Mercurial > octave
view libinterp/corefcn/symbfact.cc @ 31605:e88a07dec498 stable
maint: Use macros to begin/end C++ namespaces.
* oct-conf-post-public.in.h: Define two macros (OCTAVE_BEGIN_NAMESPACE,
OCTAVE_END_NAMESPACE) that can be used to start/end a namespace.
* mk-opts.pl, build-env.h, build-env.in.cc, __betainc__.cc, __contourc__.cc,
__dsearchn__.cc, __eigs__.cc, __expint__.cc, __ftp__.cc, __gammainc__.cc,
__ichol__.cc, __ilu__.cc, __isprimelarge__.cc, __lin_interpn__.cc,
__magick_read__.cc, __pchip_deriv__.cc, __qp__.cc, amd.cc, auto-shlib.cc,
auto-shlib.h, balance.cc, base-text-renderer.cc, base-text-renderer.h,
besselj.cc, bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
call-stack.cc, call-stack.h, ccolamd.cc, cellfun.cc, chol.cc, colamd.cc,
colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc, data.h, debug.cc,
defaults.cc, defaults.h, defun-int.h, defun.cc, det.cc, dirfns.cc, display.cc,
display.h, dlmread.cc, dmperm.cc, dot.cc, dynamic-ld.cc, dynamic-ld.h, eig.cc,
ellipj.cc, environment.cc, environment.h, error.cc, error.h, errwarn.h,
event-manager.cc, event-manager.h, event-queue.cc, event-queue.h, fcn-info.cc,
fcn-info.h, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
ft-text-renderer.cc, ft-text-renderer.h, gcd.cc, getgrent.cc, getpwent.cc,
getrusage.cc, givens.cc, gl-render.cc, gl-render.h, gl2ps-print.cc,
gl2ps-print.h, graphics-toolkit.cc, graphics-toolkit.h, graphics.cc,
graphics.in.h, gsvd.cc, gtk-manager.cc, gtk-manager.h, hash.cc, help.cc,
help.h, hess.cc, hex2num.cc, hook-fcn.cc, hook-fcn.h, input.cc, input.h,
interpreter-private.cc, interpreter-private.h, interpreter.cc, interpreter.h,
inv.cc, jsondecode.cc, jsonencode.cc, kron.cc, latex-text-renderer.cc,
latex-text-renderer.h, load-path.cc, load-path.h, load-save.cc, load-save.h,
lookup.cc, ls-ascii-helper.cc, ls-ascii-helper.h, ls-oct-text.cc, ls-utils.cc,
ls-utils.h, lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex-private.h,
mex.cc, mgorth.cc, nproc.cc, oct-fstrm.cc, oct-fstrm.h, oct-hdf5-types.cc,
oct-hdf5-types.h, oct-hist.cc, oct-hist.h, oct-iostrm.cc, oct-iostrm.h,
oct-opengl.h, oct-prcstrm.cc, oct-prcstrm.h, oct-procbuf.cc, oct-procbuf.h,
oct-process.cc, oct-process.h, oct-stdstrm.h, oct-stream.cc, oct-stream.h,
oct-strstrm.cc, oct-strstrm.h, oct-tex-lexer.in.ll, oct-tex-parser.yy,
ordqz.cc, ordschur.cc, pager.cc, pager.h, pinv.cc, pow2.cc, pr-flt-fmt.cc,
pr-output.cc, procstream.cc, procstream.h, psi.cc, qr.cc, quad.cc, quadcc.cc,
qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, settings.cc, settings.h,
sighandlers.cc, sighandlers.h, sparse-xdiv.cc, sparse-xdiv.h, sparse-xpow.cc,
sparse-xpow.h, sparse.cc, spparms.cc, sqrtm.cc, stack-frame.cc, stack-frame.h,
stream-euler.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc, sylvester.cc,
symbfact.cc, syminfo.cc, syminfo.h, symrcm.cc, symrec.cc, symrec.h,
symscope.cc, symscope.h, symtab.cc, symtab.h, syscalls.cc, sysdep.cc, sysdep.h,
text-engine.cc, text-engine.h, text-renderer.cc, text-renderer.h, time.cc,
toplev.cc, tril.cc, tsearch.cc, typecast.cc, url-handle-manager.cc,
url-handle-manager.h, urlwrite.cc, utils.cc, utils.h, variables.cc,
variables.h, xdiv.cc, xdiv.h, xnorm.cc, xnorm.h, xpow.cc, xpow.h,
__delaunayn__.cc, __fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __ode15__.cc, __voronoi__.cc, audiodevinfo.cc,
audioread.cc, convhulln.cc, fftw.cc, gzip.cc, mk-build-env-features.sh,
mk-builtins.pl, cdef-class.cc, cdef-class.h, cdef-fwd.h, cdef-manager.cc,
cdef-manager.h, cdef-method.cc, cdef-method.h, cdef-object.cc, cdef-object.h,
cdef-package.cc, cdef-package.h, cdef-property.cc, cdef-property.h,
cdef-utils.cc, cdef-utils.h, ov-base.cc, ov-base.h, ov-bool-mat.cc,
ov-builtin.h, ov-cell.cc, ov-class.cc, ov-class.h, ov-classdef.cc,
ov-classdef.h, ov-complex.cc, ov-fcn-handle.cc, ov-fcn-handle.h, ov-fcn.h,
ov-java.cc, ov-java.h, ov-mex-fcn.h, ov-null-mat.cc, ov-oncleanup.cc,
ov-struct.cc, ov-typeinfo.cc, ov-typeinfo.h, ov-usr-fcn.cc, ov-usr-fcn.h,
ov.cc, ov.h, octave.cc, octave.h, mk-ops.sh, op-b-b.cc, op-b-bm.cc,
op-b-sbm.cc, op-bm-b.cc, op-bm-bm.cc, op-bm-sbm.cc, op-cdm-cdm.cc, op-cell.cc,
op-chm.cc, op-class.cc, op-cm-cm.cc, op-cm-cs.cc, op-cm-m.cc, op-cm-s.cc,
op-cm-scm.cc, op-cm-sm.cc, op-cs-cm.cc, op-cs-cs.cc, op-cs-m.cc, op-cs-s.cc,
op-cs-scm.cc, op-cs-sm.cc, op-dm-dm.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-fcdm-fcdm.cc, op-fcm-fcm.cc,
op-fcm-fcs.cc, op-fcm-fm.cc, op-fcm-fs.cc, op-fcn.cc, op-fcs-fcm.cc,
op-fcs-fcs.cc, op-fcs-fm.cc, op-fcs-fs.cc, op-fdm-fdm.cc, op-fm-fcm.cc,
op-fm-fcs.cc, op-fm-fm.cc, op-fm-fs.cc, op-fs-fcm.cc, op-fs-fcs.cc,
op-fs-fm.cc, op-fs-fs.cc, op-i16-i16.cc, op-i32-i32.cc, op-i64-i64.cc,
op-i8-i8.cc, op-int-concat.cc, op-m-cm.cc, op-m-cs.cc, op-m-m.cc, op-m-s.cc,
op-m-scm.cc, op-m-sm.cc, op-mi.cc, op-pm-pm.cc, op-pm-scm.cc, op-pm-sm.cc,
op-pm-template.cc, op-range.cc, op-s-cm.cc, op-s-cs.cc, op-s-m.cc, op-s-s.cc,
op-s-scm.cc, op-s-sm.cc, op-sbm-b.cc, op-sbm-bm.cc, op-sbm-sbm.cc,
op-scm-cm.cc, op-scm-cs.cc, op-scm-m.cc, op-scm-s.cc, op-scm-scm.cc,
op-scm-sm.cc, op-sm-cm.cc, op-sm-cs.cc, op-sm-m.cc, op-sm-s.cc, op-sm-scm.cc,
op-sm-sm.cc, op-str-m.cc, op-str-s.cc, op-str-str.cc, op-struct.cc,
op-ui16-ui16.cc, op-ui32-ui32.cc, op-ui64-ui64.cc, op-ui8-ui8.cc, ops.h,
anon-fcn-validator.cc, anon-fcn-validator.h, bp-table.cc, bp-table.h,
comment-list.cc, comment-list.h, filepos.h, lex.h, lex.ll, oct-lvalue.cc,
oct-lvalue.h, oct-parse.yy, parse.h, profiler.cc, profiler.h,
pt-anon-scopes.cc, pt-anon-scopes.h, pt-arg-list.cc, pt-arg-list.h,
pt-args-block.cc, pt-args-block.h, pt-array-list.cc, pt-array-list.h,
pt-assign.cc, pt-assign.h, pt-binop.cc, pt-binop.h, pt-bp.cc, pt-bp.h,
pt-cbinop.cc, pt-cbinop.h, pt-cell.cc, pt-cell.h, pt-check.cc, pt-check.h,
pt-classdef.cc, pt-classdef.h, pt-cmd.h, pt-colon.cc, pt-colon.h, pt-const.cc,
pt-const.h, pt-decl.cc, pt-decl.h, pt-eval.cc, pt-eval.h, pt-except.cc,
pt-except.h, pt-exp.cc, pt-exp.h, pt-fcn-handle.cc, pt-fcn-handle.h, pt-id.cc,
pt-id.h, pt-idx.cc, pt-idx.h, pt-jump.h, pt-loop.cc, pt-loop.h, pt-mat.cc,
pt-mat.h, pt-misc.cc, pt-misc.h, pt-pr-code.cc, pt-pr-code.h, pt-select.cc,
pt-select.h, pt-spmd.cc, pt-spmd.h, pt-stmt.cc, pt-stmt.h, pt-tm-const.cc,
pt-tm-const.h, pt-unop.cc, pt-unop.h, pt-vm-eval.cc, pt-walk.cc, pt-walk.h,
pt.cc, pt.h, token.cc, token.h, Range.cc, Range.h, idx-vector.cc, idx-vector.h,
range-fwd.h, CollocWt.cc, CollocWt.h, aepbalance.cc, aepbalance.h, chol.cc,
chol.h, gepbalance.cc, gepbalance.h, gsvd.cc, gsvd.h, hess.cc, hess.h,
lo-mappers.cc, lo-mappers.h, lo-specfun.cc, lo-specfun.h, lu.cc, lu.h,
oct-convn.cc, oct-convn.h, oct-fftw.cc, oct-fftw.h, oct-norm.cc, oct-norm.h,
oct-rand.cc, oct-rand.h, oct-spparms.cc, oct-spparms.h, qr.cc, qr.h, qrp.cc,
qrp.h, randgamma.cc, randgamma.h, randmtzig.cc, randmtzig.h, randpoisson.cc,
randpoisson.h, schur.cc, schur.h, sparse-chol.cc, sparse-chol.h, sparse-lu.cc,
sparse-lu.h, sparse-qr.cc, sparse-qr.h, svd.cc, svd.h, child-list.cc,
child-list.h, dir-ops.cc, dir-ops.h, file-ops.cc, file-ops.h, file-stat.cc,
file-stat.h, lo-sysdep.cc, lo-sysdep.h, lo-sysinfo.cc, lo-sysinfo.h,
mach-info.cc, mach-info.h, oct-env.cc, oct-env.h, oct-group.cc, oct-group.h,
oct-password.cc, oct-password.h, oct-syscalls.cc, oct-syscalls.h, oct-time.cc,
oct-time.h, oct-uname.cc, oct-uname.h, action-container.cc, action-container.h,
base-list.h, cmd-edit.cc, cmd-edit.h, cmd-hist.cc, cmd-hist.h, f77-fcn.h,
file-info.cc, file-info.h, lo-array-errwarn.cc, lo-array-errwarn.h, lo-hash.cc,
lo-hash.h, lo-ieee.h, lo-regexp.cc, lo-regexp.h, lo-utils.cc, lo-utils.h,
oct-base64.cc, oct-base64.h, oct-glob.cc, oct-glob.h, oct-inttypes.h,
oct-mutex.cc, oct-mutex.h, oct-refcount.h, oct-shlib.cc, oct-shlib.h,
oct-sparse.cc, oct-sparse.h, oct-string.h, octave-preserve-stream-state.h,
pathsearch.cc, pathsearch.h, quit.cc, quit.h, unwind-prot.cc, unwind-prot.h,
url-transfer.cc, url-transfer.h : Use new macros to begin/end C++ namespaces.
author | Rik <rik@octave.org> |
---|---|
date | Thu, 01 Dec 2022 14:23:45 -0800 |
parents | 83f9f8bda883 |
children | 597f3ee61a48 |
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//////////////////////////////////////////////////////////////////////// // // Copyright (C) 1998-2022 The Octave Project Developers // // See the file COPYRIGHT.md in the top-level directory of this // distribution or <https://octave.org/copyright/>. // // This file is part of Octave. // // Octave is free software: you can redistribute it and/or modify it // under the terms of the GNU General Public License as published by // the Free Software Foundation, either version 3 of the License, or // (at your option) any later version. // // Octave is distributed in the hope that it will be useful, but // WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // // You should have received a copy of the GNU General Public License // along with Octave; see the file COPYING. If not, see // <https://www.gnu.org/licenses/>. // //////////////////////////////////////////////////////////////////////// #if defined (HAVE_CONFIG_H) # include "config.h" #endif #include <cmath> #include <algorithm> #include <string> #include "CSparse.h" #include "boolSparse.h" #include "dColVector.h" #include "dSparse.h" #include "oct-locbuf.h" #include "oct-sparse.h" #include "oct-spparms.h" #include "sparse-util.h" #include "defun.h" #include "error.h" #include "errwarn.h" #include "ovl.h" #include "parse.h" #include "utils.h" OCTAVE_BEGIN_NAMESPACE(octave) DEFUN (symbfact, args, nargout, doc: /* -*- texinfo -*- @deftypefn {} {[@var{count}, @var{h}, @var{parent}, @var{post}, @var{R}] =} symbfact (@var{S}) @deftypefnx {} {[@dots{}] =} symbfact (@var{S}, @var{typ}) @deftypefnx {} {[@dots{}] =} symbfact (@var{S}, @var{typ}, @var{mode}) Perform a symbolic factorization analysis of the sparse matrix @var{S}. The input variables are @table @var @item S @var{S} is a real or complex sparse matrix. @item typ Is the type of the factorization and can be one of @table @asis @item @qcode{"sym"} (default) Factorize @var{S}. Assumes @var{S} is symmetric and uses the upper triangular portion of the matrix. @item @qcode{"col"} Factorize @tcode{@var{S}' * @var{S}}. @item @qcode{"row"} Factorize @tcode{@var{S} * @var{S}'}. @item @qcode{"lo"} Factorize @tcode{@var{S}'}. Assumes @var{S} is symmetric and uses the lower triangular portion of the matrix. @end table @item mode When @var{mode} is unspecified return the Cholesky@tie{}factorization for @var{R}. If @var{mode} is @qcode{"lower"} or @qcode{"L"} then return the conjugate transpose @tcode{@var{R}'} which is a lower triangular factor. The conjugate transpose version is faster and uses less memory, but still returns the same values for all other outputs: @var{count}, @var{h}, @var{parent}, and @var{post}. @end table The output variables are: @table @var @item count The row counts of the Cholesky@tie{}factorization as determined by @var{typ}. The computational difficulty of performing the true factorization using @code{chol} is @code{sum (@var{count} .^ 2)}. @item h The height of the elimination tree. @item parent The elimination tree itself. @item post A sparse boolean matrix whose structure is that of the Cholesky@tie{}factorization as determined by @var{typ}. @end table @seealso{chol, etree, treelayout} @end deftypefn */) { #if defined (HAVE_CHOLMOD) int nargin = args.length (); if (nargin < 1 || nargin > 3) print_usage (); octave_value_list retval; double dummy; cholmod_sparse Astore; cholmod_sparse *A = &Astore; A->packed = true; A->sorted = true; A->nz = nullptr; #if defined (OCTAVE_ENABLE_64) A->itype = CHOLMOD_LONG; #else A->itype = CHOLMOD_INT; #endif A->dtype = CHOLMOD_DOUBLE; A->stype = 1; A->x = &dummy; SparseMatrix sm; SparseComplexMatrix scm; if (args(0).isreal ()) { sm = args(0).sparse_matrix_value (); A->nrow = sm.rows (); A->ncol = sm.cols (); A->p = sm.cidx (); A->i = sm.ridx (); A->nzmax = sm.nnz (); A->xtype = CHOLMOD_REAL; if (A->nrow > 0 && A->ncol > 0) A->x = sm.data (); } else if (args(0).iscomplex ()) { scm = args(0).sparse_complex_matrix_value (); A->nrow = scm.rows (); A->ncol = scm.cols (); A->p = scm.cidx (); A->i = scm.ridx (); A->nzmax = scm.nnz (); A->xtype = CHOLMOD_COMPLEX; if (A->nrow > 0 && A->ncol > 0) A->x = scm.data (); } else err_wrong_type_arg ("symbfact", args(0)); bool coletree = false; octave_idx_type n = A->nrow; if (nargin > 1) { std::string str = args(1).xstring_value ("TYP must be a string"); // FIXME: The input validation could be improved to use strncmp char ch; ch = tolower (str[0]); if (ch == 'r') // 'row' A->stype = 0; else if (ch == 'c') // 'col' { n = A->ncol; coletree = true; A->stype = 0; } else if (ch == 's') // 'sym' (default) A->stype = 1; else if (ch == 'l') // 'lo' A->stype = -1; else error (R"(symbfact: unrecognized TYP "%s")", str.c_str ()); } if (nargin == 3) { std::string str = args(2).xstring_value ("MODE must be a string"); // FIXME: The input validation could be improved to use strncmp char ch; ch = toupper (str[0]); if (ch != 'L') error (R"(symbfact: unrecognized MODE "%s")", str.c_str ()); } if (A->stype && A->nrow != A->ncol) err_square_matrix_required ("symbfact", "S"); OCTAVE_LOCAL_BUFFER (suitesparse_integer, Parent, n); OCTAVE_LOCAL_BUFFER (suitesparse_integer, Post, n); OCTAVE_LOCAL_BUFFER (suitesparse_integer, ColCount, n); OCTAVE_LOCAL_BUFFER (suitesparse_integer, First, n); OCTAVE_LOCAL_BUFFER (octave_idx_type, Level, n); cholmod_common Common; cholmod_common *cm = &Common; CHOLMOD_NAME(start) (cm); double spu = sparse_params::get_key ("spumoni"); if (spu == 0.0) { cm->print = -1; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, nullptr); } else { cm->print = static_cast<int> (spu) + 2; SUITESPARSE_ASSIGN_FPTR (printf_func, cm->print_function, &SparseCholPrint); } cm->error_handler = &SparseCholError; SUITESPARSE_ASSIGN_FPTR2 (divcomplex_func, cm->complex_divide, divcomplex); SUITESPARSE_ASSIGN_FPTR2 (hypot_func, cm->hypotenuse, hypot); cholmod_sparse *F = CHOLMOD_NAME(transpose) (A, 0, cm); cholmod_sparse *Aup, *Alo; if (A->stype == 1 || coletree) { Aup = A; Alo = F; } else { Aup = F; Alo = A; } CHOLMOD_NAME(etree) (Aup, Parent, cm); ColumnVector tmp (n); // Declaration must precede any goto cleanup. std::string err_msg; if (cm->status < CHOLMOD_OK) { err_msg = "symbfact: matrix corrupted"; goto cleanup; } if (CHOLMOD_NAME(postorder) (Parent, n, nullptr, Post, cm) != n) { err_msg = "symbfact: postorder failed"; goto cleanup; } CHOLMOD_NAME(rowcolcounts) (Alo, nullptr, 0, Parent, Post, nullptr, ColCount, First, to_suitesparse_intptr (Level), cm); if (cm->status < CHOLMOD_OK) { err_msg = "symbfact: matrix corrupted"; goto cleanup; } if (nargout > 4) { cholmod_sparse *A1, *A2; if (A->stype == 1) { A1 = A; A2 = nullptr; } else if (A->stype == -1) { A1 = F; A2 = nullptr; } else if (coletree) { A1 = F; A2 = A; } else { A1 = A; A2 = F; } // count the total number of entries in L octave_idx_type lnz = 0; for (octave_idx_type j = 0 ; j < n ; j++) lnz += ColCount[j]; // allocate the output matrix L (pattern-only) SparseBoolMatrix L (dim_vector (n, n), lnz); // initialize column pointers lnz = 0; for (octave_idx_type j = 0 ; j < n ; j++) { L.xcidx(j) = lnz; lnz += ColCount[j]; } L.xcidx(n) = lnz; // create a copy of the column pointers suitesparse_integer *W = First; for (octave_idx_type j = 0 ; j < n ; j++) W[j] = L.xcidx (j); // get workspace for computing one row of L cholmod_sparse *R = CHOLMOD_NAME(allocate_sparse) (n, 1, n, false, true, 0, CHOLMOD_PATTERN, cm); octave_idx_type *Rp = static_cast<octave_idx_type *> (R->p); octave_idx_type *Ri = static_cast<octave_idx_type *> (R->i); // compute L one row at a time for (octave_idx_type k = 0 ; k < n ; k++) { // get the kth row of L and store in the columns of L CHOLMOD_NAME(row_subtree) (A1, A2, k, Parent, R, cm); for (octave_idx_type p = 0 ; p < Rp[1] ; p++) L.xridx (W[Ri[p]]++) = k; // add the diagonal entry L.xridx (W[k]++) = k; } // free workspace CHOLMOD_NAME(free_sparse) (&R, cm); // fill L with one's std::fill_n (L.xdata (), lnz, true); // transpose L to get R, or leave as is if (nargin < 3) L = L.transpose (); retval(4) = L; } if (nargout > 3) { for (octave_idx_type i = 0; i < n; i++) tmp(i) = Post[i] + 1; retval(3) = tmp; } if (nargout > 2) { for (octave_idx_type i = 0; i < n; i++) tmp(i) = Parent[i] + 1; retval(2) = tmp; } if (nargout > 1) { // compute the elimination tree height octave_idx_type height = 0; for (int i = 0 ; i < n ; i++) height = std::max (height, Level[i]); height++; retval(1) = static_cast<double> (height); } for (octave_idx_type i = 0; i < n; i++) tmp(i) = ColCount[i]; retval(0) = tmp; cleanup: CHOLMOD_NAME(free_sparse) (&F, cm); CHOLMOD_NAME(finish) (cm); if (! err_msg.empty ()) error ("%s", err_msg.c_str ()); return retval; #else octave_unused_parameter (args); octave_unused_parameter (nargout); err_disabled_feature ("symbfact", "CHOLMOD"); #endif } /* %!testif HAVE_CHOLMOD %! A = sparse (magic (3)); %! [count, h, parent, post, r] = symbfact (A); %! assert (count, [3; 2; 1]); %! assert (h, 3); %! assert (parent, [2; 3; 0]); %! assert (r, sparse (triu (true (3)))); %!testif HAVE_CHOLMOD %! ## Test MODE "lower" %! A = sparse (magic (3)); %! [~, ~, ~, ~, l] = symbfact (A, "sym", "lower"); %! assert (l, sparse (tril (true (3)))); %!testif HAVE_CHOLMOD <*42587> %! ## singular matrix %! A = sparse ([1 0 8;0 1 8;8 8 1]); %! [count, h, parent, post, r] = symbfact (A); ## Test input validation %!testif HAVE_CHOLMOD %! fail ("symbfact ()"); %! fail ("symbfact (1,2,3,4)"); %! fail ("symbfact ({1})", "wrong type argument 'cell'"); %! fail ("symbfact (sparse (1), {1})", "TYP must be a string"); %! fail ("symbfact (sparse (1), 'foobar')", 'unrecognized TYP "foobar"'); %! fail ("symbfact (sparse (1), 'sym', {'L'})", "MODE must be a string"); %! fail ('symbfact (sparse (1), "sym", "foobar")', %! 'unrecognized MODE "foobar"'); %! fail ("symbfact (sparse ([1, 2; 3, 4; 5, 6]))", "S must be a square matrix"); */ OCTAVE_END_NAMESPACE(octave)