Mercurial > octave
annotate libinterp/dldfcn/colamd.cc @ 21724:aba2e6293dd8
use "#if ..." consistently instead of "#ifdef" and "#ifndef"
* configure.ac, Doxyfile.in, make_int.cc, Backend.cc, BaseControl.cc,
ButtonControl.cc, Canvas.cc, CheckBoxControl.cc, Container.cc,
ContextMenu.cc, EditControl.cc, Figure.cc, FigureWindow.cc,
GLCanvas.cc, KeyMap.cc, ListBoxControl.cc, Logger.cc, Menu.cc,
MouseModeActionGroup.cc, Object.cc, ObjectFactory.cc,
ObjectProxy.cc, Panel.cc, PopupMenuControl.cc, PushButtonControl.cc,
PushTool.cc, QtHandlesUtils.cc, RadioButtonControl.cc,
SliderControl.cc, TextControl.cc, TextEdit.cc,
ToggleButtonControl.cc, ToggleTool.cc, ToolBar.cc, __init_qt__.cc,
annotation-dialog.cc, gl-select.cc, module.mk, color-picker.cc,
dialog.cc, documentation-dock-widget.cc, files-dock-widget.cc,
find-files-dialog.cc, find-files-model.cc, history-dock-widget.cc,
liboctgui-build-info.in.cc, file-editor-tab.cc, file-editor.cc,
find-dialog.cc, marker.cc, marker.h, octave-qscintilla.cc,
octave-txt-lexer.cc, main-window.cc, octave-cmd.cc,
octave-dock-widget.cc, octave-gui.cc, octave-interpreter.cc,
octave-qt-link.cc, parser.cc, webinfo.cc, resource-manager.cc,
settings-dialog.cc, shortcut-manager.cc, terminal-dock-widget.cc,
thread-manager.cc, welcome-wizard.cc, workspace-model.cc,
workspace-view.cc, build-env.in.cc, Cell.cc, __contourc__.cc,
__dispatch__.cc, __dsearchn__.cc, __ichol__.cc, __ilu__.cc,
__lin_interpn__.cc, __luinc__.cc, __magick_read__.cc,
__pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc, betainc.cc,
bitfcns.cc, bsxfun.cc, c-file-ptr-stream.cc, c-file-ptr-stream.h,
cdisplay.c, cdisplay.h, cellfun.cc, coct-hdf5-types.c, colloc.cc,
comment-list.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
debug.cc, defaults.cc, defaults.in.h, defun.cc, det.cc, dirfns.cc,
display.cc, dlmread.cc, dot.cc, dynamic-ld.cc, eig.cc, ellipj.cc,
error.cc, errwarn.cc, event-queue.cc, fft.cc, fft2.cc, fftn.cc,
file-io.cc, filter.cc, find.cc, ft-text-renderer.cc, gammainc.cc,
gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc,
gl-render.cc, gl2ps-print.cc, graphics.cc, gripes.cc, hash.cc,
help.cc, hess.cc, hex2num.cc, input.cc, inv.cc, jit-ir.cc, jit-ir.h,
jit-typeinfo.cc, jit-typeinfo.h, jit-util.cc, jit-util.h, kron.cc,
load-path.cc, load-save.cc, lookup.cc, ls-ascii-helper.cc,
ls-hdf5.cc, ls-mat-ascii.cc, ls-mat4.cc, ls-mat5.cc,
ls-oct-binary.cc, ls-oct-text.cc, ls-oct-text.h, ls-utils.cc,
lsode.cc, lu.cc, mappers.cc, matrix_type.cc, max.cc, mex.cc, mex.h,
mexproto.h, mgorth.cc, nproc.cc, oct-errno.in.cc, oct-fstrm.cc,
oct-hdf5-types.cc, oct-hdf5-types.h, oct-hist.cc, oct-iostrm.cc,
oct-lvalue.cc, oct-map.cc, oct-prcstrm.cc, oct-procbuf.cc,
oct-stdstrm.h, oct-stream.cc, oct-strstrm.cc, oct-tex-lexer.in.ll,
oct-tex-parser.in.yy, octave-link.cc, ordschur.cc, pager.cc,
pinv.cc, pr-output.cc, procstream.cc, profiler.cc, psi.cc,
pt-jit.cc, pt-jit.h, quad.cc, quadcc.cc, qz.cc, rand.cc, rcond.cc,
regexp.cc, schur.cc, sighandlers.cc, sighandlers.h, siglist.c,
siglist.h, sparse-xdiv.cc, sparse-xpow.cc, sparse.cc, spparms.cc,
sqrtm.cc, str2double.cc, strfind.cc, strfns.cc, sub2ind.cc, svd.cc,
sylvester.cc, symtab.cc, syscalls.cc, sysdep.cc, text-renderer.cc,
time.cc, toplev.cc, tril.cc, tsearch.cc, txt-eng.cc, typecast.cc,
urlwrite.cc, utils.cc, variables.cc, xdiv.cc, xgl2ps.c, xnorm.cc,
xpow.cc, zfstream.cc, zfstream.h, __delaunayn__.cc, __eigs__.cc,
__fltk_uigetfile__.cc, __glpk__.cc, __init_fltk__.cc,
__init_gnuplot__.cc, __osmesa_print__.cc, __voronoi__.cc, amd.cc,
audiodevinfo.cc, audioread.cc, ccolamd.cc, chol.cc, colamd.cc,
convhulln.cc, dmperm.cc, fftw.cc, qr.cc, symbfact.cc, symrcm.cc,
liboctinterp-build-info.in.cc, mkbuiltins, mkops, ov-base.cc,
ov-bool-mat.cc, ov-bool-sparse.cc, ov-bool.cc, ov-builtin.cc,
ov-cell.cc, ov-ch-mat.cc, ov-class.cc, ov-classdef.cc, ov-colon.cc,
ov-complex.cc, ov-cs-list.cc, ov-cx-diag.cc, ov-cx-mat.cc,
ov-cx-sparse.cc, ov-dld-fcn.cc, ov-fcn-handle.cc, ov-fcn-inline.cc,
ov-fcn.cc, ov-float.cc, ov-flt-complex.cc, ov-flt-cx-diag.cc,
ov-flt-cx-mat.cc, ov-flt-re-diag.cc, ov-flt-re-mat.cc, ov-int16.cc,
ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.cc, ov-lazy-idx.cc,
ov-mex-fcn.cc, ov-null-mat.cc, ov-oncleanup.cc, ov-perm.cc,
ov-range.cc, ov-re-diag.cc, ov-re-mat.cc, ov-re-sparse.cc,
ov-scalar.cc, ov-str-mat.cc, ov-struct.cc, ov-typeinfo.cc,
ov-uint16.cc, ov-uint32.cc, ov-uint64.cc, ov-uint8.cc,
ov-usr-fcn.cc, ov-usr-fcn.h, ov.cc, ovl.cc, octave.cc, octave.h,
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-cdm-cm.cc, op-cdm-dm.cc,
op-cdm-m.cc, op-cell.cc, op-chm.cc, op-class.cc, op-cm-cdm.cc,
op-cm-cm.cc, op-cm-cs.cc, op-cm-dm.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-cdm.cc, op-dm-cm.cc,
op-dm-dm.cc, op-dm-m.cc, op-dm-scm.cc, op-dm-sm.cc,
op-dm-template.cc, op-dms-template.cc, op-double-conv.cc,
op-fcdm-fcdm.cc, op-fcdm-fcm.cc, op-fcdm-fdm.cc, op-fcdm-fm.cc,
op-fcm-fcdm.cc, op-fcm-fcm.cc, op-fcm-fcs.cc, op-fcm-fdm.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-fcdm.cc, op-fdm-fcm.cc,
op-fdm-fdm.cc, op-fdm-fm.cc, op-float-conv.cc, op-fm-fcdm.cc,
op-fm-fcm.cc, op-fm-fcs.cc, op-fm-fdm.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-int-conv.cc, op-m-cdm.cc, op-m-cm.cc, op-m-cs.cc, op-m-dm.cc,
op-m-m.cc, op-m-s.cc, op-m-scm.cc, op-m-sm.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,
lex.ll, oct-parse.in.yy, pt-arg-list.cc, pt-array-list.cc,
pt-assign.cc, pt-binop.cc, pt-bp.cc, pt-cbinop.cc, pt-cell.cc,
pt-check.cc, pt-classdef.cc, pt-cmd.cc, pt-colon.cc, pt-const.cc,
pt-decl.cc, pt-eval.cc, pt-except.cc, pt-exp.cc, pt-fcn-handle.cc,
pt-funcall.cc, pt-id.cc, pt-idx.cc, pt-jump.cc, pt-loop.cc,
pt-loop.h, pt-mat.cc, pt-misc.cc, pt-pr-code.cc, pt-select.cc,
pt-stmt.cc, pt-unop.cc, pt.cc, token.cc, Array-jit.cc, Array-tc.cc,
version.cc, Array-C.cc, Array-b.cc, Array-ch.cc, Array-d.cc,
Array-f.cc, Array-fC.cc, Array-i.cc, Array-idx-vec.cc, Array-s.cc,
Array-str.cc, Array-util.cc, Array-voidp.cc, Array.cc,
CColVector.cc, CDiagMatrix.cc, CMatrix.cc, CNDArray.cc,
CRowVector.cc, CSparse.cc, MArray-C.cc, MArray-d.cc, MArray-f.cc,
MArray-fC.cc, MArray-i.cc, MArray-s.cc, MSparse-C.cc, MSparse-d.cc,
MatrixType.cc, PermMatrix.cc, Range.cc, Sparse-C.cc, Sparse-b.cc,
Sparse-d.cc, boolMatrix.cc, boolNDArray.cc, boolSparse.cc,
chMatrix.cc, chNDArray.cc, dColVector.cc, dDiagMatrix.cc,
dMatrix.cc, dNDArray.cc, dRowVector.cc, dSparse.cc, dim-vector.cc,
dim-vector.h, fCColVector.cc, fCDiagMatrix.cc, fCMatrix.cc,
fCNDArray.cc, fCRowVector.cc, fColVector.cc, fDiagMatrix.cc,
fMatrix.cc, fNDArray.cc, fRowVector.cc, idx-vector.cc,
int16NDArray.cc, int32NDArray.cc, int64NDArray.cc, int8NDArray.cc,
uint16NDArray.cc, uint32NDArray.cc, uint64NDArray.cc,
uint8NDArray.cc, Faddeeva.cc, blaswrap.c, cquit.c, f77-extern.cc,
f77-fcn.c, f77-fcn.h, lo-error.c, lo-error.h, quit.cc, quit.h,
liboctave-build-info.in.cc, CollocWt.cc, DASPK.cc, DASRT.cc,
DASSL.cc, EIG.cc, LSODE.cc, ODES.cc, Quad.cc, aepbalance.cc,
chol.cc, eigs-base.cc, fEIG.cc, gepbalance.cc, hess.cc,
lo-mappers.cc, lo-specfun.cc, lu.cc, oct-convn.cc, oct-fftw.cc,
oct-norm.cc, oct-rand.cc, oct-spparms.cc, qr.cc, qrp.cc,
randmtzig.cc, randpoisson.cc, schur.cc, sparse-chol.cc,
sparse-dmsolve.cc, sparse-lu.cc, sparse-qr.cc, svd.cc, mk-ops.awk,
mx-defs.h, dir-ops.cc, file-ops.cc, file-stat.cc, lo-sysdep.cc,
mach-info.cc, oct-env.cc, oct-group.cc, oct-passwd.cc,
oct-syscalls.cc, oct-time.cc, oct-uname.cc, pathlen.h, syswait.h,
cmd-edit.cc, cmd-hist.cc, data-conv.cc, f2c-main.c, glob-match.cc,
kpse.cc, lo-array-errwarn.cc, lo-array-gripes.cc, lo-cutils.c,
lo-cutils.h, lo-ieee.cc, lo-ieee.h, lo-regexp.cc, lo-utils.cc,
oct-base64.cc, oct-glob.cc, oct-inttypes.cc, oct-inttypes.h,
oct-locbuf.cc, oct-mutex.cc, oct-rl-edit.c, oct-rl-edit.h,
oct-rl-hist.c, oct-rl-hist.h, oct-shlib.cc, oct-sort.cc,
pathsearch.cc, singleton-cleanup.cc, sparse-sort.cc, sparse-util.cc,
statdefs.h, str-vec.cc, unwind-prot.cc, url-transfer.cc,
acinclude.m4, display-available.c, display-available.h, main-cli.cc,
main-gui.cc, main.in.cc, mkoctfile.in.cc, octave-build-info.in.cc,
octave-config.in.cc, shared-fcns.h:
Use "#if ..." consistently instead of "#ifdef" and "#ifndef".
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 17 May 2016 12:09:30 -0400 |
parents | 263d18409fdf |
children | b571fc85953f |
rev | line source |
---|---|
5164 | 1 /* |
2 | |
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3 Copyright (C) 2004-2015 David Bateman |
11523 | 4 Copyright (C) 1998-2004 Andy Adler |
7016 | 5 |
6 This file is part of Octave. | |
5164 | 7 |
8 Octave is free software; you can redistribute it and/or modify it | |
9 under the terms of the GNU General Public License as published by the | |
7016 | 10 Free Software Foundation; either version 3 of the License, or (at your |
11 option) any later version. | |
5164 | 12 |
13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
16 for more details. | |
17 | |
18 You should have received a copy of the GNU General Public License | |
7016 | 19 along with Octave; see the file COPYING. If not, see |
20 <http://www.gnu.org/licenses/>. | |
5164 | 21 |
22 */ | |
23 | |
24 // This is the octave interface to colamd, which bore the copyright given | |
25 // in the help of the functions. | |
26 | |
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27 #if defined (HAVE_CONFIG_H) |
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28 # include "config.h" |
5164 | 29 #endif |
30 | |
31 #include <cstdlib> | |
32 | |
33 #include <string> | |
34 #include <vector> | |
35 | |
36 #include "ov.h" | |
37 #include "defun-dld.h" | |
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38 #include "errwarn.h" |
5164 | 39 #include "pager.h" |
40 #include "ov-re-mat.h" | |
41 | |
42 #include "ov-re-sparse.h" | |
43 #include "ov-cx-sparse.h" | |
44 | |
5451 | 45 #include "oct-sparse.h" |
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46 #include "oct-locbuf.h" |
5164 | 47 |
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48 #if defined (OCTAVE_ENABLE_64) |
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49 # define COLAMD_NAME(name) colamd_l ## name |
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50 # define SYMAMD_NAME(name) symamd_l ## name |
5440 | 51 #else |
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52 # define COLAMD_NAME(name) colamd ## name |
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53 # define SYMAMD_NAME(name) symamd ## name |
5440 | 54 #endif |
55 | |
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56 // The symmetric column elimination tree code take from the Davis LDL code. |
5164 | 57 // Copyright given elsewhere in this file. |
7924 | 58 static void |
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59 symetree (const octave_idx_type *ridx, const octave_idx_type *cidx, |
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60 octave_idx_type *Parent, octave_idx_type *P, octave_idx_type n) |
5164 | 61 { |
5440 | 62 OCTAVE_LOCAL_BUFFER (octave_idx_type, Flag, n); |
63 OCTAVE_LOCAL_BUFFER (octave_idx_type, Pinv, (P ? n : 0)); | |
5164 | 64 if (P) |
65 // If P is present then compute Pinv, the inverse of P | |
5440 | 66 for (octave_idx_type k = 0 ; k < n ; k++) |
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67 Pinv[P[k]] = k; |
5164 | 68 |
5440 | 69 for (octave_idx_type k = 0 ; k < n ; k++) |
5164 | 70 { |
71 // L(k,:) pattern: all nodes reachable in etree from nz in A(0:k-1,k) | |
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72 Parent[k] = n ; // parent of k is not yet known |
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73 Flag[k] = k ; // mark node k as visited |
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74 octave_idx_type kk = (P) ? P[k] // kth original, or permuted, column |
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75 : (k); |
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76 octave_idx_type p2 = cidx[kk+1]; |
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77 for (octave_idx_type p = cidx[kk] ; p < p2 ; p++) |
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78 { |
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79 // A (i,k) is nonzero (original or permuted A) |
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80 octave_idx_type i = (Pinv) ? (Pinv[ridx[p]]) : (ridx[p]); |
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81 if (i < k) |
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82 { |
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83 // follow path from i to root of etree, stop at flagged node |
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84 for ( ; Flag[i] != k ; i = Parent[i]) |
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85 { |
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86 // find parent of i if not yet determined |
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87 if (Parent[i] == n) |
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88 Parent[i] = k; |
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89 Flag[i] = k ; // mark i as visited |
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90 } |
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91 } |
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92 } |
5164 | 93 } |
94 } | |
95 | |
96 // The elimination tree post-ordering code below is taken from SuperLU | |
7924 | 97 static inline octave_idx_type |
98 make_set (octave_idx_type i, octave_idx_type *pp) | |
5164 | 99 { |
100 pp[i] = i; | |
101 return i; | |
102 } | |
103 | |
7924 | 104 static inline octave_idx_type |
105 link (octave_idx_type s, octave_idx_type t, octave_idx_type *pp) | |
5164 | 106 { |
107 pp[s] = t; | |
108 return t; | |
109 } | |
110 | |
7924 | 111 static inline octave_idx_type |
112 find (octave_idx_type i, octave_idx_type *pp) | |
5164 | 113 { |
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114 octave_idx_type p = pp[i]; |
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115 octave_idx_type gp = pp[p]; |
7924 | 116 |
117 while (gp != p) | |
118 { | |
119 pp[i] = gp; | |
120 i = gp; | |
121 p = pp[i]; | |
122 gp = pp[p]; | |
123 } | |
124 | |
125 return p; | |
5164 | 126 } |
127 | |
7924 | 128 static octave_idx_type |
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129 etdfs (octave_idx_type v, octave_idx_type *first_kid, |
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130 octave_idx_type *next_kid, octave_idx_type *post, |
7924 | 131 octave_idx_type postnum) |
5164 | 132 { |
7924 | 133 for (octave_idx_type w = first_kid[v]; w != -1; w = next_kid[w]) |
5164 | 134 postnum = etdfs (w, first_kid, next_kid, post, postnum); |
7924 | 135 |
5164 | 136 post[postnum++] = v; |
137 | |
138 return postnum; | |
139 } | |
140 | |
7924 | 141 static void |
142 tree_postorder (octave_idx_type n, octave_idx_type *parent, | |
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143 octave_idx_type *post) |
5164 | 144 { |
145 // Allocate storage for working arrays and results | |
5440 | 146 OCTAVE_LOCAL_BUFFER (octave_idx_type, first_kid, n+1); |
147 OCTAVE_LOCAL_BUFFER (octave_idx_type, next_kid, n+1); | |
5164 | 148 |
149 // Set up structure describing children | |
7924 | 150 for (octave_idx_type v = 0; v <= n; first_kid[v++] = -1) |
20946 | 151 ; // do nothing |
7924 | 152 |
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153 for (octave_idx_type v = n-1; v >= 0; v--) |
5164 | 154 { |
5440 | 155 octave_idx_type dad = parent[v]; |
5164 | 156 next_kid[v] = first_kid[dad]; |
157 first_kid[dad] = v; | |
158 } | |
159 | |
160 // Depth-first search from dummy root vertex #n | |
161 etdfs (n, first_kid, next_kid, post, 0); | |
162 } | |
163 | |
7924 | 164 static void |
165 coletree (const octave_idx_type *ridx, const octave_idx_type *colbeg, | |
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166 octave_idx_type *colend, octave_idx_type *parent, |
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167 octave_idx_type nr, octave_idx_type nc) |
5164 | 168 { |
5440 | 169 OCTAVE_LOCAL_BUFFER (octave_idx_type, root, nc); |
170 OCTAVE_LOCAL_BUFFER (octave_idx_type, pp, nc); | |
171 OCTAVE_LOCAL_BUFFER (octave_idx_type, firstcol, nr); | |
5164 | 172 |
173 // Compute firstcol[row] = first nonzero column in row | |
7924 | 174 for (octave_idx_type row = 0; row < nr; firstcol[row++] = nc) |
20946 | 175 ; // do nothing |
7924 | 176 |
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177 for (octave_idx_type col = 0; col < nc; col++) |
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178 for (octave_idx_type p = colbeg[col]; p < colend[col]; p++) |
5164 | 179 { |
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180 octave_idx_type row = ridx[p]; |
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181 if (firstcol[row] > col) |
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182 firstcol[row] = col; |
5164 | 183 } |
184 | |
185 // Compute etree by Liu's algorithm for symmetric matrices, | |
186 // except use (firstcol[r],c) in place of an edge (r,c) of A. | |
187 // Thus each row clique in A'*A is replaced by a star | |
188 // centered at its first vertex, which has the same fill. | |
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189 for (octave_idx_type col = 0; col < nc; col++) |
5164 | 190 { |
5440 | 191 octave_idx_type cset = make_set (col, pp); |
5164 | 192 root[cset] = col; |
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193 parent[col] = nc; |
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194 for (octave_idx_type p = colbeg[col]; p < colend[col]; p++) |
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195 { |
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196 octave_idx_type row = firstcol[ridx[p]]; |
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197 if (row >= col) |
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198 continue; |
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199 octave_idx_type rset = find (row, pp); |
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200 octave_idx_type rroot = root[rset]; |
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201 if (rroot != col) |
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202 { |
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203 parent[rroot] = col; |
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204 cset = link (cset, rset, pp); |
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205 root[cset] = col; |
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206 } |
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207 } |
5164 | 208 } |
209 } | |
210 | |
211 DEFUN_DLD (colamd, args, nargout, | |
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212 "-*- texinfo -*-\n\ |
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213 @deftypefn {} {@var{p} =} colamd (@var{S})\n\ |
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214 @deftypefnx {} {@var{p} =} colamd (@var{S}, @var{knobs})\n\ |
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215 @deftypefnx {} {[@var{p}, @var{stats}] =} colamd (@var{S})\n\ |
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216 @deftypefnx {} {[@var{p}, @var{stats}] =} colamd (@var{S}, @var{knobs})\n\ |
5164 | 217 \n\ |
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218 Compute the column approximate minimum degree permutation.\n\ |
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219 \n\ |
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220 @code{@var{p} = colamd (@var{S})} returns the column approximate minimum\n\ |
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221 degree permutation vector for the sparse matrix @var{S}. For a\n\ |
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222 non-symmetric matrix @var{S}, @code{@var{S}(:,@var{p})} tends to have\n\ |
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223 sparser LU@tie{}factors than @var{S}. The Cholesky@tie{}factorization of\n\ |
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224 @code{@var{S}(:,@var{p})' * @var{S}(:,@var{p})} also tends to be sparser\n\ |
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225 than that of @code{@var{S}' * @var{S}}.\n\ |
5164 | 226 \n\ |
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227 @var{knobs} is an optional one- to three-element input vector. If @var{S}\n\ |
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228 is m-by-n, then rows with more than @code{max(16,@var{knobs}(1)*sqrt(n))}\n\ |
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229 entries are ignored. Columns with more than\n\ |
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230 @code{max (16,@var{knobs}(2)*sqrt(min(m,n)))} entries are removed prior to\n\ |
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231 ordering, and ordered last in the output permutation @var{p}. Only\n\ |
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232 completely dense rows or columns are removed if @code{@var{knobs}(1)} and\n\ |
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233 @code{@var{knobs}(2)} are < 0, respectively. If @code{@var{knobs}(3)} is\n\ |
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234 nonzero, @var{stats} and @var{knobs} are printed. The default is\n\ |
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235 @code{@var{knobs} = [10 10 0]}. Note that @var{knobs} differs from earlier\n\ |
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236 versions of colamd.\n\ |
5164 | 237 \n\ |
238 @var{stats} is an optional 20-element output vector that provides data\n\ | |
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239 about the ordering and the validity of the input matrix @var{S}. Ordering\n\ |
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240 statistics are in @code{@var{stats}(1:3)}. @code{@var{stats}(1)} and\n\ |
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241 @code{@var{stats}(2)} are the number of dense or empty rows and columns\n\ |
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242 ignored by @sc{colamd} and @code{@var{stats}(3)} is the number of garbage\n\ |
10840 | 243 collections performed on the internal data structure used by @sc{colamd}\n\ |
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244 (roughly of size @code{2.2 * nnz(@var{S}) + 4 * @var{m} + 7 * @var{n}}\n\ |
5164 | 245 integers).\n\ |
246 \n\ | |
247 Octave built-in functions are intended to generate valid sparse matrices,\n\ | |
248 with no duplicate entries, with ascending row indices of the nonzeros\n\ | |
249 in each column, with a non-negative number of entries in each column (!)\n\ | |
10840 | 250 and so on. If a matrix is invalid, then @sc{colamd} may or may not be able\n\ |
5164 | 251 to continue. If there are duplicate entries (a row index appears two or\n\ |
252 more times in the same column) or if the row indices in a column are out\n\ | |
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253 of order, then @sc{colamd} can correct these errors by ignoring the\n\ |
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254 duplicate entries and sorting each column of its internal copy of the\n\ |
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255 matrix @var{S} (the input matrix @var{S} is not repaired, however). If a\n\ |
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256 matrix is invalid in other ways then @sc{colamd} cannot continue, an error\n\ |
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257 message is printed, and no output arguments (@var{p} or @var{stats}) are\n\ |
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258 returned.\n\ |
10840 | 259 @sc{colamd} is thus a simple way to check a sparse matrix to see if it's\n\ |
5164 | 260 valid.\n\ |
261 \n\ | |
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262 @code{@var{stats}(4:7)} provide information if @sc{colamd} was able to\n\ |
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263 continue. The matrix is OK if @code{@var{stats}(4)} is zero, or 1 if\n\ |
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264 invalid. @code{@var{stats}(5)} is the rightmost column index that is\n\ |
5164 | 265 unsorted or contains duplicate entries, or zero if no such column exists.\n\ |
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266 @code{@var{stats}(6)} is the last seen duplicate or out-of-order row\n\ |
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267 index in the column index given by @code{@var{stats}(5)}, or zero if no\n\ |
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268 such row index exists. @code{@var{stats}(7)} is the number of duplicate\n\ |
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269 or out-of-order row indices. @code{@var{stats}(8:20)} is always zero in\n\ |
10840 | 270 the current version of @sc{colamd} (reserved for future use).\n\ |
5164 | 271 \n\ |
272 The ordering is followed by a column elimination tree post-ordering.\n\ | |
273 \n\ | |
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274 The authors of the code itself are @nospell{Stefan I. Larimore} and\n\ |
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275 @nospell{Timothy A. Davis @email{davis@@cise.ufl.edu}}, University of Florida. The algorithm was developed in collaboration with @nospell{John Gilbert},\n\ |
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276 Xerox PARC, and @nospell{Esmond Ng}, Oak Ridge National Laboratory. (see\n\ |
5164 | 277 @url{http://www.cise.ufl.edu/research/sparse/colamd})\n\ |
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278 @seealso{colperm, symamd, ccolamd}\n\ |
5642 | 279 @end deftypefn") |
5164 | 280 { |
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281 #if defined (HAVE_COLAMD) |
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282 |
5164 | 283 int nargin = args.length (); |
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284 |
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285 if (nargin < 1 || nargin > 2) |
5823 | 286 print_usage (); |
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287 |
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288 octave_value_list retval (nargout == 2 ? 2 : 1); |
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289 int spumoni = 0; |
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290 |
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291 // Get knobs |
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292 OCTAVE_LOCAL_BUFFER (double, knobs, COLAMD_KNOBS); |
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293 COLAMD_NAME (_set_defaults) (knobs); |
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295 // Check for user-passed knobs |
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296 if (nargin == 2) |
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297 { |
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298 NDArray User_knobs = args(1).array_value (); |
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299 int nel_User_knobs = User_knobs.numel (); |
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300 |
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301 if (nel_User_knobs > 0) |
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302 knobs[COLAMD_DENSE_ROW] = User_knobs(0); |
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303 if (nel_User_knobs > 1) |
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304 knobs[COLAMD_DENSE_COL] = User_knobs(1); |
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305 if (nel_User_knobs > 2) |
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306 spumoni = static_cast<int> (User_knobs(2)); |
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308 // print knob settings if spumoni is set |
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309 if (spumoni) |
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310 { |
5164 | 311 |
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312 octave_stdout << "\ncolamd version " << COLAMD_MAIN_VERSION |
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313 << "." << COLAMD_SUB_VERSION |
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314 << ", " << COLAMD_DATE << ":\n"; |
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316 if (knobs[COLAMD_DENSE_ROW] >= 0) |
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317 octave_stdout << "knobs(1): " << User_knobs (0) |
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318 << ", rows with > max (16," |
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319 << knobs[COLAMD_DENSE_ROW] << "*sqrt (size(A,2)))" |
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320 << " entries removed\n"; |
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321 else |
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322 octave_stdout << "knobs(1): " << User_knobs (0) |
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323 << ", only completely dense rows removed\n"; |
5440 | 324 |
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325 if (knobs[COLAMD_DENSE_COL] >= 0) |
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326 octave_stdout << "knobs(2): " << User_knobs (1) |
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327 << ", cols with > max (16," |
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328 << knobs[COLAMD_DENSE_COL] << "*sqrt (size(A)))" |
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329 << " entries removed\n"; |
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330 else |
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331 octave_stdout << "knobs(2): " << User_knobs (1) |
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332 << ", only completely dense columns removed\n"; |
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334 octave_stdout << "knobs(3): " << User_knobs (2) |
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335 << ", statistics and knobs printed\n"; |
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336 |
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337 } |
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338 } |
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339 |
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340 octave_idx_type n_row, n_col, nnz; |
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341 octave_idx_type *ridx, *cidx; |
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342 SparseComplexMatrix scm; |
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343 SparseMatrix sm; |
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344 |
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345 if (args(0).is_sparse_type ()) |
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346 { |
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347 if (args(0).is_complex_type ()) |
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348 { |
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349 scm = args(0). sparse_complex_matrix_value (); |
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350 n_row = scm.rows (); |
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351 n_col = scm.cols (); |
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352 nnz = scm.nnz (); |
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353 ridx = scm.xridx (); |
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354 cidx = scm.xcidx (); |
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355 } |
5164 | 356 else |
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357 { |
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358 sm = args(0).sparse_matrix_value (); |
5164 | 359 |
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360 n_row = sm.rows (); |
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361 n_col = sm.cols (); |
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362 nnz = sm.nnz (); |
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363 ridx = sm.xridx (); |
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364 cidx = sm.xcidx (); |
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365 } |
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366 } |
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367 else |
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368 { |
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369 if (args(0).is_complex_type ()) |
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370 sm = SparseMatrix (real (args(0).complex_matrix_value ())); |
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371 else |
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372 sm = SparseMatrix (args(0).matrix_value ()); |
5164 | 373 |
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374 n_row = sm.rows (); |
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375 n_col = sm.cols (); |
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376 nnz = sm.nnz (); |
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377 ridx = sm.xridx (); |
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378 cidx = sm.xcidx (); |
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379 } |
5164 | 380 |
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381 // Allocate workspace for colamd |
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382 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, n_col+1); |
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383 for (octave_idx_type i = 0; i < n_col+1; i++) |
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384 p[i] = cidx[i]; |
5164 | 385 |
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386 octave_idx_type Alen = COLAMD_NAME (_recommended) (nnz, n_row, n_col); |
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387 OCTAVE_LOCAL_BUFFER (octave_idx_type, A, Alen); |
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388 for (octave_idx_type i = 0; i < nnz; i++) |
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389 A[i] = ridx[i]; |
5164 | 390 |
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391 // Order the columns (destroys A) |
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392 OCTAVE_LOCAL_BUFFER (octave_idx_type, stats, COLAMD_STATS); |
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393 if (! COLAMD_NAME () (n_row, n_col, Alen, A, p, knobs, stats)) |
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394 { |
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395 COLAMD_NAME (_report)(stats); |
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396 |
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397 error ("colamd: internal error!"); |
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398 } |
5164 | 399 |
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400 // column elimination tree post-ordering (reuse variables) |
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401 OCTAVE_LOCAL_BUFFER (octave_idx_type, colbeg, n_col + 1); |
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402 OCTAVE_LOCAL_BUFFER (octave_idx_type, colend, n_col + 1); |
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403 OCTAVE_LOCAL_BUFFER (octave_idx_type, etree, n_col + 1); |
5164 | 404 |
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405 for (octave_idx_type i = 0; i < n_col; i++) |
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406 { |
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407 colbeg[i] = cidx[p[i]]; |
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408 colend[i] = cidx[p[i]+1]; |
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409 } |
5164 | 410 |
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411 coletree (ridx, colbeg, colend, etree, n_row, n_col); |
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412 |
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413 // Calculate the tree post-ordering |
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414 tree_postorder (n_col, etree, colbeg); |
5164 | 415 |
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416 // return the permutation vector |
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417 NDArray out_perm (dim_vector (1, n_col)); |
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418 for (octave_idx_type i = 0; i < n_col; i++) |
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419 out_perm(i) = p[colbeg[i]] + 1; |
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420 |
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421 retval(0) = out_perm; |
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422 |
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423 // print stats if spumoni > 0 |
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424 if (spumoni > 0) |
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425 COLAMD_NAME (_report)(stats); |
5164 | 426 |
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427 // Return the stats vector |
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428 if (nargout == 2) |
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429 { |
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430 NDArray out_stats (dim_vector (1, COLAMD_STATS)); |
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431 for (octave_idx_type i = 0 ; i < COLAMD_STATS ; i++) |
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432 out_stats(i) = stats[i]; |
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433 retval(1) = out_stats; |
5164 | 434 |
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435 // fix stats (5) and (6), for 1-based information on |
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436 // jumbled matrix. note that this correction doesn't |
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437 // occur if symamd returns FALSE |
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438 out_stats(COLAMD_INFO1)++; |
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439 out_stats(COLAMD_INFO2)++; |
5164 | 440 } |
441 | |
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442 return retval; |
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443 |
5451 | 444 #else |
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445 |
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446 octave_unused_parameter (args); |
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447 octave_unused_parameter (nargout); |
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448 |
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449 err_disabled_feature ("colamd", "COLAMD"); |
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450 |
5451 | 451 #endif |
5164 | 452 } |
453 | |
454 DEFUN_DLD (symamd, args, nargout, | |
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455 "-*- texinfo -*-\n\ |
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456 @deftypefn {} {@var{p} =} symamd (@var{S})\n\ |
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457 @deftypefnx {} {@var{p} =} symamd (@var{S}, @var{knobs})\n\ |
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458 @deftypefnx {} {[@var{p}, @var{stats}] =} symamd (@var{S})\n\ |
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459 @deftypefnx {} {[@var{p}, @var{stats}] =} symamd (@var{S}, @var{knobs})\n\ |
5164 | 460 \n\ |
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461 For a symmetric positive definite matrix @var{S}, returns the permutation\n\ |
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462 vector p such that @code{@var{S}(@var{p}, @var{p})} tends to have a\n\ |
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463 sparser Cholesky@tie{}factor than @var{S}.\n\ |
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464 \n\ |
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465 Sometimes @code{symamd} works well for symmetric indefinite matrices too.\n\ |
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466 The matrix @var{S} is assumed to be symmetric; only the strictly lower\n\ |
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467 triangular part is referenced. @var{S} must be square.\n\ |
5164 | 468 \n\ |
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469 @var{knobs} is an optional one- to two-element input vector. If @var{S} is\n\ |
5440 | 470 n-by-n, then rows and columns with more than\n\ |
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471 @code{max (16,@var{knobs}(1)*sqrt(n))} entries are removed prior to\n\ |
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472 ordering, and ordered last in the output permutation @var{p}. No\n\ |
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473 rows/columns are removed if @code{@var{knobs}(1) < 0}. If\n\ |
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474 @code{@var{knobs} (2)} is nonzero, @code{stats} and @var{knobs} are\n\ |
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475 printed. The default is @code{@var{knobs} = [10 0]}. Note that\n\ |
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476 @var{knobs} differs from earlier versions of @code{symamd}.\n\ |
5164 | 477 \n\ |
478 @var{stats} is an optional 20-element output vector that provides data\n\ | |
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479 about the ordering and the validity of the input matrix @var{S}. Ordering\n\ |
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480 statistics are in @code{@var{stats}(1:3)}.\n\ |
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481 @code{@var{stats}(1) = @var{stats}(2)} is the number of dense or empty rows\n\ |
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482 and columns ignored by SYMAMD and @code{@var{stats}(3)} is the number of\n\ |
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483 garbage collections performed on the internal data structure used by SYMAMD\n\ |
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484 (roughly of size @code{8.4 * nnz (tril (@var{S}, -1)) + 9 * @var{n}}\n\ |
5164 | 485 integers).\n\ |
486 \n\ | |
487 Octave built-in functions are intended to generate valid sparse matrices,\n\ | |
488 with no duplicate entries, with ascending row indices of the nonzeros\n\ | |
489 in each column, with a non-negative number of entries in each column (!)\n\ | |
490 and so on. If a matrix is invalid, then SYMAMD may or may not be able\n\ | |
491 to continue. If there are duplicate entries (a row index appears two or\n\ | |
492 more times in the same column) or if the row indices in a column are out\n\ | |
493 of order, then SYMAMD can correct these errors by ignoring the duplicate\n\ | |
494 entries and sorting each column of its internal copy of the matrix S (the\n\ | |
495 input matrix S is not repaired, however). If a matrix is invalid in\n\ | |
496 other ways then SYMAMD cannot continue, an error message is printed, and\n\ | |
497 no output arguments (@var{p} or @var{stats}) are returned. SYMAMD is\n\ | |
498 thus a simple way to check a sparse matrix to see if it's valid.\n\ | |
499 \n\ | |
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500 @code{@var{stats}(4:7)} provide information if SYMAMD was able to\n\ |
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501 continue. The matrix is OK if @code{@var{stats} (4)} is zero, or 1\n\ |
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502 if invalid. @code{@var{stats}(5)} is the rightmost column index that\n\ |
5164 | 503 is unsorted or contains duplicate entries, or zero if no such column\n\ |
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504 exists. @code{@var{stats}(6)} is the last seen duplicate or out-of-order\n\ |
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505 row index in the column index given by @code{@var{stats}(5)}, or zero\n\ |
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506 if no such row index exists. @code{@var{stats}(7)} is the number of\n\ |
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507 duplicate or out-of-order row indices. @code{@var{stats}(8:20)} is\n\ |
5164 | 508 always zero in the current version of SYMAMD (reserved for future use).\n\ |
509 \n\ | |
510 The ordering is followed by a column elimination tree post-ordering.\n\ | |
511 \n\ | |
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512 The authors of the code itself are @nospell{Stefan I. Larimore} and\n\ |
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513 @nospell{Timothy A. Davis @email{davis@@cise.ufl.edu}}, University of Florida. The algorithm was developed in collaboration with @nospell{John Gilbert},\n\ |
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514 Xerox PARC, and @nospell{Esmond Ng}, Oak Ridge National Laboratory. (see\n\ |
5164 | 515 @url{http://www.cise.ufl.edu/research/sparse/colamd})\n\ |
5642 | 516 @seealso{colperm, colamd}\n\ |
517 @end deftypefn") | |
5164 | 518 { |
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519 #if defined (HAVE_COLAMD) |
5451 | 520 |
5164 | 521 int nargin = args.length (); |
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522 |
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523 if (nargin < 1 || nargin > 2) |
5823 | 524 print_usage (); |
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525 |
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526 octave_value_list retval (nargin == 2 ? 2 : 1); |
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527 int spumoni = 0; |
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528 |
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529 // Get knobs |
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530 OCTAVE_LOCAL_BUFFER (double, knobs, COLAMD_KNOBS); |
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531 COLAMD_NAME (_set_defaults) (knobs); |
5164 | 532 |
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533 // Check for user-passed knobs |
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534 if (nargin == 2) |
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535 { |
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536 NDArray User_knobs = args(1).array_value (); |
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537 int nel_User_knobs = User_knobs.numel (); |
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538 |
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539 if (nel_User_knobs > 0) |
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540 knobs[COLAMD_DENSE_ROW] = User_knobs(COLAMD_DENSE_ROW); |
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541 if (nel_User_knobs > 1) |
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542 spumoni = static_cast<int> (User_knobs (1)); |
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543 } |
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544 |
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545 // print knob settings if spumoni is set |
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546 if (spumoni > 0) |
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547 octave_stdout << "symamd: dense row/col fraction: " |
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548 << knobs[COLAMD_DENSE_ROW] << std::endl; |
5164 | 549 |
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550 octave_idx_type n_row, n_col; |
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551 octave_idx_type *ridx, *cidx; |
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552 SparseMatrix sm; |
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553 SparseComplexMatrix scm; |
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554 |
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555 if (args(0).is_sparse_type ()) |
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556 { |
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557 if (args(0).is_complex_type ()) |
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558 { |
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559 scm = args(0).sparse_complex_matrix_value (); |
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560 n_row = scm.rows (); |
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561 n_col = scm.cols (); |
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562 ridx = scm.xridx (); |
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563 cidx = scm.xcidx (); |
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564 } |
5164 | 565 else |
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566 { |
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567 sm = args(0).sparse_matrix_value (); |
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568 n_row = sm.rows (); |
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569 n_col = sm.cols (); |
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570 ridx = sm.xridx (); |
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571 cidx = sm.xcidx (); |
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572 } |
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573 } |
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574 else |
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575 { |
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576 if (args(0).is_complex_type ()) |
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577 sm = SparseMatrix (real (args(0).complex_matrix_value ())); |
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578 else |
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579 sm = SparseMatrix (args(0).matrix_value ()); |
5164 | 580 |
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581 n_row = sm.rows (); |
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582 n_col = sm.cols (); |
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583 ridx = sm.xridx (); |
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584 cidx = sm.xcidx (); |
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585 } |
5164 | 586 |
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587 if (n_row != n_col) |
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588 err_square_matrix_required ("symamd", "S"); |
5164 | 589 |
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590 // Allocate workspace for symamd |
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591 OCTAVE_LOCAL_BUFFER (octave_idx_type, perm, n_col+1); |
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592 OCTAVE_LOCAL_BUFFER (octave_idx_type, stats, COLAMD_STATS); |
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593 if (! SYMAMD_NAME () (n_col, ridx, cidx, perm, |
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594 knobs, stats, &calloc, &free)) |
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595 { |
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596 SYMAMD_NAME (_report)(stats); |
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597 |
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598 error ("symamd: internal error!"); |
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599 } |
5164 | 600 |
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601 // column elimination tree post-ordering |
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602 OCTAVE_LOCAL_BUFFER (octave_idx_type, etree, n_col + 1); |
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603 symetree (ridx, cidx, etree, perm, n_col); |
5164 | 604 |
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605 // Calculate the tree post-ordering |
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606 OCTAVE_LOCAL_BUFFER (octave_idx_type, post, n_col + 1); |
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607 tree_postorder (n_col, etree, post); |
5164 | 608 |
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609 // return the permutation vector |
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610 NDArray out_perm (dim_vector (1, n_col)); |
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611 for (octave_idx_type i = 0; i < n_col; i++) |
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612 out_perm(i) = perm[post[i]] + 1; |
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613 |
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614 retval(0) = out_perm; |
5164 | 615 |
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616 // print stats if spumoni > 0 |
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617 if (spumoni > 0) |
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618 SYMAMD_NAME (_report)(stats); |
5164 | 619 |
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620 // Return the stats vector |
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621 if (nargout == 2) |
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622 { |
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623 NDArray out_stats (dim_vector (1, COLAMD_STATS)); |
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624 for (octave_idx_type i = 0 ; i < COLAMD_STATS ; i++) |
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625 out_stats(i) = stats[i]; |
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626 retval(1) = out_stats; |
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627 |
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628 // fix stats (5) and (6), for 1-based information on |
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629 // jumbled matrix. note that this correction doesn't |
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630 // occur if symamd returns FALSE |
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631 out_stats(COLAMD_INFO1)++; |
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632 out_stats(COLAMD_INFO2)++; |
5164 | 633 } |
634 | |
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635 return retval; |
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636 |
5451 | 637 #else |
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638 |
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639 octave_unused_parameter (args); |
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640 octave_unused_parameter (nargout); |
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641 |
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642 err_disabled_feature ("symamd", "COLAMD"); |
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643 |
5451 | 644 #endif |
5164 | 645 } |
646 | |
647 DEFUN_DLD (etree, args, nargout, | |
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648 "-*- texinfo -*-\n\ |
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649 @deftypefn {} {@var{p} =} etree (@var{S})\n\ |
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650 @deftypefnx {} {@var{p} =} etree (@var{S}, @var{typ})\n\ |
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651 @deftypefnx {} {[@var{p}, @var{q}] =} etree (@var{S}, @var{typ})\n\ |
5164 | 652 \n\ |
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653 Return the elimination tree for the matrix @var{S}.\n\ |
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654 \n\ |
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655 By default @var{S} is assumed to be symmetric and the symmetric elimination\n\ |
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656 tree is returned. The argument @var{typ} controls whether a symmetric or\n\ |
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657 column elimination tree is returned. Valid values of @var{typ} are\n\ |
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658 @qcode{\"sym\"} or @qcode{\"col\"}, for symmetric or column elimination tree\n\ |
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659 respectively.\n\ |
5164 | 660 \n\ |
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661 Called with a second argument, @code{etree} also returns the postorder\n\ |
5164 | 662 permutations on the tree.\n\ |
663 @end deftypefn") | |
664 { | |
665 int nargin = args.length (); | |
666 | |
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667 if (nargin < 1 || nargin > 2) |
5823 | 668 print_usage (); |
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669 |
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670 octave_value_list retval (nargout == 2 ? 2 : 1); |
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671 |
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672 octave_idx_type n_row = 0; |
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673 octave_idx_type n_col = 0; |
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674 octave_idx_type *ridx = 0; |
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675 octave_idx_type *cidx = 0; |
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676 |
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677 if (args(0).is_sparse_type ()) |
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678 error ("etree: S must be a sparse matrix"); |
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679 |
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680 if (args(0).is_complex_type ()) |
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681 { |
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682 SparseComplexMatrix scm = args(0).sparse_complex_matrix_value (); |
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683 |
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684 n_row = scm.rows (); |
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685 n_col = scm.cols (); |
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686 ridx = scm.xridx (); |
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687 cidx = scm.xcidx (); |
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688 } |
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689 else |
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690 { |
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691 SparseMatrix sm = args(0).sparse_matrix_value (); |
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692 |
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693 n_row = sm.rows (); |
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694 n_col = sm.cols (); |
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695 ridx = sm.xridx (); |
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696 cidx = sm.xcidx (); |
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697 } |
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698 |
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699 bool is_sym = true; |
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700 |
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701 if (nargin == 2) |
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702 { |
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703 std::string str = args(1).xstring_value ("etree: TYP must be a string"); |
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704 if (str.find ("C") == 0 || str.find ("c") == 0) |
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705 is_sym = false; |
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706 } |
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707 |
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708 // column elimination tree post-ordering (reuse variables) |
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709 OCTAVE_LOCAL_BUFFER (octave_idx_type, etree, n_col + 1); |
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710 |
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711 if (is_sym) |
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712 { |
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713 if (n_row != n_col) |
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714 error ("etree: S is marked as symmetric, but is not square"); |
5164 | 715 |
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716 symetree (ridx, cidx, etree, 0, n_col); |
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717 } |
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718 else |
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719 { |
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720 OCTAVE_LOCAL_BUFFER (octave_idx_type, colbeg, n_col); |
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721 OCTAVE_LOCAL_BUFFER (octave_idx_type, colend, n_col); |
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722 |
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723 for (octave_idx_type i = 0; i < n_col; i++) |
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724 { |
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725 colbeg[i] = cidx[i]; |
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726 colend[i] = cidx[i+1]; |
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727 } |
7924 | 728 |
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729 coletree (ridx, colbeg, colend, etree, n_row, n_col); |
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730 } |
7924 | 731 |
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732 NDArray tree (dim_vector (1, n_col)); |
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733 for (octave_idx_type i = 0; i < n_col; i++) |
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734 // We flag a root with n_col while Matlab does it with zero |
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735 // Convert for matlab compatiable output |
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736 if (etree[i] == n_col) |
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737 tree(i) = 0; |
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738 else |
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739 tree(i) = etree[i] + 1; |
5164 | 740 |
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741 retval(0) = tree; |
5164 | 742 |
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743 if (nargout == 2) |
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744 { |
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745 // Calculate the tree post-ordering |
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746 OCTAVE_LOCAL_BUFFER (octave_idx_type, post, n_col + 1); |
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747 tree_postorder (n_col, etree, post); |
5164 | 748 |
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749 NDArray postorder (dim_vector (1, n_col)); |
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750 for (octave_idx_type i = 0; i < n_col; i++) |
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751 postorder(i) = post[i] + 1; |
5164 | 752 |
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753 retval(1) = postorder; |
5164 | 754 } |
755 | |
756 return retval; | |
757 } |