fk(int)h(DV_readFromFile)d(\() │ │ │ │ j(DV)g(*dv,)g(char)g(*fn)g(\))g(;)227 547 y Fl(This)33 │ │ │ │ b(metho)s(d)g(reads)g(a)h Fk(DV)f Fl(ob)5 b(ject)35 b(from)e(a)h │ │ │ │ (\014le.)50 b(It)34 b(tries)f(to)i(op)s(en)e(the)g(\014le)h(and)f(if)g │ │ │ │ (it)h(is)g(successful,)g(it)227 660 y(then)j(calls)g │ │ │ │ Fk(DV)p 751 660 29 4 v 34 w(readFromFormattedFile\(\))30 │ │ │ │ b Fl(or)37 b Fk(DV)p 2133 660 V 34 w(readFromBinaryFile\(\))p │ │ │ │ Fl(,)32 b(closes)38 b(the)f(\014le)g(and)227 772 y(returns)29 │ │ │ │ @@ -4764,17 +4775,17 @@ │ │ │ │ (\))h(;)227 5259 y Fl(This)30 b(metho)s(d)g(writes)g(the)h(header)f │ │ │ │ (and)g(statistics)i(to)f(a)g(\014le.)41 b(The)29 b(v)-5 │ │ │ │ b(alue)31 b Fk(1)f Fl(is)h(returned.)227 5407 y Ff(Err)-5 │ │ │ │ b(or)34 b(che)-5 b(cking:)40 b Fl(If)30 b Fk(dv)g Fl(or)g │ │ │ │ Fk(fp)g Fl(are)h Fk(NULL)p Fl(,)e(an)i(error)f(message)h(is)g(prin)m │ │ │ │ (ted)f(and)f(zero)i(is)g(returned.)p eop end │ │ │ │ %%Page: 8 8 │ │ │ │ -TeXDict begin 8 7 bop 0 100 a Fl(8)p 136 100 1206 4 v │ │ │ │ -1388 w Fk(DV)29 b Fg(:)i Ff(DRAFT)f Fg(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2695 100 V 111 399 a Fl(9.)46 b Fk(int)h(DV_writeForMatlab)c(\()48 │ │ │ │ +TeXDict begin 8 7 bop 0 100 a Fl(8)p 136 100 1183 4 v │ │ │ │ +1365 w Fk(DV)30 b Fg(:)g Ff(DRAFT)g Fg(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2717 100 V 111 399 a Fl(9.)46 b Fk(int)h(DV_writeForMatlab)c(\()48 │ │ │ │ b(DV)f(*dv,)g(char)f(*name,)g(FILE)h(*fp)g(\))g(;)227 │ │ │ │ 549 y Fl(This)37 b(metho)s(d)h(writes)f(the)i(en)m(tries)f(of)g(the)g │ │ │ │ (v)m(ector)i(to)e(a)g(\014le)g(suitable)h(to)f(b)s(e)g(read)f(b)m(y)h │ │ │ │ (Matlab.)64 b(The)227 662 y(c)m(haracter)31 b(string)e │ │ │ │ Fk(name)f Fl(is)h(the)g(name)g(of)g(the)g(v)m(ector,)i(e.g,)g(if)e │ │ │ │ Fk(name)46 b(=)i("A")p Fl(,)28 b(then)h(w)m(e)g(ha)m(v)m(e)h(lines)g │ │ │ │ (of)f(the)227 775 y(form)227 1000 y Fk(A\(1\))47 b(=)g │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -22,15 +22,15 @@ │ │ │ │ │ simplest operations, and so when we need to manipulate an double vector inside a loop, we extract │ │ │ │ │ out the size and pointer to the base array from the DV object. On the other hand, the convenience │ │ │ │ │ makes it a widely used object. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ The DV structure has three fields. │ │ │ │ │ • int size : present size of the vector. │ │ │ │ │ 1 │ │ │ │ │ - 2 DV : DRAFT January 6, 2026 │ │ │ │ │ + 2 DV : DRAFT January 17, 2026 │ │ │ │ │ • int maxsize : maximum size of the vector. │ │ │ │ │ • int owned : owner flag for the data. When owned = 1, storage for owned double’s has been │ │ │ │ │ allocated by this object and can be free’d by the object. When owned == 0 but size > 0 , │ │ │ │ │ this object points to entries that have been allocated elsewhere, and these entries will not be │ │ │ │ │ free’d by this object. │ │ │ │ │ • double *vec : pointer to the base address of the double vector │ │ │ │ │ The size, maxsize, nowned and vec fields need never be accessed directly — see the DV size(), │ │ │ │ │ @@ -53,15 +53,15 @@ │ │ │ │ │ the storage for vec is free’d by a call to DVfree(). The structure’s default fields are then set │ │ │ │ │ with a call to DV setDefaultFields(). │ │ │ │ │ Error checking: If dv is NULL an error message is printed and the program exits. │ │ │ │ │ 4. void DV_free ( DV *dv ) ; │ │ │ │ │ This method releases any storage by a call to DV clearData() then free’s the storage for the │ │ │ │ │ structure with a call to free(). │ │ │ │ │ Error checking: If dv is NULL an error message is printed and the program exits. │ │ │ │ │ - DV : DRAFT January 6, 2026 3 │ │ │ │ │ + DV : DRAFT January 17, 2026 3 │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ These method allow access to information in the data fields without explicitly following pointers. │ │ │ │ │ There is overhead involved with these method due to the function call and error checking inside │ │ │ │ │ the methods. │ │ │ │ │ 1. int DV_owned ( DV *dv ) ; │ │ │ │ │ This method returns the value of owned. If owned > 0, then the object owns the data pointed │ │ │ │ │ to by vec and will free this data with a call to DVfree() when its data is cleared by a call to │ │ │ │ │ @@ -85,15 +85,15 @@ │ │ │ │ │ This method fills *psize with the size of the vector and **pentries with the base address │ │ │ │ │ of the vector. │ │ │ │ │ Error checking: If dv, psize or pentriesis NULL, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 7. void DV_setEntry ( DV *dv, int loc, double value ) ; │ │ │ │ │ This method sets the loc’th entry of the vector to value. │ │ │ │ │ Error checking: If dv is NULL or loc < 0, an error message is printed and the program exits. │ │ │ │ │ - 4 DV : DRAFT January 6, 2026 │ │ │ │ │ + 4 DV : DRAFT January 17, 2026 │ │ │ │ │ 1.2.3 Initializer methods │ │ │ │ │ There are three initializer methods. │ │ │ │ │ 1. void DV_init ( DV *dv, int size, double *entries ) ; │ │ │ │ │ This method initializes the object given a size for the vector and a possible pointer to the │ │ │ │ │ vectors’ storage. Any previous data is cleared with a call to DV clearData(). If entries != │ │ │ │ │ NULL then the vec field is set to entries, the size and maxsize fields are set to size, and │ │ │ │ │ owned is set to zero because the object does not own the entries. If entries is NULL and size │ │ │ │ │ @@ -123,15 +123,15 @@ │ │ │ │ │ increased with a call to DV setMaxsize(). The size field is set to newsize. │ │ │ │ │ Error checking: If dv is NULL, or newsize < 0, or if 0 < maxsize < newsize and owned = │ │ │ │ │ 0, an error message is printed and the program exits. │ │ │ │ │ 1.2.4 Utility methods │ │ │ │ │ 1. void DV_shiftBase ( DV *dv, int offset ) ; │ │ │ │ │ This method shifts the base entries of the vector and decrements the present size and max- │ │ │ │ │ imum size of the vector by offset. This is a dangerous method to use because the state of │ │ │ │ │ - DV : DRAFT January 6, 2026 5 │ │ │ │ │ + DV : DRAFT January 17, 2026 5 │ │ │ │ │ the vector is lost, namely vec, the base of the entries, is corrupted. If the object owns its │ │ │ │ │ entries and DV free(), DV setSize() or DV setMaxsize() is called before the base has been │ │ │ │ │ shifted back to its original position, a segmentation violation will likely result. This is a very │ │ │ │ │ useful method, but use with caution. │ │ │ │ │ Error checking: If dv is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. void DV_push ( DV *dv, double val ) ; │ │ │ │ │ This method pushes an entry onto the vector. If the vector is full, i.e., if size == maxsize │ │ │ │ │ @@ -159,15 +159,15 @@ │ │ │ │ │ This method shuffles the entries in the vector using seed as a seed to a random number │ │ │ │ │ generator. │ │ │ │ │ Error checking: If dv is NULL, size <= 0 or if vec == NULL, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 7. int DV_sizeOf ( DV *dv ) ; │ │ │ │ │ This method returns the number of bytes taken by the object. │ │ │ │ │ Error checking: If dv is NULL an error message is printed and the program exits. │ │ │ │ │ - 6 DV : DRAFT January 6, 2026 │ │ │ │ │ + 6 DV : DRAFT January 17, 2026 │ │ │ │ │ 8. double * DV_first ( DV *dv ) ; │ │ │ │ │ double * DV_next ( DV *dv, int *pd ) ; │ │ │ │ │ These two methods are used as iterators, e.g., │ │ │ │ │ for ( pd = DV_first(dv) ; pd != NULL ; pd = DV_next(dv, pd) ) { │ │ │ │ │ do something with entry *pd │ │ │ │ │ } │ │ │ │ │ Each method checks to see if dv or pd is NULL, if so an error message is printed and the │ │ │ │ │ @@ -193,15 +193,15 @@ │ │ │ │ │ smaller than tausmall, or larger than taubig are placed into pnzero, *pnsmall and *pnbig, │ │ │ │ │ respectively. On return, the size of the xDV and yDV objects is npts. │ │ │ │ │ Error checking: If dv, xDV, yDV, pnsmall or pnbig are NULL, or if npts ≤ 0, or if taubig < 0.0 │ │ │ │ │ or if tausmall > taubig, an error message is printed and the program exits. │ │ │ │ │ 1.2.5 IO methods │ │ │ │ │ There are the usual eight IO routines. The file structure of a DV object is simple: the first entry is │ │ │ │ │ size, followed by the size entries found in vec[]. │ │ │ │ │ - DV : DRAFT January 6, 2026 7 │ │ │ │ │ + DV : DRAFT January 17, 2026 7 │ │ │ │ │ 1. int DV_readFromFile ( DV *dv, char *fn ) ; │ │ │ │ │ This method reads a DV object from a file. It tries to open the file and if it is successful, it │ │ │ │ │ then calls DV readFromFormattedFile() or DV readFromBinaryFile(), closes the file and │ │ │ │ │ returns the value returned from the called routine. │ │ │ │ │ Error checking: If dv or fn are NULL, or if fn is not of the form *.dvf (for a formatted file) │ │ │ │ │ or *.dvb (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 2. int DV_readFromFormattedFile ( DV *dv, FILE *fp ) ; │ │ │ │ │ @@ -230,15 +230,15 @@ │ │ │ │ │ This method writes a DV object to a file in a human readable format. is called to write out │ │ │ │ │ the header and statistics. The entries of the vector then follow in eighty column format using │ │ │ │ │ the DVfprintf() method. The value 1 is returned. │ │ │ │ │ Error checking: If dv or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 8. int DV_writeStats ( DV *dv, FILE *fp ) ; │ │ │ │ │ This method writes the header and statistics to a file. The value 1 is returned. │ │ │ │ │ Error checking: If dv or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ - 8 DV : DRAFT January 6, 2026 │ │ │ │ │ + 8 DV : DRAFT January 17, 2026 │ │ │ │ │ 9. int DV_writeForMatlab ( DV *dv, char *name, FILE *fp ) ; │ │ │ │ │ This method writes the entries of the vector to a file suitable to be read by Matlab. The │ │ │ │ │ character string name is the name of the vector, e.g, if name = "A", then we have lines of the │ │ │ │ │ form │ │ │ │ │ A(1) = 1.000000000000e0 ; │ │ │ │ │ A(2) = 2.000000000000e0 ; │ │ │ │ │ ... │ │ ├── ./usr/share/doc/spooles-doc/DenseMtx.ps.gz │ │ │ ├── DenseMtx.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o DenseMtx.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg 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29 w(REAL)f Fj(nor)g Fi(SPOOLES)p 2442 │ │ │ │ @@ -4152,17 +4163,17 @@ │ │ │ │ Fi(irowB)e Fj(is)h(out)h(of)f(range,)h(or)f(if)h Fi(mtxA)e │ │ │ │ Fj(is)h Fi(NULL)p Fj(,)f(or)h(if)h Fi(irowA)e Fj(is)h(out)h(of)208 │ │ │ │ 5308 y(range,)23 b(or)h(if)g(the)h(n)n(um)n(b)r(er)f(of)h(columns)f(in) │ │ │ │ g Fi(mtxB)f Fj(and)h Fi(mtxA)f Fj(are)g(not)h(the)h(same,)g(an)f(error) │ │ │ │ e(message)h(is)h(prin)n(ted)g(and)208 5407 y(the)k(program)d(exits.)p │ │ │ │ eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fj(6)p 125 100 1135 4 v │ │ │ │ -1300 w Fi(DenseMtx)24 b Fe(:)37 b Fh(DRAFT)28 b Fe(Jan)n(uary)d(6,)i │ │ │ │ -(2026)p 2766 100 V 101 390 a Fj(9.)42 b Fi(void)f(DenseMtx_addRow)d(\() │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fj(6)p 125 100 1114 4 v │ │ │ │ +1279 w Fi(DenseMtx)25 b Fe(:)37 b Fh(DRAFT)27 b Fe(Jan)n(uary)e(17,)i │ │ │ │ +(2026)p 2786 100 V 101 390 a Fj(9.)42 b Fi(void)f(DenseMtx_addRow)d(\() │ │ │ │ 43 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│ │ │ │ -b Fe(:)37 b Fh(DRAFT)110 b Fe(Jan)n(uary)26 b(6,)h(2026)p │ │ │ │ -2726 100 V 1135 w Fj(7)0 390 y Fc(1.2.5)112 b(IO)38 b(metho)s(ds)0 │ │ │ │ +TeXDict begin 7 6 bop 83 100 1114 4 v 1280 100 a Fi(DenseMtx)24 │ │ │ │ +b Fe(:)37 b Fh(DRAFT)110 b Fe(Jan)n(uary)26 b(17,)h(2026)p │ │ │ │ +2747 100 V 1114 w Fj(7)0 390 y Fc(1.2.5)112 b(IO)38 b(metho)s(ds)0 │ │ │ │ 573 y Fj(The)23 b(\014le)g(structure)f(of)h(a)g Fi(DenseMtx)c │ │ │ │ Fj(ob)5 b(ject)23 b(is)g(simple.)35 b(First)23 b(comes)f(sev)n(en)g │ │ │ │ (scalars,)g Fi(type)p Fj(,)h Fi(rowid)p Fj(,)e Fi(colid)p │ │ │ │ Fj(,)h Fi(nrow)p Fj(,)h Fi(ncol)p Fj(,)0 672 y Fi(inc1)g │ │ │ │ Fj(and)h Fi(inc2)p Fj(,)f(follo)n(w)n(ed)g(b)n(y)h(the)h(ro)n(w)e │ │ │ │ (indices,)i(follo)n(w)n(ed)e(b)n(y)h(the)g(column)g(indices,)h(and)f │ │ │ │ (then)h(follo)n(w)n(ed)e(b)n(y)h(the)h(matrix)0 772 y(en)n(tries.)101 │ │ │ │ @@ -4332,17 +4343,17 @@ │ │ │ │ 5270 y Fj(This)27 b(metho)r(d)h(writes)f(a)h Fi(DenseMtx)c │ │ │ │ Fj(ob)5 b(ject)27 b(to)h(a)f(\014le)h(in)g(an)f(easily)g(readable)f │ │ │ │ (format.)208 5407 y Fh(Err)l(or)k(che)l(cking:)38 b Fj(If)28 │ │ │ │ b Fi(mtx)f Fj(or)g Fi(fp)f Fj(are)h Fi(NULL)p Fj(,)f(an)h(error)f │ │ │ │ (message)g(is)i(prin)n(ted)f(and)h(zero)e(is)i(returned.)p │ │ │ │ eop end │ │ │ │ %%Page: 8 8 │ │ │ │ -TeXDict begin 8 7 bop 0 100 a Fj(8)p 125 100 1135 4 v │ │ │ │ -1300 w Fi(DenseMtx)24 b Fe(:)37 b Fh(DRAFT)28 b Fe(Jan)n(uary)d(6,)i │ │ │ │ -(2026)p 2766 100 V 101 390 a Fj(9.)42 b Fi(void)f(DenseMtx_writeFor)o │ │ │ │ +TeXDict begin 8 7 bop 0 100 a Fj(8)p 125 100 1114 4 v │ │ │ │ +1279 w Fi(DenseMtx)25 b Fe(:)37 b Fh(DRAFT)27 b Fe(Jan)n(uary)e(17,)i │ │ │ │ +(2026)p 2786 100 V 101 390 a Fj(9.)42 b Fi(void)f(DenseMtx_writeFor)o │ │ │ │ (Mat)o(la)o(b)d(\()43 b(DenseMtx)d(*mtx,)i(char)f(*mtxname,)f(FILE)i │ │ │ │ (*fp)h(\))g(;)208 523 y Fj(This)27 b(metho)r(d)h(writes)f(out)h(a)f │ │ │ │ Fi(DenseMtx)e Fj(ob)5 b(ject)27 b(to)g(a)h(\014le)f(in)h(a)f(Matlab)h │ │ │ │ (format.)36 b(A)28 b(sample)f(line)h(is)208 722 y Fi(a\(10,5\))40 │ │ │ │ b(=)87 b(-1.550328201511e)o(-01)37 b(+)130 b(1.848033378871e+)o(00*)o │ │ │ │ (i)37 b(;)208 922 y Fj(for)27 b(complex)g(matrices,)g(or)208 │ │ │ │ 1121 y Fi(a\(10,5\))40 b(=)87 b(-1.550328201511e)o(-01)37 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -22,15 +22,15 @@ │ │ │ │ │ • double *entries : pointer to the base address of the double vector that contains the entries. │ │ │ │ │ • DV wrkDV : object that manages the owned working storage. │ │ │ │ │ • DenseMtx *next : link to a next object in a singly linked list. │ │ │ │ │ One can query the type of entries via two macros. │ │ │ │ │ • DENSEMTX IS REAL(mtx) returns 1 if the matrix has real entries, and 0 otherwise. │ │ │ │ │ • DENSEMTX IS COMPLEX(mtx) returns 1 if the matrix has complex entries, and 0 otherwise. │ │ │ │ │ 1 │ │ │ │ │ - 2 DenseMtx : DRAFT January 6, 2026 │ │ │ │ │ + 2 DenseMtx : DRAFT January 17, 2026 │ │ │ │ │ 1.2 Prototypes and descriptions of DenseMtx methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the DenseMtx │ │ │ │ │ object. │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ Asusual, there are four basic methods to support object creation, setting default fields, clearing any allocated │ │ │ │ │ data, and free’ing the object. │ │ │ │ │ 1. DenseMtx * DenseMtx_new ( void ) ; │ │ │ │ │ @@ -58,15 +58,15 @@ │ │ │ │ │ 3. void DenseMtx_dimensions ( DenseMtx *mtx, int *pnrow, int *pncol ) ; │ │ │ │ │ This method fills *pnrow and *pncol with nrow and ncol. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. int DenseMtx_columnIncrement ( DenseMtx *mtx ) ; │ │ │ │ │ This method returns the row increment of the object, the difference in memory locations of two entries │ │ │ │ │ in consecutive columns in the same row. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ - DenseMtx : DRAFT January 6, 2026 3 │ │ │ │ │ + DenseMtx : DRAFT January 17, 2026 3 │ │ │ │ │ 5. int DenseMtx_rowIncrement ( DenseMtx *mtx ) ; │ │ │ │ │ This method returns the row increment of the object, the difference in memory locations of two entries │ │ │ │ │ in consecutive rows in the same column. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 6. void DenseMtx_rowIndices ( DenseMtx *mtx, int *pnrow, **prowind ) ; │ │ │ │ │ This method fills *pnrow with nrow, the number of rows, and *prowind with rowind, a pointer to the │ │ │ │ │ row indices. │ │ │ │ │ @@ -97,15 +97,15 @@ │ │ │ │ │ message is printed and the program exits. │ │ │ │ │ 13. void DenseMtx_setComplexEntry ( DenseMtx *mtx, int irow, int jcol, │ │ │ │ │ double real, double imag ) ; │ │ │ │ │ This method sets the real and imaginary parts of the entry in row irow and column jcol to be │ │ │ │ │ (real,imag). │ │ │ │ │ Error checking: If mtx is NULL, or if the matrix is not complex, or if irow or jcol is out of range, an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ - 4 DenseMtx : DRAFT January 6, 2026 │ │ │ │ │ + 4 DenseMtx : DRAFT January 17, 2026 │ │ │ │ │ 14. int DenseMtx_row ( DenseMtx *mtx, int irow, double **prowent ) ; │ │ │ │ │ This method fills *prowent with the first location of the entries in row irow. │ │ │ │ │ Return codes: 1 is a normal return, -1 means mtx is NULL, -2 means invalid type for mtx, -3 means │ │ │ │ │ irow is out-of-range, -4 means prowent is NULL. │ │ │ │ │ 15. int DenseMtx_column ( DenseMtx *mtx, int jcol, double **pcolent ) ; │ │ │ │ │ This method fills *pcolent with the first location of the entries in column jcol. │ │ │ │ │ Return codes: 1 is a normal return, -1 means mtx is NULL, -2 means invalid type for mtx, -3 means │ │ │ │ │ @@ -139,15 +139,15 @@ │ │ │ │ │ 4. void DenseMtx_initFromBuffer ( DenseMtx *mtx ) ; │ │ │ │ │ This method initializes the object using information present in the workspace buffer. This method is │ │ │ │ │ used to initialize the DenseMtx object when it has been received as an MPI message. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 5. void DenseMtx_setA2 ( DenseMtx *mtx, A2 *a2 ) ; │ │ │ │ │ This method initializes the a2 object to point into the entries of the matrix. │ │ │ │ │ Error checking: If mtx or a2 is NULL, an error message is printed and the program exits. │ │ │ │ │ - DenseMtx : DRAFT January 6, 2026 5 │ │ │ │ │ + DenseMtx : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.4 Utility methods │ │ │ │ │ 1. int DenseMtx_nbytesNeeded ( int type, int nrow, int ncol ) ; │ │ │ │ │ This method returns the number of bytes required to store the object’s information in its buffer. │ │ │ │ │ Error checking: If type is neither SPOOLES REAL nor SPOOLES COMPLEX, or if nrow or ncol is less than │ │ │ │ │ zero, an error message is printed and the program exits. │ │ │ │ │ 2. int DenseMtx_nbytesInWorkspace ( DenseMtx *mtx ) ; │ │ │ │ │ This method returns the number of bytes in the workspace owned by this object. │ │ │ │ │ @@ -180,15 +180,15 @@ │ │ │ │ │ 8. void DenseMtx_copyRowAndIndex ( DenseMtx *mtxB, int irowB, │ │ │ │ │ DenseMtx *mtxA, int irowA ) ; │ │ │ │ │ This method copies row irowA from matrix mtxA into row irowB of matrix mtxB, and copies the index │ │ │ │ │ of row irowA of mtxA into location irowB of the row indices for mtxB. │ │ │ │ │ Error checking: If mtxB is NULL, or if irowB is out of range, or if mtxA is NULL, or if irowA is out of │ │ │ │ │ range, or if the number of columns in mtxB and mtxA are not the same, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ - 6 DenseMtx : DRAFT January 6, 2026 │ │ │ │ │ + 6 DenseMtx : DRAFT January 17, 2026 │ │ │ │ │ 9. void DenseMtx_addRow ( DenseMtx *mtxB, int irowB, DenseMtx *mtxA, int irowA ) ; │ │ │ │ │ This method adds row irowA from matrix mtxA into row irowB of matrix mtxB. │ │ │ │ │ Error checking: If mtxB is NULL, or if irowB is out of range, or if mtxA is NULL, or if irowA is out of │ │ │ │ │ range, or if the number of columns in mtxB and mtxA are not the same, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 10. void DenseMtx_zero ( DenseMtx *mtx ) ; │ │ │ │ │ This method zeros the entries in the matrix. │ │ │ │ │ @@ -219,15 +219,15 @@ │ │ │ │ │ This method copies vector vec[] into row irow of matrix mtx. │ │ │ │ │ Error checking: If mtx or vec is NULL, or if irow < 0 or irow ≥ nrow, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 18. double DenseMtx_addVectorIntoRow ( DenseMtx *mtx, int irow, double vec[] ) ; │ │ │ │ │ This method adds vector vec[] into row irow of matrix mtx. │ │ │ │ │ Error checking: If mtx or vec is NULL, or if irow < 0 or irow ≥ nrow, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ - DenseMtx : DRAFT January 6, 2026 7 │ │ │ │ │ + DenseMtx : DRAFT January 17, 2026 7 │ │ │ │ │ 1.2.5 IO methods │ │ │ │ │ Thefile structure of a DenseMtxobject is simple. First comes seven scalars, type, rowid, colid, nrow, ncol, │ │ │ │ │ inc1 and inc2, followed by the row indices, followed by the column indices, and then followed by the matrix │ │ │ │ │ entries. │ │ │ │ │ 1. int DenseMtx_readFromFile ( DenseMtx *mtx, char *fn ) ; │ │ │ │ │ This method reads an DenseMtx object from a file. If the the file can be opened successfully, the │ │ │ │ │ method calls DenseMtx readFromFormattedFile() or DenseMtx readFromBinaryFile(), closes the │ │ │ │ │ @@ -258,15 +258,15 @@ │ │ │ │ │ Error checking: If mtx or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 7. int DenseMtx_writeStats ( DenseMtx *mtx, FILE *fp ) ; │ │ │ │ │ This method writes out a header and statistics to a file. The value 1 is returned. │ │ │ │ │ Error checking: If mtx or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 8. void DenseMtx_writeForHumanEye ( DenseMtx *mtx, FILE *fp ) ; │ │ │ │ │ This method writes a DenseMtx object to a file in an easily readable format. │ │ │ │ │ Error checking: If mtx or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ - 8 DenseMtx : DRAFT January 6, 2026 │ │ │ │ │ + 8 DenseMtx : DRAFT January 17, 2026 │ │ │ │ │ 9. void DenseMtx_writeForMatlab ( DenseMtx *mtx, char *mtxname, FILE *fp ) ; │ │ │ │ │ This method writes out a DenseMtx object to a file in a Matlab format. A sample line is │ │ │ │ │ a(10,5) = -1.550328201511e-01 + 1.848033378871e+00*i ; │ │ │ │ │ for complex matrices, or │ │ │ │ │ a(10,5) = -1.550328201511e-01 ; │ │ │ │ │ for real matrices, where mtxname = "a". The matrix indices come from the rowind[] and colind[] │ │ │ │ │ vectors, and are incremented by one to follow the Matlab and FORTRAN convention. │ │ ├── ./usr/share/doc/spooles-doc/Drand.ps.gz │ │ │ ├── Drand.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Drand.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 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b Fj(If)30 b Fh(drand)f │ │ │ │ Fj(is)i Fh(NULL)p Fj(,)e(an)h(error)g(message)i(is)e(prin)m(ted)g(and)g │ │ │ │ (the)h(program)f(exits.)227 862 y Fc(Err)-5 b(or)33 b(che)-5 │ │ │ │ b(cking:)39 b Fj(If)29 b Fh(drand)e Fj(is)i Fh(NULL)p │ │ │ │ @@ -3823,18 +3834,18 @@ │ │ │ │ Fh(n)47 b(<)h(0)f Fj(,)35 b(an)f(error)f(message)i(is)e(prin)m(ted)h │ │ │ │ (and)f(the)227 4852 y(program)d(exits.)0 5175 y Fg(1.3)135 │ │ │ │ b(Driv)l(er)46 b(programs)g(for)f(the)g Fe(Drand)d Fg(ob)7 │ │ │ │ b(ject)0 5407 y Fj(This)30 b(section)h(con)m(tains)h(brief)e │ │ │ │ (descriptions)g(of)g(the)h(driv)m(er)f(programs.)p eop │ │ │ │ end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fj(4)p 136 100 1129 4 v │ │ │ │ -1311 w Fh(Drand)29 b Fd(:)40 b Fc(DRAFT)31 b Fd(Jan)m(uary)f(6,)h(2026) │ │ │ │ -p 2771 100 V 111 399 a Fj(1.)46 b Fh(testDrand)g(msglvl)g(msgFile)f │ │ │ │ -(distribution)g(param1)h(param2)g(seed1)g(seed2)h(n)227 │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fj(4)p 136 100 1106 4 v │ │ │ │ +1288 w Fh(Drand)29 b Fd(:)41 b Fc(DRAFT)30 b Fd(Jan)m(uary)g(17,)h │ │ │ │ +(2026)p 2794 100 V 111 399 a Fj(1.)46 b Fh(testDrand)g(msglvl)g │ │ │ │ +(msgFile)f(distribution)g(param1)h(param2)g(seed1)g(seed2)h(n)227 │ │ │ │ 549 y Fj(This)30 b(driv)m(er)g(program)g(test)h(the)g │ │ │ │ Fh(Drand)e Fj(random)g(n)m(um)m(b)s(er)h(generator.)337 │ │ │ │ 761 y Ff(\210)45 b Fj(The)30 b Fh(msglvl)f Fj(parameter)i(determines)f │ │ │ │ (the)h(amoun)m(t)f(of)h(output.)337 907 y Ff(\210)45 │ │ │ │ b Fj(The)33 b Fh(msgFile)e Fj(parameter)j(determines)f(the)h(message)g │ │ │ │ (\014le)f(|)h(if)f Fh(msgFile)e Fj(is)i Fh(stdout)p Fj(,)g(then)g(the) │ │ │ │ 427 1020 y(message)27 b(\014le)f(is)g Fc(stdout)p Fj(,)i(otherwise)e(a) │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -15,15 +15,15 @@ │ │ │ │ │ • double mean : mean for a normal distribution │ │ │ │ │ • double sigma : variation for a normal distribution │ │ │ │ │ • int mode: mode of the object, uniform is 1, normal is 2 │ │ │ │ │ 1.2 Prototypes and descriptions of Drand methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ Drand object. │ │ │ │ │ 1 │ │ │ │ │ - 2 Drand : DRAFT January 6, 2026 │ │ │ │ │ + 2 Drand : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. Drand * Drand_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Drand structure and then sets the default fields │ │ │ │ │ by a call to Drand setDefaultFields(). │ │ │ │ │ 2. void Drand_setDefaultFields ( Drand *drand ) ; │ │ │ │ │ @@ -47,15 +47,15 @@ │ │ │ │ │ 1. void Drand_init ( Drand *drand ) ; │ │ │ │ │ This initializer simply sets the default fields with a call to Drand setDefaultFields(). │ │ │ │ │ Error checking: If drand is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. void Drand_setSeed ( Drand *drand, int seed1 ) ; │ │ │ │ │ This method sets the random number seeds using a single input seed. │ │ │ │ │ Error checking: If drand is NULL, or if seed1 ≤ 0, or if seed1 ≥ 2147483563, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ - Drand : DRAFT January 6, 2026 3 │ │ │ │ │ + Drand : DRAFT January 17, 2026 3 │ │ │ │ │ 3. void Drand_setSeeds ( Drand *drand, int seed1, int seed2 ) ; │ │ │ │ │ This method sets the random number seeds using two input seeds. │ │ │ │ │ Error checking: If drand is NULL, an error message is printed and the program exits. │ │ │ │ │ Error checking: If drand is NULL, or if seed1 ≤ 0, or if seed1 ≥ 2147483563, or if seed2 ≤ 0, │ │ │ │ │ or if seed2 ≥ 2147483399, an error message is printed and the program exits. │ │ │ │ │ 4. void Drand_setNormal ( Drand *drand, double mean, double sigma ) ; │ │ │ │ │ This method sets the mode to be a normal distribution with mean mean and variation sigma. │ │ │ │ │ @@ -79,15 +79,15 @@ │ │ │ │ │ program exits. │ │ │ │ │ 4. void Drand_fillIvector ( Drand *drand, int n, int vec[] ) ; │ │ │ │ │ This method fills vec[] with n int random numbers. │ │ │ │ │ Error checking: If drand or vec are NULL or if n < 0 , an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 1.3 Driver programs for the Drand object │ │ │ │ │ This section contains brief descriptions of the driver programs. │ │ │ │ │ - 4 Drand : DRAFT January 6, 2026 │ │ │ │ │ + 4 Drand : DRAFT January 17, 2026 │ │ │ │ │ 1. testDrand msglvl msgFile distribution param1 param2 seed1 seed2 n │ │ │ │ │ This driver program test the Drand random number generator. │ │ │ │ │ • The msglvl parameter determines the amount of output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The distribution parameter specifies the mode of the object. If 1, the distribution is │ │ ├── ./usr/share/doc/spooles-doc/EGraph.ps.gz │ │ │ ├── EGraph.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o EGraph.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1405,16 +1405,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 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│ ├── ps2ascii {} │ │ │ │ │ @@ -21,15 +21,15 @@ │ │ │ │ │ • int nvtx : number of vertices in the graph │ │ │ │ │ • IVL *adjIVL : pointer to a IVL structure that holds the vertex lists for the elements. │ │ │ │ │ • int *vwghts : when type = 1, vwghts points to an int vector of size nvtx that holds the │ │ │ │ │ node weights. │ │ │ │ │ A correctly initialized and nontrivial EGraph object will have positive nelem and nvtx values, a │ │ │ │ │ valid adjIVL field. If type = 1, the vwghts will be non-NULL. │ │ │ │ │ 1 │ │ │ │ │ - 2 EGraph : DRAFT January 6, 2026 │ │ │ │ │ + 2 EGraph : DRAFT January 17, 2026 │ │ │ │ │ 1.2 Prototypes and descriptions of EGraph methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ EGraph object. │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. EGraph * EGraph_new ( void ) ; │ │ │ │ │ @@ -55,15 +55,15 @@ │ │ │ │ │ This method initializes an EGraph object given the type of vertices, number of elements, │ │ │ │ │ number of vertices, and storage type for the IVL element list object. It then clears any │ │ │ │ │ previous data with a call to EGraph clearData(). The IVL object is initialized by a call │ │ │ │ │ to IVL init1(). If type = 1, the vwghts is initialized via a call to IVinit(). See the IVL │ │ │ │ │ object for a description of the IVL type parameter. │ │ │ │ │ Error checking: If egraph is NULL or type is not zero or one, or if either nelem or nvtx are │ │ │ │ │ nonpositive, an error message is printed and the program exits. │ │ │ │ │ - EGraph : DRAFT January 6, 2026 3 │ │ │ │ │ + EGraph : DRAFT January 17, 2026 3 │ │ │ │ │ 1.2.3 Utility methods │ │ │ │ │ 1. Graph EGraph_mkAdjGraph ( EGraph *egraph ) ; │ │ │ │ │ This method creates and returns a Graph object with vertex adjacency lists from the element │ │ │ │ │ graph object. │ │ │ │ │ Error checking: If egraph is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. EGraph * EGraph_make9P ( int n1, int n2, int ncomp ) ; │ │ │ │ │ This method creates and returns a EGraph object for a n1 × n2 grid for a 9-point operator │ │ │ │ │ @@ -92,15 +92,15 @@ │ │ │ │ │ This method reads in an EGraph object from a formatted file. If there are no errors in reading │ │ │ │ │ the data, the value 1 is returned. If an IO error is encountered from fscanf, zero is returned. │ │ │ │ │ Error checking: If egraph or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 3. int EGraph_readFromBinaryFile ( EGraph *egraph, FILE *fp ) ; │ │ │ │ │ This method reads in an EGraph object from a binary file. If there are no errors in reading │ │ │ │ │ the data, the value 1 is returned. If an IO error is encountered from fread, zero is returned. │ │ │ │ │ Error checking: If egraph or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ - 4 EGraph : DRAFT January 6, 2026 │ │ │ │ │ + 4 EGraph : DRAFT January 17, 2026 │ │ │ │ │ 4. int EGraph_writeToFile ( EGraph *egraph, char *fn ) ; │ │ │ │ │ This method writes an EGraph object to a file. It tries to open the file and if it is successful, │ │ │ │ │ it then calls EGraph writeFromFormattedFile()or EGraph writeFromBinaryFile(),closes │ │ │ │ │ the file and returns the value returned from the called routine. │ │ │ │ │ Error checking: If egraph or fn are NULL, or if fn is not of the form *.egraphf (for a │ │ │ │ │ formatted file) or *.egraphb (for a binary file), an error message is printed and the method │ │ │ │ │ returns zero. │ │ │ │ │ @@ -128,15 +128,15 @@ │ │ │ │ │ binary files and vice versa. One can also read in a EGraph file and print out just the header │ │ │ │ │ information (see the EGraph writeStats() method). │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the EGraph object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ - EGraph : DRAFT January 6, 2026 5 │ │ │ │ │ + EGraph : DRAFT January 17, 2026 5 │ │ │ │ │ • The inFile parameter is the input file for the EGraph object. It must be of the form │ │ │ │ │ *.egraphfor*.egraphb. TheEGraphobjectisreadfromthefileviatheEGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The outFileparameter is the output file for the EGraph object. If outFile is none then │ │ │ │ │ the EGraphobject is not written to a file. Otherwise, the EGraph writeToFile()method │ │ │ │ │ is called to write the object to a formatted file (if outFile is of the form *.egraphf), │ │ │ │ │ or a binary file (if outFile is of the form *.egraphb). │ │ │ │ │ @@ -166,15 +166,15 @@ │ │ │ │ │ data. │ │ │ │ │ • n1 is the number of grid points in the first direction, must be greater than one. │ │ │ │ │ • n2 is the number of grid points in the second direction, must be greater than one. │ │ │ │ │ • n3 is the number of grid points in the third direction, must be greater than or equal to │ │ │ │ │ one. │ │ │ │ │ • ncomp is the number of components (i.e., the number of degrees of freedom) at each grid │ │ │ │ │ point, must be greater than or equal to one. │ │ │ │ │ - 6 EGraph : DRAFT January 6, 2026 │ │ │ │ │ + 6 EGraph : DRAFT January 17, 2026 │ │ │ │ │ • TheoutEGraphFileparameteristheoutputfilefortheEGraphobject. IfoutEGraphFile │ │ │ │ │ is nonethentheEGraphobjectisnotwrittentoafile. Otherwise,theEGraph writeToFile() │ │ │ │ │ method is called to write the object to a formatted file (if outEGraphFile is of the form │ │ │ │ │ *.egraphf), or a binary file (if outEGraphFile is of the form *.egraphb). │ │ │ │ │ Index │ │ │ │ │ EGraph clearData(), 2 │ │ │ │ │ EGraph free(), 2 │ │ ├── ./usr/share/doc/spooles-doc/ETree.ps.gz │ │ │ ├── ETree.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o ETree.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 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│ │ │ 246 624 V 33 w(wrapMap\(\))p Fo(,)h(15)0 737 y Fn(ETree)p │ │ │ │ 246 737 V 33 w(writeForHumanEye\(\))p Fo(,)e(18)0 850 │ │ │ │ y Fn(ETree)p 246 850 V 33 w(writeStats\(\))p Fo(,)h(18)0 │ │ │ │ 963 y Fn(ETree)p 246 963 V 33 w(writeToBinaryFile\(\))p │ │ │ │ Fo(,)e(18)0 1076 y Fn(ETree)p 246 1076 V 33 w(writeToFile\(\))p │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -21,15 +21,15 @@ │ │ │ │ │ • int nfront : number of fronts in the tree │ │ │ │ │ • int nvtx : number of vertices in the tree │ │ │ │ │ • Tree *tree : pointer to a Tree structure │ │ │ │ │ • IV *nodwghtsIV : pointer to an IV object to hold front weights, size nfront │ │ │ │ │ • IV *bndwghtsIV : pointer to an IV object to hold the weights of the fronts’ boundaries, size │ │ │ │ │ nfront │ │ │ │ │ 1 │ │ │ │ │ - 2 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 2 ETree : DRAFT January 17, 2026 │ │ │ │ │ • IV *vtxToFrontIV : pointer to an IV object to hold the map from vertices to fronts, size │ │ │ │ │ nfront │ │ │ │ │ A correctly initialized and nontrivial ETree object will have positive nfront and nvtx values, a │ │ │ │ │ valid tree field and non-NULL nodwghtsIV, bndwghtsIV and vtxToFrontIV pointers. │ │ │ │ │ 1.2 Prototypes and descriptions of ETree methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ ETree object. │ │ │ │ │ @@ -53,15 +53,15 @@ │ │ │ │ │ This method releases any storage by a call to ETree clearData() then free’s the storage for │ │ │ │ │ the structure with a call to free(). │ │ │ │ │ Error checking: If etree is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ 1. int ETree_nfront ( ETree *etree ) ; │ │ │ │ │ This method returns the number of fronts. │ │ │ │ │ Error checking: If etree is NULL, an error message is printed and the program exits. │ │ │ │ │ - ETree : DRAFT January 6, 2026 3 │ │ │ │ │ + ETree : DRAFT January 17, 2026 3 │ │ │ │ │ 2. int ETree_nvtx ( ETree *etree ) ; │ │ │ │ │ This method returns the number of vertices. │ │ │ │ │ Error checking: If etree is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. Tree * ETree_tree ( ETree *etree ) ; │ │ │ │ │ This method returns a pointer to the Tree object. │ │ │ │ │ Error checking: If etree is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. int ETree_root ( ETree *etree ) ; │ │ │ │ │ @@ -86,15 +86,15 @@ │ │ │ │ │ 9. int * ETree_nodwghts ( ETree *etree ) ; │ │ │ │ │ This method returns a pointer to the nodwghts vector. │ │ │ │ │ Error checking: If etree or etree->nodwghtsIV is NULL, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 10. IV * ETree_bndwghtsIV ( ETree *etree ) ; │ │ │ │ │ This method returns a pointer to the bndwghtsIV object. │ │ │ │ │ Error checking: If etree is NULL, an error message is printed and the program exits. │ │ │ │ │ - 4 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 4 ETree : DRAFT January 17, 2026 │ │ │ │ │ 11. int * ETree_bndwghts ( ETree *etree ) ; │ │ │ │ │ This method returns a pointer to the bndwghts vector. │ │ │ │ │ Error checking: If etree or etree->bndwghtsIV is NULL, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 12. IV * ETree_vtxToFrontIV ( ETree *etree ) ; │ │ │ │ │ This method returns a pointer to the vtxToFrontIV object. │ │ │ │ │ Error checking: If etree is NULL, an error message is printed and the program exits. │ │ │ │ │ @@ -121,15 +121,15 @@ │ │ │ │ │ Error checking: If etree is NULL, or if symflag is invalid, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 1.2.3 Initializer methods │ │ │ │ │ There are four initializer methods. │ │ │ │ │ 1. void ETree_init1 ( ETree *etree, int nfront, int nvtx ) ; │ │ │ │ │ This method initializes an ETree object given the number of fronts and number of vertices. │ │ │ │ │ Anyprevious data is cleared with a call to ETree clearData(), The Tree object is initialized │ │ │ │ │ - ETree : DRAFT January 6, 2026 5 │ │ │ │ │ + ETree : DRAFT January 17, 2026 5 │ │ │ │ │ with a call to Tree init1(). The nodwghtsIV, bndwghtsIV and vtxToFrontIV objects are │ │ │ │ │ initialized with calls to IV init(). The entries in nodwghtsIV and bndwghtsIV are set to 0, │ │ │ │ │ while the entries in vtxToFrontIV are set to -1. │ │ │ │ │ Error checking: If etree is NULL, or if nfront is negative, or if nvtx < nfront, an error │ │ │ │ │ message is printed and the program exits. │ │ │ │ │ 2. void ETree_initFromGraph ( ETree *etree, Graph *g ) ; │ │ │ │ │ This method generates an elimination tree from a graph. The nodwghtsIV vector object is │ │ │ │ │ @@ -160,15 +160,15 @@ │ │ │ │ │ permutes to vertex-to-front map, and returns an IV object that contains the old-to-new │ │ │ │ │ permutation. │ │ │ │ │ Error checking: If etree is NULL or inETreeFileName is “none”, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ 6. int ETree_initFromSubtree ( ETree *subtree, IV *nodeidsIV, ETree *etree, IV *vtxIV ) ; │ │ │ │ │ This method initializes subtree from tree using the nodes of etree that are found in │ │ │ │ │ nodeidsIV. The map from nodes in subtree to nodes in etree is returned in vtxIV. │ │ │ │ │ - 6 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 6 ETree : DRAFT January 17, 2026 │ │ │ │ │ Return code: 1 for a normal return, -1 if subtree is NULL, -2 if nodeidsIV is NULL, -3 if │ │ │ │ │ etree is NULL, -4 if nodeidsIV is invalid, -5 if vtxIV is NULL. │ │ │ │ │ 1.2.4 Utility methods │ │ │ │ │ Theutility methods return the number of bytes taken by the object, or the number of factor indices, │ │ │ │ │ entries or operations required by the object. │ │ │ │ │ 1. int ETree_sizeOf ( ETree *etree ) ; │ │ │ │ │ This method returns the number of bytes taken by this object (which includes the bytes taken │ │ │ │ │ @@ -195,15 +195,15 @@ │ │ │ │ │ Error checking: If etree or tree is NULL, or if nfront < 1, or if nvtx < 1, or if type or │ │ │ │ │ symflag is invalid, an error message is printed and the program exits. │ │ │ │ │ 5. double ETree_nFactorEntriesInFront ( ETree *etree, int symflag, int J ) ; │ │ │ │ │ ThismethodreturnsthenumberofentriesinfrontJforanLU factorization. Thesymflagpa- │ │ │ │ │ rameter can be one of SPOOLES SYMMETRIC, SPOOLES HERMITIAN or SPOOLES NONSYMMETRIC. │ │ │ │ │ Error checking: If etree or tree is NULL, or if nfront < 1, or if symflag is invalid, or if │ │ │ │ │ J < 0, or if J ≥ nfront, an error message is printed and the program exits. │ │ │ │ │ - ETree : DRAFT January 6, 2026 7 │ │ │ │ │ + ETree : DRAFT January 17, 2026 7 │ │ │ │ │ 6. double ETree_nInternalOpsInFront ( ETree *etree, int type, int symflag, int J ) ; │ │ │ │ │ ThismethodreturnsthenumberofinternaloperationsperformedbyfrontJonits(1,1), (2,1), │ │ │ │ │ and (1,2) blocks during a factorization. The type parameter can be one of SPOOLES REAL │ │ │ │ │ or SPOOLES COMPLEX. symflag must be one of SPOOLES SYMMETRIC, SPOOLES HERMITIAN or │ │ │ │ │ SPOOLES NONSYMMETRIC. │ │ │ │ │ Error checking: If etree or tree is NULL, or if nfront < 1, or if type or symflag is invalid, │ │ │ │ │ or if J < 0, or if J ≥ nfront, an error message is printed and the program exits. │ │ │ │ │ @@ -233,15 +233,15 @@ │ │ │ │ │ Error checking: If etree is NULL, or if type or symflag is invalid, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ 11. ETree * ETree_expand ( ETree *etree, IV *eqmapIV ) ; │ │ │ │ │ This method creates and returns an ETree object for an uncompressed graph. The map from │ │ │ │ │ compressed vertices to uncompressed vertices is found in the eqmapIV object. │ │ │ │ │ Error checking: If etree or eqmapIV is NULL, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - 8 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 8 ETree : DRAFT January 17, 2026 │ │ │ │ │ 12. ETree * ETree_spliceTwoEtrees ( ETree *etree0, Graph *graph, IV *mapIV, ETree *etree1 ) ; │ │ │ │ │ This method creates and returns an ETree object that is formed by splicing together two │ │ │ │ │ front trees, etree0 for the vertices the eliminated domains, etree1 for the vertices the Schur │ │ │ │ │ complement. The mapIV object maps vertices to domains or the Schur complement — if the │ │ │ │ │ entry is 0, the vertex is in the Schur complement, otherwise it is in a domain. │ │ │ │ │ Error checking: If etree0, graph, mapIV or etree1 is NULL, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ @@ -266,15 +266,15 @@ │ │ │ │ │ 3. DV * ETree_nopsMetric ( ETree *etree, int type, int symflag ) ; │ │ │ │ │ AnDVobjectofsize nfrontis created and returned. Each entry of the vector is filled with the │ │ │ │ │ number of factor operations associated with the corresponding front. The type parameter │ │ │ │ │ can be one of SPOOLES REAL or SPOOLES COMPLEX. The symflag parameter can be one of │ │ │ │ │ SPOOLES SYMMETRIC, SPOOLES HERMITIAN or SPOOLES NONSYMMETRIC. │ │ │ │ │ Error checking: If etree is NULL, or if nfront < 1, or if nvtx < 1, or if type or symflag is │ │ │ │ │ invalid, an error message is printed and the program exits. │ │ │ │ │ - ETree : DRAFT January 6, 2026 9 │ │ │ │ │ + ETree : DRAFT January 17, 2026 9 │ │ │ │ │ 1.2.6 Compression methods │ │ │ │ │ Frequently an ETree object will need to be compressed in some manner. Elimination trees usually │ │ │ │ │ have long chains of vertices at the higher levels, where each chain of vertices corresponds to a │ │ │ │ │ supernode. Liu’s generalized row envelope methods partition the vertices by longest chains [?]. In │ │ │ │ │ both cases, we can construct a map from each node to a set of nodes to define a smaller, more │ │ │ │ │ compact ETree object. Given such a map, we construct the smaller etree. │ │ │ │ │ Afundamental chain is a set of vertices v ,...,v such that │ │ │ │ │ @@ -308,15 +308,15 @@ │ │ │ │ │ Error checking: If etree or tree is NULL, or if nfront < 1, or if nvtx < 1, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 2. IV * ETree_fundSupernodeMap ( ETree *etree ) ; │ │ │ │ │ An IV object of size nfront is created, filled with the map from vertices to fundamental │ │ │ │ │ supernodes, then returned. │ │ │ │ │ Error checking: If etree or tree is NULL, or if nfront < 1, or if nvtx < 1, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ - 10 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 10 ETree : DRAFT January 17, 2026 │ │ │ │ │ 3. ETree * ETree_compress ( ETree *etree, IV *frontMapIV ) ; │ │ │ │ │ Using frontMapIV, a new ETree object is created and returned. If frontMapIV does not │ │ │ │ │ define each inverse map of a new node to be connected set of nodes in the old ETree object, │ │ │ │ │ the new ETree object will not be well defined. │ │ │ │ │ Error checking: If etree or frontMapIV is NULL, or if nfront < 1, or if nvtx < 1, an error │ │ │ │ │ message is printed and the program exits. │ │ │ │ │ 1.2.7 Justification methods │ │ │ │ │ @@ -342,15 +342,15 @@ │ │ │ │ │ 1. IV * ETree_newToOldFrontPerm ( ETree *etree ) ; │ │ │ │ │ IV * ETree_oldToNewFrontPerm ( ETree *etree ) ; │ │ │ │ │ An IV object is created with size nfront. A post-order traversal of the Tree object fills │ │ │ │ │ the new-to-old permutation. A reversal of the new-to-old permutation gives the old-to-new │ │ │ │ │ permutation. Both methods are simply wrappers around the respective Tree methods. │ │ │ │ │ Error checking: If etree is NULL, or if nfront < 1, or if nvtx < 1, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ - ETree : DRAFT January 6, 2026 11 │ │ │ │ │ + ETree : DRAFT January 17, 2026 11 │ │ │ │ │ 2. IV * ETree_newToOldVtxPerm ( ETree *etree ) ; │ │ │ │ │ IV * ETree_oldToNewVtxPerm ( ETree *etree ) ; │ │ │ │ │ AnIVobject is created with size nvtx. First we find a new-to-old permutation of the fronts. │ │ │ │ │ Then we search over the fronts in their new order to fill the vertex new-to-old permutation │ │ │ │ │ vector. The old-to-new vertex permutation vector is found by first finding the new-to-old │ │ │ │ │ vertex permutation vector, then inverting it. │ │ │ │ │ Error checking: If etree is NULL, or if nfront < 1, or if nvtx < 1, an error message is printed │ │ │ │ │ @@ -380,15 +380,15 @@ │ │ │ │ │ of the subtree is more than cutoff times the vertex weight, the vertex is in the multisector. │ │ │ │ │ Error checking: If etree is NULL, or if nfront < 1, or if nvtx < 1, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ 3. IV * ETree_msByNentCutoff ( ETree *etree, double cutoff, int symflag ) ; │ │ │ │ │ An IV object is created to hold the multisector nodes and returned. Multisector nodes │ │ │ │ │ have their component id zero, domain nodes have their component id one. Inclusion in the │ │ │ │ │ multisector is based on the number of factor entries in the subtree that a vertex belongs, or │ │ │ │ │ - 12 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 12 ETree : DRAFT January 17, 2026 │ │ │ │ │ strictly speaking, the number of factor entries in the subtree of the front to which a vertex │ │ │ │ │ belongs. If weight of the subtree is more than cutoff times the number of factor entries, │ │ │ │ │ the vertex is in the multisector. The symflag parameter can be one of SPOOLES SYMMETRIC, │ │ │ │ │ SPOOLES HERMITIAN or SPOOLES NONSYMMETRIC. │ │ │ │ │ Error checking: If etree is NULL, or if nfront < 1, or if nvtx < 1, or if symflag is invalid, │ │ │ │ │ an error message is printed and the program exits. │ │ │ │ │ 4. IV * ETree_msByNopsCutoff ( ETree *etree, double cutoff, int type, int symflag ) ; │ │ │ │ │ @@ -423,15 +423,15 @@ │ │ │ │ │ ∂J,J ∂J,J J,J │ │ │ │ │ α = 0, we minimize active storage, when α = 1, we minimize solve operations. On return, │ │ │ │ │ *ptotalgain is filled with the total gain. The return value is a pointer to compidsIV, where │ │ │ │ │ compids[J] = 0 means that J is in the Schur complement, and compids[J] != 0 means │ │ │ │ │ that J is in domain compids[J]. │ │ │ │ │ Error checking: If etree, graph or symbfacIVL is NULL, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ - ETree : DRAFT January 6, 2026 13 │ │ │ │ │ + ETree : DRAFT January 17, 2026 13 │ │ │ │ │ 1.2.10 Transformation methods │ │ │ │ │ Often the elimination tree or front tree that we obtain from an ordering of the graph is not as │ │ │ │ │ appropriate for a factorization as we would like. There are two important cases. │ │ │ │ │ • Near the leaves of the tree the fronts are typically small in size. There is an overhead │ │ │ │ │ associated with each front, and though the overhead varies with regard to the factorization │ │ │ │ │ algorithm, it can be beneficial to group small subtrees together into one front. The expense is │ │ │ │ │ added storage for the logically zero entries and the factor operations on them. In this library, │ │ │ │ │ @@ -464,15 +464,15 @@ │ │ │ │ │ restriction. │ │ │ │ │ • The method ETree mergeFrontsAll() tries to merge a front with all of its children, if the │ │ │ │ │ resulting front does not contain too many zero entries. This has the effect of merging small │ │ │ │ │ bushy subtrees, but will not merge a top level separator with one of its children. │ │ │ │ │ For a serial application, ETree mergeFrontsAny()is suitable. For a parallel application, we recom- │ │ │ │ │ mend first using ETree mergeFrontsOne() followed by ETree mergeFrontsAll(). See the driver │ │ │ │ │ programs testTransform and mkNDETree for examples of how to call the methods. │ │ │ │ │ - 14 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 14 ETree : DRAFT January 17, 2026 │ │ │ │ │ 1. ETree * ETree_mergeFrontsOne ( ETree *etree, int maxzeros, IV *nzerosIV ) ; │ │ │ │ │ This method only tries to merge a front with its only child. It returns an ETree object where │ │ │ │ │ one or more subtrees that contain multiple fronts have been merged into single fronts. The │ │ │ │ │ parameter that governs the merging process is maxzeros, the number of zero entries that can │ │ │ │ │ be introduced by merging a child and parent front together. On input, nzerosIV contains │ │ │ │ │ the number of zeros presently in each front. It is modified on output to correspond with the │ │ │ │ │ new front tree. This method only tries to merge a front with its only child. │ │ │ │ │ @@ -505,15 +505,15 @@ │ │ │ │ │ is NULL, then the vertices have unit weight. The way the vertices in a front to be split are │ │ │ │ │ assigned to smaller fronts is random; the seed parameter is a seed to a random number │ │ │ │ │ generator that permutes the vertices in a front. │ │ │ │ │ Error checking: If etree is NULL, or if nfront < 1, or if nvtx < 1, or if maxfrontsize ≤ 0, │ │ │ │ │ an error message is printed and the program exits. │ │ │ │ │ 5. ETree * ETree_transform ( ETree *etree, int vwghts[], int maxzeros, │ │ │ │ │ int maxfrontsize, int seed ) ; │ │ │ │ │ - ETree : DRAFT January 6, 2026 15 │ │ │ │ │ + ETree : DRAFT January 17, 2026 15 │ │ │ │ │ ETree * ETree_transform2 ( ETree *etree, int vwghts[], int maxzeros, │ │ │ │ │ int maxfrontsize, int seed ) ; │ │ │ │ │ These methods returns an ETree object where one or more subtrees that contain multiple │ │ │ │ │ fronts have been merged into single fronts and where one or more large fronts have been split │ │ │ │ │ into smaller fronts. The two methods differ slightly. ETree transform2() is better suited │ │ │ │ │ for parallel computing because it tends to preserve the tree branching properties. (A front is │ │ │ │ │ merged with either an only child or all children. ETree transform() can merge a front with │ │ │ │ │ @@ -544,15 +544,15 @@ │ │ │ │ │ where the fronts are visited in a post-order traversal of the tree and a front is assigned │ │ │ │ │ to a thread or processor with the least number of accumulated operations thus far. │ │ │ │ │ • The subtree-subset map is the most complex, where subsets of threads or processors are │ │ │ │ │ assigned to subtrees via a pre-order traversal of the tree. (Each root of the tree can be │ │ │ │ │ assigned to all processors.) The tree is then visited in a post-order traversal, and each │ │ │ │ │ front is assigned to an eligible thread or processor with the least number of accumulated │ │ │ │ │ ops so far. │ │ │ │ │ - 16 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 16 ETree : DRAFT January 17, 2026 │ │ │ │ │ • The domain decomposition map is also complex, where domains are mapped to threads, │ │ │ │ │ then the fronts in the schur complement are mapped to threads, both using independent │ │ │ │ │ balanced maps. The method ETree ddMapNew() is more robust than ETree ddMap(), │ │ │ │ │ and is more general in the sense that it takes a multisector vector as input. The msIV │ │ │ │ │ object is a map from the vertices to {0,1}. A vertex mapped to 0 lies in the Schur │ │ │ │ │ complement, a vertex mapped to 1 lies in a domain. │ │ │ │ │ Error checking: If etree or cumopsDV is NULL, or if type or symflag is invalid, an error │ │ │ │ │ @@ -580,15 +580,15 @@ │ │ │ │ │ can be one of SPOOLES SYMMETRIC, SPOOLES HERMITIAN or SPOOLES NONSYMMETRIC. │ │ │ │ │ Error checking: If etree or dvec are NULL, or if symflag is invalid, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ 4. void ETree_forwSolveProfile ( ETree *etree, double dvec[] ) ; │ │ │ │ │ Onreturn, dvec[J] contains the amount of stack storage to solve for J using the multifrontal- │ │ │ │ │ based forward solve. │ │ │ │ │ Error checking: If etree or dvec are NULL, an error message is printed and the program exits. │ │ │ │ │ - ETree : DRAFT January 6, 2026 17 │ │ │ │ │ + ETree : DRAFT January 17, 2026 17 │ │ │ │ │ 5. void ETree_backSolveProfile ( ETree *etree, double dvec[] ) ; │ │ │ │ │ Onreturn, dvec[J] contains the amount of stack storage to solve for J using the multifrontal- │ │ │ │ │ based backward solve. │ │ │ │ │ Error checking: If etree or dvec are NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.13 IO methods │ │ │ │ │ There are the usual eight IO routines. The file structure of a tree object is simple: nfront, nvtx, │ │ │ │ │ a Tree object followed by the nodwghtsIV, bndwghtsIV and vtxToFrontIV objects. │ │ │ │ │ @@ -615,15 +615,15 @@ │ │ │ │ │ Error checking: If etree or fn are NULL, or if fn is not of the form *.etreef (for a formatted │ │ │ │ │ file) or *.etreeb (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 5. int ETree_writeToFormattedFile ( ETree *etree, FILE *fp ) ; │ │ │ │ │ This method writes an ETree object to a formatted file. Otherwise, the data is written to │ │ │ │ │ the file. If there are no errors in writing the data, the value 1 is returned. If an IO error is │ │ │ │ │ encountered from fprintf, zero is returned. │ │ │ │ │ Error checking: If etree or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ - 18 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 18 ETree : DRAFT January 17, 2026 │ │ │ │ │ 6. int ETree_writeToBinaryFile ( ETree *etree, FILE *fp ) ; │ │ │ │ │ This method writes an ETree object to a binary file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ Error checking: If etree or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 7. int ETree_writeForHumanEye ( ETree *etree, FILE *fp ) ; │ │ │ │ │ This method writes an ETree object to a file in a readable format. Otherwise, the method │ │ │ │ │ ETree writeStats() is called to write out the header and statistics. Then the parent, first │ │ │ │ │ @@ -650,15 +650,15 @@ │ │ │ │ │ • The inPermFile parameter is the input file for the Perm object. It must be of the form │ │ │ │ │ *.permfor*.permb. ThePermobjectisreadfromthefileviathePerm readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The outIVfile parameter is the output file for the vertex-to-front map IV object. │ │ │ │ │ If outIVfile is none then the IV object is not written to a file. Otherwise, the │ │ │ │ │ IV writeToFile()methodis called to write the object to a formatted file (if outIVfile │ │ │ │ │ is of the form *.ivf), or a binary file (if outIVfile is of the form *.ivb). │ │ │ │ │ - ETree : DRAFT January 6, 2026 19 │ │ │ │ │ + ETree : DRAFT January 17, 2026 19 │ │ │ │ │ • TheoutETreeFileparameter is the output file for the ETree object. If outETreeFileis │ │ │ │ │ nonethentheETreeobjectisnotwrittentoafile. Otherwise,theETree writeToFile() │ │ │ │ │ method is called to write the object to a formatted file (if outETreeFile is of the form │ │ │ │ │ *.etreef), or a binary file (if outETreeFile is of the form *.etreeb). │ │ │ │ │ 2. extractTopSep msglvl msgFile inETreeFile outIVfile │ │ │ │ │ ThisdriverprogramcreatesanIVobjectthatcontainsacompids[]vector, wherecompids[v] │ │ │ │ │ = 0 if vertex v is in the top level separator and -1 otherwise. The IV object is optionally │ │ │ │ │ @@ -689,15 +689,15 @@ │ │ │ │ │ Here is some typical output for a 15×15×15 grid matrix with maxzeros = 64 and maxsize │ │ │ │ │ = 32. │ │ │ │ │ vtx tree : 3375 fronts, 367237 indices, 367237 |L|, 63215265 ops │ │ │ │ │ fs tree : 1023 fronts, 39661 indices, 367237 |L|, 63215265 ops │ │ │ │ │ merge1 : 1023 fronts, 39661 indices, 367237 |L|, 63215265 ops │ │ │ │ │ merge2 : 511 fronts, 29525 indices, 373757 |L|, 63590185 ops │ │ │ │ │ split : 536 fronts, 34484 indices, 373757 |L|, 63590185 ops │ │ │ │ │ - 20 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 20 ETree : DRAFT January 17, 2026 │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the ETree object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • n1 is the number of grid points in the first direction. │ │ │ │ │ • n2 is the number of grid points in the second direction. │ │ │ │ │ @@ -729,15 +729,15 @@ │ │ │ │ │ • n3 is the number of grid points in the third direction. │ │ │ │ │ • The maxzeros parameter is an upper bound on the number of logically zero entries that │ │ │ │ │ will be allowed in a new front. │ │ │ │ │ • The maxsize parameter is an upper bound on the number of vertices in a front — any │ │ │ │ │ original front that contains more than maxsize vertices will be broken up into smaller │ │ │ │ │ fronts. │ │ │ │ │ • The nthread parameter is the number of threads. │ │ │ │ │ - ETree : DRAFT January 6, 2026 21 │ │ │ │ │ + ETree : DRAFT January 17, 2026 21 │ │ │ │ │ • The maptype parameter is the type of map. │ │ │ │ │ – 1 — wrap map │ │ │ │ │ – 2 — balanced map │ │ │ │ │ – 3 — subtree-subset map │ │ │ │ │ – 4 — domain decomposition map │ │ │ │ │ • The cutoff parameter is used by the domain decomposition map only. Try setting │ │ │ │ │ cutoff = 1/nthread or cutoff = 1/(2*nthread). │ │ │ │ │ @@ -771,15 +771,15 @@ │ │ │ │ │ nonethentheETreeobjectisnotwrittentoafile. Otherwise,theETree writeToFile() │ │ │ │ │ method is called to write the object to a formatted file (if outETreeFile is of the form │ │ │ │ │ *.etreef), or a binary file (if outETreeFile is of the form *.etreeb). │ │ │ │ │ • The outIVFile parameter is the output file for the old-to-new IV object. If outIVFile │ │ │ │ │ is none then the IV object is not written to a file. Otherwise, the IV writeToFile() │ │ │ │ │ method is called to write the object to a formatted file (if outIVFile is of the form │ │ │ │ │ *.ivf), or a binary file (if outIVFile is of the form *.ivb). │ │ │ │ │ - 22 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 22 ETree : DRAFT January 17, 2026 │ │ │ │ │ 6. testExpand msglvl msgFile inETreeFile inEqmapFile outETreeFile │ │ │ │ │ This driver program is used to translate an ETree object for a compressed graph into an │ │ │ │ │ ETree object for the unit weight graph. │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the ETree object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ @@ -812,15 +812,15 @@ │ │ │ │ │ • TheinETreeFileparameteristheinputfilefortheETreeobject. It mustbeof theform │ │ │ │ │ *.etreefor*.etreeb. TheETreeobjectisreadfromthefileviatheETree readFromFile() │ │ │ │ │ method. │ │ │ │ │ • If labelflag = 1, the node ids are written on the nodes in the two plots. │ │ │ │ │ • Each node will have a circle with radius radius. │ │ │ │ │ • The firstEPSfile and secondEPSfile parameters is the output EPS file for the two │ │ │ │ │ plots. │ │ │ │ │ - ETree : DRAFT January 6, 2026 23 │ │ │ │ │ + ETree : DRAFT January 17, 2026 23 │ │ │ │ │ Figure 1.1: GRD7x7: Working storage for the forward sparse factorization of the nested dissection │ │ │ │ │ b │ │ │ │ │ ordering. On the left is the storage required to factor J and its update matrix. On the right is the │ │ │ │ │ storage required to factor J and all of its ancestors. Both plots have the same scale. │ │ │ │ │ 29 30 14 22 16 10 4 │ │ │ │ │ 23 15 11 3 │ │ │ │ │ 26 25 24 19 18 17 12 8 7 5 1 0 │ │ │ │ │ @@ -846,15 +846,15 @@ │ │ │ │ │ method. │ │ │ │ │ 9. testIO msglvl msgFile inFile outFile │ │ │ │ │ This driver program reads and writes ETree files, useful for converting formatted files to │ │ │ │ │ binary files and vice versa. One can also read in a ETree file and print out just the header │ │ │ │ │ information (see the ETree writeStats() method). │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the ETree object is written to the message file. │ │ │ │ │ - 24 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 24 ETree : DRAFT January 17, 2026 │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The inFile parameter is the input file for the ETree object. It must be of the form │ │ │ │ │ *.etreefor*.etreeb. TheETreeobjectisreadfromthefileviatheETree readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The outFile parameter is the output file for the ETree object. If outFile is none then │ │ │ │ │ @@ -886,15 +886,15 @@ │ │ │ │ │ Thecutoff defines the multisector, 0 ≤ cutoff ≤ 1. If front J has a subtree metric based │ │ │ │ │ on forward operations that is greater than or equalt to cutoff times the total number │ │ │ │ │ of operations, then front J belongs to the multisector. │ │ │ │ │ 11. testMS msglvl msgFile inETreeFile outIVfile flag cutoff │ │ │ │ │ This program is used to extract a multisector from a front tree ETree object. It partitions the │ │ │ │ │ vertices into domains and a multisector, where each domain is a subtree of the elimination │ │ │ │ │ tree and the multisector is the rest of the vertices. The choice of the subtrees depends on │ │ │ │ │ - ETree : DRAFT January 6, 2026 25 │ │ │ │ │ + ETree : DRAFT January 17, 2026 25 │ │ │ │ │ the flag and cutoff parameters — it can be based on depth of a subtree or the number of │ │ │ │ │ vertices, factor entries or factor operations associated with the subtree. The component ids │ │ │ │ │ IV object is optionally written to a file. Here is some sample output for BCSSTK30 ordered by │ │ │ │ │ nested dissection, where the multisector is defined by subtree vertex weight (flag = 2) with │ │ │ │ │ cutoff = 0.125. │ │ │ │ │ region vertices entries operations metric/(avg domain) │ │ │ │ │ 0 1671 597058 255691396 0.797 2.201 3.967 │ │ │ │ │ @@ -927,15 +927,15 @@ │ │ │ │ │ • TheinETreeFileparameteristheinputfilefortheETreeobject. It mustbeof theform │ │ │ │ │ *.etreefor*.etreeb. TheETreeobjectisreadfromthefileviatheETree readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The outIVFile parameter is the output file for the IV object. If outIVFile is none │ │ │ │ │ then the IV object is not written to a file. Otherwise, the IV writeToFile() method is │ │ │ │ │ called to write the object to a formatted file (if outIVFile is of the form *.ivf), or a │ │ │ │ │ binary file (if outIVFile is of the form *.ivb). │ │ │ │ │ - 26 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 26 ETree : DRAFT January 17, 2026 │ │ │ │ │ • The flag parameter specifies the type of multisector. │ │ │ │ │ – flag == 1 — the multisector is based on the depth of the front, i.e., if the front is │ │ │ │ │ more than depth steps removed from the root, it forms the root of a domain. │ │ │ │ │ – flag == 2 — the multisector is based on the number of vertices in a subtree, i.e., │ │ │ │ │ if the subtree rooted at a front contains more than cutoff times the total number │ │ │ │ │ of vertices, it is a domain. │ │ │ │ │ – flag == 3 — the multisector is based on the number of factor entries in a subtree, │ │ │ │ │ @@ -967,15 +967,15 @@ │ │ │ │ │ data. │ │ │ │ │ • TheinETreeFileparameteristheinputfilefortheETreeobject. It mustbeof theform │ │ │ │ │ *.etreefor*.etreeb. TheETreeobjectisreadfromthefileviatheETree readFromFile() │ │ │ │ │ method. │ │ │ │ │ • TheinGraphFileparameteristheinputfilefortheGraphobject. It mustbeof theform │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ - ETree : DRAFT January 6, 2026 27 │ │ │ │ │ + ETree : DRAFT January 17, 2026 27 │ │ │ │ │ • The outEPSfile parameter is the name of the EPS file to hold the tree. │ │ │ │ │ • The metricType parameter defines the type of metric to be illustrated. See above for │ │ │ │ │ values. │ │ │ │ │ • For information about the heightflag and coordflag parameters, see Section ??. │ │ │ │ │ • If labelflag = 1, the node ids are written on the nodes in the two plots. │ │ │ │ │ • The fontscale parameter is the font size when labels are drawn. │ │ │ │ │ 13. testStorage msglvl msgFile inETreeFile inGraphFile │ │ │ │ │ @@ -1007,21 +1007,21 @@ │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ 14. testTransform msglvl msgFile inETreeFile inGraphFile │ │ │ │ │ outETreeFile maxzeros maxsize seed │ │ │ │ │ This driver program is used to transform a front tree ETree object into a (possibly) merged │ │ │ │ │ and (possibly) split front tree. Merging the front tree means combining fronts together that │ │ │ │ │ do not introduce more than maxzeros zero entries in a front. (See [?] and [?] for a description │ │ │ │ │ - 28 ETree : DRAFT January 6, 2026 │ │ │ │ │ + 28 ETree : DRAFT January 17, 2026 │ │ │ │ │ Figure 1.2: GRD7x7x7: Four tree plots for a 7×7×7 grid matrix ordered using nested dissection. │ │ │ │ │ The top left tree measure number of original matrix entries in a front. The top right tree measure │ │ │ │ │ numberoffactormatrixentries inafront. Thebottomlefttree measurenumberoffactor operations │ │ │ │ │ in a front for a forward looking factorization, e.g., forward sparse. The bottom right tree measure │ │ │ │ │ number of factor operations in a front for a backward looking factorization, e.g., general sparse. │ │ │ │ │ - ETree : DRAFT January 6, 2026 29 │ │ │ │ │ + ETree : DRAFT January 17, 2026 29 │ │ │ │ │ of this supernode amalgamation or relaxation.) Splitting a front means breaking a front up │ │ │ │ │ into a chain of smaller fronts; this allows more processors to work on the original front in │ │ │ │ │ a straightforward manner. The new front tree is optionally written to a file. Here is some │ │ │ │ │ output for the R3D13824 matrix using maxzeros = 1000 and maxsize = 64. │ │ │ │ │ CPU #fronts #indices #entries #ops │ │ │ │ │ original : 6001 326858 3459359 1981403337 │ │ │ │ │ merge one : 0.209 3477 158834 3497139 2000297117 │ │ │ │ │ @@ -1094,15 +1094,15 @@ │ │ │ │ │ ETree mergeFrontsAll(), 14 ETree spliceTwoEtrees(), 8 │ │ │ │ │ ETree mergeFrontsAny(), 14 ETree splitFronts(), 14 │ │ │ │ │ ETree mergeFrontsOne(), 14 ETree subtreeSubsetMap(), 15 │ │ │ │ │ ETree MFstackProfile(), 16 ETree transform(), 15 │ │ │ │ │ ETree msByDepth(), 11 ETree transform2(), 15 │ │ │ │ │ ETree msByNentCutoff(), 11 ETree tree(), 3 │ │ │ │ │ 30 │ │ │ │ │ - ETree : DRAFT January 6, 2026 31 │ │ │ │ │ + ETree : DRAFT January 17, 2026 31 │ │ │ │ │ ETree vtxToFront(), 4 │ │ │ │ │ ETree vtxToFrontIV(), 4 │ │ │ │ │ ETree wrapMap(), 15 │ │ │ │ │ ETree writeForHumanEye(), 18 │ │ │ │ │ ETree writeStats(), 18 │ │ │ │ │ ETree writeToBinaryFile(), 18 │ │ │ │ │ ETree writeToFile(), 17 │ │ ├── ./usr/share/doc/spooles-doc/Eigen.ps.gz │ │ │ ├── Eigen.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Eigen.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1594,16 +1594,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ 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│ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 65 /A put │ │ │ │ dup 66 /B put │ │ │ │ dup 67 /C put │ │ │ │ dup 74 /J put │ │ │ │ dup 80 /P put │ │ │ │ dup 87 /W put │ │ │ │ dup 97 /a put │ │ │ │ @@ -6731,177 +6744,184 @@ │ │ │ │ 82032FBD2FCB6E403D34B85ED4053A8CB619BDD4DE001F4C3007B1F317579651 │ │ │ │ E6D6662189CC2D95AB85D7473F65C5D7B4AC63B0FE928F3400035D5A9D443D0D │ │ │ │ F3532B99F3AC26CB25EA3CD64C341159061E02EFBC7C033C05CD919BBD827A6A │ │ │ │ BFCF3BD739E32E7FE909AEE068D50FAC33605FFF98C7D0115FB860178FD03DB9 │ │ │ │ 7985B78E0AC21F2EA065FA841F5928FB85163B2E2D8F850DC7EE313912C45C28 │ │ │ │ 2783F6762C67882EFEDDC7E7567F91C16B16FD8D5A1ABF35B5586307701B91AD │ │ │ │ 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│ │ │ │ 689 y(----------------)o(--)o(--)o(---)o(--)o(---)o(--)o(---)o(--)o(--) │ │ │ │ o(---)o(--)o(---)o(--)o(-)0 789 y(*/)131 888 y(inpmtxA)f(=)k │ │ │ │ (InpMtx_new\(\))38 b(;)131 988 y(InpMtx_init\(inpm)o(tx)o(A,)f │ │ │ │ (INPMTX_BY_CHEVRO)o(NS,)g(SPOOLES_REAL,)h(0,)43 b(0\))g(;)131 │ │ │ │ @@ -9602,17 +9622,17 @@ │ │ │ │ 4774 y(JimSolveMPI)g(\))k(;)0 4873 y(MARKTIME\(t2\))c(;)0 │ │ │ │ 4973 y(fprintf\(msgFile,)e("\\n)42 b(CPU)h(\0458.3f)e(:)i(time)f(for)h │ │ │ │ (lanczos)d(run",)i(t2)h(-)g(t1\))f(;)0 5073 y(fflush\(msgFile\))37 │ │ │ │ b(;)0 5172 y(if)43 b(\()g(myid)f(==)h(0)g(\))g({)0 5272 │ │ │ │ y(/*)131 5372 y(----------------)o(--)o(--)o(---)o(--)o(---)o(--)o(---) │ │ │ │ o(--)o(--)o(---)o(--)o(---)o(-)p eop end │ │ │ │ %%Page: 40 41 │ │ │ │ -TeXDict begin 40 40 bop 83 100 781 4 v 947 100 a Fn(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fe(:)120 │ │ │ │ -b(Jan)n(uary)26 b(6,)h(2026)p 3038 100 V 781 w Fm(40)131 │ │ │ │ +TeXDict begin 40 40 bop 83 100 760 4 v 926 100 a Fn(SPOOLES)32 │ │ │ │ +b(2.2)f(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fe(:)120 │ │ │ │ +b(Jan)n(uary)25 b(17,)i(2026)p 3059 100 V 760 w Fm(40)131 │ │ │ │ 390 y Fl(processor)40 b(0)j(deals)e(with)h(eigenvalues)d(and)k(vectors) │ │ │ │ 131 490 y(----------------)o(--)o(--)o(---)o(--)o(---)o(--)o(---)o(--)o │ │ │ │ (--)o(---)o(--)o(---)o(-)0 589 y(*/)131 689 y(MARKTIME\(t1\))38 │ │ │ │ b(;)131 789 y(neig)129 b(=)43 b(nfound)e(+)i(ndiscd)e(;)131 │ │ │ │ 888 y(lstevl)g(=)i(nfound)e(;)131 988 y(lanczos_eigenval)o(ue)o(s)c │ │ │ │ (\(&lanczos_wksp,)h(eigval,)j(&neig,)g(&retc\);)131 1088 │ │ │ │ y(fstevl)g(=)i(1)g(;)131 1187 y(if)g(\()g(nfound)e(==)i(0)g(\))g │ │ │ │ @@ -9642,17 +9662,17 @@ │ │ │ │ (ksp)o(\))e(;)0 4774 y(MARKTIME\(t2\))i(;)0 4873 y(fprintf\(msgFile,)e │ │ │ │ ("\\n)42 b(CPU)h(\0458.3f)e(:)i(free)f(lanczos)f(workspace",)e(t2)k(-)g │ │ │ │ (t1\))f(;)0 4973 y(fflush\(msgFile\))37 b(;)0 5073 y(MARKTIME\(t1\))i │ │ │ │ (;)0 5172 y(CleanupMPI\(&brid)o(ge\))e(;)0 5272 y(MARKTIME\(t2\))i(;)0 │ │ │ │ 5372 y(fprintf\(msgFile,)e("\\n)42 b(CPU)h(\0458.3f)e(:)i(free)f │ │ │ │ (solver)f(workspace",)e(t2)k(-)g(t1\))g(;)p eop end │ │ │ │ %%Page: 41 42 │ │ │ │ -TeXDict begin 41 41 bop 83 100 781 4 v 947 100 a Fn(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fe(:)120 │ │ │ │ -b(Jan)n(uary)26 b(6,)h(2026)p 3038 100 V 781 w Fm(41)0 │ │ │ │ +TeXDict begin 41 41 bop 83 100 760 4 v 926 100 a Fn(SPOOLES)32 │ │ │ │ +b(2.2)f(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fe(:)120 │ │ │ │ +b(Jan)n(uary)25 b(17,)i(2026)p 3059 100 V 760 w Fm(41)0 │ │ │ │ 390 y Fl(fflush\(msgFile\))37 b(;)0 589 y(MPI_Finalize\(\))h(;)0 │ │ │ │ 789 y(fprintf\(msgFile,)f("\\n"\))k(;)0 888 y(fclose\(msgFile\))c(;)0 │ │ │ │ 1088 y(return)k(;)i(})p eop end │ │ │ │ %%Page: 42 43 │ │ │ │ TeXDict begin 42 42 bop 0 866 a Fo(Index)0 1281 y Fl(Cleanup\(\))p │ │ │ │ Fm(,)24 b(7)0 1380 y Fl(CleanupMPI\(\))p Fm(,)f(19)0 │ │ │ │ 1480 y Fl(CleanupMT\(\))p Fm(,)g(12)0 1663 y Fl(Factor\(\))p │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -1,12 +1,12 @@ │ │ │ │ │ Integrating the SPOOLES 2.2 Sparse Linear Algebra Library │ │ │ │ │ into the LANCZOS Block-shifted Lanczos Eigensolver │ │ │ │ │ Cleve Ashcraft Jim Patterson │ │ │ │ │ Boeing Phantom Works1 Boeing Phantom Works2 │ │ │ │ │ - January 6, 2026 │ │ │ │ │ + January 17, 2026 │ │ │ │ │ 1P. O. Box 24346, Mail Stop 7L-22, Seattle, Washington 98124, cleve.ashcraft@boeing.com. This research │ │ │ │ │ was supported in part by the DARPA Contract DABT63-95-C-0122 and the DoD High Performance Computing │ │ │ │ │ Modernization Program Common HPC Software Support Initiative. │ │ │ │ │ 2P. O. Box 24346, Mail Stop 7L-22, Seattle, Washington 98124, pattersn@redwood.rt.cs.boeing.com. This re- │ │ │ │ │ search was supportedin part bytheDARPAContractDABT63-95-C-0122 andtheDoDHighPerformanceComputing │ │ │ │ │ Modernization Program Common HPC Software Support Initiative. │ │ │ │ │ Contents │ │ │ │ │ @@ -55,18 +55,18 @@ │ │ │ │ │ b b │ │ │ │ │ izations and solves involving A and B. This permutation matrix P is typically found by ordering the graph │ │ │ │ │ of A +B using a variant of minimum degree or nested dissection. The ordering is performed prior to any │ │ │ │ │ action by the eigensolver. This “setup phase” includes more than just finding the permutation matrix, e.g., │ │ │ │ │ various data structures must be initialized. In a parallel environment, there is even more setup work to do, │ │ │ │ │ analyzing the factorization and solves and specifying which threads or processors perform what computations │ │ │ │ │ 2 │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 3 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 3 │ │ │ │ │ and store what data. In a distributed environment, the entries of A and B must also be distributed among │ │ │ │ │ the processors in preparation for the factors and multiplies. │ │ │ │ │ - For each of the three environments — serial, multithreaded and MPI — the SPOOLES solver has │ │ │ │ │ + For each of the three environments — serial, multithreaded and MPI — the SPOOLES solver has │ │ │ │ │ constructed a “bridge” object to span the interface between the linear system solver and the eigensolver. │ │ │ │ │ Each of the Bridge, BridgeMT and BridgeMPI objects have five methods: set-up, factor, solve, matrix- │ │ │ │ │ multiply and cleanup. The factor, solve and matrix-multiply methods follow the calling sequence convention │ │ │ │ │ imposed by the eigensolver, and are passed to the eigensolver at the beginning of the Lanczos run. The │ │ │ │ │ set-up method is called prior to the eigensolver, and the cleanup method is called after the eigenvalues and │ │ │ │ │ eigenvectors have been determined. │ │ │ │ │ Chapter 2 │ │ │ │ │ @@ -91,55 +91,55 @@ │ │ │ │ │ and are used in the solves. │ │ │ │ │ • FrontMtx *frontmtx : object that stores the L, D and U factor matrices. │ │ │ │ │ • IV *oldToNewIV : object that stores old-to-new permutation vector. │ │ │ │ │ • IV *newToOldIV : object that stores new-to-old permutation vector. │ │ │ │ │ • DenseMtx *X : dense matrix object that is used during the matrix multiples and solves. │ │ │ │ │ • DenseMtx *Y : dense matrix object that is used during the matrix multiples and solves. │ │ │ │ │ 4 │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 5 │ │ │ │ │ - • int msglvl : message level for output. When 0, no output, When 1, just statistics and cpu times. │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 5 │ │ │ │ │ + • int msglvl : message level for output. When 0, no output, When 1, just statistics and cpu times. │ │ │ │ │ When greater than 1, more and more output. │ │ │ │ │ - • FILE *msgFile : message file for output. When msglvl > 0, msgFile must not be NULL. │ │ │ │ │ - 2.2 Prototypes and descriptions of Bridge methods │ │ │ │ │ + • FILE *msgFile : message file for output. When msglvl > 0, msgFile must not be NULL. │ │ │ │ │ + 2.2 Prototypes and descriptions of Bridge methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the Bridge object. │ │ │ │ │ 1. int Setup ( void *data, int *pprbtype, int *pneqns, int *pmxbsz, │ │ │ │ │ - InpMtx *A, InpMtx *B, int *pseed, int *pmsglvl, FILE *msgFile ) ; │ │ │ │ │ + InpMtx *A, InpMtx *B, int *pseed, int *pmsglvl, FILE *msgFile ) ; │ │ │ │ │ All calling sequence parameters are pointers to more easily allow an interface with Fortran. │ │ │ │ │ - • void *data — a pointer to the Bridge object. │ │ │ │ │ - • int *pprbtype — *pprbtype holds the problem type. │ │ │ │ │ - – 1 — vibration, a multiply with B is required. │ │ │ │ │ - – 2 — buckling, a multiply with A is required. │ │ │ │ │ - – 3 — simple, no multiply is required. │ │ │ │ │ - • int *pneqns — *pneqns is the number of equations. │ │ │ │ │ - • int *pmxbsz — *pmxbsz is an upper bound on the block size. │ │ │ │ │ - • InpMtx *A — A is a SPOOLES object that holds the matrix A. │ │ │ │ │ - • InpMtx *B — B is a SPOOLES object that holds the matrix B. For an ordinary eigenproblem, │ │ │ │ │ - B is the identity and B is NULL. │ │ │ │ │ - • int *pseed — *pseed is a random number seed. │ │ │ │ │ - • int *pmsglvl—*pmsglvlisamessagelevelforthebridgemethodsandtheSPOOLESmethods │ │ │ │ │ - they call. │ │ │ │ │ - • FILE *pmsglvl— msgFileis the message file for the bridge methods and the SPOOLES meth- │ │ │ │ │ - ods they call. │ │ │ │ │ + • void *data — a pointer to the Bridge object. │ │ │ │ │ + • int *pprbtype — *pprbtype holds the problem type. │ │ │ │ │ + – 1 — vibration, a multiply with B is required. │ │ │ │ │ + – 2 — buckling, a multiply with A is required. │ │ │ │ │ + – 3 — simple, no multiply is required. │ │ │ │ │ + • int *pneqns — *pneqns is the number of equations. │ │ │ │ │ + • int *pmxbsz — *pmxbsz is an upper bound on the block size. │ │ │ │ │ + • InpMtx *A — A is a SPOOLES object that holds the matrix A. │ │ │ │ │ + • InpMtx *B — B is a SPOOLES object that holds the matrix B. For an ordinary eigenproblem, │ │ │ │ │ + B is the identity and B is NULL. │ │ │ │ │ + • int *pseed — *pseed is a random number seed. │ │ │ │ │ + • int *pmsglvl—*pmsglvlisamessagelevelforthebridgemethodsandtheSPOOLESmethods │ │ │ │ │ + they call. │ │ │ │ │ + • FILE *pmsglvl— msgFileis the message file for the bridge methods and the SPOOLES meth- │ │ │ │ │ + ods they call. │ │ │ │ │ This method must be called in the driver program prior to invoking the eigensolver via a call to │ │ │ │ │ lanczos run(). It then follows this sequence of action. │ │ │ │ │ - • Themethodbeginsbycheckingalltheinput data, andsetting the appropriatefields of the Bridge │ │ │ │ │ - object. │ │ │ │ │ - • The pencil object is initialized with A and B. │ │ │ │ │ - • A and B are converted to storage by rows and vector mode. │ │ │ │ │ - • A Graph object is created that contains the sparsity pattern of the union of A and B. │ │ │ │ │ - • The graph is ordered by first finding a recursive dissection partition, and then evaluating the │ │ │ │ │ - orderings produced by nested dissection and multisection, and choosing the better of the two. │ │ │ │ │ - The frontETree object is produced and placed into the bridge object. │ │ │ │ │ - • Old-to-new and new-to-old permutations are extracted from the front tree and loaded into the │ │ │ │ │ - Bridge object. │ │ │ │ │ - • The vertices in the front tree are permuted, as well as the entries in A and B. Entries in the lower │ │ │ │ │ - triangle of A and B are mapped into the upper triangle, and the storage modes of A and B are │ │ │ │ │ - changed to chevrons and vectors, in preparation for the first factorization. │ │ │ │ │ - • The symbolic factorization is then computed and loaded in the Bridge object. │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 6 │ │ │ │ │ + • Themethodbeginsbycheckingalltheinput data, andsetting the appropriatefields of the Bridge │ │ │ │ │ + object. │ │ │ │ │ + • The pencil object is initialized with A and B. │ │ │ │ │ + • A and B are converted to storage by rows and vector mode. │ │ │ │ │ + • A Graph object is created that contains the sparsity pattern of the union of A and B. │ │ │ │ │ + • The graph is ordered by first finding a recursive dissection partition, and then evaluating the │ │ │ │ │ + orderings produced by nested dissection and multisection, and choosing the better of the two. │ │ │ │ │ + The frontETree object is produced and placed into the bridge object. │ │ │ │ │ + • Old-to-new and new-to-old permutations are extracted from the front tree and loaded into the │ │ │ │ │ + Bridge object. │ │ │ │ │ + • The vertices in the front tree are permuted, as well as the entries in A and B. Entries in the lower │ │ │ │ │ + triangle of A and B are mapped into the upper triangle, and the storage modes of A and B are │ │ │ │ │ + changed to chevrons and vectors, in preparation for the first factorization. │ │ │ │ │ + • The symbolic factorization is then computed and loaded in the Bridge object. │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 6 │ │ │ │ │ • A FrontMtx object is created to hold the factorization and loaded into the Bridge object. │ │ │ │ │ • A SubMtxManager object is created to hold the factor’s submatrices and loaded into the Bridge │ │ │ │ │ object. │ │ │ │ │ • Two DenseMtx objects are created to be used during the matrix multiplies and solves. │ │ │ │ │ The A and B matrices are now in their permuted ordering, i.e., PAPT and PBPT, and all data struc- │ │ │ │ │ tures are with respect to this ordering. After the Lanczos run completes, any generated eigenvectors │ │ │ │ │ must be permuted back into their original ordering using the oldToNewIV and newToOldIV objects. │ │ │ │ │ @@ -173,15 +173,15 @@ │ │ │ │ │ • double X[] — this is the X matrix, stored column major with leading dimension *pnrows. │ │ │ │ │ • double Y[] — this is the Y matrix, stored column major with leading dimension *pnrows. │ │ │ │ │ • int *pprbtype — *pprbtype holds the problem type. │ │ │ │ │ – 1 — vibration, a multiply with B is required. │ │ │ │ │ – 2 — buckling, a multiply with A is required. │ │ │ │ │ – 3 — simple, no multiply is required. │ │ │ │ │ • void *data — a pointer to the Bridge object. │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 7 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 7 │ │ │ │ │ 4. void Solve ( int *pnrows, int *pncols, double X[], double Y[], │ │ │ │ │ void *data, int *perror ) ; │ │ │ │ │ This method solves (A−σB)X = Y, where (A−σB) has been factored by a previous call to Factor(). │ │ │ │ │ All calling sequence parameters are pointers to more easily allow an interface with Fortran. │ │ │ │ │ • int *pnrows — *pnrows contains the number of rows in X and Y. │ │ │ │ │ • int *pncols — *pncols contains the number of columns in X and Y. │ │ │ │ │ • double X[] — this is the X matrix, stored column major with leading dimension *pnrows. │ │ │ │ │ @@ -207,15 +207,15 @@ │ │ │ │ │ • inFileB is the Harwell-Boeing file for the matrix B. │ │ │ │ │ This program is executed for some sample matrices by the do ST * shell scripts in the drivers directory. │ │ │ │ │ Here is a short description of the steps in the driver program. See Chapter A for the listing. │ │ │ │ │ 1. The command line inputs are decoded. │ │ │ │ │ 2. The header of the Harwell-Boeing file for A is read. This yields the number of equations. │ │ │ │ │ 3. The parameters that define the eigensystem to be solved are read in from the parmFile file. │ │ │ │ │ 4. The Lanczos eigensolver workspace is initialized. │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 8 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 8 │ │ │ │ │ 5. The Lanczos communication structure is filled with some parameters. │ │ │ │ │ 6. The A and possibly B matrices are read in from the Harwell-Boeing files and converted into InpMtx │ │ │ │ │ objects from the SPOOLES library. │ │ │ │ │ 7. The linear solver environment is then initialized via a call to Setup(). │ │ │ │ │ 8. The eigensolver is invoked via a call to lanczos run(). The FactorMT(), SolveMT() and MatMulMT() │ │ │ │ │ methods are passed to this routine. │ │ │ │ │ 9. The eigenvalues are extracted and printed via a call to lanczos eigenvalues(). │ │ │ │ │ @@ -243,15 +243,15 @@ │ │ │ │ │ where it is contained. │ │ │ │ │ • IVL *symbfacIVL : object that contains the symbolic factorization of the matrix. │ │ │ │ │ • SubMtxManager *mtxmanager : object that manages the SubMtx objects that store the factor entries │ │ │ │ │ and are used in the solves. │ │ │ │ │ • FrontMtx *frontmtx : object that stores the L, D and U factor matrices. │ │ │ │ │ • IV *oldToNewIV : object that stores old-to-new permutation vector. │ │ │ │ │ 9 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 10 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 10 │ │ │ │ │ • IV *newToOldIV : object that stores new-to-old permutation vector. │ │ │ │ │ • DenseMtx *X : dense matrix object that is used during the matrix multiples and solves. │ │ │ │ │ • DenseMtx *Y : dense matrix object that is used during the matrix multiples and solves. │ │ │ │ │ • IV *ownersIV : object that maps fronts to owning threads for the factorization and matrix-multiplies. │ │ │ │ │ • SolveMap *solvemap : object that maps factor submatrices to owning threads for the solve. │ │ │ │ │ • int msglvl : message level for output. When 0, no output, When 1, just statistics and cpu times. │ │ │ │ │ When greater than 1, more and more output. │ │ │ │ │ @@ -281,15 +281,15 @@ │ │ │ │ │ • FILE *pmsglvl— msgFileis the message file for the bridge methods and the SPOOLES meth- │ │ │ │ │ ods they call. │ │ │ │ │ This method must be called in the driver program prior to invoking the eigensolver via a call to │ │ │ │ │ lanczos run(). It then follows this sequence of action. │ │ │ │ │ • The method begins by checking all the input data, and setting the appropriate fields of the │ │ │ │ │ BridgeMT object. │ │ │ │ │ • The pencil object is initialized with A and B. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 11 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 11 │ │ │ │ │ • A and B are converted to storage by rows and vector mode. │ │ │ │ │ • A Graph object is created that contains the sparsity pattern of the union of A and B. │ │ │ │ │ • The graph is ordered by first finding a recursive dissection partition, and then evaluating the │ │ │ │ │ orderings produced by nested dissection and multisection, and choosing the better of the two. │ │ │ │ │ The frontETree object is produced and placed into the bridge object. │ │ │ │ │ • Old-to-new and new-to-old permutations are extracted from the front tree and loaded into the │ │ │ │ │ BridgeMT object. │ │ │ │ │ @@ -326,15 +326,15 @@ │ │ │ │ │ by 1/(∗ppvttol). │ │ │ │ │ • void *data — a pointer to the BridgeMT object. │ │ │ │ │ • int *pinertia — on return, *pinertia holds the number of negative eigenvalues. │ │ │ │ │ • int *perror — on return, *perror holds an error code. │ │ │ │ │ 1 error in the factorization -2 ppvttol is NULL │ │ │ │ │ 0 normal return -3 data is NULL │ │ │ │ │ -1 psigma is NULL -4 pinertia is NULL │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 12 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 12 │ │ │ │ │ 3. void MatMulMT ( int *pnrows, int *pncols, double X[], double Y[], │ │ │ │ │ int *pprbtype, void *data ) ; │ │ │ │ │ This method computes a multiply of the form Y = IX, Y = AX or Y = BX. All calling sequence │ │ │ │ │ parameters are pointers to more easily allow an interface with Fortran. │ │ │ │ │ • int *pnrows — *pnrows contains the number of rows in X and Y. │ │ │ │ │ • int *pncols — *pncols contains the number of columns in X and Y. │ │ │ │ │ • double X[] — this is the X matrix, stored column major with leading dimension *pnrows. │ │ │ │ │ @@ -363,15 +363,15 @@ │ │ │ │ │ 3.3 The testMT Driver Program │ │ │ │ │ A complete listing of the multithreaded driver program is found in chapter B. The program is invoked by │ │ │ │ │ this command sequence. │ │ │ │ │ testMT msglvl msgFile parmFile seed nthread inFileA inFileB │ │ │ │ │ where │ │ │ │ │ • msglvl is the message level for the BridgeMT methods and the SPOOLES software. │ │ │ │ │ • msgFile is the message file for the BridgeMT methods and the SPOOLES software. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 13 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 13 │ │ │ │ │ • parmFile is the input file for the parameters of the eigensystem to be solved. │ │ │ │ │ • seed is a random number seed used by the SPOOLES software. │ │ │ │ │ • nthread is the number of threads to use in the factors, solves and matrix-multiplies. │ │ │ │ │ • inFileA is the Harwell-Boeing file for the matrix A. │ │ │ │ │ • inFileB is the Harwell-Boeing file for the matrix B. │ │ │ │ │ This program is executed for some sample matrices by the do ST * shell scripts in the drivers directory. │ │ │ │ │ Here is a short description of the steps in the driver program. See Chapter A for the listing. │ │ │ │ │ @@ -411,15 +411,15 @@ │ │ │ │ │ • ETree *frontETree : object that defines the factorizations, e.g., the number of fronts, the tree they │ │ │ │ │ form, the number of internal and external rows for each front, and the map from vertices to the front │ │ │ │ │ where it is contained. │ │ │ │ │ • IVL *symbfacIVL : object that contains the symbolic factorization of the matrix. │ │ │ │ │ • SubMtxManager *mtxmanager : object that manages the SubMtx objects that store the factor entries │ │ │ │ │ and are used in the solves. │ │ │ │ │ 14 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 15 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 15 │ │ │ │ │ • FrontMtx *frontmtx : object that stores the L, D and U factor matrices. │ │ │ │ │ • IV *oldToNewIV : object that stores old-to-new permutation vector. │ │ │ │ │ • IV *newToOldIV : object that stores new-to-old permutation vector. │ │ │ │ │ • DenseMtx *Xloc : dense local matrix object that is used during the matrix multiples and solves. │ │ │ │ │ • DenseMtx *Yloc : dense local matrix object that is used during the matrix multiples and solves. │ │ │ │ │ • IV *vtxmapIV : object that maps vertices to owning processors for the factorization and matrix- │ │ │ │ │ multiplies. │ │ │ │ │ @@ -450,15 +450,15 @@ │ │ │ │ │ inside the LANCZOS software a global Krylov block is assembled on each processor prior to calling the │ │ │ │ │ solve or matrix-multiply methods. To “translate” between the global blocks to local blocks, and then back │ │ │ │ │ to global blocks, we have written two wrapper methods, JimMatMulMPI() and JimSolveMPI(). Each takes │ │ │ │ │ the global input block, compresses it into a local block, call the bridge matrix-multiply or solve method, │ │ │ │ │ then takes the local output blocks and gathers them on all the processors into each of their global output │ │ │ │ │ blocks. These operations add a considerable cost to the solve and matrix-multiplies, but the next release of │ │ │ │ │ the LANCZOS software will remove these steps. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 16 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 16 │ │ │ │ │ 1. int SetupMPI ( void *data, int *pprbtype, int *pneqns, │ │ │ │ │ int *pmxbsz, InpMtx *A, InpMtx *B, int *pseed, │ │ │ │ │ int *pmsglvl, FILE *msgFile, MPI_Comm comm ) ; │ │ │ │ │ All calling sequence parameters are pointers to more easily allow an interface with Fortran. │ │ │ │ │ • void *data — a pointer to the BridgeMPI object. │ │ │ │ │ • int *pprbtype — *pprbtype holds the problem type. │ │ │ │ │ – 1 — vibration, a multiply with B is required. │ │ │ │ │ @@ -493,15 +493,15 @@ │ │ │ │ │ • The ownersIV, vtxmapIV and myownedIV objects are created, that map fronts and vertices to │ │ │ │ │ processors. │ │ │ │ │ • The entries in A and B are permuted. Entries in the permuted lower triangle are mapped into │ │ │ │ │ the upper triangle. The storage modes of A and B are changed to chevrons and vectors, and the │ │ │ │ │ entries of A and B are redistributed to the processors that own them. │ │ │ │ │ • The symbolic factorization is then computed and loaded in the BridgeMPI object. │ │ │ │ │ • A FrontMtx object is created to hold the factorization and loaded into the BridgeMPI object. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 17 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 17 │ │ │ │ │ • ASubMtxManagerobjectiscreatedtoholdthefactor’ssubmatricesandloadedintotheBridgeMPI │ │ │ │ │ object. │ │ │ │ │ • Themapfromfactorsubmatricestotheir owningthreadsis computed and stored in the solvemap │ │ │ │ │ object. │ │ │ │ │ • The distributed matrix-multiplies are set up. │ │ │ │ │ The A and B matrices are now in their permuted ordering, i.e., PAPT and PBPT, and all data struc- │ │ │ │ │ tures are with respect to this ordering. After the Lanczos run completes, any generated eigenvectors │ │ │ │ │ @@ -536,15 +536,15 @@ │ │ │ │ │ • int *pnrows — *pnrows contains the number of global rows in X and Y. │ │ │ │ │ • int *pncols — *pncols contains the number of global columns in X and Y. │ │ │ │ │ • double X[] — this is the global X matrix, stored column major with leading dimension *pnrows. │ │ │ │ │ • double Y[] — this is the global Y matrix, stored column major with leading dimension *pnrows. │ │ │ │ │ • int *pprbtype — *pprbtype holds the problem type. │ │ │ │ │ – 1 — vibration, a multiply with B is required. │ │ │ │ │ – 2 — buckling, a multiply with A is required. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 18 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 18 │ │ │ │ │ – 3 — simple, no multiply is required. │ │ │ │ │ • void *data — a pointer to the BridgeMPI object. │ │ │ │ │ 4. void MatMulMPI ( int *pnrows, int *pncols, double X[], double Y[], │ │ │ │ │ int *pprbtype, void *data ) ; │ │ │ │ │ This method computes a multiply of the form Y = IX, Y = AX or Y = BX. All calling sequence │ │ │ │ │ parameters are pointers to more easily allow an interface with Fortran. │ │ │ │ │ • int *pnrows — *pnrows contains the number of local rows in X and Y. │ │ │ │ │ @@ -578,15 +578,15 @@ │ │ │ │ │ • double X[] — this is the local X matrix, stored column major with leading dimension *pnrows. │ │ │ │ │ • double Y[] — this is the local Y matrix, stored column major with leading dimension *pnrows. │ │ │ │ │ • void *data — a pointer to the BridgeMPI object. │ │ │ │ │ • int *perror — on return, *perror holds an error code. │ │ │ │ │ 1 normal return -3 X is NULL │ │ │ │ │ -1 pnrows is NULL -4 Y is NULL │ │ │ │ │ -2 pncols is NULL -5 data is NULL │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 19 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 19 │ │ │ │ │ 7. int CleanupMPI ( void *data ) ; │ │ │ │ │ This method releases all the storage used by the SPOOLES library functions. │ │ │ │ │ Return value: 1 for a normal return, -1 if a data is NULL. │ │ │ │ │ 4.3 The testMPI Driver Program │ │ │ │ │ A complete listing of the multithreaded driver program is found in chapter C. The program is invoked by │ │ │ │ │ this command sequence. │ │ │ │ │ testMPI msglvl msgFile parmFile seed inFileA inFileB │ │ │ │ │ @@ -644,15 +644,15 @@ │ │ │ │ │ double eigval[1000], sigma[2]; │ │ │ │ │ double *evec; │ │ │ │ │ int error, fstevl, lfinit, lstevl, mxbksz, msglvl, ncol, ndiscd, │ │ │ │ │ neig, neigvl, nfound, nnonzeros, nrhs, nrow, prbtyp, rc, │ │ │ │ │ retc, rfinit, seed, warnng ; │ │ │ │ │ int c__5 = 5, output = 6 ; │ │ │ │ │ 20 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 21 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 21 │ │ │ │ │ int *lanczos_wksp; │ │ │ │ │ InpMtx *inpmtxA, *inpmtxB ; │ │ │ │ │ FILE *msgFile, *parmFile; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ if ( argc != 7 ) { │ │ │ │ │ fprintf(stdout, │ │ │ │ │ "\n\n usage : %s msglvl msgFile parmFile seed inFileA inFileB" │ │ │ │ │ @@ -694,15 +694,15 @@ │ │ │ │ │ /* │ │ │ │ │ --------------------------------------------- │ │ │ │ │ read in the Harwell-Boeing matrix information │ │ │ │ │ --------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ if ( strcmp(inFileName_A, "none") == 0 ) { │ │ │ │ │ fprintf(msgFile, "\n no file to read from") ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 22 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 22 │ │ │ │ │ exit(0) ; │ │ │ │ │ } │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ readHB_info (inFileName_A, &nrow, &ncol, &nnonzeros, &type, &nrhs) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : read in header information for A", │ │ │ │ │ t2 - t1) ; │ │ │ │ │ @@ -746,15 +746,15 @@ │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : read in eigenvalue problem data", │ │ │ │ │ t2 - t1) ; │ │ │ │ │ /* │ │ │ │ │ ---------------------------------------- │ │ │ │ │ check and set the problem type parameter │ │ │ │ │ ---------------------------------------- │ │ │ │ │ */ │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 23 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 23 │ │ │ │ │ switch ( pbtype[1] ) { │ │ │ │ │ case ’v’ : case ’V’ : prbtyp = 1 ; break ; │ │ │ │ │ case ’b’ : case ’B’ : prbtyp = 2 ; break ; │ │ │ │ │ case ’o’ : case ’O’ : prbtyp = 3 ; break ; │ │ │ │ │ default : │ │ │ │ │ fprintf(stderr, "\n invalid problem type %s", pbtype) ; │ │ │ │ │ exit(-1) ; │ │ │ │ │ @@ -798,15 +798,15 @@ │ │ │ │ │ InpMtx_readFromHBfile ( inpmtxA, inFileName_A ) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : read in A", t2 - t1) ; │ │ │ │ │ if ( msglvl > 2 ) { │ │ │ │ │ fprintf(msgFile, "\n\n InpMtx A object after loading") ; │ │ │ │ │ InpMtx_writeForHumanEye(inpmtxA, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 24 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 24 │ │ │ │ │ } │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "matrix-type", &c__1, &retc ); │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : set A’s parameters", t2 - t1) ; │ │ │ │ │ if ( prbtyp != 3 ) { │ │ │ │ │ if ( strcmp(inFileName_B, "none") == 0 ) { │ │ │ │ │ @@ -850,15 +850,15 @@ │ │ │ │ │ invoke eigensolver │ │ │ │ │ nfound -- # of eigenvalues found and kept │ │ │ │ │ ndisc -- # of additional eigenvalues discarded │ │ │ │ │ ----------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ lanczos_run(&neigvl, &which[1] , &pbtype[1], &lfinit, &lftend, │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 25 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 25 │ │ │ │ │ &rfinit, &rhtend, ¢er, &lanczos_wksp, &bridge, &nfound, │ │ │ │ │ &ndiscd, &warnng, &error, Factor, MatMul, Solve ) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : time for lanczos run", t2 - t1) ; │ │ │ │ │ /* │ │ │ │ │ ------------------------- │ │ │ │ │ get eigenvalues and print │ │ │ │ │ @@ -901,15 +901,15 @@ │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ lanczos_free( &lanczos_wksp ) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : free lanczos workspace ", t2 - t1) ; │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ rc = Cleanup(&bridge) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 26 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 26 │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : free solver workspace ", t2 - t1) ; │ │ │ │ │ if ( rc != 1 ) { │ │ │ │ │ fprintf(stderr, "\n error return %d from Cleanup()", rc) ; │ │ │ │ │ exit(-1) ; │ │ │ │ │ } │ │ │ │ │ fprintf(msgFile, "\n") ; │ │ │ │ │ fclose(msgFile) ; │ │ │ │ │ @@ -942,15 +942,15 @@ │ │ │ │ │ double *evec; │ │ │ │ │ int error, fstevl, lfinit, lstevl, msglvl, mxbksz, ncol, ndiscd, │ │ │ │ │ neig, neigvl, nfound, nnonzeros, nrhs, nrow, nthreads, │ │ │ │ │ prbtyp, rc, retc, rfinit, seed, warnng ; │ │ │ │ │ int c__5 = 5, output = 6 ; │ │ │ │ │ int *lanczos_wksp; │ │ │ │ │ 27 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 28 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 28 │ │ │ │ │ InpMtx *inpmtxA, *inpmtxB ; │ │ │ │ │ FILE *msgFile, *parmFile ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ if ( argc != 8 ) { │ │ │ │ │ fprintf(stdout, │ │ │ │ │ "\n\n usage : %s msglvl msgFile parmFile seed nthread inFileA inFileB" │ │ │ │ │ "\n msglvl -- message level" │ │ │ │ │ @@ -994,15 +994,15 @@ │ │ │ │ │ --------------------------------------------- │ │ │ │ │ read in the Harwell-Boeing matrix information │ │ │ │ │ --------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ if ( strcmp(inFileName_A, "none") == 0 ) { │ │ │ │ │ fprintf(msgFile, "\n no file to read from") ; │ │ │ │ │ exit(0) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 29 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 29 │ │ │ │ │ } │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ readHB_info (inFileName_A, &nrow, &ncol, &nnonzeros, &type, &nrhs) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : read in harwell-boeing header info", │ │ │ │ │ t2 - t1) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ @@ -1046,15 +1046,15 @@ │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : read in eigenvalue problem data", │ │ │ │ │ t2 - t1) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ /* │ │ │ │ │ ---------------------------------------- │ │ │ │ │ check and set the problem type parameter │ │ │ │ │ ---------------------------------------- │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 30 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 30 │ │ │ │ │ */ │ │ │ │ │ switch ( pbtype[1] ) { │ │ │ │ │ case ’v’ : │ │ │ │ │ case ’V’ : │ │ │ │ │ prbtyp = 1 ; │ │ │ │ │ break ; │ │ │ │ │ case ’b’ : │ │ │ │ │ @@ -1098,15 +1098,15 @@ │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ --------------------------------------------- │ │ │ │ │ create the InpMtx objects for matrix A and B │ │ │ │ │ --------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ if ( strcmp(inFileName_A, "none") == 0 ) { │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 31 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 31 │ │ │ │ │ fprintf(msgFile, "\n no file to read A from") ; │ │ │ │ │ exit(-1) ; │ │ │ │ │ } │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ inpmtxA = InpMtx_new() ; │ │ │ │ │ InpMtx_readFromHBfile ( inpmtxA, inFileName_A ) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ @@ -1150,15 +1150,15 @@ │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : set up the solver environment", │ │ │ │ │ t2 - t1) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ if ( rc != 1 ) { │ │ │ │ │ fprintf(stderr, "\n error return %d from SetupMT()", rc) ; │ │ │ │ │ exit(-1) ; │ │ │ │ │ } │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 32 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 32 │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ----------------------------------------------- │ │ │ │ │ invoke eigensolver │ │ │ │ │ nfound -- # of eigenvalues found and kept │ │ │ │ │ ndisc -- # of additional eigenvalues discarded │ │ │ │ │ ----------------------------------------------- │ │ │ │ │ @@ -1202,15 +1202,15 @@ │ │ │ │ │ hdslp5_ ( "computed eigenvector returned by hdserc", │ │ │ │ │ &neig, evec, &output, 39L ) ; │ │ │ │ │ } │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : get and print eigenvectors", t2 - t1) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ */ │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 33 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 33 │ │ │ │ │ /* │ │ │ │ │ ------------------------ │ │ │ │ │ free the working storage │ │ │ │ │ ------------------------ │ │ │ │ │ */ │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ lanczos_free( &lanczos_wksp ) ; │ │ │ │ │ @@ -1254,15 +1254,15 @@ │ │ │ │ │ InpMtx *inpmtxA, *inpmtxB ; │ │ │ │ │ FILE *msgFile, *parmFile ; │ │ │ │ │ double lftend, rhtend, center, shfscl, t1, t2 ; │ │ │ │ │ double c__1 = 1.0, c__4 = 4.0, tolact = 2.309970868130169e-11 ; │ │ │ │ │ double eigval[1000], sigma[2] ; │ │ │ │ │ double *evec; │ │ │ │ │ 34 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 35 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 35 │ │ │ │ │ /* │ │ │ │ │ --------------------------------------------------------------- │ │ │ │ │ find out the identity of this process and the number of process │ │ │ │ │ --------------------------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ MPI_Init(&argc, &argv) ; │ │ │ │ │ MPI_Comm_dup(MPI_COMM_WORLD, &comm) ; │ │ │ │ │ @@ -1306,15 +1306,15 @@ │ │ │ │ │ } │ │ │ │ │ parmFileName = argv[3] ; │ │ │ │ │ seed = atoi(argv[4]) ; │ │ │ │ │ inFileName_A = argv[5] ; │ │ │ │ │ inFileName_B = argv[6] ; │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n %s " │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 36 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 36 │ │ │ │ │ "\n msglvl -- %d" │ │ │ │ │ "\n message file -- %s" │ │ │ │ │ "\n parameter file -- %s" │ │ │ │ │ "\n stiffness matrix file -- %s" │ │ │ │ │ "\n mass matrix file -- %s" │ │ │ │ │ "\n random number seed -- %d" │ │ │ │ │ "\n", │ │ │ │ │ @@ -1358,15 +1358,15 @@ │ │ │ │ │ with K positive semidefinite │ │ │ │ │ with K_s posibly indefinite (buckling problem) │ │ │ │ │ ’o’ or ’O’ ordinary symmetric eigenproblem │ │ │ │ │ lfinit -- if true, lftend is restriction on lower bound of │ │ │ │ │ eigenvalues. if false, no restriction on lower bound │ │ │ │ │ lftend -- left endpoint of interval │ │ │ │ │ rfinit -- if true, rhtend is restriction on upper bound of │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 37 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 37 │ │ │ │ │ eigenvalues. if false, no restriction on upper bound │ │ │ │ │ rhtend -- right endpoint of interval │ │ │ │ │ center -- center of interval │ │ │ │ │ mxbksz -- upper bound on block size for Lanczos recurrence │ │ │ │ │ shfscl -- shift scaling parameter, an estimate on the magnitude │ │ │ │ │ of the smallest nonzero eigenvalues │ │ │ │ │ --------------------------------------------------------------- │ │ │ │ │ @@ -1410,15 +1410,15 @@ │ │ │ │ │ initialize communication structure │ │ │ │ │ ---------------------------------- │ │ │ │ │ */ │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "order-of-problem", &nrow, &retc ); │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "accuracy-tolerance", &tolact, &retc ); │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "max-block-size", &mxbksz, &retc ); │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 38 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 38 │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "shift-scale", &shfscl, &retc ); │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "message_level", &msglvl, &retc ); │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "mpi-communicator", &comm, &retc ); │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "qfile-pathname", "lqfil", &retc ); │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "mqfil-pathname", "lmqfil", &retc ); │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "evfil-pathname", "evcfil", &retc ); │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ @@ -1462,15 +1462,15 @@ │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ } else { │ │ │ │ │ inpmtxB = NULL ; │ │ │ │ │ lanczos_set_parm( &lanczos_wksp, "matrix-type", &c__4, &retc ); │ │ │ │ │ } │ │ │ │ │ } else { │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 39 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 39 │ │ │ │ │ /* │ │ │ │ │ ------------------------------------------------ │ │ │ │ │ other processors initialize their local matrices │ │ │ │ │ ------------------------------------------------ │ │ │ │ │ */ │ │ │ │ │ inpmtxA = InpMtx_new() ; │ │ │ │ │ InpMtx_init(inpmtxA, INPMTX_BY_CHEVRONS, SPOOLES_REAL, 0, 0) ; │ │ │ │ │ @@ -1514,15 +1514,15 @@ │ │ │ │ │ JimSolveMPI ) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : time for lanczos run", t2 - t1) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ if ( myid == 0 ) { │ │ │ │ │ /* │ │ │ │ │ ---------------------------------------------- │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 40 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 40 │ │ │ │ │ processor 0 deals with eigenvalues and vectors │ │ │ │ │ ---------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ neig = nfound + ndiscd ; │ │ │ │ │ lstevl = nfound ; │ │ │ │ │ lanczos_eigenvalues (&lanczos_wksp, eigval, &neig, &retc); │ │ │ │ │ @@ -1566,15 +1566,15 @@ │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : free lanczos workspace", t2 - t1) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ MARKTIME(t1) ; │ │ │ │ │ CleanupMPI(&bridge) ; │ │ │ │ │ MARKTIME(t2) ; │ │ │ │ │ fprintf(msgFile, "\n CPU %8.3f : free solver workspace", t2 - t1) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 41 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 41 │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ MPI_Finalize() ; │ │ │ │ │ fprintf(msgFile, "\n") ; │ │ │ │ │ fclose(msgFile) ; │ │ │ │ │ return ; } │ │ │ │ │ Index │ │ │ │ │ Cleanup(), 7 │ │ ├── ./usr/share/doc/spooles-doc/FrontMtx.ps.gz │ │ │ ├── FrontMtx.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o FrontMtx.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1758,16 +1758,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1955,79 +1957,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ 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Fm(20)p 182 100 1012 │ │ │ │ +4 v 1194 w Fl(FrontMtx)28 b Ff(:)41 b Fh(DRAFT)30 b Ff(Jan)m(uary)g │ │ │ │ +(17,)i(2026)p 2888 100 V 227 399 a Fm(This)d(metho)s(d)g(computes)g │ │ │ │ +(and)g(return)f(the)i(n)m(um)m(b)s(er)e(of)h(\015oating)i(p)s(oin)m(t)e │ │ │ │ +(op)s(erations)h(for)f(a)h(solv)m(e)g(with)g(a)227 511 │ │ │ │ +y(single)h(righ)m(t)g(hand)f(side.)227 664 y Fh(Err)-5 │ │ │ │ +b(or)29 b(che)-5 b(cking:)37 b Fm(If)24 b Fl(frontmtx)e │ │ │ │ +Fm(is)i Fl(NULL)p Fm(,)g(or)g(if)g Fl(type)f Fm(or)i │ │ │ │ +Fl(symmetryflag)c Fm(are)j(in)m(v)-5 b(alid,)27 b(an)d(error)g(message) │ │ │ │ +227 777 y(is)31 b(prin)m(ted)f(and)f(the)i(program)f(exits.)0 │ │ │ │ +1053 y Fb(1.2.13)113 b(IO)37 b(metho)s(ds)111 1252 y │ │ │ │ +Fm(1.)46 b Fl(int)h(FrontMtx_readFromFile)42 b(\()48 │ │ │ │ +b(FrontMtx)d(*frontmtx,)g(char)i(*fn)g(\))g(;)227 1405 │ │ │ │ +y Fm(This)25 b(metho)s(d)g(reads)g(a)h Fl(FrontMtx)45 │ │ │ │ b(object)24 b Fm(from)h(a)h(\014le.)39 b(It)26 b(tries)g(to)g(op)s(en)e │ │ │ │ (the)i(\014le)g(and)f(if)g(it)h(is)f(success-)227 1518 │ │ │ │ y(ful,)g(it)f(then)g(calls)h Fl(FrontMtx)p 1252 1518 │ │ │ │ 29 4 v 32 w(readFromFormattedFile\(\))17 b Fm(or)24 b │ │ │ │ Fl(FrontMtx)p 2894 1518 V 32 w(readFromBinaryFile\(\))p │ │ │ │ Fm(,)227 1631 y(closes)32 b(the)e(\014le)h(and)f(returns)f(the)h(v)-5 │ │ │ │ b(alue)31 b(returned)e(from)h(the)h(called)g(routine.)227 │ │ │ │ @@ -6625,17 +6637,17 @@ │ │ │ │ b Fl(1)f Fm(is)g(returned.)40 b(If)30 b(an)g(IO)g(error)g(is)g(encoun)m │ │ │ │ (tered)h(from)f Fl(fwrite)p Fm(,)f(zero)i(is)g(returned.)227 │ │ │ │ 5407 y Fh(Err)-5 b(or)33 b(che)-5 b(cking:)40 b Fm(If)28 │ │ │ │ b Fl(frontmtx)f Fm(or)i Fl(fp)g Fm(are)g Fl(NULL)f Fm(an)h(error)g │ │ │ │ (message)h(is)f(prin)m(ted)f(and)h(zero)h(is)f(returned.)p │ │ │ │ eop end │ │ │ │ %%Page: 21 21 │ │ │ │ -TeXDict begin 21 20 bop 91 100 1035 4 v 1216 100 a Fl(FrontMtx)28 │ │ │ │ -b Ff(:)41 b Fh(DRAFT)121 b Ff(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2773 100 V 1035 w Fm(21)111 399 y(7.)46 b Fl(int)h │ │ │ │ +TeXDict begin 21 20 bop 91 100 1012 4 v 1193 100 a Fl(FrontMtx)28 │ │ │ │ +b Ff(:)41 b Fh(DRAFT)121 b Ff(Jan)m(uary)30 b(17,)i(2026)p │ │ │ │ +2796 100 V 1012 w Fm(21)111 399 y(7.)46 b Fl(int)h │ │ │ │ (FrontMtx_writeForHumanEye)41 b(\()48 b(FrontMtx)d(*frontmtx,)g(FILE)i │ │ │ │ (*fp)g(\))g(;)227 547 y Fm(This)36 b(metho)s(d)g(writes)h(a)g │ │ │ │ Fl(FrontMtx)d Fm(ob)5 b(ject)37 b(to)g(a)g(\014le)g(in)f(a)h(h)m(uman)f │ │ │ │ (readable)h(format.)59 b(The)36 b(metho)s(d)227 660 y │ │ │ │ Fl(FrontMtx)p 617 660 29 4 v 32 w(writeStats\(\))41 b │ │ │ │ Fm(is)i(called)i(to)f(write)g(out)f(the)h(header)f(and)g(statistics.)82 │ │ │ │ b(The)43 b(v)-5 b(alue)44 b Fl(1)f Fm(is)227 773 y(returned.)227 │ │ │ │ @@ -6698,18 +6710,18 @@ │ │ │ │ 4980 y Fm(metho)s(d.)337 5122 y Fi(\210)45 b Fm(The)30 │ │ │ │ b Fl(seed)f Fm(parameter)i(is)g(a)f(random)g(n)m(um)m(b)s(er)f(seed.) │ │ │ │ 337 5265 y Fi(\210)45 b Fm(The)30 b Fl(type)f Fm(parameter)i(sp)s │ │ │ │ (eci\014es)f(a)h(real)g(or)f(complex)h(linear)g(system.)500 │ │ │ │ 5407 y Fe({)45 b Fl(type)i(=)g(1)h(\(SPOOLES)p 1417 5407 │ │ │ │ V 32 w(REAL\))29 b Fm(for)h(real,)p eop end │ │ │ │ %%Page: 22 22 │ │ │ │ -TeXDict begin 22 21 bop 0 100 a Fm(22)p 182 100 1035 │ │ │ │ -4 v 1217 w Fl(FrontMtx)28 b Ff(:)41 b Fh(DRAFT)30 b Ff(Jan)m(uary)g(6,) │ │ │ │ -h(2026)p 2866 100 V 500 399 a Fe({)45 b Fl(type)i(=)g(2)h(\(SPOOLES)p │ │ │ │ -1417 399 29 4 v 32 w(COMPLEX\))28 b Fm(for)i(complex.)337 │ │ │ │ +TeXDict begin 22 21 bop 0 100 a Fm(22)p 182 100 1012 │ │ │ │ +4 v 1194 w Fl(FrontMtx)28 b Ff(:)41 b Fh(DRAFT)30 b Ff(Jan)m(uary)g │ │ │ │ +(17,)i(2026)p 2888 100 V 500 399 a Fe({)45 b Fl(type)i(=)g(2)h │ │ │ │ +(\(SPOOLES)p 1417 399 29 4 v 32 w(COMPLEX\))28 b Fm(for)i(complex.)337 │ │ │ │ 544 y Fi(\210)45 b Fm(The)30 b Fl(symmetryflag)d Fm(parameter)k(sp)s │ │ │ │ (eci\014es)f(the)h(symmetry)f(of)g(the)h(matrix.)500 │ │ │ │ 690 y Fe({)45 b Fl(type)i(=)g(0)h(\(SPOOLES)p 1417 690 │ │ │ │ V 32 w(SYMMETRIC\))28 b Fm(for)i Fk(A)g Fm(real)h(or)g(complex)g │ │ │ │ (symmetric,)500 820 y Fe({)45 b Fl(type)i(=)g(1)h(\(SPOOLES)p │ │ │ │ 1417 820 V 32 w(HERMITIAN\))28 b Fm(for)i Fk(A)g Fm(complex)h │ │ │ │ (Hermitian,)500 949 y Fe({)45 b Fl(type)i(=)g(2)h(\(SPOOLES)p │ │ │ │ @@ -6778,17 +6790,17 @@ │ │ │ │ 5115 y Fi(\210)45 b Fl(n2)30 b Fm(is)g(the)h(n)m(um)m(b)s(er)e(of)i(p)s │ │ │ │ (oin)m(ts)f(in)g(the)g(second)h(grid)f(direction.)337 │ │ │ │ 5261 y Fi(\210)45 b Fl(n3)30 b Fm(is)g(the)h(n)m(um)m(b)s(er)e(of)i(p)s │ │ │ │ (oin)m(ts)f(in)g(the)g(third)g(grid)g(direction.)337 │ │ │ │ 5407 y Fi(\210)45 b Fm(The)30 b Fl(seed)f Fm(parameter)i(is)g(a)f │ │ │ │ (random)g(n)m(um)m(b)s(er)f(seed.)p eop end │ │ │ │ %%Page: 23 23 │ │ │ │ -TeXDict begin 23 22 bop 91 100 1035 4 v 1216 100 a Fl(FrontMtx)28 │ │ │ │ -b Ff(:)41 b Fh(DRAFT)121 b Ff(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2773 100 V 1035 w Fm(23)337 399 y Fi(\210)45 b Fm(The)30 │ │ │ │ +TeXDict begin 23 22 bop 91 100 1012 4 v 1193 100 a Fl(FrontMtx)28 │ │ │ │ +b Ff(:)41 b Fh(DRAFT)121 b Ff(Jan)m(uary)30 b(17,)i(2026)p │ │ │ │ +2796 100 V 1012 w Fm(23)337 399 y Fi(\210)45 b Fm(The)30 │ │ │ │ b Fl(nrhs)f Fm(parameter)i(is)g(the)f(n)m(um)m(b)s(er)f(of)i(righ)m(t)g │ │ │ │ (hand)e(sides)h(to)h(solv)m(e)h(as)f(one)f(blo)s(c)m(k.)337 │ │ │ │ 545 y Fi(\210)45 b Fm(The)30 b Fl(type)f Fm(parameter)i(sp)s(eci\014es) │ │ │ │ f(a)h(real)g(or)f(complex)h(linear)g(system.)500 691 │ │ │ │ y Fe({)45 b Fl(type)i(=)g(1)h(\(SPOOLES)p 1417 691 29 │ │ │ │ 4 v 32 w(REAL\))29 b Fm(for)h(real,)500 820 y Fe({)45 │ │ │ │ b Fl(type)i(=)g(2)h(\(SPOOLES)p 1417 820 V 32 w(COMPLEX\))28 │ │ │ │ @@ -6878,16 +6890,16 @@ │ │ │ │ Fm(,)i(9)1992 5064 y Fl(FrontMtx)p 2382 5064 V 32 w │ │ │ │ (writeForHumanEye\(\))p Fm(,)d(20)1992 5178 y Fl(FrontMtx)p │ │ │ │ 2382 5178 V 32 w(writeStats\(\))p Fm(,)i(21)1992 5293 │ │ │ │ y Fl(FrontMtx)p 2382 5293 V 32 w(writeToBinaryFile\(\))p │ │ │ │ Fm(,)e(20)1992 5407 y Fl(FrontMtx)p 2382 5407 V 32 w(writeToFile\(\))p │ │ │ │ Fm(,)i(20)1905 5656 y(24)p eop end │ │ │ │ %%Page: 25 25 │ │ │ │ -TeXDict begin 25 24 bop 91 100 1035 4 v 1216 100 a Fl(FrontMtx)28 │ │ │ │ -b Ff(:)41 b Fh(DRAFT)121 b Ff(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2773 100 V 1035 w Fm(25)0 399 y Fl(FrontMtx)p 390 399 │ │ │ │ +TeXDict begin 25 24 bop 91 100 1012 4 v 1193 100 a Fl(FrontMtx)28 │ │ │ │ +b Ff(:)41 b Fh(DRAFT)121 b Ff(Jan)m(uary)30 b(17,)i(2026)p │ │ │ │ +2796 100 V 1012 w Fm(25)0 399 y Fl(FrontMtx)p 390 399 │ │ │ │ 29 4 v 32 w(writeToFormattedFile\(\))p Fm(,)25 b(20)p │ │ │ │ eop end │ │ │ │ %%Trailer │ │ │ │ │ │ │ │ userdict /end-hook known{end-hook}if │ │ │ │ %%EOF │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -23,15 +23,15 @@ │ │ │ │ │ are disjoint. P is a permutation matrix. If pivoting is not used, P is the identity. │ │ │ │ │ 2. (A + σB) = P(L + I)D(I + U)QT for a square nonsymmetric matrix A with symmetric │ │ │ │ │ structure. D is a diagonal matrix. U is strictly upper triangular. L is strictly lower triangular. │ │ │ │ │ P and Q are permutation matrices. If pivoting is not used, P and Q are the identity. │ │ │ │ │ 3. A = QR for square or rectangular A. Q is an orthogonal matrix that is not explicitly │ │ │ │ │ computed or stored. R is upper triangular. │ │ │ │ │ 1 │ │ │ │ │ - 2 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 2 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ The factorization is performed using a one dimensional decomposition of the global sparse │ │ │ │ │ matrix. A typical front of the matrix is found the shaded portion of the figure below. │ │ │ │ │ Afront is indivisible, it is found on one processor, and one processor or one thread is responsible │ │ │ │ │ for its internal computations. This is extremely important if we want to support pivoting for │ │ │ │ │ stability, for deciding how to choose the pivot elements in the front requires continuous up-to- │ │ │ │ │ date information about all the entries in the front. If a front were partitioned among threads or │ │ │ │ │ processors, the cost of the communication to select pivot elements would be intolerable. │ │ │ │ │ @@ -56,15 +56,15 @@ │ │ │ │ │ • The linear combination A+σB is found in a Pencil object. │ │ │ │ │ • The ETree object contains the front tree that governs the factorization and solve. Inside │ │ │ │ │ this object are the dimensions of each front (the number of internal and external rows and │ │ │ │ │ columns), the tree connectivity of the fronts, and a map from each vertex to the front that │ │ │ │ │ contains it as an internal row and column. The FrontMtx object contains a pointer to an │ │ │ │ │ ETree object, but it does not modify the object, nor does it own the storage for the ETree │ │ │ │ │ object. Thus multiple front matrices can all point to the same ETree object simultaneously. │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 3 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 3 │ │ │ │ │ • An IVL object (Integer Vector List), contains the symbolic factorization. For each front, it │ │ │ │ │ gives the list of internal and external rows and columns, used to initialize a front prior to its │ │ │ │ │ factorization. For a factorization without pivoting, this object stores the index information │ │ │ │ │ for the factors, and so is used during the forward and backsolves. For a factorization with │ │ │ │ │ pivoting, the index information for a front may change, so this object is not used during the │ │ │ │ │ solves. As for the ETree object, the symbolic factorization is neither modified or owned by │ │ │ │ │ the front matrix object. │ │ │ │ │ @@ -96,15 +96,15 @@ │ │ │ │ │ postponed data (when pivoting is enabled) or aggregate data (in a parallel factorization), and │ │ │ │ │ the factorization of the fully assembled front, take place within the context of this object. │ │ │ │ │ • The SubMtx object is used to store a submatrix of the factor matrices D, L and U. Once a │ │ │ │ │ front is factored it is split into one or more of these submatrix objects. After the factorization │ │ │ │ │ is complete, the data structures are postprocessed to yield submatrices that contain the │ │ │ │ │ coupling between fronts. The working storage during the solves is also managed by SubMtx │ │ │ │ │ objects. │ │ │ │ │ - 4 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 4 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ • Each submatrix represents the coupling between two fronts, I and J. To enable rapid random │ │ │ │ │ access to these submatrices, we use a I2Ohash object that is a hash table whose keys are two │ │ │ │ │ integers and whose data is a void * pointer. │ │ │ │ │ • The set of nonzero submatrices, i.e., the nonzero couplings between two fronts, is kept in │ │ │ │ │ one or two IVL objects. This information is necessary for the factorization and forward and │ │ │ │ │ backsolves. │ │ │ │ │ • The factorization and solves require lists of fronts and submatrices to manage assembly of │ │ │ │ │ @@ -131,15 +131,15 @@ │ │ │ │ │ • int pivotingflag : flag to specify pivoting for stability, │ │ │ │ │ – SPOOLES NO PIVOTING — pivoting not used │ │ │ │ │ – SPOOLES PIVOTING — pivoting used │ │ │ │ │ • int sparsityflag : flag to specify storage of factors. │ │ │ │ │ – 0 — each front is dense │ │ │ │ │ – 1 — a front may be sparse due to entries dropped because they are below a drop │ │ │ │ │ tolerance. │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 5 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 5 │ │ │ │ │ • int dataMode : flag to specify data storage. │ │ │ │ │ – 1 — one-dimensional, used during the factorization. │ │ │ │ │ – 2 — two-dimensional, used during the solves. │ │ │ │ │ • int nentD : number of entries in D │ │ │ │ │ • int nentL : number of entries in L │ │ │ │ │ • int nentU : number of entries in U │ │ │ │ │ • Tree *tree: Treeobjectthatholdsthetreeoffronts. Note, normallythisisfrontETree->tree, │ │ │ │ │ @@ -165,15 +165,15 @@ │ │ │ │ │ used only during a nonsymmetric factorization. │ │ │ │ │ • SubMtx **p mtxLNJ : a vector of pointers to submatrices in L that are off the block diagonal, │ │ │ │ │ used only during a nonsymmetric factorization. │ │ │ │ │ • I2Ohash *lowerhash : pointer to a I2Ohash hash table for submatrices in L, used during │ │ │ │ │ the solves. │ │ │ │ │ • I2Ohash *upperhash : pointer to a I2Ohash hash table for submatrices in U, used during │ │ │ │ │ the solves. │ │ │ │ │ - 6 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 6 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ • SubMtxManager *manager : pointer to an object that manages the instances of submatrices │ │ │ │ │ during the factors and solves. │ │ │ │ │ • Lock *lock : pointer to a Lock lock used in a multithreaded environment to ensure exlusive │ │ │ │ │ access while allocating storage in the IV and IVL objects. This is not used in a serial or MPI │ │ │ │ │ environment. │ │ │ │ │ • int nlocks : number of times the lock has been locked. │ │ │ │ │ • PatchAndGo *info : this is a pointer to an object that is used by the Chv object during the │ │ │ │ │ @@ -196,15 +196,15 @@ │ │ │ │ │ • FRONTMTX IS 1D MODE(frontmtx) is 1 if the factor are still stored as a one-dimensional data │ │ │ │ │ decomposition (i.e., the matrix has not yet been post-processed), and 0 otherwise. │ │ │ │ │ • FRONTMTX IS 2D MODE(frontmtx) is 1 if the factor are stored as a two-dimensional data │ │ │ │ │ decomposition (i.e., the matrix has been post-processed), and 0 otherwise. │ │ │ │ │ 1.2 Prototypes and descriptions of FrontMtx methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ FrontMtx object. │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 7 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 7 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. FrontMtx * FrontMtx_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the FrontMtx structure and then sets the default │ │ │ │ │ fields by a call to FrontMtx setDefaultFields(). │ │ │ │ │ 2. void FrontMtx_setDefaultFields ( FrontMtx *frontmtx ) ; │ │ │ │ │ @@ -231,15 +231,15 @@ │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ 1. int FrontMtx_nfront ( FrontMtx *frontmtx ) ; │ │ │ │ │ This method returns the number of fronts in the matrix. │ │ │ │ │ Error checking: If frontmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. int FrontMtx_neqns ( FrontMtx *frontmtx ) ; │ │ │ │ │ This method returns the number of equations in the matrix. │ │ │ │ │ Error checking: If frontmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ - 8 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 8 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ 3. Tree * FrontMtx_frontTree ( FrontMtx *frontmtx ) ; │ │ │ │ │ This method returns the Tree object for the fronts. │ │ │ │ │ Error checking: If frontmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void FrontMtx_initialFrontDimensions ( FrontMtx *frontmtx, int J, │ │ │ │ │ int *pnD, int *pnL, int *pnU, int *pnbytes ) ; │ │ │ │ │ This method fills the four pointer arguments with the number of internal rows and columns, │ │ │ │ │ number of rows in the lower block, number of columns in the upper block, and number of │ │ │ │ │ @@ -269,15 +269,15 @@ │ │ │ │ │ Error checking: If frontmtx, pnrow or pindices is NULL, or if J is not in [0,nfront), an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ 9. SubMtx * FrontMtx_diagMtx ( FrontMtx *frontmtx, int J ) ; │ │ │ │ │ This method returns a pointer to the object that contains submatrix D . │ │ │ │ │ J,J │ │ │ │ │ Error checking: If frontmtx is NULL, or if J is not in [0,nfront), an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 9 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 9 │ │ │ │ │ 10. SubMtx * FrontMtx_upperMtx ( FrontMtx *frontmtx, int J, int K ) ; │ │ │ │ │ This method returns a pointer to the object that contains submatrix UJ,K. If K = nfront, │ │ │ │ │ then the object containing UJ,∂J is returned. │ │ │ │ │ Error checking: If frontmtx is NULL, or if J is not in [0,nfront), or if K is not in [0,nfront], │ │ │ │ │ an error message is printed and the program exits. │ │ │ │ │ 11. SubMtx * FrontMtx_lowerMtx ( FrontMtx *frontmtx, int K, int J ) ; │ │ │ │ │ This method returns a pointer to the object that contains submatrix LK,J. If K = nfront, │ │ │ │ │ @@ -304,15 +304,15 @@ │ │ │ │ │ Error checking: If frontmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 16. IVL * FrontMtx_upperBlockIVL ( FrontMtx *frontmtx ) ; │ │ │ │ │ This method returns a pointer to the IVL object that holds the upper blocks. │ │ │ │ │ Error checking: If frontmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 17. IVL * FrontMtx_lowerBlockIVL ( FrontMtx *frontmtx ) ; │ │ │ │ │ This method returns a pointer to the IVL object that holds the lower blocks. │ │ │ │ │ Error checking: If frontmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ - 10 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 10 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ 1.2.3 Initialization methods │ │ │ │ │ 1. void FrontMtx_init ( FrontMtx *frontmtx, ETree *frontETree, │ │ │ │ │ IVL *symbfacIVL, int type, int symmetryflag, int sparsityflag, │ │ │ │ │ int pivotingflag, int lockflag, int myid, IV *ownersIV, │ │ │ │ │ SubMtxManager *manager, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method initializes the object, allocating and initializing the internal objects as necessary. │ │ │ │ │ See the previous section on data structures for the meanings of the type, symmetryflag, │ │ │ │ │ @@ -342,15 +342,15 @@ │ │ │ │ │ 1. void FrontMtx_initializeFront ( FrontMtx *frontmtx, Chv *frontJ, int J ) ; │ │ │ │ │ This method is called to initialize a front. The number of internal rows and columns is found │ │ │ │ │ from the front ETree object and the row and column indices are obtained from the symbolic │ │ │ │ │ factorization IVL object. The front Chv object is initialized via a call to Chv init(), and the │ │ │ │ │ column indices and row indices (when nonsymemtric) are copied. Finally the front’s entries │ │ │ │ │ are zeroed via a call to Chv zero(). │ │ │ │ │ Error checking: None presently. │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 11 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 11 │ │ │ │ │ 2. char FrontMtx_factorVisit ( FrontMtx *frontmtx, Pencil *pencil, int J, │ │ │ │ │ int myid, int owners[], Chv *fronts[], int lookahead, double tau, │ │ │ │ │ double droptol, char status[], IP *heads[], IV *pivotsizesIV, DV *workDV, │ │ │ │ │ int parent[], ChvList *aggList, ChvList *postList, ChvManager *chvmanager, │ │ │ │ │ int stats[], double cpus[], int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method is called during the serial, multithreaded and MPI factorizations when front J │ │ │ │ │ is visited during the bottom-up traversal of the tree. │ │ │ │ │ @@ -382,15 +382,15 @@ │ │ │ │ │ Error checking: If frontmtx, owners or status is NULL, or if myid < 0, an error message is │ │ │ │ │ printed and the program exits. │ │ │ │ │ 7. void FrontMtx_loadActiveLeaves ( FrontMtx *frontmtx, char status[], │ │ │ │ │ char activeFlag, Ideq *dequeue ) ; │ │ │ │ │ This method is called by the multithreaded and MPI factor and solve methods to load the │ │ │ │ │ dequeue with the active leaves in the front tree with respect to the thread or processor. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ - 12 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 12 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ 8. ChvList * FrontMtx_postList ( FrontMtx *frontmtx, IV *frontOwnersIV, │ │ │ │ │ int lockflag ) ; │ │ │ │ │ This method is called by the multithreaded and MPI factor methods to create and return a │ │ │ │ │ list object to hold postponed chevrons and help synchronize the factorization. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ 9. ChvList * FrontMtx_aggregateList ( FrontMtx *frontmtx, │ │ │ │ │ IV *frontOwnersIV, int lockflag ) ; │ │ │ │ │ @@ -421,15 +421,15 @@ │ │ │ │ │ the list in postponedlist. If this list is empty, a new front is created to hold the aggregate │ │ │ │ │ updates and the postponed data, and the chvmanager object receives the aggregate and │ │ │ │ │ postponed Chv objects. The number of delayed rows and columns is returned in *pndelay — │ │ │ │ │ this is used during the factorization of the front that follows immediately. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ 13. FrontMtx_storePostponedData ( FrontMtx *frontmtx, Chv *frontJ, │ │ │ │ │ int npost, int K, ChvList *postponedlist, ChvManager *chvmanager ) ; │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 13 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 13 │ │ │ │ │ This method is used to store any postponed rows and columns from the current front frontJ │ │ │ │ │ into a Chv object obtained from the chvmanager object and place it into the list of postponed │ │ │ │ │ objects for K, its parent, found in the postponedlist object. The frontJ object is unchanged │ │ │ │ │ by this method. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ 14. FrontMtx_storeFront ( FrontMtx *frontmtx, Chv *frontJ, IV *pivotsizesIV, │ │ │ │ │ double droptol, int msglvl, FILE *msgFile ) ; │ │ │ │ │ @@ -459,15 +459,15 @@ │ │ │ │ │ following information. │ │ │ │ │ • cpus[0] — time spent initializing the fronts. │ │ │ │ │ • cpus[1] — time spent loading the original entries. │ │ │ │ │ • cpus[2] — time spent accumulating updates from descendents. │ │ │ │ │ • cpus[3] — time spent assembling postponed data. │ │ │ │ │ • cpus[4] — time spent to factor the fronts. │ │ │ │ │ • cpus[5] — time spent to extract postponed data. │ │ │ │ │ - 14 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 14 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ • cpus[6] — time spent to store the factor entries. │ │ │ │ │ • cpus[7] — miscellaneous time. │ │ │ │ │ • cpus[8] — total time in the method. │ │ │ │ │ Onreturn, the stats[] vector is filled with the following information. │ │ │ │ │ • stats[0] — number of pivots. │ │ │ │ │ • stats[1] — number of pivot tests. │ │ │ │ │ • stats[2] — number of delayed rows and columns. │ │ │ │ │ @@ -495,15 +495,15 @@ │ │ │ │ │ workDV, cpus or pfacops is NULL, or if msglvl > 0 and msgFile is NULL, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 3. A2 * FrontMtx_QR_assembleFront ( FrontMtx *frontmtx, int J, InpMtx *mtxA, │ │ │ │ │ IVL *rowsIVL, int firstnz[], int colmap[], Chv *firstchild, │ │ │ │ │ DV *workDV, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method creates an A2 object to hold the front, assembles any original rows of A and │ │ │ │ │ any update matrices from the children into the front, and then returns the front. The rows │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 15 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 15 │ │ │ │ │ and update matrices are assembled into staircase form, so no subsequent permutations of the │ │ │ │ │ rows is necessary. │ │ │ │ │ Error checking: If frontmtx, mtxA, rowsIVL, firstnz, colmap or workDV is NULL, or if msglvl │ │ │ │ │ > 0 and msgFile is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void FrontMtx_QR_storeFront ( FrontMtx *frontmtx, int J, A2 *frontJ, │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method takes as input frontJ, the front in trapezoidal or triangular form. It scales the │ │ │ │ │ @@ -533,15 +533,15 @@ │ │ │ │ │ • cpus[4] – time to store the update entries │ │ │ │ │ • cpus[5] – miscellaneous time │ │ │ │ │ • cpus[6] – total time │ │ │ │ │ Onreturn, *pfacops contains the number of floating point operations done by the factoriza- │ │ │ │ │ tion. │ │ │ │ │ Error checking: If frontmtx, frontJ or chvmanager is NULL, or if msglvl > 0 and msgFile │ │ │ │ │ is NULL, an error message is printed and the program exits. │ │ │ │ │ - 16 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 16 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ 1.2.8 Postprocessing methods │ │ │ │ │ 1. void FrontMtx_postProcess ( FrontMtx *frontmtx, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method does post-processing chores after the factorization is complete. If pivoting was │ │ │ │ │ enabled, the method permutes the row and column adjacency objects, permutes the lower and │ │ │ │ │ upper matrices, and updates the block adjacency objects. The chevron submatrices L∂J,J │ │ │ │ │ and UJ,∂J are split into LK,J and UJ,K where K ∩∂J 6= ∅. │ │ │ │ │ Error checking: If frontmtx is NULL, or if msglvl ¿ 0 and msgFile is NULL, an error message │ │ │ │ │ @@ -572,15 +572,15 @@ │ │ │ │ │ Error checking: If frontmtx is NULL, or if msglvl ¿ 0 and msgFile is NULL, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 1.2.9 Utility Solve methods │ │ │ │ │ The following methods are called by all the solve methods — serial, multithreaded and MPI. │ │ │ │ │ 1. SubMtx ** FrontMtx_loadRightHandSide ( FrontMtx *frontmtx, DenseMtx *mtxB, │ │ │ │ │ int owners[], int myid, SubMtxManager *mtxmanager, │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 17 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 17 │ │ │ │ │ This method creates and returns a vector of pointers to SubMtx objects that hold pointers to │ │ │ │ │ the right hand side submatrices owned by the thread or processor. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ 2. void FrontMtx_forwardVisit ( FrontMtx *frontmtx, int J, int nrhs, │ │ │ │ │ int *owners, int myid, SubMtxManager *mtxmanager, SubMtxList *aggList, │ │ │ │ │ SubMtx *p_mtx[], char frontIsDone[], IP *heads[], SubMtx *p_agg[], │ │ │ │ │ char status[], int msglvl, FILE *msgFile) ; │ │ │ │ │ @@ -610,15 +610,15 @@ │ │ │ │ │ this thread or processor. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ 7. IP ** FrontMtx_backwardSetup ( FrontMtx *frontmtx, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method is used to set up a data structure of IP objects that hold the updates of the │ │ │ │ │ form Z := Z −U X that will be performed by this thread or processor. │ │ │ │ │ J J J,K K │ │ │ │ │ Error checking: None presently. │ │ │ │ │ - 18 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 18 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ 8. void FrontMtx_loadActiveRoots ( FrontMtx *frontmtx, char status[], │ │ │ │ │ char activeFlag, Ideq *dequeue ) ; │ │ │ │ │ This method loads the active roots for a thread or a processor into the dequeue for the │ │ │ │ │ backward solve. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ 1.2.10 Serial Solve method │ │ │ │ │ 1. void FrontMtx_solve ( FrontMtx *frontmtx, DenseMtx *mtxX, DenseMtx *mtxB, │ │ │ │ │ @@ -648,15 +648,15 @@ │ │ │ │ │ the seminormal equations (U +I)D(I +U)X = A B or (U +I)D(I +U)X = A B for │ │ │ │ │ X. The mtxmanager object manages the working storage used in the solves. On return the │ │ │ │ │ cpus[] vector is filled with the following. │ │ │ │ │ • cpus[0] — set up the solves │ │ │ │ │ • cpus[1] — fetch right hand side and store solution │ │ │ │ │ • cpus[2] — forward solve │ │ │ │ │ • cpus[3] — diagonal solve │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 19 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 19 │ │ │ │ │ • cpus[4] — backward solve │ │ │ │ │ • cpus[5] — total time in the solve method. │ │ │ │ │ T H │ │ │ │ │ • cpus[6] — time to compute A B or A B. │ │ │ │ │ • cpus[7] — total time. │ │ │ │ │ Error checking: If frontmtx, mtxA, mtxX, mtxB or cpus is NULL, or if msglvl ¿ 0 and msgFile │ │ │ │ │ is NULL, an error message is printed and the program exits. │ │ │ │ │ @@ -685,15 +685,15 @@ │ │ │ │ │ This method determines the inertia of a symmetric matrix based on the (UT + I)D(I + U) │ │ │ │ │ factorization. The number of negative eigenvalues is returned in *pnneg, the number of zero │ │ │ │ │ eigenvalues is returned in *pnzero, and the number of positive eigenvalues is returned in │ │ │ │ │ *pnpos. │ │ │ │ │ Error checking: If frontmtx, pnneg, pnzero or pnpos is NULL, or if symmetryflag 6= 0 an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ 5. int FrontMtx_nSolveOps ( FrontMtx *frontmtx ) ; │ │ │ │ │ - 20 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 20 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ This method computes and return the number of floating point operations for a solve with a │ │ │ │ │ single right hand side. │ │ │ │ │ Error checking: If frontmtx is NULL, or if type or symmetryflag are invalid, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 1.2.13 IO methods │ │ │ │ │ 1. int FrontMtx_readFromFile ( FrontMtx *frontmtx, char *fn ) ; │ │ │ │ │ This method reads a FrontMtx object from a file. It tries to open the file and if it is success- │ │ │ │ │ @@ -721,15 +721,15 @@ │ │ │ │ │ This method writes a FrontMtx object to a formatted file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fprintf, zero is returned. │ │ │ │ │ Error checking: If frontmtx or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 6. int FrontMtx_writeToBinaryFile ( FrontMtx *frontmtx, FILE *fp ) ; │ │ │ │ │ This method writes a FrontMtx object to a binary file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ Error checking: If frontmtx or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 21 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 21 │ │ │ │ │ 7. int FrontMtx_writeForHumanEye ( FrontMtx *frontmtx, FILE *fp ) ; │ │ │ │ │ This method writes a FrontMtx object to a file in a human readable format. The method │ │ │ │ │ FrontMtx writeStats() is called to write out the header and statistics. The value 1 is │ │ │ │ │ returned. │ │ │ │ │ Error checking: If frontmtx or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 8. int FrontMtx_writeStats ( FrontMtx *frontmtx, FILE *fp ) ; │ │ │ │ │ The header and statistics are written to a file. The value 1 is returned. │ │ │ │ │ @@ -758,15 +758,15 @@ │ │ │ │ │ • maxzeros is used to merge small fronts together into larger fronts. Look at the ETree │ │ │ │ │ object for the ETree mergeFronts{One,All,Any}() methods. │ │ │ │ │ • maxsize is used to split large fronts into smaller fronts. See the ETree splitFronts() │ │ │ │ │ method. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The type parameter specifies a real or complex linear system. │ │ │ │ │ – type = 1 (SPOOLES REAL) for real, │ │ │ │ │ - 22 FrontMtx : DRAFT January 6, 2026 │ │ │ │ │ + 22 FrontMtx : DRAFT January 17, 2026 │ │ │ │ │ – type = 2 (SPOOLES COMPLEX) for complex. │ │ │ │ │ • The symmetryflag parameter specifies the symmetry of the matrix. │ │ │ │ │ – type = 0 (SPOOLES SYMMETRIC) for A real or complex symmetric, │ │ │ │ │ – type = 1 (SPOOLES HERMITIAN) for A complex Hermitian, │ │ │ │ │ – type = 2 (SPOOLES NONSYMMETRIC) │ │ │ │ │ for A real or complex nonsymmetric. │ │ │ │ │ • The sparsityflag parameter signals a direct or approximate factorization. │ │ │ │ │ @@ -798,15 +798,15 @@ │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • n1 is the number of points in the first grid direction. │ │ │ │ │ • n2 is the number of points in the second grid direction. │ │ │ │ │ • n3 is the number of points in the third grid direction. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 23 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 23 │ │ │ │ │ • The nrhs parameter is the number of right hand sides to solve as one block. │ │ │ │ │ • The type parameter specifies a real or complex linear system. │ │ │ │ │ – type = 1 (SPOOLES REAL) for real, │ │ │ │ │ – type = 2 (SPOOLES COMPLEX) for complex. │ │ │ │ │ Index │ │ │ │ │ FrontMtx aggregateList(), 12 FrontMtx ownedColumns(), 19 │ │ │ │ │ FrontMtx assemblePostponedData(), 12 FrontMtx ownedRows(), 19 │ │ │ │ │ @@ -842,9 +842,9 @@ │ │ │ │ │ FrontMtx nactiveChild(), 11 FrontMtx upperBlockIVL(), 9 │ │ │ │ │ FrontMtx neqns(), 7 FrontMtx upperMtx(), 9 │ │ │ │ │ FrontMtx new(), 7 FrontMtx writeForHumanEye(), 20 │ │ │ │ │ FrontMtx nfront(), 7 FrontMtx writeStats(), 21 │ │ │ │ │ FrontMtx nLowerBlocks(), 9 FrontMtx writeToBinaryFile(), 20 │ │ │ │ │ FrontMtx nUpperBlocks(), 9 FrontMtx writeToFile(), 20 │ │ │ │ │ 24 │ │ │ │ │ - FrontMtx : DRAFT January 6, 2026 25 │ │ │ │ │ + FrontMtx : DRAFT January 17, 2026 25 │ │ │ │ │ FrontMtx writeToFormattedFile(), 20 │ │ ├── ./usr/share/doc/spooles-doc/FrontTrees.ps.gz │ │ │ ├── FrontTrees.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o FrontTrees.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2033 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -3344,16 +3344,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 70 /F put │ │ │ │ dup 74 /J put │ │ │ │ dup 79 /O put │ │ │ │ dup 84 /T put │ │ │ │ dup 97 /a put │ │ │ │ dup 100 /d put │ │ │ │ dup 101 /e put │ │ │ │ @@ -3546,130 +3548,139 @@ │ │ │ │ 60F5C3F629F7BC5A27C207D70DE63FBE0E023452097D5B7AA5B2CAC668D4D075 │ │ │ │ 1A0F70683E96AE35A6BA0B59619C215A7012568991AFC0C35789DD0ECE45C649 │ │ │ │ F44580845F0FA422868CFCC8029513235C0286B76196E350498845EA934DF289 │ │ │ │ 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0000000000000000000000000000000000000000000000000000000000000000 │ │ │ │ 0000000000000000000000000000000000000000000000000000000000000000 │ │ │ │ 0000000000000000000000000000000000000000000000000000000000000000 │ │ │ │ @@ -6741,16 +6752,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 65 /A put │ │ │ │ dup 66 /B put │ │ │ │ dup 67 /C put │ │ │ │ dup 71 /G put │ │ │ │ dup 74 /J put │ │ │ │ dup 83 /S put │ │ │ │ dup 97 /a put │ │ │ │ @@ -6948,168 +6961,175 @@ │ │ │ │ 82032FBD2FCB6E403D34B85ED4053A8CB619BDD4DE001F4C3007B1F317579651 │ │ │ │ E6D6662189CC2D95AB85D7473F65C5D7B4AC63B0FE928F3400035D5A9D443D0D │ │ │ │ F3532B99F3AC26CB25EA3CD64C341159061E02EFBC7C033C05CD919BBD827A6A │ │ │ │ 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w(Orderings)g(and)h(F)-7 b(ron)n(t)27 │ │ │ │ b(T)-7 b(rees)327 b Fr(19)844 448 y(T)-7 b(able)27 b(3:)36 │ │ │ │ b(R3D13824:)f(the)28 b(in\015uence)g(of)f Fg(maxzeros)e │ │ │ │ Fr(and)i Fg(maxsize)p Fr(.)p 1241 639 4 100 v 1674 609 │ │ │ │ a(factor)942 b(solv)n(e)276 b(total)440 709 y Fg(maxzeros)96 │ │ │ │ b(maxsize)p 1241 738 V 97 w Fr(init)105 b(CPU)g(m\015ops)99 │ │ │ │ b(p)r(ostpro)r(cess)f(CPU)i(m\015ops)k(CPU)p 390 742 │ │ │ │ 3121 4 v 663 811 a(0)294 b Fo(1)p 1241 841 4 100 v 220 │ │ │ │ @@ -12974,16 +12995,16 @@ │ │ │ │ 5308 y([12])41 b(A.)27 b(Gupta.)37 b(W)n(GPP:)27 b(Watson)g(Graph)g │ │ │ │ (Partitioning)f(and)h(sparse)f(matrix)h(ordering)e(Pac)n(k)-5 │ │ │ │ b(age.)34 b(T)-7 b(ec)n(hnical)27 b(Rep)r(ort)171 5407 │ │ │ │ y(Users)g(Man)n(ual,)f(IBM)i(T.J.)f(W)-7 b(atson)28 b(Researc)n(h)e │ │ │ │ (Cen)n(ter,)h(New)h(Y)-7 b(ork,)27 b(1996.)p eop end │ │ │ │ %%Page: 20 20 │ │ │ │ TeXDict begin 20 19 bop 0 100 a Fr(20)327 b Fj(Orderings)25 │ │ │ │ -b(and)j(F)-7 b(ron)n(t)27 b(T)-7 b(rees)p 1484 100 1756 │ │ │ │ -4 v 1948 w(Jan)n(uary)26 b(6,)h(2026)0 390 y Fr([13])41 │ │ │ │ +b(and)j(F)-7 b(ron)n(t)27 b(T)-7 b(rees)p 1484 100 1714 │ │ │ │ +4 v 1907 w(Jan)n(uary)25 b(17,)i(2026)0 390 y Fr([13])41 │ │ │ │ b(B.)24 b(Hendric)n(kson)e(and)i(R.)g(Leland.)31 b(An)24 │ │ │ │ b(impro)n(v)n(ed)f(sp)r(ectral)g(graph)g(partitioning)g(algorithm)g │ │ │ │ (for)h(mapping)f(parallel)171 490 y(computations.)28 │ │ │ │ b(T)-7 b(ec)n(hnical)23 b(Rep)r(ort)f(SAND92-1460,)g(Sandia)h(National) │ │ │ │ f(Lab)r(oratories,)g(Albuquerque,)h(NM,)h(1992.)0 656 │ │ │ │ y([14])41 b(B.)f(Hendric)n(kson)f(and)h(R.)g(Leland.)74 │ │ │ │ b(The)40 b(Chaco)f(user's)g(guide.)74 b(T)-7 b(ec)n(hnical)39 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -1,11 +1,11 @@ │ │ │ │ │ Ordering Sparse Matrices and Transforming Front Trees │ │ │ │ │ ∗ │ │ │ │ │ Cleve Ashcraft, Boeing Shared Services Group │ │ │ │ │ - January 6, 2026 │ │ │ │ │ + January 17, 2026 │ │ │ │ │ 1 Introduction │ │ │ │ │ If the ultimate goal is to solve linear systems of the form AX = B, one must compute an A = LDU, │ │ │ │ │ A=UTDU orA=UHDU factorization, depending on whether the matrix A is nonsymmetric, symmetric │ │ │ │ │ or Hermitian. D is a diagonal or block diagonal matrix, L is unit lower triangular, and U is unit upper │ │ │ │ │ triangular. A is sparse, but the sparsity structure of L and U will likely be much larger than that of A, │ │ │ │ │ i.e., they will suffer fill-in. It is crucial to find a permutation matrix such that the factors of PAPT have as │ │ │ │ │ moderate fill-in as can be reasonably expected. │ │ │ │ │ @@ -35,15 +35,15 @@ │ │ │ │ │ Section 2 introduces some background on sparse matrix orderings and describes the SPOOLES or- │ │ │ │ │ dering software. Section 3 presents the front tree object that controls the factorization, and its various │ │ │ │ │ transformations to improve performance. │ │ │ │ │ ∗P. O. Box 24346, Mail Stop 7L-21, Seattle, Washington 98124. This research was supported in part by the DARPA │ │ │ │ │ Contract DABT63-95-C-0122 and the DoD High Performance Computing Modernization Program Common HPC Software │ │ │ │ │ Support Initiative. │ │ │ │ │ 1 │ │ │ │ │ - 2 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 2 Orderings and Front Trees January 17, 2026 │ │ │ │ │ 2 Sparse matrix orderings │ │ │ │ │ Thepast few years have seen a resurgence of interest and accompanying improvement in algorithms and soft- │ │ │ │ │ ware to order sparse matrices. The minimum degree algorithm, specifically the multiple external minimum │ │ │ │ │ degree algorithm [19], was the preferred algorithm of choice for the better part of a decade. Alternative min- │ │ │ │ │ imum priority codes have recently pushed multiple minimum degree aside, including approximate minimum │ │ │ │ │ degree [1] and approximate deficiency [21], [25]. They offer improved quality or improved run time, and on │ │ │ │ │ occasion, both. │ │ │ │ │ @@ -81,15 +81,15 @@ │ │ │ │ │ One can construct the IVL object directly. There are methods to set the number of lists, to set the size │ │ │ │ │ of a list, to copy entries in a list into the object. It resizes itself as necessary. However, if one already has │ │ │ │ │ the matrix entries of A stored in an InpMtx object (which is the way that SPOOLES deals with sparse │ │ │ │ │ matrices), there is an easier way. One can create an IVL object from the InpMtx object, as follows. │ │ │ │ │ InpMtx *A ; │ │ │ │ │ IVL *adjIVL ; │ │ │ │ │ adjIVL = InpMtx_fullAdjacency(A) ; │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 3 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 3 │ │ │ │ │ Figure 1: A 3×4 9-point grid with its adjacency structure │ │ │ │ │ IVL : integer vector list object : │ │ │ │ │ type 1, chunked storage │ │ │ │ │ 12 lists, 12 maximum lists, 70 tsize, 4240 total bytes │ │ │ │ │ 1 chunks, 70 active entries, 1024 allocated, 6.84 % used │ │ │ │ │ 0 : 0 1 3 4 │ │ │ │ │ 9 10 11 1 : 0 1 2 3 4 5 │ │ │ │ │ @@ -121,15 +121,15 @@ │ │ │ │ │ This is an initializer for the Graph object, one that takes as input a complete IVL adjacency object. The │ │ │ │ │ 0 and NULL fields are not applicable here. (The Graph object is sophisticated — it can have weighted or │ │ │ │ │ unweighted vertices, weighted or unweighted edges, or both, and it can have boundary vertices. Neither is │ │ │ │ │ relevant now.) │ │ │ │ │ 2.2 Constructing an ordering │ │ │ │ │ Once we have a Graph object, we can construct an ordering. There are four choices: │ │ │ │ │ • minimum degree, (actually multiple external minimum degree, from [19]), │ │ │ │ │ - 4 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 4 Orderings and Front Trees January 17, 2026 │ │ │ │ │ • generalized nested dissection, │ │ │ │ │ • multisection, and │ │ │ │ │ • the better of generalized nested dissection and multisection. │ │ │ │ │ Minimum degree takes the least amount of CPU time. Generalized nested dissection and multisection both │ │ │ │ │ require the a partition of the graph, which can be much more expensive to compute than a minimum degree │ │ │ │ │ ordering. By and large, for larger graphs nested dissection generates better orderings than minimum degree, │ │ │ │ │ and the difference in quality increases as the graph size increases. Multisection is an ordering which almost │ │ │ │ │ @@ -161,15 +161,15 @@ │ │ │ │ │ etree = orderViaBestOfNDandMS(graph, maxdomainsize, maxzeros, │ │ │ │ │ maxsize, seed, msglvl, msgFile) ; │ │ │ │ │ Now let us describe the different parameters. │ │ │ │ │ • The msglvl and msgFile parameters are used to control output. When msglvl = 0, there is no │ │ │ │ │ output. When msglvl > 0, output goes to the msgFile file. The SPOOLES library is a research │ │ │ │ │ code, we have left a great deal of monitoring and debug code in the software. Large values of msglvl │ │ │ │ │ mayresult in large message files. To see the statistics generated during the ordering, use msglvl = 1. │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 5 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 5 │ │ │ │ │ • Theseedparameterisusedasarandomnumberseed. (Therearemanyplacesinthegraphpartitioning │ │ │ │ │ and minimum degree algorithms where randomness plays a part. Using a random number seed ensures │ │ │ │ │ repeatability.) │ │ │ │ │ • maxdomainsize is used for the nested dissection and multisection orderings. This parameter is used │ │ │ │ │ during the graph partition. Any subgraph that is larger than maxdomainsize is split. We recommend │ │ │ │ │ using a value of neqns/16 or neqns/32. Note: maxdomainsize must be greater than zero. │ │ │ │ │ • maxzeros and maxsize are used to transform the front tree. In effect, we have placed the ordering │ │ │ │ │ @@ -203,15 +203,15 @@ │ │ │ │ │ 10102 4.6 210364 10651916 6.2 211089 10722231 │ │ │ │ │ 10103 4.6 215795 11760095 6.4 217141 11606103 │ │ │ │ │ 10104 4.6 210989 10842091 6.1 212828 11168728 │ │ │ │ │ 10105 4.8 209201 10335761 6.1 210468 10582750 │ │ │ │ │ For the nested dissection and multisection orderings, we used maxdomainsize = 100. We see that there is │ │ │ │ │ really little difference in ordering quality, while the minimum degree ordering takes much less time than the │ │ │ │ │ other orderings. │ │ │ │ │ - 6 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 6 Orderings and Front Trees January 17, 2026 │ │ │ │ │ Let us now look at a random triangulation of a unit cube. This matrix has 13824 rows and columns. │ │ │ │ │ Each face of the cube has a 22×22 regular grid of points. The remainder of the vertices are placed in the │ │ │ │ │ interior using quasi-random points, and the Delauney triangulation is computed. │ │ │ │ │ minimum degree nested dissection │ │ │ │ │ seed CPU #entries #ops CPU #entries #ops │ │ │ │ │ 10101 9.2 5783892 6119141542 27.8 3410222 1921402246 │ │ │ │ │ 10102 8.8 5651678 5959584620 31.4 3470063 1998795621 │ │ │ │ │ @@ -245,15 +245,15 @@ │ │ │ │ │ ETree *vetree ; │ │ │ │ │ int *newToOld, *oldToNew ; │ │ │ │ │ Graph *graph ; │ │ │ │ │ vetree = ETree_new() ; │ │ │ │ │ ETree_initFromGraphWithPerms(vetree, graph, newToOld, oldToNew) ; │ │ │ │ │ Thevetreeobjectinthecodefragmentaboveisavertex elimination tree [20], [26], where each front contains │ │ │ │ │ one vertex. │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 7 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 7 │ │ │ │ │ Figure 2: R2D100: randomly triangulated, 100 grid points │ │ │ │ │ 48 49 51 50 55 91 8 11 10 9 │ │ │ │ │ 52 │ │ │ │ │ 53 69 54 17 18 │ │ │ │ │ 67 95 │ │ │ │ │ 70 19 │ │ │ │ │ 66 68 5 3 │ │ │ │ │ @@ -300,15 +300,15 @@ │ │ │ │ │ tree [2] has these property: any node in the tree is │ │ │ │ │ • either a leaf, │ │ │ │ │ • or has two or more children, │ │ │ │ │ • or its nonzero structure is not contained in that of its one child. │ │ │ │ │ The top tree in Figure 4 shows the vertex elimination tree with the “front” number of each vertex superim- │ │ │ │ │ posed on the vertex. The bottom tree is the fundamental supernode tree. Figure 5 shows the block partition │ │ │ │ │ 1Vertex j is the parent of i if j is the first vertex greater than i such that Lj,i 6= 0. │ │ │ │ │ - 8 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 8 Orderings and Front Trees January 17, 2026 │ │ │ │ │ Figure 3: Vertex elimination tree for R2D100, 100 rows and columns │ │ │ │ │ 99 │ │ │ │ │ 98 │ │ │ │ │ 97 │ │ │ │ │ 96 │ │ │ │ │ 95 │ │ │ │ │ 94 │ │ │ │ │ @@ -327,15 +327,15 @@ │ │ │ │ │ 7 17 31 39 55 65 71 78 81 │ │ │ │ │ 6 11 16 27 30 38 53 54 64 75 77 80 │ │ │ │ │ 2 5 8 10 13 15 22 26 29 37 52 59 63 76 79 │ │ │ │ │ 1 4 9 12 14 25 28 36 51 58 62 │ │ │ │ │ 0 3 24 35 49 50 57 60 61 │ │ │ │ │ 23 34 48 56 │ │ │ │ │ 33 │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 9 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 9 │ │ │ │ │ superimposed on the structure of the factor L. Note this one important property: within any block column │ │ │ │ │ and below the diagonal block, a row is either zero or dense. │ │ │ │ │ The code fragment to convert a tree into a fundamental supernode tree is given below. │ │ │ │ │ ETree *fsetree, *vetree ; │ │ │ │ │ int maxzeros ; │ │ │ │ │ IV *nzerosIV ; │ │ │ │ │ nzerosIV = IV_new() ; │ │ │ │ │ @@ -368,15 +368,15 @@ │ │ │ │ │ This method will merge a node with all of its children if it will not result in more than maxzeros zeros inside │ │ │ │ │ the new block. On input, nzerosIV object keeps count of the number of zeroes already in the blocks of │ │ │ │ │ fsetree, and on return it will contain the number of zeros in the blocks of ametree. │ │ │ │ │ 3.4 Splitting large fronts │ │ │ │ │ There is one final step to constructing the tree that governs the factorization and solve. Large matrices will │ │ │ │ │ generate large supernodes at the topmost levels of the tree. For example, a k × k × k grid with a 27 point │ │ │ │ │ finite difference operator, when ordered by nested dissection, has a root supernode with k2 rows and columns. │ │ │ │ │ - 10 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 10 Orderings and Front Trees January 17, 2026 │ │ │ │ │ Figure 4: Top: vertex elimination tree with the vertices mapped to the fundamental supernode that contains │ │ │ │ │ them. Bottom: fundamental supernode tree. │ │ │ │ │ 71 │ │ │ │ │ 71 │ │ │ │ │ 71 │ │ │ │ │ 71 │ │ │ │ │ 71 │ │ │ │ │ @@ -407,17 +407,17 @@ │ │ │ │ │ 2 5 10 15 23 26 34 43 44 49 53 57 58 67 │ │ │ │ │ 1 4 7 9 12 14 18 22 25 33 42 48 52 56 63 66 │ │ │ │ │ 0 3 8 11 13 21 24 32 41 47 50 51 60 62 65 │ │ │ │ │ 20 31 39 40 46 61 64 │ │ │ │ │ 19 30 38 │ │ │ │ │ 29 │ │ │ │ │ 28 │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 11 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 11 │ │ │ │ │ Figure 5: Block structure of L with the fundamental supernode partition. │ │ │ │ │ - 12 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 12 Orderings and Front Trees January 17, 2026 │ │ │ │ │ Figure 6: Top: fundamental supernode tree with the supernodes mapped to the amalgamated supernode │ │ │ │ │ that contains them. Bottom: amalgamated supernode tree. │ │ │ │ │ 24 │ │ │ │ │ 24 │ │ │ │ │ 24 │ │ │ │ │ 24 │ │ │ │ │ 24 │ │ │ │ │ @@ -442,17 +442,17 @@ │ │ │ │ │ 6 10 13 15 │ │ │ │ │ 10 │ │ │ │ │ 24 │ │ │ │ │ 4 12 18 23 │ │ │ │ │ 0 1 2 3 9 11 14 17 19 22 │ │ │ │ │ 7 8 10 13 15 16 20 21 │ │ │ │ │ 5 6 │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 13 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 13 │ │ │ │ │ Figure 7: Block structure of L with the amalgamated supernode partition. │ │ │ │ │ - 14 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 14 Orderings and Front Trees January 17, 2026 │ │ │ │ │ The data structure for a top level supernode can be very large, too large to fit into memory. In a parallel │ │ │ │ │ environment, we follow the convention that each node in the tree is handled by one process. Having a very │ │ │ │ │ large node at the top levels of the tree will severely decrease the parallelism available to the computations. │ │ │ │ │ The solution to both problems, large data structures and limited parallelism, is to split large supernodes │ │ │ │ │ into pieces. We can specify a maximum size for the nodes in the tree, and split the large supernode into pieces │ │ │ │ │ no larger than this maximum size. This will keep the data structures to a manageable size and increase the │ │ │ │ │ available parallelism. We call the resulting tree the front tree because it represents the final computational │ │ │ │ │ @@ -488,15 +488,15 @@ │ │ │ │ │ of front trees. The original front tree came from our nested dissection ordering. │ │ │ │ │ There are 13824 rows and columns in the matrix, and 6001 fronts in the nested dissection tree. While │ │ │ │ │ there is an average of two rows and columns per front, most of the fronts are singleton fronts at the lower │ │ │ │ │ levels of the tree. The top level front has 750 internal rows and columns. │ │ │ │ │ • In the first step we create an fundamental supernode tree with a call to ETree mergeFrontsOne()with │ │ │ │ │ maxzeros = 0. We see that the number of fronts decreases by one and the number of entries does not │ │ │ │ │ change. │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 15 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 15 │ │ │ │ │ Figure 8: Left: tree after the large supernodes have been split. Right: tree with nodes mapped back to their │ │ │ │ │ amalgamated supernode. │ │ │ │ │ 26 │ │ │ │ │ 26 │ │ │ │ │ 26 │ │ │ │ │ 26 │ │ │ │ │ 27 │ │ │ │ │ @@ -525,26 +525,26 @@ │ │ │ │ │ 28 │ │ │ │ │ 27 │ │ │ │ │ 26 │ │ │ │ │ 5 13 20 25 │ │ │ │ │ 4 10 12 19 21 24 │ │ │ │ │ 0 1 2 3 8 9 11 15 18 22 23 │ │ │ │ │ 6 7 14 16 17 │ │ │ │ │ - 16 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 16 Orderings and Front Trees January 17, 2026 │ │ │ │ │ Figure 9: Block structure of L with the amalgamated and split supernode partition. │ │ │ │ │ Table 1: R3D13824: front tree transformations │ │ │ │ │ CPU #fronts #indices # entries #operations │ │ │ │ │ original 6001 326858 3459359 1981403337 │ │ │ │ │ fs tree 0.040 6000 326103 3459359 1981403337 │ │ │ │ │ merge one 0.032 3477 158834 3497139 2000297117 │ │ │ │ │ merge all 0.020 748 95306 3690546 2021347776 │ │ │ │ │ merge any 0.012 597 85366 3753241 2035158539 │ │ │ │ │ split 0.043 643 115139 3753241 2035158539 │ │ │ │ │ final 0.423 643 115128 3752694 2034396840 │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 17 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 17 │ │ │ │ │ • The second step is also a call to ETree mergeFrontsOne(), this time with maxzeros = 1000. Here │ │ │ │ │ we merge fronts with only one child with that child, in other words, only chains of nodes can merge │ │ │ │ │ together. Note how the number of fronts is decreased by almost one half, and the number of factor │ │ │ │ │ entries and operations increase by 1%. │ │ │ │ │ • The third step is a call to ETree mergeFrontsAll()with maxzeros = 1000, where we try to merge a │ │ │ │ │ node with all of its children if possible. The number of fronts decreases again by a factor of five, while │ │ │ │ │ the number of factor entries and operations increases by 7% and 2%, respectively, when compared with │ │ │ │ │ @@ -582,15 +582,15 @@ │ │ │ │ │ the final front tree, for the intra-front computations are a small fraction of the total number of operations. │ │ │ │ │ The solve time improves dramatically when small fronts are merged together into larger fronts. Our │ │ │ │ │ solves are submatrix algorithms, where the fundamental kernel is an operation Y := B −L X and │ │ │ │ │ J J J,I I │ │ │ │ │ X :=Y −U Y ,andisdesigned to be a BLAS2 kernel (when X and Y have a single column) or BLAS3 │ │ │ │ │ J J I,J J │ │ │ │ │ kernel (when X and Y are matrices). When fronts are small, particularly with one internal row and column, │ │ │ │ │ - 18 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 18 Orderings and Front Trees January 17, 2026 │ │ │ │ │ the submatrices that take part are very small. The overhead for the computations takes far more time than │ │ │ │ │ the computations themselves. │ │ │ │ │ This multistep process of merging, merging again, etc, and finally splitting the front trees is tedious. │ │ │ │ │ There are simple methods that do the process in one step. │ │ │ │ │ ETree *etree, *etree2, *etree3 ; │ │ │ │ │ int maxfrontsize, maxzeros, seed ; │ │ │ │ │ etree2 = ETree_transform(etree, NULL, maxzeros, maxfrontsize, seed) ; │ │ │ │ │ @@ -624,15 +624,15 @@ │ │ │ │ │ computations in the factorization and solve. If maxsize is too large, then too much of the computations in │ │ │ │ │ the factorization is done inside a front, which uses a slow kernel. If maxsize is too small, then the fronts are │ │ │ │ │ too small to get much computational efficiency. We recommend using a value between 32 and 96. Luckily, │ │ │ │ │ the factor and solve times are fairly flat within this range. A value of 64 is what we customarily use. │ │ │ │ │ References │ │ │ │ │ [1] P. Amestoy, T. Davis, and I. Duff. An approximate minimum degree ordering algorithm. SIAM J. │ │ │ │ │ Matrix Anal. Appl., 17:886–905, 1996. │ │ │ │ │ - January 6, 2026 Orderings and Front Trees 19 │ │ │ │ │ + January 17, 2026 Orderings and Front Trees 19 │ │ │ │ │ Table 3: R3D13824: the influence of maxzeros and maxsize. │ │ │ │ │ factor solve total │ │ │ │ │ maxzeros maxsize init CPU mflops postprocess CPU mflops CPU │ │ │ │ │ 0 ∞ 3.3 129.8 15.3 5.3 7.8 7.1 146.2 │ │ │ │ │ 10 ∞ 3.5 129.2 15.3 3.3 5.3 10.5 141.3 │ │ │ │ │ 100 ∞ 3.0 119.3 16.7 2.0 3.9 14.4 128.2 │ │ │ │ │ 1000 ∞ 3.0 121.8 16.7 1.4 3.5 17.0 129.7 │ │ │ │ │ @@ -665,15 +665,15 @@ │ │ │ │ │ Trans. Math. Software, 6:302–325, 1983. │ │ │ │ │ [10] J. A. George. Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal., 10:345–363, │ │ │ │ │ 1973. │ │ │ │ │ [11] J. A. George and J. W. H. Liu. Computer Solution of Large Sparse Positive Definite Systems. Prentice- │ │ │ │ │ Hall, Englewood Cliffs, NJ, 1981. │ │ │ │ │ [12] A. Gupta. WGPP: Watson Graph Partitioning and sparse matrix ordering Package. Technical Report │ │ │ │ │ Users Manual, IBM T.J. Watson Research Center, New York, 1996. │ │ │ │ │ - 20 Orderings and Front Trees January 6, 2026 │ │ │ │ │ + 20 Orderings and Front Trees January 17, 2026 │ │ │ │ │ [13] B. Hendrickson and R. Leland. An improved spectral graph partitioning algorithm for mapping parallel │ │ │ │ │ computations. Technical Report SAND92-1460, Sandia National Laboratories, Albuquerque, NM, 1992. │ │ │ │ │ [14] B. Hendrickson and R. Leland. The Chaco user’s guide. Technical Report SAND93-2339, Sandia │ │ │ │ │ National Laboratories, Albuquerque, NM, 1993. │ │ │ │ │ [15] B. Hendrickson and E. Rothberg. Improving the runtime and quality of nested dissection ordering. │ │ │ │ │ SIAM J. Sci. Comput., 20:468–489, 1998. │ │ │ │ │ [16] G. Karypis and V. Kumar. 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b(;)15 │ │ │ │ b(W)e Fp(]\))30 b(=)f Fi(j)p Fl(S)5 b Fi(j)1776 551 y │ │ │ │ Fh(\022)1838 670 y Fp(1)20 b(+)g Fl(\013)2062 608 y Fp(max)q │ │ │ │ @@ -6143,17 +6154,17 @@ │ │ │ │ Fp(\))p Fi(g)969 5407 y Fl(Y)1022 5421 y Fk(3)1144 5407 │ │ │ │ y Fp(=)83 b Fi(f)p Fl(y)28 b Fi(2)d Fl(Y)50 b Fi(j)31 │ │ │ │ b Fl(y)d Fi(2)d Fl(Ad)-10 b(j)5 b Fp(\()p Fl(B)26 b Fi(n)21 │ │ │ │ b Fl(Y)f Fp(\))30 b(and)g Fl(y)e Fi(2)d Fl(Ad)-10 b(j)5 │ │ │ │ b Fp(\()p Fl(W)34 b Fi(n)21 b Fl(Y)f Fp(\))p Fi(g)p eop │ │ │ │ end │ │ │ │ %%Page: 8 8 │ │ │ │ -TeXDict begin 8 7 bop 0 100 a Fp(8)p 136 100 1129 4 v │ │ │ │ -1311 w Fo(GPart)29 b Fg(:)40 b Fm(DRAFT)31 b Fg(Jan)m(uary)f(6,)h(2026) │ │ │ │ -p 2771 100 V 227 399 a Fp(The)e Fo(YVmapIV)e Fp(ob)5 │ │ │ │ +TeXDict begin 8 7 bop 0 100 a Fp(8)p 136 100 1106 4 v │ │ │ │ +1288 w Fo(GPart)29 b Fg(:)41 b Fm(DRAFT)30 b Fg(Jan)m(uary)g(17,)h │ │ │ │ +(2026)p 2794 100 V 227 399 a Fp(The)e Fo(YVmapIV)e Fp(ob)5 │ │ │ │ b(ject)30 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Fp(parameter)k(is)f(the)g │ │ │ │ @@ -6560,17 +6571,17 @@ │ │ │ │ y Fn(\210)45 b Fp(The)30 b Fo(alpha)f Fp(parameter)i(con)m(trols)h(the) │ │ │ │ e(partition)h(ev)-5 b(aluation)32 b(function.)337 5294 │ │ │ │ y Fn(\210)45 b Fp(The)i Fo(maxdomweight)e Fp(parameter)j(con)m(trols)g │ │ │ │ (the)g(recursiv)m(e)g(bisection)h(|)e(no)g(subgraph)f(with)427 │ │ │ │ 5407 y(w)m(eigh)m(t)32 b(less)f(than)f Fo(maxdomweight)d │ │ │ │ Fp(is)j(further)f(split.)p eop end │ │ │ │ %%Page: 13 13 │ │ │ │ -TeXDict begin 13 12 bop 91 100 1106 4 v 1288 100 a Fo(GPart)29 │ │ │ │ -b Fg(:)40 b Fm(DRAFT)121 b Fg(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2701 100 V 1106 w Fp(13)337 399 y Fn(\210)45 b Fp(The)c │ │ │ │ +TeXDict begin 13 12 bop 91 100 1084 4 v 1265 100 a Fo(GPart)29 │ │ │ │ +b Fg(:)41 b Fm(DRAFT)121 b Fg(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2724 100 V 1084 w Fp(13)337 399 y Fn(\210)45 b Fp(The)c │ │ │ │ Fo(DDoption)e Fp(parameter)j(con)m(trols)h(the)f(initial)h │ │ │ │ (domain/segmen)m(t)g(partition)f(on)f(eac)m(h)i(sub-)427 │ │ │ │ 511 y(graph.)60 b(When)37 b Fo(DDDoption)45 b(=)j(1)37 │ │ │ │ b Fp(w)m(e)g(use)g(the)g(\014shnet)f(algorithm)i(for)f(eac)m(h)h │ │ │ │ (subgraph.)59 b(When)427 624 y Fo(DDDoption)46 b(=)h(1)32 │ │ │ │ b Fp(w)m(e)h(use)f(the)h(\014shnet)e(algorithm)j(once)f(for)f(the)g(en) │ │ │ │ m(tire)i(graph)e(and)f(this)i(is)f(then)427 737 y(pro)5 │ │ │ │ @@ -6640,17 +6651,17 @@ │ │ │ │ 5275 y Ff({)45 b Fo(nlayer)h(=)i(2)30 b Fp(|)g(eac)m(h)i(net)m(w)m(ork) │ │ │ │ f(has)f(t)m(w)m(o)i(la)m(y)m(ers)f(but)f(need)g(not)h(b)s(e)f │ │ │ │ (bipartite.)500 5407 y Ff({)45 b Fo(nlayer)h(>)i(2)30 │ │ │ │ b Fp(|)g(eac)m(h)i(net)m(w)m(ork)f(has)f Fo(option/2)e │ │ │ │ Fp(la)m(y)m(ers)k(on)e(eac)m(h)i(side)e(of)h(the)f(separator.)p │ │ │ │ eop end │ │ │ │ %%Page: 14 14 │ │ │ │ -TeXDict begin 14 13 bop 0 100 a Fp(14)p 182 100 1106 │ │ │ │ -4 v 1289 w Fo(GPart)29 b Fg(:)40 b Fm(DRAFT)30 b Fg(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2794 100 V 337 399 a Fn(\210)45 b Fp(The)34 b │ │ │ │ +TeXDict begin 14 13 bop 0 100 a Fp(14)p 182 100 1084 │ │ │ │ +4 v 1266 w Fo(GPart)29 b Fg(:)40 b Fm(DRAFT)31 b Fg(Jan)m(uary)f(17,)h │ │ │ │ +(2026)p 2817 100 V 337 399 a Fn(\210)45 b Fp(The)34 b │ │ │ │ Fo(outDSTreeFile)d Fp(parameter)k(is)f(the)h(output)f(\014le)g(for)g │ │ │ │ (the)h Fo(DSTree)e Fp(ob)5 b(ject.)53 b(It)35 b(m)m(ust)f(b)s(e)g(of) │ │ │ │ 427 511 y(the)29 b(form)f Fo(*.dstreef)e Fp(or)j Fo(*.dstreeb)p │ │ │ │ Fp(.)37 b(If)29 b Fo(outDSTreeFile)24 b Fp(is)29 b(not)g │ │ │ │ Fo("none")p Fp(,)e(the)i Fo(DSTree)e Fp(ob)5 b(ject)427 │ │ │ │ 624 y(is)31 b(written)f(to)h(the)g(\014le)f(via)h(the)g │ │ │ │ Fo(DSTree)p 1851 624 29 4 v 33 w(writeToFile\(\))26 b │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -30,15 +30,15 @@ │ │ │ │ │ condensed into the source while the nodes in W \Y are condensed into the sink. The rest of │ │ │ │ │ the network is formed using the structure of the subgraph induced by Y. Given a min-cut of │ │ │ │ │ b │ │ │ │ │ the network we can identify a separator S ⊆ Y that has minimal weight. We examine two │ │ │ │ │ (possibly) different min-cuts and evaluate the partitions induced via their minimal weight │ │ │ │ │ separators, and accept a better partition if present. │ │ │ │ │ 1 │ │ │ │ │ - 2 GPart : DRAFT January 6, 2026 │ │ │ │ │ + 2 GPart : DRAFT January 17, 2026 │ │ │ │ │ This process we call DDSEP, which is short for Domain Decomposition SEParator, explained in more │ │ │ │ │ detail in [?] and [?]. │ │ │ │ │ 1.1 Data Structures │ │ │ │ │ The GPart structure has a pointer to a Graph object and other fields that contain information │ │ │ │ │ about the partition of the graph. │ │ │ │ │ The following fields are always active. │ │ │ │ │ • Graph *graph : pointer to the Graph object │ │ │ │ │ @@ -61,15 +61,15 @@ │ │ │ │ │ • GPart *sib : pointer to a sibling GPart object │ │ │ │ │ • IV vtxMapIV : an IV object of size nvtx + nvbnd, contains a map from the vertices of the │ │ │ │ │ graph to either the vertices of its parent or to the vertices of the root graph │ │ │ │ │ The DDsepInfo helper-object is used during the DDSEP recursive bisection process. It contains │ │ │ │ │ input parameters for the different stages of the DDSEP algorithm, and collects statistics about the │ │ │ │ │ CPUtime spent in each stage. │ │ │ │ │ • These parameters are used to generate the domain decomposition. │ │ │ │ │ - GPart : DRAFT January 6, 2026 3 │ │ │ │ │ + GPart : DRAFT January 17, 2026 3 │ │ │ │ │ – int minweight: minimum target weight for a domain │ │ │ │ │ – int maxweight: maximum target weight for a domain │ │ │ │ │ – double freeze: multiplier used to freeze vertices of high degree into the multisector. │ │ │ │ │ If the degree of v is more than freeze times the median degree, v is placed into the │ │ │ │ │ multisector. │ │ │ │ │ – int seed: random number seed │ │ │ │ │ – int DDoption: If 1, a new domain decomposition is constructed for each subgraph. If │ │ │ │ │ @@ -98,15 +98,15 @@ │ │ │ │ │ – int ntreeobj: number of tree objects in the tree, used to set gpart->id and used to │ │ │ │ │ initialize the DSTree object. │ │ │ │ │ – int msglvl : message level │ │ │ │ │ – FILE *msgFile : message file pointer │ │ │ │ │ 1.2 Prototypes and descriptions of GPart methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ GPart object. There are no IO methods. │ │ │ │ │ - 4 GPart : DRAFT January 6, 2026 │ │ │ │ │ + 4 GPart : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. GPart * GPart_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the GPart structure and then sets the default fields │ │ │ │ │ by a call to GPart setDefaultFields(). │ │ │ │ │ 2. void GPart_setDefaultFields ( GPart *gpart ) ; │ │ │ │ │ @@ -132,15 +132,15 @@ │ │ │ │ │ compidsIV and cweightsIV IV objects are initialized. The remaining fields are not changed │ │ │ │ │ from their default values. │ │ │ │ │ Error checking: If gpart or g is NULL, or if g->nvtx ≤ 0, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 2. void GPart_setMessageInfo ( GPart *gpart, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method sets the msglvl and msgFile fields. │ │ │ │ │ Error checking: If gpart is NULL, an error message is printed and the program exits. │ │ │ │ │ - GPart : DRAFT January 6, 2026 5 │ │ │ │ │ + GPart : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.3 Utility methods │ │ │ │ │ 1. void GPart_setCweights ( GPart *gpart ) ; │ │ │ │ │ This method sets the component weights vector cweightsIV. We assume that the compidsIV │ │ │ │ │ vector has been set prior to entering this method. The weight of a component is not simply │ │ │ │ │ the sum of the weights of the vertices with that component’s id. We accept the separator or │ │ │ │ │ multisector vertices (those v with compids[v] == 0) but then find the connected components │ │ │ │ │ of the remaining vertices, renumbering the compidsIV vector where necessary. Thus, ncomp │ │ │ │ │ @@ -171,15 +171,15 @@ │ │ │ │ │ This method determines whether the vertex v is adjacent to just one domain or not. We use │ │ │ │ │ this method to make a separator or multisector minimal. If the vertex is adjacent to only one │ │ │ │ │ domain, the return value is 1 and *pdomid is set to the domain’s id. If a vertex is adjacent │ │ │ │ │ to zero or two or more domains, the return value is zero. If a vertex belongs to a domain, it │ │ │ │ │ is considered adjacent to that domain. │ │ │ │ │ Error checking: If gpart, g or domid is NULL, or if v is out of range (i.e., v < 0 or nvtx ≤ v), │ │ │ │ │ an error message is printed and the program exits. │ │ │ │ │ - 6 GPart : DRAFT January 6, 2026 │ │ │ │ │ + 6 GPart : DRAFT January 17, 2026 │ │ │ │ │ 6. IV * GPart_bndWeightsIV ( GPart *gpart ) ; │ │ │ │ │ This method returns an IV object that contains the weights of the vertices on the boundaries │ │ │ │ │ of the components. │ │ │ │ │ Error checking: If gpart or g is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.4 Domain decomposition methods │ │ │ │ │ There are presently two methods that create a domain decomposition of a graph or a subgraph. │ │ │ │ │ 1. void GPart_DDviaFishnet ( GPart *gpart, double frac, int minweight, │ │ │ │ │ @@ -209,15 +209,15 @@ │ │ │ │ │ double cpus[] ) ; │ │ │ │ │ This method takes a domain decomposition {Φ,Ω ,...,Ω } defined by the compidsIV vector │ │ │ │ │ 1 m │ │ │ │ │ and generates a two set partition [S,B,W]. We first compute the map from vertices to │ │ │ │ │ domains and segments (the segments partition the interface nodes Φ). We then construct the │ │ │ │ │ bipartite graph that represents the connectivity of the domains and segments. Each segment │ │ │ │ │ is an “edge” that connects two “adjacent” domains. This allows us to use a variant of the │ │ │ │ │ - GPart : DRAFT January 6, 2026 7 │ │ │ │ │ + GPart : DRAFT January 17, 2026 7 │ │ │ │ │ Kernighan-Lin algorithm to find an “edge” separator formed of segments, which is really a │ │ │ │ │ vertex separator, a subset of Φ. The alpha parameter is used in the cost function evaluation │ │ │ │ │ for the partition, cost([S,B,W]) = |S|1+αmax{|B|,|W|}. The seed parameter is used │ │ │ │ │ min{|B|,|W|} │ │ │ │ │ to randomize the algorithm. One can make several runswith different seeds and chose the best │ │ │ │ │ partition. The cpus[] array is used to store execution times for segments of the algorithm: │ │ │ │ │ cpus[0] stores the time to compute the domain/segment map; cpus[2] stores the time to │ │ │ │ │ @@ -253,15 +253,15 @@ │ │ │ │ │ 0 │ │ │ │ │ Y = {y∈Y | y∈Adj(B\Y) and y ∈/ Adj(W \Y)} │ │ │ │ │ 1 │ │ │ │ │ Y = {y∈Y | y∈/ Adj(B \Y) and y ∈ Adj(W \Y)} │ │ │ │ │ 2 │ │ │ │ │ Y = {y∈Y | y∈Adj(B\Y) and y ∈Adj(W \Y)} │ │ │ │ │ 3 │ │ │ │ │ - 8 GPart : DRAFT January 6, 2026 │ │ │ │ │ + 8 GPart : DRAFT January 17, 2026 │ │ │ │ │ The YVmapIV object contains the list of vertices in the wide separator Y . The IV object that │ │ │ │ │ is returned, (called YCmapIV in the calling method) contains the subscripts of the Y , Y , Y │ │ │ │ │ 0 1 2 │ │ │ │ │ or Y sets that contains each vertex. │ │ │ │ │ 3 │ │ │ │ │ Error checking: If gpart, g or YVmapIV is NULL, or if nvtx ≤ 0, or if YVmapIV is empty, an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ @@ -303,15 +303,15 @@ │ │ │ │ │ improves it (if possible). The methods returns the cost of a (possibly) new two-set partition │ │ │ │ │ b b c │ │ │ │ │ [S,B,W] defined by the compidsIV vector. The wide separator Y that is constructed is │ │ │ │ │ centered around S, i.e., Y includes all nodes in B and W that are nlayer distance or less │ │ │ │ │ from S. This method calls GPart smoothYSep(). │ │ │ │ │ Error checking: If gpart is NULL, or if nlevel < 0, or if alpha < 0.0, an error message is │ │ │ │ │ printed and the program exits. │ │ │ │ │ - GPart : DRAFT January 6, 2026 9 │ │ │ │ │ + GPart : DRAFT January 17, 2026 9 │ │ │ │ │ 1.2.7 Recursive Bisection method │ │ │ │ │ There is presently one method to construct the domain/separator tree. │ │ │ │ │ 1. DSTree * GPart_RBviaDDsep ( GPart *gpart, DDsepInfo *info ) ; │ │ │ │ │ This method performs a recursive bisection of the graph using the DDSEP algorithm and │ │ │ │ │ returns a DSTree object that represents the domain/separator tree and the map from vertices │ │ │ │ │ to domains and separators. The DDsepInfo structure contains all the parameters to the │ │ │ │ │ different steps of the DDSEP algorithm (the fishnet method to find the domain decomposition, │ │ │ │ │ @@ -341,15 +341,15 @@ │ │ │ │ │ info->DDoption = 1 ; info->msglvl = 0 ; │ │ │ │ │ info->nlayer = 3 ; info->msgFile = stdout ; │ │ │ │ │ Error checking: If info is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. void DDsepInfo_clearData ( DDsepInfo *info ) ; │ │ │ │ │ This method checks to see whether info is NULL. DDsepInfo setDefaultFields() is called │ │ │ │ │ to set the default values. │ │ │ │ │ Error checking: If info is NULL, an error message is printed and the program exits. │ │ │ │ │ - 10 GPart : DRAFT January 6, 2026 │ │ │ │ │ + 10 GPart : DRAFT January 17, 2026 │ │ │ │ │ 4. void DDsepInfo_free ( DDsepInfo *info ) ; │ │ │ │ │ This method checks to see whether info is NULL. If so, an error message is printed and the │ │ │ │ │ program exits. Otherwise, it releases any storage by a call to DDsepInfo clearData() then │ │ │ │ │ free’s the storage for the structure with a call to free(). │ │ │ │ │ Error checking: If info is NULL, an error message is printed and the program exits. │ │ │ │ │ 5. void DDsepInfo_writeCpuTimes ( DDsepInfo *info, FILE *msgFile ) ; │ │ │ │ │ This method writes a breakdown of the CPU times in a meaningful format. Here is sample │ │ │ │ │ @@ -379,15 +379,15 @@ │ │ │ │ │ data. │ │ │ │ │ • TheinGraphFileparameteristheinputfilefortheGraphobject. It mustbeof theform │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The freeze parameter is used to place nodes of high degree into the multisector. If the │ │ │ │ │ external degree of a vertex is freeze times the average degree, then it is placed in the │ │ │ │ │ multisector. │ │ │ │ │ - GPart : DRAFT January 6, 2026 11 │ │ │ │ │ + GPart : DRAFT January 17, 2026 11 │ │ │ │ │ • The target minimum weight for a domain is minweight. │ │ │ │ │ • The target maximum weight for a domain is maxweight. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The outIVfile parameter is the output file for the IV object that contains the map │ │ │ │ │ from vertices to components. If outIVfile is "none", then there is no output, otherwise │ │ │ │ │ outIVfile must be of the form *.ivf or *.ivb. │ │ │ │ │ 2. testTwoSetViaBKL msglvl msgFile inGraphFile inIVfile │ │ │ │ │ @@ -417,15 +417,15 @@ │ │ │ │ │ problems. It reads in a Graph object and an IV object that holds the map from vertices to │ │ │ │ │ components (e.g., the output from the driver program testTwoSetViaBKL) from two files, │ │ │ │ │ smooths the separator and then optionally writes out the new component ids map to a file. │ │ │ │ │ • The msglvl parameter determines the amount of output. │ │ │ │ │ • The msgFile parameter determines the output file — if msgFile is stdout, then the │ │ │ │ │ output file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ - 12 GPart : DRAFT January 6, 2026 │ │ │ │ │ + 12 GPart : DRAFT January 17, 2026 │ │ │ │ │ • TheinGraphFileparameteristheinputfilefortheGraphobject. It mustbeof theform │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The inIVfile parameter is the input file for the IV object that contains the map from │ │ │ │ │ vertices to domains and multisector. It inIVfile must be of the form *.ivf or *.ivb. │ │ │ │ │ • The option parameter specifies the type of network optimization problem that will be │ │ │ │ │ solved. │ │ │ │ │ @@ -457,15 +457,15 @@ │ │ │ │ │ • The target maximum weight for a domain is maxweight. │ │ │ │ │ • The freeze parameter is used to place nodes of high degree into the multisector. If the │ │ │ │ │ external degree of a vertex is freeze times the average degree, then it is placed in the │ │ │ │ │ multisector. │ │ │ │ │ • The alpha parameter controls the partition evaluation function. │ │ │ │ │ • The maxdomweight parameter controls the recursive bisection — no subgraph with │ │ │ │ │ weight less than maxdomweight is further split. │ │ │ │ │ - GPart : DRAFT January 6, 2026 13 │ │ │ │ │ + GPart : DRAFT January 17, 2026 13 │ │ │ │ │ • The DDoption parameter controls the initial domain/segment partition on each sub- │ │ │ │ │ graph. When DDDoption = 1 we use the fishnet algorithm for each subgraph. When │ │ │ │ │ DDDoption = 1 we use the fishnet algorithm once for the entire graph and this is then │ │ │ │ │ projected down onto each subgraph. │ │ │ │ │ • The nlayer parameter governs the smoothing process by specifying the type of network │ │ │ │ │ optimization problem that will be solved. │ │ │ │ │ – nlayer = 1 — each network has two layers and is bipartite. │ │ │ │ │ @@ -496,15 +496,15 @@ │ │ │ │ │ DDDoption = 1 we use the fishnet algorithm once for the entire graph and this is then │ │ │ │ │ projected down onto each subgraph. │ │ │ │ │ • The nlayer parameter governs the smoothing process by specifying the type of network │ │ │ │ │ optimization problem that will be solved. │ │ │ │ │ – nlayer = 1 — each network has two layers and is bipartite. │ │ │ │ │ – nlayer = 2 — each network has two layers but need not be bipartite. │ │ │ │ │ – nlayer > 2 — each network has option/2 layers on each side of the separator. │ │ │ │ │ - 14 GPart : DRAFT January 6, 2026 │ │ │ │ │ + 14 GPart : DRAFT January 17, 2026 │ │ │ │ │ • The outDSTreeFile parameter is the output file for the DSTree object. It must be of │ │ │ │ │ the form *.dstreef or *.dstreeb. If outDSTreeFile is not "none", the DSTree object │ │ │ │ │ is written to the file via the DSTree writeToFile() method. │ │ │ │ │ Index │ │ │ │ │ DDsepInfo clearData(), 9 │ │ │ │ │ DDsepInfo free(), 10 │ │ │ │ │ DDsepInfo new(), 9 │ │ ├── ./usr/share/doc/spooles-doc/Graph.ps.gz │ │ │ ├── Graph.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Graph.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1202,16 +1202,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1399,79 +1401,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 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Fo(parameter)i(is)g(the)g(input)e(\014le)i(for)f(the)h │ │ │ │ Fn(Graph)e Fo(ob)5 b(ject.)64 b(It)37 b(m)m(ust)h(b)s(e)f(of)h(the)f │ │ │ │ (form)427 511 y Fn(*.graphf)18 b Fo(or)j Fn(*.graphb)p │ │ │ │ Fo(.)35 b(The)19 b Fn(Graph)g Fo(ob)5 b(ject)21 b(is)g(read)f(from)g │ │ │ │ (the)g(\014le)h(via)f(the)h Fn(Graph)p 3368 511 29 4 │ │ │ │ v 33 w(readFromFile\(\))427 624 y Fo(metho)s(d.)111 1065 │ │ │ │ y(7.)46 b Fn(testWirebasket)e(msglvl)i(msgFile)g(inGraphFile)f │ │ │ │ @@ -6557,17 +6570,17 @@ │ │ │ │ Fo(15)29 b(grid.)40 b(They)27 b(sho)m(w)h(the)h(stages)227 │ │ │ │ 5294 y(for)36 b Fn(radius)46 b(=)i(1)36 b Fo(on)g(the)g(left)h(and)f │ │ │ │ Fn(radius)46 b(=)i(2)35 b Fo(on)i(the)f(righ)m(t.)59 │ │ │ │ b(The)36 b(domains)g(are)g(3)25 b Fi(\002)f Fo(3)36 b(subgrids)227 │ │ │ │ 5407 y(whose)30 b(v)m(ertices)i(ha)m(v)m(e)g(lab)s(els)f(equal)g(to)g │ │ │ │ (zero.)p eop end │ │ │ │ %%Page: 12 12 │ │ │ │ -TeXDict begin 12 11 bop 0 100 a Fo(12)p 182 100 1106 │ │ │ │ -4 v 1289 w Fn(Graph)29 b Fe(:)40 b Fl(DRAFT)30 b Fe(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2794 100 V 429 1927 a @beginspecial 0 @llx 0 │ │ │ │ +TeXDict begin 12 11 bop 0 100 a Fo(12)p 182 100 1084 │ │ │ │ +4 v 1266 w Fn(Graph)29 b Fe(:)40 b Fl(DRAFT)31 b Fe(Jan)m(uary)f(17,)h │ │ │ │ +(2026)p 2817 100 V 429 1927 a @beginspecial 0 @llx 0 │ │ │ │ @lly 600 @urx 600 @ury 1943 @rwi 1943 @rhi @setspecial │ │ │ │ %%BeginDocument: ../../Graph/doc/rad1.eps │ │ │ │ %!PS-Adobe-2.0 EPSF-1.2 │ │ │ │ %%BoundingBox: 0.0 0.0 600.0 600.0 │ │ │ │ /radius 15 def │ │ │ │ /Helvetica findfont 18.75 scalefont setfont │ │ │ │ /M {moveto} def │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -27,15 +27,15 @@ │ │ │ │ │ weight vertices in the weighted vertex. The weight of an edge is w(u,v), the number of (u,v) edges │ │ │ │ │ in the unit weight graph where u ∈ u and v ∈ v. │ │ │ │ │ Thenaturalcompressedgraph[?],[?]isveryimportantformanymatricesfromstructralanalysis │ │ │ │ │ and computational fluid mechanics. This type of graph has one special property: │ │ │ │ │ w(u,v) = w(u)·w(v) │ │ │ │ │ 1The EGraph object represents a graph of the matrix, but stores a list of covering cliques in an IVL object. │ │ │ │ │ 1 │ │ │ │ │ - 2 Graph : DRAFT January 6, 2026 │ │ │ │ │ + 2 Graph : DRAFT January 17, 2026 │ │ │ │ │ and it is the smallest graph with this property. The compression is loss-less, for given G(V,E) │ │ │ │ │ and φ, we can reconstruct the unit weight graph G(V,E). In effect, we can work with the natural │ │ │ │ │ compressed graph to find separators and orderings and map back to the unit weight graph. The │ │ │ │ │ savings in time and space can be considerable. │ │ │ │ │ The Graph object has a method to find the φ map for the natural compressed graph; it requires │ │ │ │ │ O(|V|) space and O(|E|) time. There is a method to compress a graph (i.e., given G(V,E) and │ │ │ │ │ an arbitrary φ, construct G(V,E)) and a method to expand a graph (i.e., given G(V,E) and an │ │ │ │ │ @@ -57,15 +57,15 @@ │ │ │ │ │ • int totewght : total edge weight │ │ │ │ │ • IVL *adjIVL : pointer to IVL object to hold adjacency lists │ │ │ │ │ • int *vwghts : pointer to a vertex to hold vertex weights non-NULL if type % 2 == 1 │ │ │ │ │ • IVL *ewghtIVL : pointer to IVL object to hold edge weight lists, non-NULL if type / 2 == 1 │ │ │ │ │ 1.2 Prototypes and descriptions of Graph methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ Graph object. │ │ │ │ │ - Graph : DRAFT January 6, 2026 3 │ │ │ │ │ + Graph : DRAFT January 17, 2026 3 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. Graph * Graph_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Graph structure and then sets the default fields │ │ │ │ │ by a call to Graph setDefaultFields(). │ │ │ │ │ 2. void Graph_setDefaultFields ( Graph *graph ) ; │ │ │ │ │ @@ -91,15 +91,15 @@ │ │ │ │ │ int adjType, int ewghtType ) ; │ │ │ │ │ Thisisthebasicinitializer method. Anypreviousdataisclearedwithacall toGraph clearData(). │ │ │ │ │ Thenthescalar fields are set and the adjIVL object is initialized. If type is 1 or 3, the vwghts │ │ │ │ │ vector is initialized to zeros. If type is 2 or 3, the ewghtIVL object is initialized. │ │ │ │ │ Error checking: If graph is NULL, type is invalid (type must be in [0,3]), nvtx is non- │ │ │ │ │ positive, nvbnd or nedges is negative, or adjType of ewghtType is invalid (they must be │ │ │ │ │ IVL CHUNKED, IVL SOLO or IVL UNKNOWN). an error message is printed and the program exits. │ │ │ │ │ - 4 Graph : DRAFT January 6, 2026 │ │ │ │ │ + 4 Graph : DRAFT January 17, 2026 │ │ │ │ │ 2. void Graph_init2 ( Graph *graph, int type, int nvtx, int nvbnd, int nedges, │ │ │ │ │ int totvwght, int totewght, IVL *adjIVL, int *vwghts, IVL *ewghtIVL) │ │ │ │ │ This method is used by the IO read methods. When a Graph object is read from a file, │ │ │ │ │ the IVL object(s) must be initialized and then read in from the file. Therefore, we need an │ │ │ │ │ initialization method that allows us to set pointers to the IVL objects and the vwghts vector. │ │ │ │ │ Note, adjIVL, vwghts and ewghtIVL are owned by the Graph object and will be free’d when │ │ │ │ │ the Graph object is free’d. │ │ │ │ │ @@ -130,15 +130,15 @@ │ │ │ │ │ 1.2.3 Compress and Expand methods │ │ │ │ │ These three methods find an equivalence map for the natural compressed graph, compress a graph, │ │ │ │ │ and expand a graph. │ │ │ │ │ 1. IV * Graph_equivMap ( Graph *graph ) ; │ │ │ │ │ This method constructs the equivalence map from the graph to its natural compressed graph. │ │ │ │ │ The map φ : V 7→ V is then constructed (see the Introduction in this section) and put into │ │ │ │ │ an IV object that is then returned. │ │ │ │ │ - Graph : DRAFT January 6, 2026 5 │ │ │ │ │ + Graph : DRAFT January 17, 2026 5 │ │ │ │ │ Error checking: If graph is NULL or nvtx <= 0, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 2. Graph * Graph_compress ( Graph *graph, int map[], int coarseType ) ; │ │ │ │ │ Graph * Graph_compress2 ( Graph *graph, IV *mapIV, int coarseType ) ; │ │ │ │ │ This Graph and map objects (map[] or mapIV) are checked and if any errors are found, │ │ │ │ │ the appropriate message is printed and the program exits. The compressed graph object │ │ │ │ │ is constructed and returned. Note, the compressed graph does not have a boundary, even │ │ │ │ │ @@ -164,15 +164,15 @@ │ │ │ │ │ 1. int Graph_sizeOf ( Graph *graph ) ; │ │ │ │ │ This method returns the number of bytes taken by this object. │ │ │ │ │ Error checking: If graph is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. Graph_externalDegree ( Graph *graph, int v ) ; │ │ │ │ │ This method returns the weight of adj(v). │ │ │ │ │ Error checking: If graph is NULL, or v is out of range, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ - 6 Graph : DRAFT January 6, 2026 │ │ │ │ │ + 6 Graph : DRAFT January 17, 2026 │ │ │ │ │ 3. int Graph_adjAndSize ( Graph *graph, int u, int *pusize, int **puadj) ; │ │ │ │ │ This method fills *pusize with the size of the adjacency list for u and *puadj points to the │ │ │ │ │ start of the list vector. │ │ │ │ │ Error checking: If graph is NULL, or if u < 0 or u >= nvtx or if pusize or puadj is NULL, an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ 4. int Graph_adjAndEweights ( Graph *graph, int u, int *pusize, │ │ │ │ │ int **puadj, int **puewghts) ; │ │ │ │ │ @@ -205,15 +205,15 @@ │ │ │ │ │ list for the vertex in the parent graph. Each adjacency list for a boundary vertex of the │ │ │ │ │ subgraph is new storage, and only these lists are free’d when the subgraph is free’d. A map │ │ │ │ │ vector is created that maps the subgraphs’s vertices (both internal and boundary) into the │ │ │ │ │ parent graph’s vertices; the address of the map vector is put into *pmap. The adjacency lists │ │ │ │ │ for the subgraph are overwritten by the map[] vector. This renders the graph object invalid. │ │ │ │ │ The graph partitioning methods map the vertices back to their original values. Presently, │ │ │ │ │ only graphs with unit edge weights are allowed as input. │ │ │ │ │ - Graph : DRAFT January 6, 2026 7 │ │ │ │ │ + Graph : DRAFT January 17, 2026 7 │ │ │ │ │ Error checking: If graph is NULL or icomp < 0 or compids or pmap is NULL, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 8. int Graph_isSymmetric ( Graph *graph ) ; │ │ │ │ │ This method returns 1 if the graph is symmetric (i.e., edge (i,j) is present if and only if │ │ │ │ │ edge (j,i) is present) and 0 otherwise. │ │ │ │ │ Error checking: If graph is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.6 IO methods │ │ │ │ │ @@ -242,15 +242,15 @@ │ │ │ │ │ file and returns the value returned from the called routine. │ │ │ │ │ Error checking: If graph or fn are NULL, or if fn is not of the form *.graphf (for a formatted │ │ │ │ │ file) or *.graphb (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 5. int Graph_writeToFormattedFile ( Graph *graph, FILE *fp ) ; │ │ │ │ │ This method writes a Graph object to a formatted file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fprintf, zero is returned. │ │ │ │ │ Error checking: If graph or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ - 8 Graph : DRAFT January 6, 2026 │ │ │ │ │ + 8 Graph : DRAFT January 17, 2026 │ │ │ │ │ 6. int Graph_writeToBinaryFile ( Graph *graph, FILE *fp ) ; │ │ │ │ │ This method writes a Graph object to a binary file. If there are no errors in writing the data, │ │ │ │ │ the value 1 is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ Error checking: If graph or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 7. int Graph_writeForHumanEye ( Graph *graph, FILE *fp ) ; │ │ │ │ │ This method writes a Graph object to a file in a human readable format. The method │ │ │ │ │ Graph writeStats()is called to write out the header and statistics. The value 1 is returned. │ │ │ │ │ @@ -276,15 +276,15 @@ │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ 2. compressGraph msglvl msgFile inGraphFile coarseType outMapFile outGraphFile │ │ │ │ │ This driver program reads in a Graph object from a file, computes the equivalence map to │ │ │ │ │ its natural compressed graph (the first graph need not be unit weight), and constructs the │ │ │ │ │ natural compressed graph. The equivalence map and compressed graph are optionally written │ │ │ │ │ out to files. │ │ │ │ │ - Graph : DRAFT January 6, 2026 9 │ │ │ │ │ + Graph : DRAFT January 17, 2026 9 │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ that all objects are written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • TheinGraphFileparameteristheinputfilefortheGraphobject. It mustbeof theform │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ @@ -317,15 +317,15 @@ │ │ │ │ │ (if inMapFile is of the form *.ivf), or a binary file (if inMapFile is of the form *.ivb). │ │ │ │ │ • The outGraphFile parameter is the output file for the compressed Graph object. If │ │ │ │ │ outGraphFile is none then the Graph object is not written to a file. Otherwise, │ │ │ │ │ the Graph writeToFile() method is called to write the graph to a formatted file (if │ │ │ │ │ outGraphFile is of the form *.graphf), or a binary file (if outGraphFile is of the form │ │ │ │ │ *.graphb). │ │ │ │ │ 4. mkGridGraph msglvl msgFile stencil n1 n2 n3 outFile │ │ │ │ │ - 10 Graph : DRAFT January 6, 2026 │ │ │ │ │ + 10 Graph : DRAFT January 17, 2026 │ │ │ │ │ This driver program creates a Graph object for a finite difference operator on a n1×n2×n3 │ │ │ │ │ regular grid. │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ that all objects are written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ @@ -355,15 +355,15 @@ │ │ │ │ │ Graph isSymmetric() method. This was useful in one application where the Graph object │ │ │ │ │ was constructed improperly. │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the Graph object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ - Graph : DRAFT January 6, 2026 11 │ │ │ │ │ + Graph : DRAFT January 17, 2026 11 │ │ │ │ │ • The inFile parameter is the input file for the Graph object. It must be of the form │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ 7. testWirebasket msglvl msgFile inGraphFile inStagesFile │ │ │ │ │ outStagesFile radius │ │ │ │ │ This driver program reads in a Graph object and and a file that contains the stages ids of the │ │ │ │ │ vertices, (stage equal to zero means the vertex is in the Schur complement), and overwrites the │ │ │ │ │ @@ -386,15 +386,15 @@ │ │ │ │ │ the form *.ivf or *.ivb. The IV object is written to the file via the IV writeToFile() │ │ │ │ │ method. │ │ │ │ │ • The radius parameter is used to define the stage of a Schur complement vertex, namely │ │ │ │ │ the stage is the number of domains that are found within radius edges of the vertex. │ │ │ │ │ The two plots below illustrate the wirebasket stages for a 15×15 grid. They show the stages │ │ │ │ │ for radius = 1 on the left and radius = 2 on the right. The domains are 3 × 3 subgrids │ │ │ │ │ whose vertices have labels equal to zero. │ │ │ │ │ - 12 Graph : DRAFT January 6, 2026 │ │ │ │ │ + 12 Graph : DRAFT January 17, 2026 │ │ │ │ │ 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 │ │ │ │ │ 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 │ │ │ │ │ 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 4 0 0 0 4 0 0 0 4 0 0 0 │ │ │ │ │ 2 2 2 4 2 2 2 4 2 2 2 4 2 2 2 2 2 4 4 4 2 4 4 4 2 4 4 4 2 2 │ │ │ │ │ 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 4 0 0 0 4 0 0 0 4 0 0 0 │ │ │ │ │ 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 │ │ │ │ │ 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 4 0 0 0 4 0 0 0 4 0 0 0 │ │ ├── ./usr/share/doc/spooles-doc/I2Ohash.ps.gz │ │ │ ├── I2Ohash.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o I2Ohash.ps │ │ │ │ %DVIPSParameters: dpi=600 │ 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Fi(DRAFT)30 b Fh(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2819 100 V 0 399 a Fj(1.3)135 b(Driv)l(er)46 │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fm(4)p 136 100 1059 4 v │ │ │ │ +1240 w Fl(I2Ohash)29 b Fh(:)40 b Fi(DRAFT)31 b Fh(Jan)m(uary)f(17,)h │ │ │ │ +(2026)p 2842 100 V 0 399 a Fj(1.3)135 b(Driv)l(er)46 │ │ │ │ b(programs)g(for)f(the)g Fg(I2Ohash)58 b(object)111 626 │ │ │ │ y Fm(1.)46 b Fl(test_hash)g(msglvl)g(msgFile)f(size)i(grow)g(maxkey)f │ │ │ │ (nent)g(seed)227 777 y Fm(This)34 b(driv)m(er)h(program)g(tests)h(the)f │ │ │ │ Fl(I2Ohash)e Fm(insert)i(metho)s(d.)54 b(It)35 b(inserts)f(a)i(n)m(um)m │ │ │ │ (b)s(er)d(of)i(triples)h(in)m(to)g(a)227 890 y(hash)d(table)h(and)e │ │ │ │ (prin)m(ts)h(out)g(the)h(\\measure")g(of)f(ho)m(w)g(w)m(ell)h │ │ │ │ (distributed)f(the)g(en)m(tries)h(are)f(in)g(the)h(hash)227 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -21,15 +21,15 @@ │ │ │ │ │ • int nlist : number of lists in the hash table │ │ │ │ │ • int grow : when no I2OP objects are available to insert a new triple, │ │ │ │ │ the object can allocate grow more I2OP objects and put them on the free list. │ │ │ │ │ • nitem : number of items in the hash table. │ │ │ │ │ • I2OP *baseI2OP : pointer to an I2OP object that keeps track of all the I2OP objects that │ │ │ │ │ have been allocated by the hash table. │ │ │ │ │ 1 │ │ │ │ │ - 2 I2Ohash : DRAFT January 6, 2026 │ │ │ │ │ + 2 I2Ohash : DRAFT January 17, 2026 │ │ │ │ │ • I2OP *freeI2OP : pointer to the first I2OP object on the free list. │ │ │ │ │ • I2OP **heads : pointer to a vector of pointers to I2OP objects, used to hold a pointer to the │ │ │ │ │ first I2OP object in each list. │ │ │ │ │ Acorrectly initialized and nontrivial I2Ohash object will have nlist > 0. If grow is zero and │ │ │ │ │ a new triple is given to the hash table to be inserted, a fatal error occurs. │ │ │ │ │ 1.2 Prototypes and descriptions of I2Ohash methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ @@ -51,15 +51,15 @@ │ │ │ │ │ Error checking: If hashtable is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void I2Ohash_free ( I2Ohash *hashtable ) ; │ │ │ │ │ This method releases any storage by a call to I2Ohash clearData() then free’s the storage │ │ │ │ │ for the structure with a call to free(). │ │ │ │ │ Error checking: If hashtable is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.2 Initializer methods │ │ │ │ │ There is one initializer method. │ │ │ │ │ - I2Ohash : DRAFT January 6, 2026 3 │ │ │ │ │ + I2Ohash : DRAFT January 17, 2026 3 │ │ │ │ │ 1. void I2Ohash_init ( I2Ohash *hashtable, int nlist, int nobj, int grow ) ; │ │ │ │ │ This method is the basic initializer method. It clears any previous data with a call to │ │ │ │ │ I2Ohash clearData(). It allocates storage for nlist lists and if nobj is positive, it loads the │ │ │ │ │ free list with nobj I2OP objects. │ │ │ │ │ Error checking: If hashtable is NULL, or if nlist ≤ 0, or if nobj and grow are both zero, an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ 1.2.3 Utility methods │ │ │ │ │ @@ -92,15 +92,15 @@ │ │ │ │ │ the triples are evenly distributed among nlist/k lists, the value is √k. │ │ │ │ │ Error checking: If hashtable is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.4 IO methods │ │ │ │ │ 1. void I2Ohash_writeForHumanEye ( I2Ohash *hashtable, FILE *fp ) ; │ │ │ │ │ This method prints the hash table in a human-readable format. │ │ │ │ │ Error checking: If hashtable or fp is NULL, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - 4 I2Ohash : DRAFT January 6, 2026 │ │ │ │ │ + 4 I2Ohash : DRAFT January 17, 2026 │ │ │ │ │ 1.3 Driver programs for the I2Ohash object │ │ │ │ │ 1. test_hash msglvl msgFile size grow maxkey nent seed │ │ │ │ │ This driver program tests the I2Ohash insert method. It inserts a number of triples into a │ │ │ │ │ hash table and prints out the “measure” of how well distributed the entries are in the hash │ │ │ │ │ table. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ timing output. │ │ ├── ./usr/share/doc/spooles-doc/IIheap.ps.gz │ │ │ ├── IIheap.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o IIheap.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1276,16 +1276,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ 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│ │ │ A correctly initialized and nontrivial IIheap object will have maxsize > 0 and 0 <= size < │ │ │ │ │ maxsize. │ │ │ │ │ 1.2 Prototypes and descriptions of IIheap methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ IIheap object. │ │ │ │ │ 1 │ │ │ │ │ - 2 IIheap : DRAFT January 6, 2026 │ │ │ │ │ + 2 IIheap : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. IIheap * IIheap_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the IIheap structure and then sets the default fields │ │ │ │ │ by a call to IIheap setDefaultFields(). │ │ │ │ │ 2. void IIheap_setDefaultFields ( IIheap *heap ) ; │ │ │ │ │ @@ -49,15 +49,15 @@ │ │ │ │ │ IVinit(). The entries in the three vectors are set to -1. │ │ │ │ │ Error checking: If heap is NULL, or if maxsize ≤ 0, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 1.2.3 Utility methods │ │ │ │ │ 1. int IIheap_sizeOf ( IIheap *heap ) ; │ │ │ │ │ This method returns the number of bytes taken by this object. │ │ │ │ │ Error checking: If heap is NULL, an error message is printed and the program exits. │ │ │ │ │ - IIheap : DRAFT January 6, 2026 3 │ │ │ │ │ + IIheap : DRAFT January 17, 2026 3 │ │ │ │ │ 2. void IIheap_root ( IIheap *heap, int *pkey, int *pvalue ) ; │ │ │ │ │ This method fills *pid and *pkey with the key and value, respectively, of the root element, │ │ │ │ │ an element with minimum value. If size == 0 then -1 is returned. │ │ │ │ │ Error checking: If heap, pkey or pvalue is NULL, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 3. void IIheap_insert ( IIheap *heap, int key, int value ) ; │ │ │ │ │ This method inserts the pair (key,value) into the heap. │ │ ├── ./usr/share/doc/spooles-doc/IV.ps.gz │ │ │ ├── IV.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o IV.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ 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(int)h(*entries)f(\))h(;)227 747 y Fj(This)36 b(metho)s(d)g │ │ │ │ (initializes)j(the)d(ob)5 b(ject)38 b(giv)m(en)f(a)g(size)h(for)e(the)h │ │ │ │ (v)m(ector)h(and)e(a)h(p)s(ossible)f(p)s(oin)m(ter)g(to)i(the)227 │ │ │ │ 860 y(v)m(ectors)28 b(storage.)41 b(An)m(y)26 b(previous)g(data)h(with) │ │ │ │ f(a)h(call)g(to)g Fi(IV)p 2277 860 29 4 v 34 w(clearData\(\))p │ │ │ │ Fj(.)36 b(If)26 b Fi(entries)46 b(!=)h(NULL)25 b Fj(then)227 │ │ │ │ @@ -4110,17 +4121,17 @@ │ │ │ │ (v)m(ector)j(b)m(y)d Fi(offset)p Fj(.)46 b(This)31 b(is)i(a)g │ │ │ │ (dangerous)f(metho)s(d)g(to)h(use)g(b)s(ecause)f(the)h(state)h(of)227 │ │ │ │ 5407 y(the)j(v)m(ector)h(is)e(lost,)j(namely)e Fi(vec)p │ │ │ │ Fj(,)g(the)g(base)f(of)h(the)f(en)m(tries,)j(is)e(corrupted.)58 │ │ │ │ b(If)35 b(the)i(ob)5 b(ject)37 b(o)m(wns)g(its)p eop │ │ │ │ end │ │ │ │ %%Page: 5 5 │ │ │ │ -TeXDict begin 5 4 bop 91 100 1206 4 v 1387 100 a Fi(IV)30 │ │ │ │ -b Fe(:)g Fd(DRAFT)121 b Fe(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2647 100 V 1206 w Fj(5)227 399 y(en)m(tries)e(and)e Fi(IV)p │ │ │ │ +TeXDict begin 5 4 bop 91 100 1183 4 v 1364 100 a Fi(IV)30 │ │ │ │ +b Fe(:)h Fd(DRAFT)121 b Fe(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2670 100 V 1183 w Fj(5)227 399 y(en)m(tries)e(and)e Fi(IV)p │ │ │ │ 792 399 29 4 v 34 w(free\(\))p Fj(,)g Fi(IV)p 1262 399 │ │ │ │ V 34 w(setSize\(\))e Fj(or)j Fi(IV)p 1958 399 V 34 w(setMaxsize\(\))d │ │ │ │ Fj(is)j(called)h(b)s(efore)f(the)g(base)g(has)g(b)s(een)227 │ │ │ │ 511 y(shifted)h(bac)m(k)g(to)g(its)h(original)f(p)s(osition,)h(a)f │ │ │ │ (segmen)m(tation)i(violation)f(will)f(lik)m(ely)i(result.)40 │ │ │ │ b(This)28 b(is)g(a)i(v)m(ery)227 624 y(useful)g(metho)s(d,)g(but)g(use) │ │ │ │ g(with)g(caution.)227 779 y Fd(Err)-5 b(or)34 b(che)-5 │ │ │ │ @@ -4181,17 +4192,17 @@ │ │ │ │ (;)227 5294 y Fj(This)24 b(metho)s(d)f(examines)i(the)g(en)m(tries)g │ │ │ │ (in)f(the)g(v)m(ector.)40 b(Let)25 b Fi(k)f Fj(b)s(e)g(en)m(try)g │ │ │ │ Fi(i)g Fj(in)g(the)h(v)m(ector.)40 b(If)24 b Fi(tags[k])46 │ │ │ │ b(!=)227 5407 y(keepTag)p Fj(,)28 b(the)i(en)m(try)g(is)g(mo)m(v)m(ed)g │ │ │ │ (to)h(the)f(end)f(of)g(the)h(v)m(ector,)i(otherwise)e(it)g(is)g(mo)m(v) │ │ │ │ m(ed)g(to)h(the)f(b)s(eginning)p eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fj(6)p 136 100 1206 4 v │ │ │ │ -1388 w Fi(IV)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2695 100 V 227 399 a Fj(of)f(the)g(v)m(ector.)42 b(The)29 │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fj(6)p 136 100 1183 4 v │ │ │ │ +1365 w Fi(IV)30 b Fe(:)g Fd(DRAFT)g Fe(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2717 100 V 227 399 a Fj(of)e(the)g(v)m(ector.)42 b(The)29 │ │ │ │ b(size)h(of)g(the)g(v)m(ector)h(is)e(reset)i(to)f(b)s(e)f(the)g(n)m(um) │ │ │ │ m(b)s(er)g(of)g(tagged)i(en)m(tries)g(that)f(are)g(no)m(w)227 │ │ │ │ 511 y(in)g(the)h(leading)g(lo)s(cations.)227 660 y Fd(Err)-5 │ │ │ │ b(or)34 b(che)-5 b(cking:)40 b Fj(If)30 b Fi(iv)g Fj(of)h │ │ │ │ Fi(tags)e Fj(is)h Fi(NULL)f Fj(an)i(error)f(message)h(is)g(prin)m(ted)f │ │ │ │ (and)f(the)i(program)f(exits.)111 844 y(9.)46 b Fi(void)h │ │ │ │ (IV_filterPurge)d(\()j(IV)g(*iv,)g(int)g(tags[],)f(int)h(purgeTag)e(\)) │ │ │ │ @@ -4250,17 +4261,17 @@ │ │ │ │ Fi(loc)p Fj('th)g(lo)s(cation)h(of)g(the)f Fi(iv)f Fj(ob)5 │ │ │ │ b(ject)39 b(b)m(y)f(one)h(and)e(returns)g(the)h(new)227 │ │ │ │ 5146 y(v)-5 b(alue.)227 5294 y Fd(Err)g(or)38 b(che)-5 │ │ │ │ b(cking:)49 b Fj(If)34 b Fi(iv)g Fj(is)h Fi(NULL)f Fj(or)g(if)h │ │ │ │ Fi(loc)f Fj(is)h(out)g(of)f(range,)j(an)d(error)h(message)h(is)e(prin)m │ │ │ │ (ted)h(and)f(the)227 5407 y(program)c(exits.)p eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 91 100 1206 4 v 1387 100 a Fi(IV)30 │ │ │ │ -b Fe(:)g Fd(DRAFT)121 b Fe(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2647 100 V 1206 w Fj(7)66 399 y(15.)46 b Fi(int)h(IV_findValue)e(\()i │ │ │ │ +TeXDict begin 7 6 bop 91 100 1183 4 v 1364 100 a Fi(IV)30 │ │ │ │ +b Fe(:)h Fd(DRAFT)121 b Fe(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2670 100 V 1183 w Fj(7)66 399 y(15.)46 b Fi(int)h(IV_findValue)e(\()i │ │ │ │ (IV)g(*iv,)g(int)g(value)f(\))i(;)227 547 y Fj(This)30 │ │ │ │ b(metho)s(d)f(lo)s(oks)i(for)e Fi(value)g Fj(in)h(its)g(en)m(tries.)42 │ │ │ │ b(If)29 b Fi(value)g Fj(is)h(presen)m(t,)g(the)h(\014rst)e(lo)s(cation) │ │ │ │ j(is)e(returned,)227 660 y(otherwise)h Fi(-1)f Fj(is)g(returned.)40 │ │ │ │ b(The)30 b(cost)h(is)f(linear)h(in)f(the)h(n)m(um)m(b)s(er)e(of)h(en)m │ │ │ │ (tries.)227 808 y Fd(Err)-5 b(or)34 b(che)-5 b(cking:)40 │ │ │ │ b Fj(If)30 b Fi(iv)g Fj(is)h Fi(NULL)p Fj(,)e(an)h(error)g(message)i │ │ │ │ @@ -4331,17 +4342,17 @@ │ │ │ │ 5294 y Fd(Err)-5 b(or)36 b(che)-5 b(cking:)43 b Fj(If)31 │ │ │ │ b Fi(iv)g Fj(or)h Fi(fn)f Fj(are)i Fi(NULL)p Fj(,)d(or)i(if)g │ │ │ │ Fi(fn)f Fj(is)h(not)g(of)g(the)g(form)g Fi(*.ivf)e Fj(\(for)i(a)g │ │ │ │ (formatted)g(\014le\))227 5407 y(or)f Fi(*.ivb)e Fj(\(for)h(a)h(binary) │ │ │ │ e(\014le\),)j(an)e(error)g(message)h(is)g(prin)m(ted)f(and)f(the)i │ │ │ │ (metho)s(d)f(returns)f(zero.)p eop end │ │ │ │ %%Page: 8 8 │ │ │ │ -TeXDict begin 8 7 bop 0 100 a Fj(8)p 136 100 1206 4 v │ │ │ │ -1388 w Fi(IV)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2695 100 V 111 399 a Fj(2.)46 b Fi(int)h(IV_readFromFormattedFile)41 │ │ │ │ +TeXDict begin 8 7 bop 0 100 a Fj(8)p 136 100 1183 4 v │ │ │ │ +1365 w Fi(IV)30 b Fe(:)g Fd(DRAFT)g Fe(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2717 100 V 111 399 a Fj(2.)46 b Fi(int)h(IV_readFromFormattedFile)41 │ │ │ │ b(\()48 b(IV)f(*iv,)g(FILE)f(*fp)h(\))h(;)227 550 y Fj(This)27 │ │ │ │ b(metho)s(d)g(reads)h(in)f(an)g Fi(IV)g Fj(ob)5 b(ject)29 │ │ │ │ b(from)e(a)h(formatted)g(\014le.)40 b(If)27 b(there)h(are)g(no)g │ │ │ │ (errors)f(in)g(reading)h(the)227 663 y(data,)k(the)e(v)-5 │ │ │ │ b(alue)31 b Fi(1)f Fj(is)g(returned.)40 b(If)30 b(an)g(IO)g(error)g(is) │ │ │ │ g(encoun)m(tered)h(from)f Fi(fscanf)p Fj(,)f(zero)i(is)g(returned.)227 │ │ │ │ 815 y Fd(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fj(If)30 │ │ │ │ @@ -4419,17 +4430,17 @@ │ │ │ │ h(separated)g(b)m(y)g(a)g(whitespace.)40 b(The)227 5255 │ │ │ │ y(v)-5 b(alue)31 b Fi(1)f Fj(is)h(returned.)227 5407 │ │ │ │ y Fd(Err)-5 b(or)27 b(che)-5 b(cking:)36 b Fj(If)22 b │ │ │ │ Fi(iv)g Fj(or)g Fi(fp)g Fj(or)g Fi(pierr)f Fj(are)i Fi(NULL)p │ │ │ │ Fj(,)e(an)i(error)f(message)h(is)g(prin)m(ted)e(and)h(zero)h(is)g │ │ │ │ (returned.)p eop end │ │ │ │ %%Page: 9 9 │ │ │ │ -TeXDict begin 9 8 bop 91 100 1206 4 v 1387 100 a Fi(IV)30 │ │ │ │ -b Fe(:)g Fd(DRAFT)121 b Fe(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2647 100 V 1206 w Fj(9)66 399 y(10.)46 b Fi(int)h(IV_writeForMatlab)c │ │ │ │ +TeXDict begin 9 8 bop 91 100 1183 4 v 1364 100 a Fi(IV)30 │ │ │ │ +b Fe(:)h Fd(DRAFT)121 b Fe(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2670 100 V 1183 w Fj(9)66 399 y(10.)46 b Fi(int)h(IV_writeForMatlab)c │ │ │ │ (\()48 b(IV)f(*iv,)g(char)f(*name,)g(FILE)h(*fp)g(\))g(;)227 │ │ │ │ 549 y Fj(This)37 b(metho)s(d)h(writes)f(the)i(en)m(tries)f(of)g(the)g │ │ │ │ (v)m(ector)i(to)e(a)g(\014le)g(suitable)h(to)f(b)s(e)g(read)f(b)m(y)h │ │ │ │ (Matlab.)64 b(The)227 662 y(c)m(haracter)31 b(string)e │ │ │ │ Fi(name)f Fj(is)h(the)g(name)g(of)g(the)g(v)m(ector,)i(e.g,)g(if)e │ │ │ │ Fi(name)46 b(=)i("A")p Fj(,)28 b(then)h(w)m(e)g(ha)m(v)m(e)h(lines)g │ │ │ │ (of)f(the)227 775 y(form)227 1000 y Fi(A\(1\))47 b(=)g(32)h(;)227 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -24,15 +24,15 @@ │ │ │ │ │ IV setMaxsize() methods) than it is to duplicate code to work on an int vector. │ │ │ │ │ Onemustchoose where to use this object. There is a substantial performance penalty for doing the │ │ │ │ │ simplest operations, and so when we need to manipulate an int vector inside a loop, we extract │ │ │ │ │ out the size and pointer to the base array from the IV object. On the other hand, the convenience │ │ │ │ │ makes it a widely used object. Originally its use was restricted to reading and writing *.iv{f,b} │ │ │ │ │ files, but now IV objects appear much more frequently in new development. │ │ │ │ │ 1 │ │ │ │ │ - 2 IV : DRAFT January 6, 2026 │ │ │ │ │ + 2 IV : DRAFT January 17, 2026 │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ The IV structure has four fields. │ │ │ │ │ • int size : present size of the vector. │ │ │ │ │ • int maxsize : maximum size of the vector. │ │ │ │ │ • int owned : owner flag for the data. When owned = 1, storage for maxsize int’s has been │ │ │ │ │ allocated by this object and can be free’d by the object. When nowned = 0 but maxsize > │ │ │ │ │ 0, this object points to entries that have been allocated elsewhere, and these entries will not │ │ │ │ │ @@ -58,15 +58,15 @@ │ │ │ │ │ the storage for vec is free’d by a call to IVfree(). The structure’s default fields are then set │ │ │ │ │ with a call to IV setDefaultFields(). │ │ │ │ │ Error checking: If iv is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void IV_free ( IV *iv ) ; │ │ │ │ │ This method releases any storage by a call to IV clearData() then free’s the storage for the │ │ │ │ │ structure with a call to free(). │ │ │ │ │ Error checking: If iv is NULL, an error message is printed and the program exits. │ │ │ │ │ - IV : DRAFT January 6, 2026 3 │ │ │ │ │ + IV : DRAFT January 17, 2026 3 │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ These method allow access to information in the data fields without explicitly following pointers. │ │ │ │ │ There is overhead involved with these method due to the function call and error checking inside │ │ │ │ │ the methods. │ │ │ │ │ 1. int IV_owned ( IV *iv ) ; │ │ │ │ │ This method returns the value of owned. If owned = 1, then the object owns the data pointed │ │ │ │ │ to by vec and will free this data with a call to IVfree() when its data is cleared by a call to │ │ │ │ │ @@ -91,15 +91,15 @@ │ │ │ │ │ the vector. │ │ │ │ │ Error checking: If iv, psize or pentries is NULL an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 7. void IV_setEntry ( IV *iv, int loc, int value ) ; │ │ │ │ │ This method sets the loc’th entry of the vector to value. │ │ │ │ │ Error checking: If iv, loc < 0 or loc >= size, or if vec is NULL an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ - 4 IV : DRAFT January 6, 2026 │ │ │ │ │ + 4 IV : DRAFT January 17, 2026 │ │ │ │ │ 1.2.3 Initializer methods │ │ │ │ │ 1. void IV_init ( IV *iv, int size, int *entries ) ; │ │ │ │ │ This method initializes the object given a size for the vector and a possible pointer to the │ │ │ │ │ vectors storage. Any previous data with a call to IV clearData(). If entries != NULL then │ │ │ │ │ the vec field is set to entries, the size and maxsize fields are set to size , and owned is │ │ │ │ │ set to zero because the object does not own the entries. If entries is NULL and if size > 0 │ │ │ │ │ then a vector is allocated by the object, and the object owns this storage. │ │ │ │ │ @@ -128,15 +128,15 @@ │ │ │ │ │ Error checking: If iv is NULL or newsize < 0, or if 0 < maxsize < newsize and owned == │ │ │ │ │ 0, an error message is printed and the program exits. │ │ │ │ │ 1.2.4 Utility methods │ │ │ │ │ 1. void IV_shiftBase ( IV *iv, int offset ) ; │ │ │ │ │ This method shifts the base entries of the vector and decrements the present size and max- │ │ │ │ │ imum size of the vector by offset. This is a dangerous method to use because the state of │ │ │ │ │ the vector is lost, namely vec, the base of the entries, is corrupted. If the object owns its │ │ │ │ │ - IV : DRAFT January 6, 2026 5 │ │ │ │ │ + IV : DRAFT January 17, 2026 5 │ │ │ │ │ entries and IV free(), IV setSize() or IV setMaxsize() is called before the base has been │ │ │ │ │ shifted back to its original position, a segmentation violation will likely result. This is a very │ │ │ │ │ useful method, but use with caution. │ │ │ │ │ Error checking: If iv is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. void IV_push ( IV *iv, int val ) ; │ │ │ │ │ This method pushes an entry onto the vector. If the vector is full, i.e., if size = maxsize │ │ │ │ │ - 1, then the size of the vector is doubled if possible. If the storage cannot grow, i.e., if the │ │ │ │ │ @@ -164,15 +164,15 @@ │ │ │ │ │ the program exits. │ │ │ │ │ 7. int IV_sizeOf ( IV *iv ) ; │ │ │ │ │ This method returns the number of bytes taken by the object. │ │ │ │ │ Error checking: If iv is NULL an error message is printed and the program exits. │ │ │ │ │ 8. void IV_filterKeep ( IV *iv, int tags[], int keepTag ) ; │ │ │ │ │ This method examines the entries in the vector. Let k be entry i in the vector. If tags[k] != │ │ │ │ │ keepTag, the entry is moved to the end of the vector, otherwise it is moved to the beginning │ │ │ │ │ - 6 IV : DRAFT January 6, 2026 │ │ │ │ │ + 6 IV : DRAFT January 17, 2026 │ │ │ │ │ of the vector. The size of the vector is reset to be the number of tagged entries that are now │ │ │ │ │ in the leading locations. │ │ │ │ │ Error checking: If iv of tags is NULL an error message is printed and the program exits. │ │ │ │ │ 9. void IV_filterPurge ( IV *iv, int tags[], int purgeTag ) ; │ │ │ │ │ This method examines the entries in the vector. Let k be entry i in the vector. If tags[k] == │ │ │ │ │ purgeTag, the entry is moved to the end of the vector, otherwise it is moved to the beginning │ │ │ │ │ of the vector. The size of the vector is reset to be the number of untagged entries that are │ │ │ │ │ @@ -201,15 +201,15 @@ │ │ │ │ │ Error checking: If iv is NULL or if loc is out of range, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 14. int IV_decrement ( IV *iv, int loc ) ; │ │ │ │ │ This method decrements the loc’th location of the iv object by one and returns the new │ │ │ │ │ value. │ │ │ │ │ Error checking: If iv is NULL or if loc is out of range, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ - IV : DRAFT January 6, 2026 7 │ │ │ │ │ + IV : DRAFT January 17, 2026 7 │ │ │ │ │ 15. int IV_findValue ( IV *iv, int value ) ; │ │ │ │ │ This method looks for value in its entries. If value is present, the first location is returned, │ │ │ │ │ otherwise -1 is returned. The cost is linear in the number of entries. │ │ │ │ │ Error checking: If iv is NULL, an error message is printed and the program exits. │ │ │ │ │ 16. int IV_findValueAscending ( IV *iv, int value ) ; │ │ │ │ │ Thismethodlooksforvalueinitsentries. Ifvalueispresent, alocation isreturned, otherwise │ │ │ │ │ -1 is returned. This method assumes that the entries are sorted in ascending order. The cost │ │ │ │ │ @@ -238,15 +238,15 @@ │ │ │ │ │ is size, followed by the size entries found in vec[]. │ │ │ │ │ 1. int IV_readFromFile ( IV *iv, char *fn ) ; │ │ │ │ │ This method reads an IV object from a formatted file. It tries to open the file and if it is │ │ │ │ │ successful, it then calls IV readFromFormattedFile() or IV readFromBinaryFile(), closes │ │ │ │ │ the file and returns the value returned from the called routine. │ │ │ │ │ Error checking: If iv or fn are NULL, or if fn is not of the form *.ivf (for a formatted file) │ │ │ │ │ or *.ivb (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ - 8 IV : DRAFT January 6, 2026 │ │ │ │ │ + 8 IV : DRAFT January 17, 2026 │ │ │ │ │ 2. int IV_readFromFormattedFile ( IV *iv, FILE *fp ) ; │ │ │ │ │ This method reads in an IV object from a formatted file. If there are no errors in reading the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fscanf, zero is returned. │ │ │ │ │ Error checking: If iv or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 3. int IV_readFromBinaryFile ( IV *iv, FILE *fp ) ; │ │ │ │ │ This method reads in an IV object from a binary file. If there are no errors in reading the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fread, zero is returned. │ │ │ │ │ @@ -274,15 +274,15 @@ │ │ │ │ │ This method writes the header and statistics to a file. The value 1 is returned. │ │ │ │ │ Error checking: If iv or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 9. int IV_fp80 ( IV *iv, FILE *fp, int column, int *pierr ) ; │ │ │ │ │ This method is just a wrapper around the IVfp80() method for an int method. The entries │ │ │ │ │ in the vector are found on lines with eighty columns and are separated by a whitespace. The │ │ │ │ │ value 1 is returned. │ │ │ │ │ Error checking: If iv or fp or pierr are NULL, an error message is printed and zero is returned. │ │ │ │ │ - IV : DRAFT January 6, 2026 9 │ │ │ │ │ + IV : DRAFT January 17, 2026 9 │ │ │ │ │ 10. int IV_writeForMatlab ( IV *iv, char *name, FILE *fp ) ; │ │ │ │ │ This method writes the entries of the vector to a file suitable to be read by Matlab. The │ │ │ │ │ character string name is the name of the vector, e.g, if name = "A", then we have lines of the │ │ │ │ │ form │ │ │ │ │ A(1) = 32 ; │ │ │ │ │ A(2) = -433 ; │ │ │ │ │ ... │ │ ├── ./usr/share/doc/spooles-doc/IVL.ps.gz │ │ │ ├── IVL.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o IVL.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 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b(storage)i(held)d(b)m(y)h(the)g │ │ │ │ Fi(Ichunk)e Fj(structures)h(is)h(free'd,)h(and)227 792 │ │ │ │ y(if)c Fi(sizes)e Fj(or)h Fi(p)p 745 792 V 34 w(vec)f │ │ │ │ @@ -4072,17 +4083,17 @@ │ │ │ │ (int)g(incr)f(\))i(;)227 5126 y Fj(This)30 b(metho)s(d)g(sets)g(the)h │ │ │ │ (storage)h(incremen)m(t)f(to)g Fi(incr)p Fj(.)227 5294 │ │ │ │ y Fd(Err)-5 b(or)27 b(che)-5 b(cking:)36 b Fj(If)21 b │ │ │ │ Fi(ivl)g Fj(is)i Fi(NULL)e Fj(or)h Fi(incr)f Fj(is)h(negativ)m(e,)k(an) │ │ │ │ c(error)f(message)j(is)e(prin)m(ted)f(and)h(the)g(program)227 │ │ │ │ 5407 y(exits.)p eop end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fj(4)p 136 100 1182 4 v │ │ │ │ -1364 w Fi(IVL)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2719 100 V 0 399 a Fa(1.2.3)112 b(Initialization)39 b(and)f(resizing)g │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fj(4)p 136 100 1159 4 v │ │ │ │ +1341 w Fi(IVL)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2741 100 V 0 399 a Fa(1.2.3)112 b(Initialization)39 b(and)f(resizing)g │ │ │ │ (metho)s(ds)111 606 y Fj(1.)46 b Fi(void)h(IVL_init1)e(\()j(IVL)f │ │ │ │ (*ivl,)f(int)h(type,)f(int)h(maxnlist)f(\))h(;)227 767 │ │ │ │ y Fj(This)34 b(metho)s(d)g(is)g(used)g(when)f(only)i(the)f(n)m(um)m(b)s │ │ │ │ (er)f(of)i(lists)g(is)f(kno)m(wn.)52 b(An)m(y)35 b(previous)e(data)j │ │ │ │ (is)e(cleared)227 879 y(with)c(a)f(call)i(to)g Fi(IVL)p │ │ │ │ 935 879 29 4 v 33 w(clearData\(\))p Fj(.)37 b(The)30 │ │ │ │ b Fi(type)e Fj(\014eld)h(is)h(set.)41 b(If)29 b Fi(maxnlist)45 │ │ │ │ @@ -4161,17 +4172,17 @@ │ │ │ │ 5085 y Fd(Err)-5 b(or)32 b(che)-5 b(cking:)40 b Fj(If)27 │ │ │ │ b Fi(ivl)h Fj(is)g Fi(NULL)f Fj(or)i(if)f Fi(newmaxnlist)d │ │ │ │ Fj(is)k(negativ)m(e,)i(an)d(error)g(message)h(is)g(prin)m(ted)f(and)227 │ │ │ │ 5198 y(the)j(program)f(exits.)111 5407 y(6.)46 b Fi(void)h │ │ │ │ (IVL_setNlist)d(\()k(IVL)f(*ivl,)f(int)h(newnlist)f(\))h(;)p │ │ │ │ eop end │ │ │ │ %%Page: 5 5 │ │ │ │ -TeXDict begin 5 4 bop 91 100 1182 4 v 1363 100 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(ossibly\))i(p)s(oin)m(ter)f(to)h(a)g(list)f(of)h(en)m(tries.)68 │ │ │ │ b(The)39 b(b)s(eha)m(vior)g(of)h(the)227 5407 y(metho)s(d)30 │ │ │ │ b(dep)s(ends)f(on)h(the)g(t)m(yp)s(e)h(of)g(the)f Fi(ivl)g │ │ │ │ Fj(ob)5 b(ject.)41 b(Here)31 b(is)f(the)h(\015o)m(w)f(c)m(hart:)p │ │ │ │ eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fj(6)p 136 100 1182 4 v │ │ │ │ -1364 w Fi(IVL)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2719 100 V 605 311 2918 4 v 605 2506 4 2196 v 663 414 │ │ │ │ -a Fj(if)g Fi(ilist)46 b(>=)h(maxnlist)28 b Fj(then)898 │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fj(6)p 136 100 1159 4 v │ │ │ │ +1341 w Fi(IVL)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2741 100 V 605 311 2918 4 v 605 2506 4 2196 v 663 414 │ │ │ │ +a Fj(if)f Fi(ilist)46 b(>=)h(maxnlist)28 b Fj(then)898 │ │ │ │ 527 y(the)j(n)m(um)m(b)s(er)e(of)h(lists)h(is)g(increased)f(via)h(a)g │ │ │ │ (call)h(to)f Fi(IVL)p 2816 527 29 4 v 33 w(setMaxnlist\(\))663 │ │ │ │ 640 y Fj(endif)663 753 y(if)g Fi(ilist)46 b(>=)h(nlist)29 │ │ │ │ b Fj(then)898 866 y Fi(nlist)g Fj(is)i(increased)663 │ │ │ │ 979 y(endif)663 1092 y(if)g Fi(isize)46 b(=)i(0)30 b │ │ │ │ Fj(then)898 1205 y(release)i(the)e(storage)i(for)f(that)f(list,)i │ │ │ │ (reclaim)f(storage)h(if)e(p)s(ossible)663 1318 y(else)i(if)e │ │ │ │ @@ -4267,17 +4278,17 @@ │ │ │ │ y(int)g(IVL_sum)f(\()h(IVL)g(*ivl)g(\))g(;)227 5246 y │ │ │ │ Fj(These)30 b(metho)s(ds)g(return)f(some)i(simple)f(information)h(ab)s │ │ │ │ (out)f(the)h(ob)5 b(ject.)227 5407 y Fd(Err)-5 b(or)34 │ │ │ │ b(che)-5 b(cking:)40 b Fj(If)30 b Fi(ivl)g Fj(is)g Fi(NULL)f │ │ │ │ Fj(then)i(an)f(error)g(message)h(is)g(prin)m(ted)f(and)f(the)i(program) │ │ │ │ f(exits.)p eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 91 100 1182 4 v 1363 100 a Fi(IVL)30 │ │ │ │ -b Fe(:)g Fd(DRAFT)121 b Fe(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2671 100 V 1182 w Fj(7)111 399 y(3.)46 b Fi(int)h(IVL_sortUp)e(\()j │ │ │ │ +TeXDict begin 7 6 bop 91 100 1159 4 v 1340 100 a Fi(IVL)30 │ │ │ │ +b Fe(:)g Fd(DRAFT)122 b Fe(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2694 100 V 1159 w Fj(7)111 399 y(3.)46 b Fi(int)h(IVL_sortUp)e(\()j │ │ │ │ (IVL)f(*ivl)f(\))i(;)227 559 y Fj(This)30 b(metho)s(d)g(sorts)g(eac)m │ │ │ │ (h)i(list)f(in)m(to)g(ascending)g(order.)227 720 y Fd(Err)-5 │ │ │ │ b(or)28 b(che)-5 b(cking:)37 b Fj(If)23 b Fi(ivl)g Fj(is)g │ │ │ │ Fi(NULL)g Fj(or)g Fi(nlist)46 b(<)i(0)23 b Fj(then)g(an)h(error)f │ │ │ │ (message)i(is)e(prin)m(ted)g(and)g(the)h(program)227 │ │ │ │ 833 y(exits.)111 1042 y(4.)46 b Fi(int)h(*)h(IVL_equivMap1)c(\()j(IVL)g │ │ │ │ (*ivl)g(\))g(;)227 1155 y(IV)95 b(*)48 b(IVL_equivMap2)c(\()j(IVL)g │ │ │ │ @@ -4345,17 +4356,17 @@ │ │ │ │ b(so)227 5246 y(w)m(e)31 b(create)h(and)e(return)f(a)i(new)f │ │ │ │ Fi(IVL)f Fj(ob)5 b(ject)31 b(that)g(con)m(tains)h(en)m(tries)f(for)f │ │ │ │ (the)h(uncompressed)e(graph.)227 5407 y Fd(Err)-5 b(or)30 │ │ │ │ b(che)-5 b(cking:)38 b Fj(If)26 b Fi(ivl)f Fj(or)h Fi(eqmapIV)e │ │ │ │ Fj(is)i Fi(NULL)p Fj(,)f(an)h(error)f(message)i(is)f(prin)m(ted)g(and)f │ │ │ │ (the)h(program)g(exits.)p eop end │ │ │ │ %%Page: 8 8 │ │ │ │ -TeXDict begin 8 7 bop 0 100 a Fj(8)p 136 100 1182 4 v │ │ │ │ -1364 w Fi(IVL)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2719 100 V 0 399 a Fa(1.2.6)112 b(Miscellaneous)40 b(metho)s(ds)111 │ │ │ │ +TeXDict begin 8 7 bop 0 100 a Fj(8)p 136 100 1159 4 v │ │ │ │ +1341 w Fi(IVL)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2741 100 V 0 399 a Fa(1.2.6)112 b(Miscellaneous)40 b(metho)s(ds)111 │ │ │ │ 598 y Fj(1.)46 b Fi(IVL)h(*)h(IVL_make9P)d(\()i(int)g(n1,)g(int)g(n2,)g │ │ │ │ (int)g(ncomp)f(\))h(;)227 752 y Fj(This)35 b(metho)s(d)g(returns)f(an)h │ │ │ │ Fi(IVL)f Fj(ob)5 b(ject)36 b(that)g(con)m(tains)h(the)e(full)g │ │ │ │ (adjacency)i(structure)d(for)h(a)h(9-p)s(oin)m(t)227 │ │ │ │ 865 y(op)s(erator)31 b(on)f(a)h Fi(n1)20 b Fc(\002)g │ │ │ │ Fi(n2)29 b Fj(grid)h(with)g Fi(ncomp)f Fj(comp)s(onen)m(ts)i(at)g(eac)m │ │ │ │ (h)h(grid)e(p)s(oin)m(t.)227 1018 y Fd(Err)-5 b(or)37 │ │ │ │ @@ -4419,17 +4430,17 @@ │ │ │ │ 5254 y(data,)h(the)e(v)-5 b(alue)31 b Fi(1)f Fj(is)g(returned.)40 │ │ │ │ b(If)30 b(an)g(IO)g(error)g(is)g(encoun)m(tered)h(from)f │ │ │ │ Fi(fscanf)p Fj(,)f(zero)i(is)g(returned.)227 5407 y Fd(Err)-5 │ │ │ │ b(or)34 b(che)-5 b(cking:)40 b Fj(If)30 b Fi(ivl)g Fj(or)g │ │ │ │ Fi(fp)g Fj(are)h Fi(NULL)e Fj(an)h(error)g(message)i(is)e(prin)m(ted)g │ │ │ │ (and)g(zero)h(is)f(returned.)p eop end │ │ │ │ %%Page: 9 9 │ │ │ │ -TeXDict begin 9 8 bop 91 100 1182 4 v 1363 100 a Fi(IVL)30 │ │ │ │ -b Fe(:)g Fd(DRAFT)121 b Fe(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2671 100 V 1182 w Fj(9)111 399 y(3.)46 b Fi(int)h │ │ │ │ +TeXDict begin 9 8 bop 91 100 1159 4 v 1340 100 a Fi(IVL)30 │ │ │ │ +b Fe(:)g Fd(DRAFT)122 b Fe(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2694 100 V 1159 w Fj(9)111 399 y(3.)46 b Fi(int)h │ │ │ │ (IVL_readFromBinaryFile)42 b(\()47 b(IVL)g(*ivl,)g(FILE)f(*fp)h(\))h(;) │ │ │ │ 227 556 y Fj(This)25 b(metho)s(d)g(reads)g(an)g Fi(IVL)g │ │ │ │ Fj(ob)5 b(ject)26 b(from)f(a)h(binary)f(\014le.)39 b(If)25 │ │ │ │ b(there)h(are)f(no)h(errors)f(in)g(reading)g(the)h(data,)227 │ │ │ │ 669 y(the)31 b(v)-5 b(alue)31 b Fi(1)f Fj(is)g(returned.)40 │ │ │ │ b(If)30 b(an)g(IO)g(error)g(is)g(encoun)m(tered)h(from)f │ │ │ │ Fi(fread)p Fj(,)f(zero)i(is)g(returned.)227 826 y Fd(Err)-5 │ │ │ │ @@ -4496,17 +4507,17 @@ │ │ │ │ Fi(IVL)e Fj(ob)5 b(ject)29 b(from)e Fi(inFile)e Fj(and)i(writes)h(out)g │ │ │ │ (the)f(ob)5 b(ject)29 b(to)f Fi(outFile)337 5294 y Ff(\210)45 │ │ │ │ b Fj(The)28 b Fi(msglvl)f Fj(parameter)i(determines)g(the)g(amoun)m(t)g │ │ │ │ (of)f(output)h(|)f(taking)i Fi(msglvl)46 b(>=)h(3)28 │ │ │ │ b Fj(means)427 5407 y(the)j Fi(IVL)e Fj(ob)5 b(ject)32 │ │ │ │ b(is)e(written)g(to)i(the)e(message)i(\014le.)p eop end │ │ │ │ %%Page: 10 10 │ │ │ │ -TeXDict begin 10 9 bop 0 100 a Fj(10)p 182 100 1159 4 │ │ │ │ -v 1341 w Fi(IVL)30 b Fe(:)g Fd(DRAFT)h Fe(Jan)m(uary)f(6,)h(2026)p │ │ │ │ -2741 100 V 337 399 a Ff(\210)45 b Fj(The)33 b Fi(msgFile)e │ │ │ │ +TeXDict begin 10 9 bop 0 100 a Fj(10)p 182 100 1136 4 │ │ │ │ +v 1319 w Fi(IVL)29 b Fe(:)i Fd(DRAFT)f Fe(Jan)m(uary)g(17,)h(2026)p │ │ │ │ +2764 100 V 337 399 a Ff(\210)45 b Fj(The)33 b Fi(msgFile)e │ │ │ │ Fj(parameter)j(determines)f(the)h(message)g(\014le)f(|)h(if)f │ │ │ │ Fi(msgFile)e Fj(is)i Fi(stdout)p Fj(,)g(then)g(the)427 │ │ │ │ 511 y(message)27 b(\014le)f(is)g Fd(stdout)p Fj(,)i(otherwise)e(a)h │ │ │ │ (\014le)f(is)f(op)s(ened)g(with)h Fd(app)-5 b(end)28 │ │ │ │ b Fj(status)e(to)g(receiv)m(e)i(an)m(y)e(output)427 624 │ │ │ │ y(data.)337 770 y Ff(\210)45 b Fj(The)25 b Fi(inFile)e │ │ │ │ Fj(parameter)i(is)g(the)g(input)f(\014le)g(for)h(the)g │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -22,15 +22,15 @@ │ │ │ │ │ Each list is allocated separately using the IVinit() function. When the IVL object is │ │ │ │ │ free’d, each list is free’d separately using the IVfree() function. │ │ │ │ │ – IVL UNKNOWN │ │ │ │ │ This storage mode is available for the cases where storage for a list is aliased to another │ │ │ │ │ location. Absolutely no free’ing of data is done when the IVL object is free’d. │ │ │ │ │ The storage management is handled by IVL setList() and IVL setPointerToList(). │ │ │ │ │ 1 │ │ │ │ │ - 2 IVL : DRAFT January 6, 2026 │ │ │ │ │ + 2 IVL : DRAFT January 17, 2026 │ │ │ │ │ • int maxnlist : maximum number of lists. │ │ │ │ │ int nlist : number of lists. │ │ │ │ │ We may not know how many lists we will need for the object — maxnlist is the dimension │ │ │ │ │ of the sizes[] and p vec[] arrays and nlist is the present number of active lists. When │ │ │ │ │ we initialize the object using one of the IVL init{1,2,3}() methods, we set nlist equal to │ │ │ │ │ maxnlist. We resize the object using IVL setMaxnlist(). │ │ │ │ │ • int tsize : total number of list entries. │ │ │ │ │ @@ -57,15 +57,15 @@ │ │ │ │ │ 1. IVL * IVL_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the IVL structure and then sets the default fields by │ │ │ │ │ a call to IVL setDefaultFields(). │ │ │ │ │ 2. void IVL_setDefaultFields ( IVL *ivl ) ; │ │ │ │ │ This method sets the default fields of the object — type = IVL NOTYPE, maxnlist, nlist │ │ │ │ │ and tsize are zero, incr is 1024, and sizes, p vec and chunk are NULL. │ │ │ │ │ Error checking: If ivl is NULL, an error message is printed and the program exits. │ │ │ │ │ - IVL : DRAFT January 6, 2026 3 │ │ │ │ │ + IVL : DRAFT January 17, 2026 3 │ │ │ │ │ 3. void IVL_clearData ( IVL *ivl ) ; │ │ │ │ │ This method clears any data allocated by this object and then sets the default fields with a │ │ │ │ │ call to IVL setDefaultFields(). Any storage held by the Ichunk structures is free’d, and │ │ │ │ │ if sizes or p vec are not NULL, they are free’d. │ │ │ │ │ Error checking: If ivl is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void IVL_free ( IVL *ivl ) ; │ │ │ │ │ This method releases any storage by a call to IVL clearData() then free’s the storage for │ │ │ │ │ @@ -87,15 +87,15 @@ │ │ │ │ │ 5. int IVL_incr ( IVL *ivl ) ; │ │ │ │ │ This method returns incr, the storage increment. │ │ │ │ │ Error checking: If ivl is NULL, an error message is printed and the program exits. │ │ │ │ │ 6. int IVL_setincr ( IVL *ivl, int incr ) ; │ │ │ │ │ This method sets the storage increment to incr. │ │ │ │ │ Error checking: If ivl is NULL or incr is negative, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - 4 IVL : DRAFT January 6, 2026 │ │ │ │ │ + 4 IVL : DRAFT January 17, 2026 │ │ │ │ │ 1.2.3 Initialization and resizing methods │ │ │ │ │ 1. void IVL_init1 ( IVL *ivl, int type, int maxnlist ) ; │ │ │ │ │ This method is used when only the number of lists is known. Any previous data is cleared │ │ │ │ │ with a call to IVL clearData(). The type field is set. If maxnlist > 0, storage is allocated │ │ │ │ │ for the sizes[] and p vec[] arrays and nlist is set to maxnlist. │ │ │ │ │ Error checking: If ivl is NULL or type is invalid or maxnlist is negative, an error message is │ │ │ │ │ printed and the program exits. │ │ │ │ │ @@ -124,15 +124,15 @@ │ │ │ │ │ newmaxnlist == maxnlist,nothingisdone. Otherwise,newstorageforsizes[]andp vec[] │ │ │ │ │ is allocated, the information for the first nlist lists is copied over, and the old storage │ │ │ │ │ free’d. Note, maxnlist is set to newmaxnlist and nlist is set to the minimum of nlist and │ │ │ │ │ newmaxnlist. │ │ │ │ │ Error checking: If ivl is NULL or if newmaxnlist is negative, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 6. void IVL_setNlist ( IVL *ivl, int newnlist ) ; │ │ │ │ │ - IVL : DRAFT January 6, 2026 5 │ │ │ │ │ + IVL : DRAFT January 17, 2026 5 │ │ │ │ │ This method is used to change the number of lists. If newnlist > maxnlist, storage for │ │ │ │ │ the lists is increased via a call to the IVL setMaxnlist() method. Then nlist is set to │ │ │ │ │ newnlist. │ │ │ │ │ Error checking: If ivl is NULL, or if newnlist is negative, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 1.2.4 List manipulation methods │ │ │ │ │ 1. void IVL_listAndSize ( IVL *ivl, int ilist, int *psize, int **pivec) ; │ │ │ │ │ @@ -151,15 +151,15 @@ │ │ │ │ │ if so an error message is printed and the program exits. In method IVL firstInList(), if │ │ │ │ │ sizes[ilist] > 0 and p vec[ilist] = NULL, an error message is printed and the program │ │ │ │ │ exits. In method IVL nextInList(), if pi is not in the valid range for list ilist, an error │ │ │ │ │ message is printed and the program exits. │ │ │ │ │ 3. void IVL_setList ( IVL *ivl, int ilist, int isize, int ivec[] ) ; │ │ │ │ │ This method sets the size and (possibly) pointer to a list of entries. The behavior of the │ │ │ │ │ method depends on the type of the ivl object. Here is the flow chart: │ │ │ │ │ - 6 IVL : DRAFT January 6, 2026 │ │ │ │ │ + 6 IVL : DRAFT January 17, 2026 │ │ │ │ │ if ilist >= maxnlist then │ │ │ │ │ the number of lists is increased via a call to IVL setMaxnlist() │ │ │ │ │ endif │ │ │ │ │ if ilist >= nlist then │ │ │ │ │ nlist is increased │ │ │ │ │ endif │ │ │ │ │ if isize = 0 then │ │ │ │ │ @@ -189,15 +189,15 @@ │ │ │ │ │ Error checking: If ivl is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. int IVL_min ( IVL *ivl ) ; │ │ │ │ │ int IVL_max ( IVL *ivl ) ; │ │ │ │ │ int IVL_maxListSize ( IVL *ivl ) ; │ │ │ │ │ int IVL_sum ( IVL *ivl ) ; │ │ │ │ │ These methods return some simple information about the object. │ │ │ │ │ Error checking: If ivl is NULL then an error message is printed and the program exits. │ │ │ │ │ - IVL : DRAFT January 6, 2026 7 │ │ │ │ │ + IVL : DRAFT January 17, 2026 7 │ │ │ │ │ 3. int IVL_sortUp ( IVL *ivl ) ; │ │ │ │ │ This method sorts each list into ascending order. │ │ │ │ │ Error checking: If ivl is NULL or nlist < 0 then an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 4. int * IVL_equivMap1 ( IVL *ivl ) ; │ │ │ │ │ IV * IVL_equivMap2 ( IVL *ivl ) ; │ │ │ │ │ Two lists are equivalent if their contents are identical. These methods are used to find the │ │ │ │ │ @@ -226,15 +226,15 @@ │ │ │ │ │ and the program exits. │ │ │ │ │ 8. IVL * IVL_expand ( IVL *ivl, IV *eqmapIV ) ; │ │ │ │ │ This method was created in support of a symbolic factorization. An IVL object is constructed │ │ │ │ │ using a compressed graph. it must be expanded to reflect the compressed graph. The number │ │ │ │ │ of lists does not change (there is one list per front) but the size of each list may change. so │ │ │ │ │ we create and return a new IVL object that contains entries for the uncompressed graph. │ │ │ │ │ Error checking: If ivl or eqmapIV is NULL, an error message is printed and the program exits. │ │ │ │ │ - 8 IVL : DRAFT January 6, 2026 │ │ │ │ │ + 8 IVL : DRAFT January 17, 2026 │ │ │ │ │ 1.2.6 Miscellaneous methods │ │ │ │ │ 1. IVL * IVL_make9P ( int n1, int n2, int ncomp ) ; │ │ │ │ │ This method returns an IVL object that contains the full adjacency structure for a 9-point │ │ │ │ │ operator on a n1×n2 grid with ncomp components at each grid point. │ │ │ │ │ Error checking: If n1, n2 or ncomp is less than or equal to zero, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ 2. IVL * IVL_make13P ( int n1, int n2 ) ; │ │ │ │ │ @@ -261,15 +261,15 @@ │ │ │ │ │ and returns the value returned from the called routine. │ │ │ │ │ Error checking: If ivl or fn are NULL, or if fn is not of the form *.ivlf (for a formatted file) │ │ │ │ │ or *.ivlb (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 2. int IVL_readFromFormattedFile ( IVL *ivl, FILE *fp ) ; │ │ │ │ │ This method reads an IVL object from a formatted file. If there are no errors in reading the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fscanf, zero is returned. │ │ │ │ │ Error checking: If ivl or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ - IVL : DRAFT January 6, 2026 9 │ │ │ │ │ + IVL : DRAFT January 17, 2026 9 │ │ │ │ │ 3. int IVL_readFromBinaryFile ( IVL *ivl, FILE *fp ) ; │ │ │ │ │ This method reads an IVL object from a binary file. If there are no errors in reading the data, │ │ │ │ │ the value 1 is returned. If an IO error is encountered from fread, zero is returned. │ │ │ │ │ Error checking: If ivl or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 4. int IVL_writeToFile ( IVL *ivl, char *fn ) ; │ │ │ │ │ This method writes an IVL object to a file. If the the file can be opened successfully, the │ │ │ │ │ method calls IVL writeFromFormattedFile() or IVL writeFromBinaryFile(), closes the │ │ │ │ │ @@ -293,15 +293,15 @@ │ │ │ │ │ Error checking: If ivl or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 1.3 Driver programs for the IVL object │ │ │ │ │ This section contains brief descriptions of six driver programs. │ │ │ │ │ 1. testIO msglvl msgFile inFile outFile │ │ │ │ │ This driver program reads in a IVL object from inFile and writes out the object to outFile │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the IVL object is written to the message file. │ │ │ │ │ - 10 IVL : DRAFT January 6, 2026 │ │ │ │ │ + 10 IVL : DRAFT January 17, 2026 │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The inFileparameter is the input file for the IVL object. It must be of the form *.ivlf │ │ │ │ │ or *.ivlb. The IVL object is read from the file via the IVL readFromFile() method. │ │ │ │ │ • The outFile parameter is the output file for the IVL object. It must be of the form │ │ │ │ │ *.ivlf or *.ivlb. The IVL object is written to the file via the IVL writeToFile() │ │ ├── ./usr/share/doc/spooles-doc/Ideq.ps.gz │ │ │ ├── Ideq.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Ideq.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1255,16 +1255,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1452,79 +1454,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ B7D99CD533EC5F931B18E6B39BECF67FA2D6DD1AEC76772B068BE06335A94C05 │ │ │ │ 7A4DDEE77B66101DA855C17AC312600370B34E31F5EC3A01300A8EB60B4C9767 │ │ │ │ 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y(2.)46 b Fh(int)h(Ideq_head)e(\()j │ │ │ │ @@ -3457,17 +3468,17 @@ │ │ │ │ 3130 5136 V 34 w(resize\(\))d Fi(metho)s(d.)227 5248 │ │ │ │ y(Otherwise,)f(the)f(item)h(is)g(placed)f(in)m(to)i(the)e(list)h(and)f │ │ │ │ Fh(1)g Fi(is)h(returned.)227 5407 y Fg(Err)-5 b(or)34 │ │ │ │ b(che)-5 b(cking:)40 b Fi(If)30 b Fh(deq)g Fi(is)g Fh(NULL)p │ │ │ │ Fi(,)g(an)g(error)g(message)h(is)g(prin)m(ted)f(and)g(the)g(program)g │ │ │ │ (exits.)p eop end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fi(4)p 136 100 1153 4 v │ │ │ │ -1335 w Fh(Ideq)29 b Fc(:)41 b Fg(DRAFT)30 b Fc(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2748 100 V 0 399 a Fb(1.2.4)112 b(IO)38 b(metho)s(ds)111 │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fi(4)p 136 100 1130 4 v │ │ │ │ +1312 w Fh(Ideq)29 b Fc(:)41 b Fg(DRAFT)30 b Fc(Jan)m(uary)g(17,)i(2026) │ │ │ │ +p 2770 100 V 0 399 a Fb(1.2.4)112 b(IO)38 b(metho)s(ds)111 │ │ │ │ 595 y Fi(1.)46 b Fh(void)h(Ideq_writeForHumanEye)42 b(\()47 │ │ │ │ b(Ideq)g(*deq)g(\))g(;)227 745 y Fi(This)31 b(metho)s(d)g(write)h(the)f │ │ │ │ (state)i(of)f(the)f(ob)5 b(ject,)33 b(\(the)f(size,)h(head)f(and)e │ │ │ │ (tail\))k(and)c(the)i(list)g(of)g(en)m(tries)g(to)227 │ │ │ │ 858 y(a)f(\014le.)227 1008 y Fg(Err)-5 b(or)34 b(che)-5 │ │ │ │ b(cking:)40 b Fi(If)30 b Fh(deq)g Fi(or)g Fh(fp)g Fi(is)g │ │ │ │ Fh(NULL)p Fi(,)g(an)g(error)g(message)i(is)e(prin)m(ted)g(and)g(the)g │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -16,15 +16,15 @@ │ │ │ │ │ • IV iv : an IV object to hold the list vector. │ │ │ │ │ A correctly initialized and nontrivial Ideq object will have maxsize > 0. When the dequeue is │ │ │ │ │ empty, head = tail = -1. │ │ │ │ │ 1.2 Prototypes and descriptions of Ideq methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the Ideq │ │ │ │ │ object. │ │ │ │ │ 1 │ │ │ │ │ - 2 Ideq : DRAFT January 6, 2026 │ │ │ │ │ + 2 Ideq : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. Ideq * Ideq_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Ideq structure and then sets the default fields │ │ │ │ │ by a call to Ideq setDefaultFields(). │ │ │ │ │ 2. void Ideq_setDefaultFields ( Ideq *deq ) ; │ │ │ │ │ @@ -47,50 +47,50 @@ │ │ │ │ │ initializer. │ │ │ │ │ If the present size of the list (the number of entries between head and tail inclusive) is larger │ │ │ │ │ than newsize, the method returns -1. Otherwise, a new int vector is allocated and filled │ │ │ │ │ with the entries in the list. The old int vector is free’d, the new vector is spliced into the IV │ │ │ │ │ object, and the head, tail and maxsize fields are set. The method then returns 1. │ │ │ │ │ Error checking: If deq is NULL, or if newsize < 0, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - Ideq : DRAFT January 6, 2026 3 │ │ │ │ │ + Ideq : DRAFT January 17, 2026 3 │ │ │ │ │ 1.2.3 Utility methods │ │ │ │ │ - 1. void Ideq_clear ( Ideq *deq ) ; │ │ │ │ │ + 1. void Ideq_clear ( Ideq *deq ) ; │ │ │ │ │ This method clears the dequeue. The head and tail fields are set to -1. │ │ │ │ │ Error checking: If deq is NULL, an error message is printed and the program exits. │ │ │ │ │ - 2. int Ideq_head ( Ideq *deq ) ; │ │ │ │ │ + 2. int Ideq_head ( Ideq *deq ) ; │ │ │ │ │ This method returns the value at the head of the list without removing that value. If head │ │ │ │ │ == -1 then -1 is returned. Note, the list may be nonempty and the first value may be -1, so │ │ │ │ │ -1 may signal an empty list or a terminating element. │ │ │ │ │ Error checking: If deq is NULL, an error message is printed and the program exits. │ │ │ │ │ - 3. int Ideq_removeFromHead ( Ideq *deq ) ; │ │ │ │ │ + 3. int Ideq_removeFromHead ( Ideq *deq ) ; │ │ │ │ │ This method returns the value at the head of the list and removes that value. If head == -1 │ │ │ │ │ then -1 is returned. Note, the list may be nonempty and the first value may be -1, so -1 │ │ │ │ │ may signal an empty list or a terminating element. │ │ │ │ │ Error checking: If deq is NULL, an error message is printed and the program exits. │ │ │ │ │ - 4. int Ideq_insertAtHead ( Ideq *deq, int val ) ; │ │ │ │ │ + 4. int Ideq_insertAtHead ( Ideq *deq, int val ) ; │ │ │ │ │ This method inserts a value val into the list at the head of the list. If there is no room in │ │ │ │ │ the list, -1 is returned and the dequeue must be resized using the Ideq resize() method. │ │ │ │ │ Otherwise, the item is placed into the list and 1 is returned. │ │ │ │ │ Error checking: If deq is NULL, an error message is printed and the program exits. │ │ │ │ │ - 5. int Ideq_tail ( Ideq *deq ) ; │ │ │ │ │ + 5. int Ideq_tail ( Ideq *deq ) ; │ │ │ │ │ This method returns the value at the tail of the list without removing that value. If tail == │ │ │ │ │ -1 then -1 is returned. Note, the list may be nonempty and the first value may be -1, so -1 │ │ │ │ │ may signal an empty list or a terminating element. │ │ │ │ │ Error checking: If deq is NULL, an error message is printed and the program exits. │ │ │ │ │ - 6. int Ideq_removeFromTail ( Ideq *deq ) ; │ │ │ │ │ + 6. int Ideq_removeFromTail ( Ideq *deq ) ; │ │ │ │ │ This method returns the value at the tail of the list and removes that value. If tail == -1 │ │ │ │ │ then -1 is returned. Note, the list may be nonempty and the first value may be -1, so -1 │ │ │ │ │ may signal an empty list or a terminating element. │ │ │ │ │ Error checking: If deq is NULL, an error message is printed and the program exits. │ │ │ │ │ - 7. int Ideq_insertAtTail ( Ideq *deq, int val ) ; │ │ │ │ │ + 7. int Ideq_insertAtTail ( Ideq *deq, int val ) ; │ │ │ │ │ This method inserts a value val into the list at the tail of the list. If there is no room in │ │ │ │ │ the list, -1 is returned and the dequeue must be resized using the Ideq resize() method. │ │ │ │ │ Otherwise, the item is placed into the list and 1 is returned. │ │ │ │ │ Error checking: If deq is NULL, an error message is printed and the program exits. │ │ │ │ │ - 4 Ideq : DRAFT January 6, 2026 │ │ │ │ │ + 4 Ideq : DRAFT January 17, 2026 │ │ │ │ │ 1.2.4 IO methods │ │ │ │ │ 1. void Ideq_writeForHumanEye ( Ideq *deq ) ; │ │ │ │ │ This method write the state of the object, (the size, head and tail) and the list of entries to │ │ │ │ │ a file. │ │ │ │ │ Error checking: If deq or fp is NULL, an error message is printed and the program exits. │ │ │ │ │ Index │ │ │ │ │ Ideq clear(), 3 │ │ ├── ./usr/share/doc/spooles-doc/InpMtx.ps.gz │ │ │ ├── InpMtx.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o InpMtx.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -2762,16 +2762,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J 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y(tations)f(for)g(the)h(matrix-v)n(ector)e(m)n(ultiply)-7 │ │ │ │ @@ -7589,17 +7600,17 @@ │ │ │ │ 4969 y(...)556 5069 y(xnpts)42 b(ynpts)f(])i(;)208 5308 │ │ │ │ y Fp(whic)n(h)24 b(can)h(b)r(e)g(used)g(to)g(generate)e(the)i(follo)n │ │ │ │ (wing)f(matlab)h(plot.)36 b(An)25 b(example)f(is)h(giv)n(en)f(b)r(elo)n │ │ │ │ (w)h(for)f(the)h Fa(bcsstk23)208 5407 y Fp(matrix,)i(where)g │ │ │ │ Fo(npts)42 b(=)h(200)p Fp(,)26 b Fo(tausmall)41 b(=)i(1.e-10)25 │ │ │ │ b Fp(and)i Fo(taubig)42 b(=)h(1.e100)p Fp(.)p eop end │ │ │ │ %%Page: 21 21 │ │ │ │ -TeXDict begin 21 20 bop 83 100 1158 4 v 1323 100 a Fo(InpMtx)26 │ │ │ │ -b Fj(:)36 b Fm(DRAFT)111 b Fj(Jan)n(uary)25 b(6,)j(2026)p │ │ │ │ -2662 100 V 1158 w Fp(21)1154 1747 y @beginspecial 47 │ │ │ │ +TeXDict begin 21 20 bop 83 100 1137 4 v 1303 100 a Fo(InpMtx)25 │ │ │ │ +b Fj(:)37 b Fm(DRAFT)110 b Fj(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +2682 100 V 1137 w Fp(21)1154 1747 y @beginspecial 47 │ │ │ │ @llx 197 @lly 550 @urx 604 @ury 2160 @rwi 1728 @rhi @setspecial │ │ │ │ %%BeginDocument: ../../InpMtx/doc/BCSSTK23.eps │ │ │ │ %!PS-Adobe-2.0 EPSF-1.2 │ │ │ │ %%Creator: MATLAB, The Mathworks, Inc. │ │ │ │ %%Title: profile.eps │ │ │ │ %%CreationDate: 03/13/97 09:20:11 │ │ │ │ %%DocumentNeededFonts: Helvetica │ │ │ │ @@ -8004,17 +8015,17 @@ │ │ │ │ Fo(InpMtx)c Fp(ob)5 b(ject)43 b(that)g(holds)g(the)g(matrix.)83 │ │ │ │ b(It)390 5308 y(m)n(ust)40 b(b)r(e)f(of)h(the)f(form)g │ │ │ │ Fo(*.inpmtxf)d Fp(or)j Fo(*.inpmtxb)p Fp(.)68 b(The)39 │ │ │ │ b Fo(InpMtx)e Fp(ob)5 b(ject)39 b(is)h(written)f(to)g(the)h(\014le)g │ │ │ │ (via)390 5407 y(the)28 b Fo(InpMtx)p 802 5407 V 29 w(writeToFile\(\))22 │ │ │ │ b Fp(metho)r(d.)p eop end │ │ │ │ %%Page: 22 22 │ │ │ │ -TeXDict begin 22 21 bop 0 100 a Fp(22)p 166 100 1158 │ │ │ │ -4 v 1322 w Fo(InpMtx)26 b Fj(:)37 b Fm(DRAFT)27 b Fj(Jan)n(uary)e(6,)j │ │ │ │ -(2026)p 2743 100 V 60 390 a Fp(12.)41 b Fo(testMMM)f(msglvl)h(msgFile)g │ │ │ │ +TeXDict begin 22 21 bop 0 100 a Fp(22)p 166 100 1137 │ │ │ │ +4 v 1302 w Fo(InpMtx)25 b Fj(:)37 b Fm(DRAFT)27 b Fj(Jan)n(uary)f(17,)g │ │ │ │ +(2026)p 2763 100 V 60 390 a Fp(12.)41 b Fo(testMMM)f(msglvl)h(msgFile)g │ │ │ │ (dataType)f(symflag)h(coordType)f(transpose)556 490 y(nrow)i(ncol)g │ │ │ │ (nitem)g(nrhs)g(seed)f(alphaReal)f(alphaImag)208 623 │ │ │ │ y Fp(This)32 b(driv)n(er)f(program)f(tests)i(the)h(matrix-matrix)e(m)n │ │ │ │ (ultiply)h(metho)r(ds.)52 b(This)32 b(driv)n(er)f(program)f(generates)h │ │ │ │ Fl(A)p Fp(,)i(a)208 723 y Fo(nrow)14 b Fg(\002)i Fo(ncol)25 │ │ │ │ b Fp(matrix)h(using)g Fo(nitem)f Fp(input)i(en)n(tries,)f │ │ │ │ Fl(X)33 b Fp(and)26 b Fl(Y)19 b Fp(,)27 b Fo(nrow)15 │ │ │ │ @@ -8114,17 +8125,17 @@ │ │ │ │ (the)g(matrix.)307 5274 y Fn(\210)42 b Fo(nrhs)26 b Fp(is)i(the)g(n)n │ │ │ │ (um)n(b)r(er)f(of)h(columns)f(in)h Fl(X)34 b Fp(and)27 │ │ │ │ b Fl(Y)19 b Fp(.)307 5407 y Fn(\210)42 b Fp(The)21 b │ │ │ │ Fo(seed)e Fp(parameter)g(is)h(a)g(random)g(n)n(um)n(b)r(er)g(seed)g │ │ │ │ (used)g(to)h(\014ll)f(the)h(matrix)f(en)n(tries)g(with)h(random)f(n)n │ │ │ │ (um)n(b)r(ers.)p eop end │ │ │ │ %%Page: 23 23 │ │ │ │ -TeXDict begin 23 22 bop 83 100 1158 4 v 1323 100 a Fo(InpMtx)26 │ │ │ │ -b Fj(:)36 b Fm(DRAFT)111 b Fj(Jan)n(uary)25 b(6,)j(2026)p │ │ │ │ -2662 100 V 1158 w Fp(23)307 390 y Fn(\210)42 b Fo(alphaReal)24 │ │ │ │ +TeXDict begin 23 22 bop 83 100 1137 4 v 1303 100 a Fo(InpMtx)25 │ │ │ │ +b Fj(:)37 b Fm(DRAFT)110 b Fj(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +2682 100 V 1137 w Fp(23)307 390 y Fn(\210)42 b Fo(alphaReal)24 │ │ │ │ b Fp(and)k Fo(alphaImag)c Fp(form)j(the)h Fl(\013)g Fp(scalar)e(in)i │ │ │ │ (the)g(m)n(ultiply)-7 b(.)307 523 y Fn(\210)42 b Fo(betaReal)25 │ │ │ │ b Fp(and)i Fo(betaImag)d Fp(form)k(the)g Fl(\014)k Fp(scalar)26 │ │ │ │ b(in)h(the)h(m)n(ultiply)-7 b(.)60 706 y(14.)41 b Fo(testGMVM)f(msglvl) │ │ │ │ h(msgFile)g(dataType)f(symflag)h(coordType)e(transpose)600 │ │ │ │ 805 y(nrow)j(ncol)g(nitem)f(seed)h(alphaReal)e(alphaImag)g(betaReal)g │ │ │ │ (betaImag)208 938 y Fp(This)18 b(driv)n(er)g(program)e(tests)j(the)g │ │ │ │ @@ -8305,18 +8316,18 @@ │ │ │ │ y Fo(InpMtx)p 2261 5005 V 28 w(storageMode\(\))p Fp(,)h(5)1992 │ │ │ │ 5105 y Fo(InpMtx)p 2261 5105 V 28 w(supportNonsym\(\))p │ │ │ │ Fp(,)f(9)1992 5206 y Fo(InpMtx)p 2261 5206 V 28 w(supportNonsymH\(\))p │ │ │ │ Fp(,)g(9)1992 5307 y Fo(InpMtx)p 2261 5307 V 28 w(supportNonsymT\(\))p │ │ │ │ Fp(,)g(9)1992 5407 y Fo(InpMtx)p 2261 5407 V 28 w(supportSym\(\))p │ │ │ │ Fp(,)h(9)1908 5656 y(24)p eop end │ │ │ │ %%Page: 25 25 │ │ │ │ -TeXDict begin 25 24 bop 83 100 1158 4 v 1323 100 a Fo(InpMtx)26 │ │ │ │ -b Fj(:)36 b Fm(DRAFT)111 b Fj(Jan)n(uary)25 b(6,)j(2026)p │ │ │ │ -2662 100 V 1158 w Fp(25)0 390 y Fo(InpMtx)p 269 390 27 │ │ │ │ -4 v 29 w(supportSymH\(\))p Fp(,)22 b(9)0 490 y Fo(InpMtx)p │ │ │ │ +TeXDict begin 25 24 bop 83 100 1137 4 v 1303 100 a Fo(InpMtx)25 │ │ │ │ +b Fj(:)37 b Fm(DRAFT)110 b Fj(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +2682 100 V 1137 w Fp(25)0 390 y Fo(InpMtx)p 269 390 27 │ │ │ │ +4 v 29 w(supportSymH\(\))p Fp(,)c(9)0 490 y Fo(InpMtx)p │ │ │ │ 269 490 V 29 w(sym)p 430 490 V 30 w(gmmm\(\))p Fp(,)j(11)0 │ │ │ │ 589 y Fo(InpMtx)p 269 589 V 29 w(sym)p 430 589 V 30 w(gmvm\(\))p │ │ │ │ Fp(,)g(11)0 689 y Fo(InpMtx)p 269 689 V 29 w(sym)p 430 │ │ │ │ 689 V 30 w(mmm\(\))p Fp(,)h(10)0 789 y Fo(InpMtx)p 269 │ │ │ │ 789 V 29 w(vecids\(\))p Fp(,)e(6)0 888 y Fo(InpMtx)p │ │ │ │ 269 888 V 29 w(vector\(\))p Fp(,)g(6)0 988 y Fo(InpMtx)p │ │ │ │ 269 988 V 29 w(writeForHumanEye)o(\(\))o Fp(,)e(15)0 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -28,15 +28,15 @@ │ │ │ │ │ be efficient to have sufficient elbow room to minimize the number of sorts and compressions. In this │ │ │ │ │ case, a tight upper bound on the necessary storage is the sum of the sizes of the elemental matrices. │ │ │ │ │ The entries are assembled by a call to InpMtx changeStorageMode(). │ │ │ │ │ T │ │ │ │ │ 5. CreateanIVLobjectthatcontainsthefull adjacencyofA+A bycallingtheInpMtx fullAdjacency() │ │ │ │ │ method. │ │ │ │ │ 1 │ │ │ │ │ - 2 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 2 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ 6. Create a Graph object using the Graph init2() method and the IVL object as an input argument. │ │ │ │ │ A similar functionality exists for creating a Graph object from a linear combination of two InpMtx objects │ │ │ │ │ that contains the matrices A and B. The InpMtx fullAdjacency2() method returns an IVL object with │ │ │ │ │ the full adjacency of (A+B)+(A+B)T. These two methods are called by the DPencil fullAdjacency() │ │ │ │ │ methods to return the full adjacency of a matrix pencil. │ │ │ │ │ Here is a common sequence of events to use this object when we want to assemble the entries of a sparse │ │ │ │ │ matrix. │ │ │ │ │ @@ -68,15 +68,15 @@ │ │ │ │ │ j,j j,k k,j │ │ │ │ │ – INPMTX CUSTOM — custom coordinates. │ │ │ │ │ • int storageMode : mode of storage │ │ │ │ │ – INPMTX RAW DATA — data is raw pairs or triples, two coordinates and (optionally) one or two │ │ │ │ │ double precision values. │ │ │ │ │ – INPMTX SORTED — data is sorted and distinct triples, the primary key is the first coordinate, the │ │ │ │ │ secondary key is the second coordinate. │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 3 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 3 │ │ │ │ │ – INPMTX BY VECTORS — data is sorted and distinct vectors. All entries in a vector share some- │ │ │ │ │ thing in common. For example, when coordType is INPMTX BY ROWS, INPMTX BY COLUMNS or │ │ │ │ │ INPMTX BY CHEVRONS, row vectors, column vectors, or chevron vectors are stored, respectively. │ │ │ │ │ WhencoordTypeis INPMTX CUSTOM, a custom type, entries in the same vector have something in │ │ │ │ │ common but it need not be a common row, column or chevron coordinate. │ │ │ │ │ • int inputMode : mode of data input │ │ │ │ │ – INPMTX INDICES ONLY — only indices are stored, not entries. │ │ │ │ │ @@ -106,15 +106,15 @@ │ │ │ │ │ • INPMTX IS BY COLUMNS(mtx) returns 1 if the entries are stored by columns, and 0 otherwise. │ │ │ │ │ • INPMTX IS BY CHEVRONS(mtx) returns 1 if the entries are stored by chevrons, and 0 otherwise. │ │ │ │ │ • INPMTX IS BY CUSTOM(mtx) returns 1 if the entries are stored by some custom coordinate, and 0 │ │ │ │ │ otherwise. │ │ │ │ │ • INPMTX IS RAW DATA(mtx) returns 1 if the entries are stored as unsorted pairs or triples, and 0 other- │ │ │ │ │ wise. │ │ │ │ │ • INPMTX IS SORTED(mtx) returns 1 if the entries are stored as sorted pairs or triples, and 0 otherwise. │ │ │ │ │ - 4 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 4 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ • INPMTX IS BY VECTORS(mtx) returns 1 if the entries are stored as vectors, and 0 otherwise. │ │ │ │ │ • INPMTX IS INDICES ONLY(mtx) returns 1 if the entries are not stored, and 0 otherwise. │ │ │ │ │ • INPMTX IS REAL ENTRIES(mtx) returns 1 if the entries are real, and 0 otherwise. │ │ │ │ │ • INPMTX IS COMPLEX ENTRIES(mtx) returns 1 if the entries are complex, and 0 otherwise. │ │ │ │ │ 1.2 Prototypes and descriptions of InpMtx methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the InpMtx object. │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ @@ -140,15 +140,15 @@ │ │ │ │ │ 1. int InpMtx_coordType ( InpMtx *inpmtx ) ; │ │ │ │ │ This method returns the coordinate type. │ │ │ │ │ • INPMTX NO TYPE – none specified │ │ │ │ │ • INPMTX BY ROWS – storage by row triples │ │ │ │ │ • INPMTX BY COLUMNS – storage by column triples │ │ │ │ │ • INPMTX BY CHEVRONS – storage by chevron triples │ │ │ │ │ • INPMTX CUSTOM – custom type │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 5 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 5 │ │ │ │ │ Error checking: If inpmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. int InpMtx_storageMode ( InpMtx *inpmtx ) ; │ │ │ │ │ This method returns the storage mode. │ │ │ │ │ • INPMTX NO MODE – none specified │ │ │ │ │ • INPMTX RAW DATA – raw triples │ │ │ │ │ • INPMTX SORTED – sorted and distinct triples │ │ │ │ │ • INPMTX BY VECTORS – vectors by the first coordinate │ │ │ │ │ @@ -176,15 +176,15 @@ │ │ │ │ │ Error checking: If inpmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 9. int * InpMtx_ivec1 ( InpMtx *inpmtx ) ; │ │ │ │ │ This method returns the base address of the ivec1[] vector. │ │ │ │ │ Error checking: If inpmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 10. int * InpMtx_ivec2 ( InpMtx *inpmtx ) ; │ │ │ │ │ This method returns the base address of the ivec2[] vector. │ │ │ │ │ Error checking: If inpmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ - 6 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 6 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ 11. double * InpMtx_dvec ( InpMtx *inpmtx ) ; │ │ │ │ │ This method returns the base address of the dvec[] vector. │ │ │ │ │ Error checking: If inpmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 12. int * InpMtx_vecids ( InpMtx *inpmtx ) ; │ │ │ │ │ This method returns the base address of the vecids[] vector. │ │ │ │ │ Error checking: If inpmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 13. int * InpMtx_sizes ( InpMtx *inpmtx ) ; │ │ │ │ │ @@ -217,15 +217,15 @@ │ │ │ │ │ This method sets the maxinum number of entries in the indices and entries vectors. │ │ │ │ │ Error checking: If inpmtx is NULL, or if newmaxnent < 0, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 18. void InpMtx_setNent ( InpMtx *inpmtx, int newnent ) ; │ │ │ │ │ This method sets the present number of entries in the indices and entries vectors. │ │ │ │ │ Error checking: If inpmtx is NULL, or if newnent < 0, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 7 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 7 │ │ │ │ │ 19. void InpMtx_setMaxnvector ( InpMtx *inpmtx, int newmaxnvector ) ; │ │ │ │ │ This method sets the maxinum number of vectors. │ │ │ │ │ Error checking: If inpmtx is NULL, or if newmaxnvector < 0, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 20. void InpMtx_setNvector ( InpMtx *inpmtx, int newnvector ) ; │ │ │ │ │ This method sets the present number of vectors. │ │ │ │ │ Error checking: If inpmtx is NULL, or if newnvector < 0, an error message is printed and the program │ │ │ │ │ @@ -261,15 +261,15 @@ │ │ │ │ │ exits. │ │ │ │ │ 3. void InpMtx_changeStorageMode ( InpMtx *inpmtx, int newMode ) ; │ │ │ │ │ If storageMode = newMode, the method returns. Otherwise, a translation between the three valid │ │ │ │ │ modes is made by calling InpMtx sortAndCompress()and InpMtx convertToVectors(),as appropri- │ │ │ │ │ ate. │ │ │ │ │ Error checking: If inpmtx is NULL or newMode is invalid, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - 8 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 8 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ 1.2.4 Input methods │ │ │ │ │ 1. void InpMtx_inputEntry ( InpMtx *inpmtx, int row, int col ) ; │ │ │ │ │ void InpMtx_inputRealEntry ( InpMtx *inpmtx, int row, int col, double value ) ; │ │ │ │ │ void InpMtx_inputComplexEntry ( InpMtx *inpmtx, int row, int col, │ │ │ │ │ double real, double imag ) ; │ │ │ │ │ This method places a single entry into the matrix object. The coordinate type of the object must be │ │ │ │ │ INPMTX BY ROWS, INPMTX BY COLUMNS or INPMTX BY CHEVRONS. The triple is formed and inserted into │ │ │ │ │ @@ -307,15 +307,15 @@ │ │ │ │ │ Error checking: If inpmtx is NULL, or chv or chvsize are negative, or chvind or chvent are NULL, an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ 5. void InpMtx_inputMatrix ( InpMtx *inpmtx, int nrow, int col, │ │ │ │ │ int rowstride, int colstride, int rowind[], int colind[] ) ; │ │ │ │ │ void InpMtx_inputRealMatrix ( InpMtx *inpmtx, int nrow, int col, │ │ │ │ │ int rowstride, int colstride, int rowind[], int colind[], double mtxent[] ) ; │ │ │ │ │ void InpMtx_inputComplexMatrix ( InpMtx *inpmtx, int nrow, int col, │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 9 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 9 │ │ │ │ │ int rowstride, int colstride, int rowind[], int colind[], double mtxent[] ) ; │ │ │ │ │ This method places a dense submatrix into the matrix object. The coordinate type of the object must │ │ │ │ │ be INPMTX BY ROWS, INPMTX BY COLUMNS or INPMTX BY CHEVRONS. The individual entries of the matrix │ │ │ │ │ are placed into the vector storage as triples, and the vectors are resized if necessary. │ │ │ │ │ Error checking: If inpmtx is NULL, or col or row are negative, or rowstride or colstride are less │ │ │ │ │ than 1, or rowind, colind or mtxent are NULL, an error message is printed and the program exits. │ │ │ │ │ 6. void InpMtx_inputTriples ( InpMtx *inpmtx, int ntriples, │ │ │ │ │ @@ -351,15 +351,15 @@ │ │ │ │ │ and A will contain only part of the larger global matrix A. Finding the row an column support enables │ │ │ │ │ one to construct local data structures for X and the product αAX. │ │ │ │ │ Error checking: If A or supIV is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. void InpMtx_mapEntries ( InpMtx *A, IV *rowmapIV, IV *colmapIV ) ; │ │ │ │ │ These methods are used to map a matrix from one numbering system to another. The primary use of │ │ │ │ │ this method is to map a part of a distributed matrix between the global and local numberings. │ │ │ │ │ Error checking: If A, rowmapIV or colmapIV is NULL, an error message is printed and the program exits. │ │ │ │ │ - 10 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 10 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ 4. void InpMtx_permute ( InpMtx *inpmtx, int rowOldToNew[], int colOldToNew[] ) ; │ │ │ │ │ This method permutes the rows and or columns of the matrix. If rowOldToNew and colOldToNew are │ │ │ │ │ both NULL, or if there are no entries in the matrix, the method returns. Note, either rowOldToNew or │ │ │ │ │ colOldToNew can be NULL. If coordType == INPMTX BY CHEVRONS, then the coordinates are changed │ │ │ │ │ to row coordinates. The coordinates are then mapped to their new values. The storageMode is set to │ │ │ │ │ 1, (raw triples). │ │ │ │ │ Error checking: If inpmtx is NULL, an error message is printed and the program exits. │ │ │ │ │ @@ -395,15 +395,15 @@ │ │ │ │ │ InpMtx nonsym mmm H() Y := Y +αA X nonsymmetric complex │ │ │ │ │ A, X and Y must all be real or all be complex. When A is real, then α = alpha[0]. When A is complex, │ │ │ │ │ then α = alpha[0] + i* alpha[1]. The values of α must be loaded into an array of length 1 or 2. │ │ │ │ │ Error checking: If A, Y or X are NULL, or if coordType is not INPMTX BY ROWS, INPMTX BY COLUMNS or │ │ │ │ │ INPMTX BY CHEVRONS,orifstorageModeisnotoneofINPMTX RAW DATA,INPMTX SORTEDorINPMTX BY VECTORS, │ │ │ │ │ or if inputModeis not SPOOLES REAL or SPOOLES COMPLEX,an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 11 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 11 │ │ │ │ │ 2. void InpMtx_nonsym_mmmVector ( InpMtx *A, DenseMtx *Y, double alpha[], DenseMtx *X ) ; │ │ │ │ │ void InpMtx_sym_mmmVector ( InpMtx *A, DenseMtx *Y, double alpha[], DenseMtx *X ) ; │ │ │ │ │ void InpMtx_herm_mmmVector ( InpMtx *A, DenseMtx *Y, double alpha[], DenseMtx *X ) ; │ │ │ │ │ void InpMtx_nonsym_mmmVector_T ( InpMtx *A, DenseMtx *Y, double alpha[], DenseMtx *X ) ; │ │ │ │ │ void InpMtx_nonsym_mmmVector_H ( InpMtx *A, DenseMtx *Y, double alpha[], DenseMtx *X ) ; │ │ │ │ │ These five methods perform the following computations. │ │ │ │ │ InpMtx nonsym mmm() y := y +αAx nonsymmetric real or complex │ │ │ │ │ @@ -443,15 +443,15 @@ │ │ │ │ │ -1 A is NULL -9 alpha is NULL │ │ │ │ │ -2 type of A is invalid -10 X is NULL │ │ │ │ │ -3 indices of entries of A are NULL -11 type of X is invalid │ │ │ │ │ -4 beta is NULL -12 bad dimensions and strides for X │ │ │ │ │ -5 Y is NULL -13 entries of X are NULL │ │ │ │ │ -6 type of Y is invalid -14 types of A, X and Y are not identical │ │ │ │ │ -7 bad dimensions and strides for Y -15 number of columns in X and Y are not equal │ │ │ │ │ - 12 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 12 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ 4. int InpMtx_nonsym_gmvm ( InpMtx *A, double beta[], int ny, double y[], │ │ │ │ │ double alpha[], int nx, double x[] ) ; │ │ │ │ │ int InpMtx_sym_gmvm ( InpMtx *A, double beta[], int ny, double y[], │ │ │ │ │ double alpha[], int nx, double x[] ) ; │ │ │ │ │ int InpMtx_herm_gmvm ( InpMtx *A, double beta[], int ny, double y[], │ │ │ │ │ double alpha[], int nx, double x[] ) ; │ │ │ │ │ int InpMtx_nonsym_gmvm_T ( InpMtx *A, double beta[], int ny, double y[], │ │ │ │ │ @@ -492,15 +492,15 @@ │ │ │ │ │ Error checking: If inpmtxAisNULL,orifthecoordinatetypeisnotINPMTX BY ROWSorINPMTX BY COLUMNS, │ │ │ │ │ or if the storage mode is not INPMTX BY VECTORS, an error message is printed and the program exits. │ │ │ │ │ 3. IVL * InpMtx_adjForATA ( InpMtx *inpmtxA ) ; │ │ │ │ │ T │ │ │ │ │ This method creates and returns an IVL object that holds the full adjacency structure of A A, where │ │ │ │ │ inpmtxA contains the entries in A. │ │ │ │ │ Error checking: If inpmtxA is NULL, an error message is printed and the program exits. │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 13 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 13 │ │ │ │ │ 1.2.8 Submatrix extraction method │ │ │ │ │ 1. int InpMtx_initFromSubmatrix ( InpMtx *B, InpMtx *A, IV *BrowsIV, │ │ │ │ │ IV *BcolsIV, int symmetryflag, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method fills B with the submatrix formed from the rows and columns of A found in BrowsIV and │ │ │ │ │ BcolsIV. The row and column indices in B are local with respect to BrowsIV and BcolsIV. │ │ │ │ │ Whensymmetryflagis SPOOLES SYMMETRICor SPOOLES HERMITIAN, then we assume that when i 6= j, │ │ │ │ │ A orA isstored, but not both. (A could be stored by rows of its upper triangle, or by columns of │ │ │ │ │ @@ -538,15 +538,15 @@ │ │ │ │ │ void InpMtx_mapToUpperTriangleH ( InpMtx *inpmtx ) ; │ │ │ │ │ If the InpMtxobject holds only the loweror upper triangle of a matrix (as when the matrix is symmetric │ │ │ │ │ or Hermitian), and is then permuted, it is not likely that the permuted object will only have entries in │ │ │ │ │ the lower or upper triangle. The first method moves a for i < j to a . The second method moves │ │ │ │ │ i,j j,i │ │ │ │ │ a for i > j to a , (If the matrix is Hermitian, the sign of the imaginary part of an entry is dealt with │ │ │ │ │ i,j j,i │ │ │ │ │ - 14 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 14 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ in the correct fashion.) In other words, using these methods will restore the lower or upper triangular │ │ │ │ │ structure after a permutation. │ │ │ │ │ Error checking: If inpmtx is NULL, or if coordType is invalid, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 5. void InpMtx_log10profile ( InpMtx *inpmtx, int npts, DV *xDV, DV *yDV, │ │ │ │ │ double tausmall, double taubig, │ │ │ │ │ int *pnzero, int *pnsmall, int *pnbig ) ; │ │ │ │ │ @@ -582,15 +582,15 @@ │ │ │ │ │ returned. If nitem is not positive, -9 is returned. Otherwise, 1 is returned. │ │ │ │ │ Return codes: │ │ │ │ │ 1 normal return -5 nrow or ncol negative │ │ │ │ │ -1 inpmtx is NULL -6 symflag is invalid │ │ │ │ │ -2 inputMode invalid -7 (symflag,inputMode)invalid │ │ │ │ │ -3 coordType invalid -8 (symflag,nrow,ncol)invalid │ │ │ │ │ -4 storageMode invalid -9 nitem negative │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 15 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 15 │ │ │ │ │ 1.2.10 IO methods │ │ │ │ │ There are the usual eight IO routines. The file structure of a InpMtx object is simple: The first en- │ │ │ │ │ tries in the file are coordType, storageMode, inputMode, nent and nvector. If nent > 0, then the │ │ │ │ │ ivec1IV and ivec2IV vectors follow, If nent > 0 and inputMode = SPOOLES REAL or SPOOLES COMPLEX, │ │ │ │ │ the dvecDVvectorfollows. If storageMode = INPMTX BY VECTORSand nvector > 0, the vecidsIV,sizesIV │ │ │ │ │ and offsetsIV vectors follow. │ │ │ │ │ 1. int InpMtx_readFromFile ( InpMtx *inpmtx, char *fn ) ; │ │ │ │ │ @@ -624,15 +624,15 @@ │ │ │ │ │ is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ Error checking: If inpmtx or fp is NULL, an error message is printed and the method returns zero. │ │ │ │ │ 7. int InpMtx_writeForHumanEye ( InpMtx *inpmtx, FILE *fp ) ; │ │ │ │ │ Thismethodwritestheobjecttoafilesuitableforreadingbyahuman. ThemethodInpMtx writeStats() │ │ │ │ │ is called to write out the header and statistics. The data is written out in the appropriate way, e.g., if │ │ │ │ │ the storage mode is by triples, triples are written out. The value 1 is returned. │ │ │ │ │ Error checking: If inpmtx or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ - 16 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 16 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ 8. int InpMtx_writeStats ( InpMtx *inpmtx, FILE *fp ) ; │ │ │ │ │ This method writes the statistics about the object to a file. human. The value 1 is returned. │ │ │ │ │ Error checking: If inpmtx or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 9. void InpMtx_writeForMatlab ( InpMtx *mtx, char *mtxname, FILE *fp ) ; │ │ │ │ │ This method writes out a InpMtx object to a file in a Matlab format. A sample line is │ │ │ │ │ a(10,5) = -1.550328201511e-01 + 1.848033378871e+00*i ; │ │ │ │ │ for complex matrices, or │ │ │ │ │ @@ -663,15 +663,15 @@ │ │ │ │ │ to write the object to a formatted file (if outFile is of the form *.inpmtxf), or a binary file (if │ │ │ │ │ outFile is of the form *.inpmtxb). │ │ │ │ │ 2. testFullAdj msglvl msgFile nvtx nent seed │ │ │ │ │ This driver program tests the InpMtx fullAdjacency() method. If first generates a InpMtx object │ │ │ │ │ filled with random entries of a matrix A and then constructs an IVL object that contains the full │ │ │ │ │ adjacency structure of A +AT, diagonal edges included. │ │ │ │ │ 1http://math.nist.gov/mcsd/Staff/KRemington/harwell io/harwell io.html │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 17 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 17 │ │ │ │ │ • Themsglvlparameterdeterminestheamountofoutput—takingmsglvl >= 3meanstheInpMtx │ │ │ │ │ object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • The nvtx parameter is the number of rows and columns in A. │ │ │ │ │ • The nent parameter is an upper bound on the number of entries in A. (Since the locations of the │ │ │ │ │ entries are generated via random numbers, there may be duplicate entries.) │ │ │ │ │ @@ -707,15 +707,15 @@ │ │ │ │ │ • The outFile parameter is the output file for the InpMtx object. If outFile is none then the │ │ │ │ │ InpMtx object is not written to a file. Otherwise, the InpMtx writeToFile() method is called │ │ │ │ │ to write the object to a formatted file (if outFile is of the form *.inpmtxf), or a binary file (if │ │ │ │ │ outFile is of the form *.inpmtxb). │ │ │ │ │ 5. createGraphForATA msglvl msgFile inFile outFile │ │ │ │ │ This driver program reads in InpMtx object from the file inFile that holds a matrix A. It then creates │ │ │ │ │ a Graph object for B = ATA and writes it to the file outFile. │ │ │ │ │ - 18 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 18 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ • Themsglvlparameterdeterminestheamountofoutput—takingmsglvl >= 3meanstheInpMtx │ │ │ │ │ object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • The inFile parameter is the input file for the InpMtx object. It must be of the form *.inpmtxf │ │ │ │ │ or *.inpmtxb. The InpMtx object is read from the file via the InpMtx readFromFile() method. │ │ │ │ │ • The outFile parameter is the output file for the InpMtx object. If outFile is none then the │ │ │ │ │ @@ -752,15 +752,15 @@ │ │ │ │ │ binary file (if outGraphFile is of the form *.graphb). │ │ │ │ │ • The flag parameter is used to specify whether the offsets and indices are 0-indexed (as in C) or │ │ │ │ │ 1-indexed (as in Fortran). If they are 1-indexed, the offsets and indices are decremented prior to │ │ │ │ │ loading into the InpMtx object. │ │ │ │ │ 7. weightedAdjToGraph msglvl msgFile inAdjacencyFile outGraphFile flag │ │ │ │ │ This driver program was used to generate a type 1 Graph object (weighted vertices, unit weight edges) │ │ │ │ │ from a file that contained the adjacency structure of a matrix in the following form. │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 19 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 19 │ │ │ │ │ nvtx nadj │ │ │ │ │ vwghts[nvtx] │ │ │ │ │ offsets[nvtx+1] │ │ │ │ │ indices[nadj] │ │ │ │ │ There are nvtx vertices in the graph and the adjacency vector has nadj entries. It was not known │ │ │ │ │ whether the adjacency structure contained (v,v) entries or if it was only the upper or lower triangle. │ │ │ │ │ Our Graph object is symmetric with loops, i.e., (u,v) is present if and only if (v,u) is present, and │ │ │ │ │ @@ -798,15 +798,15 @@ │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any message data. │ │ │ │ │ • The EGraphFile is the file that holds the EGraph object — must be of the form *.egraphf or │ │ │ │ │ *.egraphb. │ │ │ │ │ • The CoordsFile is the file that holds the Coords object — must be of the form *.coordsf or │ │ │ │ │ *.coordsb. │ │ │ │ │ • The coordType determines the coordinate type for the InpMtx object. │ │ │ │ │ - 20 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 20 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ – 1 — storage of entries by rows │ │ │ │ │ – 2 — storage of entries by columns │ │ │ │ │ – 3 — storage of entries by chevrons │ │ │ │ │ • The seed parameter is used as a random number seed to determine the row and column permu- │ │ │ │ │ tations for the matrix-vector multiply. │ │ │ │ │ • The outInpMtxFileparameteris the output file for the InpMtx object. If outInpMtxFileis none │ │ │ │ │ then the InpMtx object is not written to a file. Otherwise, the InpMtx writeToFile() method is │ │ │ │ │ @@ -839,15 +839,15 @@ │ │ │ │ │ profile plot. The message file will contain line of the form. │ │ │ │ │ data = [ ... │ │ │ │ │ x1 y1 │ │ │ │ │ ... │ │ │ │ │ xnpts ynpts ] ; │ │ │ │ │ which can be used to generate the following matlab plot. An example is given below for the bcsstk23 │ │ │ │ │ matrix, where npts = 200, tausmall = 1.e-10 and taubig = 1.e100. │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 21 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 21 │ │ │ │ │ BCSSTK23: profile of magnitudes of matrix entries │ │ │ │ │ 1600 │ │ │ │ │ 1400 │ │ │ │ │ 1200 │ │ │ │ │ 1000 │ │ │ │ │ 800 │ │ │ │ │ # of entries │ │ │ │ │ @@ -883,15 +883,15 @@ │ │ │ │ │ • n1 is the number of points in the first direction. │ │ │ │ │ • n2 is the number of points in the second direction. │ │ │ │ │ • n3 is the number of points in the third direction. │ │ │ │ │ • Theseedparameterisarandomnumberseedusedtofillthematrixentrieswithrandomnumbers. │ │ │ │ │ • The outFile parameter is the output file for the InpMtx object that holds the matrix. It │ │ │ │ │ must be of the form *.inpmtxf or *.inpmtxb. The InpMtx object is written to the file via │ │ │ │ │ the InpMtx writeToFile() method. │ │ │ │ │ - 22 InpMtx : DRAFT January 6, 2026 │ │ │ │ │ + 22 InpMtx : DRAFT January 17, 2026 │ │ │ │ │ 12. testMMM msglvl msgFile dataType symflag coordType transpose │ │ │ │ │ nrow ncol nitem nrhs seed alphaReal alphaImag │ │ │ │ │ This driver program tests the matrix-matrix multiply methods. This driver program generates A, a │ │ │ │ │ nrow×ncol matrix using nitem input entries, X and Y, nrow×nrhs matrices, and all are filled with │ │ │ │ │ T H │ │ │ │ │ random numbers. It then computes Y := Y + αAX, Y := Y + αA X or Y := Y + αA X. The │ │ │ │ │ program’s output is a file which when sent into Matlab, outputs the error in the computation. │ │ │ │ │ @@ -930,15 +930,15 @@ │ │ │ │ │ T │ │ │ │ │ Y := βY +αA X. │ │ │ │ │ • nrowA is the number of rows in A │ │ │ │ │ • ncolA is the number of columns in A │ │ │ │ │ • nitem is the number of matrix entries that are assembled into the matrix. │ │ │ │ │ • nrhs is the number of columns in X and Y. │ │ │ │ │ • Theseedparameterisarandomnumberseedusedtofillthematrixentrieswithrandomnumbers. │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 23 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 23 │ │ │ │ │ • alphaReal and alphaImag form the α scalar in the multiply. │ │ │ │ │ • betaReal and betaImag form the β scalar in the multiply. │ │ │ │ │ 14. testGMVM msglvl msgFile dataType symflag coordType transpose │ │ │ │ │ nrow ncol nitem seed alphaReal alphaImag betaReal betaImag │ │ │ │ │ Thisdriverprogramteststhegeneralizedmatrix-vectormultiplymethods. ItgeneratesA, anrow×ncol │ │ │ │ │ matrix using nitem input entries, x and y, and fills the matrices with random numbers. It then │ │ │ │ │ T H │ │ │ │ │ @@ -1013,15 +1013,15 @@ │ │ │ │ │ InpMtx inputRealTriples(), 9 InpMtx sortAndCompress(), 13 │ │ │ │ │ InpMtx inputRow(), 8 InpMtx storageMode(), 5 │ │ │ │ │ InpMtx inputTriples(), 9 InpMtx supportNonsym(), 9 │ │ │ │ │ InpMtx ivec1(), 5 InpMtx supportNonsymH(), 9 │ │ │ │ │ InpMtx ivec2(), 5 InpMtx supportNonsymT(), 9 │ │ │ │ │ InpMtx log10profile(), 13 InpMtx supportSym(), 9 │ │ │ │ │ 24 │ │ │ │ │ - InpMtx : DRAFT January 6, 2026 25 │ │ │ │ │ + InpMtx : DRAFT January 17, 2026 25 │ │ │ │ │ InpMtx supportSymH(), 9 │ │ │ │ │ InpMtx sym gmmm(), 11 │ │ │ │ │ InpMtx sym gmvm(), 11 │ │ │ │ │ InpMtx sym mmm(), 10 │ │ │ │ │ InpMtx vecids(), 6 │ │ │ │ │ InpMtx vector(), 6 │ │ │ │ │ InpMtx writeForHumanEye(), 15 │ │ ├── ./usr/share/doc/spooles-doc/LinSol.ps.gz │ │ │ ├── LinSol.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ 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│ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 65 /A put │ │ │ │ dup 66 /B put │ │ │ │ dup 67 /C put │ │ │ │ dup 71 /G put │ │ │ │ dup 74 /J put │ │ │ │ dup 80 /P put │ │ │ │ dup 82 /R put │ │ │ │ @@ -6745,184 +6758,192 @@ │ │ │ │ 82032FBD2FCB6E403D34B85ED4053A8CB619BDD4DE001F4C3007B1F317579651 │ │ │ │ E6D6662189CC2D95AB85D7473F65C5D7B4AC63B0FE928F3400035D5A9D443D0D │ │ │ │ F3532B99F3AC26CB25EA3CD64C341159061E02EFBC7C033C05CD919BBD827A6A │ │ │ │ BFCF3BD739E32E7FE909AEE068D50FAC33605FFF98C7D0115FB860178FD03DB9 │ │ │ │ 7985B78E0AC21F2EA065FA841F5928FB85163B2E2D8F850DC7EE313912C45C28 │ │ │ │ 2783F6762C67882EFEDDC7E7567F91C16B16FD8D5A1ABF35B5586307701B91AD │ │ │ │ 54984598F2AD46FEE3D68A2731BEAA754C8E730FE0E84952EF77930E4118F8D7 │ │ │ │ -2F3AD7547D3E54167FB0B315756753DC0DF935CC3D1CBB93A9A575EBF5BBB34F │ │ │ │ -2CBD38692849D484C11BB5CF75F095251A87F37EC4727933F21C3932EEE24157 │ │ │ │ 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│ b(if)28 b(the)g Fm(Neqns)d Fj(<)i Fm(compressCutoff)21 │ │ │ │ b Fc(\003)27 b Fm(neqns)p Fo(,)e(then)j(the)f(compressed)f(graph)390 │ │ │ │ 490 y(is)i(formed,)f(ordered)f(and)i(used)f(to)h(create)e(the)i(sym)n │ │ │ │ (b)r(olic)g(factorization.)125 642 y Ff(\210)42 b Fo(Matrix)27 │ │ │ │ b(parameters:)301 795 y Fp({)41 b Fm(int)i(type)26 b │ │ │ │ Fo(:)37 b(t)n(yp)r(e)27 b(of)h(en)n(tries,)f Fm(SPOOLES)p │ │ │ │ @@ -8506,17 +8527,17 @@ │ │ │ │ b(factor)g(time)2242 5120 y Fm(cpus[10])d Fo(:)100 b(time)28 │ │ │ │ b(to)f(p)r(erm)n(ute)h(rhs)2242 5220 y Fm(cpus[11])c │ │ │ │ Fo(:)100 b(time)28 b(to)f(solv)n(e)2242 5319 y Fm(cpus[12])d │ │ │ │ Fo(:)100 b(time)28 b(to)f(p)r(erm)n(ute)h(solution)2242 │ │ │ │ 5419 y Fm(cpus[13])c Fo(:)100 b(total)27 b(solv)n(e)g(time)p │ │ │ │ eop end │ │ │ │ %%Page: 15 17 │ │ │ │ -TeXDict begin 15 16 bop 83 100 781 4 v 947 100 a Fp(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ -b(Jan)n(uary)26 b(6,)h(2026)p 3038 100 V 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5208 y Fm(mtxY)41 │ │ │ │ b(=)j(DenseMtx_new\(\))37 b(;)208 5308 y(rc)42 b(=)h(DenseMtx_readFrom) │ │ │ │ o(Fil)o(e\()o(mtx)o(Y,)37 b(mtxFileName\))i(;)208 5407 │ │ │ │ y(DenseMtx_dimens)o(ion)o(s\()o(mt)o(xY,)e(&nrow,)k(&nrhs\))g(;)p │ │ │ │ eop end │ │ │ │ %%Page: 20 22 │ │ │ │ -TeXDict begin 20 21 bop 83 100 781 4 v 947 100 a Fp(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ -b(Jan)n(uary)26 b(6,)h(2026)p 3038 100 V 781 w Fo(20)208 │ │ │ │ +TeXDict begin 20 21 bop 83 100 760 4 v 926 100 a Fp(SPOOLES)32 │ │ │ │ +b(2.2)f(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ +b(Jan)n(uary)25 b(17,)i(2026)p 3059 100 V 760 w Fo(20)208 │ │ │ │ 390 y(The)h Fm(nrhs)f Fo(parameter)g(con)n(tains)g(the)i(n)n(um)n(b)r │ │ │ │ (er)f(of)g(righ)n(t)g(hand)g(sides,)g(or)g(equiv)-5 b(alen)n(tly)e(,)28 │ │ │ │ b(the)h(n)n(um)n(b)r(er)f(of)g(columns)208 490 y(in)f │ │ │ │ Fj(Y)19 b Fo(.)125 656 y Ff(\210)42 b Fo(Create)26 b(and)i(setup)g(the) │ │ │ │ g Fm(BridgeMT)c Fo(ob)5 b(ject.)208 855 y Fm(bridge)41 │ │ │ │ b(=)i(BridgeMT_new\(\))38 b(;)208 955 y(BridgeMT_setMat)o(rix)o(Pa)o │ │ │ │ (ra)o(ms\()o(br)o(idg)o(e,)f(neqns,)k(type,)h(symmetryflag\))c(;)208 │ │ │ │ @@ -8902,17 +8923,17 @@ │ │ │ │ b(The)28 b(solution)g(is)g(then)g(solv)n(ed.)208 5006 │ │ │ │ y(Again,)d(note)h(the)g(presence)g(of)f Fm(permuteflag)p │ │ │ │ Fo(.)32 b(When)27 b Fm(1)p Fo(,)f Fm(mtxY)e Fo(needs)i(to)f(b)r(e)i(p)r │ │ │ │ (erm)n(uted)f(in)n(to)f(the)i(new)f(ordering,)208 5106 │ │ │ │ y(and)h Fm(mtxX)f Fo(is)h(returned)h(in)g(the)f(original)g(ordering.)p │ │ │ │ eop end │ │ │ │ %%Page: 21 23 │ │ │ │ -TeXDict begin 21 22 bop 83 100 781 4 v 947 100 a Fp(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ -b(Jan)n(uary)26 b(6,)h(2026)p 3038 100 V 781 w Fo(21)0 │ │ │ │ +TeXDict begin 21 22 bop 83 100 760 4 v 926 100 a Fp(SPOOLES)32 │ │ │ │ +b(2.2)f(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ +b(Jan)n(uary)25 b(17,)i(2026)p 3059 100 V 760 w Fo(21)0 │ │ │ │ 390 y Fe(4.2)135 b(The)45 b Fd(BridgeMT)c Fe(Data)46 │ │ │ │ b(Structure)0 596 y Fo(The)28 b Fm(BridgeMT)c Fo(structure)j(has)g(the) │ │ │ │ h(follo)n(wing)f(\014elds.)125 784 y Ff(\210)42 b Fo(Graph)27 │ │ │ │ b(parameters:)301 949 y Fp({)41 b Fm(int)i(neqns)25 b │ │ │ │ Fo(:)37 b(n)n(um)n(b)r(er)27 b(of)h(equations,)f(i.e.,)h(n)n(um)n(b)r │ │ │ │ (er)f(of)h(v)n(ertices)e(in)i(the)g(graph.)301 1081 y │ │ │ │ Fp({)41 b Fm(int)i(nedges)25 b Fo(:)37 b(n)n(um)n(b)r(er)27 │ │ │ │ @@ -8990,17 +9011,17 @@ │ │ │ │ b Fo(:)k(ob)5 b(ject)28 b(that)g(con)n(tains)e(the)i(sym)n(b)r(olic)f │ │ │ │ (factorization)g(of)g(the)h(matrix.)301 5308 y Fp({)41 │ │ │ │ b Fm(SubMtxManager)d(*mtxmanager)33 b Fo(:)55 b(ob)5 │ │ │ │ b(ject)37 b(that)g(manages)f(the)h Fm(SubMtx)d Fo(ob)5 │ │ │ │ b(jects)37 b(that)g(store)f(the)h(factor)390 5407 y(en)n(tries)27 │ │ │ │ b(and)h(are)e(used)i(in)g(the)g(solv)n(es.)p eop end │ │ │ │ %%Page: 22 24 │ │ │ │ -TeXDict begin 22 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│ │ │ 818 621 27 4 v 28 w(setDefaultFields\()o(\))p Fo(.)101 │ │ │ │ 783 y(2.)42 b Fm(int)g(BridgeMT_setDefa)o(ul)o(tFi)o(el)o(ds)37 │ │ │ │ b(\()43 b(BridgeMT)e(*bridge)f(\))j(;)208 913 y Fo(The)27 │ │ │ │ @@ -9148,17 +9169,17 @@ │ │ │ │ b Fm(int)g(BridgeMT_symbfac)o(IV)o(L)c(\()43 b(BridgeMT)d(*bridge,)g │ │ │ │ (IVL)j(**pobj)e(\))i(;)208 5276 y Fo(This)27 b(metho)r(d)h(\014lls)g │ │ │ │ Fm(*pobj)e Fo(with)i(its)f Fm(symbfacIVL)d Fo(p)r(oin)n(ter.)208 │ │ │ │ 5407 y Fg(R)l(eturn)k(value:)38 b Fo(1)27 b(for)g(a)g(normal)g(return,) │ │ │ │ g(-1)g(if)34 b Fm(bridge)25 b Fo(is)j Fm(NULL)p Fo(.)e(-2)h(if)34 │ │ │ │ b Fm(pobj)26 b Fo(is)i Fm(NULL)p Fo(.)p eop end │ │ │ │ %%Page: 24 26 │ │ │ │ -TeXDict begin 24 25 bop 83 100 781 4 v 947 100 a Fp(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ -b(Jan)n(uary)26 b(6,)h(2026)p 3038 100 V 781 w Fo(24)101 │ │ │ │ +TeXDict begin 24 25 bop 83 100 760 4 v 926 100 a Fp(SPOOLES)32 │ │ │ │ +b(2.2)f(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ +b(Jan)n(uary)25 b(17,)i(2026)p 3059 100 V 760 w Fo(24)101 │ │ │ │ 390 y(5.)42 b Fm(int)g(BridgeMT_mtxmana)o(ge)o(r)c(\()43 │ │ │ │ b(BridgeMT)d(*bridge,)g(SubMtxManager)f(**pobj)i(\))i(;)208 │ │ │ │ 523 y Fo(This)27 b(metho)r(d)h(\014lls)g Fm(*pobj)e Fo(with)i(its)f │ │ │ │ Fm(mtxmanager)d Fo(p)r(oin)n(ter.)208 656 y Fg(R)l(eturn)k(value:)38 │ │ │ │ b Fo(1)27 b(for)g(a)g(normal)g(return,)g(-1)g(if)34 b │ │ │ │ Fm(bridge)25 b Fo(is)j Fm(NULL)p Fo(.)e(-2)h(if)34 b │ │ │ │ Fm(pobj)26 b Fo(is)i Fm(NULL)p Fo(.)101 822 y(6.)42 b │ │ │ │ @@ -9219,17 +9240,17 @@ │ │ │ │ (Par)o(am)o(s)c(\()43 b(BridgeMT)d(*bridge,)g(int)j(sparsityflag,)38 │ │ │ │ b(int)k(pivotingflag,)818 5125 y(double)f(tau,)h(double)f(droptol,)f │ │ │ │ (int)j(lookahead,)c(PatchAndGoInfo)f(*patchinfo)h(\))k(;)208 │ │ │ │ 5258 y Fo(This)27 b(metho)r(d)h(sets)g(parameters)d(needed)j(for)f(the) │ │ │ │ h(factorization.)208 5391 y Fg(R)l(eturn)g(value:)p eop │ │ │ │ end │ │ │ │ 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b(whic)n(h)h(sp)r(eci\014es)g(the)g(relativ)n(e)f(size)g(of)h(a)g │ │ │ │ (subtree)f(that)h(forms)f(a)208 5132 y(domain.)49 b(If)39 │ │ │ │ b Fm(maptype)30 b Fo(is)i(not)g(one)f(of)h(1,)h(2,)g(3)f(or)f(4,)i(the) │ │ │ │ f(default)h(map)f(is)g(used:)45 b(domain)32 b(decomp)r(osition)g(with) │ │ │ │ 208 5232 y Fm(cutoff)25 b Fo(=)i(1/\(2*)p Fm(nthread)p │ │ │ │ Fo(\).)208 5365 y Fg(R)l(eturn)h(value:)p eop end │ │ │ │ %%Page: 26 28 │ │ │ │ -TeXDict begin 26 27 bop 83 100 781 4 v 947 100 a Fp(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ -b(Jan)n(uary)26 b(6,)h(2026)p 3038 100 V 781 w Fo(26)618 │ │ │ │ +TeXDict begin 26 27 bop 83 100 760 4 v 926 100 a Fp(SPOOLES)32 │ │ │ │ +b(2.2)f(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ +b(Jan)n(uary)25 b(17,)i(2026)p 3059 100 V 760 w Fo(26)618 │ │ │ │ 377 y(1)99 b(normal)26 b(return,)i(factorization)e(did)i(complete)590 │ │ │ │ 477 y(-1)99 b Fm(bridge)25 b Fo(is)i Fm(NULL)2393 377 │ │ │ │ y Fo(-2)99 b Fm(nthread)24 b Fj(<)k Fo(1)2393 477 y(-5)99 │ │ │ │ b Fm(frontETree)23 b Fo(is)28 b(not)f(presen)n(t)101 │ │ │ │ 672 y(2.)42 b Fm(int)g(BridgeMT_factor)37 b(\()43 b(BridgeMT)e │ │ │ │ (*bridge,)f(InpMtx)h(*mtxA,)g(int)i(permuteflag,)38 b(int)43 │ │ │ │ b(*perror)d(\))j(;)208 805 y Fo(This)24 b(metho)r(d)g(p)r(erm)n(utes)g │ │ │ │ @@ -9399,17 +9420,17 @@ │ │ │ │ Fm(BridgeMPI)d Fo(driv)n(er)i(program)f(\(whose)i(complete)g(listing)g │ │ │ │ (is)g(found)h(in)0 5164 y(App)r(endix)32 b(C\).)49 b(Section)32 │ │ │ │ b(5.2)e(describ)r(es)h(the)h(in)n(ternal)f(data)g(\014elds)g(of)h(the)g │ │ │ │ Fm(BridgeMPI)c Fo(ob)5 b(ject.)48 b(Section)31 b(3.3)g(con)n(tains)0 │ │ │ │ 5264 y(the)d(protot)n(yp)r(es)e(and)i(descriptions)f(of)g(all)h │ │ │ │ Fm(Bridge)d Fo(metho)r(ds.)1908 5656 y(27)p eop end │ │ │ │ %%Page: 28 30 │ │ │ │ -TeXDict begin 28 29 bop 83 100 781 4 v 947 100 a Fp(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ -b(Jan)n(uary)26 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│ │ │ (-----)h(PARALLEL)e(SOLVE)i(SETUP)f(-----\\n")349 1187 │ │ │ │ @@ -10939,17 +10960,17 @@ │ │ │ │ (time)f(to)h(solve)e(linear)g(system")349 5073 y("\\n)173 │ │ │ │ b(CPU)42 b(\0458.3f)g(:)h(time)f(to)h(gather)e(solution)f(")349 │ │ │ │ 5172 y("\\n)173 b(CPU)42 b(\0458.3f)g(:)h(time)f(to)h(permute)d │ │ │ │ (solution)g(into)i(old)h(ordering")349 5272 y("\\n)f(CPU)g(\0458.3f)g │ │ │ │ (:)h(total)f(solve)f(time")349 5372 y("\\n\\n)g(solve:)g(raw)i(mflops)e │ │ │ │ (\0458.3f,)g(overall)g(mflops)g(\0458.3f",)p eop end │ │ │ │ %%Page: 57 59 │ │ │ │ -TeXDict begin 57 58 bop 83 100 781 4 v 947 100 a Fp(SPOOLES)32 │ │ │ │ -b(2.2)e(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ -b(Jan)n(uary)26 b(6,)h(2026)p 3038 100 V 781 w Fo(57)349 │ │ │ │ +TeXDict begin 57 58 bop 83 100 760 4 v 926 100 a Fp(SPOOLES)32 │ │ │ │ +b(2.2)f(W)-8 b(rapp)s(er)32 b(Ob)5 b(jects)28 b Fl(:)120 │ │ │ │ +b(Jan)n(uary)25 b(17,)i(2026)p 3059 100 V 760 w Fo(57)349 │ │ │ │ 390 y Fm(bridge->cpus[15)o(],)37 b(bridge->cpus[16],)g │ │ │ │ (bridge->cpus[17])o(,)349 490 y(bridge->cpus[18)o(],)g │ │ │ │ (bridge->cpus[19],)g(bridge->cpus[20])o(,)349 589 y(bridge->cpus[21)o │ │ │ │ (],)349 689 y(1.e-6*nsolveops)o(/br)o(id)o(ge-)o(>c)o(pus)o([1)o(8])o │ │ │ │ (,)349 789 y(1.e-6*nsolveops)o(/br)o(id)o(ge-)o(>c)o(pus)o([2)o(1])o │ │ │ │ (\))h(;)0 888 y(fflush\(msgFile\))f(;)0 988 y(if)43 b(\()g(myid)f(==)h │ │ │ │ (0)g(\))g({)131 1088 y(if)g(\()g(msglvl)e(>)i(0)g(\))g({)262 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -1,13 +1,13 @@ │ │ │ │ │ Wrapper Objects for Solving │ │ │ │ │ a Linear System of Equations │ │ │ │ │ using SPOOLES 2.2 │ │ │ │ │ Cleve Ashcraft Peter Schartz │ │ │ │ │ Boeing Shared Services Group1 CSARCorporation2 │ │ │ │ │ - January 6, 2026 │ │ │ │ │ + January 17, 2026 │ │ │ │ │ 1P. O. Box 24346, Mail Stop 7L-21, Seattle, Washington 98124. This research was supported in part by the │ │ │ │ │ DARPAContract DABT63-95-C-0122 and the DoD High Performance Computing Modernization Program Common │ │ │ │ │ HPCSoftware Support Initiative. │ │ │ │ │ 228035 Dorothy Drive, Agoura Hills, CA 91301. This research was supported in part by the DARPA Contract │ │ │ │ │ DABT63-95-C-0122 and the DoD High Performance Computing Modernization Program Common HPC Software │ │ │ │ │ Support Initiative. │ │ │ │ │ Abstract │ │ │ │ │ @@ -51,15 +51,15 @@ │ │ │ │ │ 4.3.5 Factor methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 │ │ │ │ │ 4.3.6 Solve methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 │ │ │ │ │ 5 The MPI Wrapper Object and Driver 27 │ │ │ │ │ 5.1 Aquick look at the MPI driver program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 │ │ │ │ │ 5.2 The BridgeMPI Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 │ │ │ │ │ 5.3 Prototypes and descriptions of BridgeMPI methods . . . . . . . . . . . . . . . . . . . . . . . . 32 │ │ │ │ │ 1 │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 2 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 2 │ │ │ │ │ 5.3.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 │ │ │ │ │ 5.3.2 Instance methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 │ │ │ │ │ 5.3.3 Parameter methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 │ │ │ │ │ 5.3.4 Setup methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 │ │ │ │ │ 5.3.5 Factor methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 │ │ │ │ │ 5.3.6 Solve methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 │ │ │ │ │ A testWrapper.c — A Serial Driver Program 37 │ │ │ │ │ @@ -104,25 +104,25 @@ │ │ │ │ │ the user must generate two SPOOLES objects — a InpMtx object for A and DenseMtx objects for Y and │ │ │ │ │ X. This process is described in section 2. │ │ │ │ │ Serial code has one process and one address space. Multithreaded code can have multiple threads sharing │ │ │ │ │ one address space. The SPOOLES library utilizes multiple threads only in the factorization and solve steps. │ │ │ │ │ All other operations act on the global data structures using serial methods. In the MPI environment, the │ │ │ │ │ data structures for A, X and Y may be distributed, and all working data structures that contain the factor │ │ │ │ │ 3 │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 4 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 4 │ │ │ │ │ matrices and their supporting information are distributed. The MPI code is much more complex than the │ │ │ │ │ serial or multithreaded codes, for not only are the factor and solves parallel and distributed (as is the symbolic │ │ │ │ │ factorization), but there is a great deal of support code necessary because of the distributed data structures. │ │ │ │ │ - ThewrappermethodsdescribedinthispaperdonotexerciseallthefunctionalityoftheMPIenvironment. │ │ │ │ │ + ThewrappermethodsdescribedinthispaperdonotexerciseallthefunctionalityoftheMPIenvironment. │ │ │ │ │ This is due to the present state of the CSAR-Nastran code from CSAR, where the matrix A and right hand │ │ │ │ │ side Y are generated on one processor. We chose to do all the serial preprocessing │ │ │ │ │ - • generate a graph of the matrix, │ │ │ │ │ - • order the graph, │ │ │ │ │ - • compute the symbolic factorization, │ │ │ │ │ - • and construct the permutations │ │ │ │ │ + • generate a graph of the matrix, │ │ │ │ │ + • order the graph, │ │ │ │ │ + • compute the symbolic factorization, │ │ │ │ │ + • and construct the permutations │ │ │ │ │ on processor 0 that reads in A and Y from the CSAR-Nastran files. Since the bulk of the overall time for a │ │ │ │ │ CSAR-Nastran run is dominated by the factor and solves, this approach was considered acceptable. For the │ │ │ │ │ user who is interested in using the MPI environment for the entire process, e.g., when A and Y cannot fit │ │ │ │ │ on one processor, see the SPOOLES User Manual for driver programs. │ │ │ │ │ Chapter 2 │ │ │ │ │ Setting up the linear system │ │ │ │ │ Ourtypical user is interested in solving AX = Y , where A is square, large and sparse, and X and Y are dense │ │ │ │ │ @@ -150,15 +150,15 @@ │ │ │ │ │ • INPMTX BY COLUMNS, where r(i,j) = j, c(i,j) = i. │ │ │ │ │ • INPMTX BY CHEVRONS, where r(i,j) = min(i,j), c(i,j) = j −i. │ │ │ │ │ Rows and columns are self-explanatory, the first coordinate r(i,j) is either the row or column of ai,j. The │ │ │ │ │ j-th “chevron” is composed of the diagonal entry aj,j, entries in the j-th row of the upper triangle, and │ │ │ │ │ entries in the j-th column of the lower triangle. It is the natural data structure for the assembly of the │ │ │ │ │ matrix entries into the “fronts” used to factor the matrix. │ │ │ │ │ 5 │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 6 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 6 │ │ │ │ │ The InpMtx object can hold one of three types of entries as “indices only” (no entries are present), real │ │ │ │ │ entries, or complex entries. The type is specified by the inputModeparameter to the InpMtx init() method. │ │ │ │ │ • INPMTX INDICES ONLY where the triples langler(i,j),c(i,j),−i are really only pairs, i.e., no numerical │ │ │ │ │ values are present. This mode is useful for assembling graphs. │ │ │ │ │ • SPOOLES REAL where ai,j is a real number, a double value. │ │ │ │ │ • SPOOLES COMPLEX where a is a complex number, really two consecutive double values. │ │ │ │ │ i,j │ │ │ │ │ @@ -192,15 +192,15 @@ │ │ │ │ │ to assemble finite element matrices.) The knowledgeable user can change the storage mode as necessary, │ │ │ │ │ and thus avoiding expensive sorts when possible. For example, after reading in the matrix data from the │ │ │ │ │ CSAR-Nastran file, the entries are already in sorted form, and the explicit sort can be avoided. │ │ │ │ │ Now let us see how we “input” information into the InpMtx object. There are several input methods, │ │ │ │ │ e.g., single entries, rows, columns, and submatrices, and each input method has three types of input, e.g, │ │ │ │ │ indices only, real entries, or complex entries. Here are the prototypes below. │ │ │ │ │ • Input methods for “indices only” mode. │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 7 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 7 │ │ │ │ │ void InpMtx_inputEntry ( InpMtx *mtxA, int row, int col ) ; │ │ │ │ │ void InpMtx_inputRow ( InpMtx *mtxA, int row, int rowsize, int rowind[] ) ; │ │ │ │ │ void InpMtx_inputColumn ( InpMtx *mtxA, int col, int colsize, int colind[] ) ; │ │ │ │ │ void InpMtx_inputMatrix ( InpMtx *mtxA, int nrow, int ncol, int rowstride, │ │ │ │ │ int colstride, int rowind[], colind[] ) ; │ │ │ │ │ • Input methods for real entries. │ │ │ │ │ void InpMtx_inputRealEntry ( InpMtx *mtxA, int row, int col, double value ) ; │ │ │ │ │ @@ -238,94 +238,94 @@ │ │ │ │ │ if ( ii < n1 ) { │ │ │ │ │ indices[count] = ij + 1 ; │ │ │ │ │ entries[count] = -1.0 ; │ │ │ │ │ count++ ; │ │ │ │ │ } │ │ │ │ │ if ( jj < n2 ) { │ │ │ │ │ indices[count] = ij + n1 ; │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 8 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 8 │ │ │ │ │ entries[count] = -1.0 ; │ │ │ │ │ count++ ; │ │ │ │ │ - } │ │ │ │ │ - InpMtx_inputRealRow(mtxA, ij, count, indices, entries) ; │ │ │ │ │ - } │ │ │ │ │ + } │ │ │ │ │ + InpMtx_inputRealRow(mtxA, ij, count, indices, entries) ; │ │ │ │ │ + } │ │ │ │ │ } │ │ │ │ │ InpMtx_changeStorageMode(mtxA, INPMTX_BY_VECTORS) ; │ │ │ │ │ The process begins by allocating an InpMtx object mtxA using the InpMtx new() method, initializing it with │ │ │ │ │ the InpMtx init() method, and filling it with matrix entries with the InpMtx inputRealRow() method. │ │ │ │ │ The last method, InpMtx changeStorageMode(), “assembles” the data (not really necessary because the │ │ │ │ │ entries are disjoint, “sorts” the data (again not necessary since the entries were input in ascending order, │ │ │ │ │ and creates a vector structure inside the InpMtx object that allows easy access to each individual row. │ │ │ │ │ - We could have input all the entries and treated it as a nonsymmetric matrix, but that would not be │ │ │ │ │ + We could have input all the entries and treated it as a nonsymmetric matrix, but that would not be │ │ │ │ │ efficient with respect to storage or factorization cost. Alternatively, we could have input all the entries and │ │ │ │ │ called the InpMtx dropLowerTriangle() method to drop the lower triangular entries. │ │ │ │ │ - 2.2 Constructing an DenseMtx object │ │ │ │ │ + 2.2 Constructing an DenseMtx object │ │ │ │ │ The DenseMtx stores a real or complex dense matrix. It is not just an array of numbers, it also has row │ │ │ │ │ indices and column indices. This allows it to exist in a distributed MPI environment where each processors │ │ │ │ │ has only a submatrix of the matrix. Here is how to initialize a DenseMtx object. │ │ │ │ │ - int type, rowid, colid, nrow, ncol, inc1, inc2 ; │ │ │ │ │ - DenseMtx *mtx = DenseMtx_new() ; │ │ │ │ │ + int type, rowid, colid, nrow, ncol, inc1, inc2 ; │ │ │ │ │ + DenseMtx *mtx = DenseMtx_new() ; │ │ │ │ │ DenseMtx_init(mtx, type, rowid, colid, nrow, ncol, inc1, inc2) ; │ │ │ │ │ - • The type is either SPOOLES REAL or SPOOLES COMPLEX. │ │ │ │ │ - • The rowid and colid values are used to identify a DenseMtx as a submatrix of a larger matrix. Any │ │ │ │ │ + • The type is either SPOOLES REAL or SPOOLES COMPLEX. │ │ │ │ │ + • The rowid and colid values are used to identify a DenseMtx as a submatrix of a larger matrix. Any │ │ │ │ │ values are suitable. │ │ │ │ │ - • nrow and ncol are the number of rows and columns in the matrix, respectively. │ │ │ │ │ - • The entries of the matrix can be stored in either row major or column major form. For row major, use │ │ │ │ │ + • nrow and ncol are the number of rows and columns in the matrix, respectively. │ │ │ │ │ + • The entries of the matrix can be stored in either row major or column major form. For row major, use │ │ │ │ │ inc1 = ncol and inc2 = 1. For column major, use inc1 = 1 and inc2 = nrow. Note, all solve and │ │ │ │ │ matrix-matrix multiply methods require that the DenseMtx object be column major. │ │ │ │ │ For example, here is the call to initialize a DenseMtx object to have real entries, 100 rows and 5 columns, │ │ │ │ │ entries column major. │ │ │ │ │ DenseMtx_init(mtx, SPOOLES_REAL, 0, 0, 100, 5, 1, 100) ; │ │ │ │ │ During the initialization, the row indices are set to 0,1,...,nrow−1 and the column indices are set to │ │ │ │ │ 0,1,...,ncol−1. The entries are not initialized. Zero the entries with a call to DenseMtx zero(). (This is │ │ │ │ │ crucial when loading a sparse right hand side into the DenseMtx object.) │ │ │ │ │ - Once we have the DenseMtx object initialized, we want to be able to access the row indices, the column │ │ │ │ │ + Once we have the DenseMtx object initialized, we want to be able to access the row indices, the column │ │ │ │ │ indices and the entries. We do this through instance methods. │ │ │ │ │ void DenseMtx_rowIndices ( DenseMtx *mtx, int *pnrow, int *prowind ) ; │ │ │ │ │ void DenseMtx_columnIndices ( DenseMtx *mtx, int *pncol, int *pcolind ) ; │ │ │ │ │ double * DenseMtx_entries ( DenseMtx *mtx ) ; │ │ │ │ │ - SPOOLES2.2 Wrapper Objects : January 6, 2026 9 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 9 │ │ │ │ │ Wewould use them as follows. │ │ │ │ │ double *entries ; │ │ │ │ │ int ncol, nrow, *colind, *rowind ; │ │ │ │ │ DenseMtx_rowIndices(mtx, &nrow, &rowind) ; │ │ │ │ │ DenseMtx_columnIndices(mtx, &ncol, &colind) ; │ │ │ │ │ entries = DenseMtx_entries(mtx) ; │ │ │ │ │ We can now fill the indices or the entries. The location of the (irow,jcol) entry is found at offset = │ │ │ │ │ irow*inc1 + jcol*inc2. The row and column increments can be found as follows. │ │ │ │ │ int inc1 = DenseMtx_rowIncrement(mtx) ; │ │ │ │ │ int inc2 = DenseMtx_columnIncrement(mtx) ; │ │ │ │ │ - To avoid dealing with row and column increments, we can retrieve and set values of a particular entry. │ │ │ │ │ + To avoid dealing with row and column increments, we can retrieve and set values of a particular entry. │ │ │ │ │ double value, real, imag ; │ │ │ │ │ int irow, jcol ; │ │ │ │ │ DenseMtx_realEntry(mtx, irow, jcol, &value) ; │ │ │ │ │ DenseMtx_complexEntry(mtx, irow, jcol, &real, &imag) ; │ │ │ │ │ DenseMtx_setRealEntry(mtx, irow, jcol, value + 10.) ; │ │ │ │ │ DenseMtx_setComplexEntry(mtx, irow, jcol, real + 1., imag + 2.) ; │ │ │ │ │ As a real example, consider the n1 × n2 grid from the previous subsection, where we assembled a finite │ │ │ │ │ difference matrix. Assume that the right hand side is zero except for points where (n1-1,0:n2-1), where a │ │ │ │ │ unit load is applied. Here is the code to generate the DenseMtx object. │ │ │ │ │ mtxY = DenseMtx_new(); │ │ │ │ │ DenseMtx_init(mtxY, SPOOLES_REAL, 0, 0, n1*n2, 1, 1, n1*n2) ; │ │ │ │ │ DenseMtx_zero(mtxY) ; │ │ │ │ │ ii = n1 - 1 ; │ │ │ │ │ for ( jj = 0 ; jj < n2 ; jj++ ) { │ │ │ │ │ - ij = ii + jj*n1 ; │ │ │ │ │ - DenseMtx_setRealEntry(mtxY, ij, 1, 1.0) ; │ │ │ │ │ + ij = ii + jj*n1 ; │ │ │ │ │ + DenseMtx_setRealEntry(mtxY, ij, 1, 1.0) ; │ │ │ │ │ } │ │ │ │ │ Do not forget to zero the entries in mtxY before setting any entries. │ │ │ │ │ - 2.3 IO for the InpMtx and DenseMtx objects │ │ │ │ │ + 2.3 IO for the InpMtx and DenseMtx objects │ │ │ │ │ The three driver programs that we describe in the next sections read A and Y from files and write X to a │ │ │ │ │ file. So the first thing we know is that the InpMtx and DenseMtx objects can read and write themselves from │ │ │ │ │ and to files. This convention is supported by most of the objects in the SPOOLES library. In fact, there │ │ │ │ │ is a common protocol that is followed. Let us take a look at the common IO methods for the InpMtx. │ │ │ │ │ - • int InpMtx readFromFile ( InpMtx *obj, char *filename ) ; │ │ │ │ │ - • int InpMtx readFromFormattedFile ( InpMtx *obj, FILE *fp ) ; │ │ │ │ │ - • int InpMtx readFromBinaryFile ( InpMtx *obj, FILE *fp ) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 10 │ │ │ │ │ + • int InpMtx readFromFile ( InpMtx *obj, char *filename ) ; │ │ │ │ │ + • int InpMtx readFromFormattedFile ( InpMtx *obj, FILE *fp ) ; │ │ │ │ │ + • int InpMtx readFromBinaryFile ( InpMtx *obj, FILE *fp ) ; │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 10 │ │ │ │ │ • int InpMtx writeToFile ( InpMtx *obj, char *filename ) ; │ │ │ │ │ • int InpMtx writeToFormattedFile ( InpMtx *obj, FILE *fp ) ; │ │ │ │ │ • int InpMtx writeToBinaryFile ( InpMtx *obj, FILE *fp ) ; │ │ │ │ │ • int InpMtx writeForHumanEye ( InpMtx *obj, FILE *fp ) ; │ │ │ │ │ There are corresponding methods for the DenseMtx object, just replace “Inp” by “Dense” in the above │ │ │ │ │ prototypes. │ │ │ │ │ Two methods take as input char * file names. Each object can be archived in its own file with a │ │ │ │ │ @@ -375,15 +375,15 @@ │ │ │ │ │ ordering, factor and solve processes. │ │ │ │ │ Section 3.1 takes a quick look at the Bridge driver program (whose complete listing is found in Ap- │ │ │ │ │ pendix A). Section 3.2 describes the internal data fields of the Bridge object. Section 3.3 contains the │ │ │ │ │ prototypes and descriptions of all Bridge methods. │ │ │ │ │ 3.1 Aquick look at serial driver program │ │ │ │ │ The entire listing of this serial driver is found in Appendix A. We now extract parts of the code. │ │ │ │ │ 11 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 12 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 12 │ │ │ │ │ • Decode the input. │ │ │ │ │ msglvl = atoi(argv[1]) ; │ │ │ │ │ msgFileName = argv[6] ; │ │ │ │ │ neqns = atoi(argv[3]) ; │ │ │ │ │ type = atoi(argv[4]) ; │ │ │ │ │ symmetryflag = atoi(argv[5]) ; │ │ │ │ │ mtxFileName = argv[6] ; │ │ │ │ │ @@ -414,15 +414,15 @@ │ │ │ │ │ • Read in the DenseMtx object for Y. │ │ │ │ │ mtxY = DenseMtx_new() ; │ │ │ │ │ rc = DenseMtx_readFromFile(mtxY, mtxFileName) ; │ │ │ │ │ DenseMtx_dimensions(mtxY, &nrow, &nrhs) ; │ │ │ │ │ The nrhs parameter contains the number of right hand sides, or equivalently, the number of columns │ │ │ │ │ in Y . │ │ │ │ │ • Create and setup the Bridge object. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 13 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 13 │ │ │ │ │ bridge = Bridge_new() ; │ │ │ │ │ Bridge_setMatrixParams(bridge, neqns, type, symmetryflag) ; │ │ │ │ │ Bridge_setMessageInfo(bridge, msglvl, msgFile) ; │ │ │ │ │ rc = Bridge_setup(bridge, mtxA) ; │ │ │ │ │ TheBridgeobjectisallocatedbyBridge new(),andvariousparametersareset. Theactualorderingof │ │ │ │ │ the matrix, symbolic factorization, and permutation creation are performed inside the Bridge setup() │ │ │ │ │ method. │ │ │ │ │ @@ -451,15 +451,15 @@ │ │ │ │ │ • Ordering parameters: │ │ │ │ │ – int maxdomainsize : maximum size of a subgraph to not split any further during the nested │ │ │ │ │ dissection process. │ │ │ │ │ – int maxnzeros : maximum number of zeros to allow in a front during the supernode amalgama- │ │ │ │ │ tion process. │ │ │ │ │ – int maxsize : maximum size of a front when the fronts are split. │ │ │ │ │ – int seed : random number seed. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 14 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 14 │ │ │ │ │ – double compressCutoff : if the Neqns < compressCutoff ∗ neqns, then the compressed graph │ │ │ │ │ is formed, ordered and used to create the symbolic factorization. │ │ │ │ │ • Matrix parameters: │ │ │ │ │ – int type : type of entries, SPOOLES REAL or SPOOLES COMPLEX, default value is SPOOLES REAL. │ │ │ │ │ – int symmetryflag: type of symmetry for the matrix, SPOOLES SYMMETRIC, SPOOLES HERMITIAN │ │ │ │ │ or SPOOLES NONSYMMETRIC, default value is SPOOLES SYMMETRIC. │ │ │ │ │ • Factorization parameters: │ │ │ │ │ @@ -496,15 +496,15 @@ │ │ │ │ │ cpus[0] : time to construct Graph cpus[7] : time to factor matrix │ │ │ │ │ cpus[1] : time to compress Graph cpus[8] : time to post-process matrix │ │ │ │ │ cpus[2] : time to order Graph cpus[9] : total factor time │ │ │ │ │ cpus[3] : time for symbolic factorization cpus[10] : time to permute rhs │ │ │ │ │ cpus[4] : total setup time cpus[11] : time to solve │ │ │ │ │ cpus[5] : time to permute matrix cpus[12] : time to permute solution │ │ │ │ │ cpus[6] : time to initialize front matrix cpus[13] : total solve time │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 15 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 15 │ │ │ │ │ 3.3 Prototypes and descriptions of Bridge methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the Bridge object. │ │ │ │ │ 3.3.1 Basic methods │ │ │ │ │ Asusual, there are four basic methods to support object creation, setting default fields, clearing any allocated │ │ │ │ │ data, and free’ing the object. │ │ │ │ │ 1. Bridge * Bridge_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Bridge structure and then sets the default fields by a call │ │ │ │ │ @@ -531,15 +531,15 @@ │ │ │ │ │ 3.3.2 Instance methods │ │ │ │ │ 1. int Bridge_oldToNewIV ( Bridge *bridge, IV **pobj ) ; │ │ │ │ │ This method fills *pobj with its oldToNewIV pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 2. int Bridge_newToOldIV ( Bridge *bridge, IV **pobj ) ; │ │ │ │ │ This method fills *pobj with its newToOldIV pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 16 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 16 │ │ │ │ │ 3. int Bridge_frontETree ( Bridge *bridge, ETree **pobj ) ; │ │ │ │ │ This method fills *pobj with its frontETree pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 4. int Bridge_symbfacIVL ( Bridge *bridge, IVL **pobj ) ; │ │ │ │ │ This method fills *pobj with its symbfacIVL pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 5. int Bridge_mtxmanager ( Bridge *bridge, SubMtxManager **pobj ) ; │ │ │ │ │ @@ -568,15 +568,15 @@ │ │ │ │ │ Return value: │ │ │ │ │ 1 normal return -3 pivotingflag is invalid │ │ │ │ │ -1 bridge is NULL -4 tau < 2.0 │ │ │ │ │ -2 sparsityflag is invalid -5 droptol < 0.0 │ │ │ │ │ 4. int Bridge_setMessagesInfo ( Bridge *bridge, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method sets the message level and file. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL, -2 if msglvl > 0 and msgFile is NULL. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 17 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 17 │ │ │ │ │ 3.3.4 Setup methods │ │ │ │ │ 1. int Bridge_setup ( Bridge *bridge, InpMtx *mtxA ) ; │ │ │ │ │ This method orders the graph, generates the front tree, computes the symbolic factorization, and │ │ │ │ │ creates the two permutation vectors. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL, -2 if mtxA is NULL. │ │ │ │ │ 2. int Bridge_factorStats ( Bridge *bridge, int type, int symmetryflag, int *pnfront, │ │ │ │ │ int *pnfactorind, int *pnfactorent, int *pnsolveops, double *pnfactorops ) ; │ │ │ │ │ @@ -635,15 +635,15 @@ │ │ │ │ │ (if pivoting is requested), the drop tolerance (for an approximate factorization), and so on. Rather than │ │ │ │ │ burden the user with the knowledge of and setting these parameters, there are decent default values built │ │ │ │ │ into the object. │ │ │ │ │ Section 4.1 takes a quick look at the BridgeMT driver program (whose complete listing is found in │ │ │ │ │ Appendix B). Section 4.2 describes the internal data fields of the BridgeMT object. Section 3.3 contains the │ │ │ │ │ prototypes and descriptions of all Bridge methods. │ │ │ │ │ 18 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 19 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 19 │ │ │ │ │ 4.1 Aquick look at the multithreaded driver program │ │ │ │ │ The entire listing of this multithreaded driver is found in Appendix B. We now extract parts of the code. │ │ │ │ │ • Decode the input. │ │ │ │ │ msglvl = atoi(argv[1]) ; │ │ │ │ │ msgFileName = argv[6] ; │ │ │ │ │ neqns = atoi(argv[3]) ; │ │ │ │ │ type = atoi(argv[4]) ; │ │ │ │ │ @@ -675,15 +675,15 @@ │ │ │ │ │ rc = InpMtx_readFromFile(mtxA, mtxFileName) ; │ │ │ │ │ The rc parameter is the error return. In the driver it is tested for an error, but we omit this from the │ │ │ │ │ present discussion. │ │ │ │ │ • Read in the DenseMtx object for Y. │ │ │ │ │ mtxY = DenseMtx_new() ; │ │ │ │ │ rc = DenseMtx_readFromFile(mtxY, mtxFileName) ; │ │ │ │ │ DenseMtx_dimensions(mtxY, &nrow, &nrhs) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 20 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 20 │ │ │ │ │ The nrhs parameter contains the number of right hand sides, or equivalently, the number of columns │ │ │ │ │ in Y . │ │ │ │ │ • Create and setup the BridgeMT object. │ │ │ │ │ bridge = BridgeMT_new() ; │ │ │ │ │ BridgeMT_setMatrixParams(bridge, neqns, type, symmetryflag) ; │ │ │ │ │ BridgeMT_setMessageInfo(bridge, msglvl, msgFile) ; │ │ │ │ │ rc = BridgeMT_setup(bridge, mtxA) ; │ │ │ │ │ @@ -711,15 +711,15 @@ │ │ │ │ │ DenseMtx_init(mtxX, type, 0, 0, neqns, nrhs, 1, neqns) ; │ │ │ │ │ DenseMtx_zero(mtxX) ; │ │ │ │ │ rc = BridgeMT_solve(bridge, permuteflag, mtxX, mtxY) ; │ │ │ │ │ The DenseMtx object mtxX is created and initialized to be the same type and size as mtxY. Its entries │ │ │ │ │ are explicitly zeroed (this is not necessary but is a good idea in general). The solution is then solved. │ │ │ │ │ Again, note the presence of permuteflag. When 1, mtxY needs to be permuted into the new ordering, │ │ │ │ │ and mtxX is returned in the original ordering. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 21 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 21 │ │ │ │ │ 4.2 The BridgeMT Data Structure │ │ │ │ │ The BridgeMT structure has the following fields. │ │ │ │ │ • Graph parameters: │ │ │ │ │ – int neqns : number of equations, i.e., number of vertices in the graph. │ │ │ │ │ – int nedges : number of edges (includes (u,v), (v,u) and (u,u)). │ │ │ │ │ – int Neqns : number of equations in the compressed graph. │ │ │ │ │ – int Nedges : number of edges in the compressed graph. │ │ │ │ │ @@ -751,15 +751,15 @@ │ │ │ │ │ • Pointers to objects: │ │ │ │ │ – ETree *frontETree : object that defines the factorizations, e.g., the number of fronts, the tree │ │ │ │ │ they form, the number of internal and external rows for each front, and the map from vertices to │ │ │ │ │ the front where it is contained. │ │ │ │ │ – IVL *symbfacIVL : object that contains the symbolic factorization of the matrix. │ │ │ │ │ – SubMtxManager *mtxmanager : object that manages the SubMtx objects that store the factor │ │ │ │ │ entries and are used in the solves. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 22 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 22 │ │ │ │ │ – FrontMtx *frontmtx : object that stores the L, D and U factor matrices. │ │ │ │ │ – IV *oldToNewIV : object that stores old-to-new permutation vector. │ │ │ │ │ – IV *newToOldIV : object that stores new-to-old permutation vector. │ │ │ │ │ • Multithreaded information: │ │ │ │ │ – int nthread : number of threads to be used during the factor and solve. │ │ │ │ │ – int lookahead : this parameter is used to possibly reduce the idle time of threads during the │ │ │ │ │ factorization. When lookahead is 0, the factorization uses the least amount of working storage │ │ │ │ │ @@ -790,15 +790,15 @@ │ │ │ │ │ cpus[7] : time to initialize front matrix cpus[15] : total solve time │ │ │ │ │ 4.3 Prototypes and descriptions of BridgeMT methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the BridgeMT │ │ │ │ │ object. │ │ │ │ │ 4.3.1 Basic methods │ │ │ │ │ Asusual, there are four basic methods to support object creation, setting default fields, clearing any allocated │ │ │ │ │ data, and free’ing the object. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 23 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 23 │ │ │ │ │ 1. BridgeMT * BridgeMT_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the BridgeMT structure and then sets the default fields by a │ │ │ │ │ call to BridgeMT setDefaultFields(). │ │ │ │ │ 2. int BridgeMT_setDefaultFields ( BridgeMT *bridge ) ; │ │ │ │ │ The structure’s fields are set to default values: │ │ │ │ │ • neqns = nedges = Neqns = Nedges = 0. │ │ │ │ │ • maxdomainsize = maxnzeros = maxsize = seed = -1. compressCutoff = 0. │ │ │ │ │ @@ -828,15 +828,15 @@ │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 3. int BridgeMT_frontETree ( BridgeMT *bridge, ETree **pobj ) ; │ │ │ │ │ This method fills *pobj with its frontETree pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 4. int BridgeMT_symbfacIVL ( BridgeMT *bridge, IVL **pobj ) ; │ │ │ │ │ This method fills *pobj with its symbfacIVL pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 24 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 24 │ │ │ │ │ 5. int BridgeMT_mtxmanager ( BridgeMT *bridge, SubMtxManager **pobj ) ; │ │ │ │ │ This method fills *pobj with its mtxmanager pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 6. int BridgeMT_frontmtx ( BridgeMT *bridge, FrontMtx **pobj ) ; │ │ │ │ │ This method fills *pobj with its frontmtx pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 7. int BridgeMT_ownersIV ( BridgeMT *bridge, IV **pobj ) ; │ │ │ │ │ @@ -865,15 +865,15 @@ │ │ │ │ │ 1 normal return -3 maxsize ≤ 0 │ │ │ │ │ -1 bridge is NULL -4 compressCutoff> 1 │ │ │ │ │ -2 maxdomainsize ≤ 0 │ │ │ │ │ 3. int BridgeMT_setFactorParams ( BridgeMT *bridge, int sparsityflag, int pivotingflag, │ │ │ │ │ double tau, double droptol, int lookahead, PatchAndGoInfo *patchinfo ) ; │ │ │ │ │ This method sets parameters needed for the factorization. │ │ │ │ │ Return value: │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 25 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 25 │ │ │ │ │ 1 normal return -4 tau < 2.0 │ │ │ │ │ -1 bridge is NULL -5 droptol < 0.0 │ │ │ │ │ -2 sparsityflag is invalid -6 lookahead < 0 │ │ │ │ │ -3 pivotingflag is invalid │ │ │ │ │ 4. int BridgeMT_setMessagesInfo ( BridgeMT *bridge, int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method sets the message level and file. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL, -2 if msglvl > 0 and msgFile is NULL. │ │ │ │ │ @@ -905,15 +905,15 @@ │ │ │ │ │ Thewrapmapandbalancedmaparenotrecommended. Thesubtree-subsetmapisagoodmapwitha │ │ │ │ │ very well balanced nested dissection ordering. The domain decomposition map is recommended when │ │ │ │ │ the nested dissection tree is imbalanced or for the multisection ordering. The domain decomposition │ │ │ │ │ map requires a cutoff parameter in [0,1] which specifies the relative size of a subtree that forms a │ │ │ │ │ domain. If maptype is not one of 1, 2, 3 or 4, the default map is used: domain decomposition with │ │ │ │ │ cutoff = 1/(2*nthread). │ │ │ │ │ Return value: │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 26 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 26 │ │ │ │ │ 1 normal return, factorization did complete -2 nthread < 1 │ │ │ │ │ -1 bridge is NULL -5 frontETree is not present │ │ │ │ │ 2. int BridgeMT_factor ( BridgeMT *bridge, InpMtx *mtxA, int permuteflag, int *perror ) ; │ │ │ │ │ This method permutes the matrix into the new ordering (if permuteflagis 1), factors the matrix, and │ │ │ │ │ then post-processes the factors. │ │ │ │ │ Return value: │ │ │ │ │ 1 normal return, factorization did complete -1 bridge is NULL │ │ │ │ │ @@ -960,15 +960,15 @@ │ │ │ │ │ burden the user with the knowledge of and setting these parameters, there are decent default values built │ │ │ │ │ into the object. Using the BridgeMPI object to solve a linear system of equations can be broken down into │ │ │ │ │ three steps. │ │ │ │ │ Section 5.1 takes a quick look at the BridgeMPI driver program (whose complete listing is found in │ │ │ │ │ Appendix C). Section 5.2 describes the internal data fields of the BridgeMPI object. Section 3.3 contains │ │ │ │ │ the prototypes and descriptions of all Bridge methods. │ │ │ │ │ 27 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 28 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 28 │ │ │ │ │ 5.1 Aquick look at the MPI driver program │ │ │ │ │ The entire listing of this MPI driver is found in Appendix C. We now extract parts of the code. │ │ │ │ │ • Decode the input. │ │ │ │ │ msglvl = atoi(argv[1]) ; │ │ │ │ │ msgFileName = argv[6] ; │ │ │ │ │ neqns = atoi(argv[3]) ; │ │ │ │ │ type = atoi(argv[4]) ; │ │ │ │ │ @@ -1001,15 +1001,15 @@ │ │ │ │ │ • Processor 0 reads in the DenseMtx object for Y. │ │ │ │ │ mtxY = DenseMtx_new() ; │ │ │ │ │ rc = DenseMtx_readFromFile(mtxY, mtxFileName) ; │ │ │ │ │ DenseMtx_dimensions(mtxY, &nrow, &nrhs) ; │ │ │ │ │ The nrhs parameter contains the number of right hand sides, or equivalently, the number of columns │ │ │ │ │ in Y . Processor 0 then broadcasts the error return to the other processors. If an error occured reading │ │ │ │ │ in the matrix, all processors call MPI Finalize() and exit. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 29 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 29 │ │ │ │ │ • Create and setup the BridgeMPI object. │ │ │ │ │ bridge = BridgeMPI_new() ; │ │ │ │ │ BridgeMPI_setMPIparams(bridge, nproc, myid, MPI_COMM_WORLD) ; │ │ │ │ │ BridgeMPI_setMatrixParams(bridge, neqns, type, symmetryflag) ; │ │ │ │ │ BridgeMPI_setMessageInfo(bridge, msglvl, msgFile) ; │ │ │ │ │ rc = BridgeMPI_setup(bridge, mtxA) ; │ │ │ │ │ The BridgeMPI object is allocated by BridgeMPI new(), and various parameters are set. The actual │ │ │ │ │ @@ -1037,15 +1037,15 @@ │ │ │ │ │ mtxX = DenseMtx_new() ; │ │ │ │ │ DenseMtx_init(mtxX, type, 0, 0, neqns, nrhs, 1, neqns) ; │ │ │ │ │ DenseMtx_zero(mtxX) ; │ │ │ │ │ All processors then cooperate to compute the solution X. │ │ │ │ │ rc = BridgeMPI_solve(bridge, permuteflag, mtxX, mtxY) ; │ │ │ │ │ Again, note the presence of permuteflag. When 1, mtxY needs to be permuted into the new ordering, │ │ │ │ │ and mtxX is returned in the original ordering. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 30 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 30 │ │ │ │ │ 5.2 The BridgeMPI Data Structure │ │ │ │ │ The BridgeMPI structure has the following fields. │ │ │ │ │ • Graph parameters: │ │ │ │ │ – int neqns : number of equations, i.e., number of vertices in the graph. │ │ │ │ │ – int nedges : number of edges (includes (u,v), (v,u) and (u,u)). │ │ │ │ │ – int Neqns : number of equations in the compressed graph. │ │ │ │ │ – int Nedges : number of edges in the compressed graph. │ │ │ │ │ @@ -1078,15 +1078,15 @@ │ │ │ │ │ factorization. When lookahead is 0, the factorization uses the least amount of working storage │ │ │ │ │ but threads can be idle. Larger values of lookahead tend to increase the working storage but │ │ │ │ │ may decrease the execution time. Values of lookahead greater than nthread are not useful. │ │ │ │ │ • Pointers to objects: │ │ │ │ │ – ETree *frontETree : object that defines the factorizations, e.g., the number of fronts, the tree │ │ │ │ │ they form, the number of internal and external rows for each front, and the map from vertices to │ │ │ │ │ the front where it is contained. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 31 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 31 │ │ │ │ │ – IVL *symbfacIVL : object that contains the symbolic factorization of the matrix. │ │ │ │ │ – SubMtxManager *mtxmanager : object that manages the SubMtx objects that store the factor │ │ │ │ │ entries and are used in the solves. │ │ │ │ │ – FrontMtx *frontmtx : object that stores the L, D and U factor matrices. │ │ │ │ │ – IV *oldToNewIV : object that stores old-to-new permutation vector. │ │ │ │ │ – IV *newToOldIV : object that stores new-to-old permutation vector. │ │ │ │ │ • MPI information: │ │ │ │ │ @@ -1124,15 +1124,15 @@ │ │ │ │ │ cpus[4] : broadcast the front tree cpus[15] : permute rhs │ │ │ │ │ cpus[5] : broadcast symbolic factor cpus[16] : distribute rhs │ │ │ │ │ cpus[6] : total setup time cpus[17] : create solution matrix │ │ │ │ │ cpus[7] : setup the factorization cpus[18] : solve │ │ │ │ │ cpus[8] : permute matrix cpus[19] : gather solution │ │ │ │ │ cpus[9] : distribute matrix cpus[20] : permute solution │ │ │ │ │ cpus[10] : initialize front matrix cpus[21] : total solve time │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 32 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 32 │ │ │ │ │ 5.3 Prototypes and descriptions of BridgeMPI methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the BridgeMPI │ │ │ │ │ object. │ │ │ │ │ 5.3.1 Basic methods │ │ │ │ │ Asusual, there are four basic methods to support object creation, setting default fields, clearing any allocated │ │ │ │ │ data, and free’ing the object. │ │ │ │ │ 1. BridgeMPI * BridgeMPI_new ( void ) ; │ │ │ │ │ @@ -1157,15 +1157,15 @@ │ │ │ │ │ 3. int BridgeMPI_clearData ( BridgeMPI *bridge ) ; │ │ │ │ │ Thismethodclearstheobjectandfree’sanyowneddata. ItthencallsBridgeMPI setDefaultFields(). │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. │ │ │ │ │ 4. int BridgeMPI_free ( BridgeMPI *bridge ) ; │ │ │ │ │ This method releases any storage by a call to BridgeMPI clearData() and then free the space for │ │ │ │ │ bridge. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 33 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 33 │ │ │ │ │ 5.3.2 Instance methods │ │ │ │ │ 1. int BridgeMPI_oldToNewIV ( BridgeMPI *bridge, IV **pobj ) ; │ │ │ │ │ This method fills *pobj with its oldToNewIV pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 2. int BridgeMPI_newToOldIV ( BridgeMPI *bridge, IV **pobj ) ; │ │ │ │ │ This method fills *pobj with its newToOldIV pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ @@ -1192,15 +1192,15 @@ │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 10. int BridgeMPI_rowmapIV ( BridgeMPI *bridge, IV **pobj ) ; │ │ │ │ │ This method fills *pobj with its rowmapIV pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 11. int BridgeMPI_ownedColumns ( BridgeMPI *bridge, IV **pobj ) ; │ │ │ │ │ This method fills *pobj with its ownedColumnsIV pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 34 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 34 │ │ │ │ │ 12. int BridgeMPI_Xloc ( BridgeMPI *bridge, DenseMtx **pobj ) ; │ │ │ │ │ This method fills *pobj with its Xloc pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 13. int BridgeMPI_Yloc ( BridgeMPI *bridge, DenseMtx **pobj ) ; │ │ │ │ │ This method fills *pobj with its Yloc pointer. │ │ │ │ │ Return value: 1 for a normal return, -1 if bridge is NULL. -2 if pobj is NULL. │ │ │ │ │ 14. int BridgeMPI_nproc ( BridgeMPI *bridge, int *pnproc ) ; │ │ │ │ │ @@ -1227,15 +1227,15 @@ │ │ │ │ │ 3. int BridgeMPI_setOrderingParams ( BridgeMPI *bridge, int maxdomainsize, int maxnzeros, │ │ │ │ │ int maxsize, int seed, double compressCutoff ) ; │ │ │ │ │ This method sets parameters needed for the ordering. │ │ │ │ │ Return value: │ │ │ │ │ 1 normal return -3 maxsize ≤ 0 │ │ │ │ │ -1 bridge is NULL -4 compressCutoff> 1 │ │ │ │ │ -2 maxdomainsize ≤ 0 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 35 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 35 │ │ │ │ │ 4. int BridgeMPI_setFactorParams ( BridgeMPI *bridge, int sparsityflag, int pivotingflag, │ │ │ │ │ double tau, double droptol, int lookahead, PatchAndGoInfo *patchinfo ) ; │ │ │ │ │ This method sets parameters needed for the factorization. │ │ │ │ │ Return value: │ │ │ │ │ 1 normal return -4 tau < 2.0 │ │ │ │ │ -1 bridge is NULL -5 droptol < 0.0 │ │ │ │ │ -2 sparsityflag is invalid -6 lookahead < 0 │ │ │ │ │ @@ -1264,15 +1264,15 @@ │ │ │ │ │ 1. int BridgeMPI_factorSetup ( BridgeMPI *bridge, int maptype, double cutoff ) ; │ │ │ │ │ This method constructs the map from fronts to owning processors, and computes the number of factor │ │ │ │ │ operations that each thread will execute. The maptype parameter can be one of four values: │ │ │ │ │ • 1 — wrap map │ │ │ │ │ • 2 — balanced map │ │ │ │ │ • 3 — subtree-subset map │ │ │ │ │ • 4 — domain decomposition map │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 36 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 36 │ │ │ │ │ Thewrapmapandbalancedmaparenotrecommended. Thesubtree-subsetmapisagoodmapwitha │ │ │ │ │ very well balanced nested dissection ordering. The domain decomposition map is recommended when │ │ │ │ │ the nested dissection tree is imbalanced or for the multisection ordering. The domain decomposition │ │ │ │ │ map requires a cutoff parameter in [0,1] which specifies the relative size of a subtree that forms a │ │ │ │ │ domain. If maptype is not one of 1, 2, 3 or 4, the default map is used: domain decomposition with │ │ │ │ │ cutoff = 1/(2*nthread). │ │ │ │ │ Return value: 1 normal return, factorization did complete, -1 bridge is NULL, -2 frontETree is not │ │ │ │ │ @@ -1328,15 +1328,15 @@ │ │ │ │ │ get input parameters │ │ │ │ │ -------------------- │ │ │ │ │ */ │ │ │ │ │ if ( argc != 10 ) { │ │ │ │ │ fprintf(stdout, │ │ │ │ │ "\n\n usage : %s msglvl msgFile neqns type symmetryflag" │ │ │ │ │ 37 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 38 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 38 │ │ │ │ │ "\n mtxFile rhsFile seed" │ │ │ │ │ "\n msglvl -- message level" │ │ │ │ │ "\n 0 -- no output" │ │ │ │ │ "\n 1 -- timings and statistics" │ │ │ │ │ "\n 2 and greater -- lots of output" │ │ │ │ │ "\n msgFile -- message file" │ │ │ │ │ "\n neqns -- # of equations" │ │ │ │ │ @@ -1380,15 +1380,15 @@ │ │ │ │ │ "\n msglvl = %d" │ │ │ │ │ "\n msgFile = %s" │ │ │ │ │ "\n neqns = %d" │ │ │ │ │ "\n type = %d" │ │ │ │ │ "\n symmetryflag = %d" │ │ │ │ │ "\n mtxFile = %s" │ │ │ │ │ "\n rhsFile = %s" │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 39 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 39 │ │ │ │ │ "\n solFile = %s" │ │ │ │ │ "\n seed = %d" │ │ │ │ │ "\n", │ │ │ │ │ argv[0], msglvl, argv[2], neqns, type, symmetryflag, │ │ │ │ │ mtxFileName, rhsFileName, solFileName, seed) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ @@ -1431,15 +1431,15 @@ │ │ │ │ │ DenseMtx_dimensions(mtxY, &nrow, &nrhs) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ -------------------------------- │ │ │ │ │ create and setup a Bridge object │ │ │ │ │ -------------------------------- │ │ │ │ │ */ │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 40 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 40 │ │ │ │ │ bridge = Bridge_new() ; │ │ │ │ │ Bridge_setMatrixParams(bridge, neqns, type, symmetryflag) ; │ │ │ │ │ Bridge_setMessageInfo(bridge, msglvl, msgFile) ; │ │ │ │ │ rc = Bridge_setup(bridge, mtxA) ; │ │ │ │ │ if ( rc != 1 ) { │ │ │ │ │ fprintf(stderr, "\n error return %d from Bridge_setup()", rc) ; │ │ │ │ │ exit(-1) ; │ │ │ │ │ @@ -1483,15 +1483,15 @@ │ │ │ │ │ exit(-1) ; │ │ │ │ │ } │ │ │ │ │ fprintf(msgFile, "\n\n ----- FACTORIZATION -----\n") ; │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n CPU %8.3f : time to permute original matrix" │ │ │ │ │ "\n CPU %8.3f : time to initialize factor matrix" │ │ │ │ │ "\n CPU %8.3f : time to compute factorization" │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 41 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 41 │ │ │ │ │ "\n CPU %8.3f : time to post-process factorization" │ │ │ │ │ "\n CPU %8.3f : total factorization time\n", │ │ │ │ │ bridge->cpus[5], bridge->cpus[6], bridge->cpus[7], │ │ │ │ │ bridge->cpus[8], bridge->cpus[9]) ; │ │ │ │ │ fprintf(msgFile, "\n\n factorization statistics" │ │ │ │ │ "\n %d pivots, %d pivot tests, %d delayed vertices" │ │ │ │ │ "\n %d entries in D, %d entries in L, %d entries in U", │ │ │ │ │ @@ -1535,15 +1535,15 @@ │ │ │ │ │ DenseMtx_writeForHumanEye(mtxX, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ if ( strcmp(solFileName, "none") != 0 ) { │ │ │ │ │ /* │ │ │ │ │ ----------------------------------- │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 42 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 42 │ │ │ │ │ write the solution matrix to a file │ │ │ │ │ ----------------------------------- │ │ │ │ │ */ │ │ │ │ │ rc = DenseMtx_writeToFile(mtxX, solFileName) ; │ │ │ │ │ if ( rc != 1 ) { │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n fatal error writing mtxX to file %s, rc = %d", │ │ │ │ │ @@ -1595,15 +1595,15 @@ │ │ │ │ │ /* │ │ │ │ │ -------------------- │ │ │ │ │ get input parameters │ │ │ │ │ -------------------- │ │ │ │ │ */ │ │ │ │ │ if ( argc != 11 ) { │ │ │ │ │ 43 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 44 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 44 │ │ │ │ │ fprintf(stdout, │ │ │ │ │ "\n\n usage : %s msglvl msgFile neqns type symmetryflag " │ │ │ │ │ "\n mtxFile rhsFile solFile seed nthread\n" │ │ │ │ │ "\n msglvl -- message level" │ │ │ │ │ "\n 0 -- no output" │ │ │ │ │ "\n 1 -- timings and statistics" │ │ │ │ │ "\n 2 and greater -- lots of output" │ │ │ │ │ @@ -1647,15 +1647,15 @@ │ │ │ │ │ seed = atoi(argv[9]) ; │ │ │ │ │ nthread = atoi(argv[10]) ; │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n\n %s input :" │ │ │ │ │ "\n msglvl = %d" │ │ │ │ │ "\n msgFile = %s" │ │ │ │ │ "\n neqns = %d" │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 45 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 45 │ │ │ │ │ "\n type = %d" │ │ │ │ │ "\n symmetryflag = %d" │ │ │ │ │ "\n mtxFile = %s" │ │ │ │ │ "\n rhsFile = %s" │ │ │ │ │ "\n solFile = %s" │ │ │ │ │ "\n nthread = %d" │ │ │ │ │ "\n", │ │ │ │ │ @@ -1699,15 +1699,15 @@ │ │ │ │ │ DenseMtx_writeForHumanEye(mtxY, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ DenseMtx_dimensions(mtxY, &nrow, &nrhs) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ---------------------------------- │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 46 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 46 │ │ │ │ │ create and setup a BridgeMT object │ │ │ │ │ ---------------------------------- │ │ │ │ │ */ │ │ │ │ │ bridge = BridgeMT_new() ; │ │ │ │ │ BridgeMT_setMatrixParams(bridge, neqns, type, symmetryflag) ; │ │ │ │ │ BridgeMT_setMessageInfo(bridge, msglvl, msgFile) ; │ │ │ │ │ rc = BridgeMT_setup(bridge, mtxA) ; │ │ │ │ │ @@ -1751,15 +1751,15 @@ │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n CPU %8.3f : time to setup parallel factorization", │ │ │ │ │ bridge->cpus[5]) ; │ │ │ │ │ if ( msglvl > 0 ) { │ │ │ │ │ fprintf(msgFile, "\n total factor operations = %.0f", │ │ │ │ │ DV_sum(bridge->cumopsDV)) ; │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 47 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 47 │ │ │ │ │ "\n upper bound on speedup due to load balance = %.2f", │ │ │ │ │ DV_sum(bridge->cumopsDV)/DV_max(bridge->cumopsDV)) ; │ │ │ │ │ fprintf(msgFile, "\n operations distributions over threads") ; │ │ │ │ │ DV_writeForHumanEye(bridge->cumopsDV, msgFile) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ @@ -1803,15 +1803,15 @@ │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------ │ │ │ │ │ setup the parallel solve │ │ │ │ │ ------------------------ │ │ │ │ │ */ │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 48 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 48 │ │ │ │ │ rc = BridgeMT_solveSetup(bridge) ; │ │ │ │ │ fprintf(msgFile, "\n\n ----- PARALLEL SOLVE SETUP -----\n") ; │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n CPU %8.3f : time to setup parallel solve", │ │ │ │ │ bridge->cpus[11]) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ @@ -1855,15 +1855,15 @@ │ │ │ │ │ */ │ │ │ │ │ rc = DenseMtx_writeToFile(mtxX, solFileName) ; │ │ │ │ │ if ( rc != 1 ) { │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n fatal error writing mtxX to file %s, rc = %d", │ │ │ │ │ solFileName, rc) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 49 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 49 │ │ │ │ │ exit(-1) ; │ │ │ │ │ } │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ --------------------- │ │ │ │ │ free the working data │ │ │ │ │ @@ -1906,15 +1906,15 @@ │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ --------------------------------------------------------------- │ │ │ │ │ find out the identity of this process and the number of process │ │ │ │ │ --------------------------------------------------------------- │ │ │ │ │ */ │ │ │ │ │ 50 │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 51 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 51 │ │ │ │ │ MPI_Init(&argc, &argv) ; │ │ │ │ │ MPI_Comm_rank(MPI_COMM_WORLD, &myid) ; │ │ │ │ │ MPI_Comm_size(MPI_COMM_WORLD, &nproc) ; │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ -------------------- │ │ │ │ │ get input parameters │ │ │ │ │ @@ -1958,15 +1958,15 @@ │ │ │ │ │ if ( (msgFile = fopen(buffer, "w")) == NULL ) { │ │ │ │ │ fprintf(stderr, "\n fatal error in %s" │ │ │ │ │ "\n unable to open file %s\n", │ │ │ │ │ argv[0], argv[2]) ; │ │ │ │ │ MPI_Finalize() ; │ │ │ │ │ return(0) ; │ │ │ │ │ } │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 52 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 52 │ │ │ │ │ CVfree(buffer) ; │ │ │ │ │ } │ │ │ │ │ neqns = atoi(argv[3]) ; │ │ │ │ │ type = atoi(argv[4]) ; │ │ │ │ │ symmetryflag = atoi(argv[5]) ; │ │ │ │ │ mtxFileName = argv[6] ; │ │ │ │ │ rhsFileName = argv[7] ; │ │ │ │ │ @@ -2010,15 +2010,15 @@ │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ } │ │ │ │ │ } │ │ │ │ │ /* │ │ │ │ │ --------------------------------------------------------------- │ │ │ │ │ processor 0 broadcasts the error return to the other processors │ │ │ │ │ --------------------------------------------------------------- │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 53 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 53 │ │ │ │ │ */ │ │ │ │ │ MPI_Bcast((void *) &rc, 1, MPI_INT, 0, MPI_COMM_WORLD) ; │ │ │ │ │ if ( rc != 1 ) { │ │ │ │ │ MPI_Finalize() ; │ │ │ │ │ return(-1) ; │ │ │ │ │ } │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ @@ -2062,15 +2062,15 @@ │ │ │ │ │ ------------------------------------------ │ │ │ │ │ create and setup a BridgeMPI object │ │ │ │ │ set the MPI, matrix and message parameters │ │ │ │ │ ------------------------------------------ │ │ │ │ │ */ │ │ │ │ │ bridge = BridgeMPI_new() ; │ │ │ │ │ BridgeMPI_setMPIparams(bridge, nproc, myid, MPI_COMM_WORLD) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 54 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 54 │ │ │ │ │ BridgeMPI_setMatrixParams(bridge, neqns, type, symmetryflag) ; │ │ │ │ │ BridgeMPI_setMessageInfo(bridge, msglvl, msgFile) ; │ │ │ │ │ /* │ │ │ │ │ ----------------- │ │ │ │ │ setup the problem │ │ │ │ │ ----------------- │ │ │ │ │ */ │ │ │ │ │ @@ -2114,15 +2114,15 @@ │ │ │ │ │ MPI_Finalize() ; │ │ │ │ │ exit(-1) ; │ │ │ │ │ } │ │ │ │ │ fprintf(msgFile, "\n\n ----- PARALLEL FACTOR SETUP -----\n") ; │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n CPU %8.3f : time to setup parallel factorization", │ │ │ │ │ bridge->cpus[7]) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 55 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 55 │ │ │ │ │ if ( msglvl > 0 ) { │ │ │ │ │ fprintf(msgFile, "\n total factor operations = %.0f" │ │ │ │ │ "\n upper bound on speedup due to load balance = %.2f", │ │ │ │ │ DV_sum(bridge->cumopsDV), │ │ │ │ │ DV_sum(bridge->cumopsDV)/DV_max(bridge->cumopsDV)) ; │ │ │ │ │ fprintf(msgFile, "\n operations distributions over processors") ; │ │ │ │ │ DV_writeForHumanEye(bridge->cumopsDV, msgFile) ; │ │ │ │ │ @@ -2166,15 +2166,15 @@ │ │ │ │ │ tstats[0], tstats[1], tstats[2], │ │ │ │ │ tstats[3], tstats[4], tstats[5]) ; │ │ │ │ │ fprintf(msgFile, │ │ │ │ │ "\n\n factorization: raw mflops %8.3f, overall mflops %8.3f", │ │ │ │ │ 1.e-6*nfactorops/bridge->cpus[11], │ │ │ │ │ 1.e-6*nfactorops/bridge->cpus[13]) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 56 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 56 │ │ │ │ │ /*--------------------------------------------------------------------*/ │ │ │ │ │ /* │ │ │ │ │ ------------------------ │ │ │ │ │ setup the parallel solve │ │ │ │ │ ------------------------ │ │ │ │ │ */ │ │ │ │ │ rc = BridgeMPI_solveSetup(bridge) ; │ │ │ │ │ @@ -2218,15 +2218,15 @@ │ │ │ │ │ "\n CPU %8.3f : time to distribute rhs " │ │ │ │ │ "\n CPU %8.3f : time to initialize solution matrix " │ │ │ │ │ "\n CPU %8.3f : time to solve linear system" │ │ │ │ │ "\n CPU %8.3f : time to gather solution " │ │ │ │ │ "\n CPU %8.3f : time to permute solution into old ordering" │ │ │ │ │ "\n CPU %8.3f : total solve time" │ │ │ │ │ "\n\n solve: raw mflops %8.3f, overall mflops %8.3f", │ │ │ │ │ - SPOOLES 2.2 Wrapper Objects : January 6, 2026 57 │ │ │ │ │ + SPOOLES 2.2 Wrapper Objects : January 17, 2026 57 │ │ │ │ │ bridge->cpus[15], bridge->cpus[16], bridge->cpus[17], │ │ │ │ │ bridge->cpus[18], bridge->cpus[19], bridge->cpus[20], │ │ │ │ │ bridge->cpus[21], │ │ │ │ │ 1.e-6*nsolveops/bridge->cpus[18], │ │ │ │ │ 1.e-6*nsolveops/bridge->cpus[21]) ; │ │ │ │ │ fflush(msgFile) ; │ │ │ │ │ if ( myid == 0 ) { │ │ ├── ./usr/share/doc/spooles-doc/Lock.ps.gz │ │ │ ├── Lock.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Lock.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ 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creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. Lock * Lock_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Lock structure and then sets the default fields │ │ │ │ │ by a call to Lock setDefaultFields(). │ │ │ │ │ @@ -53,15 +53,15 @@ │ │ │ │ │ thread package, lockflag != 0 means the lock will be initialized to synchronize only threads │ │ │ │ │ in this process. │ │ │ │ │ Error checking: If lock is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.3 Utility methods │ │ │ │ │ 1. void Lock_lock ( Lock *lock ) ; │ │ │ │ │ This method locks the lock. │ │ │ │ │ Error checking: If lock is NULL, an error message is printed and the program exits. │ │ │ │ │ - Lock : DRAFT January 6, 2026 3 │ │ │ │ │ + Lock : DRAFT January 17, 2026 3 │ │ │ │ │ 2. void Lock_unlock ( Lock *lock ) ; │ │ │ │ │ This method unlocks the lock. │ │ │ │ │ Error checking: If lock is NULL, an error message is printed and the program exits. │ │ │ │ │ Index │ │ │ │ │ Lock clearData(), 2 │ │ │ │ │ Lock free(), 2 │ │ │ │ │ Lock 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│ │ │ │ (\014le)f Fl(do)p 1997 5407 27 4 v 31 w(patchAndGo)d │ │ │ │ Fn(for)j(testing.)p eop end │ │ │ │ %%Page: 14 14 │ │ │ │ -TeXDict begin 14 13 bop 0 100 a Fn(14)p 166 100 1228 │ │ │ │ -4 v 1392 w Fl(MPI)27 b Fd(:)h Fm(DRAFT)f Fd(Jan)n(uary)e(6,)j(2026)p │ │ │ │ -2673 100 V 307 390 a Ff(\210)42 b Fn(The)23 b Fl(msglvl)e │ │ │ │ +TeXDict begin 14 13 bop 0 100 a Fn(14)p 166 100 1207 │ │ │ │ +4 v 1372 w Fl(MPI)26 b Fd(:)i Fm(DRAFT)f Fd(Jan)n(uary)f(17,)g(2026)p │ │ │ │ +2693 100 V 307 390 a Ff(\210)42 b Fn(The)23 b Fl(msglvl)e │ │ │ │ Fn(parameter)g(determines)i(the)h(amoun)n(t)e(of)h(output.)36 │ │ │ │ b(Use)23 b Fl(msglvl)41 b(=)i(1)23 b Fn(for)g(just)g(timing)g(output.) │ │ │ │ 307 528 y Ff(\210)42 b Fn(The)32 b Fl(msgFile)c Fn(parameter)i │ │ │ │ (determines)h(the)h(message)e(\014le)i(|)f(if)h Fl(msgFile)d │ │ │ │ Fn(is)i Fl(stdout)p Fn(,)f(then)i(the)g(message)390 628 │ │ │ │ y(\014le)c(is)f Fm(stdout)p Fn(,)h(otherwise)e(a)i(\014le)f(is)h(op)r │ │ │ │ (ened)f(with)i Fm(app)l(end)g Fn(status)e(to)g(receiv)n(e)g(an)n(y)g │ │ │ │ @@ -6236,17 +6248,17 @@ │ │ │ │ Fl(X)p Fn(.)307 5131 y Ff(\210)42 b Fl(inc1)26 b Fn(is)i(the)g(ro)n(w)e │ │ │ │ (incremen)n(t)h(for)g Fl(X)p Fn(.)307 5269 y Ff(\210)42 │ │ │ │ b Fl(inc2)26 b Fn(is)i(the)g(column)f(incremen)n(t)h(for)f │ │ │ │ Fl(X)p Fn(.)307 5407 y Ff(\210)42 b Fn(The)28 b Fl(seed)e │ │ │ │ Fn(parameter)g(is)h(a)h(random)e(n)n(um)n(b)r(er)i(seed.)p │ │ │ │ eop end │ │ │ │ %%Page: 15 15 │ │ │ │ -TeXDict begin 15 14 bop 83 100 1228 4 v 1393 100 a Fl(MPI)27 │ │ │ │ -b Fd(:)h Fm(DRAFT)110 b Fd(Jan)n(uary)25 b(6,)j(2026)p │ │ │ │ -2592 100 V 1228 w Fn(15)101 390 y(4.)42 b Fl(testGraph_Bcast)37 │ │ │ │ +TeXDict begin 15 14 bop 83 100 1207 4 v 1373 100 a Fl(MPI)26 │ │ │ │ +b Fd(:)i Fm(DRAFT)110 b Fd(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +2612 100 V 1207 w Fn(15)101 390 y(4.)42 b Fl(testGraph_Bcast)37 │ │ │ │ b(msglvl)k(msgFile)g(type)h(nvtx)g(nitem)f(root)h(seed)208 │ │ │ │ 528 y Fn(This)35 b(driv)n(er)g(program)f(tests)h(the)h(distributed)h │ │ │ │ Fl(Graph)p 2007 528 27 4 v 29 w(MPI)p 2168 528 V 30 w(Bcast\(\))c │ │ │ │ Fn(metho)r(d.)62 b(Pro)r(cessor)33 b Fl(root)h Fn(generates)g(a)208 │ │ │ │ 628 y(random)g(graph)f(of)i(t)n(yp)r(e)g Fl(type)f Fn(\(see)g(the)i(do) │ │ │ │ r(cumen)n(tation)e(for)h(the)g Fl(Graph)e Fn(ob)5 b(ject)35 │ │ │ │ b(in)g(c)n(hapter)f Fe(??)p Fn(\))h(with)h Fl(nvtx)208 │ │ │ │ @@ -6338,17 +6350,17 @@ │ │ │ │ b Fn(The)29 b Fl(type)e Fn(parameter)g(sp)r(eci\014es)i(whether)g(the)g │ │ │ │ (linear)f(system)g(is)h(real)f(or)g(complex.)40 b(Use)28 │ │ │ │ b Fl(1)h Fn(for)f(real)g(and)g Fl(2)390 5270 y Fn(for)f(complex.)307 │ │ │ │ 5407 y Ff(\210)42 b Fn(The)28 b Fl(symmetryflag)23 b │ │ │ │ Fn(parameter)j(denotes)h(the)h(presence)f(or)f(absence)h(of)h(symmetry) │ │ │ │ -7 b(.)p eop end │ │ │ │ %%Page: 16 16 │ │ │ │ -TeXDict begin 16 15 bop 0 100 a Fn(16)p 166 100 1228 │ │ │ │ -4 v 1392 w Fl(MPI)27 b Fd(:)h Fm(DRAFT)f Fd(Jan)n(uary)e(6,)j(2026)p │ │ │ │ -2673 100 V 456 390 a Fe({)41 b Fn(Use)f Fl(0)g Fn(for)f(a)g(real)g(or)g │ │ │ │ +TeXDict begin 16 15 bop 0 100 a Fn(16)p 166 100 1207 │ │ │ │ +4 v 1372 w Fl(MPI)26 b Fd(:)i Fm(DRAFT)f Fd(Jan)n(uary)f(17,)g(2026)p │ │ │ │ +2693 100 V 456 390 a Fe({)41 b Fn(Use)f Fl(0)g Fn(for)f(a)g(real)g(or)g │ │ │ │ (complex)g(symmetric)g(matrix)g Fh(A)p Fn(.)74 b(A)40 │ │ │ │ b(\()p Fh(U)2703 360 y Fg(T)2782 390 y Fn(+)26 b Fh(I)7 │ │ │ │ b Fn(\))p Fh(D)r Fn(\()p Fh(I)34 b Fn(+)26 b Fh(U)9 b │ │ │ │ Fn(\))40 b(factorization)e(is)545 490 y(computed.)456 │ │ │ │ 601 y Fe({)j Fn(Use)28 b Fl(1)f Fn(for)g(a)h(complex)f(Hermitian)g │ │ │ │ (matrix)g Fh(A)p Fn(.)38 b(A)28 b(\()p Fh(U)2273 571 │ │ │ │ y Fg(H)2354 601 y Fn(+)18 b Fh(I)7 b Fn(\))p Fh(D)r Fn(\()p │ │ │ │ @@ -6446,17 +6458,17 @@ │ │ │ │ (stored)f(con)n(tiguously)f(or)h(at)g(least)h(in)f(one)208 │ │ │ │ 5279 y(blo)r(c)n(k)h(of)g(storage,)f(w)n(e)h(could)h(ha)n(v)n(e)e(used) │ │ │ │ i(the)f Fl(MPI)p 1835 5279 V 31 w(Alltoallv\(\))c Fn(metho)r(d.)208 │ │ │ │ 5407 y(Use)k(the)h(script)f(\014le)h Fl(do)p 968 5407 │ │ │ │ V 31 w(IVL)p 1131 5407 V 30 w(alltoall)c Fn(for)j(testing.)p │ │ │ │ eop end │ │ │ │ %%Page: 17 17 │ │ │ │ -TeXDict begin 17 16 bop 83 100 1228 4 v 1393 100 a Fl(MPI)27 │ │ │ │ -b Fd(:)h Fm(DRAFT)110 b Fd(Jan)n(uary)25 b(6,)j(2026)p │ │ │ │ -2592 100 V 1228 w Fn(17)307 390 y Ff(\210)42 b Fn(The)23 │ │ │ │ +TeXDict begin 17 16 bop 83 100 1207 4 v 1373 100 a Fl(MPI)26 │ │ │ │ +b Fd(:)i Fm(DRAFT)110 b Fd(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +2612 100 V 1207 w Fn(17)307 390 y Ff(\210)42 b Fn(The)23 │ │ │ │ b Fl(msglvl)e Fn(parameter)g(determines)i(the)h(amoun)n(t)e(of)h │ │ │ │ (output.)36 b(Use)23 b Fl(msglvl)41 b(=)i(1)23 b Fn(for)g(just)g │ │ │ │ (timing)g(output.)307 524 y Ff(\210)42 b Fn(The)32 b │ │ │ │ Fl(msgFile)c Fn(parameter)i(determines)h(the)h(message)e(\014le)i(|)f │ │ │ │ (if)h Fl(msgFile)d Fn(is)i Fl(stdout)p Fn(,)f(then)i(the)g(message)390 │ │ │ │ 624 y(\014le)c(is)f Fm(stdout)p Fn(,)h(otherwise)e(a)i(\014le)f(is)h │ │ │ │ (op)r(ened)f(with)i Fm(app)l(end)g Fn(status)e(to)g(receiv)n(e)g(an)n │ │ │ │ @@ -6555,17 +6567,17 @@ │ │ │ │ y Ff(\210)42 b Fn(The)32 b Fl(msgFile)c Fn(parameter)i(determines)h │ │ │ │ (the)h(message)e(\014le)i(|)f(if)h Fl(msgFile)d Fn(is)i │ │ │ │ Fl(stdout)p Fn(,)f(then)i(the)g(message)390 5407 y(\014le)c(is)f │ │ │ │ Fm(stdout)p Fn(,)h(otherwise)e(a)i(\014le)f(is)h(op)r(ened)f(with)i │ │ │ │ Fm(app)l(end)g Fn(status)e(to)g(receiv)n(e)g(an)n(y)g(output)h(data.)p │ │ │ │ eop end │ │ │ │ %%Page: 18 18 │ │ │ │ -TeXDict begin 18 17 bop 0 100 a Fn(18)p 166 100 1228 │ │ │ │ -4 v 1392 w Fl(MPI)27 b Fd(:)h Fm(DRAFT)f Fd(Jan)n(uary)e(6,)j(2026)p │ │ │ │ -2673 100 V 307 390 a Ff(\210)42 b Fn(The)28 b Fl(nrowA)d │ │ │ │ +TeXDict begin 18 17 bop 0 100 a Fn(18)p 166 100 1207 │ │ │ │ +4 v 1372 w Fl(MPI)26 b Fd(:)i Fm(DRAFT)f Fd(Jan)n(uary)f(17,)g(2026)p │ │ │ │ +2693 100 V 307 390 a Ff(\210)42 b Fn(The)28 b Fl(nrowA)d │ │ │ │ Fn(parameter)i(is)g(the)h(n)n(um)n(b)r(er)f(of)h(ro)n(ws)e(in)i │ │ │ │ Fh(A)p Fn(.)307 524 y Ff(\210)42 b Fn(The)28 b Fl(ncolA)d │ │ │ │ Fn(parameter)i(is)g(the)h(n)n(um)n(b)r(er)f(of)h(columns)f(in)h │ │ │ │ Fh(A)p Fn(.)307 658 y Ff(\210)42 b Fn(The)28 b Fl(nentA)d │ │ │ │ Fn(parameter)i(is)g(the)h(n)n(um)n(b)r(er)f(of)h(en)n(tries)f(to)g(b)r │ │ │ │ (e)h(put)h(in)n(to)e Fh(A)p Fn(.)307 792 y Ff(\210)42 │ │ │ │ b Fn(The)28 b Fl(nrowX)d Fn(parameter)i(is)g(the)h(n)n(um)n(b)r(er)f │ │ │ │ @@ -6655,17 +6667,17 @@ │ │ │ │ (timing)g(output.)307 5308 y Ff(\210)42 b Fn(The)32 b │ │ │ │ Fl(msgFile)c Fn(parameter)i(determines)h(the)h(message)e(\014le)i(|)f │ │ │ │ (if)h Fl(msgFile)d Fn(is)i Fl(stdout)p Fn(,)f(then)i(the)g(message)390 │ │ │ │ 5407 y(\014le)c(is)f Fm(stdout)p Fn(,)h(otherwise)e(a)i(\014le)f(is)h │ │ │ │ (op)r(ened)f(with)i Fm(app)l(end)g Fn(status)e(to)g(receiv)n(e)g(an)n │ │ │ │ (y)g(output)h(data.)p eop end │ │ │ │ %%Page: 19 19 │ │ │ │ -TeXDict begin 19 18 bop 83 100 1228 4 v 1393 100 a Fl(MPI)27 │ │ │ │ -b Fd(:)h Fm(DRAFT)110 b Fd(Jan)n(uary)25 b(6,)j(2026)p │ │ │ │ -2592 100 V 1228 w Fn(19)307 390 y Ff(\210)42 b Fn(The)28 │ │ │ │ +TeXDict begin 19 18 bop 83 100 1207 4 v 1373 100 a Fl(MPI)26 │ │ │ │ +b Fd(:)i Fm(DRAFT)110 b Fd(Jan)n(uary)26 b(17,)g(2026)p │ │ │ │ +2612 100 V 1207 w Fn(19)307 390 y Ff(\210)42 b Fn(The)28 │ │ │ │ b Fl(neqns)d Fn(parameter)i(is)g(the)h(n)n(um)n(b)r(er)f(of)h │ │ │ │ (equations)f(for)g(the)h(matrix.)307 518 y Ff(\210)42 │ │ │ │ b Fn(The)28 b Fl(seed)e Fn(parameter)g(is)h(a)h(random)e(n)n(um)n(b)r │ │ │ │ (er)i(seed.)307 647 y Ff(\210)42 b Fn(The)24 b Fl(coordType)c │ │ │ │ Fn(parameter)i(de\014nes)i(the)g(co)r(ordinate)e(t)n(yp)r(e)i(that)g │ │ │ │ (will)g(b)r(e)g(used)f(during)g(the)h(redistribution.)390 │ │ │ │ 746 y(V)-7 b(alid)28 b(v)-5 b(alues)27 b(are)g Fl(1)g │ │ │ │ @@ -6758,17 +6770,17 @@ │ │ │ │ g Fl(IVL)208 5308 y Fn(ob)5 b(ject)39 b(that)h(con)n(tains)f(the)h │ │ │ │ (necessary)e(parts)h(of)g(a)h(sym)n(b)r(olic)f(factorization)f(for)h │ │ │ │ (eac)n(h)g(pro)r(cessor.)71 b(The)40 b(pro-)208 5407 │ │ │ │ y(gram)34 b(reads)g(in)i(the)g(global)f Fl(Graph)e Fn(and)j │ │ │ │ Fl(ETree)d Fn(ob)5 b(jects.)60 b(Eac)n(h)35 b(pro)r(cessor)e(creates)i │ │ │ │ (a)g(global)f Fl(InpMtx)f Fn(ob)5 b(ject)p eop end │ │ │ │ %%Page: 20 20 │ │ │ │ -TeXDict begin 20 19 bop 0 100 a Fn(20)p 166 100 1228 │ │ │ │ -4 v 1392 w Fl(MPI)27 b Fd(:)h Fm(DRAFT)f Fd(Jan)n(uary)e(6,)j(2026)p │ │ │ │ -2673 100 V 208 390 a Fn(from)i(the)i(structure)e(of)h(the)h(graph)e │ │ │ │ +TeXDict begin 20 19 bop 0 100 a Fn(20)p 166 100 1207 │ │ │ │ +4 v 1372 w Fl(MPI)26 b Fd(:)i Fm(DRAFT)f Fd(Jan)n(uary)f(17,)g(2026)p │ │ │ │ +2693 100 V 208 390 a Fn(from)k(the)i(structure)e(of)h(the)h(graph)e │ │ │ │ (and)h(computes)f(a)h(global)f(sym)n(b)r(olic)h(factorization)e(ob)5 │ │ │ │ b(ject)31 b(using)g(the)g(serial)208 490 y Fl(SymbFac)p │ │ │ │ 521 490 27 4 v 28 w(initFromInpMtx\(\))23 b Fn(metho)r(d.)43 │ │ │ │ b(The)30 b(pro)r(cessors)d(then)j(compute)f(a)h(map)f(from)g(fron)n(ts) │ │ │ │ g(to)g(pro)r(cessors,)208 589 y(and)g(eac)n(h)f(pro)r(cessor)f(thro)n │ │ │ │ (ws)h(a)n(w)n(a)n(y)f(the)i(uno)n(wned)g(matrix)g(en)n(tries)f(from)h │ │ │ │ (the)g Fl(InpMtx)e Fn(ob)5 b(ject.)41 b(The)29 b(pro)r(cessors)208 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -31,15 +31,15 @@ │ │ │ │ │ scatter/added into Y. │ │ │ │ │ TheMatMulInfoobjectstoresallthenecessaryinformationtomakethishappen. ThereisoneMatMulInfo │ │ │ │ │ object per processor. It has the following fields. │ │ │ │ │ • symflag — symmetry flag for A │ │ │ │ │ – 0 (SPOOLES SYMMETRIC) – symmetric matrix │ │ │ │ │ – 1 (SPOOLES HERMITIAN) – hermitian matrix │ │ │ │ │ 1 │ │ │ │ │ - 2 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 2 MPI : DRAFT January 17, 2026 │ │ │ │ │ – 2 (SPOOLES NONSYMMETRIC) – nonsymmetric matrix │ │ │ │ │ • opflag — operation flag for the multiply │ │ │ │ │ – 0 (MMM WITH A) — perform Y := Y +αAX │ │ │ │ │ – 1 (MMM WITH AT) — perform Y := Y +αATX │ │ │ │ │ – 2 (MMM WITH AH) — perform Y := Y +αAHX │ │ │ │ │ • IV *XownedIV — list of rows of X that are owned by this processor, these form the rows of Xq. │ │ │ │ │ • IV *XsupIV — list of rows of X that are accessed by this processor, these form the rows of Xq │ │ │ │ │ @@ -73,15 +73,15 @@ │ │ │ │ │ In a distributed environment, data must be distributed, and sometimes during a computation, data must be │ │ │ │ │ re-distributed. These methods split and redistribute four data objects. │ │ │ │ │ 1. void DenseMtx_MPI_splitByRows ( DenseMtx *mtx, IV *mapIV, int stats[], int msglvl, │ │ │ │ │ FILE *msgFile, int firsttag, MPI_Comm comm ) ; │ │ │ │ │ This method splits and redistributes the DenseMtx object based on the mapIV object that maps rows to │ │ │ │ │ processes. The messages that will be sent require nproc consecutive tags — the first is the parameter │ │ │ │ │ firsttag. On return, the stats[] vector contains the following information. │ │ │ │ │ - MPI : DRAFT January 6, 2026 3 │ │ │ │ │ + MPI : DRAFT January 17, 2026 3 │ │ │ │ │ stats[0] — #ofmessagessent stats[1] — #ofbytessent │ │ │ │ │ stats[2] — #ofmessagesreceived stats[3] — #ofbytesreceived │ │ │ │ │ Note, the values in stats[] are incremented, i.e., the stats[] vector is not zeroed at the start of the │ │ │ │ │ method, and so can be used to accumulated information with multiple calls. │ │ │ │ │ Error checking: If mtx or rowmapIV is NULL, or if msglvl > 0 and msgFile is NULL, or if firsttag < │ │ │ │ │ 0 or firsttag + nproc is larger than the largest available tag, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ @@ -117,15 +117,15 @@ │ │ │ │ │ use the chevron coordinate type to store the matrix entries. This method will redistribute a matrix │ │ │ │ │ by rows if the coordinate type is 1 (for rows) and mapIV is a row map. Similarly, this method will │ │ │ │ │ redistribute a matrix by columns if the coordinate type is 2 (for columns) and mapIV is a column map. │ │ │ │ │ See the InpMtx object for details. The messages that will be sent require nproc consecutive tags — the │ │ │ │ │ first is the parameter firsttag. On return, the stats[] vector contains the following information. │ │ │ │ │ stats[0] — #ofmessagessent stats[1] — #ofbytessent │ │ │ │ │ stats[2] — #ofmessagesreceived stats[3] — #ofbytesreceived │ │ │ │ │ - 4 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 4 MPI : DRAFT January 17, 2026 │ │ │ │ │ Note, the values in stats[] are incremented, i.e., the stats[] vector is not zeroed at the start of the │ │ │ │ │ method, and so can be used to accumulated information with multiple calls. │ │ │ │ │ Error checking: If firsttag < 0 or firsttag + nproc is larger than the largest available tag, an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ 5. InpMtx * InpMtx_MPI_splitFromGlobal ( InpMtx *Aglobal, InpMtx *Alocal, │ │ │ │ │ IV *mapIV, int root, int stats[], int msglvl, │ │ │ │ │ FILE *msgFile, int firsttag, MPI_Comm comm ) ; │ │ │ │ │ @@ -158,15 +158,15 @@ │ │ │ │ │ knownpriortoenteringthis method. Onreturn, the stats[]vectorcontainsthe followinginformation. │ │ │ │ │ stats[0] — #ofmessagessent stats[1] — #ofbytessent │ │ │ │ │ stats[2] — #ofmessagesreceived stats[3] — #ofbytesreceived │ │ │ │ │ Note, the values in stats[] are incremented, i.e., the stats[] vector is not zeroed at the start of the │ │ │ │ │ method, and so can be used to accumulated information with multiple calls. │ │ │ │ │ Error checking: If mtx or rowmapIV is NULL, or if msglvl > 0 and msgFile is NULL, or if firsttag < │ │ │ │ │ 0 is larger than the largest available tag, an error message is printed and the program exits. │ │ │ │ │ - MPI : DRAFT January 6, 2026 5 │ │ │ │ │ + MPI : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.2 Gather and scatter methods │ │ │ │ │ These method gather and scatter/add rows of DenseMtx objects. These operations are performed during the │ │ │ │ │ distributed matrix-matrixmultiply. ThegatheroperationXq ←XisperformedbyDenseMtx MPI gatherRows(), │ │ │ │ │ P supp │ │ │ │ │ while the scatter/add operation Y q := Y q + Yr is performed by DenseMtx MPI scatterAddRows(). │ │ │ │ │ r supp │ │ │ │ │ 1. void DenseMtx_MPI_gatherRows ( DenseMtx *Y, DenseMtx *X, IVL *sendIVL, │ │ │ │ │ @@ -202,15 +202,15 @@ │ │ │ │ │ 1.2.3 Symbolic Factorization methods │ │ │ │ │ 1. IVL * SymbFac_MPI_initFromInpMtx ( ETree *etree, IV *frontOwnersIV, │ │ │ │ │ InpMtx *inpmtx, int stats[], int msglvl, │ │ │ │ │ FILE *msgFile, int firsttag, MPI_Comm comm ) ; │ │ │ │ │ IVL * SymbFac_MPI_initFromPencil ( ETree *etree, IV *frontOwnersIV, │ │ │ │ │ Pencil *pencil, int stats[], int msglvl, │ │ │ │ │ FILE *msgFile, int firsttag, MPI_Comm comm ) ; │ │ │ │ │ - 6 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 6 MPI : DRAFT January 17, 2026 │ │ │ │ │ ThesemethodsareusedinplaceoftheSymbfac initFrom{InpMtx,Pencil}()methodstocomputethe │ │ │ │ │ symbolic factorization. The ETree object is assumed to be replicated over the processes. The InpMtx │ │ │ │ │ and Pencil objects are partitioned among the processes. Therefore, to compute the IVL object that │ │ │ │ │ contains the symbolic factorization is a distributed, cooperative process. At the end of the symbolic │ │ │ │ │ factorization, each process will own a portion of the IVL object. The IVL object is neither replicated │ │ │ │ │ nor partitioned (except in trivial cases), but the IVL object on each process contains just a portion, │ │ │ │ │ usually not much more than what it needs to know for its part of the factorization and solves. │ │ │ │ │ @@ -247,15 +247,15 @@ │ │ │ │ │ cpus[0] – initialize fronts cpus[7] – extract postponed data │ │ │ │ │ cpus[1] – load original entries cpus[8] – store factor entries │ │ │ │ │ cpus[2] – update fronts cpus[9] – post initial receives │ │ │ │ │ cpus[3] – insert aggregate data cpus[10] – check for received messages │ │ │ │ │ cpus[4] – assemble aggregate data cpus[11] – post initial sends │ │ │ │ │ cpus[5] – assemble postponed data cpus[12] – check for sent messages │ │ │ │ │ cpus[6] – factor fronts │ │ │ │ │ - MPI : DRAFT January 6, 2026 7 │ │ │ │ │ + MPI : DRAFT January 17, 2026 7 │ │ │ │ │ Onreturn, the stats[] vector has the following information. │ │ │ │ │ stats[0] — #ofpivots │ │ │ │ │ stats[1] — #ofpivot tests │ │ │ │ │ stats[2] — #ofdelayed rows and columns │ │ │ │ │ stats[3] — #ofentries in D │ │ │ │ │ stats[4] — #ofentries in L │ │ │ │ │ stats[5] — #ofentries in U │ │ │ │ │ @@ -293,15 +293,15 @@ │ │ │ │ │ Error checking: If frontmtx, frontOwnersIV or stats is NULL, or if firsttag < 0 or firsttag + │ │ │ │ │ nproc, is larger than the largest available tag, or if msglvl > 0 and msgFile is NULL, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 3. void IV_MPI_allgather ( IV *iv, IV *ownersIV, int stats[], int msglvl, │ │ │ │ │ FILE *msgFile, int firsttag, MPI_Comm comm ) ; │ │ │ │ │ After a factorization with pivoting, the frontsizesIVobject needs to be made globalon eachprocessor. │ │ │ │ │ This methods takes the individual entries of an IV object whose owners are specified by the ownersIV │ │ │ │ │ - 8 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 8 MPI : DRAFT January 17, 2026 │ │ │ │ │ object, and communicates the entries around the processors until the global IV object is present on │ │ │ │ │ each. The messagesthat will be sent require at most nprocconsecutive tags — the first is the parameter │ │ │ │ │ firsttag. │ │ │ │ │ Error checking: If iv, ownersIV or stats is NULL, or if firsttag < 0 or firsttag + nproc, is larger │ │ │ │ │ than the largest available tag, or if msglvl > 0 and msgFile is NULL, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ 4. void IVL_MPI_allgather ( IVL *ivl, IV *ownersIV, int stats[], int msglvl, │ │ │ │ │ @@ -334,15 +334,15 @@ │ │ │ │ │ stats[4] — #ofsolution messages received │ │ │ │ │ stats[5] — #ofaggregatemessages received │ │ │ │ │ stats[6] — #ofsolution bytes received │ │ │ │ │ stats[7] — #ofaggregatebytes received │ │ │ │ │ Error checking: If frontmtx, mtxX,mtxB, mtxmanager,solvemap,cpusorstatsisNULL,oriffirsttag │ │ │ │ │ < 0 or firsttag + 2*nfront is larger than the largest available tag, or if msglvl > 0 and msgFile │ │ │ │ │ is NULL, an error message is printed and the program exits. │ │ │ │ │ - MPI : DRAFT January 6, 2026 9 │ │ │ │ │ + MPI : DRAFT January 17, 2026 9 │ │ │ │ │ 1.2.7 Matrix-matrix multiply methods │ │ │ │ │ The usual sequence of events is as follows. │ │ │ │ │ • Set up the data structure via a call to MatMul MPI setup(). │ │ │ │ │ • Convert the local Aq matrix to local indices via a call to MatMul setLocalIndices(). │ │ │ │ │ • Compute the matrix-matrix multiply with a call to MatMul MPI mmm(). Inside this method, the MPI │ │ │ │ │ methods DenseMtx MPI gatherRows()and DenseMtx MPI scatterAddRows()are called, along with a │ │ │ │ │ serial InpMtx matrix-matrix multiply method. │ │ │ │ │ @@ -371,15 +371,15 @@ │ │ │ │ │ 2. void MatMul_setLocalIndices ( MatMulInfo *info, InpMtx *A ) ; │ │ │ │ │ void MatMul_setGlobalIndices ( MatMulInfo *info, InpMtx *A ) ; │ │ │ │ │ The first method maps the indices of A (which are assumed to be global) into local indices. The second │ │ │ │ │ method maps the indices of A (which are assumed to be local) back into global indices. It uses the │ │ │ │ │ XmapIV, XsupIV YmapIV and YsupIV objects that are contained in the info object. These are serial │ │ │ │ │ methods, performed independently on each processor. │ │ │ │ │ Error checking: If info or A is NULL, an error message is printed and the program exits. │ │ │ │ │ - 10 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 10 MPI : DRAFT January 17, 2026 │ │ │ │ │ 3. void MatMul_MPI_mmm ( MatMulInfo *info, DenseMtx *Yloc, double alpha[], InpMtx *A, │ │ │ │ │ DenseMtx *Xloc, int stats[], int msglvl, FILE *msgFile, MPI_Comm comm) ; │ │ │ │ │ This method computes a distributed matrix-matrix multiply Y := Y + αAX, Y := Y + αATX or │ │ │ │ │ H │ │ │ │ │ Y := Y +αA X, depending on how the info object was set up. NOTE: A must have local indices, │ │ │ │ │ use MatMul setLocalIndices() to convert from global to local indices. Xloc and Yloc contain the │ │ │ │ │ owned rows of X and Y, respectively. │ │ │ │ │ @@ -413,15 +413,15 @@ │ │ │ │ │ Error checking: None presently. │ │ │ │ │ 4. IV * IV_MPI_Bcast ( IV *obj, int root, │ │ │ │ │ int msglvl, FILE *msgFile, MPI_Comm comm ) ; │ │ │ │ │ This method is a broadcast method for an IV object. The root processor broadcasts its IV object to │ │ │ │ │ the other nodes and returns a pointer to its IV object. A node other than root, clears the data in its │ │ │ │ │ IV object, receives the IV object from the root and returns a pointer to it. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ - MPI : DRAFT January 6, 2026 11 │ │ │ │ │ + MPI : DRAFT January 17, 2026 11 │ │ │ │ │ 1.2.9 Utility methods │ │ │ │ │ 1. IVL * InpMtx_MPI_fullAdjacency ( InpMtx *inpmtx, int stats[], │ │ │ │ │ int msglvl, FILE *msgFile, MPI_Comm comm ) ; │ │ │ │ │ IVL * Pencil_MPI_fullAdjacency ( Pencil *pencil, int stats[], │ │ │ │ │ int msglvl, FILE *msgFile, MPI_Comm comm ) ; │ │ │ │ │ These methods are used to return an IVL object that contains the full adjacency structure of the │ │ │ │ │ graph of the matrix or matrix pencil. The matrix or matrix pencil is distributed among the processes, │ │ │ │ │ @@ -458,15 +458,15 @@ │ │ │ │ │ IVL_MPI_alltoall ( IVL *sendIVL, IVL *recvIVL, int stats[], int msglvl, │ │ │ │ │ FILE *msgFile, int firsttag, MPI_Comm comm ) ; │ │ │ │ │ This method is used during the setup for matrix-vector multiplies. Each processor has computed │ │ │ │ │ the vertices it needs from other processors, these lists are contained in sendIVL. On return, recvIVL │ │ │ │ │ contains the lists of vertices this processor must send to all others. │ │ │ │ │ This method uses tags in the range [tag,tag+nproc-1). On return, the following statistics will have │ │ │ │ │ been added. │ │ │ │ │ - 12 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 12 MPI : DRAFT January 17, 2026 │ │ │ │ │ stats[0] — #ofmessagessent stats[1] — #ofbytessent │ │ │ │ │ stats[2] — #ofmessagesreceived stats[3] — #ofbytesreceived │ │ │ │ │ This method is safe in the sense that it uses only MPI Sendrecv(). │ │ │ │ │ Error checking: If sendIVL or stats is NULL, or if msglvl > 0 and msgFile is NULL, or if tag < 0 │ │ │ │ │ or tag + nproc is larger than the largest available tag, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 5. void * makeSendRecvIVLs ( IV *supportedIV, IV *globalmapIV, IVL *sendIVL, IVL *recvIVL, │ │ │ │ │ @@ -497,15 +497,15 @@ │ │ │ │ │ the matrix, factoring the matrix, and solving the system. Use the script file do AllInOne for testing. │ │ │ │ │ The files names for the matrix and right hand side entries are hardcoded. Processor q reads in matrix │ │ │ │ │ entries from file matrix.q.input and right hand side entries from file rhs.q.input. The format for │ │ │ │ │ the matrix files is as follows: │ │ │ │ │ neqns neqns nent │ │ │ │ │ irow jcol entry │ │ │ │ │ ... ... ... │ │ │ │ │ - MPI : DRAFT January 6, 2026 13 │ │ │ │ │ + MPI : DRAFT January 17, 2026 13 │ │ │ │ │ where neqns is the global number of equations and nent is the number of entries in this file. There │ │ │ │ │ follows nent lines, each containing a row index, a column index and one or two floating point numbers, │ │ │ │ │ one if real, two if complex. The format for the right hand side file is similar: │ │ │ │ │ nrow nrhs │ │ │ │ │ irow entry ... entry │ │ │ │ │ ... ... ... ... │ │ │ │ │ where nrow is the number of rows in this file and nrhs is the number of rigght and sides. There follows │ │ │ │ │ @@ -540,15 +540,15 @@ │ │ │ │ │ one if real, two if complex. The format for the right hand side file is similar: │ │ │ │ │ nrow nrhs │ │ │ │ │ irow entry ... entry │ │ │ │ │ ... ... ... ... │ │ │ │ │ where nrow is the number of rows in this file and nrhs is the number of rigght and sides. There follows │ │ │ │ │ nrow lines, each containing a row index and either nrhs or 2*nrhs floating point numbers, the first if │ │ │ │ │ real, the second if complex. Use the script file do patchAndGo for testing. │ │ │ │ │ - 14 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 14 MPI : DRAFT January 17, 2026 │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • The type parameter specifies a real or complex linear system. │ │ │ │ │ – type = 1 (SPOOLES REAL) for real, │ │ │ │ │ – type = 2 (SPOOLES COMPLEX) for complex. │ │ │ │ │ • The symmetryflag parameter specifies the symmetry of the matrix. │ │ │ │ │ @@ -582,15 +582,15 @@ │ │ │ │ │ • The type parameter specifies whether the linear system is real (type = 1) or complex (type = │ │ │ │ │ 2). │ │ │ │ │ • nrow is the number of rows in X. │ │ │ │ │ • ncol is the number of columns in X. │ │ │ │ │ • inc1 is the row increment for X. │ │ │ │ │ • inc2 is the column increment for X. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ - MPI : DRAFT January 6, 2026 15 │ │ │ │ │ + MPI : DRAFT January 17, 2026 15 │ │ │ │ │ 4. testGraph_Bcast msglvl msgFile type nvtx nitem root seed │ │ │ │ │ This driver program tests the distributed Graph MPI Bcast() method. Processor root generates a │ │ │ │ │ random graph of type type (see the documentation for the Graph object in chapter ??) with nvtx │ │ │ │ │ vertices. The random graph is constructed via an InpMtx object using nitem edges. Processor root │ │ │ │ │ then sends its Graph object to the other processors. Each processor computes a checksum for its object, │ │ │ │ │ and the error are collected on processor 0. Use the script file do Graph Bcast for testing. │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ @@ -625,15 +625,15 @@ │ │ │ │ │ • The n3 parameter is the number of grid points in the third direction. │ │ │ │ │ • The maxzeros parameter is the maximum number of zero entries allowed in a front. │ │ │ │ │ • The maxsize parameter is the maximum number of internal rows and columns allowed in a front. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The type parameter specifies whether the linear system is real or complex. Use 1 for real and 2 │ │ │ │ │ for complex. │ │ │ │ │ • The symmetryflag parameter denotes the presence or absence of symmetry. │ │ │ │ │ - 16 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 16 MPI : DRAFT January 17, 2026 │ │ │ │ │ – Use 0 for a real or complex symmetric matrix A. A (UT + I)D(I + U) factorization is │ │ │ │ │ computed. │ │ │ │ │ – Use 1 for a complex Hermitian matrix A. A (UH +I)D(I +U) factorization is computed. │ │ │ │ │ – Use 2 for a real or complex nonsymmetric matrix A. A (L + I)D(I + U) factorization is │ │ │ │ │ computed. │ │ │ │ │ • The sparsityflag parameter denotes a direct or approximate factorization. Valid values are 0 │ │ │ │ │ for a direct factorization and 1 is for an approximate factorization. │ │ │ │ │ @@ -671,15 +671,15 @@ │ │ │ │ │ IVL object with nproc lists. List iproc contains a set of ids of items that this processor will receive │ │ │ │ │ from processor iproc. The processors then call IVL MPI allgather to create their “send” IVL object, │ │ │ │ │ where list iproc contains a set of ids of items that this processor will send to processor iproc. The set │ │ │ │ │ of lists in all the “receive” IVL objects is exactly the same as the set of lists in all the “send” objects. │ │ │ │ │ This is an “all-to-all” scatter/gather operation. Had the lists be stored contiguously or at least in one │ │ │ │ │ block of storage, we could have used the MPI Alltoallv() method. │ │ │ │ │ Use the script file do IVL alltoall for testing. │ │ │ │ │ - MPI : DRAFT January 6, 2026 17 │ │ │ │ │ + MPI : DRAFT January 17, 2026 17 │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • The n parameter is an upper bound on list size and element value. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ 8. testIVL_allgather msglvl msgFile nlist seed │ │ │ │ │ This driver program tests the distributed IVL MPI allgather() method. Each processor generates │ │ │ │ │ @@ -716,15 +716,15 @@ │ │ │ │ │ local coordinates. The matrix-matrix multiply is computed, and then all the Yq local matrices are │ │ │ │ │ gathered onto processor zero into Y , which is then compared with Z that was computed using a serial │ │ │ │ │ matrix-matrix multiply. The error is written to the message file by processor zero. Use the script file │ │ │ │ │ do MMM for testing. │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ - 18 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 18 MPI : DRAFT January 17, 2026 │ │ │ │ │ • The nrowA parameter is the number of rows in A. │ │ │ │ │ • The ncolA parameter is the number of columns in A. │ │ │ │ │ • The nentA parameter is the number of entries to be put into A. │ │ │ │ │ • The nrowX parameter is the number of rows in X. │ │ │ │ │ • The coordTypeparameter defines the coordinate type that will be used during the redistribution. │ │ │ │ │ Valid values are 1 for rows, 2 for columns and 3 for chevrons. │ │ │ │ │ • The inputMode parameter defines the mode of input. Valid values are 1 for real entries and 2 for │ │ │ │ │ @@ -759,15 +759,15 @@ │ │ │ │ │ This driver program tests the distributed InpMtx MPI splitFromGlobal() method to split a InpMtx │ │ │ │ │ sparse matrix object. Process root reads in the InpMtx object. A random map is generated (the same │ │ │ │ │ maponall processes) and the object is scattered from processor root to the other processors. Use the │ │ │ │ │ script file do ScatterInpMtx for testing. │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ - MPI : DRAFT January 6, 2026 19 │ │ │ │ │ + MPI : DRAFT January 17, 2026 19 │ │ │ │ │ • The neqns parameter is the number of equations for the matrix. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The coordTypeparameter defines the coordinate type that will be used during the redistribution. │ │ │ │ │ Valid values are 1 for rows, 2 for columns and 3 for chevrons. │ │ │ │ │ • The inputMode parameter defines the mode of input. Valid values are 0 for indices only, 1 for │ │ │ │ │ real entries and 2 for complex entries. │ │ │ │ │ • The inInpMtxFile parameter is the name of the file that contain the InpMtx object. │ │ │ │ │ @@ -802,15 +802,15 @@ │ │ │ │ │ • The inputMode parameter defines the mode of input. Valid values are 0 for indices only, 1 for │ │ │ │ │ real entries and 2 for complex entries. │ │ │ │ │ • The inInpMtxFile parameter is the name of the file that contain the InpMtx object. │ │ │ │ │ 15. testSymbFac msglvl msgFile inGraphFile inETreeFile seed │ │ │ │ │ This driver program tests the distributed SymbFac MPI initFromInpMtx() method that forms a IVL │ │ │ │ │ object that contains the necessary parts of a symbolic factorization for each processor. The pro- │ │ │ │ │ gram reads in the global Graph and ETree objects. Each processor creates a global InpMtx object │ │ │ │ │ - 20 MPI : DRAFT January 6, 2026 │ │ │ │ │ + 20 MPI : DRAFT January 17, 2026 │ │ │ │ │ from the structure of the graph and computes a global symbolic factorization object using the serial │ │ │ │ │ SymbFac initFromInpMtx() method. The processors then compute a map from fronts to processors, │ │ │ │ │ and each processor throws away the unowned matrix entries from the InpMtx object. The processors │ │ │ │ │ then compute their necessary symbolic factorizations in parallel. For a check, they compare the two │ │ │ │ │ symbolic factorizations for error. Use the script file do symbfac for testing. │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ ├── ./usr/share/doc/spooles-doc/MSMD.ps.gz │ │ │ ├── MSMD.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o MSMD.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1227,16 +1227,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1424,79 +1426,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ B7D99CD533EC5F931B18E6B39BECF67FA2D6DD1AEC76772B068BE06335A94C05 │ │ │ │ 7A4DDEE77B66101DA855C17AC312600370B34E31F5EC3A01300A8EB60B4C9767 │ │ │ │ -1B2FA10DF7E91D3BB34A1B1CE7A0015A57C813E0280D873ADB88440048702D1F │ │ │ │ -77994EE04EC3B4531D6E1888C86A8F0DA6CF1F056F16AB0DD76C862830F89DA4 │ │ │ │ -28923B3AA543E0D6E41D3BD283E600BC11F889315EE92C675C109C81065ED1BC │ │ │ │ -82A5583D1B723D50051B0557A367887F5B263014C6E77288B4883C50889473D3 │ │ │ │ -3787BAD4BEB88BD1353AFA5B73E61814819537E7FF09F53EF94792BB3DD36ED0 │ │ │ │ -002D0E7A6CDAB85A9C17AF5664BCB5A71663B861880F3ECCABC8E7A2FC81A4CC │ │ │ │ -AE7A87503FDC1CE0077BA51ECC7B43B60793FED8E9AAD5BBD03ADD6183DCD26D │ │ │ │ -24A74163611C05562437644EF9B8889FD4F9D311911204FEFD35237486F2D2D0 │ │ │ │ -B6783A03BF12EA6D19D6D0F87E4D08515F12F9CBF1961CAA71E0D69FE3C4C4D2 │ │ │ │ -7C7FB64ED24F8684C8F00C2BEDEA53EA390CDC0B5BEBD7DD982580B2EA1F1F89 │ │ │ │ -CFED5916630DC2BA32BB9180277E1ABC339B3B7DE086717BD93F7FF3681BA5B3 │ │ │ │ -FCF671C4B293C2DE4A322F0AA3323A4934444C69F23EF90120B8755482757759 │ │ │ │ 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(eigh)m(t)g(of)f(v)m(ertices)h(eliminated,)f(etc.)137 │ │ │ │ 702 y Fm(\210)45 b Fn(MSMDvtx)29 b Fo(:)40 b(an)31 b(ob)5 │ │ │ │ b(ject)31 b(that)g(mo)s(dels)f(a)h(v)m(ertex.)0 917 y(A)f(user)g(needs) │ │ │ │ g(to)h(understand)e(the)h Fn(MSMDinfo)e Fo(ob)5 b(ject,)32 │ │ │ │ @@ -5454,17 +5466,17 @@ │ │ │ │ (ultiple)f(minim)m(um)e(degree.)330 5294 y Fi({)45 b │ │ │ │ Fn(stepType)h(>)h(1)22 b Fo(|)g(an)g(indep)s(enden)m(t)f(set)i(of)f(v)m │ │ │ │ (ertices)i(is)e(eliminated)i(whose)e(priorities)g(lie)h(b)s(et)m(w)m │ │ │ │ (een)427 5407 y(the)31 b(minim)m(um)e(priorit)m(y)i(and)f(the)h(minim)m │ │ │ │ (um)e(priorit)m(y)i(m)m(ultiplied)g(b)m(y)f Fn(stepType)p │ │ │ │ Fo(.)p eop end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fo(4)p 136 100 1158 4 v │ │ │ │ -1340 w Fn(MSMD)29 b Fe(:)i Fk(DRAFT)f Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2742 100 V 227 399 a Fo(The)f(default)h(v)-5 b(alue)31 │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fo(4)p 136 100 1135 4 v │ │ │ │ +1317 w Fn(MSMD)29 b Fe(:)i Fk(DRAFT)f Fe(Jan)m(uary)g(17,)h(2026)p │ │ │ │ +2765 100 V 227 399 a Fo(The)f(default)h(v)-5 b(alue)31 │ │ │ │ b(is)f Fn(1)p Fo(,)g(m)m(ultiple)h(elimination)h(of)f(v)m(ertices)h │ │ │ │ (with)e(minim)m(um)f(priorit)m(y)-8 b(.)137 625 y Fm(\210)45 │ │ │ │ b Fn(int)i(seed)26 b Fo(|)g(a)h(seed)g(used)f(for)h(a)g(random)f(n)m │ │ │ │ (um)m(b)s(er)f(generator,)k(this)e(in)m(tro)s(duces)f(a)i(necessary)f │ │ │ │ (random)227 738 y(elemen)m(t)32 b(to)f(the)g(ordering.)137 │ │ │ │ 964 y Fm(\210)45 b Fn(int)i(msglvl)33 b Fo({)i(message)g(lev)m(el)h │ │ │ │ (for)e(statistics,)k(diagnostics)e(and)d(monitoring.)54 │ │ │ │ @@ -5509,17 +5521,17 @@ │ │ │ │ Fo(ob)5 b(jects)31 b(that)g(represen)m(t)g(the)f(v)m(ertices.)137 │ │ │ │ 5181 y Fm(\210)45 b Fn(IV)i(ivtmpIV)29 b Fo({)i Fn(IV)e │ │ │ │ Fo(ob)5 b(ject)32 b(that)f(holds)e(an)i(in)m(teger)g(temp)s(orary)f(v)m │ │ │ │ (ector.)137 5407 y Fm(\210)45 b Fn(IV)i(reachIV)29 b │ │ │ │ Fo({)i Fn(IV)e Fo(ob)5 b(ject)32 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Fo(|)h(n)m(um)m(b)s(er)f(of)i(fron)m(ts)f(created)h(at)h(this)e │ │ │ │ @@ -5561,17 +5573,17 @@ │ │ │ │ h(\(priorit)m(y\))h(heap)330 5112 y Fi({)45 b Fn('R')30 │ │ │ │ b Fo({)h(v)m(ertex)g(on)f(reac)m(h)h(set)330 5260 y Fi({)45 │ │ │ │ b Fn('I')30 b Fo({)h(v)m(ertex)g(found)e(to)i(b)s(e)f │ │ │ │ (indistinguishable)g(to)h(another)330 5407 y Fi({)45 │ │ │ │ b Fn('B')30 b Fo({)h(b)s(oundary)d(v)m(ertex,)k(to)f(b)s(e)e │ │ │ │ (eliminated)j(in)e(another)h(stage)p eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fo(6)p 136 100 1158 4 v │ │ │ │ -1340 w Fn(MSMD)29 b Fe(:)i Fk(DRAFT)f Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2742 100 V 137 399 a Fm(\210)45 b Fn(int)i(stage)29 b │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fo(6)p 136 100 1135 4 v │ │ │ │ +1317 w Fn(MSMD)29 b Fe(:)i Fk(DRAFT)f Fe(Jan)m(uary)g(17,)h(2026)p │ │ │ │ +2765 100 V 137 399 a Fm(\210)45 b Fn(int)i(stage)29 b │ │ │ │ Fo(|)h(stage)i(of)f(the)f(v)m(ertex.)42 b(Stage)32 b(0)e(no)s(des)g │ │ │ │ (are)h(eliminated)g(b)s(efore)f(stage)i(1)f(no)s(des,)e(etc.)137 │ │ │ │ 581 y Fm(\210)45 b Fn(int)i(wght)29 b Fo(|)i(w)m(eigh)m(t)g(of)g(the)g │ │ │ │ (v)m(ertex)137 763 y Fm(\210)45 b Fn(int)i(nadj)29 b │ │ │ │ Fo(|)i(size)g(of)f(the)h Fn(adj)e Fo(v)m(ector)137 945 │ │ │ │ y Fm(\210)45 b Fn(int)i(*adj)27 b Fo(|)i(for)f(an)g(uneliminated)g(v)m │ │ │ │ (ertex,)j Fn(adj)c Fo(p)s(oin)m(ts)h(to)h(a)g(list)g(of)g(unco)m(v)m │ │ │ │ @@ -5628,17 +5640,17 @@ │ │ │ │ (a)h(call)g(to)g Fn(MSMDinfo)p 2440 5147 V 32 w(clearData\(\))d │ │ │ │ Fo(then)i(free's)g(the)g(storage)227 5260 y(for)h(the)h(structure)f │ │ │ │ (with)g(a)h(call)g(to)g Fn(free\(\))p Fo(.)227 5407 y │ │ │ │ Fk(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fo(If)30 b Fn(info)g │ │ │ │ Fo(is)g Fn(NULL)p Fo(,)f(an)i(error)f(message)h(is)g(prin)m(ted)f(and)f │ │ │ │ (the)i(program)f(exits.)p eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 91 100 1158 4 v 1339 100 a Fn(MSMD)30 │ │ │ │ -b Fe(:)g Fk(DRAFT)121 b Fe(Jan)m(uary)30 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Fo(.)227 5407 y │ │ │ │ Fk(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fo(If)30 b Fn(msmd)g │ │ │ │ Fo(is)g Fn(NULL)p Fo(,)f(an)i(error)f(message)h(is)g(prin)m(ted)f(and)f │ │ │ │ (the)i(program)f(exits.)p eop end │ │ │ │ %%Page: 8 8 │ │ │ │ -TeXDict begin 8 7 bop 0 100 a Fo(8)p 136 100 1158 4 v │ │ │ │ -1340 w Fn(MSMD)29 b Fe(:)i Fk(DRAFT)f Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2742 100 V 0 399 a Fc(1.3.2)112 b(Initialization)39 b(metho)s(ds)f(|)g │ │ │ │ +TeXDict begin 8 7 bop 0 100 a Fo(8)p 136 100 1135 4 v │ │ │ │ +1317 w Fn(MSMD)29 b Fe(:)i Fk(DRAFT)f Fe(Jan)m(uary)g(17,)h(2026)p │ │ │ │ +2765 100 V 0 399 a Fc(1.3.2)112 b(Initialization)39 b(metho)s(ds)f(|)g │ │ │ │ (public)0 595 y Fo(There)30 b(is)g(one)h(initialization)i(metho)s(d.) │ │ │ │ 111 834 y(1.)46 b Fn(void)h(MSMD_init)e(\()j(MSMD)e(*msmd,)g(Graph)h │ │ │ │ (*graph,)f(int)g(stages[],)g(MSMD)g(*info)h(\))g(;)227 │ │ │ │ 985 y Fo(This)35 b(metho)s(d)h(initializes)i(the)e Fn(MSMD)f │ │ │ │ Fo(ob)5 b(ject)37 b(prior)e(to)i(an)e(ordering.)58 b(It)36 │ │ │ │ b(is)g(called)h(b)m(y)f Fn(MSMD)p 3539 985 29 4 v 33 │ │ │ │ w(order\(\))227 1098 y Fo(metho)s(d,)25 b(and)f(so)h(it)f(is)h(curren)m │ │ │ │ @@ -5768,17 +5780,17 @@ │ │ │ │ Fo(,)e(this)h(metho)s(d)g(\014lls)g(the)g Fn(IV)f Fo(ob)5 │ │ │ │ b(ject)34 b(with)f(the)h(new-to-old)g(p)s(erm)m(utation)227 │ │ │ │ 5407 y(of)i(the)f(v)m(ertices,)j(resizing)e(the)f Fn(IV)g │ │ │ │ Fo(ob)5 b(ject)36 b(if)f(necessary)-8 b(.)56 b(If)34 │ │ │ │ b Fn(oldToNewIV)f Fo(is)i(not)g Fn(NULL)p Fo(,)f(this)h(metho)s(d)p │ │ │ │ eop end │ │ │ │ %%Page: 9 9 │ │ │ │ -TeXDict begin 9 8 bop 91 100 1158 4 v 1339 100 a Fn(MSMD)30 │ │ │ │ -b Fe(:)g Fk(DRAFT)121 b Fe(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2695 100 V 1158 w Fo(9)227 399 y(\014lls)j(the)h Fn(IV)f │ │ │ │ +TeXDict begin 9 8 bop 91 100 1135 4 v 1317 100 a Fn(MSMD)29 │ │ │ │ +b Fe(:)h Fk(DRAFT)121 b Fe(Jan)m(uary)30 b(17,)i(2026)p │ │ │ │ +2718 100 V 1135 w Fo(9)227 399 y(\014lls)i(the)h Fn(IV)f │ │ │ │ Fo(ob)5 b(ject)35 b(with)f(the)g(old-to-new)i(p)s(erm)m(utation)e(of)h │ │ │ │ (the)f(v)m(ertices,)k(resizing)d(the)f Fn(IV)g Fo(ob)5 │ │ │ │ b(ject)35 b(if)227 511 y(necessary)-8 b(.)227 661 y Fk(Err)j(or)33 │ │ │ │ b(che)-5 b(cking:)40 b Fo(If)28 b Fn(msmd)g Fo(is)h Fn(NULL)p │ │ │ │ Fo(,)f(or)h(if)g Fn(newToOldIV)d Fo(and)j Fn(oldToNewIV)d │ │ │ │ Fo(is)j Fn(NULL)p Fo(,)f(an)h(error)g(message)227 774 │ │ │ │ y(is)i(prin)m(ted)f(and)f(the)i(program)f(exits.)111 │ │ │ │ @@ -5836,17 +5848,17 @@ │ │ │ │ 29 4 v 33 w(cleanSubtreeList\(\))37 b Fo(and)227 5258 │ │ │ │ y Fn(MSMD)p 425 5258 V 34 w(clearEdgeList\(\))p Fo(.)227 │ │ │ │ 5407 y Fk(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fo(If)30 │ │ │ │ b Fn(msmd)g Fo(or)g Fn(info)f Fo(is)i Fn(NULL)p Fo(,)e(an)h(error)g │ │ │ │ (message)i(is)e(prin)m(ted)g(and)g(the)g(program)h(exits.)p │ │ │ │ eop end │ │ │ │ %%Page: 10 10 │ │ │ │ -TeXDict begin 10 9 bop 0 100 a Fo(10)p 182 100 1135 4 │ │ │ │ -v 1318 w Fn(MSMD)29 b Fe(:)h Fk(DRAFT)g 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(of)g(a)f(v)m(ertex,)i(used)e(for)g(debugging.)227 5407 │ │ │ │ y Fk(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fo(If)30 b │ │ │ │ Fn(v)g Fo(or)h Fn(fp)f Fo(is)g Fn(NULL)p Fo(,)f(an)i(error)f(message)h │ │ │ │ (is)g(prin)m(ted)e(and)h(the)h(program)f(exits.)p eop │ │ │ │ end │ │ │ │ %%Page: 11 11 │ │ │ │ -TeXDict begin 11 10 bop 91 100 1135 4 v 1317 100 a Fn(MSMD)29 │ │ │ │ -b Fe(:)h Fk(DRAFT)121 b Fe(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2672 100 V 1135 w Fo(11)0 399 y Fd(1.5)135 b(Driv)l(er)46 │ │ │ │ +TeXDict begin 11 10 bop 91 100 1113 4 v 1294 100 a Fn(MSMD)29 │ │ │ │ +b Fe(:)i Fk(DRAFT)121 b Fe(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2695 100 V 1113 w Fo(11)0 399 y Fd(1.5)135 b(Driv)l(er)46 │ │ │ │ b(programs)g(for)f(the)g Fa(MSMD)e Fd(ob)7 b(ject)0 631 │ │ │ │ y Fo(This)30 b(section)h(con)m(tains)h(brief)e(descriptions)g(of)g │ │ │ │ (four)g(driv)m(er)g(programs.)111 881 y(1.)46 b Fn(orderViaMMD)f │ │ │ │ (msglvl)h(msgFile)g(inGraphFile)f(seed)h(compressFlag)f(prioType)370 │ │ │ │ 994 y(stepType)h(outOldToNewIVfile)d(outNewToOldIVfile)g(outETreeFile) │ │ │ │ 227 1149 y Fo(This)28 b(driv)m(er)g(program)g(orders)f(a)i(graph)f │ │ │ │ (using)f(the)i(m)m(ultiple)g(minim)m(um)e(degree)i(algorithm)g(|)f │ │ │ │ @@ -5983,17 +5995,17 @@ │ │ │ │ Fn(IV)e Fo(ob)5 b(ject)40 b(that)f(con)m(tains)427 5294 │ │ │ │ y(the)34 b(old-to-new)h(p)s(erm)m(utation)f(v)m(ector.)52 │ │ │ │ b(If)34 b Fn(outOldToNewIVfile)29 b Fo(is)34 b Fn("none")p │ │ │ │ Fo(,)f(then)g(there)h(is)g(no)427 5407 y(output,)d(otherwise)f │ │ │ │ Fn(outOldToNewIVfile)c Fo(m)m(ust)k(b)s(e)g(of)g(the)h(form)f │ │ │ │ Fn(*.ivf)f Fo(or)h Fn(*.ivb)p Fo(.)p eop end │ │ │ │ %%Page: 12 12 │ │ │ │ -TeXDict begin 12 11 bop 0 100 a Fo(12)p 182 100 1135 │ │ │ │ -4 v 1318 w Fn(MSMD)29 b Fe(:)h Fk(DRAFT)g Fe(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2765 100 V 337 399 a Fm(\210)45 b Fo(The)38 b Fn(outNewToOldIVfile)c │ │ │ │ +TeXDict begin 12 11 bop 0 100 a Fo(12)p 182 100 1113 │ │ │ │ +4 v 1295 w Fn(MSMD)29 b Fe(:)i Fk(DRAFT)f Fe(Jan)m(uary)g(17,)h(2026)p │ │ │ │ +2788 100 V 337 399 a Fm(\210)45 b Fo(The)38 b Fn(outNewToOldIVfile)c │ │ │ │ Fo(parameter)39 b(is)f(the)h(output)f(\014le)h(for)f(the)h │ │ │ │ Fn(IV)e Fo(ob)5 b(ject)40 b(that)f(con)m(tains)427 511 │ │ │ │ y(the)34 b(new-to-old)h(p)s(erm)m(utation)f(v)m(ector.)52 │ │ │ │ b(If)34 b Fn(outNewToOldIVfile)29 b Fo(is)34 b Fn("none")p │ │ │ │ Fo(,)f(then)g(there)h(is)g(no)427 624 y(output,)d(otherwise)f │ │ │ │ Fn(outNewToOldIVfile)c Fo(m)m(ust)k(b)s(e)g(of)g(the)h(form)f │ │ │ │ Fn(*.ivf)f Fo(or)h Fn(*.ivb)p Fo(.)337 770 y Fm(\210)45 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -21,15 +21,15 @@ │ │ │ │ │ • approximate external degree, (d from [?]) and [?], or │ │ │ │ │ ˜ │ │ │ │ │ • half external and half approximate, (d from [?]), or │ │ │ │ │ • a constant priority (to induce maximal independent set elimination). │ │ │ │ │ 1The ETree object has the Tree object that defines the connectivity of the fronts, knows the internal and external │ │ │ │ │ size of each front, and has a map from the vertices to the fronts. │ │ │ │ │ 1 │ │ │ │ │ - 2 MSMD : DRAFT January 6, 2026 │ │ │ │ │ + 2 MSMD : DRAFT January 17, 2026 │ │ │ │ │ We intend to add more priorities, e.g., approximate deficiency from [?], [?] and [?]. │ │ │ │ │ Choose a priority, then specify the definition of a step, how to choose an independent set of │ │ │ │ │ vertices to eliminate at a time. Then provide a map from each vertex to the stage at which it will │ │ │ │ │ be eliminated. │ │ │ │ │ Presently there is one ordering method, MSMD order(). It orders the vertices by stages, i.e. │ │ │ │ │ vertices in stage k will be ordered before vertices in stage k + 1. Inside each stage the vertices are │ │ │ │ │ ordered by steps. At each step an independent set of vertices is eliminated, and the choice is based │ │ │ │ │ @@ -57,15 +57,15 @@ │ │ │ │ │ The tools are largely written so any of these three algorithms can be prototyped in a small amount │ │ │ │ │ of time and effort. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ There are four typed objects. │ │ │ │ │ • MSMD : the main object. │ │ │ │ │ • MSMDinfo : an object that communicate parameter choices from the caller to the MSMD object │ │ │ │ │ and information and statistics from the MSMD object to the caller. │ │ │ │ │ - MSMD : DRAFT January 6, 2026 3 │ │ │ │ │ + MSMD : DRAFT January 17, 2026 3 │ │ │ │ │ • MSMDstageInfo : an object that contains statistics for a stage of elimination, e.g., number of │ │ │ │ │ steps, number of vertices eliminated, weight of vertices eliminated, etc. │ │ │ │ │ • MSMDvtx : an object that models a vertex. │ │ │ │ │ Auser needs to understand the MSMDinfo object, so this is where we will start our description. │ │ │ │ │ 1.1.1 MSMDinfo : define your algorithm │ │ │ │ │ • int compressFlag – define initial and subsequent compressions of the graph. │ │ │ │ │ Wecompress a graph using a checksum technique. At some point in the elimination, vertices │ │ │ │ │ @@ -93,15 +93,15 @@ │ │ │ │ │ • double stepType — define the elimination steps. │ │ │ │ │ – stepType == 0 — only one vertex of minimum priority is eliminated at each step, e.g., │ │ │ │ │ as used in SPARSPAK’s GENQMD, YSMP’s ordering, and AMD [?]. │ │ │ │ │ – stepType == 1 — an independent set of vertices of minimum priority is eliminated at │ │ │ │ │ each step, e.g., as used in GENMMD, multiple minimum degree. │ │ │ │ │ – stepType > 1—anindependentsetofvertices iseliminated whoseprioritieslie between │ │ │ │ │ the minimum priority and the minimum priority multiplied by stepType. │ │ │ │ │ - 4 MSMD : DRAFT January 6, 2026 │ │ │ │ │ + 4 MSMD : DRAFT January 17, 2026 │ │ │ │ │ The default value is 1, multiple elimination of vertices with minimum priority. │ │ │ │ │ • int seed — a seed used for a random number generator, this introduces a necessary random │ │ │ │ │ element to the ordering. │ │ │ │ │ • int msglvl – message level for statistics, diagnostics and monitoring. The default value is │ │ │ │ │ zero, no statistics. Set msglvl to one and get elimination monitoring. Increase msglvl slowly │ │ │ │ │ to get more mostly debug information. │ │ │ │ │ • FILE *msgFile – message file, default is stdout. │ │ │ │ │ @@ -119,15 +119,15 @@ │ │ │ │ │ • IIheap *heap – pointer to a IIheap object that maintains the priority queue. │ │ │ │ │ • IP *baseIP – pointer to the base IP objects, used to hold subtree lists │ │ │ │ │ • IP *freeIP – pointer to the list of free IP objects │ │ │ │ │ • int incrIP – integer that holds the increment factor for the IP objects. │ │ │ │ │ • MSMDvtx *vertices – pointer to vector of MSMDvtx objects that represent the vertices. │ │ │ │ │ • IV ivtmpIV – IV object that holds an integer temporary vector. │ │ │ │ │ • IV reachIV – IV object that holds the reach vector. │ │ │ │ │ - MSMD : DRAFT January 6, 2026 5 │ │ │ │ │ + MSMD : DRAFT January 17, 2026 5 │ │ │ │ │ 1.1.3 MSMDstageInfo : statistics object for a stage of the elimination │ │ │ │ │ This object stores information about the elimination process at a stage of the elimination. │ │ │ │ │ • int nstep — number of elimination steps in this stage │ │ │ │ │ • int nfront — number of fronts created at this stage │ │ │ │ │ • int welim — weight of the vertices eliminated at this stage │ │ │ │ │ • int nfind — number of front indices │ │ │ │ │ • int nzf — number of factor entries (for a Cholesky factorization) │ │ │ │ │ @@ -148,15 +148,15 @@ │ │ │ │ │ – ’L’ – eliminated leaf vertex │ │ │ │ │ – ’E’ – eliminated interior vertex │ │ │ │ │ – ’O’ – outmatched vertex │ │ │ │ │ – ’D’ – vertex on degree (priority) heap │ │ │ │ │ – ’R’ – vertex on reach set │ │ │ │ │ – ’I’ – vertex found to be indistinguishable to another │ │ │ │ │ – ’B’ – boundary vertex, to be eliminated in another stage │ │ │ │ │ - 6 MSMD : DRAFT January 6, 2026 │ │ │ │ │ + 6 MSMD : DRAFT January 17, 2026 │ │ │ │ │ • int stage — stage of the vertex. Stage 0 nodes are eliminated before stage 1 nodes, etc. │ │ │ │ │ • int wght — weight of the vertex │ │ │ │ │ • int nadj — size of the adj vector │ │ │ │ │ • int *adj — for an uneliminated vertex, adj points to a list of uncovered adjacent edges; for │ │ │ │ │ an eliminated vertex, adj points points to a list of its boundary vertices (only valid when the │ │ │ │ │ vertex is a leaf of the elimination tree or a root of a subtree of uneliminated vertices). │ │ │ │ │ • int bndwght — for an eliminated vertex, the weight of the vertices on its boundary. │ │ │ │ │ @@ -181,15 +181,15 @@ │ │ │ │ │ This method clears any data owned by the object and then sets the structure’s default fields │ │ │ │ │ with a call to MSMDinfo setDefaultFields(). │ │ │ │ │ Error checking: If info is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void MSMDinfo_free ( MSMDinfo *info ) ; │ │ │ │ │ This method releases any storage by a call to MSMDinfo clearData() then free’s the storage │ │ │ │ │ for the structure with a call to free(). │ │ │ │ │ Error checking: If info is NULL, an error message is printed and the program exits. │ │ │ │ │ - MSMD : DRAFT January 6, 2026 7 │ │ │ │ │ + MSMD : DRAFT January 17, 2026 7 │ │ │ │ │ 1.2.2 Utility methods │ │ │ │ │ There are two utility methods, one to print the object, one to check to see if it is valid. │ │ │ │ │ 1. void MSMDinfo_print ( MSMDinfo *info, FILE *fp ) ; │ │ │ │ │ This method prints out the information to a file. │ │ │ │ │ Error checking: If info or fp is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. int MSMDinfo_isValid ( MSMDinfo *info ) ; │ │ │ │ │ This method checks that the object is valid. The return value is 1 for a valid object, 0 for an │ │ │ │ │ @@ -213,15 +213,15 @@ │ │ │ │ │ This method clears any data owned by the object, then sets the structure’s default fields with │ │ │ │ │ a call to MSMD setDefaultFields(). │ │ │ │ │ Error checking: If msmd is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void MSMD_free ( MSMD *msmd ) ; │ │ │ │ │ This method releases any storage by a call to MSMD clearData() then free’s the storage for │ │ │ │ │ the structure with a call to free(). │ │ │ │ │ Error checking: If msmd is NULL, an error message is printed and the program exits. │ │ │ │ │ - 8 MSMD : DRAFT January 6, 2026 │ │ │ │ │ + 8 MSMD : DRAFT January 17, 2026 │ │ │ │ │ 1.3.2 Initialization methods — public │ │ │ │ │ There is one initialization method. │ │ │ │ │ 1. void MSMD_init ( MSMD *msmd, Graph *graph, int stages[], MSMD *info ) ; │ │ │ │ │ This method initializes the MSMD object prior to an ordering. It is called by MSMD order() │ │ │ │ │ method, and so it is currently a private method for the object. However, when designing more │ │ │ │ │ complicated ordering methods, this object is necessary to set up the data structures. There │ │ │ │ │ are two input arguments: graph is a pointer to a Graph object that holds the adjacency lists │ │ │ │ │ @@ -249,15 +249,15 @@ │ │ │ │ │ 1.3.4 Extraction methods — public │ │ │ │ │ There are two methods to extract the ordering. The first fills one or two IV objects with the │ │ │ │ │ permutation vector(s). The second returns an ETree object that holds the front tree for the │ │ │ │ │ ordering. │ │ │ │ │ 1. void MSMD_fillPerms ( MSMD *msmd, IV *newToOldIV, IV *oldToNewIV ) ; │ │ │ │ │ If newToOldIV is not NULL, this method fills the IV object with the new-to-old permutation │ │ │ │ │ of the vertices, resizing the IV object if necessary. If oldToNewIV is not NULL, this method │ │ │ │ │ - MSMD : DRAFT January 6, 2026 9 │ │ │ │ │ + MSMD : DRAFT January 17, 2026 9 │ │ │ │ │ fills the IV object with the old-to-new permutation of the vertices, resizing the IV object if │ │ │ │ │ necessary. │ │ │ │ │ Error checking: If msmd is NULL, or if newToOldIV and oldToNewIV is NULL, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 2. ETree * MSMD_frontETree ( MSMD *msmd ) ; │ │ │ │ │ This method constructs and returns a ETree object that contains the front tree for the │ │ │ │ │ ordering. │ │ │ │ │ @@ -283,15 +283,15 @@ │ │ │ │ │ The order of the nodes in the reach set may be permuted, but any indistinguishable nodes in │ │ │ │ │ the reach set are not purged from the reach set. │ │ │ │ │ Error checking: If msmd or info is NULL, an error message is printed and the program exits. │ │ │ │ │ 5. void MSMD_cleanReachSet ( MSMD *msmd, MSMD *info ) ; │ │ │ │ │ This method cleans the nodes in the reach set by calling MSMD cleanSubtreeList() and │ │ │ │ │ MSMD clearEdgeList(). │ │ │ │ │ Error checking: If msmd or info is NULL, an error message is printed and the program exits. │ │ │ │ │ - 10 MSMD : DRAFT January 6, 2026 │ │ │ │ │ + 10 MSMD : DRAFT January 17, 2026 │ │ │ │ │ 6. void MSMD_cleanSubtreeList ( MSMD *msmd, MSMDvtx *v, MSMD *info ) ; │ │ │ │ │ This method cleans the list of subtrees for vertex v, removing any node which is no longer │ │ │ │ │ the root of a subtree of eliminated nodes. │ │ │ │ │ Error checking: If msmd, v or info is NULL, an error message is printed and the program exits. │ │ │ │ │ 7. void MSMD_cleanEdgeList ( MSMD *msmd, MSMDvtx *v, MSMD *info ) ; │ │ │ │ │ This method cleans the list of uncovered edges for vertex v, removing any edge (v,w) where │ │ │ │ │ v and w share a common adjacent subtree. │ │ │ │ │ @@ -317,15 +317,15 @@ │ │ │ │ │ the program exits. │ │ │ │ │ 1.4 Prototypes and descriptions of MSMDvtx methods │ │ │ │ │ TheMSMDvtxobject is private so would not normally be accessed by the user. There is one method │ │ │ │ │ to print out the object. │ │ │ │ │ 1. void MSMDvtx_print ( MSMDvtx *v, FILE *fp ) ; │ │ │ │ │ This method prints a human-readable representation of a vertex, used for debugging. │ │ │ │ │ Error checking: If v or fp is NULL, an error message is printed and the program exits. │ │ │ │ │ - MSMD : DRAFT January 6, 2026 11 │ │ │ │ │ + MSMD : DRAFT January 17, 2026 11 │ │ │ │ │ 1.5 Driver programs for the MSMD object │ │ │ │ │ This section contains brief descriptions of four driver programs. │ │ │ │ │ 1. orderViaMMD msglvl msgFile inGraphFile seed compressFlag prioType │ │ │ │ │ stepType outOldToNewIVfile outNewToOldIVfile outETreeFile │ │ │ │ │ This driver program orders a graph using the multiple minimum degree algorithm — exactly │ │ │ │ │ which algorithm is controlled by the input parameters. │ │ │ │ │ • The msglvl parameter determines the amount of output. │ │ │ │ │ @@ -355,15 +355,15 @@ │ │ │ │ │ SPARSPAK. │ │ │ │ │ – stepType == 1 — regular multiple elimination, e.g., GENMMD. │ │ │ │ │ – stepType > 1 — vertices whose priority lies between the minimum priority and │ │ │ │ │ stepType times the minimum priority are eligible for elimination at a step. │ │ │ │ │ • The outOldToNewIVfile parameter is the output file for the IV object that contains │ │ │ │ │ the old-to-new permutation vector. If outOldToNewIVfile is "none", then there is no │ │ │ │ │ output, otherwise outOldToNewIVfile must be of the form *.ivf or *.ivb. │ │ │ │ │ - 12 MSMD : DRAFT January 6, 2026 │ │ │ │ │ + 12 MSMD : DRAFT January 17, 2026 │ │ │ │ │ • The outNewToOldIVfile parameter is the output file for the IV object that contains │ │ │ │ │ the new-to-old permutation vector. If outNewToOldIVfile is "none", then there is no │ │ │ │ │ output, otherwise outNewToOldIVfile must be of the form *.ivf or *.ivb. │ │ │ │ │ • The outETreeFile parameter is the output file for the ETree object that contains the │ │ │ │ │ front tree for the ordering. If outETreeFileis "none", then there is no output, otherwise │ │ │ │ │ outETreeFile must be of the form *.etreef or *.etreeb. │ │ │ │ │ 2. orderViaND msglvl msgFile inGraphFile inDSTreeFile seed compressFlag │ │ ├── ./usr/share/doc/spooles-doc/MT.ps.gz │ │ │ ├── MT.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o MT.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1599,16 +1599,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1796,79 +1798,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ 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Fm(AX)40 b Fn(=)33 b Fm(B)38 b Fn(for)c Fm(X)40 │ │ │ │ b Fn(using)34 b(m)n(ultithreaded)f(factors)g(and)208 │ │ │ │ 5407 y(solv)n(es.)i(Use)28 b(the)g(script)f(\014le)h │ │ │ │ Fi(do)p 1237 5407 27 4 v 30 w(gridMT)d Fn(for)i(testing.)p │ │ │ │ eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fn(6)p 125 100 1026 4 v │ │ │ │ -1191 w Fi(Multithreaded)22 b Fg(:)37 b Fh(DRAFT)28 b │ │ │ │ -Fg(Jan)n(uary)d(6,)i(2026)p 2874 100 V 307 390 a Fc(\210)42 │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fn(6)p 125 100 1005 4 v │ │ │ │ +1170 w Fi(Multithreaded)23 b Fg(:)37 b Fh(DRAFT)27 b │ │ │ │ +Fg(Jan)n(uary)e(17,)i(2026)p 2895 100 V 307 390 a Fc(\210)42 │ │ │ │ b Fn(The)23 b Fi(msglvl)e Fn(parameter)g(determines)i(the)h(amoun)n(t)e │ │ │ │ (of)h(output.)36 b(Use)23 b Fi(msglvl)41 b(=)i(1)23 b │ │ │ │ Fn(for)g(just)g(timing)g(output.)307 524 y Fc(\210)42 │ │ │ │ b Fn(The)32 b Fi(msgFile)c Fn(parameter)i(determines)h(the)h(message)e │ │ │ │ (\014le)i(|)f(if)h Fi(msgFile)d Fn(is)i Fi(stdout)p Fn(,)f(then)i(the)g │ │ │ │ (message)390 624 y(\014le)c(is)f Fh(stdout)p Fn(,)h(otherwise)e(a)i │ │ │ │ (\014le)f(is)h(op)r(ened)f(with)i Fh(app)l(end)g Fn(status)e(to)g │ │ │ │ @@ -5618,17 +5629,17 @@ │ │ │ │ b Fn(using)27 b(m)n(ultithreaded)g(factors)g(and)g(solv)n(es.)208 │ │ │ │ 5221 y(Use)g(the)h(script)f(\014le)h Fi(do)p 968 5221 │ │ │ │ V 31 w(patchAndGo)23 b Fn(for)k(testing.)307 5407 y Fc(\210)42 │ │ │ │ b Fn(The)23 b Fi(msglvl)e Fn(parameter)g(determines)i(the)h(amoun)n(t)e │ │ │ │ (of)h(output.)36 b(Use)23 b Fi(msglvl)41 b(=)i(1)23 b │ │ │ │ Fn(for)g(just)g(timing)g(output.)p eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 83 100 1026 4 v 1192 100 a Fi(Multithreaded)22 │ │ │ │ -b Fg(:)37 b Fh(DRAFT)110 b Fg(Jan)n(uary)26 b(6,)h(2026)p │ │ │ │ -2835 100 V 1026 w Fn(7)307 390 y Fc(\210)42 b Fn(The)32 │ │ │ │ +TeXDict begin 7 6 bop 83 100 1005 4 v 1171 100 a Fi(Multithreaded)22 │ │ │ │ +b Fg(:)37 b Fh(DRAFT)110 b Fg(Jan)n(uary)26 b(17,)h(2026)p │ │ │ │ +2856 100 V 1005 w Fn(7)307 390 y Fc(\210)42 b Fn(The)32 │ │ │ │ b Fi(msgFile)c Fn(parameter)i(determines)h(the)h(message)e(\014le)i(|)f │ │ │ │ (if)h Fi(msgFile)d Fn(is)i Fi(stdout)p Fn(,)f(then)i(the)g(message)390 │ │ │ │ 490 y(\014le)c(is)f Fh(stdout)p Fn(,)h(otherwise)e(a)i(\014le)f(is)h │ │ │ │ (op)r(ened)f(with)i Fh(app)l(end)g Fn(status)e(to)g(receiv)n(e)g(an)n │ │ │ │ (y)g(output)h(data.)307 620 y Fc(\210)42 b Fn(The)28 │ │ │ │ b Fi(type)e Fn(parameter)g(sp)r(eci\014es)h(a)h(real)e(or)h(complex)g │ │ │ │ (linear)g(system.)456 750 y Fa({)41 b Fi(type)h(=)i(1)f(\(SPOOLES)p │ │ │ │ @@ -5705,17 +5716,17 @@ │ │ │ │ 5277 y Fl(T)3144 5308 y Fj(\003)g Fm(X)27 b Fn(or)19 │ │ │ │ b Fm(Y)24 b Fn(+)5 b Fm(\013)g Fj(\003)g Fm(A)3690 5277 │ │ │ │ y Fl(H)3756 5308 y Fj(\003)g Fm(X)i Fn(.)208 5407 y(The)27 │ │ │ │ b(program's)f(output)i(is)f(a)g(\014le)h(whic)n(h)g(when)f(sen)n(t)h │ │ │ │ (in)n(to)f(Matlab,)h(outputs)f(the)h(error)e(in)i(the)g(computation.)p │ │ │ │ eop end │ │ │ │ %%Page: 8 8 │ │ │ │ -TeXDict begin 8 7 bop 0 100 a Fn(8)p 125 100 1026 4 v │ │ │ │ -1191 w Fi(Multithreaded)22 b Fg(:)37 b Fh(DRAFT)28 b │ │ │ │ -Fg(Jan)n(uary)d(6,)i(2026)p 2874 100 V 307 390 a Fc(\210)42 │ │ │ │ +TeXDict begin 8 7 bop 0 100 a Fn(8)p 125 100 1005 4 v │ │ │ │ +1170 w Fi(Multithreaded)23 b Fg(:)37 b Fh(DRAFT)27 b │ │ │ │ +Fg(Jan)n(uary)e(17,)i(2026)p 2895 100 V 307 390 a Fc(\210)42 │ │ │ │ b Fn(The)19 b Fi(msglvl)e Fn(parameter)g(determines)i(the)h(amoun)n(t)e │ │ │ │ (of)h(output)h(|)f(taking)f Fi(msglvl)41 b(>=)i(3)19 │ │ │ │ b Fn(means)f(the)h Fi(InpMtx)390 490 y Fn(ob)5 b(ject)28 │ │ │ │ b(is)f(written)h(to)f(the)h(message)e(\014le.)307 624 │ │ │ │ y Fc(\210)42 b Fn(The)32 b Fi(msgFile)c Fn(parameter)i(determines)h │ │ │ │ (the)h(message)e(\014le)i(|)f(if)h Fi(msgFile)d Fn(is)i │ │ │ │ Fi(stdout)p Fn(,)f(then)i(the)g(message)390 724 y(\014le)c(is)f │ │ │ │ @@ -5799,17 +5810,17 @@ │ │ │ │ V 28 w(HERMITIAN\))23 b Fn(for)k Fm(A)h Fn(complex)g(Hermitian,)456 │ │ │ │ 5138 y Fa({)41 b Fi(type)h(=)i(2)f(\(SPOOLES)p 1295 5138 │ │ │ │ V 28 w(NONSYMMETRIC\))390 5273 y Fn(for)27 b Fm(A)h Fn(real)f(or)g │ │ │ │ (complex)g(nonsymmetric.)307 5407 y Fc(\210)42 b Fn(The)28 │ │ │ │ b Fi(sparsityflag)23 b Fn(parameter)j(signals)g(a)h(direct)h(or)e │ │ │ │ (appro)n(ximate)g(factorization.)p eop end │ │ │ │ %%Page: 9 9 │ │ │ │ -TeXDict begin 9 8 bop 83 100 1026 4 v 1192 100 a Fi(Multithreaded)22 │ │ │ │ -b Fg(:)37 b Fh(DRAFT)110 b Fg(Jan)n(uary)26 b(6,)h(2026)p │ │ │ │ -2835 100 V 1026 w Fn(9)456 390 y Fa({)41 b Fi(sparsityflag)e(=)k(0)g │ │ │ │ +TeXDict begin 9 8 bop 83 100 1005 4 v 1171 100 a Fi(Multithreaded)22 │ │ │ │ +b Fg(:)37 b Fh(DRAFT)110 b Fg(Jan)n(uary)26 b(17,)h(2026)p │ │ │ │ +2856 100 V 1005 w Fn(9)456 390 y Fa({)41 b Fi(sparsityflag)e(=)k(0)g │ │ │ │ (\(FRONTMTX)p 1687 390 27 4 v 28 w(DENSE)p 1935 390 V │ │ │ │ 29 w(FRONTS\))26 b Fn(implies)j(a)f(direct)h(factorization,)f(the)h │ │ │ │ (fron)n(ts)f(will)545 490 y(b)r(e)g(stored)f(as)g(dense)h(submatrices.) │ │ │ │ 456 607 y Fa({)41 b Fi(sparsityflag)e(=)k(1)g(\(FRONTMTX)p │ │ │ │ 1687 607 V 28 w(SPARSE)p 1979 607 V 29 w(FRONTS\))29 │ │ │ │ b Fn(implies)j(an)g(appro)n(ximate)e(factorization.)48 │ │ │ │ b(The)545 706 y(fron)n(ts)26 b(will)g(b)r(e)g(stored)g(as)f(sparse)g │ │ │ │ @@ -5894,17 +5905,17 @@ │ │ │ │ b Fi(n1)27 b Fn(is)h(the)g(n)n(um)n(b)r(er)f(of)g(p)r(oin)n(ts)h(in)g │ │ │ │ (the)g(\014rst)f(grid)g(direction.)307 5273 y Fc(\210)42 │ │ │ │ b Fi(n2)27 b Fn(is)h(the)g(n)n(um)n(b)r(er)f(of)g(p)r(oin)n(ts)h(in)g │ │ │ │ (the)g(second)f(grid)g(direction.)307 5407 y Fc(\210)42 │ │ │ │ b Fi(n3)27 b Fn(is)h(the)g(n)n(um)n(b)r(er)f(of)g(p)r(oin)n(ts)h(in)g │ │ │ │ (the)g(third)g(grid)e(direction.)p eop end │ │ │ │ %%Page: 10 10 │ │ │ │ -TeXDict begin 10 9 bop 0 100 a Fn(10)p 166 100 1005 4 │ │ │ │ -v 1170 w Fi(Multithreaded)22 b Fg(:)37 b Fh(DRAFT)27 │ │ │ │ -b Fg(Jan)n(uary)f(6,)h(2026)p 2895 100 V 307 390 a Fc(\210)42 │ │ │ │ +TeXDict begin 10 9 bop 0 100 a Fn(10)p 166 100 984 4 │ │ │ │ +v 1149 w Fi(Multithreaded)22 b Fg(:)37 b Fh(DRAFT)28 │ │ │ │ +b Fg(Jan)n(uary)d(17,)i(2026)p 2916 100 V 307 390 a Fc(\210)42 │ │ │ │ b Fn(The)28 b Fi(seed)e Fn(parameter)g(is)h(a)h(random)e(n)n(um)n(b)r │ │ │ │ (er)i(seed.)307 523 y Fc(\210)42 b Fn(The)28 b Fi(nrhs)e │ │ │ │ Fn(parameter)g(is)h(the)h(n)n(um)n(b)r(er)g(of)f(righ)n(t)g(hand)h │ │ │ │ (sides)f(to)h(solv)n(e)e(as)h(one)g(blo)r(c)n(k.)307 │ │ │ │ 656 y Fc(\210)42 b Fn(The)28 b Fi(type)e Fn(parameter)g(sp)r(eci\014es) │ │ │ │ h(a)h(real)e(or)h(complex)g(linear)g(system.)456 789 │ │ │ │ y Fa({)41 b Fi(type)h(=)i(1)f(\(SPOOLES)p 1295 789 27 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -35,15 +35,15 @@ │ │ │ │ │ by independent topological traversals of the front tree. It is the list and working storage data structures (the │ │ │ │ │ ChvList, ChvManager and SubMtxManager objects) that have locks. What is done is common code between │ │ │ │ │ the serial and multithreaded environments, it is the choreography, i.e., who does what, that differs. │ │ │ │ │ Most of these same comments apply to the multithreaded solve methods. The calling sequences between │ │ │ │ │ the serial and multithreaded solves differs by one parameter, a SolveMap object that maps the submatrices │ │ │ │ │ of the factor matrix to the threads that will compute with them. │ │ │ │ │ 1 │ │ │ │ │ - 2 Multithreaded : DRAFT January 6, 2026 │ │ │ │ │ + 2 Multithreaded : DRAFT January 17, 2026 │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ There are no multithreaded specific data structures. See the Lock object which is used to hide the particular │ │ │ │ │ mutual exclusion device used by a thread library. │ │ │ │ │ 1.2 Prototypes and descriptions of MT methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods found in the MT source directory. │ │ │ │ │ 1.2.1 Matrix-matrix multiply methods │ │ │ │ │ Therearefivemethodstomultiplyavectortimesadensematrix. Thefirstthreemethods,calledInpMtx MT nonsym mmm*(), │ │ │ │ │ @@ -79,15 +79,15 @@ │ │ │ │ │ This method computes the matrix-vector product y := y+αA x, where y is found in the Y DenseMtx │ │ │ │ │ object, α is real or complex in alpha[], A is found in the A Inpmtx object, and x is found in the X │ │ │ │ │ DenseMtx object. If any of the input objects are NULL, an error message is printed and the program │ │ │ │ │ exits. A, X and Y must all be real or all be complex. When A is real, then α = alpha[0]. When A │ │ │ │ │ is complex, then α = alpha[0] + i* alpha[1]. This means that one cannot call the methods with │ │ │ │ │ a constant as the third parameter, e.g., InpMtx MT nonsym mmm(A, Y, 3.22, X, nthread, msglvl, │ │ │ │ │ msgFile), for this may result in a segmentation violation. The values of α must be loaded into an │ │ │ │ │ - Multithreaded : DRAFT January 6, 2026 3 │ │ │ │ │ + Multithreaded : DRAFT January 17, 2026 3 │ │ │ │ │ array of length 1 or 2. The number of threads is specified by the nthread parameter; if, nthread is 1, │ │ │ │ │ the serial method is called. The msglvl and msgFile parameters are used for diagnostics during the │ │ │ │ │ creation of the threads’ individual data structures. │ │ │ │ │ Error checking: If A, Y or X are NULL, or if coordType is not INPMTX BY ROWS, INPMTX BY COLUMNS or │ │ │ │ │ INPMTX BY CHEVRONS,orifstorageModeisnotoneofINPMTX RAW DATA,INPMTX SORTEDorINPMTX BY VECTORS, │ │ │ │ │ or if inputModeis not SPOOLES REAL or SPOOLES COMPLEX,an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ @@ -124,15 +124,15 @@ │ │ │ │ │ • cpus[1] — time spent initializing the fronts and loading the original entries. │ │ │ │ │ • cpus[2] — time spent accumulating updates from descendents. │ │ │ │ │ • cpus[3] — time spent inserting aggregate fronts. │ │ │ │ │ • cpus[4] — time spent removing and assembling aggregate fronts. │ │ │ │ │ • cpus[5] — time spent assembling postponed data. │ │ │ │ │ • cpus[6] — time spent to factor the fronts. │ │ │ │ │ • cpus[7] — time spent to extract postponed data. │ │ │ │ │ - 4 Multithreaded : DRAFT January 6, 2026 │ │ │ │ │ + 4 Multithreaded : DRAFT January 17, 2026 │ │ │ │ │ • cpus[8] — time spent to store the factor entries. │ │ │ │ │ • cpus[9] — miscellaneous time. │ │ │ │ │ Onreturn, the stats[] vector is filled with the following information. │ │ │ │ │ • stats[0] — number of pivots. │ │ │ │ │ • stats[1] — number of pivot tests. │ │ │ │ │ • stats[2] — number of delayed rows and columns. │ │ │ │ │ • stats[3] — number of entries in D. │ │ │ │ │ @@ -164,15 +164,15 @@ │ │ │ │ │ an error message is printed and the program exits. │ │ │ │ │ 1.2.4 Multithreaded Solve method │ │ │ │ │ 1. void FrontMtx_MT_solve ( FrontMtx *frontmtx, DenseMtx *mtxX, DenseMtx *mtxB, │ │ │ │ │ SubMtxManager *mtxmanager, SolveMap *solvemap, │ │ │ │ │ double cpus[], int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method is used to solve one of three linear systems of equations using a multithreaded solve — │ │ │ │ │ (UT +I)D(I +U)X =B, (UH +I)D(I +U)X =B or (L+I)D(I+U)X =B. Entries of B are read │ │ │ │ │ - Multithreaded : DRAFT January 6, 2026 5 │ │ │ │ │ + Multithreaded : DRAFT January 17, 2026 5 │ │ │ │ │ from mtxB and entries of X are written to mtxX. Therefore, mtxX and mtxB can be the same object. │ │ │ │ │ (Note, this does not hold true for an MPI factorization with pivoting.) The submatrix manager object │ │ │ │ │ manages the working storage. The solvemap object contains the map from submatrices to threads. │ │ │ │ │ The map from fronts to processes that own them is given in the ownersIV object. On return the │ │ │ │ │ cpus[] vector is filled with the following. The stats[] vector is not currently used. │ │ │ │ │ • cpus[0] — set up the solves │ │ │ │ │ • cpus[1] — fetch right hand side and store solution │ │ │ │ │ @@ -206,15 +206,15 @@ │ │ │ │ │ ¿ 0 and msgFile is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.3 Driver programs for the multithreaded functions │ │ │ │ │ 1. allInOneMT msglvl msgFile type symmetryflag pivotingflag │ │ │ │ │ matrixFileName rhsFileName seed nthread │ │ │ │ │ This driver program reads in a matrix A and right hand side B, generates the graph for A and orders │ │ │ │ │ the matrix, factors A and solves the linear system AX = B for X using multithreaded factors and │ │ │ │ │ solves. Use the script file do gridMT for testing. │ │ │ │ │ - 6 Multithreaded : DRAFT January 6, 2026 │ │ │ │ │ + 6 Multithreaded : DRAFT January 17, 2026 │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • The type parameter specifies a real or complex linear system. │ │ │ │ │ – type = 1 (SPOOLES REAL) for real, │ │ │ │ │ – type = 2 (SPOOLES COMPLEX) for complex. │ │ │ │ │ • The symmetryflag parameter specifies the symmetry of the matrix. │ │ │ │ │ @@ -249,15 +249,15 @@ │ │ │ │ │ Thisdriverprogramisusedtotestthe“patch-and-go”functionalityforafactorizationwithoutpivoting. │ │ │ │ │ Whensmalldiagonalpivotelements are found, one of three actions are taken. See the PatchAndGoInfo │ │ │ │ │ object for more information. │ │ │ │ │ The program reads in a matrix A and right hand side B, generates the graph for A and orders the │ │ │ │ │ matrix, factors A and solves the linear system AX = B for X using multithreaded factors and solves. │ │ │ │ │ Use the script file do patchAndGo for testing. │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ - Multithreaded : DRAFT January 6, 2026 7 │ │ │ │ │ + Multithreaded : DRAFT January 17, 2026 7 │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • The type parameter specifies a real or complex linear system. │ │ │ │ │ – type = 1 (SPOOLES REAL) for real, │ │ │ │ │ – type = 2 (SPOOLES COMPLEX) for complex. │ │ │ │ │ • The symmetryflag parameter specifies the symmetry of the matrix. │ │ │ │ │ – type = 0 (SPOOLES SYMMETRIC) for A real or complex symmetric, │ │ │ │ │ @@ -294,15 +294,15 @@ │ │ │ │ │ • The nthread parameter is the number of threads. │ │ │ │ │ 3. testMMM msglvl msgFile dataType symflag storageMode transpose │ │ │ │ │ nrow ncol nitem nrhs seed alphaReal alphaImag nthread │ │ │ │ │ ThisdriverprogramgeneratesA, anrow×ncolmatrixusingniteminputentries,X andY,nrow×nrhs │ │ │ │ │ T H │ │ │ │ │ matrices, is filled with random numbers. It then computes Y +α∗A∗X,Y +α∗A ∗X orY +α∗A ∗X. │ │ │ │ │ The program’s output is a file which when sent into Matlab, outputs the error in the computation. │ │ │ │ │ - 8 Multithreaded : DRAFT January 6, 2026 │ │ │ │ │ + 8 Multithreaded : DRAFT January 17, 2026 │ │ │ │ │ • Themsglvlparameterdeterminestheamountofoutput—takingmsglvl >= 3meanstheInpMtx │ │ │ │ │ object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • dataType is the type of entries, 0 for real, 1 for complex. │ │ │ │ │ • symflag is the symmetry flag, 0 for symmetric, 1 for Hermitian, 2 for nonsymmetric. │ │ │ │ │ • storageModeisthestoragemodefortheentries,1forbyrows,2forbycolumns, 3forbychevrons. │ │ │ │ │ @@ -336,15 +336,15 @@ │ │ │ │ │ – type = 2 (SPOOLES COMPLEX) for complex. │ │ │ │ │ • The symmetryflag parameter specifies the symmetry of the matrix. │ │ │ │ │ – type = 0 (SPOOLES SYMMETRIC) for A real or complex symmetric, │ │ │ │ │ – type = 1 (SPOOLES HERMITIAN) for A complex Hermitian, │ │ │ │ │ – type = 2 (SPOOLES NONSYMMETRIC) │ │ │ │ │ for A real or complex nonsymmetric. │ │ │ │ │ • The sparsityflag parameter signals a direct or approximate factorization. │ │ │ │ │ - Multithreaded : DRAFT January 6, 2026 9 │ │ │ │ │ + Multithreaded : DRAFT January 17, 2026 9 │ │ │ │ │ – sparsityflag = 0 (FRONTMTX DENSE FRONTS) implies a direct factorization, the fronts will │ │ │ │ │ be stored as dense submatrices. │ │ │ │ │ – sparsityflag = 1 (FRONTMTX SPARSE FRONTS) implies an approximate factorization. The │ │ │ │ │ fronts will be stored as sparse submatrices, where the entries in the triangular factors will be │ │ │ │ │ subjected to a drop tolerance test — if the magnitude of an entry is droptol or larger, it will │ │ │ │ │ be stored, otherwise it will be dropped. │ │ │ │ │ • The pivotingflag parameter signals whether pivoting for stability will be enabled or not. │ │ │ │ │ @@ -382,15 +382,15 @@ │ │ │ │ │ X F │ │ │ │ │ • The msglvlparameterdetermines the amount of output. Use msglvl = 1 for just timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ │ │ │ file is stdout, otherwise a file is opened with append status to receive any output data. │ │ │ │ │ • n1 is the number of points in the first grid direction. │ │ │ │ │ • n2 is the number of points in the second grid direction. │ │ │ │ │ • n3 is the number of points in the third grid direction. │ │ │ │ │ - 10 Multithreaded : DRAFT January 6, 2026 │ │ │ │ │ + 10 Multithreaded : DRAFT January 17, 2026 │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The nrhs parameter is the number of right hand sides to solve as one block. │ │ │ │ │ • The type parameter specifies a real or complex linear system. │ │ │ │ │ – type = 1 (SPOOLES REAL) for real, │ │ │ │ │ – type = 2 (SPOOLES COMPLEX) for complex. │ │ │ │ │ • The nthread parameter is the number of threads. │ │ │ │ │ • The maptype parameter determines the type of map from fronts to processes to be used during │ │ ├── ./usr/share/doc/spooles-doc/Network.ps.gz │ │ │ ├── Network.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Network.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1541,16 +1541,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ 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w(writeStats\(\))227 │ │ │ │ 1096 y Fn(is)29 b(called)h(to)f(write)g(out)g(the)f(header)h(and)f │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -31,15 +31,15 @@ │ │ │ │ │ B B │ │ │ │ │ Similarly, an edge (x,y) where x ∈ Y and y ∈ Y is not found in the network. │ │ │ │ │ W W │ │ │ │ │ • An edge (x,y) where x ∈ Y and y ∈ Y becomes two edges, (x,y−) and (y+,x), both with │ │ │ │ │ B I │ │ │ │ │ infinite capacity. │ │ │ │ │ 1 │ │ │ │ │ - 2 Network : DRAFT January 6, 2026 │ │ │ │ │ + 2 Network : DRAFT January 17, 2026 │ │ │ │ │ • An edge (y,z) where y ∈ Y and z ∈ Y becomes two edges, (y+,z) and (z,y−), both with │ │ │ │ │ I W │ │ │ │ │ infinite capacity. │ │ │ │ │ + − + − │ │ │ │ │ • An edge (x,y) where x ∈ Y and y ∈ Y becomes two edges, (x ,y ) and (y ,x ), both with │ │ │ │ │ I I │ │ │ │ │ infinite capacity. │ │ │ │ │ @@ -71,15 +71,15 @@ │ │ │ │ │ • ArcChunk – a structure that holds the storage for a number of arcs. Since we do not require │ │ │ │ │ the number of arcs to be known in advance when initializing the Network object, we allo- │ │ │ │ │ cate chunks of space to hold the arcs as necessary. Each chunks holds space for nnode arc │ │ │ │ │ structures. │ │ │ │ │ The Network object has six fields. │ │ │ │ │ • int nnode — the number of nodes in the network, including the source (node 0) and the sink │ │ │ │ │ (node nnode-1). │ │ │ │ │ - Network : DRAFT January 6, 2026 3 │ │ │ │ │ + Network : DRAFT January 17, 2026 3 │ │ │ │ │ • int narc — the number of arcs in the network │ │ │ │ │ • int ntrav — the number of arc traversals that we made to find a max flow. │ │ │ │ │ • Arc **inheads — pointer to a vector of pointers to Arc, inheads[v] points to the first arc │ │ │ │ │ in the in-list for node v. │ │ │ │ │ • Arc **outheads — pointer to a vector of pointers to Arc, outheads[v] points to the first │ │ │ │ │ arc in the out-list for node v. │ │ │ │ │ • ArcChunk *chunk — pointer to the first ArcChunk structure. │ │ │ │ │ @@ -99,15 +99,15 @@ │ │ │ │ │ • int size — the total number of Arc structures in this chunk. │ │ │ │ │ • int inuse — the number of active Arc structures in this chunk. │ │ │ │ │ • Arc *base — pointer to the first Arc structure in this chunk. │ │ │ │ │ • ArcChunk *next — pointer to the next ArcChunk structure in the list of chunks. │ │ │ │ │ 1.2 Prototypes and descriptions of Network methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ Network object. │ │ │ │ │ - 4 Network : DRAFT January 6, 2026 │ │ │ │ │ + 4 Network : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. Network * Network_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Network structure and then sets the default │ │ │ │ │ fields by a call to Network setDefaultFields(). │ │ │ │ │ 2. void Network_setDefaultFields ( Network *network ) ; │ │ │ │ │ @@ -135,15 +135,15 @@ │ │ │ │ │ 3. void Network_addArc ( Network *network, int firstNode, secondNode, │ │ │ │ │ int capacity, int flow ) ; │ │ │ │ │ This method adds an arc from firstNode to secondNode with flow flow and capacity │ │ │ │ │ capacity. The arc is inserted in the out-list for firstNode and the in-list for secondNode. │ │ │ │ │ Error checking: If network is NULL, or if nnode ≤ 0, or if firstNode ≤ 0, or if nnode ≤ │ │ │ │ │ firstNode, or if secondNode ≤ 0, or if nnode ≤ secondNode, or if capacity ≤ 0, an error │ │ │ │ │ message is printed and the program exits. │ │ │ │ │ - Network : DRAFT January 6, 2026 5 │ │ │ │ │ + Network : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.3 Utility methods │ │ │ │ │ 1. void Network_findMaxFlow ( Network *network ) ; │ │ │ │ │ This method finds a maximum flow over the network by repeatedly calling the method to │ │ │ │ │ find an augmenting path and then the method to augment the path. It uses an Ideq object │ │ │ │ │ to maintain a priority dequeue. │ │ │ │ │ Error checking: If network is NULL, or if nnode ≤ 0, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ @@ -172,15 +172,15 @@ │ │ │ │ │ and the program exits. │ │ │ │ │ 5. void Network_findMincutFromSink ( Network *network, Ideq deq, int mark[]) ; │ │ │ │ │ This method finds the min-cut closest to the sink by traversing a tree of flow-alternating │ │ │ │ │ paths into the sink. On return, mark[v] = 1 if the node v is in the component that contains │ │ │ │ │ the source. If the node v is in the component that contains the sink, then mark[v] = 2. │ │ │ │ │ Error checking: If network, deq or mark is NULL, or if nnode ≤ 0, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ - 6 Network : DRAFT January 6, 2026 │ │ │ │ │ + 6 Network : DRAFT January 17, 2026 │ │ │ │ │ 1.2.4 IO methods │ │ │ │ │ There are two IO routines for debugging purposes. │ │ │ │ │ 1. void Network_writeForHumanEye ( Network *network, FILE *fp ) ; │ │ │ │ │ Thismethodwritesthenetworktoafileinahumanreadableformat. ThemethodNetwork writeStats() │ │ │ │ │ is called to write out the header and statistics. Then the in-list and out-lists for the nodes in │ │ │ │ │ the network are printed. │ │ │ │ │ Error checking: If network or fp is NULL, an error message is printed and the program exits. │ │ ├── ./usr/share/doc/spooles-doc/PatchAndGoInfo.ps.gz │ │ │ ├── PatchAndGoInfo.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o PatchAndGoInfo.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale 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y(p)s(erturbation)i(is)g(noted,)h(and)f(the)g(factorization)j(pro)s │ │ │ │ (ceeds.)141 728 y(Other)27 b(strategies)h(can)f(b)s(e)g(added)f(to)i │ │ │ │ (the)f Fn(PatchAndGoInfo)c Fo(ob)5 b(ject.)40 b(F)-8 │ │ │ │ b(or)28 b(example,)g(if)f(a)g(matrix)g(is)g(b)s(eing)0 │ │ │ │ 841 y(factored)34 b(that)g(is)g(b)s(eliev)m(ed)g(to)g(b)s(e)f(p)s │ │ │ │ @@ -4967,17 +4978,17 @@ │ │ │ │ (default)h(v)-5 b(alues:)41 b Fn(strategy)28 b Fo(=)i(-1,)h │ │ │ │ Fn(toosmall)d Fo(=)h Fn(fudge)227 5255 y Fo(=)h(0.0,)i(and)e │ │ │ │ Fn(fudgeIV)e Fo(=)i Fn(fudgeDV)f Fo(=)h Fn(NULL)f Fo(.)227 │ │ │ │ 5407 y Ff(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fo(If)30 │ │ │ │ b Fn(info)g Fo(is)g Fn(NULL)p Fo(,)f(an)i(error)f(message)h(is)g(prin)m │ │ │ │ (ted)f(and)f(the)i(program)f(exits.)p eop end │ │ │ │ %%Page: 3 3 │ │ │ │ -TeXDict begin 3 2 bop 91 100 914 4 v 1096 100 a Fn(PatchAndGoInfo)26 │ │ │ │ -b Fg(:)41 b Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2939 100 V 914 w Fo(3)111 399 y(3.)46 b Fn(void)h │ │ │ │ +TeXDict begin 3 2 bop 91 100 892 4 v 1073 100 a Fn(PatchAndGoInfo)26 │ │ │ │ +b Fg(:)41 b Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(17,)i(2026)p │ │ │ │ +2962 100 V 892 w Fo(3)111 399 y(3.)46 b Fn(void)h │ │ │ │ (PatchAndGoInfo_clearData)41 b(\()48 b(PatchAndGoInfo)43 │ │ │ │ b(*info)k(\))g(;)227 549 y Fo(This)35 b(metho)s(d)f(clears)i(an)m(y)g │ │ │ │ (data)f(o)m(wned)g(b)m(y)g(the)h(ob)5 b(ject.)56 b(If)34 │ │ │ │ b Fn(fudgeIV)f Fo(is)i(not)h Fn(NULL)e Fo(it)h(is)h(free'd)f(b)m(y)g(a) │ │ │ │ 227 662 y(call)c(to)f Fn(IV)p 605 662 29 4 v 34 w(free\(\))p │ │ │ │ Fo(.)38 b(If)29 b Fn(fudgeDV)e Fo(is)i(not)h Fn(NULL)e │ │ │ │ Fo(it)i(is)f(free'd)g(b)m(y)g(a)h(call)g(to)g Fn(DV)p │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -26,15 +26,15 @@ │ │ │ │ │ If A is singular, the solution X = 0 and X = A−1B is perfectly acceptable. In other │ │ │ │ │ 1,1 1 2 2,2 2 │ │ │ │ │ cases, the location of the singularity can be communicated back to the user to supply useful │ │ │ │ │ information about the finite element model. One common practice is to not use pivoting, but │ │ │ │ │ to check the magnitude of the diagonal entry as a row and column is to be eliminated. If │ │ │ │ │ the magnitude is smaller than a user-supplied parameter, the diagonal entry is set to some │ │ │ │ │ 1 │ │ │ │ │ - 2 PatchAndGoInfo : DRAFT January 6, 2026 │ │ │ │ │ + 2 PatchAndGoInfo : DRAFT January 17, 2026 │ │ │ │ │ multiple of the largest offdiagonal entry in that row and column of the front, the location and │ │ │ │ │ perturbation is noted, and the factorization proceeds. │ │ │ │ │ Other strategies can be added to the PatchAndGoInfo object. For example, if a matrix is being │ │ │ │ │ factored that is believed to be positive definite, and a negative value is found in a pivot element, │ │ │ │ │ one could abort the factorization, or perturb the element so that it is positive. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ The PatchAndGoInfo structure has five fields. │ │ │ │ │ @@ -58,15 +58,15 @@ │ │ │ │ │ 1. PatchAndGoInfo * PatchAndGoInfo_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the PatchAndGoInfo structure and then sets the │ │ │ │ │ default fields by a call to PatchAndGoInfo setDefaultFields(). │ │ │ │ │ 2. void PatchAndGoInfo_setDefaultFields ( PatchAndGoInfo *info ) ; │ │ │ │ │ This method sets the structure’s fields to default values: strategy = -1, toosmall = fudge │ │ │ │ │ =0.0, and fudgeIV = fudgeDV = NULL . │ │ │ │ │ Error checking: If info is NULL, an error message is printed and the program exits. │ │ │ │ │ - PatchAndGoInfo : DRAFT January 6, 2026 3 │ │ │ │ │ + PatchAndGoInfo : DRAFT January 17, 2026 3 │ │ │ │ │ 3. void PatchAndGoInfo_clearData ( PatchAndGoInfo *info ) ; │ │ │ │ │ This method clears any data owned by the object. If fudgeIV is not NULL it is free’d by a │ │ │ │ │ call to IV free(). If fudgeDV is not NULL it is free’d by a call to DV free(). The structure’s │ │ │ │ │ default fields are then set with a call to PatchAndGoInfo setDefaultFields(). │ │ │ │ │ Error checking: If info is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void PatchAndGoInfo_free ( PatchAndGoInfo *info ) ; │ │ │ │ │ This method releases any storage by a call to PatchAndGoInfo clearData() then free’s the │ │ ├── ./usr/share/doc/spooles-doc/Pencil.ps.gz │ │ │ ├── Pencil.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Pencil.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 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Fe(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2746 100 V 227 399 a Fg(Note:)52 b Fl(this)36 b(metho)s(d)g(w)m(as)g │ │ │ │ (created)i(for)e(an)g(MPI)g(application.)59 b(If)36 b │ │ │ │ Fj(myid)f Fl(is)h(zero,)j(then)d(the)g(\014les)h(are)227 │ │ │ │ 511 y(read)30 b(in,)g(otherwise)h(just)e(stubs)g(are)h(created)h(for)f │ │ │ │ (the)g(in)m(ternal)h(matrix)f(ob)5 b(jects.)41 b(In)30 │ │ │ │ b(our)f(MPI)h(driv)m(ers,)227 624 y(pro)s(cess)d(zero)i(reads)e(in)g │ │ │ │ (the)h(matrices)g(and)f(then)g(starts)h(the)g(pro)s(cess)f(to)h │ │ │ │ (distribute)f(them)h(to)g(the)g(other)227 737 y(pro)s(cesses.)227 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -16,15 +16,15 @@ │ │ │ │ │ • InpMtx *inpmtxB : pointer to the matrix object for B. If inpmtxB is NULL, then B is the │ │ │ │ │ identity matrix. │ │ │ │ │ • double sigma[2] : real or complex scalar shift value. │ │ │ │ │ 1.2 Prototypes and descriptions of Pencil methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ Pencil object. │ │ │ │ │ 1 │ │ │ │ │ - 2 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 2 Chv : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. Pencil * Pencil_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Pencil structure and then sets the default fields │ │ │ │ │ by a call to Pencil setDefaultFields(). │ │ │ │ │ 2. void Pencil_setDefaultFields ( Pencil *pencil ) ; │ │ │ │ │ @@ -48,15 +48,15 @@ │ │ │ │ │ 1. void Pencil_changeCoordType ( Pencil *pencil, int newType ) ; │ │ │ │ │ ThismethodsimplycallstheInpMtx changeCoordType()methodforeachofitstwomatrices. │ │ │ │ │ Error checking: If pencil is NULL, an error message is printed and zero is returned. │ │ │ │ │ 2. void Pencil_changeStorageMode ( Pencil *pencil, int newMode ) ; │ │ │ │ │ This method simply calls the InpMtx changeStorageMode() method for each of its two ma- │ │ │ │ │ trices. │ │ │ │ │ Error checking: If pencil is NULL, an error message is printed and zero is returned. │ │ │ │ │ - Chv : DRAFT January 6, 2026 3 │ │ │ │ │ + Chv : DRAFT January 17, 2026 3 │ │ │ │ │ 3. void Pencil_sortAndCompress ( Pencil *pencil ) ; │ │ │ │ │ ThismethodsimplycallstheInpMtx sortAndCompress()methodforeachofitstwomatrices. │ │ │ │ │ Error checking: If pencil is NULL, an error message is printed and zero is returned. │ │ │ │ │ 4. void Pencil_convertToVectors ( Pencil *pencil ) ; │ │ │ │ │ ThismethodsimplycallstheInpMtx sortAndCompress()methodforeachofitstwomatrices. │ │ │ │ │ Error checking: If pencil is NULL, an error message is printed and zero is returned. │ │ │ │ │ 5. void Pencil_mapToLowerTriangle ( Pencil *pencil ) ; │ │ │ │ │ @@ -83,15 +83,15 @@ │ │ │ │ │ 1. Pencil * Pencil_setup ( int myid, int symflag, char *inpmtxAfile, │ │ │ │ │ double sigma[], char *inpmtxBfile, int randomflag, Drand *drand, │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method is used to read in the matrices from two files and initialize the objects. If │ │ │ │ │ the file name is “none”, then no matrix is read. If symflag is SPOOLES SYMMETRIC or │ │ │ │ │ SPOOLES HERMITIAN, entries in the lower triangle are dropped. If randomflag is one, the │ │ │ │ │ entries are filled with random numbers using the Drand random number generator drand. │ │ │ │ │ - 4 Chv : DRAFT January 6, 2026 │ │ │ │ │ + 4 Chv : DRAFT January 17, 2026 │ │ │ │ │ Note: this method was created for an MPI application. If myid is zero, then the files are │ │ │ │ │ read in, otherwise just stubs are created for the internal matrix objects. In our MPI drivers, │ │ │ │ │ process zero reads in the matrices and then starts the process to distribute them to the other │ │ │ │ │ processes. │ │ │ │ │ Error checking: If pencil or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 2. int Pencil_readFromFiles ( Pencil *pencil, char *fnA, char *fnB ) ; │ │ │ │ │ This method reads the two InpMtx objects from two files. If fnA is “none”, then A is not │ │ ├── ./usr/share/doc/spooles-doc/Perm.ps.gz │ │ │ ├── Perm.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Perm.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1014,16 +1014,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 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+3623,17 @@ │ │ │ │ b(to)h(the)g(old-to-new)g(v)m(ector)0 5045 y Fh(1.2)135 │ │ │ │ b(Protot)l(yp)t(es)46 b(and)f(descriptions)g(of)g Fc(Perm)e │ │ │ │ Fh(metho)t(ds)0 5294 y Fj(This)25 b(section)h(con)m(tains)h(brief)e │ │ │ │ (descriptions)h(including)f(protot)m(yp)s(es)h(of)f(all)i(metho)s(ds)d │ │ │ │ (that)j(b)s(elong)e(to)h(the)g Fi(Perm)0 5407 y Fj(ob)5 │ │ │ │ b(ject.)1927 5656 y(1)p eop end │ │ │ │ %%Page: 2 2 │ │ │ │ -TeXDict begin 2 1 bop 0 100 a Fj(2)p 136 100 1158 4 v │ │ │ │ -1340 w Fi(PERM)29 b Fb(:)i Fg(DRAFT)f Fb(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2742 100 V 0 399 a Fa(1.2.1)112 b(Basic)38 b(metho)s(ds)0 │ │ │ │ +TeXDict begin 2 1 bop 0 100 a Fj(2)p 136 100 1135 4 v │ │ │ │ +1317 w Fi(PERM)29 b Fb(:)i Fg(DRAFT)f Fb(Jan)m(uary)g(17,)h(2026)p │ │ │ │ +2765 100 V 0 399 a Fa(1.2.1)112 b(Basic)38 b(metho)s(ds)0 │ │ │ │ 601 y Fj(As)d(usual,)h(there)f(are)g(four)f(basic)h(metho)s(ds)g(to)g │ │ │ │ (supp)s(ort)e(ob)5 b(ject)36 b(creation,)i(setting)e(default)f │ │ │ │ (\014elds,)h(clearing)0 714 y(an)m(y)31 b(allo)s(cated)h(data,)f(and)f │ │ │ │ (free'ing)h(the)g(ob)5 b(ject.)111 965 y(1.)46 b Fi(Perm)h(*)g │ │ │ │ (Perm_new)f(\()h(void)g(\))g(;)227 1121 y Fj(This)32 │ │ │ │ b(metho)s(d)f(simply)h(allo)s(cates)i(storage)g(for)e(the)g │ │ │ │ Fi(Perm)f Fj(structure)h(and)f(then)h(sets)h(the)f(default)g(\014elds) │ │ │ │ @@ -3677,17 +3688,17 @@ │ │ │ │ (*perm)f(\))i(;)227 5251 y Fj(This)30 b(metho)s(d)g(returns)f(the)h(n)m │ │ │ │ (um)m(b)s(er)f(of)i(b)m(ytes)g(tak)m(en)g(b)m(y)g(this)f(ob)5 │ │ │ │ b(ject.)227 5407 y Fg(Err)-5 b(or)34 b(che)-5 b(cking:)40 │ │ │ │ b Fj(If)30 b Fi(perm)g Fj(is)g Fi(NULL)p Fj(,)f(an)i(error)f(message)h │ │ │ │ (is)g(prin)m(ted)f(and)f(the)i(program)f(exits.)p eop │ │ │ │ end │ │ │ │ %%Page: 3 3 │ │ │ │ -TeXDict begin 3 2 bop 91 100 1158 4 v 1339 100 a Fi(PERM)30 │ │ │ │ -b Fb(:)g Fg(DRAFT)121 b Fb(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2695 100 V 1158 w Fj(3)111 399 y(2.)46 b Fi(int)h(Perm_checkPerm)d(\()k │ │ │ │ +TeXDict begin 3 2 bop 91 100 1135 4 v 1317 100 a Fi(PERM)29 │ │ │ │ +b Fb(:)h Fg(DRAFT)121 b Fb(Jan)m(uary)30 b(17,)i(2026)p │ │ │ │ +2718 100 V 1135 w Fj(3)111 399 y(2.)46 b Fi(int)h(Perm_checkPerm)d(\()k │ │ │ │ (Perm)e(*perm)h(\))g(;)227 557 y Fj(This)39 b(metho)s(d)g(c)m(hec)m(ks) │ │ │ │ i(the)f(v)-5 b(alidit)m(y)41 b(of)e(the)h Fi(Perm)e Fj(ob)5 │ │ │ │ b(ject.)69 b(If)39 b Fi(oldToNew)f Fj(is)h(presen)m(t,)j(it)e(is)g(c)m │ │ │ │ (hec)m(k)m(ed)227 670 y(to)c(see)f(that)g(it)h(is)f(a)g(true)f(p)s(erm) │ │ │ │ m(utation)h(v)m(ector,)j(i.e.,)f(a)e(one-one)h(and)e(on)m(to)i(map)e │ │ │ │ (from)h Fi([0,size\))d Fj(to)227 783 y Fi([0,size\))p │ │ │ │ Fj(,)d(and)h(similarly)h(for)g Fi(newToOld)d Fj(if)j(it)g(is)f(presen)m │ │ │ │ @@ -3747,17 +3758,17 @@ │ │ │ │ b(metho)s(ds)0 4952 y Fj(There)30 b(are)h(the)f(usual)g(eigh)m(t)i(IO)e │ │ │ │ (routines.)40 b(The)30 b(\014le)h(structure)f(of)g(a)h │ │ │ │ Fi(Perm)e Fj(ob)5 b(ject)31 b(is)g(simple:)0 5181 y Fi(isPresent)d │ │ │ │ (size)0 5294 y(oldToNew[size])e Fj(\(if)31 b(presen)m(t\))0 │ │ │ │ 5407 y Fi(newToOld[size])26 b Fj(\(if)31 b(presen)m(t\))p │ │ │ │ eop end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fj(4)p 136 100 1158 4 v │ │ │ │ -1340 w Fi(PERM)29 b Fb(:)i Fg(DRAFT)f Fb(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2742 100 V 111 399 a Fj(1.)46 b Fi(int)h(Perm_readFromFile)c(\()48 │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fj(4)p 136 100 1135 4 v │ │ │ │ +1317 w Fi(PERM)29 b Fb(:)i Fg(DRAFT)f Fb(Jan)m(uary)g(17,)h(2026)p │ │ │ │ +2765 100 V 111 399 a Fj(1.)46 b Fi(int)h(Perm_readFromFile)c(\()48 │ │ │ │ b(Perm)e(*perm,)g(char)h(*fn)g(\))g(;)227 552 y Fj(This)29 │ │ │ │ b(metho)s(d)f(reads)h(a)g Fi(Perm)f Fj(ob)5 b(ject)30 │ │ │ │ b(from)f(a)g(\014le.)41 b(It)29 b(tries)g(to)h(op)s(en)e(the)i(\014le)f │ │ │ │ (and)f(if)h(it)h(is)f(successful,)g(it)227 665 y(then)35 │ │ │ │ b(calls)i Fi(Perm)p 845 665 29 4 v 33 w(readFromFormattedFile\(\))29 │ │ │ │ b Fj(or)36 b Fi(Perm)p 2320 665 V 33 w(readFromBinaryFile\(\))p │ │ │ │ Fj(,)c(closes)k(the)g(\014le)227 778 y(and)30 b(returns)f(the)i(v)-5 │ │ │ │ @@ -3837,17 +3848,17 @@ │ │ │ │ 34 w(writeStats\(\))26 b Fj(is)k(called)h(to)f(write)g(out)h(the)f │ │ │ │ (header)f(and)g(statistics.)43 b(The)29 b(v)-5 b(alue)31 │ │ │ │ b Fi(1)e Fj(is)h(returned.)227 5407 y Fg(Err)-5 b(or)34 │ │ │ │ b(che)-5 b(cking:)40 b Fj(If)30 b Fi(perm)g Fj(or)g Fi(fp)g │ │ │ │ Fj(are)g Fi(NULL)p Fj(,)g(an)g(error)g(message)i(is)e(prin)m(ted)g(and) │ │ │ │ g(zero)h(is)f(returned.)p eop end │ │ │ │ %%Page: 5 5 │ │ │ │ -TeXDict begin 5 4 bop 91 100 1158 4 v 1339 100 a Fi(PERM)30 │ │ │ │ -b Fb(:)g Fg(DRAFT)121 b Fb(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2695 100 V 1158 w Fj(5)111 399 y(8.)46 b Fi(int)h(Perm_writeStats)d(\() │ │ │ │ +TeXDict begin 5 4 bop 91 100 1135 4 v 1317 100 a Fi(PERM)29 │ │ │ │ +b Fb(:)h Fg(DRAFT)121 b Fb(Jan)m(uary)30 b(17,)i(2026)p │ │ │ │ +2718 100 V 1135 w Fj(5)111 399 y(8.)46 b Fi(int)h(Perm_writeStats)d(\() │ │ │ │ j(Perm)g(*perm,)f(FILE)h(*fp)g(\))g(;)227 549 y Fj(This)30 │ │ │ │ b(metho)s(d)g(writes)g(out)h(a)f(header)h(and)e(statistics)k(to)e(a)g │ │ │ │ (\014le.)40 b(The)30 b(v)-5 b(alue)31 b Fi(1)f Fj(is)h(returned.)227 │ │ │ │ 699 y Fg(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fj(If)30 │ │ │ │ b Fi(perm)g Fj(or)g Fi(fp)g Fj(are)g Fi(NULL)p Fj(,)g(an)g(error)g │ │ │ │ (message)i(is)e(prin)m(ted)g(and)g(zero)h(is)f(returned.)p │ │ │ │ eop end │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -14,15 +14,15 @@ │ │ │ │ │ • int size : dimension of the vectors │ │ │ │ │ • int *newToOld : pointer to the new-to-old vector │ │ │ │ │ • int *oldToNew : pointer to the old-to-new vector │ │ │ │ │ 1.2 Prototypes and descriptions of Perm methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the Perm │ │ │ │ │ object. │ │ │ │ │ 1 │ │ │ │ │ - 2 PERM : DRAFT January 6, 2026 │ │ │ │ │ + 2 PERM : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. Perm * Perm_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the Perm structure and then sets the default fields │ │ │ │ │ by a call to Perm setDefaultFields(). │ │ │ │ │ 2. void Perm_setDefaultFields ( Perm *perm ) ; │ │ │ │ │ @@ -46,15 +46,15 @@ │ │ │ │ │ isPresent == 3 then newToOld and newToOld are set with calls to IVinit(). │ │ │ │ │ Error checking: If perm is NULL, or if isPresent is invalid, or if size <= 0, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 1.2.3 Utility methods │ │ │ │ │ 1. int Perm_sizeOf ( Perm *perm ) ; │ │ │ │ │ This method returns the number of bytes taken by this object. │ │ │ │ │ Error checking: If perm is NULL, an error message is printed and the program exits. │ │ │ │ │ - PERM : DRAFT January 6, 2026 3 │ │ │ │ │ + PERM : DRAFT January 17, 2026 3 │ │ │ │ │ 2. int Perm_checkPerm ( Perm *perm ) ; │ │ │ │ │ This method checks the validity of the Perm object. If oldToNew is present, it is checked │ │ │ │ │ to see that it is a true permutation vector, i.e., a one-one and onto map from [0,size) to │ │ │ │ │ [0,size), and similarly for newToOld if it is present. If the permutation vector(s) are valid, │ │ │ │ │ 1 is returned, otherwise 0 is returned. │ │ │ │ │ Error checking: If perm is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. void Perm_fillOldToNew ( Perm *perm ) ; │ │ │ │ │ @@ -80,15 +80,15 @@ │ │ │ │ │ compressed graph. │ │ │ │ │ Error checking: If perm or eqmapIV are NULL, an error message is printed and zero is returned. │ │ │ │ │ 1.2.4 IO methods │ │ │ │ │ There are the usual eight IO routines. The file structure of a Perm object is simple: │ │ │ │ │ isPresent size │ │ │ │ │ oldToNew[size] (if present) │ │ │ │ │ newToOld[size] (if present) │ │ │ │ │ - 4 PERM : DRAFT January 6, 2026 │ │ │ │ │ + 4 PERM : DRAFT January 17, 2026 │ │ │ │ │ 1. int Perm_readFromFile ( Perm *perm, char *fn ) ; │ │ │ │ │ This method reads a Perm object from a file. It tries to open the file and if it is successful, it │ │ │ │ │ then calls Perm readFromFormattedFile() or Perm readFromBinaryFile(), closes the file │ │ │ │ │ and returns the value returned from the called routine. │ │ │ │ │ Error checking: If perm or fn are NULL, or if fn is not of the form *.permf (for a formatted │ │ │ │ │ file) or *.permb (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 2. int Perm_readFromFormattedFile ( Perm *perm, FILE *fp ) ; │ │ │ │ │ @@ -117,15 +117,15 @@ │ │ │ │ │ This method writes out a Perm object to a binary file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ Error checking: If perm or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 7. int Perm_writeForHumanEye ( Perm *perm, FILE *fp ) ; │ │ │ │ │ This method writes out a Perm object to a file in a human readable format. The method │ │ │ │ │ Perm writeStats() is called to write out the header and statistics. The value 1 is returned. │ │ │ │ │ Error checking: If perm or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ - PERM : DRAFT January 6, 2026 5 │ │ │ │ │ + PERM : DRAFT January 17, 2026 5 │ │ │ │ │ 8. int Perm_writeStats ( Perm *perm, FILE *fp ) ; │ │ │ │ │ This method writes out a header and statistics to a file. The value 1 is returned. │ │ │ │ │ Error checking: If perm or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ Index │ │ │ │ │ Perm checkPerm(), 4 │ │ │ │ │ Perm clearData(), 3 │ │ │ │ │ Perm compress(), 4 │ │ ├── ./usr/share/doc/spooles-doc/ReferenceManual.ps.gz │ │ │ ├── ReferenceManual.ps │ │ │ │ @@ -12,15 +12,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o ReferenceManual.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2033 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 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0000000000000000000000000000000000000000000000000000000000000000 │ │ │ │ 0000000000000000000000000000000000000000000000000000000000000000 │ │ │ │ 0000000000000000000000000000000000000000000000000000000000000000 │ │ │ │ 0000000000000000000000000000000000000000000000000000000000000000 │ │ │ │ @@ -10596,16 +10607,18 @@ │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 46 /period put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 65 /A put │ │ │ │ dup 67 /C put │ │ │ │ dup 68 /D put │ │ │ │ dup 74 /J put │ │ │ │ dup 75 /K put │ │ │ │ dup 80 /P put │ │ │ │ dup 87 /W put │ │ │ │ @@ -10807,166 +10820,174 @@ │ │ │ │ 34DE10D995ABCAF45FBB3B6B73E80D05F4C51F8C29D4B0F67C8A86432A6C5E86 │ │ │ │ F0126AB25A5CA2875B48C61CB8112A4CF9AA08F8B0157396CF63CBECDB8867CC │ │ │ │ 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b(Driv)n(er)27 │ │ │ │ b(programs)76 b(.)42 b(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h │ │ │ │ (.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.) │ │ │ │ h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 b(302)p │ │ │ │ eop end │ │ │ │ %%Page: 11 12 │ │ │ │ -TeXDict begin 11 11 bop 83 100 1157 4 v 1323 100 a Fz(SPOOLES)32 │ │ │ │ -b(2.2)26 b Fr(:)120 b(Jan)n(uary)26 b(6,)h(2026)p 2662 │ │ │ │ -100 V 1157 w Fy(11)0 390 y Fz(34)i Ft(PatchAndGoInfo)p │ │ │ │ +TeXDict begin 11 11 bop 83 100 1137 4 v 1302 100 a Fz(SPOOLES)32 │ │ │ │ +b(2.2)27 b Fr(:)120 b(Jan)n(uary)25 b(17,)i(2026)p 2683 │ │ │ │ +100 V 1137 w Fy(11)0 390 y Fz(34)i Ft(PatchAndGoInfo)p │ │ │ │ Fz(:)36 b(Piv)m(ot)c(Mo)s(di\014cation)f(Ob)5 b(ject)1856 │ │ │ │ b(307)125 513 y Fy(34.1)41 b(Data)28 b(Structure)61 b(.)41 │ │ │ │ b(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h │ │ │ │ (.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.) │ │ │ │ f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 b(308)125 637 y(34.2)41 │ │ │ │ b(Protot)n(yp)r(es)26 b(and)i(descriptions)f(of)g Ft(PatchAndGoInfo)22 │ │ │ │ b Fy(metho)r(ds)76 b(.)42 b(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f │ │ │ │ @@ -12849,17 +12870,17 @@ │ │ │ │ (.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.) │ │ │ │ h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 b(335)315 5407 │ │ │ │ y(38.2.4)h(IO)27 b(metho)r(ds)44 b(.)d(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h │ │ │ │ (.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.) │ │ │ │ f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 │ │ │ │ b(335)p eop end │ │ │ │ %%Page: 12 13 │ │ │ │ -TeXDict begin 12 12 bop 0 100 a Fy(12)p 166 100 1157 │ │ │ │ -4 v 1322 w Fz(SPOOLES)32 b(2.2)26 b Fr(:)37 b(Jan)n(uary)26 │ │ │ │ -b(6,)h(2026)p 2743 100 V 0 390 a Fz(39)i Ft(SubMtxManager)p │ │ │ │ +TeXDict begin 12 12 bop 0 100 a Fy(12)p 166 100 1137 │ │ │ │ +4 v 1301 w Fz(SPOOLES)32 b(2.2)27 b Fr(:)37 b(Jan)n(uary)25 │ │ │ │ +b(17,)i(2026)p 2764 100 V 0 390 a Fz(39)i Ft(SubMtxManager)p │ │ │ │ Fz(:)36 b Ft(SubMtx)29 b Fz(ob)5 b(ject)33 b(manager)2057 │ │ │ │ b(336)125 515 y Fy(39.1)41 b(Data)28 b(Structure)61 b(.)41 │ │ │ │ b(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h │ │ │ │ (.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.) │ │ │ │ f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 b(337)125 640 y(39.2)41 │ │ │ │ b(Protot)n(yp)r(es)26 b(and)i(descriptions)f(of)g Ft(SubMtxManager)22 │ │ │ │ b Fy(metho)r(ds)56 b(.)41 b(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h │ │ │ │ @@ -12945,17 +12966,17 @@ │ │ │ │ f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f │ │ │ │ (.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 b(368)315 5407 │ │ │ │ y(43.1.1)h Ft(MatMulInfo)24 b Fy(:)37 b(Matrix-matrix)26 │ │ │ │ b(m)n(ultiply)i(information)f(ob)5 b(ject)75 b(.)41 b(.)h(.)f(.)h(.)g │ │ │ │ (.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 b(368)p │ │ │ │ eop end │ │ │ │ %%Page: 13 14 │ │ │ │ -TeXDict begin 13 13 bop 83 100 1157 4 v 1323 100 a Fz(SPOOLES)32 │ │ │ │ -b(2.2)26 b Fr(:)120 b(Jan)n(uary)26 b(6,)h(2026)p 2662 │ │ │ │ -100 V 1157 w Fy(13)125 390 y(43.2)41 b(Protot)n(yp)r(es)26 │ │ │ │ +TeXDict begin 13 13 bop 83 100 1137 4 v 1302 100 a Fz(SPOOLES)32 │ │ │ │ +b(2.2)27 b Fr(:)120 b(Jan)n(uary)25 b(17,)i(2026)p 2683 │ │ │ │ +100 V 1137 w Fy(13)125 390 y(43.2)41 b(Protot)n(yp)r(es)26 │ │ │ │ b(and)i(descriptions)f(of)g Ft(MPI)g Fy(metho)r(ds)39 │ │ │ │ b(.)i(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g │ │ │ │ (.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 b(369)315 │ │ │ │ 515 y(43.2.1)h(Split)28 b(and)g(redistribution)f(metho)r(ds)59 │ │ │ │ b(.)41 b(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)h(.) │ │ │ │ f(.)h(.)g(.)f(.)h(.)f(.)h(.)f(.)h(.)g(.)f(.)h(.)f(.)51 │ │ │ │ b(369)315 639 y(43.2.2)h(Gather)27 b(and)h(scatter)f(metho)r(ds)j(.)42 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -1,13 +1,13 @@ │ │ │ │ │ The Reference Manual for SPOOLES, Release 2.2: │ │ │ │ │ An Object Oriented Software Library for Solving │ │ │ │ │ Sparse Linear Systems of Equations │ │ │ │ │ 1 2 3 4 │ │ │ │ │ Cleve Ashcraft Daniel Pierce David K. Wah Jason Wu │ │ │ │ │ - January 6, 2026 │ │ │ │ │ + January 17, 2026 │ │ │ │ │ 1Boeing Shared Services Group, P. O. Box 24346, Mail Stop 7L-22, Seattle, Washington 98124, │ │ │ │ │ cleve.ashcraft@boeing.com. This research was supported in part by the DARPA Contract DABT63-95-C-0122 │ │ │ │ │ and the DoD High Performance Computing Modernization Program Common HPC Software Support Initiative. │ │ │ │ │ 2Boeing Shared Services Group, P. O. Box 24346, Mail Stop 7L-22, Seattle, Washington 98124, │ │ │ │ │ dpierce@redwood.rt.cs.boeing.com. This research was supported in part by the DARPA Contract DABT63- │ │ │ │ │ 95-C-0122 and the DoD High Performance Computing Modernization Program Common HPC Software Support │ │ │ │ │ Initiative. │ │ │ │ │ @@ -68,15 +68,15 @@ │ │ │ │ │ 3.2 Prototypes and descriptions of Coords methods . . . . . . . . . . . . . . . . . . . . . . . . . . 34 │ │ │ │ │ 3.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 │ │ │ │ │ 3.2.2 Initializer methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 │ │ │ │ │ 3.2.3 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 │ │ │ │ │ 3.2.4 IO methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 │ │ │ │ │ 3.3 Driver programs for the Coords object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 │ │ │ │ │ 2 │ │ │ │ │ - SPOOLES2.2: January 6, 2026 3 │ │ │ │ │ + SPOOLES 2.2: January 17, 2026 3 │ │ │ │ │ 4 DV: Double Vector Object 39 │ │ │ │ │ 4.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 │ │ │ │ │ 4.2 Prototypes and descriptions of DV methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 │ │ │ │ │ 4.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 │ │ │ │ │ 4.2.2 Instance methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 │ │ │ │ │ 4.2.3 Initializer methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 │ │ │ │ │ 4.2.4 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 │ │ │ │ │ @@ -109,15 +109,15 @@ │ │ │ │ │ 8.2 Prototypes and descriptions of IV methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 │ │ │ │ │ 8.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 │ │ │ │ │ 8.2.2 Instance methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 │ │ │ │ │ 8.2.3 Initializer methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 │ │ │ │ │ 8.2.4 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 │ │ │ │ │ 8.2.5 IO methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 │ │ │ │ │ 8.3 Driver programs for the IV object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 │ │ │ │ │ - 4 SPOOLES 2.2 : January 6, 2026 │ │ │ │ │ + 4 SPOOLES 2.2 : January 17, 2026 │ │ │ │ │ 9 IVL: Integer Vector List Object 64 │ │ │ │ │ 9.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 │ │ │ │ │ 9.2 Prototypes and descriptions of IVL methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 │ │ │ │ │ 9.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 │ │ │ │ │ 9.2.2 Instance methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 │ │ │ │ │ 9.2.3 Initialization and resizing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 │ │ │ │ │ 9.2.4 List manipulation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 │ │ │ │ │ @@ -149,15 +149,15 @@ │ │ │ │ │ 13.1 Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 │ │ │ │ │ 13.2 Prototypes and descriptions of Utilities methods . . . . . . . . . . . . . . . . . . . . . . . . 81 │ │ │ │ │ 13.2.1 CV : char vector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 │ │ │ │ │ 13.2.2 DV : double vector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 │ │ │ │ │ 13.2.3 ZV : double complex vector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 │ │ │ │ │ 13.2.4 IV : int vector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 │ │ │ │ │ 13.2.5 FV : float vector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 │ │ │ │ │ - SPOOLES2.2: January 6, 2026 5 │ │ │ │ │ + SPOOLES 2.2: January 17, 2026 5 │ │ │ │ │ 13.2.6 PCV : char * vector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 │ │ │ │ │ 13.2.7 PDV : double * vector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 │ │ │ │ │ 13.2.8 PFV : float * vector methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 │ │ │ │ │ 13.2.9 Sorting routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 │ │ │ │ │ 13.2.10Sort and compress routines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 │ │ │ │ │ 13.2.11IP : (int, pointer) singly linked-list methods . . . . . . . . . . . . . . . . . . . . . . 103 │ │ │ │ │ 13.2.12I2OP : (int, int, void*, pointer) singly linked-list methods . . . . . . . . . . . . 104 │ │ │ │ │ @@ -186,15 +186,15 @@ │ │ │ │ │ 16.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 │ │ │ │ │ 16.2.2 Initializer methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 │ │ │ │ │ 16.2.3 Generate induced graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 │ │ │ │ │ 16.2.4 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 │ │ │ │ │ 16.2.5 Dulmage-Mendelsohn decomposition method . . . . . . . . . . . . . . . . . . . . . . . 123 │ │ │ │ │ 16.2.6 IO methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 │ │ │ │ │ 16.3 Driver programs for the BPG object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 │ │ │ │ │ - 6 SPOOLES 2.2 : January 6, 2026 │ │ │ │ │ + 6 SPOOLES 2.2 : January 17, 2026 │ │ │ │ │ 17 DSTree: │ │ │ │ │ ADomain/Separator Tree Object 126 │ │ │ │ │ 17.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 │ │ │ │ │ 17.2 Prototypes and descriptions of DSTree methods . . . . . . . . . . . . . . . . . . . . . . . . . . 126 │ │ │ │ │ 17.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 │ │ │ │ │ 17.2.2 Instance methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 │ │ │ │ │ 17.2.3 Initializer methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 │ │ │ │ │ @@ -226,15 +226,15 @@ │ │ │ │ │ 19.2.11Parallel factorization map methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 │ │ │ │ │ 19.2.12Storage profile methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 │ │ │ │ │ 19.2.13IO methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 │ │ │ │ │ 19.3 Driver programs for the ETree object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 │ │ │ │ │ 20 GPart: Graph Partitioning Object 162 │ │ │ │ │ 20.1 Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 │ │ │ │ │ 20.2 Prototypes and descriptions of GPart methods . . . . . . . . . . . . . . . . . . . . . . . . . . 164 │ │ │ │ │ - SPOOLES2.2: January 6, 2026 7 │ │ │ │ │ + SPOOLES 2.2: January 17, 2026 7 │ │ │ │ │ 20.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 │ │ │ │ │ 20.2.2 Initializer methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 │ │ │ │ │ 20.2.3 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 │ │ │ │ │ 20.2.4 Domain decomposition methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 │ │ │ │ │ 20.2.5 Methods to generate a 2-set partition . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 │ │ │ │ │ 20.2.6 Methods to improve a 2-set partition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 │ │ │ │ │ 20.2.7 Recursive Bisection method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 │ │ │ │ │ @@ -264,15 +264,15 @@ │ │ │ │ │ 22.3.1 Basic methods — public . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 │ │ │ │ │ 22.3.2 Initialization methods — public . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 │ │ │ │ │ 22.3.3 Ordering methods — public . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 │ │ │ │ │ 22.3.4 Extraction methods — public . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 │ │ │ │ │ 22.3.5 Internal methods — private . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 │ │ │ │ │ 22.4 Prototypes and descriptions of MSMDvtx methods . . . . . . . . . . . . . . . . . . . . . . . . . 192 │ │ │ │ │ 22.5 Driver programs for the MSMD object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 │ │ │ │ │ - 8 SPOOLES 2.2 : January 6, 2026 │ │ │ │ │ + 8 SPOOLES 2.2 : January 17, 2026 │ │ │ │ │ 23 Network: Simple Max-flow solver 195 │ │ │ │ │ 23.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 │ │ │ │ │ 23.2 Prototypes and descriptions of Network methods . . . . . . . . . . . . . . . . . . . . . . . . . 197 │ │ │ │ │ 23.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 │ │ │ │ │ 23.2.2 Initializer methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 │ │ │ │ │ 23.2.3 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 │ │ │ │ │ 23.2.4 IO methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 │ │ │ │ │ @@ -303,15 +303,15 @@ │ │ │ │ │ IV Numeric Objects and Methods 216 │ │ │ │ │ 26 Chv: Block chevron 217 │ │ │ │ │ 26.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 │ │ │ │ │ 26.2 Prototypes and descriptions of Chv methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 │ │ │ │ │ 26.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 │ │ │ │ │ 26.2.2 Instance methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 │ │ │ │ │ 26.2.3 Initialization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 │ │ │ │ │ - SPOOLES2.2: January 6, 2026 9 │ │ │ │ │ + SPOOLES 2.2: January 17, 2026 9 │ │ │ │ │ 26.2.4 Search methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 │ │ │ │ │ 26.2.5 Pivot methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 │ │ │ │ │ 26.2.6 Update methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 │ │ │ │ │ 26.2.7 Assembly methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 │ │ │ │ │ 26.2.8 Factorization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 │ │ │ │ │ 26.2.9 Copy methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 │ │ │ │ │ 26.2.10Swap methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 │ │ │ │ │ @@ -343,15 +343,15 @@ │ │ │ │ │ 30 FrontMtx: Front matrix 250 │ │ │ │ │ 30.1 Data Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 │ │ │ │ │ 30.2 Prototypes and descriptions of FrontMtx methods . . . . . . . . . . . . . . . . . . . . . . . . 255 │ │ │ │ │ 30.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 │ │ │ │ │ 30.2.2 Instance methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 │ │ │ │ │ 30.2.3 Initialization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 │ │ │ │ │ 30.2.4 Utility Factorization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 │ │ │ │ │ - 10 SPOOLES 2.2: January 6, 2026 │ │ │ │ │ + 10 SPOOLES 2.2 : January 17, 2026 │ │ │ │ │ 30.2.5 Serial Factorization method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 │ │ │ │ │ 30.2.6 QR factorization utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 │ │ │ │ │ 30.2.7 Serial QR Factorization method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 │ │ │ │ │ 30.2.8 Postprocessing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 │ │ │ │ │ 30.2.9 Utility Solve methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 │ │ │ │ │ 30.2.10Serial Solve method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 │ │ │ │ │ 30.2.11Serial QR Solve method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 │ │ │ │ │ @@ -384,15 +384,15 @@ │ │ │ │ │ 32.3 Driver programs for the InpMtx object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 │ │ │ │ │ 33 Iter: Iterative Methods 297 │ │ │ │ │ 33.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 │ │ │ │ │ 33.2 Prototypes and descriptions of Iter methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 │ │ │ │ │ 33.2.1 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 │ │ │ │ │ 33.2.2 Iterative methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 │ │ │ │ │ 33.3 Driver programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 │ │ │ │ │ - SPOOLES 2.2: January 6, 2026 11 │ │ │ │ │ + SPOOLES 2.2 : January 17, 2026 11 │ │ │ │ │ 34 PatchAndGoInfo: Pivot Modification Object 307 │ │ │ │ │ 34.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 │ │ │ │ │ 34.2 Prototypes and descriptions of PatchAndGoInfo methods . . . . . . . . . . . . . . . . . . . . 308 │ │ │ │ │ 34.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 │ │ │ │ │ 34.2.2 Initializer methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 │ │ │ │ │ 35 Pencil: Matrix pencil 310 │ │ │ │ │ 35.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 │ │ │ │ │ @@ -424,15 +424,15 @@ │ │ │ │ │ 38 SubMtxList: SubMtx list object 333 │ │ │ │ │ 38.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 │ │ │ │ │ 38.2 Prototypes and descriptions of SubMtxList methods . . . . . . . . . . . . . . . . . . . . . . . 334 │ │ │ │ │ 38.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 │ │ │ │ │ 38.2.2 Initialization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 │ │ │ │ │ 38.2.3 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 │ │ │ │ │ 38.2.4 IO methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 │ │ │ │ │ - 12 SPOOLES 2.2: January 6, 2026 │ │ │ │ │ + 12 SPOOLES 2.2 : January 17, 2026 │ │ │ │ │ 39 SubMtxManager: SubMtx object manager 336 │ │ │ │ │ 39.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 │ │ │ │ │ 39.2 Prototypes and descriptions of SubMtxManager methods . . . . . . . . . . . . . . . . . . . . . 337 │ │ │ │ │ 39.2.1 Basic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 │ │ │ │ │ 39.2.2 Initialization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 │ │ │ │ │ 39.2.3 Utility methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 │ │ │ │ │ 39.2.4 IO methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 │ │ │ │ │ @@ -459,15 +459,15 @@ │ │ │ │ │ 42.2.4 Multithreaded Solve method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 │ │ │ │ │ 42.2.5 Multithreaded QR Solve method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 │ │ │ │ │ 42.3 Driver programs for the multithreaded functions . . . . . . . . . . . . . . . . . . . . . . . . . 361 │ │ │ │ │ VII MPI Methods 367 │ │ │ │ │ 43 MPI directory 368 │ │ │ │ │ 43.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 │ │ │ │ │ 43.1.1 MatMulInfo : Matrix-matrix multiply information object . . . . . . . . . . . . . . . . 368 │ │ │ │ │ - SPOOLES 2.2: January 6, 2026 13 │ │ │ │ │ + SPOOLES 2.2 : January 17, 2026 13 │ │ │ │ │ 43.2 Prototypes and descriptions of MPI methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 │ │ │ │ │ 43.2.1 Split and redistribution methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 │ │ │ │ │ 43.2.2 Gather and scatter methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 │ │ │ │ │ 43.2.3 Symbolic Factorization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 │ │ │ │ │ 43.2.4 Numeric Factorization methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 │ │ │ │ │ 43.2.5 Post-processing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 │ │ │ │ │ 43.2.6 Numeric Solve methods . . . . . . . . . . . . . . . . . . . . . . . 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b(Sc)n(h)n(ur)g(righ)n(t)g(hand)h(side)369 │ │ │ │ 775 y Fm(cpus[4])97 b Fn(Sc)n(h)n(ur)27 b(solv)n(e)2099 │ │ │ │ 377 y Fm(cpus[5])97 b Fn(compute)27 b(domains')g(righ)n(t)g(hand)h │ │ │ │ (side)2099 477 y Fm(cpus[6])97 b Fn(second)27 b(solv)n(e)f(with)i │ │ │ │ @@ -5294,17 +5305,17 @@ │ │ │ │ (loaded)f(with)i(random)e(en)n(tries.)50 b(The)32 b(linear)208 │ │ │ │ 5240 y(system)27 b Fl(AX)j Fn(=)22 b Fl(B)32 b Fn(is)27 │ │ │ │ b(solv)n(ed)g(as)g(follo)n(ws.)307 5407 y Fg(\210)42 │ │ │ │ b Fn(First)28 b Fl(A)g Fn(is)f(factored,)g(and)g(a)h │ │ │ │ Fm(FrontMtx)c Fn(ob)5 b(ject)27 b(is)h(created)f(to)g(hold)h(the)g │ │ │ │ (factorization.)p eop end │ │ │ │ %%Page: 5 5 │ │ │ │ -TeXDict begin 5 4 bop 83 100 1070 4 v 1235 100 a Fm(SemiImplMtx)23 │ │ │ │ -b Fd(:)37 b Fe(DRAFT)110 b Fd(Jan)n(uary)26 b(6,)h(2026)p │ │ │ │ -2791 100 V 1070 w Fn(5)307 390 y Fg(\210)42 b Fn(The)28 │ │ │ │ +TeXDict begin 5 4 bop 83 100 1049 4 v 1214 100 a Fm(SemiImplMtx)24 │ │ │ │ +b Fd(:)36 b Fe(DRAFT)111 b Fd(Jan)n(uary)25 b(17,)i(2026)p │ │ │ │ +2812 100 V 1049 w Fn(5)307 390 y Fg(\210)42 b Fn(The)28 │ │ │ │ b(system)f(is)h(solv)n(ed)e(using)h(the)h Fm(FrontMtx)d │ │ │ │ Fn(ob)5 b(ject.)307 523 y Fg(\210)42 b Fn(A)28 b Fm(SemiImplMtx)23 │ │ │ │ b Fn(matrix)k(ob)5 b(ject)28 b(is)f(constructed)g(from)h(the)g │ │ │ │ Fm(FrontMtx)c Fn(ob)5 b(ject)27 b(and)h Fl(A)p Fn(.)307 │ │ │ │ 656 y Fg(\210)42 b Fn(The)28 b(system)f(is)h(solv)n(ed)e(using)h(the)h │ │ │ │ Fm(SemiImplMtx)c Fn(ob)5 b(ject.)208 822 y(V)-7 b(arious)30 │ │ │ │ b(statistics)h(and)g(CPU)g(timings)g(are)g(written)g(to)g(the)h │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -51,15 +51,15 @@ │ │ │ │ │ in a semi-implicit form) can pay off — storage can be saved when the number of entries in L and U │ │ │ │ │ 2,1 1,2 │ │ │ │ │ are larger than the number of entries in A and A . The number of solve operations is reduced by │ │ │ │ │ 2,1 1,2 │ │ │ │ │ |L | + |U | − 2|D | − |A | − |A |, where | · | denotes the number of nonzeroes in a matrix. │ │ │ │ │ 2,1 1,2 1,1 2,1 1,2 │ │ │ │ │ 1 │ │ │ │ │ - 2 SemiImplMtx : DRAFT January 6, 2026 │ │ │ │ │ + 2 SemiImplMtx : DRAFT January 17, 2026 │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ The SemiImplMtx structure has the following fields. │ │ │ │ │ • int neqns : number of equations. │ │ │ │ │ • int type : type of entries, SPOOLES REAL or SPOOLES COMPLEX. │ │ │ │ │ • int symmetryflag: typeofmatrixsymmetry,SPOOLES SYMMETRIC,SPOOLES HERMITIANorSPOOLES NONSYMMETRIC. │ │ │ │ │ • int ndomeqns : number of equations in the domains, or (1,1) block. │ │ │ │ │ • int nschureqns : number of equations in the Schur complement, or (2,2) block. │ │ │ │ │ @@ -95,15 +95,15 @@ │ │ │ │ │ Thismethodsetsthestructure’sfieldstodefaultvalues: neqns=0,type=SPOOLES REAL,symmetryflag │ │ │ │ │ =SPOOLES SYMMETRIC,ndomeqns=nschureqns=0,anddomainMtx,schurMtx,A21,A12,domRowsIV, │ │ │ │ │ schurRowsIV, domColumnsIV and schurColumnsIV are all set to NULL. │ │ │ │ │ Return codes: 1 means a normal return, -1 means mtx is NULL. │ │ │ │ │ 3. int SemiImplMtx_clearData ( SemiImplMtx *mtx ) ; │ │ │ │ │ This method releases all storage held by the object. │ │ │ │ │ Return codes: 1 means a normal return, -1 means mtx is NULL. │ │ │ │ │ - SemiImplMtx : DRAFT January 6, 2026 3 │ │ │ │ │ + SemiImplMtx : DRAFT January 17, 2026 3 │ │ │ │ │ 4. int SemiImplMtx_free ( SemiImplMtx *mtx ) ; │ │ │ │ │ This method releases all storage held by the object via a call to SemiImplMtx clearData(), then free’d │ │ │ │ │ the storage for the object. │ │ │ │ │ Return codes: 1 means a normal return, -1 means mtx is NULL. │ │ │ │ │ 1.2.2 Initialization Methods │ │ │ │ │ 1. int SemiImplMtx_initFromFrontMtx ( SemiImplMtx *semimtx, FrontMtx *frontmtx, │ │ │ │ │ InpMtx *inpmtx, IV *frontmapIV, int msglvl, FILE *msgFile) ; │ │ │ │ │ @@ -140,15 +140,15 @@ │ │ │ │ │ 1.2.3 Solve Methods │ │ │ │ │ 1. int SemiImplMtx_solve ( SemiImplMtx *mtx, DenseMtx *X, DenseMtx *B, │ │ │ │ │ SubMtxManager *mtxmanager, double cpus[], int msglvl, FILE *msgFile ) ; │ │ │ │ │ This methods solves a linear system (L + I)D(I + U)X = B, (UT + I)D(I + U)X = B or (UH + │ │ │ │ │ I)D(I + U)X = B, where X and B are DenseMtx objects. mtxmanager is an object to handle the │ │ │ │ │ working SubMtx objects during the solve. One can have X and B point to the same object, for entries │ │ │ │ │ are read from B and written to X. On return, the cpus[] vector contains the following information. │ │ │ │ │ - 4 SemiImplMtx : DRAFT January 6, 2026 │ │ │ │ │ + 4 SemiImplMtx : DRAFT January 17, 2026 │ │ │ │ │ cpus[0] initialize working matrices cpus[5] compute domains’ right hand side │ │ │ │ │ cpus[1] load right hand side cpus[6] second solve with domains │ │ │ │ │ cpus[2] first solve with domains cpus[7] store solution │ │ │ │ │ cpus[3] compute Schur right hand side cpus[8] miscellaneous time │ │ │ │ │ cpus[4] Schur solve cpus[9] total time │ │ │ │ │ Return codes: │ │ │ │ │ 1 normal return -3 B is NULL │ │ │ │ │ @@ -181,15 +181,15 @@ │ │ │ │ │ This section contains brief descriptions of the driver programs. │ │ │ │ │ 1. testGrid msglvl msgFile n1 n2 n3 maxzeros maxsize seed type symmetryflag │ │ │ │ │ sparsityflag pivotingflag tau droptol nrhs depth │ │ │ │ │ This driver program tests the SemiImplMtx creation and solve methods for a matrix from a regular │ │ │ │ │ 2-D or 3-D grid. The matrix can be real or complex and is loaded with random entries. The linear │ │ │ │ │ system AX =B is solved as follows. │ │ │ │ │ • First A is factored, and a FrontMtx object is created to hold the factorization. │ │ │ │ │ - SemiImplMtx : DRAFT January 6, 2026 5 │ │ │ │ │ + SemiImplMtx : DRAFT January 17, 2026 5 │ │ │ │ │ • The system is solved using the FrontMtx object. │ │ │ │ │ • A SemiImplMtx matrix object is constructed from the FrontMtx object and A. │ │ │ │ │ • The system is solved using the SemiImplMtx object. │ │ │ │ │ Various statistics and CPU timings are written to the message file to compare the two solution pro- │ │ │ │ │ cesses. Use the do grid shell script for testing. │ │ │ │ │ • The msglvl parameter determines the amount of output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the message │ │ ├── ./usr/share/doc/spooles-doc/SolveMap.ps.gz │ │ │ ├── SolveMap.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o SolveMap.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg 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b(17,)h(2026)p │ │ │ │ +2818 100 V 1035 w Fm(7)111 399 y(6.)46 b Fl(int)h │ │ │ │ (SolveMap_writeToBinaryFil)o(e)42 b(\()47 b(SolveMap)f(*solvemap,)f │ │ │ │ (FILE)h(*fp)h(\))h(;)227 549 y Fm(This)29 b(metho)s(d)h(writes)g(an)f │ │ │ │ Fl(SolveMap)f Fm(ob)5 b(ject)31 b(to)f(a)h(binary)e(\014le.)40 │ │ │ │ b(If)30 b(there)g(are)g(no)g(errors)f(in)h(writing)g(the)227 │ │ │ │ 662 y(data,)i(the)e(v)-5 b(alue)31 b Fl(1)f Fm(is)g(returned.)40 │ │ │ │ b(If)30 b(an)g(IO)g(error)g(is)g(encoun)m(tered)h(from)f │ │ │ │ Fl(fwrite)p Fm(,)f(zero)i(is)g(returned.)227 812 y Fk(Err)-5 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -19,15 +19,15 @@ │ │ │ │ │ • int nproc – number of threads or processes │ │ │ │ │ • int *owners – vector mapping fronts to owning threads or processes │ │ │ │ │ • int nblockUpper – number of submatrices in the upper triangle │ │ │ │ │ • int *rowidsUpper – vector of row ids for the upper triangle │ │ │ │ │ • int *colidsUpper – vector of column ids for the upper triangle │ │ │ │ │ • int *mapUpper – map from submatrices to threads or processes │ │ │ │ │ 1 │ │ │ │ │ - 2 SolveMap : DRAFT January 6, 2026 │ │ │ │ │ + 2 SolveMap : DRAFT January 17, 2026 │ │ │ │ │ • int nblockLower – number of submatrices in the lower triangle │ │ │ │ │ • int *rowidsLower – vector of row ids for the lower triangle │ │ │ │ │ • int *colidsLower – vector of column ids for the lower triangle │ │ │ │ │ • int *mapLower – map from submatrices to threads or processes processes │ │ │ │ │ 1.2 Prototypes and descriptions of SolveMap methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ SolveMap object. │ │ │ │ │ @@ -50,15 +50,15 @@ │ │ │ │ │ This method releases any storage by a call to SolveMap clearData() then free’s the storage │ │ │ │ │ for the structure with a call to free(). │ │ │ │ │ Error checking: If solvemap is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ 1. int SolveMap_symmetryflag ( SolveMap *solvemap ) ; │ │ │ │ │ This method returns symmetryflag, the symmetry flag. │ │ │ │ │ Error checking: If solvemap is NULL, an error message is printed and the program exits. │ │ │ │ │ - SolveMap : DRAFT January 6, 2026 3 │ │ │ │ │ + SolveMap : DRAFT January 17, 2026 3 │ │ │ │ │ 2. int SolveMap_nfront ( SolveMap *solvemap ) ; │ │ │ │ │ This method returns nfront, the number of fronts. │ │ │ │ │ Error checking: If solvemap is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. int SolveMap_nproc ( SolveMap *solvemap ) ; │ │ │ │ │ This method returns nproc, the number of threads or processes. │ │ │ │ │ Error checking: If solvemap is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. int SolveMap_nblockUpper ( SolveMap *solvemap ) ; │ │ │ │ │ @@ -84,15 +84,15 @@ │ │ │ │ │ This method returns mapUpper, a pointer to the vector that maps the submatrices in the │ │ │ │ │ upper triangle to threads or processes. │ │ │ │ │ Error checking: If solvemap is NULL, an error message is printed and the program exits. │ │ │ │ │ 10. int * SolveMap_rowidsLower ( SolveMap *solvemap ) ; │ │ │ │ │ This method returns rowidsLower, a pointer to the vector of row ids of the submatrices in │ │ │ │ │ the lower triangle. │ │ │ │ │ Error checking: If solvemap is NULL, an error message is printed and the program exits. │ │ │ │ │ - 4 SolveMap : DRAFT January 6, 2026 │ │ │ │ │ + 4 SolveMap : DRAFT January 17, 2026 │ │ │ │ │ 11. int * SolveMap_colidsLower ( SolveMap *solvemap ) ; │ │ │ │ │ This method returns colidsLower, a pointer to the vector of column ids of the submatrices │ │ │ │ │ in the upper triangle. │ │ │ │ │ Error checking: If solvemap is NULL, an error message is printed and the program exits. │ │ │ │ │ 12. int * SolveMap_mapLower ( SolveMap *solvemap ) ; │ │ │ │ │ This method returns mapLower, a pointer to the vector that maps the submatrices in the │ │ │ │ │ upper triangle to threads or processes. │ │ │ │ │ @@ -118,15 +118,15 @@ │ │ │ │ │ fashion. A domain is a subtree of fronts that are owned by the same thread or process. │ │ │ │ │ Furthermore, a domain is maximal, i.e., the parent of the root domain (if it exists) is owned │ │ │ │ │ by a different process. If J belongs to a domain, then for all K, LK,J and UJ,K are owned by │ │ │ │ │ the thread or process that owns the domain. All other submatrices are mapped to threads or │ │ │ │ │ processes in a random fashion. │ │ │ │ │ Error checking: If solvemap, upperBlockIVL or ownersIV is NULL, or if symmetryflag is │ │ │ │ │ invalid, an error message is printed and the program exits. │ │ │ │ │ - SolveMap : DRAFT January 6, 2026 5 │ │ │ │ │ + SolveMap : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.5 Solve setup methods │ │ │ │ │ 1. IP ** SolveMap_forwardSetup ( SolveMap *solvemap, int myid, │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ IP ** SolveMap_backwardSetup ( SolveMap *solvemap, int myid, │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ ThesetwomethodsreturnavectorofpointerstoIPobjectsthatcontainthelistofsubmatrices │ │ │ │ │ that thread or process myid will use during the forward or backward solves. │ │ │ │ │ @@ -157,15 +157,15 @@ │ │ │ │ │ submatrices process myid expects for front J. │ │ │ │ │ Error checking: If solvemap is NULL or nlist < 0 then an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 5. IV * SolveMap_lowerAggregateIV ( SolveMap *solvemap, int myid │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method returns an IV object that contains the aggregate count for a forward solve. If │ │ │ │ │ myid owns front J, then entry J of the returned IV object contains the number of processes │ │ │ │ │ - 6 SolveMap : DRAFT January 6, 2026 │ │ │ │ │ + 6 SolveMap : DRAFT January 17, 2026 │ │ │ │ │ (other than myid) that own an L submatrix, (or U submatrix if symmetric or hermitian) │ │ │ │ │ J,I I,J │ │ │ │ │ and so is the number of incoming aggregate submatrices process myid expects for front J. │ │ │ │ │ Error checking: If solvemap is NULL or nlist < 0 then an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 1.2.7 IO methods │ │ │ │ │ TherearetheusualeightIOroutines. ThefilestructureofaSolveMapobjectissimple: symmetryflag, │ │ │ │ │ @@ -194,15 +194,15 @@ │ │ │ │ │ Error checking: If solvemap or fn are NULL, or if fn is not of the form *.solvemapf (for a │ │ │ │ │ formatted file) or *.solvemapb (for a binary file), an error message is printed and the method │ │ │ │ │ returns zero. │ │ │ │ │ 5. int SolveMap_writeToFormattedFile ( SolveMap *solvemap, FILE *fp ) ; │ │ │ │ │ This method writes an SolveMap object to a formatted file. If there are no errors in writing │ │ │ │ │ the data, the value 1 is returned. If an IO error is encountered from fprintf, zero is returned. │ │ │ │ │ Error checking: If solvemap or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ - SolveMap : DRAFT January 6, 2026 7 │ │ │ │ │ + SolveMap : DRAFT January 17, 2026 7 │ │ │ │ │ 6. int SolveMap_writeToBinaryFile ( SolveMap *solvemap, FILE *fp ) ; │ │ │ │ │ This method writes an SolveMap object to a binary file. If there are no errors in writing the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ Error checking: If solvemap or fp are NULL an error message is printed and zero is returned. │ │ │ │ │ 7. int SolveMap_writeForHumanEye ( SolveMap *solvemap, FILE *fp ) ; │ │ │ │ │ This method writes an SolveMap object to a file in an easily readable format. The method │ │ │ │ │ SolveMap writeStats() is called to write out the header and statistics. The value 1 is │ │ ├── ./usr/share/doc/spooles-doc/SubMtx.ps.gz │ │ │ ├── SubMtx.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o SubMtx.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -2118,16 +2118,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ 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│ │ │ │ (a)f(random)g(n)m(um)m(b)s(er)f(seed.)p eop end │ │ │ │ %%Page: 18 18 │ │ │ │ -TeXDict begin 18 17 bop 0 100 a Fo(18)p 182 100 1082 │ │ │ │ -4 v 1265 w Fn(SubMtx)28 b Fg(:)41 b Ff(DRAFT)30 b Fg(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2818 100 V 111 399 a Fo(9.)46 b Fn(test_sort)g(msglvl)g │ │ │ │ +TeXDict begin 18 17 bop 0 100 a Fo(18)p 182 100 1060 │ │ │ │ +4 v 1242 w Fn(SubMtx)29 b Fg(:)40 b Ff(DRAFT)31 b Fg(Jan)m(uary)f(17,)h │ │ │ │ +(2026)p 2841 100 V 111 399 a Fo(9.)46 b Fn(test_sort)g(msglvl)g │ │ │ │ (msgFile)f(type)i(mode)g(nrowA)f(ncolA)g(nentA)h(seed)227 │ │ │ │ 549 y Fo(This)22 b(driv)m(er)h(program)f(tests)i(the)f │ │ │ │ Fn(SubMtx)p 1688 549 29 4 v 32 w(sortRowsUp\(\))d Fo(and)i │ │ │ │ Fn(SubMtx)p 2773 549 V 33 w(sortColumnsUp\(\))c Fo(metho)s(ds.)227 │ │ │ │ 662 y(Use)34 b(the)g(script)f(\014le)h Fn(do)p 1073 662 │ │ │ │ V 33 w(sort)f Fo(for)g(testing.)51 b(When)33 b(the)h(output)f(\014le)g │ │ │ │ (is)h(loaded)g(in)m(to)g(matlab,)h(the)f(last)227 775 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -23,15 +23,15 @@ │ │ │ │ │ – dense by columns, i.e., dense and column major │ │ │ │ │ – sparse using dense subrows │ │ │ │ │ – sparse using dense subcolumns │ │ │ │ │ – sparse using sparse rows │ │ │ │ │ – sparse using sparse columns │ │ │ │ │ – sparse using (i,j,ai,j) triples │ │ │ │ │ 1 │ │ │ │ │ - 2 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 2 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ – a diagonal matrix │ │ │ │ │ – a block diagonal symmetric matrix where the blocks are 1 × 1 or 2 × 2, used in the │ │ │ │ │ symmetric indefinite factorization. │ │ │ │ │ – a block diagonal Hermitian matrix where the blocks are 1 × 1 or 2 × 2, used in the │ │ │ │ │ hermitian indefinite factorization. │ │ │ │ │ • The SubMtx object can be self-contained, in the sense that its structure contains a DV object │ │ │ │ │ that manages a contiguous vector of workspace that is used to store all information about the │ │ │ │ │ @@ -60,15 +60,15 @@ │ │ │ │ │ information is better than using explicit structure fields. For example, if we want to extend the │ │ │ │ │ object by allowing another storage format, we do not need to increase the size of the structure at │ │ │ │ │ all — it is only necessary to provide one or more instance methods to return the new information. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ The SubMtx structure has the following fields. │ │ │ │ │ • int type : type of entries. │ │ │ │ │ – SPOOLES REAL : double precision real entries. │ │ │ │ │ - SubMtx : DRAFT January 6, 2026 3 │ │ │ │ │ + SubMtx : DRAFT January 17, 2026 3 │ │ │ │ │ – SPOOLES COMPLEX : double precision complex entries. │ │ │ │ │ • int mode : storage mode. │ │ │ │ │ – SUBMTX DENSE ROWS : dense, storage by rows. │ │ │ │ │ – SUBMTX DENSE COLUMNS : dense, storage by columns. │ │ │ │ │ – SUBMTX SPARSE ROWS : sparse, storage by rows. │ │ │ │ │ – SUBMTX SPARSE COLUMNS : sparse, storage by columns. │ │ │ │ │ – SUBMTX SPARSE TRIPLES : sparse, storage by (i,j,ai,j) triples. │ │ │ │ │ @@ -92,15 +92,15 @@ │ │ │ │ │ • SUBMTX IS DENSE ROWS(mtx)is 1 if mtx has dense rows as its storage format, and 0 otherwise. │ │ │ │ │ • SUBMTX IS DENSE COLUMNS(mtx) is 1 if mtx has dense columns as its storage format, and 0 │ │ │ │ │ otherwise. │ │ │ │ │ • SUBMTX IS SPARSE ROWS(mtx) is 1 if mtx has sparse rows as its storage format, and 0 other- │ │ │ │ │ wise. │ │ │ │ │ • SUBMTX IS SPARSE COLUMNS(mtx) is 1 if mtx has sparse columns as its storage format, and 0 │ │ │ │ │ otherwise. │ │ │ │ │ - 4 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 4 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ • SUBMTX IS SPARSE TRIPLES(mtx) is 1 if mtx has sparse triples as its storage format, 0 other- │ │ │ │ │ wise. │ │ │ │ │ • SUBMTX IS DENSE SUBROWS(mtx) is 1 if mtx has dense subrows as its storage format, 0 other- │ │ │ │ │ wise. │ │ │ │ │ • SUBMTX IS DENSE SUBCOLUMNS(mtx) is 1 if mtx has dense subcolumns as its storage format, │ │ │ │ │ 0 otherwise. │ │ │ │ │ • SUBMTX IS DIAGONAL(mtx) is 1 if mtx is diagonal, 0 otherwise. │ │ │ │ │ @@ -126,15 +126,15 @@ │ │ │ │ │ This method clears the object and free’s any owned data by invoking the clearData() │ │ │ │ │ methodsforitsinternal DVobject. Thereis a concluding call to SubMtx setDefaultFields(). │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void SubMtx_free ( SubMtx *mtx ) ; │ │ │ │ │ This method releases any storage by a call to SubMtx clearData() and then frees the space │ │ │ │ │ for mtx. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ - SubMtx : DRAFT January 6, 2026 5 │ │ │ │ │ + SubMtx : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ 1. void SubMtx_ids ( SubMtx *mtx, int *prowid, int *pcolid ) ; │ │ │ │ │ This method fills *prowid with the row id and *pcolid with the column id of the object. │ │ │ │ │ Error checking: If mtx, prowid or pcolid is NULL, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 2. void SubMtx_setIds ( SubMtx *mtx, int rowid, int colid ) ; │ │ │ │ │ This method sets the row and column id’s of the matrix. │ │ │ │ │ @@ -163,15 +163,15 @@ │ │ │ │ │ the program exits. │ │ │ │ │ 7. void SubMtx_sparseRowsInfo ( SubMtx *mtx, int *pnrow, int *pnent, │ │ │ │ │ int **psizes, int **pindices, double **pentries ) ; │ │ │ │ │ This method is used when the storage mode is sparse rows. It fills *pnrow with the number │ │ │ │ │ of rows, *pnent with the number of matrix entries, *psizes with the base address of the │ │ │ │ │ sizes[nrow]vector that contains the number of entries in each row, *indices with the base │ │ │ │ │ address of the indices[nent] vector that contains the column index for each entry, and │ │ │ │ │ - 6 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 6 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ *pentries with the base address of entries[nent] vector. The indices and entries for the │ │ │ │ │ rows are stored contiguously. │ │ │ │ │ Error checking: If mtx, pnrow, pnent, psizes, pindices or pentries is NULL, or if the matrix │ │ │ │ │ type is not SUBMTX SPARSE ROWS, an error message is printed and the program exits. │ │ │ │ │ 8. void SubMtx_sparseColumnsInfo ( SubMtx *mtx, int *pncol, int *pnent, │ │ │ │ │ int **psizes, int **pindices, double **pentries ) ; │ │ │ │ │ Thismethodisusedwhenthestoragemodeissparsecolumns. Itfills*pncolwiththenumber │ │ │ │ │ @@ -204,15 +204,15 @@ │ │ │ │ │ exits. │ │ │ │ │ 11. void SubMtx_denseSubcolumnsInfo ( SubMtx *mtx, int *pncol, int *pnent, │ │ │ │ │ int **pfirstlocs, int **plastlocs, double **pentries ) ; │ │ │ │ │ This method is used when the storage mode is dense subcolumns. It fills *pncol with │ │ │ │ │ the number of columns, *pnent with the number of matrix entries, *pfirstlocs with the │ │ │ │ │ base address of the firstlocs[ncol] vector, *plastlocs with the base address of the │ │ │ │ │ lastlocs[ncol]vector, and *pentries with the base address of entries[nent] vector. For │ │ │ │ │ - SubMtx : DRAFT January 6, 2026 7 │ │ │ │ │ + SubMtx : DRAFT January 17, 2026 7 │ │ │ │ │ column jcol, the nonzero entries are found in rows [firstlocs[jcol],lastlocs[jcol]] │ │ │ │ │ when firstlocs[jcol] ≥ 0 and firstlocs[jcol] ≤ lastlocs[jcol]. The entries for the │ │ │ │ │ columns are stored contiguously. │ │ │ │ │ Error checking: If mtx, pnrow, pnent, pfirstlocs, plastlocs or pentries is NULL, or if the │ │ │ │ │ matrix type is not SUBMTX DENSE SUBCOLUMNS, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ 12. void SubMtx_diagonalInfo ( SubMtx *mtx, int *pncol, double **pentries ) ; │ │ │ │ │ @@ -242,15 +242,15 @@ │ │ │ │ │ and 0 ≤ jcol ≤ ncol. If the (irow,jcol) entry is present, the return value is the offset │ │ │ │ │ from the start of the entries vector. (The offset is in terms of complex entries, not double │ │ │ │ │ entries.) Otherwise, -1 is returned. │ │ │ │ │ Error checking: If mtx, pReal or pImag is NULL, or if irow or jcol is out of range, an error │ │ │ │ │ message is printed and the program exits. │ │ │ │ │ 16. void SubMtx_locationOfRealEntry ( SubMtx *mtx, int irow, int jcol, │ │ │ │ │ double **ppValue ) ; │ │ │ │ │ - 8 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 8 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ If the (irow,jcol) entry is present, this method fills *ppValue with a pointer to the entry │ │ │ │ │ in row irow and columnjcol. Otherwise, *ppValue is set to NULL. Note, irow and jcol are │ │ │ │ │ local indices, i.e., 0 ≤ irow ≤ nrow and 0 ≤ jcol ≤ ncol. │ │ │ │ │ Error checking: If mtx or ppValue is NULL, or if irow or jcol is out of range, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ 17. void SubMtx_locationOfComplexEntry ( SubMtx *mtx, int irow, int jcol, │ │ │ │ │ double **ppReal, double **ppImag ) ; │ │ │ │ │ @@ -278,15 +278,15 @@ │ │ │ │ │ int nrow, int ncol, int nent, int seed ) ; │ │ │ │ │ This is used to initialize an object to have random entries and (possibly) random structure. │ │ │ │ │ The object is first initialized via a call to SubMtx init(). Its matrix entries are then filled │ │ │ │ │ with random numbers. If the matrix is sparse, its sparsity pattern is sparse and random, │ │ │ │ │ using nent when applicable. The row and column indices are ascending starting from zero. │ │ │ │ │ Error checking: If mtx is NULL, or if nrow, ncol, inc1 or inc2 is less than or equal to zero, │ │ │ │ │ or if neither inc1 nor inc2 are 1, an error message is printed and the program exits. │ │ │ │ │ - SubMtx : DRAFT January 6, 2026 9 │ │ │ │ │ + SubMtx : DRAFT January 17, 2026 9 │ │ │ │ │ 4. void SubMtx_initRandomLowerTriangle ( SubMtx *mtx, int type, int mode, │ │ │ │ │ int rowid, int colid, int nrow, int ncol, int nent, int seed, int strict ) ; │ │ │ │ │ void SubMtx_initRandomUpperTriangle ( SubMtx *mtx, int type, int mode, │ │ │ │ │ int rowid, int colid, int nrow, int ncol, int nent, int seed, int strict ) ; │ │ │ │ │ This is used to initialize an object to have random entries and (possibly) random struc- │ │ │ │ │ ture. The matrix type may not be diagonal, block diagonal, or triples. If strict = 1, the │ │ │ │ │ matrix will be strict lower or upper triangular. The object is first initialized via a call to │ │ │ │ │ @@ -317,15 +317,15 @@ │ │ │ │ │ 1. void SubMtx_solve ( SubMtx *mtxA, SubMtx *mtxB ) ; │ │ │ │ │ This method is used to solve (I + A)X = B (if A is strict lower or upper triangular) or │ │ │ │ │ AX =B (if A is diagonal or block diagonal). The solution X overwrites B, and mtxB must │ │ │ │ │ have dense columns. If A is strict lower triangular, then mtxA must have dense subrows or │ │ │ │ │ sparse rows. If A is strict upper triangular, then mtxA must have dense subcolumns or sparse │ │ │ │ │ columns. │ │ │ │ │ Error checking: If mtxA or mtxB is NULL, an error message is printed and the program exits. │ │ │ │ │ - 10 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 10 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ 2. void SubMtx_solveH ( SubMtx *mtxA, SubMtx *mtxB ) ; │ │ │ │ │ This method is used to solve (I+AH)X = B, where A is strict lower or upper triangular. The │ │ │ │ │ solution X overwrites B, and mtxB must have dense columns. If A is strict lower triangular, │ │ │ │ │ then mtxA must have dense subrows or sparse rows. If A is strict upper triangular, then mtxA │ │ │ │ │ must have dense subcolumns or sparse columns. │ │ │ │ │ Error checking: If mtxA or mtxB is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. void SubMtx_solveT ( SubMtx *mtxA, SubMtx *mtxB ) ; │ │ │ │ │ @@ -354,15 +354,15 @@ │ │ │ │ │ This method returns the number of bytes required to store the object’s information in its │ │ │ │ │ buffer. │ │ │ │ │ Error checking: If nrow or ncol is less than or equal to zero, or if nent is less than to zero, │ │ │ │ │ or if type is invalid, an error message is printed and the program exits. │ │ │ │ │ 2. int SubMtx_nbytesInUse ( SubMtx *mtx ) ; │ │ │ │ │ This method returns the actual number of bytes that are used in the workspace owned by │ │ │ │ │ this object. │ │ │ │ │ - SubMtx : DRAFT January 6, 2026 11 │ │ │ │ │ + SubMtx : DRAFT January 17, 2026 11 │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. int SubMtx_nbytesInWorkspace ( SubMtx *mtx ) ; │ │ │ │ │ This method returns the number of bytes in the workspace owned by this object. │ │ │ │ │ Error checking: If mtx is NULL, an error message is printed and the program exits. │ │ │ │ │ 4. void SubMtx_setNbytesInWorkspace ( SubMtx *mtx, int nbytes ) ; │ │ │ │ │ This method sets the number of bytes in the workspace of this object. If nbytes is less than │ │ │ │ │ the present number of bytes, the workspace is not resized. │ │ │ │ │ @@ -387,15 +387,15 @@ │ │ │ │ │ Error checking: If mtx or rowDV is NULL, or if irow is out of range, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ 10. void SubMtx_fillColumnDV ( SubMtx *mtx, int jcol, DV *rowDV ) ; │ │ │ │ │ This method is used for real submatrices. It copies the entries in column jcol of the mtx │ │ │ │ │ object into the colDV vector object. │ │ │ │ │ Error checking: If mtx or colDV is NULL, or if jcol is out of range, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ - 12 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 12 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ 11. void SubMtx_fillRowZV ( SubMtx *mtx, int irow, ZV *rowZV ) ; │ │ │ │ │ This method is used for complex submatrices. It copies the entries in row irow of the mtx │ │ │ │ │ object into the rowZV vector object. │ │ │ │ │ Error checking: If mtx or rowZV is NULL, or if irow is out of range, an error message is printed │ │ │ │ │ and the program exits. │ │ │ │ │ 12. void SubMtx_fillColumnZV ( SubMtx *mtx, int jcol, ZV *rowZV ) ; │ │ │ │ │ This method is used for complex submatrices. It copies the entries in column jcol of the mtx │ │ │ │ │ @@ -422,15 +422,15 @@ │ │ │ │ │ the data, the value 1 is returned. If an IO error is encountered from fscanf, zero is returned. │ │ │ │ │ Note, if the mtxutation vectors are one-based (as for Fortran), they are converted to zero- │ │ │ │ │ based vectors. │ │ │ │ │ Error checking: If mtx or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 3. int SubMtx_readFromBinaryFile ( SubMtx *mtx, FILE *fp ) ; │ │ │ │ │ This method reads in a SubMtx object from a binary file. If there are no errors in reading │ │ │ │ │ the data, the value 1 is returned. If an IO error is encountered from fread, zero is returned. │ │ │ │ │ - SubMtx : DRAFT January 6, 2026 13 │ │ │ │ │ + SubMtx : DRAFT January 17, 2026 13 │ │ │ │ │ Note, if the mtxutation vectors are one-based (as for Fortran), they are converted to zero- │ │ │ │ │ based vectors. │ │ │ │ │ Error checking: If mtx or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 4. int SubMtx_writeToFile ( SubMtx *mtx, char *fn ) ; │ │ │ │ │ This method writes a SubMtx object to a file. It tries to open the file and if it is successful, │ │ │ │ │ it then calls SubMtx writeFromFormattedFile()or SubMtx writeFromBinaryFile(),closes │ │ │ │ │ the file and returns the value returned from the called routine. │ │ │ │ │ @@ -457,15 +457,15 @@ │ │ │ │ │ for complex matrices, or │ │ │ │ │ a(10,5) = -1.550328201511e-01 ; │ │ │ │ │ for real matrices, where mtxname = "a". The matrix indices come from the rowind[] │ │ │ │ │ and colind[] vectors, and are incremented by one to follow the Matlab and FORTRAN │ │ │ │ │ convention. │ │ │ │ │ Error checking: If mtx, mtxname or fp are NULL, an error message is printed and zero is │ │ │ │ │ returned. │ │ │ │ │ - 14 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 14 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ 1.3 Driver programs for the SubMtx object │ │ │ │ │ 1. testIO msglvl msgFile inFile outFile │ │ │ │ │ This driver program reads in a SubMtx object from inFile and writes out the object to │ │ │ │ │ outFile │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the SubMtx object is written to the message file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ @@ -494,15 +494,15 @@ │ │ │ │ │ 3. test_solve msglvl msgFile type mode nrowA nentA ncolB seed │ │ │ │ │ This driver program tests the SubMtx solve() method which tests the solve AX = B when │ │ │ │ │ A is diagonal or block diagonal, and (I + A)X = B otherwise (A is strict upper or lower │ │ │ │ │ triangular). Use the script file do solve for testing. When the output file is loaded into │ │ │ │ │ matlab, the last lines to the screen contain the errors. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ timing output. │ │ │ │ │ - SubMtx : DRAFT January 6, 2026 15 │ │ │ │ │ + SubMtx : DRAFT January 17, 2026 15 │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The type parameter must be one of 1 (SPOOLES REAL) or 2 (SPOOLES COMPLEX). │ │ │ │ │ • Themodeparametermustbeoneof2(SUBMTX SPARSE ROWS),3(SUBMTX SPARSE COLUMNS), │ │ │ │ │ 5 (SUBMTX DENSE SUBROWS), 6 (SUBMTX DENSE SUBCOLUMNS), 7 (SUBMTX DIAGONAL), │ │ │ │ │ 8 (SUBMTX BLOCK DIAGONAL SYM) or 9 (SUBMTX BLOCK DIAGONAL HERM). │ │ │ │ │ @@ -534,15 +534,15 @@ │ │ │ │ │ T │ │ │ │ │ This driver program tests the SubMtx solve() method which tests the solve (I +A )X = B │ │ │ │ │ when A is strict upper or lower triangular and has dense subrows, dense subcolumns, sparse │ │ │ │ │ rows, or sparse columns. Use the script file do solveT for testing. When the output file is │ │ │ │ │ loaded into matlab, the last lines to the screen contain the errors. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ timing output. │ │ │ │ │ - 16 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 16 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The type parameter must be one of 1 (SPOOLES REAL) or 2 (SPOOLES COMPLEX). │ │ │ │ │ • Themodeparametermustbeoneof2(SUBMTX SPARSE ROWS),3(SUBMTX SPARSE COLUMNS), │ │ │ │ │ 5 (SUBMTX DENSE SUBROWS) or 6 (SUBMTX DENSE SUBCOLUMNS). │ │ │ │ │ • The nrowA parameter is the number of rows in the matrix. │ │ │ │ │ @@ -573,15 +573,15 @@ │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ 7. test_solveupdH msglvl msgFile type mode nrowA nentA ncolB seed │ │ │ │ │ This driver program tests the SubMtx solveupd() method which tests the update Y := │ │ │ │ │ Y −AH ∗X, used in the forward solve of a hermitian factorization. X and Y have dense │ │ │ │ │ columns, and A has dense rows or columns or sparse rows or columns. Use the script file │ │ │ │ │ do solveupdH for testing. When the output file is loaded into matlab, the last lines to the │ │ │ │ │ screen contain the errors. │ │ │ │ │ - SubMtx : DRAFT January 6, 2026 17 │ │ │ │ │ + SubMtx : DRAFT January 17, 2026 17 │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The type parameter must be 2 (SPOOLES COMPLEX). │ │ │ │ │ • Themodeparametermustbeoneof0(SUBMTX DENSE ROWS),1(SUBMTX DENSE COLUMNS), │ │ │ │ │ @@ -612,15 +612,15 @@ │ │ │ │ │ • The ncolY parameter is the number of columns in Y. │ │ │ │ │ • The nrowA parameter is the number of rows in A, nrowA ≤ nrowY. │ │ │ │ │ • The ncolA parameter is the number of columns in A, ncolA ≤ nrowX. │ │ │ │ │ • The nentA parameter is the number of nonzero entries in the submatrix, when appro- │ │ │ │ │ priate. │ │ │ │ │ • The nrowX parameter is the number of rows in X, nrowA ≤ nrowY. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ - 18 SubMtx : DRAFT January 6, 2026 │ │ │ │ │ + 18 SubMtx : DRAFT January 17, 2026 │ │ │ │ │ 9. test_sort msglvl msgFile type mode nrowA ncolA nentA seed │ │ │ │ │ Thisdriver program tests the SubMtx sortRowsUp()and SubMtx sortColumnsUp()methods. │ │ │ │ │ Use the script file do sort for testing. When the output file is loaded into matlab, the last │ │ │ │ │ lines to the screen contain the errors. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ ├── ./usr/share/doc/spooles-doc/SubMtxList.ps.gz │ │ │ ├── SubMtxList.ps │ │ │ │ @@ -10,15 +10,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o SubMtxList.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1776,16 +1776,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -1973,79 +1975,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ 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│ │ /Dotaccent/cedilla/ogonek/quotesinglbase.ts1 4{/.notdef}repeat │ │ │ │ /quotedblbase.ts1/.notdef/.notdef/twelveudash/threequartersemdash │ │ │ │ /afii61664.cap/arrowleft/arrowright/tieaccentlowercase/tieaccentcapital │ │ │ │ /tieaccentlowercase.new/tieaccentcapital.new/.notdef/afii61664.asc/uni2422 3 │ │ │ │ {/.notdef}repeat/dollar/.notdef/.notdef/quotesingle/.notdef/.notdef │ │ │ │ @@ -3433,17 +3444,17 @@ │ │ │ │ (ciated)g(with)e(a)g Fh(SubMtxList)e Fi(ob)5 b(ject)36 │ │ │ │ b(is)g(optional,)i(for)d(example,)i(it)f(is)g(not)f(needed)0 │ │ │ │ 5407 y(during)22 b(a)i(serial)g(factorization)i(nor)d(a)h(MPI)f(solv)m │ │ │ │ (e.)40 b(In)23 b(the)g(latter)i(case)f(there)g(is)f(one)h │ │ │ │ Fh(SubMtxList)d Fi(p)s(er)h(pro)s(cess.)1927 5656 y(1)p │ │ │ │ eop end │ │ │ │ %%Page: 2 2 │ │ │ │ -TeXDict begin 2 1 bop 0 100 a Fi(2)p 136 100 1010 4 v │ │ │ │ -1192 w Fh(SubMtxList)27 b Ff(:)41 b Fe(DRAFT)30 b Ff(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2891 100 V 0 399 a Fi(F)-8 b(or)26 b(a)f(m)m(ultithreaded)h │ │ │ │ +TeXDict begin 2 1 bop 0 100 a Fi(2)p 136 100 987 4 v │ │ │ │ +1169 w Fh(SubMtxList)27 b Ff(:)41 b Fe(DRAFT)30 b Ff(Jan)m(uary)g(17,)i │ │ │ │ +(2026)p 2913 100 V 0 399 a Fi(F)-8 b(or)26 b(a)f(m)m(ultithreaded)h │ │ │ │ (solv)m(e)g(there)g(is)f(one)g Fh(SubMtxList)e Fi(ob)5 │ │ │ │ b(ject)26 b(that)g(is)f(shared)f(b)m(y)h(all)h(threads.)39 │ │ │ │ b(The)25 b(m)m(utual)0 511 y(exclusion)33 b(lo)s(c)m(k)h(that)f(is)f │ │ │ │ (\(optionally\))j(em)m(b)s(edded)c(in)i(the)f Fh(SubMtxList)e │ │ │ │ Fi(ob)5 b(ject)34 b(is)e(a)h Fh(Lock)f Fi(ob)5 b(ject)33 │ │ │ │ b(from)f(this)0 624 y(library)-8 b(.)39 b(It)27 b(is)f(inside)g(the)g │ │ │ │ Fh(Lock)f Fi(ob)5 b(ject)27 b(that)g(w)m(e)f(ha)m(v)m(e)i(a)e(m)m │ │ │ │ @@ -3496,65 +3507,65 @@ │ │ │ │ (and)d Fh(heads)p Fi(,)227 5251 y Fh(counts)p Fi(,)29 │ │ │ │ b Fh(lock)g Fi(and)h Fh(flags)f Fi(are)i(set)g(to)g Fh(NULL)e │ │ │ │ Fi(.)227 5407 y Fe(Err)-5 b(or)34 b(che)-5 b(cking:)40 │ │ │ │ b Fi(If)30 b Fh(list)g Fi(is)g Fh(NULL)p Fi(,)f(an)i(error)f(message)h │ │ │ │ (is)g(prin)m(ted)f(and)f(the)i(program)f(exits.)p eop │ │ │ │ end │ │ │ │ %%Page: 3 3 │ │ │ │ -TeXDict begin 3 2 bop 91 100 1010 4 v 1191 100 a Fh(SubMtxList)28 │ │ │ │ -b Ff(:)40 b Fe(DRAFT)121 b Ff(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2843 100 V 1010 w Fi(3)111 399 y(3.)46 b Fh(void)h │ │ │ │ -(SubMtxList_clearData)42 b(\()48 b(SubMtxList)d(*list)h(\))h(;)227 │ │ │ │ -555 y Fi(This)31 b(metho)s(d)f(clears)j(the)e(ob)5 b(ject)32 │ │ │ │ -b(and)f(free's)h(an)m(y)f(o)m(wned)g(data)h(b)m(y)g(calling)g │ │ │ │ -Fh(SubMtx)p 3241 555 29 4 v 33 w(free\(\))e Fi(for)h(eac)m(h)227 │ │ │ │ -668 y(ob)5 b(ject)30 b(on)e(the)h(free)g(list.)41 b(If)28 │ │ │ │ -b Fh(heads)f Fi(is)i(not)g Fh(NULL)p Fi(,)f(it)h(is)g(free'd.)40 │ │ │ │ -b(If)28 b Fh(counts)f Fi(is)i(not)g Fh(NULL)p Fi(,)f(it)h(is)g(free'd)f │ │ │ │ -(via)227 781 y(a)i(call)g(to)f Fh(IVfree\(\))p Fi(.)38 │ │ │ │ -b(If)29 b Fh(flags)e Fi(is)i(not)g Fh(NULL)p Fi(,)f(it)h(is)g(free'd)g │ │ │ │ -(via)h(a)f(call)h(to)f Fh(CVfree\(\))p Fi(.)38 b(If)29 │ │ │ │ -b(the)g(lo)s(c)m(k)h(is)f(not)227 894 y Fh(NULL)p Fi(,)34 │ │ │ │ -b(it)i(is)f(destro)m(y)m(ed)h(via)f(a)g(call)i(to)e Fh(mutex)p │ │ │ │ -1848 894 V 33 w(destroy\(\))e Fi(and)h(then)h(free'd.)54 │ │ │ │ -b(There)34 b(is)h(a)h(concluding)227 1007 y(call)c(to)f │ │ │ │ -Fh(SubMtxList)p 991 1007 V 32 w(setDefaultFields\(\))p │ │ │ │ -Fi(.)227 1164 y Fe(Err)-5 b(or)34 b(che)-5 b(cking:)40 │ │ │ │ -b Fi(If)30 b Fh(list)g Fi(is)g Fh(NULL)p Fi(,)f(an)i(error)f(message)h │ │ │ │ -(is)g(prin)m(ted)f(and)f(the)i(program)f(exits.)111 1364 │ │ │ │ -y(4.)46 b Fh(void)h(SubMtxList_free)d(\()j(SubMtxList)e(*list)h(\))i(;) │ │ │ │ -227 1521 y Fi(This)37 b(metho)s(d)f(releases)i(an)m(y)g(storage)h(b)m │ │ │ │ -(y)e(a)g(call)i(to)e Fh(SubMtxList)p 2607 1521 V 32 w(clearData\(\))d │ │ │ │ -Fi(and)j(then)f(free)i(the)227 1634 y(space)31 b(for)f │ │ │ │ -Fh(list)p Fi(.)227 1791 y Fe(Err)-5 b(or)34 b(che)-5 │ │ │ │ -b(cking:)40 b Fi(If)30 b Fh(list)g Fi(is)g Fh(NULL)p │ │ │ │ +TeXDict begin 3 2 bop 91 100 987 4 v 1168 100 a Fh(SubMtxList)28 │ │ │ │ +b Ff(:)41 b Fe(DRAFT)121 b Ff(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2866 100 V 987 w Fi(3)111 399 y(3.)46 b Fh(void)h(SubMtxList_clearData) │ │ │ │ +42 b(\()48 b(SubMtxList)d(*list)h(\))h(;)227 555 y Fi(This)31 │ │ │ │ +b(metho)s(d)f(clears)j(the)e(ob)5 b(ject)32 b(and)f(free's)h(an)m(y)f │ │ │ │ +(o)m(wned)g(data)h(b)m(y)g(calling)g Fh(SubMtx)p 3241 │ │ │ │ +555 29 4 v 33 w(free\(\))e Fi(for)h(eac)m(h)227 668 y(ob)5 │ │ │ │ +b(ject)30 b(on)e(the)h(free)g(list.)41 b(If)28 b Fh(heads)f │ │ │ │ +Fi(is)i(not)g Fh(NULL)p Fi(,)f(it)h(is)g(free'd.)40 b(If)28 │ │ │ │ +b Fh(counts)f Fi(is)i(not)g Fh(NULL)p Fi(,)f(it)h(is)g(free'd)f(via)227 │ │ │ │ +781 y(a)i(call)g(to)f Fh(IVfree\(\))p Fi(.)38 b(If)29 │ │ │ │ +b Fh(flags)e Fi(is)i(not)g Fh(NULL)p Fi(,)f(it)h(is)g(free'd)g(via)h(a) │ │ │ │ +f(call)h(to)f Fh(CVfree\(\))p Fi(.)38 b(If)29 b(the)g(lo)s(c)m(k)h(is)f │ │ │ │ +(not)227 894 y Fh(NULL)p Fi(,)34 b(it)i(is)f(destro)m(y)m(ed)h(via)f(a) │ │ │ │ +g(call)i(to)e Fh(mutex)p 1848 894 V 33 w(destroy\(\))e │ │ │ │ +Fi(and)h(then)h(free'd.)54 b(There)34 b(is)h(a)h(concluding)227 │ │ │ │ +1007 y(call)c(to)f Fh(SubMtxList)p 991 1007 V 32 w │ │ │ │ +(setDefaultFields\(\))p Fi(.)227 1164 y Fe(Err)-5 b(or)34 │ │ │ │ +b(che)-5 b(cking:)40 b Fi(If)30 b Fh(list)g Fi(is)g Fh(NULL)p │ │ │ │ Fi(,)f(an)i(error)f(message)h(is)g(prin)m(ted)f(and)f(the)i(program)f │ │ │ │ -(exits.)0 2078 y Fb(1.2.2)112 b(Initialization)39 b(metho)s(ds)0 │ │ │ │ -2281 y Fi(There)30 b(are)h(three)f(initializer)j(metho)s(ds.)111 │ │ │ │ -2534 y(1.)46 b Fh(void)h(SubMtxList_init\()c(SubMtxList)i(*list,)h(int) │ │ │ │ -h(nlist,)f(int)h(counts[],)1277 2647 y(int)g(lockflag,)e(char)i │ │ │ │ -(flags[])f(\))h(;)227 2804 y Fi(An)m(y)35 b(data)h(is)f(cleared)h(via)f │ │ │ │ -(a)h(call)g(to)g Fh(SubMtxList)p 2054 2804 V 31 w(clearData\(\))p │ │ │ │ -Fi(.)51 b(The)35 b(n)m(um)m(b)s(er)f(of)h(lists)g(is)g(set)h(and)227 │ │ │ │ -2917 y(the)43 b Fh(heads[])d Fi(v)m(ector)j(is)f(initialized.)78 │ │ │ │ -b(If)41 b Fh(counts)g Fi(is)h(not)g Fh(NULL)p Fi(,)f(the)h(ob)5 │ │ │ │ -b(ject's)43 b Fh(counts[])d Fi(v)m(ector)k(is)227 3030 │ │ │ │ -y(allo)s(cated)31 b(and)e(\014lled)g(with)g(the)g(incoming)h(en)m │ │ │ │ -(tries.)41 b(If)29 b Fh(lockflag)e Fi(is)i(zero,)i(the)e(lo)s(c)m(k)h │ │ │ │ -(is)f(not)h(initialized.)227 3143 y(If)39 b Fh(lockflag)e │ │ │ │ -Fi(is)i Fh(1)p Fi(,)j(the)d(lo)s(c)m(k)i(is)e(initialized)i(to)f(b)s(e) │ │ │ │ -f(able)h(to)g(sync)m(hronize)f(threads)g(with)g(the)g(calling)227 │ │ │ │ -3256 y(pro)s(cess.)71 b(If)40 b Fh(lockflag)e Fi(is)j │ │ │ │ -Fh(2)p Fi(,)i(the)e(lo)s(c)m(k)g(is)g(initialized)h(to)f(b)s(e)f(able)h │ │ │ │ -(to)g(sync)m(hronize)g(threads)f(across)227 3368 y(pro)s(cesses.)49 │ │ │ │ -b(If)32 b Fh(flags)g Fi(is)h(not)g Fh(NULL)p Fi(,)f(the)h(ob)5 │ │ │ │ -b(ject's)34 b Fh(flags[])d Fi(v)m(ector)k(is)e(allo)s(cated)i(and)d │ │ │ │ -(\014lled)h(with)g(the)227 3481 y(incoming)e(en)m(tries.)227 │ │ │ │ -3638 y Fe(Err)-5 b(or)40 b(che)-5 b(cking:)53 b Fi(If)36 │ │ │ │ -b Fh(list)g Fi(is)h Fh(NULL)p Fi(,)f(or)g(if)h Fh(nlist)e │ │ │ │ +(exits.)111 1364 y(4.)46 b Fh(void)h(SubMtxList_free)d(\()j(SubMtxList) │ │ │ │ +e(*list)h(\))i(;)227 1521 y Fi(This)37 b(metho)s(d)f(releases)i(an)m(y) │ │ │ │ +g(storage)h(b)m(y)e(a)g(call)i(to)e Fh(SubMtxList)p 2607 │ │ │ │ +1521 V 32 w(clearData\(\))d Fi(and)j(then)f(free)i(the)227 │ │ │ │ +1634 y(space)31 b(for)f Fh(list)p Fi(.)227 1791 y Fe(Err)-5 │ │ │ │ +b(or)34 b(che)-5 b(cking:)40 b Fi(If)30 b Fh(list)g Fi(is)g │ │ │ │ +Fh(NULL)p Fi(,)f(an)i(error)f(message)h(is)g(prin)m(ted)f(and)f(the)i │ │ │ │ +(program)f(exits.)0 2078 y Fb(1.2.2)112 b(Initialization)39 │ │ │ │ +b(metho)s(ds)0 2281 y Fi(There)30 b(are)h(three)f(initializer)j(metho)s │ │ │ │ +(ds.)111 2534 y(1.)46 b Fh(void)h(SubMtxList_init\()c(SubMtxList)i │ │ │ │ +(*list,)h(int)h(nlist,)f(int)h(counts[],)1277 2647 y(int)g(lockflag,)e │ │ │ │ +(char)i(flags[])f(\))h(;)227 2804 y Fi(An)m(y)35 b(data)h(is)f(cleared) │ │ │ │ +h(via)f(a)h(call)g(to)g Fh(SubMtxList)p 2054 2804 V 31 │ │ │ │ +w(clearData\(\))p Fi(.)51 b(The)35 b(n)m(um)m(b)s(er)f(of)h(lists)g(is) │ │ │ │ +g(set)h(and)227 2917 y(the)43 b Fh(heads[])d Fi(v)m(ector)j(is)f │ │ │ │ +(initialized.)78 b(If)41 b Fh(counts)g Fi(is)h(not)g │ │ │ │ +Fh(NULL)p Fi(,)f(the)h(ob)5 b(ject's)43 b Fh(counts[])d │ │ │ │ +Fi(v)m(ector)k(is)227 3030 y(allo)s(cated)31 b(and)e(\014lled)g(with)g │ │ │ │ +(the)g(incoming)h(en)m(tries.)41 b(If)29 b Fh(lockflag)e │ │ │ │ +Fi(is)i(zero,)i(the)e(lo)s(c)m(k)h(is)f(not)h(initialized.)227 │ │ │ │ +3143 y(If)39 b Fh(lockflag)e Fi(is)i Fh(1)p Fi(,)j(the)d(lo)s(c)m(k)i │ │ │ │ +(is)e(initialized)i(to)f(b)s(e)f(able)h(to)g(sync)m(hronize)f(threads)g │ │ │ │ +(with)g(the)g(calling)227 3256 y(pro)s(cess.)71 b(If)40 │ │ │ │ +b Fh(lockflag)e Fi(is)j Fh(2)p Fi(,)i(the)e(lo)s(c)m(k)g(is)g │ │ │ │ +(initialized)h(to)f(b)s(e)f(able)h(to)g(sync)m(hronize)g(threads)f │ │ │ │ +(across)227 3368 y(pro)s(cesses.)49 b(If)32 b Fh(flags)g │ │ │ │ +Fi(is)h(not)g Fh(NULL)p Fi(,)f(the)h(ob)5 b(ject's)34 │ │ │ │ +b Fh(flags[])d Fi(v)m(ector)k(is)e(allo)s(cated)i(and)d(\014lled)h │ │ │ │ +(with)g(the)227 3481 y(incoming)e(en)m(tries.)227 3638 │ │ │ │ +y Fe(Err)-5 b(or)40 b(che)-5 b(cking:)53 b Fi(If)36 b │ │ │ │ +Fh(list)g Fi(is)h Fh(NULL)p Fi(,)f(or)g(if)h Fh(nlist)e │ │ │ │ Fa(\024)g Fi(0,)k(or)e(if)g Fh(lockflag)d Fi(is)j(not)g(in)f │ │ │ │ Fh([0,2])p Fi(,)i(an)e(error)227 3751 y(message)c(is)e(prin)m(ted)g │ │ │ │ (and)g(zero)h(is)f(returned.)0 4038 y Fb(1.2.3)112 b(Utilit)m(y)38 │ │ │ │ b(metho)s(ds)111 4241 y Fi(1.)46 b Fh(int)h(SubMtxList_isListNonempty) │ │ │ │ 41 b(\()48 b(SubMtxList)d(*list,)h(int)h(ilist)f(\))h(;)227 │ │ │ │ 4398 y Fi(If)30 b(list)h Fh(ilist)e Fi(is)i(empt)m(y)-8 │ │ │ │ b(,)31 b(the)g(metho)s(d)e(returns)h(0.)41 b(Otherwise,)30 │ │ │ │ @@ -3570,17 +3581,17 @@ │ │ │ │ (1.)44 b(Otherwise,)32 b(the)227 5138 y(metho)s(d)e(returns)f(0.)227 │ │ │ │ 5294 y Fe(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fi(If)29 │ │ │ │ b Fh(list)g Fi(is)h Fh(NULL)p Fi(,)f(or)h(if)g Fh(ilist)e │ │ │ │ Fi(is)i(not)h(in)e(the)h(range)h Fh([0,nlist\))p Fi(,)c(an)j(error)g │ │ │ │ (message)227 5407 y(is)h(prin)m(ted)f(and)f(zero)j(is)e(returned.)p │ │ │ │ eop end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fi(4)p 136 100 1010 4 v │ │ │ │ -1192 w Fh(SubMtxList)27 b Ff(:)41 b Fe(DRAFT)30 b Ff(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2891 100 V 111 399 a Fi(3.)46 b Fh(SubMtx)g(*)i │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fi(4)p 136 100 987 4 v │ │ │ │ +1169 w Fh(SubMtxList)27 b Ff(:)41 b Fe(DRAFT)30 b Ff(Jan)m(uary)g(17,)i │ │ │ │ +(2026)p 2913 100 V 111 399 a Fi(3.)46 b Fh(SubMtx)g(*)i │ │ │ │ (SubMtxList_getList)43 b(\()k(SubMtxList)e(*list,)h(int)h(ilist)f(\))i │ │ │ │ (;)227 549 y Fi(If)28 b(list)h Fh(ilist)e Fi(is)h(empt)m(y)-8 │ │ │ │ b(,)30 b(the)f(metho)s(d)f(returns)f Fh(NULL)p Fi(.)g(Otherwise,)i(if)f │ │ │ │ (the)h(list)g(needs)f(to)h(b)s(e)e(lo)s(c)m(k)m(ed,)k(the)227 │ │ │ │ 662 y(lo)s(c)m(k)37 b(is)e(lo)s(c)m(k)m(ed.)57 b(The)34 │ │ │ │ b(head)h(of)h(the)f(list)h(is)f(sa)m(v)m(ed)i(to)f(a)f(p)s(oin)m(ter)h │ │ │ │ (and)e(then)h(the)h(head)f(is)g(set)h(to)g Fh(NULL)p │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -22,15 +22,15 @@ │ │ │ │ │ The first two operations are queries, and can be done without locking the list. The third operation │ │ │ │ │ needs a lock only when two or more threads will be inserting objects into the list. The fourth │ │ │ │ │ operation requires a lock only when one thread will add an object while another thread removes │ │ │ │ │ the object and the incoming count is not yet zero. │ │ │ │ │ Having a lock associated with a SubMtxList object is optional, for example, it is not needed │ │ │ │ │ during a serial factorization nor a MPI solve. In the latter case there is one SubMtxList per process. │ │ │ │ │ 1 │ │ │ │ │ - 2 SubMtxList : DRAFT January 6, 2026 │ │ │ │ │ + 2 SubMtxList : DRAFT January 17, 2026 │ │ │ │ │ For a multithreaded solve there is one SubMtxList object that is shared by all threads. The mutual │ │ │ │ │ exclusion lock that is (optionally) embedded in the SubMtxList object is a Lock object from this │ │ │ │ │ library. It is inside the Lock object that we have a mutual exclusion lock. Presently we support the │ │ │ │ │ Solaris and POSIX thread packages. Porting the multithreaded codes to another platform should │ │ │ │ │ be simple if the POSIX thread package is present. Another type of thread package will require │ │ │ │ │ some modifications to the Lock object, but none to the SubMtxList objects. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ @@ -52,15 +52,15 @@ │ │ │ │ │ 1. SubMtxList * SubMtxList_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the SubMtxList structure and then sets the default │ │ │ │ │ fields by a call to SubMtxList setDefaultFields(). │ │ │ │ │ 2. void SubMtxList_setDefaultFields ( SubMtxList *list ) ; │ │ │ │ │ The structure’s fields are set to default values: nlist and nlocks set to zero, and heads, │ │ │ │ │ counts, lock and flags are set to NULL . │ │ │ │ │ Error checking: If list is NULL, an error message is printed and the program exits. │ │ │ │ │ - SubMtxList : DRAFT January 6, 2026 3 │ │ │ │ │ + SubMtxList : DRAFT January 17, 2026 3 │ │ │ │ │ 3. void SubMtxList_clearData ( SubMtxList *list ) ; │ │ │ │ │ This method clears the object and free’s any owned data by calling SubMtx free() for each │ │ │ │ │ object on the free list. If heads is not NULL, it is free’d. If counts is not NULL, it is free’d via │ │ │ │ │ a call to IVfree(). If flags is not NULL, it is free’d via a call to CVfree(). If the lock is not │ │ │ │ │ NULL, it is destroyed via a call to mutex destroy() and then free’d. There is a concluding │ │ │ │ │ call to SubMtxList setDefaultFields(). │ │ │ │ │ Error checking: If list is NULL, an error message is printed and the program exits. │ │ │ │ │ @@ -87,15 +87,15 @@ │ │ │ │ │ Error checking: If list is NULL, or if ilist is not in the range [0,nlist), an error message │ │ │ │ │ is printed and zero is returned. │ │ │ │ │ 2. int SubMtxList_isCountZero ( SubMtxList *list, int ilist ) ; │ │ │ │ │ If counts is NULL, or if counts[ilist] equal to zero, the method returns 1. Otherwise, the │ │ │ │ │ method returns 0. │ │ │ │ │ Error checking: If list is NULL, or if ilist is not in the range [0,nlist), an error message │ │ │ │ │ is printed and zero is returned. │ │ │ │ │ - 4 SubMtxList : DRAFT January 6, 2026 │ │ │ │ │ + 4 SubMtxList : DRAFT January 17, 2026 │ │ │ │ │ 3. SubMtx * SubMtxList_getList ( SubMtxList *list, int ilist ) ; │ │ │ │ │ If list ilist is empty, the method returns NULL. Otherwise, if the list needs to be locked, the │ │ │ │ │ lock is locked. The head of the list is saved to a pointer and then the head is set to NULL. │ │ │ │ │ If the list was locked, the number of locks is incremented and the lock unlocked. The saved │ │ │ │ │ pointer is returned. │ │ │ │ │ Error checking: If list is NULL, or if ilist is not in the range [0,nlist), an error message │ │ │ │ │ is printed and zero is returned. │ │ ├── ./usr/share/doc/spooles-doc/SubMtxManager.ps.gz │ │ │ ├── SubMtxManager.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o SubMtxManager.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale 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When a SubMtx object is no longer │ │ │ │ │ necessary, it is released to the manager object, which then inserts it into the free list. A list of │ │ │ │ │ SubMtx objects can be released in one call. │ │ │ │ │ One can specify whether the object is to be locked via a mutual exclusion lock. This is not │ │ │ │ │ necessary for a serial or MPI factorization or solve (where there is one SubMtxManager object for │ │ │ │ │ each processor), but it is necessary for in a multithreaded environment. │ │ │ │ │ 1 │ │ │ │ │ - 2 SubMtxManager : DRAFT January 6, 2026 │ │ │ │ │ + 2 SubMtxManager : DRAFT January 17, 2026 │ │ │ │ │ Eachmanagerobjectkeepstrackofcertainstatistics, bytesintheirworkspaces, thetotal number │ │ │ │ │ of bytes requested, the number of requests for a SubMtx objects, the number of releases, and the │ │ │ │ │ number of locks and unlocks. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ The SubMtxManager structure has the following fields. │ │ │ │ │ • SubMtx *head : head of the free list of SubMtx objects. │ │ │ │ │ • Lock *lock : mutual exclusion lock. │ │ │ │ │ @@ -55,15 +55,15 @@ │ │ │ │ │ SubMtxManager object. │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. SubMtxManager * SubMtxManager_new ( void ) ; │ │ │ │ │ This method simply allocates storage for the SubMtxManager structure and then sets the │ │ │ │ │ default fields by a call to SubMtxManager setDefaultFields(). │ │ │ │ │ - SubMtxManager : DRAFT January 6, 2026 3 │ │ │ │ │ + SubMtxManager : DRAFT January 17, 2026 3 │ │ │ │ │ 2. void SubMtxManager_setDefaultFields ( SubMtxManager *manager ) ; │ │ │ │ │ Thestructure’sfieldsaresettodefaultvalues: mode,nactive,nbytesactive,nbytesrequested, │ │ │ │ │ nbytesalloc, nrequests, nreleases, nlocks and nunlocks are set to zero, and head and │ │ │ │ │ lock are set to NULL . │ │ │ │ │ Error checking: If manager is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. void SubMtxManager_clearData ( SubMtxManager *manager ) ; │ │ │ │ │ This method clears the object and free’s any owned data by calling SubMtx free() for each │ │ │ │ │ @@ -89,15 +89,15 @@ │ │ │ │ │ its workspace. │ │ │ │ │ Error checking: If manager is NULL, or if nbytesNeeded ≤ 0, an error message is printed and │ │ │ │ │ zero is returned. │ │ │ │ │ 2. void SubMtxManager_releaseObject ( SubMtxManager *manager, SubMtx *mtx ) ; │ │ │ │ │ This method releases the mtx instance, either free’ing it (if mode = 0), or returning it to the │ │ │ │ │ free list (if mode = 1). │ │ │ │ │ Error checking: If manager or mtx is NULL, an error message is printed and zero is returned. │ │ │ │ │ - 4 SubMtxManager : DRAFT January 6, 2026 │ │ │ │ │ + 4 SubMtxManager : DRAFT January 17, 2026 │ │ │ │ │ 3. void SubMtxManager_releaseListOfObjects ( SubMtxManager *manager, SubMtx *first ) ; │ │ │ │ │ This method releases a list of SubMtx objects whose head is first, either free’ing them (if │ │ │ │ │ mode = 0), or returning them to the free list (if mode = 1). │ │ │ │ │ Error checking: If manager or head is NULL, an error message is printed and zero is returned. │ │ │ │ │ 1.2.4 IO methods │ │ │ │ │ 1. void SubMtxManager_writeForHumanEye ( SubMtxManager *manager, FILE *fp ) ; │ │ │ │ │ This method writes a SubMtxManager object to a file in an easily readable format. │ │ ├── ./usr/share/doc/spooles-doc/SymbFac.ps.gz │ │ │ ├── SymbFac.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o SymbFac.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -1006,16 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(output.)337 557 y Fa(\210)45 b Fk(The)33 b Fj(msgFile)e │ │ │ │ Fk(parameter)j(determines)f(the)h(message)g(\014le)f(|)h(if)f │ │ │ │ Fj(msgFile)e Fk(is)i Fj(stdout)p Fk(,)g(then)g(the)427 │ │ │ │ 670 y(message)27 b(\014le)f(is)g Fi(stdout)p Fk(,)i(otherwise)e(a)h │ │ │ │ (\014le)f(is)f(op)s(ened)g(with)h Fi(app)-5 b(end)28 │ │ │ │ b Fk(status)e(to)g(receiv)m(e)i(an)m(y)e(output)427 783 │ │ │ │ @@ -4239,17 +4250,17 @@ │ │ │ │ (input)e(\014le)i(for)f(the)g Fj(Graph)f Fk(ob)5 b(ject.)39 │ │ │ │ b(It)24 b(m)m(ust)f(b)s(e)f(of)i(the)f(form)427 5294 │ │ │ │ y Fj(*.graphf)18 b Fk(or)j Fj(*.graphb)p Fk(.)35 b(The)19 │ │ │ │ b Fj(Graph)g Fk(ob)5 b(ject)21 b(is)g(read)f(from)g(the)g(\014le)h(via) │ │ │ │ f(the)h Fj(Graph)p 3368 5294 V 33 w(readFromFile\(\))427 │ │ │ │ 5407 y Fk(metho)s(d.)p eop end │ │ │ │ %%Page: 4 4 │ │ │ │ -TeXDict begin 4 3 bop 0 100 a Fk(4)p 136 100 1081 4 v │ │ │ │ -1263 w Fj(SymbFac)29 b Fc(:)40 b Fi(DRAFT)30 b Fc(Jan)m(uary)g(6,)h │ │ │ │ -(2026)p 2819 100 V 337 399 a Fa(\210)45 b Fk(The)24 b │ │ │ │ +TeXDict begin 4 3 bop 0 100 a Fk(4)p 136 100 1059 4 v │ │ │ │ +1240 w Fj(SymbFac)29 b Fc(:)40 b Fi(DRAFT)31 b Fc(Jan)m(uary)f(17,)h │ │ │ │ +(2026)p 2842 100 V 337 399 a Fa(\210)45 b Fk(The)24 b │ │ │ │ Fj(outETreeFile)d Fk(parameter)k(is)f(the)h(output)f(\014le)g(for)g │ │ │ │ (the)h Fj(ETree)d Fk(ob)5 b(ject.)40 b(If)24 b Fj(outETreeFile)d │ │ │ │ Fk(is)427 511 y Fj(none)g Fk(then)h(the)g Fj(ETree)f │ │ │ │ Fk(ob)5 b(ject)22 b(is)g(not)h(written)f(to)g(a)h(\014le.)38 │ │ │ │ b(Otherwise,)23 b(the)g Fj(ETree)p 3253 511 29 4 v 33 │ │ │ │ w(writeToFile\(\))427 624 y Fk(metho)s(d)30 b(is)h(called)h(to)f(write) │ │ │ │ g(the)g(ob)5 b(ject)31 b(to)h(a)f(formatted)g(\014le)g(\(if)g │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -22,15 +22,15 @@ │ │ │ │ │ to have chevron coordinate type and storage mode must be by vectors. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ There is no struct or data associated with the SymbFac object. │ │ │ │ │ 1.2 Prototypes and descriptions of SymbFac methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ SymbFac object. │ │ │ │ │ 1 │ │ │ │ │ - 2 SymbFac : DRAFT January 6, 2026 │ │ │ │ │ + 2 SymbFac : DRAFT January 17, 2026 │ │ │ │ │ 1.2.1 Symbolic factorization methods │ │ │ │ │ 1. IVL * SymbFac_initFromGraph ( ETree *etree, Graph *graph ) ; │ │ │ │ │ This symbolic factorization method takes a Graph object as input. This method constructs │ │ │ │ │ an IVL object that contains one list per front. List ilist contains the internal and external │ │ │ │ │ vertices for front ilist. If the input graph is a compressed graph, then the lists of compressed │ │ │ │ │ vertices make little sense; they must be converted to original vertices. To do this, see the │ │ │ │ │ IVL expand() method. The nodwghtsIV and bndwghtsIV objects for the ETree object are │ │ │ │ │ @@ -61,15 +61,15 @@ │ │ │ │ │ 1. testSymbFacInpMtx msglvl msgFile inETreeFile inDInpMtxFile │ │ │ │ │ outETreeFile outIVfile outIVLfile │ │ │ │ │ This driver program reads in an ETree object and a InpMtx object and computes the symbolic │ │ │ │ │ factorization. The ETree object is updated (the front sizes and boundary sizes may change) │ │ │ │ │ andisoptionally written out to outETreeFile. The old-to-new IV object is optionally written │ │ │ │ │ to outIVfile. The IVL object that contains the symbolic factorization is optionally written │ │ │ │ │ to outIVLfile. │ │ │ │ │ - SymbFac : DRAFT January 6, 2026 3 │ │ │ │ │ + SymbFac : DRAFT January 17, 2026 3 │ │ │ │ │ • The msglvl parameter determines the amount of output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • TheinETreeFileparameteristheinputfilefortheETreeobject. It mustbeof theform │ │ │ │ │ *.etreefor*.etreeb. TheETreeobjectisreadfromthefileviatheETree readFromFile() │ │ │ │ │ method. │ │ │ │ │ @@ -101,15 +101,15 @@ │ │ │ │ │ data. │ │ │ │ │ • TheinETreeFileparameteristheinputfilefortheETreeobject. It mustbeof theform │ │ │ │ │ *.etreefor*.etreeb. TheETreeobjectisreadfromthefileviatheETree readFromFile() │ │ │ │ │ method. │ │ │ │ │ • TheinGraphFileparameteristheinputfilefortheGraphobject. It mustbeof theform │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ - 4 SymbFac : DRAFT January 6, 2026 │ │ │ │ │ + 4 SymbFac : DRAFT January 17, 2026 │ │ │ │ │ • TheoutETreeFileparameter is the output file for the ETree object. If outETreeFileis │ │ │ │ │ nonethentheETreeobjectisnotwrittentoafile. Otherwise,theETree writeToFile() │ │ │ │ │ method is called to write the object to a formatted file (if outETreeFile is of the form │ │ │ │ │ *.etreef), or a binary file (if outETreeFile is of the form *.etreeb). │ │ │ │ │ • The outIVfile parameter is the output file for the vertex-to-front map IV object. │ │ │ │ │ If outIVfile is none then the IV object is not written to a file. Otherwise, the │ │ │ │ │ IV writeToFile()methodis called to write the object to a formatted file (if outIVfile │ │ ├── ./usr/share/doc/spooles-doc/Tree.ps.gz │ │ │ ├── Tree.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Tree.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -2227,16 +2227,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly def │ │ │ │ /Encoding 256 array │ │ │ │ 0 1 255 {1 index exch /.notdef put} for │ │ │ │ dup 44 /comma put │ │ │ │ dup 48 /zero put │ │ │ │ +dup 49 /one put │ │ │ │ dup 50 /two put │ │ │ │ dup 54 /six put │ │ │ │ +dup 55 /seven put │ │ │ │ dup 58 /colon put │ │ │ │ dup 74 /J put │ │ │ │ dup 97 /a put │ │ │ │ dup 110 /n put │ │ │ │ dup 114 /r put │ │ │ │ dup 117 /u put │ │ │ │ dup 121 /y put │ │ │ │ @@ -2424,79 +2426,88 @@ │ │ │ │ 7CA1534C4D5B05FC33F83790ECFD7641DF3FB94289E2A1F6E7D29AB1228A867A │ │ │ │ 6E1EF0E9C6F899B491DC18401C2C0A05FFFED46A72C245F7529B8EA55A038082 │ │ │ │ 8512307217D2A233C37004085BA3AEE379269F9FA7D0ADB4B19A95CC2AFE686E │ │ │ │ 55D88E47257C1FE6F235FEA295910569FE6DD5995512562359CC821E85A6C7A5 │ │ │ │ 79B470A9E340A6985189FF8B6AF914A6B0ECF93F47903221F95DE894A8F05B05 │ │ │ │ B7D99CD533EC5F931B18E6B39BECF67FA2D6DD1AEC76772B068BE06335A94C05 │ │ │ │ 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Fn(:)f(domain/separator)39 b(tree.)62 b(On)37 b(the)g(left)h │ │ │ │ Fm(heightflag)45 b(=)j('H')36 b Fn(and)h Fm(coordflag)45 │ │ │ │ b(=)0 684 y('C')p Fn(,)30 b(on)g(the)h(righ)m(t)g Fm(heightflag)45 │ │ │ │ b(=)i('D')29 b Fn(and)h Fm(coordflag)45 b(=)j('C')p Fn(.)105 │ │ │ │ 2612 y @beginspecial 0 @llx 0 @lly 600 @urx 600 @ury │ │ │ │ 2159 @rwi 2159 @rhi @setspecial │ │ │ │ %%BeginDocument: ../../Tree/doc/R2D100HC.eps │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -20,15 +20,15 @@ │ │ │ │ │ • int *sib : pointer to sibling vector, size n, entries in the range [-1,n-1] │ │ │ │ │ The user should rarely if ever change these five fields. In particular, throughout the code we │ │ │ │ │ assume that the Tree object was correctly initialized using one of the three initializer methods. │ │ │ │ │ Inside almost every method we check to ensure n > 0. If n > 0 then we assume that the structure │ │ │ │ │ was intialized correctly and that the par, fch and sib fields point to storage that was allocated by │ │ │ │ │ the initializer method. │ │ │ │ │ 1 │ │ │ │ │ - 2 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 2 Tree : DRAFT January 17, 2026 │ │ │ │ │ 1.2 Prototypes and descriptions of Tree methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the Tree │ │ │ │ │ object. │ │ │ │ │ 1.2.1 Basic methods │ │ │ │ │ As usual, there are four basic methods to support object creation, setting default fields, clearing │ │ │ │ │ any allocated data, and free’ing the object. │ │ │ │ │ 1. Tree * Tree_new ( void ) ; │ │ │ │ │ @@ -52,15 +52,15 @@ │ │ │ │ │ Error checking: If tree is NULL, an error message is printed and the program exits. │ │ │ │ │ 2. int Tree_root ( Tree *tree ) ; │ │ │ │ │ This method returns the root of the tree. │ │ │ │ │ Error checking: If tree is NULL, an error message is printed and the program exits. │ │ │ │ │ 3. int * Tree_par ( Tree *tree ) ; │ │ │ │ │ This method returns a pointer to the parent vector. │ │ │ │ │ Error checking: If tree is NULL, an error message is printed and the program exits. │ │ │ │ │ - Tree : DRAFT January 6, 2026 3 │ │ │ │ │ + Tree : DRAFT January 17, 2026 3 │ │ │ │ │ 4. int * Tree_fch ( Tree *tree ) ; │ │ │ │ │ This method returns a pointer to the first child vector. │ │ │ │ │ Error checking: If tree is NULL, an error message is printed and the program exits. │ │ │ │ │ 5. int * Tree_sib ( Tree *tree ) ; │ │ │ │ │ This method returns a pointer to the sibling vector. │ │ │ │ │ Error checking: If tree is NULL, an error message is printed and the program exits. │ │ │ │ │ 1.2.3 Initializer methods │ │ │ │ │ @@ -88,15 +88,15 @@ │ │ │ │ │ The subtree object is initialized from the tree object, the nodes that are included are those │ │ │ │ │ found in nodeidsIV. A parent-child link in the subtree means that the two nodes have a │ │ │ │ │ parent-child link in the tree. │ │ │ │ │ Return codes: │ │ │ │ │ 1 normal return -3 tree is NULL │ │ │ │ │ -1 subtree is NULL -4 nodeidsIV is invalid │ │ │ │ │ -2 nodeidsIV is NULL │ │ │ │ │ - 4 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 4 Tree : DRAFT January 17, 2026 │ │ │ │ │ 5. void Tree_setFchSibRoot ( Tree *tree ) ; │ │ │ │ │ Theroot and the entries in the fch[] and sib[] vectors are set using the entries in the par[] │ │ │ │ │ vector. │ │ │ │ │ Error checking: If tree is NULL, an error message is printed and the program exits. │ │ │ │ │ 6. void Tree_setRoot ( Tree *tree ) ; │ │ │ │ │ The vertices that are roots in the tree are linked by their sib[] field and the root of the tree │ │ │ │ │ is set to the head of the list. │ │ │ │ │ @@ -122,15 +122,15 @@ │ │ │ │ │ This method returns the first node in a pre-order traversal. │ │ │ │ │ Error checking: If tree is NULL, or if tree->n < 1, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 5. int Tree_preOTnext ( Tree *tree, int v ) ; │ │ │ │ │ This method returns the node that follows v in a pre-order traversal. │ │ │ │ │ Error checking: If tree is NULL, or if tree->n < 1, or v is not in [0,tree->n-1], an error │ │ │ │ │ message is printed and the program exits. │ │ │ │ │ - Tree : DRAFT January 6, 2026 5 │ │ │ │ │ + Tree : DRAFT January 17, 2026 5 │ │ │ │ │ 6. int Tree_nleaves ( Tree *tree ) ; │ │ │ │ │ This method returns the number of leaves of the tree. │ │ │ │ │ Error checking: If tree is NULL, or if tree->n < 1, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 7. int Tree_nroots ( Tree *tree ) ; │ │ │ │ │ This method returns the number of roots of the tree (really a forest). │ │ │ │ │ Error checking: If tree is NULL, or if tree->n < 1, an error message is printed and the │ │ │ │ │ @@ -155,15 +155,15 @@ │ │ │ │ │ 12. IV * Tree_maximizeGainIV ( Tree *tree, IV *gainIV, int *ptotalgain, │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ Given a gain value assigned to each node, find a set of nodes, no two in a child-ancestor │ │ │ │ │ relationship, that maximizes the total gain. This problem arises in finding the optimal do- │ │ │ │ │ main/Schur complement partition for a semi-implicit factorization. │ │ │ │ │ Error checking: If tree, gainIV or ptotalgain is NULL, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ - 6 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 6 Tree : DRAFT January 17, 2026 │ │ │ │ │ 1.2.5 Metrics methods │ │ │ │ │ Manyoperations need to know some metric defined on the nodes in a tree. Here are three examples: │ │ │ │ │ the height of a node (the minimum distance from a descendant leaf), the depth of a node (the │ │ │ │ │ distance from its root ancestor), or the weight associated with a subtree rooted at a node. Of │ │ │ │ │ course, a weight could be associated with each node, so the height or depth becomes the weight of │ │ │ │ │ the nodes on the path. │ │ │ │ │ Metrics can be int or double. Because of the limitations of C, we need two separate methods │ │ │ │ │ @@ -191,15 +191,15 @@ │ │ │ │ │ These methods create and return IV or DV objects that contain height metrics using as input │ │ │ │ │ an IV or DV object that contains the metric for each of the nodes. If hmetric[] is the vector │ │ │ │ │ in the returned IV or DV object, then │ │ │ │ │ hmetric[v] = vmetric[v] if fch[v] == -1 │ │ │ │ │ = vmetric[v] + max_{par[u] = v} hmetric[par[v]] │ │ │ │ │ Error checking: If tree or vmetric{I,D}V is NULL, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ - Tree : DRAFT January 6, 2026 7 │ │ │ │ │ + Tree : DRAFT January 17, 2026 7 │ │ │ │ │ 1.2.6 Compression methods │ │ │ │ │ Frequently a tree will need to be compressed in some manner. Elimination trees usually have long │ │ │ │ │ chains of nodes at the higher levels, where each chain of nodes corresponds to a supernode. Liu’s │ │ │ │ │ generalized row envelope methods partition the vertices by longest chains [?]. In both cases, we can │ │ │ │ │ construct a map from each node to a set of nodes to define a smaller, more compact tree. Given │ │ │ │ │ such a map, we construct the smaller tree. │ │ │ │ │ Afundamental chain is a set of nodes v ,...,v such that (1) v is a leaf or has two or more │ │ │ │ │ @@ -232,15 +232,15 @@ │ │ │ │ │ Error checking: If tree or map is NULL, or if n < 1, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ 2. void Tree_leftJustifyI ( Tree *tree, IV *metricIV ) ; │ │ │ │ │ void Tree_leftJustifyD ( Tree *tree, DV *metricIV ) ; │ │ │ │ │ This method justifies the tree, reordering the children of each node as necessary. If u and v │ │ │ │ │ are siblings, and u comes before v in a post-order traversal, then the weight of the subtree │ │ │ │ │ rooted at u is as large or larger than the weight of the subtree rooted at v. │ │ │ │ │ - 8 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 8 Tree : DRAFT January 17, 2026 │ │ │ │ │ Error checking: If tree or metricIV is NULL, or if n < 1, or if n is not the size of metricIV, │ │ │ │ │ an error message is printed and the program exits. │ │ │ │ │ 1.2.8 Permutation methods │ │ │ │ │ Often we need to extract a permutation from a tree, e.g., a post-order traversal of an elimination │ │ │ │ │ tree gives an ordering for a sparse matrix. On other occasions, we need to permute a tree, i.e. │ │ │ │ │ re-label the nodes. │ │ │ │ │ 1. void Tree_fillNewToOldPerm ( Tree *tree, int newToOld[] ) ; │ │ │ │ │ @@ -269,15 +269,15 @@ │ │ │ │ │ Return codes: │ │ │ │ │ 1 normal return -3 coordflag is invalid │ │ │ │ │ -1 tree is NULL -3 xDV is NULL │ │ │ │ │ -2 heightflag is invalid -4 yDV is NULL │ │ │ │ │ 2. int Tree_drawToEPS ( Tree *tree, FILE *filename, DV *xDV, DV *yDV, │ │ │ │ │ double rscale, DV *radiusDV, int labelflag, │ │ │ │ │ double fontscale, IV *labelsIV, double bbox[], │ │ │ │ │ - Tree : DRAFT January 6, 2026 9 │ │ │ │ │ + Tree : DRAFT January 17, 2026 9 │ │ │ │ │ double frame[], double bounds[] ) ; │ │ │ │ │ This method draws a tree. The coordinates of the nodes are found in the xDV and yDV vectors. │ │ │ │ │ The nodes will have circles of constant radius (if radiusDV is NULL) or each circle can have a │ │ │ │ │ different radius found in radiusDV when radiusDV is not NULL. The value rscale is used to │ │ │ │ │ scale all the radii. (If radiusDV is NULL, then all radii are equal to one point — there are 72 │ │ │ │ │ points to the inch.) │ │ │ │ │ If labelflag = 1, the nodes will have a numeric label. If labelsIV is NULL, then the label │ │ │ │ │ @@ -306,15 +306,15 @@ │ │ │ │ │ and returns the value returned from the called routine. │ │ │ │ │ Error checking: If tree or fn are NULL, or if fn is not of the form *.treef (for a formatted │ │ │ │ │ file) or *.treeb (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 2. int Tree_readFromFormattedFile ( Tree *tree, FILE *fp ) ; │ │ │ │ │ This method reads in a Perm object from a formatted file. If there are no errors in reading │ │ │ │ │ the data, the value 1 is returned. If an IO error is encountered from fscanf, zero is returned. │ │ │ │ │ Error checking: If tree or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ - 10 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 10 Tree : DRAFT January 17, 2026 │ │ │ │ │ 3. int Tree_readFromBinaryFile ( Tree *tree, FILE *fp ) ; │ │ │ │ │ This method reads in a Perm object from a binary file. If there are no errors in reading the │ │ │ │ │ data, the value 1 is returned. If an IO error is encountered from fread, zero is returned. │ │ │ │ │ Error checking: If tree or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 4. int Tree_writeToFile ( Tree *tree, char *fn ) ; │ │ │ │ │ This method writes a Perm object to a file. It tries to open the file and if it is successful, │ │ │ │ │ it then calls Tree writeFromFormattedFile() or Tree writeFromBinaryFile(), closes the │ │ │ │ │ @@ -339,15 +339,15 @@ │ │ │ │ │ Error checking: If tree or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 1.3 Driver programs for the Tree object │ │ │ │ │ 1. drawTree msglvl msgFile inTreeFile inTagsFile outEPSfile │ │ │ │ │ heightflag coordflag radius bbox[4] frame[4] tagflag fontsize │ │ │ │ │ This driver program reads in a Tree file and optionally a tags IV file and creates an EPS file │ │ │ │ │ with a simple picture of a tree. │ │ │ │ │ • The msglvl parameter determines the amount of output. │ │ │ │ │ - Tree : DRAFT January 6, 2026 11 │ │ │ │ │ + Tree : DRAFT January 17, 2026 11 │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ output file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The inTreeFile parameter is the input file for the Tree object. It must be of the form │ │ │ │ │ *.treefor*.treeb. TheTreeobjectisreadfromthefileviatheTree readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The inTagsFile parameter is the input file for the IV vector object than holds the tags │ │ │ │ │ @@ -364,15 +364,15 @@ │ │ │ │ │ • The frame parameter a sequence of four numbers that form the frame of the plot within │ │ │ │ │ the bounding box: lower left x value, lower left y value, width and height. │ │ │ │ │ • When tagflag = 1, tags are drawn on the nodes. If tagsFile is NULL, then node ids │ │ │ │ │ will be drawn on the nodes. Otherwise, node ids will be taken from the tagsIV object. │ │ │ │ │ • The fontsize parameter is the size of the font to be used to draw the node labels. │ │ │ │ │ Use the doDraw script file as an example. Four plots of a tree for the R2D100 matrix ordered │ │ │ │ │ by nested dissection are found below. │ │ │ │ │ - 12 Tree : DRAFT January 6, 2026 │ │ │ │ │ + 12 Tree : DRAFT January 17, 2026 │ │ │ │ │ Figure 1.1: R2D100: domain/separator tree. On the left heightflag = ’H’ and coordflag = │ │ │ │ │ ’C’, on the right heightflag = ’D’ and coordflag = ’C’. │ │ │ │ │ 71 71 │ │ │ │ │ 70 70 32 │ │ │ │ │ 51 51 69 31 13 │ │ │ │ │ 40 32 50 40 61 68 22 30 8 12 │ │ │ │ │ 39 31 49 43 39 56 60 67 64 21 17 29 23 7 11 9 │ │ ├── ./usr/share/doc/spooles-doc/Utilities.ps.gz │ │ │ ├── Utilities.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o Utilities.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ 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a Fp(IVZVisortDown\(\))p │ │ │ │ -Fq(,)26 b(21)0 511 y Fp(IVZVisortUp\(\))p Fq(,)h(21)0 │ │ │ │ -624 y Fp(IVZVqsortDown\(\))p Fq(,)f(22)0 737 y Fp(IVZVqsortUp\(\))p │ │ │ │ +TeXDict begin 32 31 bop 0 100 a Fq(32)p 182 100 988 4 │ │ │ │ +v 1170 w Fp(Utilities)28 b Fl(:)41 b Fk(DRAFT)30 b Fl(Jan)m(uary)g(17,) │ │ │ │ +i(2026)p 2912 100 V 0 399 a Fp(IVZVisortDown\(\))p Fq(,)26 │ │ │ │ +b(21)0 511 y Fp(IVZVisortUp\(\))p Fq(,)h(21)0 624 y Fp │ │ │ │ +(IVZVqsortDown\(\))p Fq(,)f(22)0 737 y Fp(IVZVqsortUp\(\))p │ │ │ │ Fq(,)h(22)0 850 y Fp(IVZVsortUpAndCompress\(\))p Fq(,)d(23)0 │ │ │ │ 1040 y Fp(PCVcopy\(\))p Fq(,)k(19)0 1153 y Fp(PCVfree\(\))p │ │ │ │ Fq(,)g(18)0 1266 y Fp(PCVinit\(\))p Fq(,)g(18)0 1379 │ │ │ │ y Fp(PCVsetup\(\))p Fq(,)g(19)0 1491 y Fp(PDVcopy\(\))p │ │ │ │ Fq(,)g(19)0 1604 y Fp(PDVfree\(\))p Fq(,)g(19)0 1717 │ │ │ │ y Fp(PDVinit\(\))p Fq(,)g(19)0 1830 y Fp(PDVsetup\(\))p │ │ │ │ Fq(,)g(19)0 1943 y Fp(PFVcopy\(\))p Fq(,)g(20)0 2056 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -22,15 +22,15 @@ │ │ │ │ │ struct _I2OP { │ │ │ │ │ int value0 ; │ │ │ │ │ int value1 ; │ │ │ │ │ void *value2 ; │ │ │ │ │ I2OP *next ; │ │ │ │ │ } ; │ │ │ │ │ 1 │ │ │ │ │ - 2 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 2 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 1.2 Prototypes and descriptions of Utilities methods │ │ │ │ │ This section contains brief descriptions including prototypes of all methods that belong to the │ │ │ │ │ Utilities directory. │ │ │ │ │ 1.2.1 CV : char vector methods │ │ │ │ │ 1. char * CVinit ( int n, char c ) ; │ │ │ │ │ This is the allocator and initializer method for char vectors. Storage for an array with size │ │ │ │ │ n is found and each entry is filled with character c. A pointer to the array is returned. │ │ │ │ │ @@ -54,15 +54,15 @@ │ │ │ │ │ 8. int CVfscanf ( FILE *fp, int n, char y[] ) ; │ │ │ │ │ This method scans in characters from file fp and places them in the array y[]. It tries to │ │ │ │ │ read in n characters, and returns the number that were actually read. │ │ │ │ │ 1.2.2 DV : double vector methods │ │ │ │ │ 1. double * DVinit ( int n, double val ) ; │ │ │ │ │ This is the allocator and initializer method for double vectors. Storage for an array with size │ │ │ │ │ n is found and each entry is filled with val. A pointer to the array is returned. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 3 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 3 │ │ │ │ │ 2. double * DVinit2 ( int n ) ; │ │ │ │ │ This is an allocator method for double vectors. Storage for an array with size n is found. A │ │ │ │ │ pointer to the array is returned. Note, on return, there will likely be garbage in the array. │ │ │ │ │ 3. void DVfree ( int vec[] ) ; │ │ │ │ │ This method releases the storage taken by vec[]. │ │ │ │ │ 4. void DVfprintf ( FILE *fp, int n, double y[] ) ; │ │ │ │ │ This method prints n entries in y[] to file fp. The format is new line followed by lines of six │ │ │ │ │ @@ -90,15 +90,15 @@ │ │ │ │ │ This method computes this computation. │ │ │ │ │ y0[] = y0[] + alpha[0] * x0[] + alpha[1] * x1[] │ │ │ │ │ y1[] = y1[] + alpha[2] * x0[] + alpha[3] * x1[] │ │ │ │ │ y2[] = y2[] + alpha[4] * x0[] + alpha[5] * x1[] │ │ │ │ │ 11. void DVaxpy31 ( int n, double y0[], double y1[], double y2[], │ │ │ │ │ double alpha, double x0[], double x1[] ) ; │ │ │ │ │ This method computes this computation. │ │ │ │ │ - 4 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 4 Utilities : DRAFT January 17, 2026 │ │ │ │ │ y0[] = y0[] + alpha[0] * x0[] │ │ │ │ │ y1[] = y1[] + alpha[1] * x0[] │ │ │ │ │ y2[] = y2[] + alpha[2] * x0[] │ │ │ │ │ 12. void DVaxpy23 ( int n, double y0[], double y1[], │ │ │ │ │ double alpha, double x0[], double x1[], double x2[] ) ; │ │ │ │ │ This method computes this computation. │ │ │ │ │ y0[] = y0[] + alpha[0] * x0[] + alpha[1] * x1[] + alpha[2] * x2[] │ │ │ │ │ @@ -121,15 +121,15 @@ │ │ │ │ │ y0[] = y0[] + alpha[0] * x0[] + alpha[1] * x1[] │ │ │ │ │ 17. void DVaxpy11 ( int n, double y0[], double alpha, double x0[] ) ; │ │ │ │ │ This method computes this computation. │ │ │ │ │ y0[] = y0[] + alpha[0] * x0[] │ │ │ │ │ 18. void DVaxpyi ( int n, double y[], int index[], double alpha, double x[] ) ; │ │ │ │ │ This method scatteradds a scaled multiple of n entries from x[] into y[], i.e., y[index[i]] │ │ │ │ │ += alpha * x[i] for 0 <= i < n. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 5 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 5 │ │ │ │ │ 19. void DVcompress ( int n1, double x1[], double y1[], │ │ │ │ │ int n2, double x2[], double y2[] ) ; │ │ │ │ │ Given a pair of arrays x1[n1] and y1[n1], fill x2[n2] and y2[n2] with a subset of the │ │ │ │ │ (x1[j],y1[j] entries whose distribution is an approximation. │ │ │ │ │ 20. void DVcopy ( int n, double y[], double x[] ) ; │ │ │ │ │ This method copies n entries from x[] to y[], i.e., y[i] = x[i] for 0 <= i < n. │ │ │ │ │ 21. int DVdot ( int n, double y[], double x[] ) ; │ │ │ │ │ @@ -167,15 +167,15 @@ │ │ │ │ │ i=0 │ │ │ │ │ n−1 │ │ │ │ │ sums[1] = Xrow1[i]∗col0[i] │ │ │ │ │ i=0 │ │ │ │ │ n−1 │ │ │ │ │ sums[2] = Xrow2[i]∗col0[i] │ │ │ │ │ i=0 │ │ │ │ │ - 6 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 6 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 25. int DVdot23 ( int n, double row0[], double row1[], │ │ │ │ │ double col0[], double col1[], double col2[], double sums[] ) ; │ │ │ │ │ This method computes six dot products. │ │ │ │ │ n−1 n−1 n−1 │ │ │ │ │ sums[0] = Xrow0[i]∗col0[i] sums[1] = Xrow0[i]∗col1[i] sums[2] = Xrow0[i]∗col2[i] │ │ │ │ │ i=0 i=0 i=0 │ │ │ │ │ n−1 n−1 n−1 │ │ │ │ │ @@ -212,15 +212,15 @@ │ │ │ │ │ sums[0] = Xrow0[i]∗col0[i] sums[1] = Xrow0[i]∗col1[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ 30. int DVdot11 ( int n, double row0[], double col0[], double sums[] ) ; │ │ │ │ │ This method computes one dot product. │ │ │ │ │ n−1 │ │ │ │ │ sums[0] = Xrow0[i]∗col0[i] │ │ │ │ │ i=0 │ │ │ │ │ - Utilities : DRAFT January 6, 2026 7 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 7 │ │ │ │ │ 31. int DVdoti ( int n, double y[], int index[], double x[] ) ; │ │ │ │ │ n−1 │ │ │ │ │ This method returns the indexed dot product Xy[index[i]]∗x[i]. │ │ │ │ │ i=0 │ │ │ │ │ 32. void DVfill ( int n, double y[], double val ) ; │ │ │ │ │ This method fills n entries in y[] with val, i.e., y[i] = val for 0 <= i < n. │ │ │ │ │ 33. void DVgather ( int n, double y[], double x[], int index[] ) ; │ │ │ │ │ @@ -248,15 +248,15 @@ │ │ │ │ │ This method permutes the vector y as follows. i.e., y[i] := y[index[i]]. See DVinvPerm() │ │ │ │ │ for a similar function. │ │ │ │ │ 42. void DVramp ( int n, double y[], double start, double inc ) ; │ │ │ │ │ This method fills n entries in y[] with values start, start + inc, start + 2*inc, start │ │ │ │ │ + 3*inc, etc. │ │ │ │ │ 43. void DVscale ( int n, double y[], double alpha ) ; │ │ │ │ │ This method scales a vector y[] by alpha, i.e., y[i] *= alpha. for 0 <= i < n. │ │ │ │ │ - 8 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 8 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 44. void DVscale2 ( int n, double x[], double y[], │ │ │ │ │ double a, double b, double c, double d ) ; │ │ │ │ │ This method scales two vectors y[] by a 2 ×2 matrix, i.e., │ │ │ │ │ " x[0] . . . x[n−1] # := " a b #" x[0] ... x[n−1] #. │ │ │ │ │ y[0] . . . y[n−1] c d y[0] . . . y[n−1] │ │ │ │ │ 45. void DVscatter ( int n, double y[], int index[], double x[] ) ; │ │ │ │ │ This method scatters n entries of x[] into y[] as follows, y[index[i]] = x[i] for 0 <= i │ │ │ │ │ @@ -284,15 +284,15 @@ │ │ │ │ │ This method swaps the x[] and y[] vectors as follows. i.e., y[i] := x[i] and x[i] := │ │ │ │ │ y[i] for 0 <= i < n. │ │ │ │ │ 53. void DVzero ( int n, double y[] ) ; │ │ │ │ │ This method zeroes n entries in y[], i.e., y[i] = 0 for 0 <= i < n. │ │ │ │ │ 54. void DVshuffle ( int n, double y[], int seed ) ; │ │ │ │ │ This method shuffles the first n entries in y[]. The value seed is the seed to a random number │ │ │ │ │ generator, and one can get repeatable behavior by repeating seed. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 9 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 9 │ │ │ │ │ 1.2.3 ZV : double complex vector methods │ │ │ │ │ Adoubleprecisioncomplexvector oflengthnissimplya doubleprecisionvector oflength2n. There │ │ │ │ │ is a separate ZVinit() allocator and initializer method, since it requires a real and imaginary part │ │ │ │ │ to fill the vector. However, there is no ZVinit2() method (which allocates without initializing the │ │ │ │ │ entries) nor a ZVfree() method to free the entries; the DVinit2() and DVfree() methods can be │ │ │ │ │ used. Similarly, there is no ZVfscanf() method, instead the DVfscanf() method can be used. │ │ │ │ │ 1. double * ZVinit ( int n, double real, double imag ) ; │ │ │ │ │ @@ -320,15 +320,15 @@ │ │ │ │ │ 6. void ZVaxpy ( int n, double y[], double areal, double aimag, double x[] ) ; │ │ │ │ │ Thismethodaddsascaledmultipleofnentriesfromx[]intoy[],i.e., y[i] += (areal,aimag) │ │ │ │ │ * x[i] for 0 <= i < n. │ │ │ │ │ 7. void ZVaxpy2 ( int n, double z[], double areal, double aimag, │ │ │ │ │ double x[], double breal, double bimag, double y[] ) ; │ │ │ │ │ This method adds a scaled multiple of two vectors x[] and y[] to another vector z[], i.e., │ │ │ │ │ i.e., z[i] += (areal,aimag) * x[i] + (breal,bimag) * y[i] for 0 <= i < n. │ │ │ │ │ - 10 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 10 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 8. void ZVaxpy33 ( int n, double y0[], double y1[], double y2[], │ │ │ │ │ double alpha[], double x0[], double x1[], double x2[] ) ; │ │ │ │ │ This method computes the following. │ │ │ │ │ y0[] = y0[] + alpha[0:1] * x0[] + alpha[2:3] * x1[] + alpha[4:5] * x2[] │ │ │ │ │ y1[] = y1[] + alpha[6:7] * x0[] + alpha[8:9] * x1[] + alpha[10:11] * x2[] │ │ │ │ │ y2[] = y2[] + alpha[12:13] * x0[] + alpha[14:15] * x1[] + alpha[16:17] * x2[] │ │ │ │ │ 9. void ZVaxpy32 ( int n, double y0[], double y1[], double y2[], │ │ │ │ │ @@ -354,15 +354,15 @@ │ │ │ │ │ y0[] = y0[] + alpha[0:1] * x0[] + alpha[2:3] * x1[] │ │ │ │ │ y1[] = y1[] + alpha[4:5] * x0[] + alpha[6:7] * x1[] │ │ │ │ │ 13. void ZVaxpy21 ( int n, double y0[], double y1[], │ │ │ │ │ double alpha[], double x0[] ) ; │ │ │ │ │ This method computes the following. │ │ │ │ │ y0[] = y0[] + alpha[0:1] * x0[] │ │ │ │ │ y1[] = y1[] + alpha[2:3] * x0[] │ │ │ │ │ - Utilities : DRAFT January 6, 2026 11 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 11 │ │ │ │ │ 14. void ZVaxpy13 ( int n, double y0[], │ │ │ │ │ double alpha[], double x0[], double x1[], double x2[] ) ; │ │ │ │ │ This method computes the following. │ │ │ │ │ y0[] = y0[] + alpha[0:1] * x0[] + alpha[2:3] * x1[] + alpha[4:5] * x2[] │ │ │ │ │ 15. void ZVaxpy12 ( int n, double y0[], double alpha[], double x0[], double x1[] ) ; │ │ │ │ │ This method computes the following. │ │ │ │ │ y0[] = y0[] + alpha[0:1] * x0[] + alpha[2:3] * x1[] │ │ │ │ │ @@ -389,15 +389,15 @@ │ │ │ │ │ This method fills *prdot and *pidot with the real and imaginary parts of the indexed dot │ │ │ │ │ n−1 │ │ │ │ │ product Xy[index[i]]∗x[i]. │ │ │ │ │ i=0 │ │ │ │ │ 22. int ZVdotU33 ( int n, double row0[], double row1[], double row2[], │ │ │ │ │ double col0[], double col1[], double col2[], double sums[] ) ; │ │ │ │ │ This method computes nine dot products. │ │ │ │ │ - 12 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 12 Utilities : DRAFT January 17, 2026 │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[0;1] = Xrow0[i]∗col0[i] sums[2 : 3] = Xrow0[i]∗col1[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[4 : 5] = Xrow0[i]∗col2[i] sums[6 : 7] = Xrow1[i]∗col0[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ @@ -441,15 +441,15 @@ │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[4 : 5] = Xrow0[i]∗col2[i] sums[6 : 7] = Xrow1[i]∗col0[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[8 : 9] = Xrow1[i]∗col1[i] sums[10 : 11] = Xrow1[i]∗col2[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ - Utilities : DRAFT January 6, 2026 13 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 13 │ │ │ │ │ 26. int ZVdotU22 ( int n, double row0[], double row1[], │ │ │ │ │ double col0[], double col1[], double sums[] ) ; │ │ │ │ │ This method computes four dot products. │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[0 : 1] = Xrow0[i]∗col0[i] sums[2 : 3] = Xrow0[i]∗col1[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ @@ -483,15 +483,15 @@ │ │ │ │ │ This method computes one dot product. │ │ │ │ │ n−1 │ │ │ │ │ sums[0 : 1] = Xrow0[i]∗col0[i] │ │ │ │ │ i=0 │ │ │ │ │ 31. int ZVdotC33 ( int n, double row0[], double row1[], double row2[], │ │ │ │ │ double col0[], double col1[], double col2[], double sums[] ) ; │ │ │ │ │ This method computes nine dot products. │ │ │ │ │ - 14 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 14 Utilities : DRAFT January 17, 2026 │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[0;1] = Xrow0[i]∗col0[i] sums[2 : 3] = Xrow0[i]∗col1[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[4 : 5] = Xrow0[i]∗col2[i] sums[6 : 7] = Xrow1[i]∗col0[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ @@ -535,15 +535,15 @@ │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[4 : 5] = Xrow0[i]∗col2[i] sums[6 : 7] = Xrow1[i]∗col0[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[8 : 9] = Xrow1[i]∗col1[i] sums[10 : 11] = Xrow1[i]∗col2[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ - Utilities : DRAFT January 6, 2026 15 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 15 │ │ │ │ │ 35. int ZVdotC22 ( int n, double row0[], double row1[], │ │ │ │ │ double col0[], double col1[], double sums[] ) ; │ │ │ │ │ This method computes four dot products. │ │ │ │ │ n−1 n−1 │ │ │ │ │ sums[0 : 1] = Xrow0[i]∗col0[i] sums[2 : 3] = Xrow0[i]∗col1[i] │ │ │ │ │ i=0 i=0 │ │ │ │ │ n−1 n−1 │ │ │ │ │ @@ -578,15 +578,15 @@ │ │ │ │ │ n−1 │ │ │ │ │ sums[0 : 1] = Xrow0[i]∗col0[i] │ │ │ │ │ i=0 │ │ │ │ │ 40. void ZVgather ( int n, double y[], double x[], int index[] ) ; │ │ │ │ │ y[i] = x[index[i]] for 0 <= i < n. │ │ │ │ │ 41. double ZVmaxabs ( int n, double y[] ) ; │ │ │ │ │ This method returns the maximum magnitude of entries in y[0:n-1]. │ │ │ │ │ - 16 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 16 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 42. double ZVminabs ( int n, double y[] ) ; │ │ │ │ │ This method returns the minimum magnitude of entries in y[0:n-1]. │ │ │ │ │ 43. void ZVscale ( int n, double y[], double areal, double aimag ) ; │ │ │ │ │ This method scales a vector y[] by (areal,aimag), i.e., y[i] *= (areal,aimag). for 0 <= │ │ │ │ │ i < n. │ │ │ │ │ 44. void ZVscale2 ( int n, double x[], double y[], │ │ │ │ │ double areal, double aimag, double breal, double bimag, │ │ │ │ │ @@ -609,15 +609,15 @@ │ │ │ │ │ This is an allocator method for int vectors. Storage for an array with size n is found. A │ │ │ │ │ pointer to the array is returned. Note, on return, there will likely be garbage in the array. │ │ │ │ │ 3. void IVfree ( int vec[] ) ; │ │ │ │ │ This method releases the storage taken by vec[]. │ │ │ │ │ 4. void IVfprintf ( FILE *fp, int n, int y[] ) ; │ │ │ │ │ This method prints n entries in y[] to file fp. The format is new line followed by lines of five │ │ │ │ │ int’s in " %4d" format. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 17 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 17 │ │ │ │ │ 5. int IVfp80 ( FILE *fp, int n, int y[], int column, int *pierr ) ; │ │ │ │ │ Thismethodprintsnentriesiny[]tofilefp. Themethodsplicesvectorstogetherornaturally │ │ │ │ │ breaks the large vectors into lines. The column value is the present location. If the printed │ │ │ │ │ value of an array entry will not fit within the eighty columns of the present line, a newline │ │ │ │ │ character is written and the value starts a new line. The number of the present column in │ │ │ │ │ the line is returned. If *pierr < 0, an IO error has occured. │ │ │ │ │ 6. int IVfscanf ( FILE *fp, int n, int y[] ) ; │ │ │ │ │ @@ -645,15 +645,15 @@ │ │ │ │ │ returns a location where target is found. If target is not in y[], -1 is returned. │ │ │ │ │ 14. int IVmax ( int n, int y[], int *ploc ) ; │ │ │ │ │ This method returns the maximum entry in y[0:n-1] and puts the first location where it │ │ │ │ │ was found into the address ploc. │ │ │ │ │ 15. int IVmaxabs ( int n, int y[], int *ploc ) ; │ │ │ │ │ This method returns the maximum magnitude of entries in y[0:n-1] and puts the first │ │ │ │ │ location where it was found into the address ploc. │ │ │ │ │ - 18 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 18 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 16. int IVmin ( int n, int y[], int *ploc ) ; │ │ │ │ │ This method returns the minimum entry in y[0:n-1] and puts the first location where it was │ │ │ │ │ found into the address ploc. │ │ │ │ │ 17. int IVminabs ( int n, int y[], int *ploc ) ; │ │ │ │ │ This method returns the minimum magnitude of entries in y[0:n-1] and puts the first loca- │ │ │ │ │ tion where it was found into the address ploc. │ │ │ │ │ 18. void IVperm ( int n, int y[], int index[] ) ; │ │ │ │ │ @@ -681,15 +681,15 @@ │ │ │ │ │ 25. void IVshuffle ( int n, int y[], int seed ) ; │ │ │ │ │ This method shuffles the first n entries in y[]. The value seed is the seed to a random number │ │ │ │ │ generator, and one can get repeatable behavior by repeating seed. │ │ │ │ │ 1.2.5 FV : float vector methods │ │ │ │ │ 1. float * FVinit ( int n, float val ) ; │ │ │ │ │ This is the allocator and initializer method for float vectors. Storage for an array with size │ │ │ │ │ n is found and each entry is filled with val. A pointer to the array is returned. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 19 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 19 │ │ │ │ │ 2. float * FVinit2 ( int n ) ; │ │ │ │ │ This is an allocator method for float vectors. Storage for an array with size n is found. A │ │ │ │ │ pointer to the array is returned. Note, on return, there will likely be garbage in the array. │ │ │ │ │ 3. void FVfree ( int vec[] ) ; │ │ │ │ │ This method releases the storage taken by vec[]. │ │ │ │ │ 4. void FVfprintf ( FILE *fp, int n, float y[] ) ; │ │ │ │ │ This method prints n entries in y[] to file fp. The format is new line followed by lines of six │ │ │ │ │ @@ -716,15 +716,15 @@ │ │ │ │ │ i=0 │ │ │ │ │ 12. void FVfill ( int n, float y[], float val ) ; │ │ │ │ │ This method fills n entries in y[] with val, i.e., y[i] = val for 0 <= i < n. │ │ │ │ │ 13. void FVgather ( int n, float y[], float x[], int index[] ) ; │ │ │ │ │ y[i] = x[index[i]] for 0 <= i < n. │ │ │ │ │ 14. void FVgatherAddZero ( int n, float y[], float x[], int index[] ) ; │ │ │ │ │ y[i] += x[index[i]] and x[index[i]] = 0 for 0 <= i < n. │ │ │ │ │ - 20 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 20 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 15. void FVgatherZero ( int n, float y[], float x[], int index[] ) ; │ │ │ │ │ y[i] = x[index[i]] and x[index[i]] = 0 │ │ │ │ │ 16. void FVinvPerm ( int n, float y[], int index[] ) ; │ │ │ │ │ This method permutes the vector y as follows. i.e., y[index[i]] := y[i]. See FVperm() for │ │ │ │ │ a similar function. │ │ │ │ │ 17. float FVmax ( int n, float y[], int *ploc ) ; │ │ │ │ │ This method returns the maximum entry in y[0:n-1] and puts the first location where it │ │ │ │ │ @@ -751,15 +751,15 @@ │ │ │ │ │ < n. │ │ │ │ │ 25. void FVscatterAddZero ( int n, float y[], int index[], float x[] ) ; │ │ │ │ │ This method scatters/adds n entries of x[] into y[] as follows, y[index[i]] += x[i] and │ │ │ │ │ x[i] for 0 <= i < n. │ │ │ │ │ 26. void FVscatterZero ( int n, float y[], int index[], float x[] ) ; │ │ │ │ │ This method scatters n entries of x[] into y[] as follows, y[index[i]] = x[i] and x[i] for │ │ │ │ │ 0 <= i < n. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 21 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 21 │ │ │ │ │ 27. void FVsub ( int n, float y[], float x[] ) ; │ │ │ │ │ This method subtracts n entries from x[] to y[], i.e., y[i] -= x[i] for 0 <= i < n. │ │ │ │ │ 28. float FVsum ( int n, float y[] ) ; │ │ │ │ │ P │ │ │ │ │ This method returns the sum of the first n entries in the vector x[], i.e., return n−1x[i]. │ │ │ │ │ i=0 │ │ │ │ │ 29. float FVsumabs ( int n, float y[] ) ; │ │ │ │ │ @@ -787,15 +787,15 @@ │ │ │ │ │ i.e., p vec[0] = vec, and p vec[i] = p vec[i-1] + sizes[i-1] for 0 < i < n. │ │ │ │ │ 1.2.7 PDV : double * vector methods │ │ │ │ │ 1. double ** PDVinit ( int n ) ; │ │ │ │ │ This is the allocator and initializer method for double* vectors. Storage for an array with │ │ │ │ │ size n is found and each entry is filled with NULL. A pointer to the array is returned. │ │ │ │ │ 2. void PDVfree ( double **p_vec ) ; │ │ │ │ │ This method releases the storage taken by p vec[]. │ │ │ │ │ - 22 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 22 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 3. void PDVcopy ( int n, double *p_y[], double *p_x[] ) ; │ │ │ │ │ This method copies n entries from p x[] to p y[], i.e., p y[i] = p x[i] for 0 <= i < n. │ │ │ │ │ 4. void PDVsetup ( int n, int sizes[], double vec[], double *p_vec[] ) ; │ │ │ │ │ This method sets the entries of p vec[] as pointers into vec[] given by the sizes[] vector, │ │ │ │ │ i.e., p vec[0] = vec, and p vec[i] = p vec[i-1] + sizes[i-1] for 0 < i < n. │ │ │ │ │ PIV : int * vector methods │ │ │ │ │ 1. int ** PIVinit ( int n ) ; │ │ │ │ │ @@ -815,15 +815,15 @@ │ │ │ │ │ 2. void PFVfree ( float **p_vec ) ; │ │ │ │ │ This method releases the storage taken by p vec[]. │ │ │ │ │ 3. void PFVcopy ( int n, float *p_y[], float *p_x[] ) ; │ │ │ │ │ This method copies n entries from p x[] to p y[], i.e., p y[i] = p x[i] for 0 <= i < n. │ │ │ │ │ 4. void PFVsetup ( int n, int sizes[], float vec[], float *p_vec[] ) ; │ │ │ │ │ This method sets the entries of p vec[] as pointers into vec[] given by the sizes[] vector, │ │ │ │ │ i.e., p vec[0] = vec, and p vec[i] = p vec[i-1] + sizes[i-1] for 0 < i < n. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 23 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 23 │ │ │ │ │ 1.2.9 Sorting routines │ │ │ │ │ Validation routines │ │ │ │ │ 1. int IVisascending ( int n, int ivec[] ) ; │ │ │ │ │ int IVisdescending ( int n, int ivec[] ) ; │ │ │ │ │ These methods returns 1 if the array ivec[] is in ascending or descending order and returns │ │ │ │ │ 0 otherwise. │ │ │ │ │ 2. int DVisascending ( int n, double dvec[] ) ; │ │ │ │ │ @@ -852,15 +852,15 @@ │ │ │ │ │ This sorts the array ivec[] into ascending or descending order using an insertion sort and │ │ │ │ │ permutes the double precision complex companion array dvec[] in the same fashion. │ │ │ │ │ 6. void IV2ZVisortUp ( int n, int ivec1[], int ivec2[], double dvec[] ) ; │ │ │ │ │ void IV2ZVisortDown ( int n, int ivec1[], int ivec2[], double dvec[] ) ; │ │ │ │ │ These methods sort the array ivec1[] into ascending or descending order using an insertion │ │ │ │ │ sort and permutes the companion arrays ivec2[] and dvec[] in the same fashion. The │ │ │ │ │ dvec[] array is double precision complex. │ │ │ │ │ - 24 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 24 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 7. void DVisortUp ( int n, double dvec[] ) ; │ │ │ │ │ void DVisortDown ( int n, double dvec[] ) ; │ │ │ │ │ These methods sort a double array into ascending or descending order using an insertion │ │ │ │ │ sort. │ │ │ │ │ 8. void DV2isortUp ( int n, double dvec1[], double dvec2[] ) ; │ │ │ │ │ void DV2isortDown ( int n, double dvec1[], double dvec2[] ) ; │ │ │ │ │ These methods sort the array dvec1[] into ascending or descending order using an insertion │ │ │ │ │ @@ -890,15 +890,15 @@ │ │ │ │ │ These methods sort the array ivec[] into ascending or descending order using a quick sort │ │ │ │ │ and permutes the double precision complex companion array dvec[] in the same fashion. │ │ │ │ │ 6. void IV2ZVqsortUp ( int n, int ivec1[], int ivec2[], double dvec[] ) ; │ │ │ │ │ void IV2ZVqsortDown ( int n, int ivec1[], int ivec2[], double dvec[] ) ; │ │ │ │ │ These methods sort the array ivec1[] into ascending or descending order using a quick sort │ │ │ │ │ and permutes the companion arrays ivec2[] and dvec[] in the same fashion. The dvec[] │ │ │ │ │ array is double precision complex. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 25 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 25 │ │ │ │ │ 7. void DVqsortUp ( int n, double dvec[] ) ; │ │ │ │ │ void DVqsortDown ( int n, double dvec[] ) ; │ │ │ │ │ Thes methods sort a double array into ascending or descending order using a quick sort. │ │ │ │ │ 8. void DV2qsortUp ( int n, double dvec1[], double dvec2[] ) ; │ │ │ │ │ void DV2qsortDown ( int n, double dvec1[], double dvec2[] ) ; │ │ │ │ │ These methods sort the array dvec1[] into ascending or descending order using a quick sort │ │ │ │ │ and permutes the companion array dvec2[] in the same fashion. │ │ │ │ │ @@ -928,15 +928,15 @@ │ │ │ │ │ program exits. │ │ │ │ │ 4. int IV2sortUpAndCompress ( int n, int ivec1[], int ivec2[] ) ; │ │ │ │ │ This method sorts ivec1[] into ascending order with ivec2[] as a companion vector. It │ │ │ │ │ then compresses the pairs, dropping all but one of identical pairs. The return value is the │ │ │ │ │ number of unique entries stored in the leading locations of the vectors ivec1[] and ivec2[]. │ │ │ │ │ Error checking: If n < 0, or if ivec1 or ivec2 is NULL, an error message is printed and the │ │ │ │ │ program exits. │ │ │ │ │ - 26 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 26 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 5. int IV2DVsortUpAndCompress ( int n, int ivec1[], int ivec2[], double dvec[] ) ; │ │ │ │ │ This method sorts ivec1[] into ascending order with ivec2[] and dvec[] as companion │ │ │ │ │ vectors. It then compresses the pairs, summing the dvec[] entries for identical (ivec1[], │ │ │ │ │ ivec2[]) pairs. The return value is the number of unique entries stored in the leading │ │ │ │ │ locations of the vectors ivec1[], ivec2[] and dvec[]. │ │ │ │ │ Error checking: If n < 0, or if ivec1, ivec2 or dvec is NULL, an error message is printed and │ │ │ │ │ the program exits. │ │ │ │ │ @@ -965,15 +965,15 @@ │ │ │ │ │ 2. void IP_free ( IP *ip ) ; │ │ │ │ │ This method releases the storage based at *ip. │ │ │ │ │ 3. void IP_fprintf ( FILE *fp, IP *ip ) ; │ │ │ │ │ This method prints the singly linked list that starts with ip. │ │ │ │ │ 4. int IP_fp80 ( FILE *fp, int n, int y[], int column, int *pierr ) ; │ │ │ │ │ This method prints the singly linked list that starts with ip. See IVfp80() for a description │ │ │ │ │ of how the entries are placed on a line. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 27 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 27 │ │ │ │ │ 5. IP * IP_mergeUp ( IP *ip1, IP *ip2 ) ; │ │ │ │ │ This method merges two singly linked lists into one. If the two lists are in ascending order, │ │ │ │ │ the new list is also in ascending order. The head of the new list is returned. │ │ │ │ │ 6. IP * IP_mergeSortUp ( IP *ip ) ; │ │ │ │ │ This method sorts a list into ascending order using a merge sort. │ │ │ │ │ 7. IP * IP_radixSortUp ( IP *ip ) ; │ │ │ │ │ This method sorts a list into ascending order using a radix sort. │ │ │ │ │ @@ -1002,15 +1002,15 @@ │ │ │ │ │ base[i].value1 = -1. The flag parameter determines how the next field is filled. │ │ │ │ │ • If flag = I2OP NULL, the elements are not linked, i.e., ips[i].next = NULL for 0 <= │ │ │ │ │ i < n. │ │ │ │ │ • If flag = I2OP FORWARD,the elements are linked in a forward manner, i.e., ips[i].next │ │ │ │ │ = &ips[i+1] for 0 <= i < n-1 and ips[n-1].next = NULL. │ │ │ │ │ • If flag = I2OP BACKWARD,theelementsarelinkedinabackwardmanner,i.e., ips[i].next │ │ │ │ │ = &ips[i-1] for 0 < i < n and ips[0].next = NULL. │ │ │ │ │ - 28 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 28 Utilities : DRAFT January 17, 2026 │ │ │ │ │ 3. void I2OP_free ( I2OP *i2op ) ; │ │ │ │ │ This method releases the storage based at *i2op. │ │ │ │ │ 4. void I2OP_fprintf ( FILE *fp, I2OP *i2op ) ; │ │ │ │ │ This method prints the singly linked list that starts with i2op. │ │ │ │ │ 1.3 Driver programs │ │ │ │ │ 1. test_sort msglvl msgFile target sortType n range mod seed │ │ │ │ │ This driver program tests the sort methods. Use the script file do test sort for testing. │ │ │ │ │ @@ -1038,15 +1038,15 @@ │ │ │ │ │ • Integer entries are of the form k mod mod, where k in [0,range]. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ 2. test_sortUpAndCompress msglvl msgFile target n range mod seed │ │ │ │ │ This driver program tests the “sort in ascending order and compress” methods. Use the script │ │ │ │ │ file do test sortUpAndCompress for testing. │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ timing output. │ │ │ │ │ - Utilities : DRAFT January 6, 2026 29 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 29 │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The target parameter denotes the type of vector(s) to be sorted. │ │ │ │ │ – IV — int vector sort │ │ │ │ │ – IV2 — (int, int) vector sort │ │ │ │ │ – IVDV — (int, double) vector sort │ │ │ │ │ @@ -1091,15 +1091,15 @@ │ │ │ │ │ DVfree(), 3 FVaxpy(), 16 │ │ │ │ │ DVfscanf(), 3 FVaxpyi(), 16 │ │ │ │ │ DVgather(), 5 FVcompress(), 16 │ │ │ │ │ DVgatherAddZero(), 5 FVcopy(), 17 │ │ │ │ │ DVgatherZero(), 6 FVdot(), 17 │ │ │ │ │ DVinit(), 2 FVfill(), 17 │ │ │ │ │ 30 │ │ │ │ │ - Utilities : DRAFT January 6, 2026 31 │ │ │ │ │ + Utilities : DRAFT January 17, 2026 31 │ │ │ │ │ FVfprintf(), 16 IV2qsortDown(), 21 │ │ │ │ │ FVfree(), 16 IV2qsortUp(), 21 │ │ │ │ │ FVfscanf(), 16 IV2sortUpAndCompress(), 23 │ │ │ │ │ FVgather(), 17 IV2ZVisortDown(), 21 │ │ │ │ │ FVgatherAddZero(), 17 IV2ZVisortUp(), 21 │ │ │ │ │ FVgatherZero(), 17 IV2ZVqsortDown(), 22 │ │ │ │ │ FVinit(), 16 IV2ZVqsortUp(), 22 │ │ │ │ │ @@ -1137,15 +1137,15 @@ │ │ │ │ │ IV2DVisortDown(), 21 IVscatter(), 15 │ │ │ │ │ IV2DVisortUp(), 21 IVshuffle(), 16 │ │ │ │ │ IV2DVqsortDown(), 22 IVsortUpAndCompress(), 22 │ │ │ │ │ IV2DVqsortUp(), 22 IVsum(), 15 │ │ │ │ │ IV2DVsortUpAndCompress(), 23 IVsumabs(), 15 │ │ │ │ │ IV2isortDown(), 20 IVswap(), 15 │ │ │ │ │ IV2isortUp(), 20 IVzero(), 16 │ │ │ │ │ - 32 Utilities : DRAFT January 6, 2026 │ │ │ │ │ + 32 Utilities : DRAFT January 17, 2026 │ │ │ │ │ IVZVisortDown(), 21 ZVdotU23(), 10 │ │ │ │ │ IVZVisortUp(), 21 ZVdotU31(), 9 │ │ │ │ │ IVZVqsortDown(), 22 ZVdotU32(), 9 │ │ │ │ │ IVZVqsortUp(), 22 ZVdotU33(), 9 │ │ │ │ │ IVZVsortUpAndCompress(), 23 ZVfprintf(), 8 │ │ │ │ │ ZVgather(), 13 │ │ │ │ │ PCVcopy(), 19 ZVinit(), 7 │ │ ├── ./usr/share/doc/spooles-doc/ZV.ps.gz │ │ │ ├── ZV.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o ZV.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -2350,16 +2350,18 @@ │ │ │ │ /UnderlinePosition -100 def │ │ │ │ /UnderlineThickness 50 def │ │ │ │ end readonly 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100 a Fk(4)p 136 100 1183 4 v │ │ │ │ +1365 w Fj(ZV)30 b Fg(:)g Ff(DRAFT)g Fg(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2717 100 V 111 399 a Fk(8.)46 b Fj(void)h(ZV_setEntry)e(\()i(ZV)g(*zv,) │ │ │ │ g(int)g(loc,)f(double)h(real,)f(double)g(imag)h(\))g(;)227 │ │ │ │ 551 y Fk(This)30 b(metho)s(d)g(sets)g(the)h Fj(loc)p │ │ │ │ Fk('th)f(en)m(try)g(of)h(the)f(v)m(ector)i(to)f Fj(\(real,imag\))p │ │ │ │ Fk(.)227 704 y Ff(Err)-5 b(or)33 b(che)-5 b(cking:)40 │ │ │ │ b Fk(If)28 b Fj(zv)h Fk(is)g Fj(NULL)e Fk(or)j Fj(loc)46 │ │ │ │ b(<)i(0)p Fk(,)29 b(an)g(error)g(message)h(is)f(prin)m(ted)f(and)h(the) │ │ │ │ g(program)g(exits.)0 978 y Fd(1.2.3)112 b(Initializer)38 │ │ │ │ @@ -4355,17 +4366,17 @@ │ │ │ │ 5294 y Ff(Err)-5 b(or)37 b(che)-5 b(cking:)46 b Fk(If)33 │ │ │ │ b Fj(zv)g Fk(is)g Fj(NULL)p Fk(,)f(or)i Fj(newsize)46 │ │ │ │ b(<)h(0)p Fk(,)34 b(or)f(if)h Fj(0)47 b(<)h(maxsize)d(<)j(newsize)31 │ │ │ │ b Fk(and)i Fj(owned)46 b(=)227 5407 y(0)p Fk(,)31 b(an)f(error)g │ │ │ │ (message)h(is)g(prin)m(ted)f(and)f(the)i(program)f(exits.)p │ │ │ │ eop end │ │ │ │ %%Page: 5 5 │ │ │ │ -TeXDict begin 5 4 bop 91 100 1206 4 v 1387 100 a Fj(ZV)30 │ │ │ │ -b Fg(:)g Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2647 100 V 1206 w Fk(5)0 399 y Fd(1.2.4)112 b(Utilit)m(y)38 │ │ │ │ +TeXDict begin 5 4 bop 91 100 1183 4 v 1364 100 a Fj(ZV)30 │ │ │ │ +b Fg(:)h Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2670 100 V 1183 w Fk(5)0 399 y Fd(1.2.4)112 b(Utilit)m(y)38 │ │ │ │ b(metho)s(ds)111 607 y Fk(1.)46 b Fj(void)h(ZV_shiftBase)d(\()k(ZV)f │ │ │ │ (*zv,)g(int)g(offset)f(\))h(;)227 770 y Fk(This)32 b(metho)s(d)h │ │ │ │ (shifts)f(the)i(base)f(en)m(tries)g(of)h(the)f(v)m(ector)h(and)f │ │ │ │ (decremen)m(ts)g(the)g(presen)m(t)g(size)h(and)f(max-)227 │ │ │ │ 883 y(im)m(um)g(size)g(of)g(the)f(v)m(ector)j(b)m(y)d │ │ │ │ Fj(offset)p Fk(.)46 b(This)31 b(is)i(a)g(dangerous)f(metho)s(d)g(to)h │ │ │ │ (use)g(b)s(ecause)f(the)h(state)h(of)227 996 y(the)j(v)m(ector)h(is)e │ │ │ │ @@ -4425,17 +4436,17 @@ │ │ │ │ b(The)24 b(n)m(um)m(b)s(er)f(of)i(en)m(tries)g(that)g(are)g(copied)g │ │ │ │ (is)g(the)f(smaller)227 5244 y(of)31 b(the)f(t)m(w)m(o)i(sizes.)227 │ │ │ │ 5407 y Ff(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fk(If)30 │ │ │ │ b Fj(zv1)g Fk(or)g Fj(zv2)g Fk(is)g Fj(NULL)p Fk(,)g(an)g(error)g │ │ │ │ (message)h(is)g(prin)m(ted)f(and)f(the)i(program)f(exits.)p │ │ │ │ eop end │ │ │ │ %%Page: 6 6 │ │ │ │ -TeXDict begin 6 5 bop 0 100 a Fk(6)p 136 100 1206 4 v │ │ │ │ -1388 w Fj(ZV)29 b Fg(:)i Ff(DRAFT)f Fg(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2695 100 V 111 399 a Fk(8.)46 b Fj(void)h(ZV_log10profile)d(\()j(ZV)g │ │ │ │ +TeXDict begin 6 5 bop 0 100 a Fk(6)p 136 100 1183 4 v │ │ │ │ +1365 w Fj(ZV)30 b Fg(:)g Ff(DRAFT)g Fg(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2717 100 V 111 399 a Fk(8.)46 b Fj(void)h(ZV_log10profile)d(\()j(ZV)g │ │ │ │ (*zv,)g(int)g(npts,)f(DV)h(*xDV,)g(DV)g(*yDV,)f(double)g(tausmall,)1325 │ │ │ │ 511 y(double)g(taubig,)g(int)h(*pnzero,)e(int)i(*pnsmall,)f(int)g │ │ │ │ (*pnbig)h(\))g(;)227 660 y Fk(This)34 b(metho)s(d)f(scans)i(the)f(en)m │ │ │ │ (tries)h(in)f(the)g Fj(ZV)g Fk(ob)5 b(ject)35 b(and)f(\014lls)g │ │ │ │ Fj(xDV)f Fk(and)h Fj(yDV)f Fk(with)h(data)h(that)g(allo)m(ws)227 │ │ │ │ 773 y(a)c(simple)f(log)703 795 y Fc(10)808 773 y Fk(distribution)f │ │ │ │ (plot.)41 b(Only)29 b(en)m(tries)i(whose)f(magnitudes)g(lie)h(in)e(the) │ │ │ │ @@ -4517,17 +4528,17 @@ │ │ │ │ 5259 y(the)j(v)-5 b(alue)31 b Fj(1)f Fk(is)g(returned.)40 │ │ │ │ b(If)30 b(an)g(IO)g(error)g(is)g(encoun)m(tered)h(from)f │ │ │ │ Fj(fprintf)p Fk(,)e(zero)k(is)e(returned.)227 5407 y │ │ │ │ Ff(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fk(If)30 b Fj(zv)g │ │ │ │ Fk(or)g Fj(fp)g Fk(are)h Fj(NULL)p Fk(,)e(an)i(error)f(message)h(is)g │ │ │ │ (prin)m(ted)f(and)f(zero)i(is)g(returned.)p eop end │ │ │ │ %%Page: 7 7 │ │ │ │ -TeXDict begin 7 6 bop 91 100 1206 4 v 1387 100 a Fj(ZV)30 │ │ │ │ -b Fg(:)g Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(6,)h(2026)p │ │ │ │ -2647 100 V 1206 w Fk(7)111 399 y(6.)46 b Fj(int)h(ZV_writeToBinaryFile) │ │ │ │ +TeXDict begin 7 6 bop 91 100 1183 4 v 1364 100 a Fj(ZV)30 │ │ │ │ +b Fg(:)h Ff(DRAFT)121 b Fg(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2670 100 V 1183 w Fk(7)111 399 y(6.)46 b Fj(int)h(ZV_writeToBinaryFile) │ │ │ │ 42 b(\()48 b(ZV)f(*zv,)g(FILE)f(*fp)h(\))h(;)227 557 │ │ │ │ y Fk(This)27 b(metho)s(d)f(writes)h(a)h Fj(ZV)e Fk(ob)5 │ │ │ │ b(ject)28 b(to)g(a)f(binary)g(\014le.)39 b(If)27 b(there)g(are)h(no)e │ │ │ │ (errors)h(in)g(writing)g(the)g(data,)i(the)227 670 y(v)-5 │ │ │ │ b(alue)31 b Fj(1)f Fk(is)h(returned.)39 b(If)30 b(an)g(IO)g(error)g(is) │ │ │ │ h(encoun)m(tered)f(from)g Fj(fwrite)p Fk(,)f(zero)i(is)g(returned.)227 │ │ │ │ 829 y Ff(Err)-5 b(or)34 b(che)-5 b(cking:)40 b Fk(If)30 │ │ │ │ @@ -4583,17 +4594,17 @@ │ │ │ │ 5140 y(data.)337 5294 y Fi(\210)45 b Fk(The)29 b Fj(inFile)f │ │ │ │ Fk(parameter)j(is)e(the)h(name)g(of)g(the)g(\014le)f(from)h(whic)m(h)f │ │ │ │ (to)h(read)g(in)f(the)h(ob)5 b(ject.)42 b Fj(inFile)427 │ │ │ │ 5407 y Fk(m)m(ust)31 b(b)s(e)e(of)i(the)f(form)g Fj(*.zvf)f │ │ │ │ Fk(for)h(a)h(formatted)g(\014le)g(or)f Fj(*.zvb)f Fk(for)h(a)h(binary)e │ │ │ │ (\014le.)p eop end │ │ │ │ %%Page: 8 8 │ │ │ │ -TeXDict begin 8 7 bop 0 100 a Fk(8)p 136 100 1206 4 v │ │ │ │ -1388 w Fj(ZV)29 b Fg(:)i Ff(DRAFT)f Fg(Jan)m(uary)g(6,)h(2026)p │ │ │ │ -2695 100 V 337 399 a Fi(\210)45 b Fk(The)40 b Fj(outFile)f │ │ │ │ +TeXDict begin 8 7 bop 0 100 a Fk(8)p 136 100 1183 4 v │ │ │ │ +1365 w Fj(ZV)30 b Fg(:)g Ff(DRAFT)g Fg(Jan)m(uary)g(17,)i(2026)p │ │ │ │ +2717 100 V 337 399 a Fi(\210)45 b Fk(The)40 b Fj(outFile)f │ │ │ │ Fk(parameter)i(is)g(the)g(name)g(of)f(the)h(\014le)g(to)g(whic)m(h)g │ │ │ │ (to)g(write)g(out)g(the)g(ob)5 b(ject.)72 b(If)427 511 │ │ │ │ y Fj(outfile)28 b Fk(is)j(of)f(the)g(form)g Fj(*.zvf)p │ │ │ │ Fk(,)f(the)h(ob)5 b(ject)31 b(is)f(written)g(to)h(a)f(formatted)h │ │ │ │ (\014le.)41 b(If)30 b Fj(outfile)e Fk(is)i(of)427 624 │ │ │ │ y(the)e(form)g Fj(*.zvb)p Fk(,)f(the)h(ob)5 b(ject)29 │ │ │ │ b(is)f(written)g(to)h(a)f(binary)f(\014le.)40 b(When)28 │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -22,15 +22,15 @@ │ │ │ │ │ Onemustchoose where to use this object. There is a substantial performance penalty for doing the │ │ │ │ │ simplest operations, and so when we need to manipulate an double vector inside a loop, we extract │ │ │ │ │ out the size and pointer to the base array from the ZV object. On the other hand, the convenience │ │ │ │ │ makes it a widely used object. │ │ │ │ │ 1.1 Data Structure │ │ │ │ │ The ZV structure has three fields. │ │ │ │ │ 1 │ │ │ │ │ - 2 ZV : DRAFT January 6, 2026 │ │ │ │ │ + 2 ZV : DRAFT January 17, 2026 │ │ │ │ │ • int size : present size of the vector. │ │ │ │ │ • int maxsize : maximum size of the vector. │ │ │ │ │ • int owned : owner flag for the data. When owned = 1, storage for owned double’s has been │ │ │ │ │ allocated by this object and can be free’d by the object. When owned == 0 but size > 0 , │ │ │ │ │ this object points to entries that have been allocated elsewhere, and these entries will not be │ │ │ │ │ free’d by this object. │ │ │ │ │ • double *vec : pointer to the base address of the double vector │ │ │ │ │ @@ -54,15 +54,15 @@ │ │ │ │ │ the storage for vec is free’d by a call to ZVfree(). The structure’s default fields are then set │ │ │ │ │ with a call to ZV setDefaultFields(). │ │ │ │ │ Error checking: If zv is NULL an error message is printed and the program exits. │ │ │ │ │ 4. void ZV_free ( ZV *zv ) ; │ │ │ │ │ This method releases any storage by a call to ZV clearData() then free’s the storage for the │ │ │ │ │ structure with a call to free(). │ │ │ │ │ Error checking: If zv is NULL an error message is printed and the program exits. │ │ │ │ │ - ZV : DRAFT January 6, 2026 3 │ │ │ │ │ + ZV : DRAFT January 17, 2026 3 │ │ │ │ │ 1.2.2 Instance methods │ │ │ │ │ These method allow access to information in the data fields without explicitly following pointers. │ │ │ │ │ There is overhead involved with these method due to the function call and error checking inside │ │ │ │ │ the methods. │ │ │ │ │ 1. int ZV_owned ( ZV *zv ) ; │ │ │ │ │ This method returns the value of owned. If owned > 0, then the object owns the data pointed │ │ │ │ │ to by vec and will free this data with a call to ZVfree() when its data is cleared by a call to │ │ │ │ │ @@ -91,15 +91,15 @@ │ │ │ │ │ This method returns vec, a pointer to the base address of the vector. │ │ │ │ │ Error checking: If zv is NULL, an error message is printed and the program exits. │ │ │ │ │ 7. void ZV_sizeAndEntries ( ZV *zv, int *psize, double **pentries ) ; │ │ │ │ │ This method fills *psize with the size of the vector and **pentries with the base address │ │ │ │ │ of the vector. │ │ │ │ │ Error checking: If zv, psize or pentriesis NULL, an error message is printed and the program │ │ │ │ │ exits. │ │ │ │ │ - 4 ZV : DRAFT January 6, 2026 │ │ │ │ │ + 4 ZV : DRAFT January 17, 2026 │ │ │ │ │ 8. void ZV_setEntry ( ZV *zv, int loc, double real, double imag ) ; │ │ │ │ │ This method sets the loc’th entry of the vector to (real,imag). │ │ │ │ │ Error checking: If zv is NULL or loc < 0, an error message is printed and the program exits. │ │ │ │ │ 1.2.3 Initializer methods │ │ │ │ │ There are three initializer methods. │ │ │ │ │ 1. void ZV_init ( ZV *zv, int size, double *entries ) ; │ │ │ │ │ This method initializes the object given a size for the vector and a possible pointer to the │ │ │ │ │ @@ -128,15 +128,15 @@ │ │ │ │ │ Error checking: If zv is NULL or newmaxsize < 0, or if 0 < maxsize and owned == 0, an │ │ │ │ │ error message is printed and the program exits. │ │ │ │ │ 5. void ZV_setSize ( ZV *zv, int newsize ) ; │ │ │ │ │ This method sets the size of the vector. If newsize > maxsize, the length of the vector is │ │ │ │ │ increased with a call to ZV setMaxsize(). The size field is set to newsize. │ │ │ │ │ Error checking: If zv is NULL, or newsize < 0, or if 0 < maxsize < newsize and owned = │ │ │ │ │ 0, an error message is printed and the program exits. │ │ │ │ │ - ZV : DRAFT January 6, 2026 5 │ │ │ │ │ + ZV : DRAFT January 17, 2026 5 │ │ │ │ │ 1.2.4 Utility methods │ │ │ │ │ 1. void ZV_shiftBase ( ZV *zv, int offset ) ; │ │ │ │ │ This method shifts the base entries of the vector and decrements the present size and max- │ │ │ │ │ imum size of the vector by offset. This is a dangerous method to use because the state of │ │ │ │ │ the vector is lost, namely vec, the base of the entries, is corrupted. If the object owns its │ │ │ │ │ entries and ZV free(), ZV setSize() or ZV setMaxsize() is called before the base has been │ │ │ │ │ shifted back to its original position, a segmentation violation will likely result. This is a very │ │ │ │ │ @@ -162,15 +162,15 @@ │ │ │ │ │ This method fills the vector with zeros. │ │ │ │ │ Error checking: If zv is NULL, an error message is printed and the program exits. │ │ │ │ │ 7. void ZV_copy ( ZV *zv1, ZV *zv2 ) ; │ │ │ │ │ This method fills the zv1 object with entries in the iv2 object. Note, this is a mapped copy, │ │ │ │ │ zv1 and zv2 need not have the same size. The number of entries that are copied is the smaller │ │ │ │ │ of the two sizes. │ │ │ │ │ Error checking: If zv1 or zv2 is NULL, an error message is printed and the program exits. │ │ │ │ │ - 6 ZV : DRAFT January 6, 2026 │ │ │ │ │ + 6 ZV : DRAFT January 17, 2026 │ │ │ │ │ 8. void ZV_log10profile ( ZV *zv, int npts, DV *xDV, DV *yDV, double tausmall, │ │ │ │ │ double taubig, int *pnzero, int *pnsmall, int *pnbig ) ; │ │ │ │ │ This method scans the entries in the ZV object and fills xDV and yDV with data that allows │ │ │ │ │ a simple log10 distribution plot. Only entries whose magnitudes lie in the range [tausmall, │ │ │ │ │ taubig] contribute to the distribution. The number of entries whose magnitudes are zero, │ │ │ │ │ smaller than tausmall, or larger than taubig are placed into pnzero, *pnsmall and *pnbig, │ │ │ │ │ respectively. On return, the size of the xDV and yDV objects is npts. │ │ │ │ │ @@ -199,15 +199,15 @@ │ │ │ │ │ and returns the value returned from the called routine. │ │ │ │ │ Error checking: If zv or fn are NULL, or if fn is not of the form *.zvf (for a formatted file) │ │ │ │ │ or *.zvb (for a binary file), an error message is printed and the method returns zero. │ │ │ │ │ 5. int ZV_writeToFormattedFile ( ZV *zv, FILE *fp ) ; │ │ │ │ │ This method writes a ZV object to a formatted file. If there are no errors in writing the data, │ │ │ │ │ the value 1 is returned. If an IO error is encountered from fprintf, zero is returned. │ │ │ │ │ Error checking: If zv or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ - ZV : DRAFT January 6, 2026 7 │ │ │ │ │ + ZV : DRAFT January 17, 2026 7 │ │ │ │ │ 6. int ZV_writeToBinaryFile ( ZV *zv, FILE *fp ) ; │ │ │ │ │ This method writes a ZV object to a binary file. If there are no errors in writing the data, the │ │ │ │ │ value 1 is returned. If an IO error is encountered from fwrite, zero is returned. │ │ │ │ │ Error checking: If zv or fp are NULL, an error message is printed and zero is returned. │ │ │ │ │ 7. int ZV_writeForHumanEye ( ZV *zv, FILE *fp ) ; │ │ │ │ │ This method writes a ZV object to a file in a human readable format. is called to write out │ │ │ │ │ the header and statistics. The entries of the vector then follow in eighty column format using │ │ │ │ │ @@ -232,15 +232,15 @@ │ │ │ │ │ • The msglvl parameter determines the amount of output. Use msglvl = 1 for just │ │ │ │ │ timing output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The inFile parameter is the name of the file from which to read in the object. inFile │ │ │ │ │ must be of the form *.zvf for a formatted file or *.zvb for a binary file. │ │ │ │ │ - 8 ZV : DRAFT January 6, 2026 │ │ │ │ │ + 8 ZV : DRAFT January 17, 2026 │ │ │ │ │ • The outFile parameter is the name of the file to which to write out the object. If │ │ │ │ │ outfile is of the form *.zvf, the object is written to a formatted file. If outfile is of │ │ │ │ │ the form *.zvb, the object is written to a binary file. When outFile is not "none", the │ │ │ │ │ object is written to the file in a human readable format. When outFile is "none", the │ │ │ │ │ object is not written out. │ │ │ │ │ Index │ │ │ │ │ ZV clearData(), 2 │ │ ├── ./usr/share/doc/spooles-doc/misc.ps.gz │ │ │ ├── misc.ps │ │ │ │ @@ -11,15 +11,15 @@ │ │ │ │ %%EndComments │ │ │ │ %%BeginDefaults │ │ │ │ %%ViewingOrientation: 1 0 0 1 │ │ │ │ %%EndDefaults │ │ │ │ %DVIPSWebPage: (www.radicaleye.com) │ │ │ │ %DVIPSCommandLine: dvips main -o misc.ps │ │ │ │ %DVIPSParameters: dpi=600 │ │ │ │ -%DVIPSSource: TeX output 2026.01.06:2034 │ │ │ │ +%DVIPSSource: TeX output 2026.01.17:2301 │ │ │ │ %%BeginProcSet: tex.pro 0 0 │ │ │ │ %! │ │ │ │ /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S │ │ │ │ N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 │ │ │ │ mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 │ │ │ │ 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ │ │ │ │ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize │ │ │ │ @@ -2250,16 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1107 4 v 1289 100 a Fl(Misc)29 │ │ │ │ +b Fh(:)41 b Fj(DRAFT)121 b Fh(Jan)m(uary)30 b(17,)h(2026)p │ │ │ │ +2700 100 V 1107 w Fp(15)337 399 y Ff(\210)45 b Fl(type)29 │ │ │ │ b Fp(is)i(the)f(t)m(yp)s(e)h(of)g(en)m(tries)500 545 │ │ │ │ y Fo({)45 b Fl(1)30 b Fp(|)h(\()p Fl(SPOOLES)p 1174 545 │ │ │ │ 29 4 v 32 w(REAL)p Fp(\))f(for)g(real)h(en)m(tries)500 │ │ │ │ 674 y Fo({)45 b Fl(2)30 b Fp(|)h(\()p Fl(SPOOLES)p 1174 │ │ │ │ 674 V 32 w(COMPLEX)p Fp(\))e(for)h(complex)h(en)m(tries)337 │ │ │ │ 820 y Ff(\210)45 b Fp(The)27 b Fl(matrixFileName)d Fp(parameter)k(is)g │ │ │ │ (the)f(name)h(of)g(the)f(input)g(\014le)h(for)f(the)h(matrix)g(en)m │ │ │ │ ├── ps2ascii {} │ │ │ │ │ @@ -17,15 +17,15 @@ │ │ │ │ │ The method calls itself recursively. To find the permutation for an n1 x n2 x n3 grid, call │ │ │ │ │ mkNDperm(n1, n2, n3, newToOld, 0, n1-1, 0, n2-1, 0, n3-1) ; │ │ │ │ │ from a driver program. │ │ │ │ │ Error checking: If n1, n2 or n3 are less than or equal to zero, or if newToOld is NULL, or if │ │ │ │ │ west, south or bottom are less than or equal to zero, of if east ≥ n1, of if north ≥ n2, of if │ │ │ │ │ top ≥ n3, an error message is printed and the program exits. │ │ │ │ │ 1 │ │ │ │ │ - 2 Misc : DRAFT January 6, 2026 │ │ │ │ │ + 2 Misc : DRAFT January 17, 2026 │ │ │ │ │ 2. void mkNDperm2 ( int n1, int n2, int n3, int newToOld[], int west, │ │ │ │ │ int east, int south, int north, int bottom, int top ) ; │ │ │ │ │ This method this vector fills a permutation vector with the nested dissection new-to-old │ │ │ │ │ ordering of the vertices for the subgrid defined by nodes whose coordinates lie in │ │ │ │ │ [west, east] x [south, north] x [bottom, top]. │ │ │ │ │ There is one important difference between this method and mkNDperm() above; this method │ │ │ │ │ finds double-wide separators, necessary for an operator with more than nearest neighbor grid │ │ │ │ │ @@ -58,15 +58,15 @@ │ │ │ │ │ tains a dsizes1[q1] x dsizes2[q2] x disizes3[q3] subgrid of points. │ │ │ │ │ Error checking: If n1, n2 or n3 are less than or equal to zero, or if p1, p2 or p3 are less than or │ │ │ │ │ equal to zero, or if 2p1−1 > n1, or if 2p2−1 > n2, or if 2p3−1 > n3, or if oldToNew is NULL, │ │ │ │ │ or if dsizes1[], disizes2[] and dsizes3[] are not NULL but have invalid entries (all entries │ │ │ │ │ must be positive, entries in dsizes1[] must sum to n1 - p1 + 1, entries in dsizes2[] must │ │ │ │ │ sum to n2 - p2 + 1, and entries in dsizes3[] must sum to n3 - p3 + 1, an error message │ │ │ │ │ is printed and the program exits. │ │ │ │ │ - Misc : DRAFT January 6, 2026 3 │ │ │ │ │ + Misc : DRAFT January 17, 2026 3 │ │ │ │ │ 5. void fp2DGrid ( int n1, int n2, int ivec[], FILE *fp ) ; │ │ │ │ │ This method writes the ivec[] vector onto an n1 x n2 grid to file fp. This is useful to │ │ │ │ │ visualize an ordering or a metric on a grid. │ │ │ │ │ Error checking: If n1 or n2 are less than or equal to zero, or if ivec or fp are NULL, an error │ │ │ │ │ message is printed and the program exits. │ │ │ │ │ 6. void fp3DGrid ( int n1, int n2, int n3, int ivec[], FILE *fp ) ; │ │ │ │ │ This method writes the ivec[] vector onto an n1 x n2 x n3 grid to file fp. This is useful │ │ │ │ │ @@ -96,15 +96,15 @@ │ │ │ │ │ This method returns a front tree ETree object for a multiple minimum degree ordering of │ │ │ │ │ the graph graph. The seed parameter is a random number seed. The msglvl and msgFile │ │ │ │ │ parameters govern the diagnostics output. Use msglvl = 0 for no output, msglvl = 1 for │ │ │ │ │ timings and scalar statistics, and use msglvl > 1 with care, for it can generate huge amounts │ │ │ │ │ of output. │ │ │ │ │ Error checking: If graph is NULL, or if msglvl > 0 and msgFile is NULL, an error message is │ │ │ │ │ printed and the program exits. │ │ │ │ │ - 4 Misc : DRAFT January 6, 2026 │ │ │ │ │ + 4 Misc : DRAFT January 17, 2026 │ │ │ │ │ 2. ETree * orderViaND ( Graph *graph, int maxdomainsize, int seed, │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method returns a front tree ETree object for a nested dissection ordering of the graph │ │ │ │ │ graph. If a subgraph has more vertices than the maxdomainsize parameter, it is split. The │ │ │ │ │ seed parameter is a random number seed. The msglvl and msgFile parameters govern │ │ │ │ │ the diagnostics output. Use msglvl = 0 for no output, msglvl = 1 for timings and scalar │ │ │ │ │ statistics, and use msglvl > 1 with care, for it can generate huge amounts of output. │ │ │ │ │ @@ -136,15 +136,15 @@ │ │ │ │ │ double linewidth2, double radius, char *epsFileName, │ │ │ │ │ int msglvl, FILE *msgFile ) ; │ │ │ │ │ This method is used to create an EPS (Encapsulated Postscript) file that contains a picture │ │ │ │ │ of a graph in two dimensions. We use this to visualize separators and domain decompositions, │ │ │ │ │ mostly of regular grids and triangulations of a planar region. │ │ │ │ │ The graph object defines the connectivity of the vertices. The coords object defines the │ │ │ │ │ locations of the vertices. The tagsIV object is used to define whether or not an edge is │ │ │ │ │ - Misc : DRAFT January 6, 2026 5 │ │ │ │ │ + Misc : DRAFT January 17, 2026 5 │ │ │ │ │ drawn between two vertices adjacent in the graph. When tagsIV is not NULL, if there is an │ │ │ │ │ edge (u,v) in the graph and tags[u] = tags[v], then the edge with width linewidth1 is │ │ │ │ │ drawn. For edges (u,v) in the graph and tags[u] != tags[v], then the edge with width │ │ │ │ │ linewidth2is drawn, assuming linewidth2> 0. If tagsIV is NULL, than all edges are drawn │ │ │ │ │ with width linewidth1. Each vertex is draw with a filled circle with radius radius. │ │ │ │ │ The graph and its Coords object occupy a certain area in 2-D space. We try to plot the │ │ │ │ │ graph inside the area defined by the rect[] array in such a manner that the relative scales │ │ │ │ │ @@ -177,15 +177,15 @@ │ │ │ │ │ InpMtx **pmtxA, DenseMtx **pmtxX, DenseMtx **pmtxB ) ; │ │ │ │ │ This method creates a linear system AX = B for a natural factor formulation of a n1×n2×n3 │ │ │ │ │ grid. If n1, n2 and n3 are all greater than 1, the grid is formed of linear hexahedral elements │ │ │ │ │ andthematrixAhas8*n1*n2*n3rows. Ifoneofn1,n2andn3isequalto1,thegridisformed │ │ │ │ │ of linear quadrilateral elements and the matrix A has 4*n1*n2*n3 rows. The entries in A and │ │ │ │ │ X are random numbers, B is computed as the product of A with X. A can be real (type = │ │ │ │ │ 1) or complex (type = 2). The number of columns of X is given by nrhs. The linear system │ │ │ │ │ - 6 Misc : DRAFT January 6, 2026 │ │ │ │ │ + 6 Misc : DRAFT January 17, 2026 │ │ │ │ │ is ordered using theoretical nested dissection, and the front tree is transformed using the │ │ │ │ │ maxzeros and maxsize parameters. The addresses of the front tree, symbolic factorization, │ │ │ │ │ and three matrix objects are returned in the last five arguments of the calling sequence. │ │ │ │ │ Error checking: None presently. │ │ │ │ │ 1.2 Driver programs found in the Misc directory │ │ │ │ │ This section contains brief descriptions of the driver programs. │ │ │ │ │ 1. testNDperm msglvl msgFile n1 n2 n3 outPermFile │ │ │ │ │ @@ -215,15 +215,15 @@ │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The ETreeFile parameter is the output file for the ETree object. If ETreeFile is none │ │ │ │ │ then the ETree object is not written to a file. Otherwise, the ETree writeToFile() │ │ │ │ │ method is called to write the object to a formatted file (if ETreeFile is of the form │ │ │ │ │ *.etreef), or a binary file (if ETreeFile is of the form *.etreeb). │ │ │ │ │ - Misc : DRAFT January 6, 2026 7 │ │ │ │ │ + Misc : DRAFT January 17, 2026 7 │ │ │ │ │ 3. testOrderViaND msglvl msgFile GraphFile maxdomainsize seed ETreeFile │ │ │ │ │ This program reads in a Graph object from a file and computes a generalized nested dissection │ │ │ │ │ ordering of the graph. │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the Perm object is written to the output file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ @@ -254,15 +254,15 @@ │ │ │ │ │ • The seed parameter is a random number seed. │ │ │ │ │ • The ETreeFile parameter is the output file for the ETree object. If ETreeFile is none │ │ │ │ │ then the ETree object is not written to a file. Otherwise, the ETree writeToFile() │ │ │ │ │ method is called to write the object to a formatted file (if ETreeFile is of the form │ │ │ │ │ *.etreef), or a binary file (if ETreeFile is of the form *.etreeb). │ │ │ │ │ 5. drawGraph msglvl msgFile inGraphFile inCoordsFile inTagsIVfile │ │ │ │ │ outEPSfile linewidth1 linewidth2 bbox[4] rect[4] radius │ │ │ │ │ - 8 Misc : DRAFT January 6, 2026 │ │ │ │ │ + 8 Misc : DRAFT January 17, 2026 │ │ │ │ │ This driver program generates a Encapsulated Postscript file outEPSfile of a 2-D graph │ │ │ │ │ using a Graph object, a Coords object and a tags IV object that contains the component ids │ │ │ │ │ of the vertices. │ │ │ │ │ See the doDraw script file in this directory for an example calling sequence. │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ that all objects are written to the output file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ @@ -293,48 +293,48 @@ │ │ │ │ │ See Figure 1.1 for a plot of the graph of R2D100, a randomly triangulated grid with 100 │ │ │ │ │ vertices with linewidth1 = 3. Figure 1.2 illustrates a domain decomposition obtained from │ │ │ │ │ the fishnet algorithm of Chapter ?? with linewidth1 = 3 and linewidth2 = 0.1. │ │ │ │ │ 6. testSemi msglvl msgFile GraphFile ETreeFile mapFile │ │ │ │ │ This program is used to compute the effect of using a semi-implicit factorization to solve │ │ │ │ │ AX=" A0,0 A0,1 #" X0 #=" B0 #=B. │ │ │ │ │ A1,0 A1,1 X1 B1 │ │ │ │ │ - Misc : DRAFT January 6, 2026 9 │ │ │ │ │ + Misc : DRAFT January 17, 2026 9 │ │ │ │ │ Figure 1.1: R2D100 │ │ │ │ │ - 10 Misc : DRAFT January 6, 2026 │ │ │ │ │ + 10 Misc : DRAFT January 17, 2026 │ │ │ │ │ Figure 1.2: R2D100: fishnet domain decomposition │ │ │ │ │ - 3 3 3 3 3 3 3 0 0 5 │ │ │ │ │ + 3 3 3 3 3 3 3 0 0 5 │ │ │ │ │ 3 │ │ │ │ │ - 3 3 3 0 0 │ │ │ │ │ + 3 3 3 0 0 │ │ │ │ │ 3 3 │ │ │ │ │ 3 1 │ │ │ │ │ - 0 0 1 1 │ │ │ │ │ - 3 0 1 │ │ │ │ │ - 3 1 │ │ │ │ │ + 0 0 1 1 │ │ │ │ │ + 3 0 1 │ │ │ │ │ + 3 1 │ │ │ │ │ 0 1 │ │ │ │ │ - 2 0 1 1 │ │ │ │ │ + 2 0 1 1 │ │ │ │ │ 0 1 1 │ │ │ │ │ - 0 1 │ │ │ │ │ - 2 2 1 1 1 │ │ │ │ │ - 2 1 │ │ │ │ │ - 0 11 │ │ │ │ │ - 2 1 │ │ │ │ │ - 2 2 0 1 1 │ │ │ │ │ + 0 1 │ │ │ │ │ + 2 2 1 1 1 │ │ │ │ │ + 2 1 │ │ │ │ │ + 0 11 │ │ │ │ │ + 2 1 │ │ │ │ │ + 2 2 0 1 1 │ │ │ │ │ 1 1 │ │ │ │ │ - 2 1 │ │ │ │ │ - 2 2 0 1 0 │ │ │ │ │ - 0 1 │ │ │ │ │ - 2 2 0 │ │ │ │ │ - 2 2 0 4 │ │ │ │ │ - 4 0 0 │ │ │ │ │ - 0 4 │ │ │ │ │ + 2 1 │ │ │ │ │ + 2 2 0 1 0 │ │ │ │ │ + 0 1 │ │ │ │ │ + 2 2 0 │ │ │ │ │ + 2 2 0 4 │ │ │ │ │ + 4 0 0 │ │ │ │ │ + 0 4 │ │ │ │ │ 2 2 4 │ │ │ │ │ - 2 2 4 4 │ │ │ │ │ - 0 4 4 │ │ │ │ │ - 2 2 0 4 4 4 4 4 4 4 │ │ │ │ │ - Misc : DRAFT January 6, 2026 11 │ │ │ │ │ + 2 2 4 4 │ │ │ │ │ + 0 4 4 │ │ │ │ │ + 2 2 0 4 4 4 4 4 4 4 │ │ │ │ │ + Misc : DRAFT January 17, 2026 11 │ │ │ │ │ Ais factored as " # " #" # │ │ │ │ │ A A L 0 U U │ │ │ │ │ 0,0 0,1 = 0,0 0,0 0,1 , │ │ │ │ │ A A L L 0 U │ │ │ │ │ 1,0 1,1 1,0 1,1 1,1 │ │ │ │ │ and to solve AX = B, we do the following steps. │ │ │ │ │ • solve L Y =B │ │ │ │ │ @@ -378,15 +378,15 @@ │ │ │ │ │ • The msglvl parameter determines the amount of output. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ • The GraphFile parameter is the input file for the Graph object. It must be of the form │ │ │ │ │ *.graphfor*.graphb. TheGraphobjectisreadfromthefileviatheGraph readFromFile() │ │ │ │ │ method. │ │ │ │ │ - 12 Misc : DRAFT January 6, 2026 │ │ │ │ │ + 12 Misc : DRAFT January 17, 2026 │ │ │ │ │ • The ETreeFile parameter is the input file for the ETree object. It must be of the form │ │ │ │ │ *.etreefor*.etreeb. TheETreeobjectisreadfromthefileviatheETree readFromFile() │ │ │ │ │ method. │ │ │ │ │ • The mapFile parameter is the input file for the map IV object. It must be of the form │ │ │ │ │ *.ivfor *.ivb. The IV object is read from the file via the IV readFromFile() method. │ │ │ │ │ 7. allInOne msglvl msgFile type symmetryflag pivotingflag │ │ │ │ │ matrixFileName rhsFileName seed │ │ │ │ │ @@ -418,15 +418,15 @@ │ │ │ │ │ ... │ │ │ │ │ irow jcol value │ │ │ │ │ ... │ │ │ │ │ where the first line has the number of rows, columns and entries. (Note, for this driver │ │ │ │ │ program nrow must be equal to ncol since we are factoring a square matrix.) Each of │ │ │ │ │ the nent following lines contain one nonzero entry. For a complex matrix, the file has │ │ │ │ │ this structure. │ │ │ │ │ - Misc : DRAFT January 6, 2026 13 │ │ │ │ │ + Misc : DRAFT January 17, 2026 13 │ │ │ │ │ nrow ncol nent │ │ │ │ │ ... │ │ │ │ │ irow jcol real_value imag_value │ │ │ │ │ ... │ │ │ │ │ For both real and complex entries, the entries need not be disjoint, i.e., entries with the │ │ │ │ │ same irow and jcol values are summed. │ │ │ │ │ • The rhsFileNameparameter is the name of the input file for the right hand side matrix. │ │ │ │ │ @@ -457,15 +457,15 @@ │ │ │ │ │ • The type parameter specifies a real or complex linear system. │ │ │ │ │ – type = 1 (SPOOLES REAL) for real, │ │ │ │ │ – type = 2 (SPOOLES COMPLEX) for complex. │ │ │ │ │ • The symmetryflag parameter specifies the symmetry of the matrix. │ │ │ │ │ – type = 0 (SPOOLES SYMMETRIC) for A real or complex symmetric, │ │ │ │ │ – type = 1 (SPOOLES HERMITIAN) for A complex Hermitian, │ │ │ │ │ – type = 2 (SPOOLES NONSYMMETRIC) │ │ │ │ │ - 14 Misc : DRAFT January 6, 2026 │ │ │ │ │ + 14 Misc : DRAFT January 17, 2026 │ │ │ │ │ for A real or complex nonsymmetric. │ │ │ │ │ • The patchAndGoFlag specifies the “patch-and-go” strategy. │ │ │ │ │ – patchAndGoFlag = 0—ifazeropivotisdetected, stopcomputingthefactorization, │ │ │ │ │ set the error flag and return. │ │ │ │ │ – patchAndGoFlag = 1 — if a small or zero pivot is detected, set the diagonal entry │ │ │ │ │ to 1 and the offdiagonal entries to zero. │ │ │ │ │ – patchAndGoFlag = 2 — if a small or zero pivot is detected, perturb the diagonal │ │ │ │ │ @@ -497,15 +497,15 @@ │ │ │ │ │ right hand side entries are read in from a file, and the system is solved. One input parameter │ │ │ │ │ specifies the type of system (real or complex). │ │ │ │ │ • The msglvl parameter determines the amount of output — taking msglvl >= 3 means │ │ │ │ │ the Perm object is written to the output file. │ │ │ │ │ • The msgFile parameter determines the message file — if msgFile is stdout, then the │ │ │ │ │ message file is stdout, otherwise a file is opened with append status to receive any output │ │ │ │ │ data. │ │ │ │ │ - Misc : DRAFT January 6, 2026 15 │ │ │ │ │ + Misc : DRAFT January 17, 2026 15 │ │ │ │ │ • type is the type of entries │ │ │ │ │ – 1 — (SPOOLES REAL) for real entries │ │ │ │ │ – 2 — (SPOOLES COMPLEX) for complex entries │ │ │ │ │ • The matrixFileName parameter is the name of the input file for the matrix entries. For │ │ │ │ │ a real matrix, this file must have the following form. │ │ │ │ │ nrow ncol nent │ │ │ │ │ ...