Mercurial > octave-nkf
annotate libinterp/corefcn/matrix_type.cc @ 19731:4197fc428c7d
maint: Update copyright notices for 2015.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 11 Feb 2015 14:19:08 -0500 |
parents | 03067dab10ca |
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2 | |
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3 Copyright (C) 2005-2015 David Bateman |
5323 | 4 |
5720 | 5 This file is part of Octave. |
6 | |
5323 | 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. | |
5323 | 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/>. | |
5323 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
25 #endif | |
26 | |
5403 | 27 #include <algorithm> |
28 | |
5323 | 29 #include "ov.h" |
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30 #include "defun.h" |
5323 | 31 #include "error.h" |
5785 | 32 #include "ov-re-mat.h" |
33 #include "ov-cx-mat.h" | |
5323 | 34 #include "ov-re-sparse.h" |
35 #include "ov-cx-sparse.h" | |
5785 | 36 #include "MatrixType.h" |
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37 #include "oct-locbuf.h" |
5323 | 38 |
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39 DEFUN (matrix_type, args, , |
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40 "-*- texinfo -*-\n\ |
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41 @deftypefn {Built-in Function} {@var{type} =} matrix_type (@var{A})\n\ |
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42 @deftypefnx {Built-in Function} {@var{type} =} matrix_type (@var{A}, \"nocompute\")\n\ |
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43 @deftypefnx {Built-in Function} {@var{A} =} matrix_type (@var{A}, @var{type})\n\ |
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44 @deftypefnx {Built-in Function} {@var{A} =} matrix_type (@var{A}, \"upper\", @var{perm})\n\ |
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45 @deftypefnx {Built-in Function} {@var{A} =} matrix_type (@var{A}, \"lower\", @var{perm})\n\ |
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46 @deftypefnx {Built-in Function} {@var{A} =} matrix_type (@var{A}, \"banded\", @var{nl}, @var{nu})\n\ |
10840 | 47 Identify the matrix type or mark a matrix as a particular type. This allows\n\ |
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48 more rapid solutions of linear equations involving @var{A} to be performed.\n\ |
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49 Called with a single argument, @code{matrix_type} returns the type of the\n\ |
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50 matrix and caches it for future use. Called with more than one argument,\n\ |
10840 | 51 @code{matrix_type} allows the type of the matrix to be defined.\n\ |
5323 | 52 \n\ |
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53 If the option @qcode{\"nocompute\"} is given, the function will not attempt\n\ |
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54 to guess the type if it is still unknown. This is useful for debugging\n\ |
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55 purposes.\n\ |
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56 \n\ |
10840 | 57 The possible matrix types depend on whether the matrix is full or sparse, and\n\ |
58 can be one of the following\n\ | |
5323 | 59 \n\ |
60 @table @asis\n\ | |
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61 @item @qcode{\"unknown\"}\n\ |
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62 Remove any previously cached matrix type, and mark type as unknown.\n\ |
5323 | 63 \n\ |
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64 @item @qcode{\"full\"}\n\ |
5323 | 65 Mark the matrix as full.\n\ |
66 \n\ | |
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67 @item @qcode{\"positive definite\"}\n\ |
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68 Probable full positive definite matrix.\n\ |
5323 | 69 \n\ |
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70 @item @qcode{\"diagonal\"}\n\ |
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71 Diagonal matrix. (Sparse matrices only)\n\ |
5323 | 72 \n\ |
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73 @item @qcode{\"permuted diagonal\"}\n\ |
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74 Permuted Diagonal matrix. The permutation does not need to be specifically\n\ |
10840 | 75 indicated, as the structure of the matrix explicitly gives this. (Sparse\n\ |
76 matrices only)\n\ | |
5323 | 77 \n\ |
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78 @item @qcode{\"upper\"}\n\ |
10840 | 79 Upper triangular. If the optional third argument @var{perm} is given, the\n\ |
80 matrix is assumed to be a permuted upper triangular with the permutations\n\ | |
81 defined by the vector @var{perm}.\n\ | |
5323 | 82 \n\ |
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83 @item @qcode{\"lower\"}\n\ |
10840 | 84 Lower triangular. If the optional third argument @var{perm} is given, the\n\ |
85 matrix is assumed to be a permuted lower triangular with the permutations\n\ | |
86 defined by the vector @var{perm}.\n\ | |
5323 | 87 \n\ |
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88 @item @qcode{\"banded\"}\n\ |
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89 @itemx @qcode{\"banded positive definite\"}\n\ |
10840 | 90 Banded matrix with the band size of @var{nl} below the diagonal and @var{nu}\n\ |
91 above it. If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal and\n\ | |
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92 treated with specialized code. In addition the matrix can be marked as\n\ |
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93 probably a positive definite. (Sparse matrices only)\n\ |
5323 | 94 \n\ |
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95 @item @qcode{\"singular\"}\n\ |
10840 | 96 The matrix is assumed to be singular and will be treated with a minimum norm\n\ |
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97 solution.\n\ |
5323 | 98 \n\ |
99 @end table\n\ | |
100 \n\ | |
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101 Note that the matrix type will be discovered automatically on the first\n\ |
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102 attempt to solve a linear equation involving @var{A}. Therefore\n\ |
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103 @code{matrix_type} is only useful to give Octave hints of the matrix type.\n\ |
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104 Incorrectly defining the matrix type will result in incorrect results from\n\ |
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105 solutions of linear equations; it is entirely @strong{the responsibility of\n\ |
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106 the user} to correctly identify the matrix type.\n\ |
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107 \n\ |
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108 Also, the test for positive definiteness is a low-cost test for a Hermitian\n\ |
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109 matrix with a real positive diagonal. This does not guarantee that the\n\ |
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110 matrix is positive definite, but only that it is a probable candidate. When\n\ |
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111 such a matrix is factorized, a Cholesky@tie{}factorization is first\n\ |
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112 attempted, and if that fails the matrix is then treated with an\n\ |
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113 LU@tie{}factorization. Once the matrix has been factorized,\n\ |
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114 @code{matrix_type} will return the correct classification of the matrix.\n\ |
5323 | 115 @end deftypefn") |
116 { | |
117 int nargin = args.length (); | |
118 octave_value retval; | |
119 | |
120 if (nargin == 0) | |
5823 | 121 print_usage (); |
5323 | 122 else if (nargin > 4) |
123 error ("matrix_type: incorrect number of arguments"); | |
124 else | |
125 { | |
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126 bool autocomp = true; |
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127 if (nargin == 2 && args(1).is_string () |
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128 && args(1).string_value () == "nocompute") |
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129 { |
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130 nargin = 1; |
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131 autocomp = false; |
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132 } |
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133 |
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134 if (args(0).is_scalar_type ()) |
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135 { |
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136 if (nargin == 1) |
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137 retval = octave_value ("Diagonal"); |
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138 else |
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139 retval = args(0); |
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140 } |
6371 | 141 else if (args(0).is_sparse_type ()) |
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142 { |
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143 if (nargin == 1) |
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144 { |
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145 MatrixType mattyp; |
5323 | 146 |
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147 if (args(0).is_complex_type ()) |
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148 { |
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149 mattyp = args(0).matrix_type (); |
5323 | 150 |
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151 if (mattyp.is_unknown () && autocomp) |
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152 { |
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153 SparseComplexMatrix m = |
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154 args(0).sparse_complex_matrix_value (); |
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155 if (!error_state) |
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156 { |
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157 mattyp = MatrixType (m); |
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158 args(0).matrix_type (mattyp); |
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159 } |
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160 } |
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161 } |
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162 else |
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163 { |
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164 mattyp = args(0).matrix_type (); |
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166 if (mattyp.is_unknown () && autocomp) |
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167 { |
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168 SparseMatrix m = args(0).sparse_matrix_value (); |
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169 if (!error_state) |
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170 { |
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171 mattyp = MatrixType (m); |
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172 args(0).matrix_type (mattyp); |
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173 } |
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174 } |
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175 } |
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177 int typ = mattyp.type (); |
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179 if (typ == MatrixType::Diagonal) |
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180 retval = octave_value ("Diagonal"); |
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181 else if (typ == MatrixType::Permuted_Diagonal) |
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182 retval = octave_value ("Permuted Diagonal"); |
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183 else if (typ == MatrixType::Upper) |
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184 retval = octave_value ("Upper"); |
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185 else if (typ == MatrixType::Permuted_Upper) |
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186 retval = octave_value ("Permuted Upper"); |
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187 else if (typ == MatrixType::Lower) |
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188 retval = octave_value ("Lower"); |
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189 else if (typ == MatrixType::Permuted_Lower) |
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190 retval = octave_value ("Permuted Lower"); |
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191 else if (typ == MatrixType::Banded) |
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192 retval = octave_value ("Banded"); |
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193 else if (typ == MatrixType::Banded_Hermitian) |
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194 retval = octave_value ("Banded Positive Definite"); |
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195 else if (typ == MatrixType::Tridiagonal) |
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196 retval = octave_value ("Tridiagonal"); |
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197 else if (typ == MatrixType::Tridiagonal_Hermitian) |
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198 retval = octave_value ("Tridiagonal Positive Definite"); |
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199 else if (typ == MatrixType::Hermitian) |
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200 retval = octave_value ("Positive Definite"); |
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201 else if (typ == MatrixType::Rectangular) |
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202 { |
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203 if (args(0).rows () == args(0).columns ()) |
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204 retval = octave_value ("Singular"); |
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205 else |
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206 retval = octave_value ("Rectangular"); |
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207 } |
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208 else if (typ == MatrixType::Full) |
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209 retval = octave_value ("Full"); |
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210 else |
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211 retval = octave_value ("Unknown"); |
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212 } |
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213 else |
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214 { |
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215 // Ok, we're changing the matrix type |
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216 if (! args(1).is_string ()) |
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217 error ("matrix_type: TYPE must be a string"); |
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218 else |
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219 { |
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220 std::string str_typ = args(1).string_value (); |
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221 |
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222 // FIXME: why do I have to explicitly call the constructor? |
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223 MatrixType mattyp = MatrixType (); |
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224 |
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225 octave_idx_type nl = 0; |
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226 octave_idx_type nu = 0; |
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227 |
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228 // Use STL function to convert to lower case |
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229 std::transform (str_typ.begin (), str_typ.end (), |
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230 str_typ.begin (), tolower); |
5323 | 231 |
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232 if (str_typ == "diagonal") |
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233 mattyp.mark_as_diagonal (); |
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234 if (str_typ == "permuted diagonal") |
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235 mattyp.mark_as_permuted_diagonal (); |
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236 else if (str_typ == "upper") |
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237 mattyp.mark_as_upper_triangular (); |
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238 else if (str_typ == "lower") |
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239 mattyp.mark_as_lower_triangular (); |
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240 else if (str_typ == "banded" |
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241 || str_typ == "banded positive definite") |
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242 { |
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243 if (nargin != 4) |
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|
244 error ("matrix_type: banded matrix type requires 4 arguments"); |
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|
245 else |
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|
246 { |
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|
247 nl = args(2).nint_value (); |
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|
248 nu = args(3).nint_value (); |
5323 | 249 |
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250 if (error_state) |
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|
251 error ("matrix_type: band size NL, NU must be integers"); |
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252 else |
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253 { |
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254 if (nl == 1 && nu == 1) |
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255 mattyp.mark_as_tridiagonal (); |
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|
256 else |
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|
257 mattyp.mark_as_banded (nu, nl); |
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258 |
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259 if (str_typ == "banded positive definite") |
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|
260 mattyp.mark_as_symmetric (); |
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261 } |
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262 } |
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|
263 } |
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|
264 else if (str_typ == "positive definite") |
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|
265 { |
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266 mattyp.mark_as_full (); |
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267 mattyp.mark_as_symmetric (); |
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268 } |
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269 else if (str_typ == "singular") |
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270 mattyp.mark_as_rectangular (); |
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271 else if (str_typ == "full") |
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|
272 mattyp.mark_as_full (); |
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273 else if (str_typ == "unknown") |
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274 mattyp.invalidate_type (); |
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275 else |
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|
276 error ("matrix_type: Unknown matrix type %s", str_typ.c_str ()); |
5323 | 277 |
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278 if (! error_state) |
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279 { |
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280 if (nargin == 3 |
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281 && (str_typ == "upper" || str_typ == "lower")) |
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282 { |
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|
283 const ColumnVector perm = |
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|
284 ColumnVector (args(2).vector_value ()); |
5323 | 285 |
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286 if (error_state) |
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|
287 error ("matrix_type: Invalid permutation vector PERM"); |
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288 else |
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289 { |
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|
290 octave_idx_type len = perm.length (); |
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291 dim_vector dv = args(0).dims (); |
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292 |
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|
293 if (len != dv(0)) |
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|
294 error ("matrix_type: Invalid permutation vector PERM"); |
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295 else |
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296 { |
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297 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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299 for (octave_idx_type i = 0; i < len; i++) |
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300 p[i] = static_cast<octave_idx_type> |
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301 (perm (i)) |
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302 - 1; |
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304 if (str_typ == "upper") |
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305 mattyp.mark_as_permuted (len, p); |
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306 else |
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307 mattyp.mark_as_permuted (len, p); |
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308 } |
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309 } |
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310 } |
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311 else if (nargin != 2 |
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312 && str_typ != "banded positive definite" |
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313 && str_typ != "banded") |
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314 error ("matrix_type: Invalid number of arguments"); |
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316 if (! error_state) |
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317 { |
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318 // Set the matrix type |
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319 if (args(0).is_complex_type ()) |
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320 retval = |
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321 octave_value (args(0).sparse_complex_matrix_value (), |
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322 mattyp); |
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323 else |
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324 retval |
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325 = octave_value (args(0).sparse_matrix_value (), |
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326 mattyp); |
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327 } |
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328 } |
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329 } |
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330 } |
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331 } |
5323 | 332 else |
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333 { |
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334 if (nargin == 1) |
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335 { |
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336 MatrixType mattyp; |
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338 if (args(0).is_complex_type ()) |
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339 { |
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340 mattyp = args(0).matrix_type (); |
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342 if (mattyp.is_unknown () && autocomp) |
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343 { |
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344 if (args(0).is_single_type ()) |
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345 { |
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346 FloatComplexMatrix m; |
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347 m = args(0).float_complex_matrix_value (); |
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348 if (!error_state) |
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349 { |
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350 mattyp = MatrixType (m); |
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351 args(0).matrix_type (mattyp); |
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352 } |
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353 } |
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354 else |
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355 { |
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356 ComplexMatrix m = args(0).complex_matrix_value (); |
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357 if (!error_state) |
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358 { |
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359 mattyp = MatrixType (m); |
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360 args(0).matrix_type (mattyp); |
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361 } |
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362 } |
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|
363 } |
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364 } |
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|
365 else |
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|
366 { |
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|
367 mattyp = args(0).matrix_type (); |
5785 | 368 |
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369 if (mattyp.is_unknown () && autocomp) |
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370 { |
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371 if (args(0).is_single_type ()) |
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372 { |
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|
373 FloatMatrix m = args(0).float_matrix_value (); |
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374 if (!error_state) |
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375 { |
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376 mattyp = MatrixType (m); |
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377 args(0).matrix_type (mattyp); |
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|
378 } |
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|
379 } |
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|
380 else |
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|
381 { |
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|
382 Matrix m = args(0).matrix_value (); |
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383 if (!error_state) |
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|
384 { |
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|
385 mattyp = MatrixType (m); |
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|
386 args(0).matrix_type (mattyp); |
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387 } |
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|
388 } |
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|
389 } |
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|
390 } |
5785 | 391 |
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392 int typ = mattyp.type (); |
5785 | 393 |
10154
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394 if (typ == MatrixType::Upper) |
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395 retval = octave_value ("Upper"); |
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396 else if (typ == MatrixType::Permuted_Upper) |
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|
397 retval = octave_value ("Permuted Upper"); |
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|
398 else if (typ == MatrixType::Lower) |
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|
399 retval = octave_value ("Lower"); |
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|
400 else if (typ == MatrixType::Permuted_Lower) |
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|
401 retval = octave_value ("Permuted Lower"); |
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402 else if (typ == MatrixType::Hermitian) |
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|
403 retval = octave_value ("Positive Definite"); |
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404 else if (typ == MatrixType::Rectangular) |
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405 { |
14846
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|
406 if (args(0).rows () == args(0).columns ()) |
10154
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|
407 retval = octave_value ("Singular"); |
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|
408 else |
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|
409 retval = octave_value ("Rectangular"); |
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|
410 } |
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|
411 else if (typ == MatrixType::Full) |
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|
412 retval = octave_value ("Full"); |
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|
413 else |
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|
414 retval = octave_value ("Unknown"); |
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|
415 } |
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|
416 else |
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|
417 { |
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|
418 // Ok, we're changing the matrix type |
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|
419 if (! args(1).is_string ()) |
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11523
diff
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|
420 error ("matrix_type: TYPE must be a string"); |
10154
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421 else |
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|
422 { |
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|
423 std::string str_typ = args(1).string_value (); |
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424 |
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425 // FIXME: why do I have to explicitly call the constructor? |
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426 MatrixType mattyp = MatrixType (MatrixType::Unknown, true); |
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427 |
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428 // Use STL function to convert to lower case |
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429 std::transform (str_typ.begin (), str_typ.end (), |
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430 str_typ.begin (), tolower); |
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432 if (str_typ == "upper") |
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433 mattyp.mark_as_upper_triangular (); |
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434 else if (str_typ == "lower") |
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435 mattyp.mark_as_lower_triangular (); |
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436 else if (str_typ == "positive definite") |
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437 { |
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438 mattyp.mark_as_full (); |
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439 mattyp.mark_as_symmetric (); |
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440 } |
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441 else if (str_typ == "singular") |
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442 mattyp.mark_as_rectangular (); |
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443 else if (str_typ == "full") |
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444 mattyp.mark_as_full (); |
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445 else if (str_typ == "unknown") |
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446 mattyp.invalidate_type (); |
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447 else |
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448 error ("matrix_type: Unknown matrix type %s", |
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449 str_typ.c_str ()); |
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451 if (! error_state) |
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452 { |
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453 if (nargin == 3 && (str_typ == "upper" |
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454 || str_typ == "lower")) |
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455 { |
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456 const ColumnVector perm = |
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457 ColumnVector (args(2).vector_value ()); |
5785 | 458 |
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459 if (error_state) |
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460 error ("matrix_type: Invalid permutation vector PERM"); |
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461 else |
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462 { |
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463 octave_idx_type len = perm.length (); |
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464 dim_vector dv = args(0).dims (); |
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465 |
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466 if (len != dv(0)) |
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467 error ("matrix_type: Invalid permutation vector PERM"); |
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468 else |
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469 { |
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470 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
5785 | 471 |
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472 for (octave_idx_type i = 0; i < len; i++) |
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473 p[i] = static_cast<octave_idx_type> |
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474 (perm (i)) |
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475 - 1; |
5785 | 476 |
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477 if (str_typ == "upper") |
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478 mattyp.mark_as_permuted (len, p); |
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479 else |
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480 mattyp.mark_as_permuted (len, p); |
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481 } |
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482 } |
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483 } |
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484 else if (nargin != 2) |
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485 error ("matrix_type: Invalid number of arguments"); |
5785 | 486 |
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487 if (! error_state) |
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488 { |
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489 // Set the matrix type |
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490 if (args(0).is_single_type ()) |
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491 { |
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492 if (args(0).is_complex_type ()) |
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493 retval = octave_value |
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494 (args(0).float_complex_matrix_value (), |
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495 mattyp); |
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496 else |
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497 retval = octave_value |
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|
498 (args(0).float_matrix_value (), |
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499 mattyp); |
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|
500 } |
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|
501 else |
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|
502 { |
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503 if (args(0).is_complex_type ()) |
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504 retval = octave_value |
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505 (args(0).complex_matrix_value (), |
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506 mattyp); |
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507 else |
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508 retval = octave_value |
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509 (args(0).matrix_value (), |
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510 mattyp); |
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511 } |
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512 } |
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513 } |
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514 } |
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515 } |
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516 } |
5323 | 517 } |
518 | |
519 return retval; | |
520 } | |
521 | |
522 /* | |
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523 ## FIXME: |
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524 ## Disable tests for lower under-determined and upper over-determined |
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525 ## matrices as this detection is disabled in MatrixType due to issues |
5681 | 526 ## of non minimum norm solution being found. |
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527 |
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528 %!assert (matrix_type (speye (10,10)), "Diagonal") |
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529 %!assert (matrix_type (speye (10,10)([2:10,1],:)), "Permuted Diagonal") |
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530 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]]), "Upper") |
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531 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]](:,[2,1,3:11])), "Permuted Upper") |
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532 %!assert (matrix_type ([speye(10,10),sparse(10,1);1,sparse(1,9),1]), "Lower") |
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533 %!assert (matrix_type ([speye(10,10),sparse(10,1);1,sparse(1,9),1]([2,1,3:11],:)), "Permuted Lower") |
5610 | 534 |
535 %!test | |
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536 %! bnd = spparms ("bandden"); |
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537 %! spparms ("bandden", 0.5); |
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538 %! a = spdiags (rand (10,3)-0.5,[-1,0,1],10,10); |
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539 %! assert (matrix_type (a), "Tridiagonal"); |
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540 %! assert (matrix_type (a'+a+2*speye (10)), "Tridiagonal Positive Definite"); |
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541 %! spparms ("bandden", bnd); |
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542 %!test |
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543 %! bnd=spparms ("bandden"); |
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544 %! spparms ("bandden", 0.5); |
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545 %! a = spdiags (randn (10,4),[-2:1],10,10); |
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546 %! assert (matrix_type (a), "Banded"); |
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547 %! assert (matrix_type (a'*a), "Banded Positive Definite"); |
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548 %! spparms ("bandden", bnd); |
5610 | 549 %!test |
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550 %! a = [speye(10,10),[sparse(9,1);1];-1,sparse(1,9),1]; |
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551 %! assert (matrix_type (a), "Full"); |
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552 %! assert (matrix_type (a'*a), "Positive Definite"); |
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553 |
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554 %!assert (matrix_type (speye (10,11)), "Diagonal") |
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555 %!assert (matrix_type (speye (10,11)([2:10,1],:)), "Permuted Diagonal") |
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556 %!assert (matrix_type (speye (11,10)), "Diagonal") |
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557 %!assert (matrix_type (speye (11,10)([2:11,1],:)), "Permuted Diagonal") |
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558 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]]), "Upper") |
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559 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]](:,[2,1,3:12])), "Permuted Upper") |
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560 %!assert (matrix_type ([speye(11,9),[1;sparse(8,1);1;0]]), "Upper") |
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561 %!assert (matrix_type ([speye(11,9),[1;sparse(8,1);1;0]](:,[2,1,3:10])), "Permuted Upper") |
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562 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]), "Lower") |
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563 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]([2,1,3:12],:)), "Permuted Lower") |
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564 %!assert (matrix_type ([speye(9,11);[1,sparse(1,8),1,0]]), "Lower") |
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565 %!assert (matrix_type ([speye(9,11);[1,sparse(1,8),1,0]]([2,1,3:10],:)), "Permuted Lower") |
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566 %!assert (matrix_type (spdiags (randn (10,4),[-2:1],10,9)), "Rectangular") |
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567 |
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568 %!assert (matrix_type (1i*speye (10,10)), "Diagonal") |
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569 %!assert (matrix_type (1i*speye (10,10)([2:10,1],:)), "Permuted Diagonal") |
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570 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]]), "Upper") |
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571 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]](:,[2,1,3:11])), "Permuted Upper") |
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572 %!assert (matrix_type ([speye(10,10),sparse(10,1);1i,sparse(1,9),1]), "Lower") |
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573 %!assert (matrix_type ([speye(10,10),sparse(10,1);1i,sparse(1,9),1]([2,1,3:11],:)), "Permuted Lower") |
5610 | 574 |
575 %!test | |
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576 %! bnd = spparms ("bandden"); |
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577 %! spparms ("bandden", 0.5); |
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578 %! assert (matrix_type (spdiags (1i*randn (10,3),[-1,0,1],10,10)), "Tridiagonal"); |
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579 %! a = 1i*(rand (9,1)-0.5); |
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580 %! a = [[a;0],ones(10,1),[0;-a]]; |
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581 %! assert (matrix_type (spdiags (a,[-1,0,1],10,10)), "Tridiagonal Positive Definite"); |
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582 %! spparms ("bandden", bnd); |
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583 %!test |
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584 %! bnd = spparms ("bandden"); |
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585 %! spparms ("bandden", 0.5); |
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586 %! assert (matrix_type (spdiags (1i*randn (10,4),[-2:1],10,10)), "Banded"); |
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587 %! a = 1i*(rand (9,2)-0.5); |
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588 %! a = [[a;[0,0]],ones(10,1),[[0;-a(:,2)],[0;0;-a(1:8,1)]]]; |
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589 %! assert (matrix_type (spdiags (a,[-2:2],10,10)), "Banded Positive Definite"); |
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590 %! spparms ("bandden", bnd); |
5785 | 591 %!test |
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592 %! a = [speye(10,10),[sparse(9,1);1i];-1,sparse(1,9),1]; |
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593 %! assert (matrix_type (a), "Full"); |
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594 %! assert (matrix_type (a'*a), "Positive Definite"); |
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595 |
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596 %!assert (matrix_type (1i*speye (10,11)), "Diagonal") |
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597 %!assert (matrix_type (1i*speye (10,11)([2:10,1],:)), "Permuted Diagonal") |
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598 %!assert (matrix_type (1i*speye (11,10)), "Diagonal") |
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599 %!assert (matrix_type (1i*speye (11,10)([2:11,1],:)), "Permuted Diagonal") |
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600 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]]), "Upper") |
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601 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]](:,[2,1,3:12])), "Permuted Upper") |
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602 %!assert (matrix_type ([speye(11,9),[1i;sparse(8,1);1i;0]]), "Upper") |
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603 %!assert (matrix_type ([speye(11,9),[1i;sparse(8,1);1i;0]](:,[2,1,3:10])), "Permuted Upper") |
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604 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]), "Lower") |
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605 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]([2,1,3:12],:)), "Permuted Lower") |
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606 %!assert (matrix_type ([speye(9,11);[1i,sparse(1,8),1i,0]]), "Lower") |
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607 %!assert (matrix_type ([speye(9,11);[1i,sparse(1,8),1i,0]]([2,1,3:10],:)), "Permuted Lower") |
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608 %!assert (matrix_type (1i*spdiags(randn(10,4),[-2:1],10,9)), "Rectangular") |
5785 | 609 |
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610 %!test |
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611 %! a = matrix_type (spdiags (randn (10,3),[-1,0,1],10,10), "Singular"); |
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612 %! assert (matrix_type (a), "Singular"); |
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613 |
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614 %!assert (matrix_type (triu (ones(10,10))), "Upper") |
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615 %!assert (matrix_type (triu (ones(10,10),-1)), "Full") |
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616 %!assert (matrix_type (tril (ones(10,10))), "Lower") |
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617 %!assert (matrix_type (tril (ones(10,10),1)), "Full") |
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618 %!assert (matrix_type (10*eye (10,10) + ones (10,10)), "Positive Definite") |
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619 %!assert (matrix_type (ones (11,10)), "Rectangular") |
5785 | 620 %!test |
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621 %! a = matrix_type (ones (10,10), "Singular"); |
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622 %! assert (matrix_type (a), "Singular"); |
5785 | 623 |
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624 %!assert (matrix_type (triu (1i*ones (10,10))), "Upper") |
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625 %!assert (matrix_type (triu (1i*ones (10,10),-1)), "Full") |
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626 %!assert (matrix_type (tril (1i*ones (10,10))), "Lower") |
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627 %!assert (matrix_type (tril (1i*ones (10,10),1)), "Full") |
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628 %!assert (matrix_type (10*eye (10,10) + 1i*triu (ones (10,10),1) -1i*tril (ones (10,10),-1)), "Positive Definite") |
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629 %!assert (matrix_type (ones (11,10)), "Rectangular") |
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630 %!test |
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631 %! a = matrix_type (ones (10,10), "Singular"); |
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632 %! assert (matrix_type (a), "Singular"); |
5610 | 633 */ |