Mercurial > octave
annotate libinterp/corefcn/dmperm.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 | 796f54d4ddbf |
| children | 597f3ee61a48 |
| rev | line source |
|---|---|
|
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1998-2022 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
| 5610 | 25 |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
| 5610 | 28 #endif |
| 29 | |
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30 #include "CSparse.h" |
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31 #include "dRowVector.h" |
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32 #include "dSparse.h" |
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33 #include "oct-sparse.h" |
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34 |
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35 #include "defun.h" |
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36 #include "errwarn.h" |
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37 #include "ov.h" |
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38 #include "ovl.h" |
| 5610 | 39 #include "utils.h" |
| 40 | |
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41 OCTAVE_BEGIN_NAMESPACE(octave) |
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42 |
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43 #if defined (OCTAVE_ENABLE_64) |
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44 # define CXSPARSE_NAME(name) cs_dl ## name |
| 5610 | 45 #else |
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46 # define CXSPARSE_NAME(name) cs_di ## name |
| 5610 | 47 #endif |
| 48 | |
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49 #if defined (HAVE_CXSPARSE) |
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50 |
| 5610 | 51 static RowVector |
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52 put_int (suitesparse_integer *p, octave_idx_type n) |
| 5610 | 53 { |
| 54 RowVector ret (n); | |
| 55 for (octave_idx_type i = 0; i < n; i++) | |
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56 ret.xelem (i) = p[i] + 1; |
| 5610 | 57 return ret; |
| 58 } | |
| 59 | |
| 6066 | 60 static octave_value_list |
| 61 dmperm_internal (bool rank, const octave_value arg, int nargout) | |
| 5610 | 62 { |
| 63 octave_value_list retval; | |
| 64 octave_idx_type nr = arg.rows (); | |
| 65 octave_idx_type nc = arg.columns (); | |
| 66 SparseMatrix m; | |
| 67 SparseComplexMatrix cm; | |
| 5648 | 68 CXSPARSE_NAME () csm; |
| 5610 | 69 csm.m = nr; |
| 70 csm.n = nc; | |
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71 csm.x = nullptr; |
| 5610 | 72 csm.nz = -1; |
| 73 | |
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74 if (arg.isreal ()) |
| 5610 | 75 { |
| 76 m = arg.sparse_matrix_value (); | |
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77 csm.nzmax = m.nnz (); |
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78 csm.p = to_suitesparse_intptr (m.xcidx ()); |
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79 csm.i = to_suitesparse_intptr (m.xridx ()); |
| 5610 | 80 } |
| 81 else | |
| 82 { | |
| 83 cm = arg.sparse_complex_matrix_value (); | |
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84 csm.nzmax = cm.nnz (); |
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85 csm.p = to_suitesparse_intptr (cm.xcidx ()); |
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86 csm.i = to_suitesparse_intptr (cm.xridx ()); |
| 5610 | 87 } |
| 88 | |
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89 if (nargout <= 1 || rank) |
| 5610 | 90 { |
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91 suitesparse_integer *jmatch = CXSPARSE_NAME (_maxtrans) (&csm, 0); |
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92 if (rank) |
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93 { |
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94 octave_idx_type r = 0; |
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95 for (octave_idx_type i = 0; i < nc; i++) |
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96 if (jmatch[nr+i] >= 0) |
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97 r++; |
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98 retval(0) = static_cast<double> (r); |
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99 } |
| 5610 | 100 else |
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101 retval(0) = put_int (jmatch + nr, nc); |
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102 CXSPARSE_NAME (_free) (jmatch); |
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103 } |
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104 else |
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105 { |
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106 CXSPARSE_NAME (d) *dm = CXSPARSE_NAME(_dmperm) (&csm, 0); |
| 6066 | 107 |
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108 retval = ovl (put_int (dm->p, nr), put_int (dm->q, nc), |
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109 put_int (dm->r, dm->nb+1), put_int (dm->s, dm->nb+1), |
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110 put_int (dm->cc, 5), put_int (dm->rr, 5)); |
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111 |
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112 CXSPARSE_NAME (_dfree) (dm); |
| 5610 | 113 } |
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114 |
| 6066 | 115 return retval; |
| 116 } | |
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117 |
| 6066 | 118 #endif |
| 119 | |
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120 // NOTE: the docstring for dmperm is adapted from the text found in the |
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121 // file cs_dmperm.m that is distributed with the CSparse portion of the |
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122 // SuiteSparse library, version 5.6.0. CSparse is distributed under the |
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123 // terms of the LGPL v2.1 or any later version. |
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124 |
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125 DEFUN (dmperm, args, nargout, |
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126 doc: /* -*- texinfo -*- |
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127 @deftypefn {} {@var{p} =} dmperm (@var{A}) |
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128 @deftypefnx {} {[@var{p}, @var{q}, @var{r}, @var{s}, @var{cc}, @var{rr}] =} dmperm (@var{A}) |
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129 |
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130 @cindex @nospell{Dulmage-Mendelsohn} decomposition |
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131 Perform a @nospell{Dulmage-Mendelsohn} permutation of the sparse matrix |
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132 @var{A}. |
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133 |
| 28754 | 134 With a single output argument @code{dmperm}, return a maximum matching @var{p} |
| 135 such that @code{p(j) = i} if column @var{j} is matched to row @var{i}, or 0 if | |
| 136 column @var{j} is unmatched. If @var{A} is square and full structural rank, | |
| 137 @var{p} is a row permutation and @code{A(p,:)} has a zero-free diagonal. The | |
| 138 structural rank of @var{A} is @code{sprank(A) = sum(p>0)}. | |
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139 |
| 28754 | 140 Called with two or more output arguments, return the |
| 141 @nospell{Dulmage-Mendelsohn} decomposition of @var{A}. @var{p} and @var{q} are | |
| 142 permutation vectors. @var{cc} and @var{rr} are vectors of length 5. | |
| 143 @code{c = A(p,q)} is split into a 4-by-4 set of coarse blocks: | |
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144 |
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145 @example |
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146 @group |
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147 A11 A12 A13 A14 |
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148 0 0 A23 A24 |
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149 0 0 0 A34 |
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150 0 0 0 A44 |
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151 @end group |
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152 @end example |
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153 |
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154 @noindent |
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155 where @code{A12}, @code{A23}, and @code{A34} are square with zero-free |
| 28754 | 156 diagonals. The columns of @code{A11} are the unmatched columns, and the rows |
| 157 of @code{A44} are the unmatched rows. Any of these blocks can be empty. In | |
| 158 the "coarse" decomposition, the (i,j)-th block is | |
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159 @code{C(rr(i):rr(i+1)-1,cc(j):cc(j+1)-1)}. In terms of a linear system, |
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160 @code{[A11 A12]} is the underdetermined part of the system (it is always |
| 28754 | 161 rectangular and with more columns and rows, or 0-by-0), @code{A23} is the |
| 162 well-determined part of the system (it is always square), and | |
| 163 @code{[A34 ; A44]} is the over-determined part of the system (it is always | |
| 164 rectangular with more rows than columns, or 0-by-0). | |
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165 |
| 28754 | 166 The structural rank of @var{A} is @code{sprank (A) = rr(4)-1}, which is an |
| 167 upper bound on the numerical rank of @var{A}. | |
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168 @code{sprank(A) = rank(full(sprand(A)))} with probability 1 in exact |
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169 arithmetic. |
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170 |
| 28754 | 171 The @code{A23} submatrix is further subdivided into block upper triangular form |
| 172 via the "fine" decomposition (the strongly-connected components of @code{A23}). | |
| 173 If @var{A} is square and structurally non-singular, @code{A23} is the entire | |
| 174 matrix. | |
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175 |
| 28754 | 176 @code{C(r(i):r(i+1)-1,s(j):s(j+1)-1)} is the (i,j)-th block of the fine |
| 177 decomposition. The (1,1) block is the rectangular block @code{[A11 A12]}, | |
| 178 unless this block is 0-by-0. The (b,b) block is the rectangular block | |
| 179 @code{[A34 ; A44]}, unless this block is 0-by-0, where @code{b = length(r)-1}. | |
| 180 All other blocks of the form @code{C(r(i):r(i+1)-1,s(i):s(i+1)-1)} are diagonal | |
| 181 blocks of @code{A23}, and are square with a zero-free diagonal. | |
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182 |
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183 The method used is described in: @nospell{A. Pothen & C.-J. Fan.} |
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184 @cite{Computing the Block Triangular Form of a Sparse Matrix}. |
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185 @nospell{ACM} Trans.@: Math.@: Software, 16(4):303--324, 1990. |
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186 @seealso{colamd, ccolamd} |
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187 @end deftypefn */) |
| 6066 | 188 { |
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189 #if defined (HAVE_CXSPARSE) |
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190 |
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191 if (args.length () != 1) |
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192 print_usage (); |
| 6066 | 193 |
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194 return dmperm_internal (false, args(0), nargout); |
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195 |
| 5610 | 196 #else |
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197 |
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198 octave_unused_parameter (args); |
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199 octave_unused_parameter (nargout); |
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200 |
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201 err_disabled_feature ("dmperm", "CXSparse"); |
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202 |
| 5610 | 203 #endif |
| 204 } | |
| 205 | |
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206 /* |
| 7243 | 207 %!testif HAVE_CXSPARSE |
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208 %! n = 20; |
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209 %! a = speye (n,n); |
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210 %! a = a(randperm (n),:); |
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211 %! assert (a(dmperm (a),:), speye (n)); |
| 5610 | 212 |
| 7243 | 213 %!testif HAVE_CXSPARSE |
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214 %! n = 20; |
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215 %! d = 0.2; |
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216 %! a = tril (sprandn (n,n,d), -1) + speye (n,n); |
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217 %! a = a(randperm (n), randperm (n)); |
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218 %! [p,q,r,s] = dmperm (a); |
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219 %! assert (tril (a(p,q), -1), sparse (n, n)); |
| 5610 | 220 */ |
| 221 | |
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222 DEFUN (sprank, args, nargout, |
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223 doc: /* -*- texinfo -*- |
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224 @deftypefn {} {@var{p} =} sprank (@var{S}) |
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225 @cindex structural rank |
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226 |
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227 Calculate the structural rank of the sparse matrix @var{S}. |
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228 |
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229 Note that only the structure of the matrix is used in this calculation based |
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230 on a @nospell{Dulmage-Mendelsohn} permutation to block triangular form. As |
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231 such the numerical rank of the matrix @var{S} is bounded by |
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232 @code{sprank (@var{S}) >= rank (@var{S})}. Ignoring floating point errors |
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233 @code{sprank (@var{S}) == rank (@var{S})}. |
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234 @seealso{dmperm} |
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235 @end deftypefn */) |
| 6066 | 236 { |
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237 #if defined (HAVE_CXSPARSE) |
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238 |
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239 if (args.length () != 1) |
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240 print_usage (); |
| 6066 | 241 |
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242 return dmperm_internal (true, args(0), nargout); |
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243 |
| 6066 | 244 #else |
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245 |
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246 octave_unused_parameter (args); |
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247 octave_unused_parameter (nargout); |
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248 |
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249 err_disabled_feature ("sprank", "CXSparse"); |
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250 |
| 6066 | 251 #endif |
| 252 } | |
| 253 | |
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254 /* |
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255 %!testif HAVE_CXSPARSE |
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256 %! assert (sprank (speye (20)), 20); |
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258 %! assert (sprank ([1,0,2,0;2,0,4,0]), 2); |
| 6066 | 259 |
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260 %!error sprank (1,2) |
| 6066 | 261 */ |
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262 |
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263 OCTAVE_END_NAMESPACE(octave) |