Mercurial > octave
annotate libinterp/corefcn/lu.cc @ 20940:48b2ad5ee801
maint: Rename oct-obj.[cc|h] to ovl.[cc|h] for clarity.
* libinterp/corefcn/oct-obj.h: Replaced. Contains a #warning issued if used in
compilation and includes "ovl.h" instead. Original file renamed to
libinterp/octave-value/ovl.h
* libinterp/corefcn/oct-obj.cc: Renamed to libinterp/octave-value/ovl.cc.
* oct-obj.cc (ovl ()): Added new function to return empty octave_value_list.
* libinterp/corefcn/module.mk: Remove oct-obj.cc from build system.
* libinterp/octave-value/module.mk: Add ovl.h and ovl.cc to build system.
* mk-opts.pl, annotation-dialog.h, Cell.cc, __contourc__.cc, __dsearchn__.cc,
__lin_interpn__.cc, __pchip_deriv__.cc, __qp__.cc, balance.cc, besselj.cc,
betainc.cc, colloc.cc, conv2.cc, daspk.cc, dasrt.cc, dassl.cc, data.cc,
debug.cc, defaults.cc, defun.cc, det.cc, dirfns.cc, dlmread.cc, eig.cc,
error.cc, fft.cc, fft2.cc, fftn.cc, file-io.cc, filter.cc, find.cc,
gammainc.cc, gcd.cc, getgrent.cc, getpwent.cc, getrusage.cc, givens.cc,
graphics.cc, gripes.cc, help.cc, hess.cc, hex2num.cc, hook-fcn.h, input.cc,
input.h, inv.cc, kron.cc, load-save.cc, lookup.cc, ls-hdf5.cc, ls-mat-ascii.cc,
ls-mat4.cc, ls-mat5.cc, ls-oct-binary.cc, ls-oct-text.cc, lsode.cc, lu.cc,
luinc.cc, max.cc, mex.cc, oct-hist.cc, oct-lvalue.cc, oct-lvalue.h, oct-map.h,
oct-stream.cc, oct.h, ordschur.cc, pager.cc, pinv.cc, pr-output.cc, quad.cc,
quadcc.cc, qz.cc, rand.cc, rcond.cc, regexp.cc, schur.cc, sparse-xpow.cc,
strfns.cc, sub2ind.cc, svd.cc, sylvester.cc, symtab.h, syscalls.cc, sysdep.cc,
time.cc, toplev.cc, tril.cc, tsearch.cc, typecast.cc, urlwrite.cc, utils.cc,
variables.cc, xpow.cc, __delaunayn__.cc, __glpk__.cc, __voronoi__.cc,
audiodevinfo.cc, audioread.cc, chol.cc, convhulln.cc, dmperm.cc, qr.cc,
symbfact.cc, mkbuiltins, ov-base-diag.h, ov-base-int.cc, ov-base-mat.cc,
ov-base-mat.h, ov-base-scalar.cc, ov-base-sparse.cc, ov-base-sparse.h,
ov-base.cc, ov-bool-mat.cc, ov-bool.cc, ov-builtin.cc, ov-cell.cc, ov-colon.cc,
ov-complex.cc, ov-cs-list.h, ov-cx-mat.cc, ov-dld-fcn.cc, ov-fcn.cc, ov-fcn.h,
ov-float.cc, ov-flt-complex.cc, ov-flt-cx-mat.cc, ov-flt-re-mat.cc,
ov-int16.cc, ov-int32.cc, ov-int64.cc, ov-int8.cc, ov-java.h, ov-mex-fcn.cc,
ov-perm.h, ov-range.cc, ov-re-mat.cc, ov-scalar.cc, ov-str-mat.cc,
ov-uint16.cc, ov-uint32.cc, ov-uint64.cc, ov-uint8.cc, ov-usr-fcn.cc,
ov-usr-fcn.h, ov.cc, octave.cc, 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-double-conv.cc, op-fcdm-fcdm.cc,
op-fcdm-fdm.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-float-conv.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-int-conv.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-pm-pm.cc, op-pm-scm.cc, op-pm-sm.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,
parse.h, pt-arg-list.cc, pt-assign.cc, pt-binop.cc, pt-cbinop.cc, pt-cell.cc,
pt-colon.cc, pt-const.cc, pt-eval.h, pt-fcn-handle.cc, pt-funcall.h, pt-id.cc,
pt-idx.cc, pt-jump.cc, pt-mat.cc, pt-select.cc, pt-unop.cc, token.cc,
Array-sym.cc: replace '#include "oct-obj.h"' with '#include "ovl.h"'.
author | Rik <rik@octave.org> |
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date | Fri, 18 Dec 2015 16:04:56 -0800 |
parents | 4d3daf7e43f3 |
children | a4f5da7c5463 |
rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2015 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
25 #endif | |
26 | |
27 #include "CmplxLU.h" | |
28 #include "dbleLU.h" | |
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29 #include "fCmplxLU.h" |
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30 #include "floatLU.h" |
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31 #include "SparseCmplxLU.h" |
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32 #include "SparsedbleLU.h" |
2928 | 33 |
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34 #include "defun.h" |
2928 | 35 #include "error.h" |
36 #include "gripes.h" | |
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37 #include "ovl.h" |
2928 | 38 #include "utils.h" |
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39 #include "ov-re-sparse.h" |
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40 #include "ov-cx-sparse.h" |
2928 | 41 |
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42 template <class MT> |
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43 static octave_value |
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44 get_lu_l (const base_lu<MT>& fact) |
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45 { |
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46 MT L = fact.L (); |
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47 if (L.is_square ()) |
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48 return octave_value (L, MatrixType (MatrixType::Lower)); |
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49 else |
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50 return L; |
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51 } |
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52 |
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53 template <class MT> |
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54 static octave_value |
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55 get_lu_u (const base_lu<MT>& fact) |
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56 { |
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57 MT U = fact.U (); |
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58 if (U.is_square () && fact.regular ()) |
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59 return octave_value (U, MatrixType (MatrixType::Upper)); |
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60 else |
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61 return U; |
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62 } |
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63 |
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64 DEFUN (lu, args, nargout, |
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65 "-*- texinfo -*-\n\ |
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66 @deftypefn {} {[@var{L}, @var{U}] =} lu (@var{A})\n\ |
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67 @deftypefnx {} {[@var{L}, @var{U}, @var{P}] =} lu (@var{A})\n\ |
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68 @deftypefnx {} {[@var{L}, @var{U}, @var{P}, @var{Q}] =} lu (@var{S})\n\ |
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69 @deftypefnx {} {[@var{L}, @var{U}, @var{P}, @var{Q}, @var{R}] =} lu (@var{S})\n\ |
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70 @deftypefnx {} {[@dots{}] =} lu (@var{S}, @var{thres})\n\ |
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71 @deftypefnx {} {@var{y} =} lu (@dots{})\n\ |
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72 @deftypefnx {} {[@dots{}] =} lu (@dots{}, \"vector\")\n\ |
3372 | 73 @cindex LU decomposition\n\ |
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74 Compute the LU@tie{}decomposition of @var{A}.\n\ |
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75 \n\ |
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76 If @var{A} is full subroutines from @sc{lapack} are used and if @var{A} is\n\ |
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77 sparse then @sc{umfpack} is used.\n\ |
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78 \n\ |
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79 The result is returned in a permuted form, according to the optional return\n\ |
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80 value @var{P}. For example, given the matrix @code{a = [1, 2; 3, 4]},\n\ |
3372 | 81 \n\ |
82 @example\n\ | |
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83 [l, u, p] = lu (@var{a})\n\ |
3372 | 84 @end example\n\ |
85 \n\ | |
86 @noindent\n\ | |
87 returns\n\ | |
88 \n\ | |
89 @example\n\ | |
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90 @group\n\ |
3372 | 91 l =\n\ |
92 \n\ | |
93 1.00000 0.00000\n\ | |
94 0.33333 1.00000\n\ | |
95 \n\ | |
96 u =\n\ | |
97 \n\ | |
98 3.00000 4.00000\n\ | |
99 0.00000 0.66667\n\ | |
100 \n\ | |
101 p =\n\ | |
102 \n\ | |
103 0 1\n\ | |
104 1 0\n\ | |
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105 @end group\n\ |
3372 | 106 @end example\n\ |
4329 | 107 \n\ |
5457 | 108 The matrix is not required to be square.\n\ |
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109 \n\ |
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110 When called with two or three output arguments and a spare input matrix,\n\ |
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111 @code{lu} does not attempt to perform sparsity preserving column\n\ |
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112 permutations. Called with a fourth output argument, the sparsity\n\ |
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113 preserving column transformation @var{Q} is returned, such that\n\ |
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114 @code{@var{P} * @var{A} * @var{Q} = @var{L} * @var{U}}.\n\ |
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115 \n\ |
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116 Called with a fifth output argument and a sparse input matrix,\n\ |
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117 @code{lu} attempts to use a scaling factor @var{R} on the input matrix\n\ |
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118 such that\n\ |
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119 @code{@var{P} * (@var{R} \\ @var{A}) * @var{Q} = @var{L} * @var{U}}.\n\ |
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120 This typically leads to a sparser and more stable factorization.\n\ |
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121 \n\ |
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122 An additional input argument @var{thres}, that defines the pivoting\n\ |
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123 threshold can be given. @var{thres} can be a scalar, in which case\n\ |
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124 it defines the @sc{umfpack} pivoting tolerance for both symmetric and\n\ |
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125 unsymmetric cases. If @var{thres} is a 2-element vector, then the first\n\ |
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126 element defines the pivoting tolerance for the unsymmetric @sc{umfpack}\n\ |
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127 pivoting strategy and the second for the symmetric strategy. By default,\n\ |
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128 the values defined by @code{spparms} are used ([0.1, 0.001]).\n\ |
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129 \n\ |
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130 Given the string argument @qcode{\"vector\"}, @code{lu} returns the values\n\ |
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131 of @var{P} and @var{Q} as vector values, such that for full matrix,\n\ |
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132 @code{@var{A} (@var{P},:) = @var{L} * @var{U}}, and @code{@var{R}(@var{P},:)\n\ |
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133 * @var{A} (:, @var{Q}) = @var{L} * @var{U}}.\n\ |
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134 \n\ |
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135 With two output arguments, returns the permuted forms of the upper and\n\ |
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136 lower triangular matrices, such that @code{@var{A} = @var{L} * @var{U}}.\n\ |
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137 With one output argument @var{y}, then the matrix returned by the @sc{lapack}\n\ |
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138 routines is returned. If the input matrix is sparse then the matrix @var{L}\n\ |
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139 is embedded into @var{U} to give a return value similar to the full case.\n\ |
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140 For both full and sparse matrices, @code{lu} loses the permutation\n\ |
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141 information.\n\ |
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142 @seealso{luupdate, ilu, chol, hess, qr, qz, schur, svd}\n\ |
3372 | 143 @end deftypefn") |
2928 | 144 { |
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145 int nargin = args.length (); |
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146 bool issparse = (nargin > 0 && args(0).is_sparse_type ()); |
2928 | 147 |
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148 if (nargin < 1 || (issparse && nargin > 3) || (! issparse && nargin > 2)) |
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149 print_usage (); |
2928 | 150 |
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151 bool vecout = false; |
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152 Matrix thres; |
20892 | 153 int n = 1; |
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154 |
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155 while (n < nargin) |
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156 { |
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157 if (args(n).is_string ()) |
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158 { |
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159 std::string tmp = args(n++).string_value (); |
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160 |
20892 | 161 if (tmp == "vector") |
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162 vecout = true; |
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163 else |
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164 error ("lu: unrecognized string argument"); |
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165 } |
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166 else |
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167 { |
20892 | 168 if (! issparse) |
169 error ("lu: can not define pivoting threshold THRES for full matrices"); | |
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170 Matrix tmp = args(n++).matrix_value (); |
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171 |
20892 | 172 if (tmp.numel () == 1) |
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173 { |
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174 thres.resize (1,2); |
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175 thres(0) = tmp(0); |
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176 thres(1) = tmp(0); |
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177 } |
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178 else if (tmp.numel () == 2) |
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179 thres = tmp; |
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180 else |
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181 error ("lu: THRES must be a 1 or 2-element vector"); |
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182 } |
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183 } |
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184 |
20892 | 185 octave_value_list retval; |
186 bool scale = (nargout == 5); | |
187 | |
2928 | 188 octave_value arg = args(0); |
189 | |
5275 | 190 octave_idx_type nr = arg.rows (); |
191 octave_idx_type nc = arg.columns (); | |
2928 | 192 |
193 int arg_is_empty = empty_arg ("lu", nr, nc); | |
194 | |
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195 if (issparse) |
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196 { |
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197 if (arg_is_empty < 0) |
20892 | 198 return octave_value_list (); |
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199 else if (arg_is_empty > 0) |
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200 return octave_value_list (5, SparseMatrix ()); |
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201 |
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202 if (arg.is_real_type ()) |
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203 { |
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204 SparseMatrix m = arg.sparse_matrix_value (); |
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205 |
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206 if (nargout < 4) |
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207 { |
20892 | 208 ColumnVector Qinit (nc); |
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209 for (octave_idx_type i = 0; i < nc; i++) |
20892 | 210 Qinit(i) = i; |
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211 SparseLU fact (m, Qinit, thres, false, true); |
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212 |
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213 if (nargout < 2) |
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214 retval(0) = fact.Y (); |
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215 else |
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216 { |
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217 retval.resize (nargout == 3 ? 3 : 2); |
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218 retval(1) |
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219 = octave_value ( |
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220 fact.U () * fact.Pc_mat ().transpose (), |
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221 MatrixType (MatrixType::Permuted_Upper, |
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222 nc, fact.col_perm ())); |
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223 |
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224 PermMatrix P = fact.Pr_mat (); |
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225 SparseMatrix L = fact.L (); |
20892 | 226 |
227 if (nargout == 2) | |
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228 retval(0) |
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229 = octave_value (P.transpose () * L, |
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230 MatrixType (MatrixType::Permuted_Lower, |
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231 nr, fact.row_perm ())); |
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232 else |
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233 { |
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234 retval(0) = L; |
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235 if (vecout) |
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236 retval(2) = fact.Pr_vec(); |
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237 else |
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238 retval(2) = P; |
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239 } |
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240 } |
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241 } |
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242 else |
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243 { |
20892 | 244 retval.resize (scale ? 5 : 4); |
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245 SparseLU fact (m, thres, scale); |
2928 | 246 |
20892 | 247 retval(0) = octave_value (fact.L (), |
248 MatrixType (MatrixType::Lower)); | |
249 retval(1) = octave_value (fact.U (), | |
250 MatrixType (MatrixType::Upper)); | |
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251 |
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252 if (vecout) |
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253 { |
20892 | 254 retval(2) = fact.Pr_vec (); |
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255 retval(3) = fact.Pc_vec (); |
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256 } |
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257 else |
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258 { |
20892 | 259 retval(2) = fact.Pr_mat (); |
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260 retval(3) = fact.Pc_mat (); |
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261 } |
20892 | 262 |
263 if (scale) | |
264 retval(4) = fact.R (); | |
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265 } |
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266 } |
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267 else if (arg.is_complex_type ()) |
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268 { |
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269 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
2928 | 270 |
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271 if (nargout < 4) |
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272 { |
20892 | 273 ColumnVector Qinit (nc); |
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274 for (octave_idx_type i = 0; i < nc; i++) |
20892 | 275 Qinit(i) = i; |
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276 SparseComplexLU fact (m, Qinit, thres, false, true); |
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277 |
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278 if (nargout < 2) |
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279 retval(0) = fact.Y (); |
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280 else |
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281 { |
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282 retval.resize (nargout == 3 ? 3 : 2); |
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283 retval(1) |
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284 = octave_value ( |
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285 fact.U () * fact.Pc_mat ().transpose (), |
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286 MatrixType (MatrixType::Permuted_Upper, |
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287 nc, fact.col_perm ())); |
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288 |
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289 PermMatrix P = fact.Pr_mat (); |
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290 SparseComplexMatrix L = fact.L (); |
20892 | 291 if (nargout == 2) |
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292 retval(0) |
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293 = octave_value (P.transpose () * L, |
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294 MatrixType (MatrixType::Permuted_Lower, |
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295 nr, fact.row_perm ())); |
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296 else |
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297 { |
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298 retval(0) = L; |
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299 if (vecout) |
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300 retval(2) = fact.Pr_vec(); |
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301 else |
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302 retval(2) = P; |
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303 } |
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304 } |
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305 } |
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306 else |
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307 { |
20892 | 308 retval.resize (scale ? 5 : 4); |
309 SparseComplexLU fact (m, thres, scale); | |
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310 |
20892 | 311 retval(0) = octave_value (fact.L (), |
312 MatrixType (MatrixType::Lower)); | |
313 retval(1) = octave_value (fact.U (), | |
314 MatrixType (MatrixType::Upper)); | |
315 | |
316 if (vecout) | |
317 { | |
318 retval(2) = fact.Pr_vec (); | |
319 retval(3) = fact.Pc_vec (); | |
320 } | |
321 else | |
322 { | |
323 retval(2) = fact.Pr_mat (); | |
324 retval(3) = fact.Pc_mat (); | |
325 } | |
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326 |
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327 if (scale) |
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328 retval(4) = fact.R (); |
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329 } |
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330 |
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331 } |
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332 else |
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333 gripe_wrong_type_arg ("lu", arg); |
2928 | 334 } |
335 else | |
336 { | |
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337 if (arg_is_empty < 0) |
20892 | 338 return octave_value_list (); |
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339 else if (arg_is_empty > 0) |
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340 return octave_value_list (3, Matrix ()); |
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341 |
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342 if (arg.is_real_type ()) |
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343 { |
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344 if (arg.is_single_type ()) |
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345 { |
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346 FloatMatrix m = arg.float_matrix_value (); |
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347 |
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348 FloatLU fact (m); |
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349 |
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350 switch (nargout) |
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351 { |
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352 case 0: |
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353 case 1: |
20892 | 354 retval = ovl (fact.Y ()); |
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355 break; |
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356 |
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357 case 2: |
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358 { |
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359 PermMatrix P = fact.P (); |
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360 FloatMatrix L = P.transpose () * fact.L (); |
20892 | 361 retval = ovl (L, get_lu_u (fact)); |
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362 } |
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363 break; |
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364 |
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365 case 3: |
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366 default: |
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367 { |
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368 if (vecout) |
20892 | 369 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
370 fact.P_vec ()); | |
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371 else |
20892 | 372 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
373 fact.P ()); | |
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374 } |
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375 break; |
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376 } |
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377 } |
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378 else |
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379 { |
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380 Matrix m = arg.matrix_value (); |
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381 |
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382 LU fact (m); |
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383 |
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384 switch (nargout) |
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385 { |
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386 case 0: |
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387 case 1: |
20892 | 388 retval = ovl (fact.Y ()); |
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389 break; |
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390 |
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391 case 2: |
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392 { |
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393 PermMatrix P = fact.P (); |
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394 Matrix L = P.transpose () * fact.L (); |
20892 | 395 retval = ovl (L, get_lu_u (fact)); |
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396 } |
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397 break; |
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398 |
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399 case 3: |
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400 default: |
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401 { |
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402 if (vecout) |
20892 | 403 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
404 fact.P_vec ()); | |
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405 else |
20892 | 406 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
407 fact.P ()); | |
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408 } |
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409 break; |
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410 } |
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411 } |
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412 } |
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413 else if (arg.is_complex_type ()) |
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414 { |
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415 if (arg.is_single_type ()) |
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416 { |
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417 FloatComplexMatrix m = arg.float_complex_matrix_value (); |
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418 |
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419 FloatComplexLU fact (m); |
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420 |
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421 switch (nargout) |
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422 { |
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423 case 0: |
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424 case 1: |
20892 | 425 retval = ovl (fact.Y ()); |
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426 break; |
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427 |
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428 case 2: |
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429 { |
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430 PermMatrix P = fact.P (); |
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431 FloatComplexMatrix L = P.transpose () * fact.L (); |
20892 | 432 retval = ovl (L, get_lu_u (fact)); |
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433 } |
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434 break; |
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435 |
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436 case 3: |
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437 default: |
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438 { |
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439 if (vecout) |
20892 | 440 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
441 fact.P_vec ()); | |
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442 else |
20892 | 443 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
444 fact.P ()); | |
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445 } |
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446 break; |
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447 } |
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448 } |
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449 else |
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450 { |
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451 ComplexMatrix m = arg.complex_matrix_value (); |
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452 |
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453 ComplexLU fact (m); |
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454 |
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455 switch (nargout) |
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456 { |
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457 case 0: |
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458 case 1: |
20892 | 459 retval = ovl (fact.Y ()); |
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460 break; |
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461 |
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462 case 2: |
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463 { |
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464 PermMatrix P = fact.P (); |
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465 ComplexMatrix L = P.transpose () * fact.L (); |
20892 | 466 retval = ovl (L, get_lu_u (fact)); |
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467 } |
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468 break; |
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469 |
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470 case 3: |
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471 default: |
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472 { |
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473 if (vecout) |
20892 | 474 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
475 fact.P_vec ()); | |
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476 else |
20892 | 477 retval = ovl (get_lu_l (fact), get_lu_u (fact), |
478 fact.P ()); | |
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479 } |
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480 break; |
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481 } |
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482 } |
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483 } |
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484 else |
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485 gripe_wrong_type_arg ("lu", arg); |
2928 | 486 } |
487 | |
488 return retval; | |
489 } | |
490 | |
491 /* | |
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492 %!assert(lu ([1, 2; 3, 4]), [3, 4; 1/3, 2/3], eps); |
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493 |
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494 %!test |
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495 %! [l, u] = lu ([1, 2; 3, 4]); |
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496 %! assert (l, [1/3, 1; 1, 0], sqrt (eps)); |
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497 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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498 |
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499 %!test |
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500 %! [l, u, p] = lu ([1, 2; 3, 4]); |
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501 %! assert (l, [1, 0; 1/3, 1], sqrt (eps)); |
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502 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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503 %! assert (p(:,:), [0, 1; 1, 0], sqrt (eps)); |
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504 |
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505 %!test |
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506 %! [l, u, p] = lu ([1, 2; 3, 4], "vector"); |
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507 %! assert (l, [1, 0; 1/3, 1], sqrt (eps)); |
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508 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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509 %! assert (p, [2;1], sqrt (eps)); |
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510 |
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511 %!test |
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512 %! [l, u, p] = lu ([1, 2; 3, 4; 5, 6]); |
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513 %! assert (l, [1, 0; 1/5, 1; 3/5, 1/2], sqrt (eps)); |
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514 %! assert (u, [5, 6; 0, 4/5], sqrt (eps)); |
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515 %! assert (p(:,:), [0, 0, 1; 1, 0, 0; 0 1 0], sqrt (eps)); |
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516 |
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517 %!assert (lu (single ([1, 2; 3, 4])), single ([3, 4; 1/3, 2/3]), eps ("single")) |
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518 |
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519 %!test |
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520 %! [l, u] = lu (single ([1, 2; 3, 4])); |
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521 %! assert (l, single ([1/3, 1; 1, 0]), sqrt (eps ("single"))); |
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522 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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523 |
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524 %!test |
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525 %! [l, u, p] = lu (single ([1, 2; 3, 4])); |
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526 %! assert (l, single ([1, 0; 1/3, 1]), sqrt (eps ("single"))); |
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527 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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528 %! assert (p(:,:), single ([0, 1; 1, 0]), sqrt (eps ("single"))); |
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529 |
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530 %!test |
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531 %! [l, u, p] = lu (single ([1, 2; 3, 4]), "vector"); |
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532 %! assert (l, single ([1, 0; 1/3, 1]), sqrt (eps ("single"))); |
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533 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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534 %! assert (p, single ([2;1]), sqrt (eps ("single"))); |
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535 |
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536 %!test |
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537 %! [l u p] = lu (single ([1, 2; 3, 4; 5, 6])); |
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538 %! assert (l, single ([1, 0; 1/5, 1; 3/5, 1/2]), sqrt (eps ("single"))); |
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539 %! assert (u, single ([5, 6; 0, 4/5]), sqrt (eps ("single"))); |
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540 %! assert (p(:,:), single ([0, 0, 1; 1, 0, 0; 0 1 0]), sqrt (eps ("single"))); |
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541 |
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542 %!error lu () |
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543 %!error <can not define pivoting threshold> lu ([1, 2; 3, 4], 2) |
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544 |
18488
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|
545 %!testif HAVE_UMFPACK |
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546 %! Bi = [1 2 3 4 5 2 3 6 7 8 4 5 7 8 9]; |
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|
547 %! Bj = [1 3 4 5 6 7 8 9 11 12 13 14 15 16 17]; |
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548 %! Bv = [1 1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1]; |
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549 %! B = sparse (Bi, Bj, Bv); |
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550 %! [L, U] = lu (B); |
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551 %! assert (L*U, B); |
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552 %! [L, U, P] = lu(B); |
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553 %! assert (P'*L*U, B); |
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554 %! [L, U, P, Q] = lu (B); |
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555 %! assert (P'*L*U*Q', B); |
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556 |
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557 */ |
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558 |
9708 | 559 static |
560 bool check_lu_dims (const octave_value& l, const octave_value& u, | |
561 const octave_value& p) | |
562 { | |
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563 octave_idx_type m = l.rows (); |
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564 octave_idx_type k = u.rows (); |
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565 octave_idx_type n = u.columns (); |
20892 | 566 |
9708 | 567 return ((l.ndims () == 2 && u.ndims () == 2 && k == l.columns ()) |
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568 && k == std::min (m, n) |
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569 && (p.is_undefined () || p.rows () == m)); |
9708 | 570 } |
571 | |
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572 DEFUN (luupdate, args, , |
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573 "-*- texinfo -*-\n\ |
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574 @deftypefn {} {[@var{L}, @var{U}] =} luupdate (@var{L}, @var{U}, @var{x}, @var{y})\n\ |
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575 @deftypefnx {} {[@var{L}, @var{U}, @var{P}] =} luupdate (@var{L}, @var{U}, @var{P}, @var{x}, @var{y})\n\ |
9709 | 576 Given an LU@tie{}factorization of a real or complex matrix\n\ |
577 @w{@var{A} = @var{L}*@var{U}}, @var{L}@tie{}lower unit trapezoidal and\n\ | |
578 @var{U}@tie{}upper trapezoidal, return the LU@tie{}factorization\n\ | |
579 of @w{@var{A} + @var{x}*@var{y}.'}, where @var{x} and @var{y} are\n\ | |
580 column vectors (rank-1 update) or matrices with equal number of columns\n\ | |
581 (rank-k update).\n\ | |
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582 \n\ |
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583 Optionally, row-pivoted updating can be used by supplying a row permutation\n\ |
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584 (pivoting) matrix @var{P}; in that case, an updated permutation matrix is\n\ |
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585 returned. Note that if @var{L}, @var{U}, @var{P} is a pivoted\n\ |
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586 LU@tie{}factorization as obtained by @code{lu}:\n\ |
9709 | 587 \n\ |
588 @example\n\ | |
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589 [@var{L}, @var{U}, @var{P}] = lu (@var{A});\n\ |
9709 | 590 @end example\n\ |
591 \n\ | |
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592 @noindent\n\ |
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593 then a factorization of @tcode{@var{A}+@var{x}*@var{y}.'} can be obtained\n\ |
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594 either as\n\ |
9709 | 595 \n\ |
596 @example\n\ | |
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597 [@var{L1}, @var{U1}] = lu (@var{L}, @var{U}, @var{P}*@var{x}, @var{y})\n\ |
9709 | 598 @end example\n\ |
599 \n\ | |
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600 @noindent\n\ |
9709 | 601 or\n\ |
602 \n\ | |
603 @example\n\ | |
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604 [@var{L1}, @var{U1}, @var{P1}] = lu (@var{L}, @var{U}, @var{P}, @var{x}, @var{y})\n\ |
9709 | 605 @end example\n\ |
606 \n\ | |
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607 The first form uses the unpivoted algorithm, which is faster, but less\n\ |
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608 stable. The second form uses a slower pivoted algorithm, which is more\n\ |
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609 stable.\n\ |
9709 | 610 \n\ |
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611 The matrix case is done as a sequence of rank-1 updates; thus, for large\n\ |
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612 enough k, it will be both faster and more accurate to recompute the\n\ |
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613 factorization from scratch.\n\ |
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614 @seealso{lu, cholupdate, qrupdate}\n\ |
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615 @end deftypefn") |
9708 | 616 { |
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617 int nargin = args.length (); |
9708 | 618 |
619 if (nargin != 4 && nargin != 5) | |
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|
620 print_usage (); |
9708 | 621 |
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622 bool pivoted = (nargin == 5); |
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|
623 |
9708 | 624 octave_value argl = args(0); |
625 octave_value argu = args(1); | |
626 octave_value argp = pivoted ? args(2) : octave_value (); | |
627 octave_value argx = args(2 + pivoted); | |
628 octave_value argy = args(3 + pivoted); | |
629 | |
20892 | 630 if (! (argl.is_numeric_type () && argu.is_numeric_type () |
631 && argx.is_numeric_type () && argy.is_numeric_type () | |
632 && (! pivoted || argp.is_perm_matrix ()))) | |
633 error ("luupdate: L, U, X, and Y must be numeric"); | |
9708 | 634 |
20892 | 635 if (! check_lu_dims (argl, argu, argp)) |
636 error ("luupdate: dimension mismatch"); | |
9708 | 637 |
20892 | 638 PermMatrix P = (pivoted |
639 ? argp.perm_matrix_value () | |
640 : PermMatrix::eye (argl.rows ())); | |
9708 | 641 |
20892 | 642 if (argl.is_real_type () && argu.is_real_type () |
643 && argx.is_real_type () && argy.is_real_type ()) | |
644 { | |
645 // all real case | |
646 if (argl.is_single_type () || argu.is_single_type () | |
647 || argx.is_single_type () || argy.is_single_type ()) | |
648 { | |
649 FloatMatrix L = argl.float_matrix_value (); | |
650 FloatMatrix U = argu.float_matrix_value (); | |
651 FloatMatrix x = argx.float_matrix_value (); | |
652 FloatMatrix y = argy.float_matrix_value (); | |
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653 |
20892 | 654 FloatLU fact (L, U, P); |
655 if (pivoted) | |
656 fact.update_piv (x, y); | |
657 else | |
658 fact.update (x, y); | |
9708 | 659 |
20892 | 660 if (pivoted) |
20898
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|
661 return ovl (get_lu_l (fact), get_lu_u (fact), fact.P ()); |
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662 else |
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|
663 return ovl (get_lu_l (fact), get_lu_u (fact)); |
9708 | 664 } |
665 else | |
20892 | 666 { |
667 Matrix L = argl.matrix_value (); | |
668 Matrix U = argu.matrix_value (); | |
669 Matrix x = argx.matrix_value (); | |
670 Matrix y = argy.matrix_value (); | |
671 | |
672 LU fact (L, U, P); | |
673 if (pivoted) | |
674 fact.update_piv (x, y); | |
675 else | |
676 fact.update (x, y); | |
677 | |
678 if (pivoted) | |
20898
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|
679 return ovl (get_lu_l (fact), get_lu_u (fact), fact.P ()); |
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680 else |
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diff
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|
681 return ovl (get_lu_l (fact), get_lu_u (fact)); |
20892 | 682 } |
9708 | 683 } |
684 else | |
20892 | 685 { |
686 // complex case | |
687 if (argl.is_single_type () || argu.is_single_type () | |
688 || argx.is_single_type () || argy.is_single_type ()) | |
689 { | |
690 FloatComplexMatrix L = argl.float_complex_matrix_value (); | |
691 FloatComplexMatrix U = argu.float_complex_matrix_value (); | |
692 FloatComplexMatrix x = argx.float_complex_matrix_value (); | |
693 FloatComplexMatrix y = argy.float_complex_matrix_value (); | |
694 | |
695 FloatComplexLU fact (L, U, P); | |
696 if (pivoted) | |
697 fact.update_piv (x, y); | |
698 else | |
699 fact.update (x, y); | |
700 | |
701 if (pivoted) | |
20898
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702 return ovl (get_lu_l (fact), get_lu_u (fact), fact.P ()); |
8da80da1ac37
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|
703 else |
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|
704 return ovl (get_lu_l (fact), get_lu_u (fact)); |
20892 | 705 } |
706 else | |
707 { | |
708 ComplexMatrix L = argl.complex_matrix_value (); | |
709 ComplexMatrix U = argu.complex_matrix_value (); | |
710 ComplexMatrix x = argx.complex_matrix_value (); | |
711 ComplexMatrix y = argy.complex_matrix_value (); | |
712 | |
713 ComplexLU fact (L, U, P); | |
714 if (pivoted) | |
715 fact.update_piv (x, y); | |
716 else | |
717 fact.update (x, y); | |
718 | |
719 if (pivoted) | |
20898
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720 return ovl (get_lu_l (fact), get_lu_u (fact), fact.P ()); |
8da80da1ac37
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|
721 else |
8da80da1ac37
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|
722 return ovl (get_lu_l (fact), get_lu_u (fact)); |
20892 | 723 } |
724 } | |
9708 | 725 } |
726 | |
7814
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727 /* |
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728 %!shared A, u, v, Ac, uc, vc |
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|
729 %! A = [0.091364 0.613038 0.999083; |
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730 %! 0.594638 0.425302 0.603537; |
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731 %! 0.383594 0.291238 0.085574; |
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732 %! 0.265712 0.268003 0.238409; |
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|
733 %! 0.669966 0.743851 0.445057 ]; |
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|
734 %! |
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|
735 %! u = [0.85082; |
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736 %! 0.76426; |
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737 %! 0.42883; |
12df7854fa7c
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738 %! 0.53010; |
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|
739 %! 0.80683 ]; |
cf70ee43077c
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|
740 %! |
cf70ee43077c
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|
741 %! v = [0.98810; |
cf70ee43077c
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742 %! 0.24295; |
cf70ee43077c
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|
743 %! 0.43167 ]; |
cf70ee43077c
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|
744 %! |
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|
745 %! Ac = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i; |
14501
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746 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i; |
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747 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i; |
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748 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i; |
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|
749 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ]; |
10080
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750 %! |
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|
751 %! uc = [0.20351 + 0.05401i; |
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|
752 %! 0.13141 + 0.43708i; |
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753 %! 0.29808 + 0.08789i; |
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754 %! 0.69821 + 0.38844i; |
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755 %! 0.74871 + 0.25821i ]; |
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756 %! |
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757 %! vc = [0.85839 + 0.29468i; |
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758 %! 0.20820 + 0.93090i; |
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759 %! 0.86184 + 0.34689i ]; |
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760 %! |
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|
761 |
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762 %!testif HAVE_QRUPDATE_LUU |
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763 %! [L,U,P] = lu (A); |
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764 %! [L,U] = luupdate (L,U,P*u,v); |
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765 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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766 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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767 %! assert (norm (vec (P'*L*U - A - u*v.'), Inf) < norm (A)*1e1*eps); |
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|
768 %! |
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769 %!testif HAVE_QRUPDATE_LUU |
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770 %! [L,U,P] = lu (Ac); |
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771 %! [L,U] = luupdate (L,U,P*uc,vc); |
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772 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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773 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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774 %! assert (norm (vec (P'*L*U - Ac - uc*vc.'), Inf) < norm (Ac)*1e1*eps); |
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|
775 |
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776 %!testif HAVE_QRUPDATE_LUU |
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777 %! [L,U,P] = lu (single (A)); |
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778 %! [L,U] = luupdate (L,U,P*single (u), single (v)); |
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779 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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780 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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781 %! assert (norm (vec (P'*L*U - single (A) - single (u)*single (v).'), Inf) < norm (single (A))*1e1*eps ("single")); |
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|
782 %! |
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|
783 %!testif HAVE_QRUPDATE_LUU |
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784 %! [L,U,P] = lu (single (Ac)); |
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785 %! [L,U] = luupdate (L,U,P*single (uc),single (vc)); |
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786 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
787 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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788 %! assert (norm (vec (P'*L*U - single (Ac) - single (uc)*single (vc).'), Inf) < norm (single (Ac))*1e1*eps ("single")); |
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|
789 |
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|
790 %!testif HAVE_QRUPDATE_LUU |
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791 %! [L,U,P] = lu (A); |
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792 %! [L,U,P] = luupdate (L,U,P,u,v); |
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793 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
794 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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|
795 %! assert (norm (vec (P'*L*U - A - u*v.'), Inf) < norm (A)*1e1*eps); |
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|
796 %! |
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797 %!testif HAVE_QRUPDATE_LUU |
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798 %! [L,U,P] = lu (A); |
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799 %! [~,ordcols] = max (P,[],1); |
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800 %! [~,ordrows] = max (P,[],2); |
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801 %! P1 = eye (size(P))(:,ordcols); |
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802 %! P2 = eye (size(P))(ordrows,:); |
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803 %! assert(P1 == P); |
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|
804 %! assert(P2 == P); |
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805 %! [L,U,P] = luupdate (L,U,P,u,v); |
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806 %! [L,U,P1] = luupdate (L,U,P1,u,v); |
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|
807 %! [L,U,P2] = luupdate (L,U,P2,u,v); |
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808 %! assert(P1 == P); |
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|
809 %! assert(P2 == P); |
aa9ca67f09fb
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diff
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|
810 %! |
aa9ca67f09fb
make all permutation matrices column permutations (bug #42418)
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|
811 %!testif HAVE_QRUPDATE_LUU |
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812 %! [L,U,P] = lu (Ac); |
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813 %! [L,U,P] = luupdate (L,U,P,uc,vc); |
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814 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
815 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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816 %! assert (norm (vec (P'*L*U - Ac - uc*vc.'), Inf) < norm (Ac)*1e1*eps); |
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|
817 |
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|
818 %!testif HAVE_QRUPDATE_LUU |
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819 %! [L,U,P] = lu (single (A)); |
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820 %! [L,U,P] = luupdate (L,U,P,single (u),single (v)); |
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821 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
822 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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823 %! assert (norm (vec (P'*L*U - single (A) - single (u)*single (v).'), Inf) < norm (single (A))*1e1*eps ("single")); |
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|
824 %! |
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|
825 %!testif HAVE_QRUPDATE_LUU |
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826 %! [L,U,P] = lu (single (Ac)); |
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827 %! [L,U,P] = luupdate (L,U,P,single (uc),single (vc)); |
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|
828 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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|
829 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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|
830 %! assert (norm (vec (P'*L*U - single (Ac) - single (uc)*single (vc).'), Inf) < norm (single (Ac))*1e1*eps ("single")); |
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|
831 */ |