Mercurial > octave
annotate libinterp/corefcn/lu.cc @ 20228:00cf2847355d
Deprecate Array::nelem() and Range::nelem() in favour of ::numel().
* liboctave/array/Array.h (Array::nelem) deprecate in favour of numel().
(Array::capacity, Array:: length): change to call numel() directly. These
methods will be deprecated soon.
* liboctave/array/PermMatrix.h (PermMatrix::nelem): deprecate in favour of
numel().
* liboctave/array/Range.h (Range::numel) new method to replace nelem().
(Range::nelem) deprecate in favour of the new method numel.
* liboctave/array/Sparse.h (Sparse::nelem) deprecate in favour of nzmax().
This one is secially bad because unlike the other classes, it is different
from numel().
* libinterp/corefcn/debug.cc, libinterp/corefcn/jit-typeinfo.cc,
libinterp/corefcn/ls-mat4.cc, libinterp/corefcn/lu.cc,
libinterp/corefcn/luinc.cc, libinterp/corefcn/max.cc,
libinterp/corefcn/pr-output.cc, libinterp/corefcn/rand.cc,
libinterp/corefcn/xpow.cc, libinterp/dldfcn/__magick_read__.cc,
libinterp/dldfcn/audioread.cc, libinterp/octave-value/ov-base-int.cc,
libinterp/octave-value/ov-bool-mat.cc, libinterp/octave-value/ov-flt-re-mat.cc,
libinterp/octave-value/ov-perm.cc, libinterp/octave-value/ov-range.cc,
libinterp/octave-value/ov-range.h, libinterp/octave-value/ov-re-mat.cc,
libinterp/parse-tree/pt-eval.cc, liboctave/array/Array.cc,
liboctave/array/CNDArray.cc, liboctave/array/Range.cc,
liboctave/array/dNDArray.cc, liboctave/array/fCNDArray.cc,
liboctave/array/fNDArray.cc, liboctave/array/idx-vector.cc,
liboctave/array/intNDArray.cc, liboctave/numeric/SparseCmplxLU.cc,
liboctave/numeric/SparsedbleLU.cc: replace use of nelem() with numel().
author | Carnë Draug <carandraug@octave.org> |
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date | Sun, 24 May 2015 02:41:37 +0100 |
parents | 4f45eaf83908 |
children | f90c8372b7ba |
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" |
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34 #include "defun.h" |
2928 | 35 #include "error.h" |
36 #include "gripes.h" | |
37 #include "oct-obj.h" | |
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 {Built-in Function} {[@var{L}, @var{U}] =} lu (@var{A})\n\ |
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67 @deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}] =} lu (@var{A})\n\ |
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68 @deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}, @var{Q}] =} lu (@var{S})\n\ |
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69 @deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}, @var{Q}, @var{R}] =} lu (@var{S})\n\ |
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70 @deftypefnx {Built-in Function} {[@dots{}] =} lu (@var{S}, @var{thres})\n\ |
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71 @deftypefnx {Built-in Function} {@var{y} =} lu (@dots{})\n\ |
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72 @deftypefnx {Built-in Function} {[@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 { |
145 octave_value_list retval; | |
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146 int nargin = args.length (); |
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147 bool issparse = (nargin > 0 && args(0).is_sparse_type ()); |
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148 bool scale = (nargout == 5); |
2928 | 149 |
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150 if (nargin < 1 || (issparse && (nargin > 3 || nargout > 5)) |
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151 || (!issparse && (nargin > 2 || nargout > 3))) |
2928 | 152 { |
5823 | 153 print_usage (); |
2928 | 154 return retval; |
155 } | |
156 | |
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157 bool vecout = false; |
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158 Matrix thres; |
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159 |
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160 int n = 1; |
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161 while (n < nargin && ! error_state) |
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162 { |
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163 if (args(n).is_string ()) |
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164 { |
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165 std::string tmp = args(n++).string_value (); |
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166 |
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167 if (tmp.compare ("vector") == 0) |
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168 vecout = true; |
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169 else |
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170 error ("lu: unrecognized string argument"); |
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171 } |
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172 else |
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173 { |
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174 Matrix tmp = args(n++).matrix_value (); |
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175 |
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176 if (! error_state) |
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177 { |
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178 if (!issparse) |
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179 error ("lu: can not define pivoting threshold THRES for full matrices"); |
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180 else if (tmp.numel () == 1) |
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181 { |
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182 thres.resize (1,2); |
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183 thres(0) = tmp(0); |
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184 thres(1) = tmp(0); |
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185 } |
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186 else if (tmp.numel () == 2) |
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187 thres = tmp; |
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188 else |
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189 error ("lu: expecting 2-element vector for THRES"); |
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190 } |
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191 } |
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192 } |
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193 |
2928 | 194 octave_value arg = args(0); |
195 | |
5275 | 196 octave_idx_type nr = arg.rows (); |
197 octave_idx_type nc = arg.columns (); | |
2928 | 198 |
199 int arg_is_empty = empty_arg ("lu", nr, nc); | |
200 | |
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201 if (issparse) |
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202 { |
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203 if (arg_is_empty < 0) |
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204 return retval; |
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205 else if (arg_is_empty > 0) |
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206 return octave_value_list (5, SparseMatrix ()); |
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207 |
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208 if (arg.is_real_type ()) |
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209 { |
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210 |
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211 SparseMatrix m = arg.sparse_matrix_value (); |
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212 |
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213 if (nargout < 4) |
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214 { |
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215 |
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216 ColumnVector Qinit; |
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217 Qinit.resize (nc); |
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218 for (octave_idx_type i = 0; i < nc; i++) |
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219 Qinit (i) = i; |
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220 SparseLU fact (m, Qinit, thres, false, true); |
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221 |
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222 if (nargout < 2) |
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223 retval(0) = fact.Y (); |
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224 else |
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225 { |
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226 |
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227 retval(1) |
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228 = octave_value ( |
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229 fact.U () * fact.Pc_mat ().transpose (), |
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230 MatrixType (MatrixType::Permuted_Upper, |
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231 nc, fact.col_perm ())); |
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232 |
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233 PermMatrix P = fact.Pr_mat (); |
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234 SparseMatrix L = fact.L (); |
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235 if (nargout < 3) |
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236 retval(0) |
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237 = octave_value (P.transpose () * L, |
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238 MatrixType (MatrixType::Permuted_Lower, |
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239 nr, fact.row_perm ())); |
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240 else |
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241 { |
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242 retval(0) = L; |
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243 if (vecout) |
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244 retval(2) = fact.Pr_vec(); |
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245 else |
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246 retval(2) = P; |
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247 } |
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248 |
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249 } |
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250 |
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251 } |
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252 else |
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253 { |
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254 |
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255 SparseLU fact (m, thres, scale); |
2928 | 256 |
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257 if (scale) |
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258 retval(4) = fact.R (); |
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259 |
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260 if (vecout) |
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261 { |
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262 retval(3) = fact.Pc_vec (); |
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263 retval(2) = fact.Pr_vec (); |
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264 } |
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265 else |
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266 { |
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267 retval(3) = fact.Pc_mat (); |
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268 retval(2) = fact.Pr_mat (); |
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269 } |
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270 retval(1) = octave_value (fact.U (), |
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271 MatrixType (MatrixType::Upper)); |
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272 retval(0) = octave_value (fact.L (), |
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273 MatrixType (MatrixType::Lower)); |
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274 } |
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275 |
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276 } |
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277 else if (arg.is_complex_type ()) |
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278 { |
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279 SparseComplexMatrix m = arg.sparse_complex_matrix_value (); |
2928 | 280 |
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281 if (nargout < 4) |
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282 { |
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283 |
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284 ColumnVector Qinit; |
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285 Qinit.resize (nc); |
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286 for (octave_idx_type i = 0; i < nc; i++) |
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287 Qinit (i) = i; |
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288 SparseComplexLU fact (m, Qinit, thres, false, true); |
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289 |
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290 if (nargout < 2) |
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291 |
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292 retval(0) = fact.Y (); |
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293 |
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294 else |
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295 { |
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296 |
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297 retval(1) |
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298 = octave_value ( |
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299 fact.U () * fact.Pc_mat ().transpose (), |
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300 MatrixType (MatrixType::Permuted_Upper, |
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301 nc, fact.col_perm ())); |
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302 |
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303 PermMatrix P = fact.Pr_mat (); |
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304 SparseComplexMatrix L = fact.L (); |
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305 if (nargout < 3) |
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306 retval(0) |
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307 = octave_value (P.transpose () * L, |
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308 MatrixType (MatrixType::Permuted_Lower, |
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309 nr, fact.row_perm ())); |
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310 else |
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311 { |
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312 retval(0) = L; |
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313 if (vecout) |
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314 retval(2) = fact.Pr_vec(); |
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315 else |
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316 retval(2) = P; |
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317 } |
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318 |
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319 } |
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320 |
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321 } |
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322 else |
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323 { |
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324 |
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325 SparseComplexLU fact (m, thres, scale); |
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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 if (vecout) |
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331 { |
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332 retval(3) = fact.Pc_vec (); |
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333 retval(2) = fact.Pr_vec (); |
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334 } |
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335 else |
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336 { |
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337 retval(3) = fact.Pc_mat (); |
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338 retval(2) = fact.Pr_mat (); |
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339 } |
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340 retval(1) = octave_value (fact.U (), |
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341 MatrixType (MatrixType::Upper)); |
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342 retval(0) = octave_value (fact.L (), |
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343 MatrixType (MatrixType::Lower)); |
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344 } |
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345 |
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346 } |
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347 else |
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348 gripe_wrong_type_arg ("lu", arg); |
2928 | 349 } |
350 else | |
351 { | |
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352 if (arg_is_empty < 0) |
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353 return retval; |
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354 else if (arg_is_empty > 0) |
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355 return octave_value_list (3, Matrix ()); |
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356 |
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357 if (arg.is_real_type ()) |
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358 { |
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359 if (arg.is_single_type ()) |
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360 { |
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361 FloatMatrix m = arg.float_matrix_value (); |
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362 |
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363 if (! error_state) |
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364 { |
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365 FloatLU fact (m); |
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366 |
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367 switch (nargout) |
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368 { |
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369 case 0: |
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370 case 1: |
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371 retval(0) = fact.Y (); |
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372 break; |
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373 |
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374 case 2: |
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375 { |
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376 PermMatrix P = fact.P (); |
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377 FloatMatrix L = P.transpose () * fact.L (); |
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378 retval(1) = get_lu_u (fact); |
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379 retval(0) = L; |
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380 } |
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381 break; |
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382 |
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383 case 3: |
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384 default: |
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385 { |
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386 if (vecout) |
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387 retval(2) = fact.P_vec (); |
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388 else |
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389 retval(2) = fact.P (); |
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390 retval(1) = get_lu_u (fact); |
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391 retval(0) = get_lu_l (fact); |
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392 } |
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393 break; |
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394 } |
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395 } |
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396 } |
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397 else |
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398 { |
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399 Matrix m = arg.matrix_value (); |
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400 |
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401 if (! error_state) |
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402 { |
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403 LU fact (m); |
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404 |
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405 switch (nargout) |
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406 { |
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407 case 0: |
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408 case 1: |
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409 retval(0) = fact.Y (); |
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410 break; |
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411 |
10154
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412 case 2: |
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413 { |
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414 PermMatrix P = fact.P (); |
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415 Matrix L = P.transpose () * fact.L (); |
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416 retval(1) = get_lu_u (fact); |
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417 retval(0) = L; |
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418 } |
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419 break; |
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420 |
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421 case 3: |
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422 default: |
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423 { |
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424 if (vecout) |
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425 retval(2) = fact.P_vec (); |
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426 else |
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427 retval(2) = fact.P (); |
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428 retval(1) = get_lu_u (fact); |
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429 retval(0) = get_lu_l (fact); |
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430 } |
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431 break; |
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432 } |
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433 } |
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434 } |
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435 } |
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436 else if (arg.is_complex_type ()) |
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437 { |
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438 if (arg.is_single_type ()) |
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439 { |
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440 FloatComplexMatrix m = arg.float_complex_matrix_value (); |
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441 |
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442 if (! error_state) |
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443 { |
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444 FloatComplexLU fact (m); |
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445 |
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446 switch (nargout) |
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447 { |
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448 case 0: |
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449 case 1: |
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450 retval(0) = fact.Y (); |
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451 break; |
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452 |
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453 case 2: |
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454 { |
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455 PermMatrix P = fact.P (); |
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456 FloatComplexMatrix L = P.transpose () * fact.L (); |
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457 retval(1) = get_lu_u (fact); |
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458 retval(0) = L; |
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459 } |
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460 break; |
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|
461 |
10154
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462 case 3: |
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463 default: |
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464 { |
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465 if (vecout) |
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466 retval(2) = fact.P_vec (); |
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467 else |
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468 retval(2) = fact.P (); |
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469 retval(1) = get_lu_u (fact); |
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470 retval(0) = get_lu_l (fact); |
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471 } |
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472 break; |
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|
473 } |
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474 } |
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|
475 } |
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|
476 else |
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|
477 { |
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|
478 ComplexMatrix m = arg.complex_matrix_value (); |
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479 |
10154
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480 if (! error_state) |
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481 { |
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|
482 ComplexLU fact (m); |
7515
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Eliminate the rest of the dispatched sparse functions
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changeset
|
483 |
10154
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|
484 switch (nargout) |
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|
485 { |
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|
486 case 0: |
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|
487 case 1: |
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|
488 retval(0) = fact.Y (); |
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|
489 break; |
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|
490 |
10154
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|
491 case 2: |
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|
492 { |
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|
493 PermMatrix P = fact.P (); |
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494 ComplexMatrix L = P.transpose () * fact.L (); |
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495 retval(1) = get_lu_u (fact); |
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496 retval(0) = L; |
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|
497 } |
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|
498 break; |
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|
499 |
10154
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|
500 case 3: |
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|
501 default: |
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|
502 { |
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|
503 if (vecout) |
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|
504 retval(2) = fact.P_vec (); |
40dfc0c99116
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changeset
|
505 else |
40dfc0c99116
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506 retval(2) = fact.P (); |
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507 retval(1) = get_lu_u (fact); |
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508 retval(0) = get_lu_l (fact); |
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changeset
|
509 } |
40dfc0c99116
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changeset
|
510 break; |
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changeset
|
511 } |
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|
512 } |
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|
513 } |
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|
514 } |
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Eliminate the rest of the dispatched sparse functions
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|
515 else |
10154
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|
516 gripe_wrong_type_arg ("lu", arg); |
2928 | 517 } |
518 | |
519 return retval; | |
520 } | |
521 | |
522 /* | |
7814
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Second set of single precision test code and fix of resulting bugs
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523 %!assert(lu ([1, 2; 3, 4]), [3, 4; 1/3, 2/3], eps); |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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|
524 |
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Second set of single precision test code and fix of resulting bugs
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changeset
|
525 %!test |
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|
526 %! [l, u] = lu ([1, 2; 3, 4]); |
14501
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|
527 %! assert (l, [1/3, 1; 1, 0], sqrt (eps)); |
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|
528 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
7814
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Second set of single precision test code and fix of resulting bugs
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|
529 |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
530 %!test |
87865ed7405f
Second set of single precision test code and fix of resulting bugs
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changeset
|
531 %! [l, u, p] = lu ([1, 2; 3, 4]); |
14501
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Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
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532 %! assert (l, [1, 0; 1/3, 1], sqrt (eps)); |
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533 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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534 %! assert (p(:,:), [0, 1; 1, 0], sqrt (eps)); |
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535 |
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536 %!test |
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537 %! [l, u, p] = lu ([1, 2; 3, 4], "vector"); |
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538 %! assert (l, [1, 0; 1/3, 1], sqrt (eps)); |
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539 %! assert (u, [3, 4; 0, 2/3], sqrt (eps)); |
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540 %! assert (p, [2;1], sqrt (eps)); |
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541 |
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542 %!test |
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543 %! [l, u, p] = lu ([1, 2; 3, 4; 5, 6]); |
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544 %! assert (l, [1, 0; 1/5, 1; 3/5, 1/2], sqrt (eps)); |
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545 %! assert (u, [5, 6; 0, 4/5], sqrt (eps)); |
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546 %! assert (p(:,:), [0, 0, 1; 1, 0, 0; 0 1 0], sqrt (eps)); |
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547 |
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548 %!assert (lu (single ([1, 2; 3, 4])), single ([3, 4; 1/3, 2/3]), eps ("single")) |
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549 |
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550 %!test |
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551 %! [l, u] = lu (single ([1, 2; 3, 4])); |
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552 %! assert (l, single ([1/3, 1; 1, 0]), sqrt (eps ("single"))); |
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553 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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554 |
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555 %!test |
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556 %! [l, u, p] = lu (single ([1, 2; 3, 4])); |
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557 %! assert (l, single ([1, 0; 1/3, 1]), sqrt (eps ("single"))); |
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558 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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559 %! assert (p(:,:), single ([0, 1; 1, 0]), sqrt (eps ("single"))); |
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560 |
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561 %!test |
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562 %! [l, u, p] = lu (single ([1, 2; 3, 4]), "vector"); |
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563 %! assert (l, single ([1, 0; 1/3, 1]), sqrt (eps ("single"))); |
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564 %! assert (u, single ([3, 4; 0, 2/3]), sqrt (eps ("single"))); |
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565 %! assert (p, single ([2;1]), sqrt (eps ("single"))); |
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566 |
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567 %!test |
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568 %! [l u p] = lu (single ([1, 2; 3, 4; 5, 6])); |
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569 %! assert (l, single ([1, 0; 1/5, 1; 3/5, 1/2]), sqrt (eps ("single"))); |
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570 %! assert (u, single ([5, 6; 0, 4/5]), sqrt (eps ("single"))); |
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571 %! assert (p(:,:), single ([0, 0, 1; 1, 0, 0; 0 1 0]), sqrt (eps ("single"))); |
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572 |
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573 %!error lu () |
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574 %!error <can not define pivoting threshold> lu ([1, 2; 3, 4], 2) |
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575 |
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576 %!testif HAVE_UMFPACK |
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577 %! Bi = [1 2 3 4 5 2 3 6 7 8 4 5 7 8 9]; |
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578 %! Bj = [1 3 4 5 6 7 8 9 11 12 13 14 15 16 17]; |
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579 %! Bv = [1 1 1 1 1 1 -1 1 1 1 1 -1 1 -1 1]; |
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580 %! B = sparse (Bi, Bj, Bv); |
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581 %! [L, U] = lu (B); |
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582 %! assert (L*U, B); |
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583 %! [L, U, P] = lu(B); |
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584 %! assert (P'*L*U, B); |
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585 %! [L, U, P, Q] = lu (B); |
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586 %! assert (P'*L*U*Q', B); |
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587 |
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588 */ |
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589 |
9708 | 590 static |
591 bool check_lu_dims (const octave_value& l, const octave_value& u, | |
592 const octave_value& p) | |
593 { | |
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594 octave_idx_type m = l.rows (); |
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595 octave_idx_type k = u.rows (); |
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596 octave_idx_type n = u.columns (); |
9708 | 597 return ((l.ndims () == 2 && u.ndims () == 2 && k == l.columns ()) |
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598 && k == std::min (m, n) |
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599 && (p.is_undefined () || p.rows () == m)); |
9708 | 600 } |
601 | |
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602 DEFUN (luupdate, args, , |
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603 "-*- texinfo -*-\n\ |
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604 @deftypefn {Built-in Function} {[@var{L}, @var{U}] =} luupdate (@var{L}, @var{U}, @var{x}, @var{y})\n\ |
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605 @deftypefnx {Built-in Function} {[@var{L}, @var{U}, @var{P}] =} luupdate (@var{L}, @var{U}, @var{P}, @var{x}, @var{y})\n\ |
9709 | 606 Given an LU@tie{}factorization of a real or complex matrix\n\ |
607 @w{@var{A} = @var{L}*@var{U}}, @var{L}@tie{}lower unit trapezoidal and\n\ | |
608 @var{U}@tie{}upper trapezoidal, return the LU@tie{}factorization\n\ | |
609 of @w{@var{A} + @var{x}*@var{y}.'}, where @var{x} and @var{y} are\n\ | |
610 column vectors (rank-1 update) or matrices with equal number of columns\n\ | |
611 (rank-k update).\n\ | |
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612 \n\ |
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613 Optionally, row-pivoted updating can be used by supplying a row permutation\n\ |
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614 (pivoting) matrix @var{P}; in that case, an updated permutation matrix is\n\ |
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615 returned. Note that if @var{L}, @var{U}, @var{P} is a pivoted\n\ |
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616 LU@tie{}factorization as obtained by @code{lu}:\n\ |
9709 | 617 \n\ |
618 @example\n\ | |
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619 [@var{L}, @var{U}, @var{P}] = lu (@var{A});\n\ |
9709 | 620 @end example\n\ |
621 \n\ | |
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622 @noindent\n\ |
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623 then a factorization of @tcode{@var{A}+@var{x}*@var{y}.'} can be obtained\n\ |
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624 either as\n\ |
9709 | 625 \n\ |
626 @example\n\ | |
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627 [@var{L1}, @var{U1}] = lu (@var{L}, @var{U}, @var{P}*@var{x}, @var{y})\n\ |
9709 | 628 @end example\n\ |
629 \n\ | |
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630 @noindent\n\ |
9709 | 631 or\n\ |
632 \n\ | |
633 @example\n\ | |
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634 [@var{L1}, @var{U1}, @var{P1}] = lu (@var{L}, @var{U}, @var{P}, @var{x}, @var{y})\n\ |
9709 | 635 @end example\n\ |
636 \n\ | |
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637 The first form uses the unpivoted algorithm, which is faster, but less\n\ |
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638 stable. The second form uses a slower pivoted algorithm, which is more\n\ |
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639 stable.\n\ |
9709 | 640 \n\ |
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641 The matrix case is done as a sequence of rank-1 updates; thus, for large\n\ |
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642 enough k, it will be both faster and more accurate to recompute the\n\ |
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643 factorization from scratch.\n\ |
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644 @seealso{lu, cholupdate, qrupdate}\n\ |
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645 @end deftypefn") |
9708 | 646 { |
647 octave_idx_type nargin = args.length (); | |
648 octave_value_list retval; | |
649 | |
650 bool pivoted = nargin == 5; | |
651 | |
652 if (nargin != 4 && nargin != 5) | |
653 { | |
654 print_usage (); | |
655 return retval; | |
656 } | |
657 | |
658 octave_value argl = args(0); | |
659 octave_value argu = args(1); | |
660 octave_value argp = pivoted ? args(2) : octave_value (); | |
661 octave_value argx = args(2 + pivoted); | |
662 octave_value argy = args(3 + pivoted); | |
663 | |
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664 if (argl.is_numeric_type () && argu.is_numeric_type () |
9708 | 665 && argx.is_numeric_type () && argy.is_numeric_type () |
666 && (! pivoted || argp.is_perm_matrix ())) | |
667 { | |
668 if (check_lu_dims (argl, argu, argp)) | |
669 { | |
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670 PermMatrix P = (pivoted |
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671 ? argp.perm_matrix_value () |
9708 | 672 : PermMatrix::eye (argl.rows ())); |
673 | |
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674 if (argl.is_real_type () |
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675 && argu.is_real_type () |
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676 && argx.is_real_type () |
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677 && argy.is_real_type ()) |
9708 | 678 { |
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679 // all real case |
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680 if (argl.is_single_type () |
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681 || argu.is_single_type () |
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682 || argx.is_single_type () |
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683 || argy.is_single_type ()) |
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684 { |
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685 FloatMatrix L = argl.float_matrix_value (); |
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686 FloatMatrix U = argu.float_matrix_value (); |
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687 FloatMatrix x = argx.float_matrix_value (); |
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688 FloatMatrix y = argy.float_matrix_value (); |
9708 | 689 |
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690 FloatLU fact (L, U, P); |
9708 | 691 if (pivoted) |
692 fact.update_piv (x, y); | |
693 else | |
694 fact.update (x, y); | |
695 | |
696 if (pivoted) | |
697 retval(2) = fact.P (); | |
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698 retval(1) = get_lu_u (fact); |
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699 retval(0) = get_lu_l (fact); |
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700 } |
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701 else |
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702 { |
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703 Matrix L = argl.matrix_value (); |
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704 Matrix U = argu.matrix_value (); |
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705 Matrix x = argx.matrix_value (); |
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706 Matrix y = argy.matrix_value (); |
9708 | 707 |
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708 LU fact (L, U, P); |
9708 | 709 if (pivoted) |
710 fact.update_piv (x, y); | |
711 else | |
712 fact.update (x, y); | |
713 | |
714 if (pivoted) | |
715 retval(2) = fact.P (); | |
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716 retval(1) = get_lu_u (fact); |
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717 retval(0) = get_lu_l (fact); |
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718 } |
9708 | 719 } |
720 else | |
721 { | |
722 // complex case | |
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723 if (argl.is_single_type () |
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724 || argu.is_single_type () |
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725 || argx.is_single_type () |
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726 || argy.is_single_type ()) |
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727 { |
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728 FloatComplexMatrix L = argl.float_complex_matrix_value (); |
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729 FloatComplexMatrix U = argu.float_complex_matrix_value (); |
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730 FloatComplexMatrix x = argx.float_complex_matrix_value (); |
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731 FloatComplexMatrix y = argy.float_complex_matrix_value (); |
9708 | 732 |
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733 FloatComplexLU fact (L, U, P); |
9708 | 734 if (pivoted) |
735 fact.update_piv (x, y); | |
736 else | |
737 fact.update (x, y); | |
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738 |
9708 | 739 if (pivoted) |
740 retval(2) = fact.P (); | |
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741 retval(1) = get_lu_u (fact); |
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742 retval(0) = get_lu_l (fact); |
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743 } |
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744 else |
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745 { |
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746 ComplexMatrix L = argl.complex_matrix_value (); |
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747 ComplexMatrix U = argu.complex_matrix_value (); |
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748 ComplexMatrix x = argx.complex_matrix_value (); |
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749 ComplexMatrix y = argy.complex_matrix_value (); |
9708 | 750 |
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751 ComplexLU fact (L, U, P); |
9708 | 752 if (pivoted) |
753 fact.update_piv (x, y); | |
754 else | |
755 fact.update (x, y); | |
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756 |
9708 | 757 if (pivoted) |
758 retval(2) = fact.P (); | |
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759 retval(1) = get_lu_u (fact); |
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760 retval(0) = get_lu_l (fact); |
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761 } |
9708 | 762 } |
763 } | |
764 else | |
11553
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|
765 error ("luupdate: dimension mismatch"); |
9708 | 766 } |
767 else | |
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Improve docstrings for functions in DLD-FUNCTIONS directory.
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|
768 error ("luupdate: L, U, X, and Y must be numeric"); |
9708 | 769 |
770 return retval; | |
771 } | |
772 | |
7814
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|
773 /* |
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774 %!shared A, u, v, Ac, uc, vc |
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775 %! A = [0.091364 0.613038 0.999083; |
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776 %! 0.594638 0.425302 0.603537; |
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777 %! 0.383594 0.291238 0.085574; |
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778 %! 0.265712 0.268003 0.238409; |
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779 %! 0.669966 0.743851 0.445057 ]; |
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780 %! |
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781 %! u = [0.85082; |
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782 %! 0.76426; |
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|
783 %! 0.42883; |
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784 %! 0.53010; |
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785 %! 0.80683 ]; |
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786 %! |
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787 %! v = [0.98810; |
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788 %! 0.24295; |
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789 %! 0.43167 ]; |
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790 %! |
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791 %! Ac = [0.620405 + 0.956953i 0.480013 + 0.048806i 0.402627 + 0.338171i; |
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792 %! 0.589077 + 0.658457i 0.013205 + 0.279323i 0.229284 + 0.721929i; |
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793 %! 0.092758 + 0.345687i 0.928679 + 0.241052i 0.764536 + 0.832406i; |
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794 %! 0.912098 + 0.721024i 0.049018 + 0.269452i 0.730029 + 0.796517i; |
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|
795 %! 0.112849 + 0.603871i 0.486352 + 0.142337i 0.355646 + 0.151496i ]; |
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796 %! |
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797 %! uc = [0.20351 + 0.05401i; |
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798 %! 0.13141 + 0.43708i; |
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|
799 %! 0.29808 + 0.08789i; |
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|
800 %! 0.69821 + 0.38844i; |
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801 %! 0.74871 + 0.25821i ]; |
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802 %! |
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803 %! vc = [0.85839 + 0.29468i; |
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804 %! 0.20820 + 0.93090i; |
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805 %! 0.86184 + 0.34689i ]; |
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806 %! |
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807 |
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808 %!testif HAVE_QRUPDATE_LUU |
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809 %! [L,U,P] = lu (A); |
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810 %! [L,U] = luupdate (L,U,P*u,v); |
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811 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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812 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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|
813 %! assert (norm (vec (P'*L*U - A - u*v.'), Inf) < norm (A)*1e1*eps); |
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814 %! |
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815 %!testif HAVE_QRUPDATE_LUU |
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816 %! [L,U,P] = lu (Ac); |
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817 %! [L,U] = luupdate (L,U,P*uc,vc); |
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818 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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819 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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820 %! assert (norm (vec (P'*L*U - Ac - uc*vc.'), Inf) < norm (Ac)*1e1*eps); |
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821 |
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822 %!testif HAVE_QRUPDATE_LUU |
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823 %! [L,U,P] = lu (single (A)); |
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824 %! [L,U] = luupdate (L,U,P*single (u), single (v)); |
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825 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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826 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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827 %! assert (norm (vec (P'*L*U - single (A) - single (u)*single (v).'), Inf) < norm (single (A))*1e1*eps ("single")); |
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828 %! |
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829 %!testif HAVE_QRUPDATE_LUU |
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830 %! [L,U,P] = lu (single (Ac)); |
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831 %! [L,U] = luupdate (L,U,P*single (uc),single (vc)); |
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832 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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833 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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834 %! assert (norm (vec (P'*L*U - single (Ac) - single (uc)*single (vc).'), Inf) < norm (single (Ac))*1e1*eps ("single")); |
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835 |
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836 %!testif HAVE_QRUPDATE_LUU |
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837 %! [L,U,P] = lu (A); |
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838 %! [L,U,P] = luupdate (L,U,P,u,v); |
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839 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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840 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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841 %! assert (norm (vec (P'*L*U - A - u*v.'), Inf) < norm (A)*1e1*eps); |
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842 %! |
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843 %!testif HAVE_QRUPDATE_LUU |
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844 %! [L,U,P] = lu (A); |
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845 %! [~,ordcols] = max (P,[],1); |
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846 %! [~,ordrows] = max (P,[],2); |
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847 %! P1 = eye (size(P))(:,ordcols); |
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848 %! P2 = eye (size(P))(ordrows,:); |
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849 %! assert(P1 == P); |
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850 %! assert(P2 == P); |
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851 %! [L,U,P] = luupdate (L,U,P,u,v); |
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852 %! [L,U,P1] = luupdate (L,U,P1,u,v); |
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853 %! [L,U,P2] = luupdate (L,U,P2,u,v); |
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854 %! assert(P1 == P); |
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855 %! assert(P2 == P); |
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856 %! |
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857 %!testif HAVE_QRUPDATE_LUU |
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858 %! [L,U,P] = lu (Ac); |
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859 %! [L,U,P] = luupdate (L,U,P,uc,vc); |
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860 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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861 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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862 %! assert (norm (vec (P'*L*U - Ac - uc*vc.'), Inf) < norm (Ac)*1e1*eps); |
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863 |
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864 %!testif HAVE_QRUPDATE_LUU |
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865 %! [L,U,P] = lu (single (A)); |
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866 %! [L,U,P] = luupdate (L,U,P,single (u),single (v)); |
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867 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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868 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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869 %! assert (norm (vec (P'*L*U - single (A) - single (u)*single (v).'), Inf) < norm (single (A))*1e1*eps ("single")); |
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870 %! |
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871 %!testif HAVE_QRUPDATE_LUU |
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872 %! [L,U,P] = lu (single (Ac)); |
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873 %! [L,U,P] = luupdate (L,U,P,single (uc),single (vc)); |
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874 %! assert (norm (vec (tril (L)-L), Inf) == 0); |
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875 %! assert (norm (vec (triu (U)-U), Inf) == 0); |
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876 %! assert (norm (vec (P'*L*U - single (Ac) - single (uc)*single (vc).'), Inf) < norm (single (Ac))*1e1*eps ("single")); |
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877 */ |