Mercurial > octave
annotate libinterp/corefcn/matrix_type.cc @ 29359:7854d5752dd2
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 10:10:40 -0500 |
parents | c40a367a84c0 0a5b15007766 |
children | 32c3a5805893 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 2005-2021 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
5323 | 28 #endif |
29 | |
5403 | 30 #include <algorithm> |
31 | |
5323 | 32 #include "ov.h" |
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33 #include "defun.h" |
5323 | 34 #include "error.h" |
5785 | 35 #include "ov-re-mat.h" |
36 #include "ov-cx-mat.h" | |
5323 | 37 #include "ov-re-sparse.h" |
38 #include "ov-cx-sparse.h" | |
5785 | 39 #include "MatrixType.h" |
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40 #include "oct-locbuf.h" |
5323 | 41 |
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42 DEFUN (matrix_type, args, , |
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43 doc: /* -*- texinfo -*- |
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44 @deftypefn {} {@var{type} =} matrix_type (@var{A}) |
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45 @deftypefnx {} {@var{type} =} matrix_type (@var{A}, "nocompute") |
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46 @deftypefnx {} {@var{A} =} matrix_type (@var{A}, @var{type}) |
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47 @deftypefnx {} {@var{A} =} matrix_type (@var{A}, "upper", @var{perm}) |
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48 @deftypefnx {} {@var{A} =} matrix_type (@var{A}, "lower", @var{perm}) |
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49 @deftypefnx {} {@var{A} =} matrix_type (@var{A}, "banded", @var{nl}, @var{nu}) |
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50 Identify the matrix type or mark a matrix as a particular type. |
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51 |
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52 This allows more rapid solutions of linear equations involving @var{A} to be |
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53 performed. |
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54 |
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55 Called with a single argument, @code{matrix_type} returns the type of the |
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56 matrix and caches it for future use. |
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57 |
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58 Called with more than one argument, @code{matrix_type} allows the type of |
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59 the matrix to be defined. |
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60 |
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61 If the option @qcode{"nocompute"} is given, the function will not attempt |
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62 to guess the type if it is still unknown. This is useful for debugging |
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63 purposes. |
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64 |
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65 The possible matrix types depend on whether the matrix is full or sparse, |
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66 and can be one of the following |
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67 |
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68 @table @asis |
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69 @item @qcode{"unknown"} |
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70 Remove any previously cached matrix type, and mark type as unknown. |
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71 |
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72 @item @qcode{"full"} |
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73 Mark the matrix as full. |
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74 |
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75 @item @qcode{"positive definite"} |
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76 Probable full positive definite matrix. |
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77 |
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78 @item @qcode{"diagonal"} |
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79 Diagonal matrix. (Sparse matrices only) |
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80 |
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81 @item @qcode{"permuted diagonal"} |
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82 Permuted Diagonal matrix. The permutation does not need to be specifically |
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83 indicated, as the structure of the matrix explicitly gives this. (Sparse |
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84 matrices only) |
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85 |
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86 @item @qcode{"upper"} |
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87 Upper triangular. If the optional third argument @var{perm} is given, the |
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88 matrix is assumed to be a permuted upper triangular with the permutations |
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89 defined by the vector @var{perm}. |
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90 |
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91 @item @qcode{"lower"} |
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92 Lower triangular. If the optional third argument @var{perm} is given, the |
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93 matrix is assumed to be a permuted lower triangular with the permutations |
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94 defined by the vector @var{perm}. |
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95 |
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96 @item @qcode{"banded"} |
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97 @itemx @qcode{"banded positive definite"} |
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98 Banded matrix with the band size of @var{nl} below the diagonal and @var{nu} |
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99 above it. If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal |
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100 and treated with specialized code. In addition the matrix can be marked as |
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101 probably a positive definite. (Sparse matrices only) |
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102 |
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103 @item @qcode{"singular"} |
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104 The matrix is assumed to be singular and will be treated with a minimum norm |
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105 solution. |
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106 |
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107 @end table |
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108 |
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109 Note that the matrix type will be discovered automatically on the first |
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110 attempt to solve a linear equation involving @var{A}. Therefore |
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111 @code{matrix_type} is only useful to give Octave hints of the matrix type. |
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112 Incorrectly defining the matrix type will result in incorrect results from |
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113 solutions of linear equations; it is entirely @strong{the responsibility of |
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114 the user} to correctly identify the matrix type. |
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115 |
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116 Also, the test for positive definiteness is a low-cost test for a Hermitian |
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117 matrix with a real positive diagonal. This does not guarantee that the |
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118 matrix is positive definite, but only that it is a probable candidate. When |
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119 such a matrix is factorized, a Cholesky@tie{}factorization is first |
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120 attempted, and if that fails the matrix is then treated with an |
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121 LU@tie{}factorization. Once the matrix has been factorized, |
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122 @code{matrix_type} will return the correct classification of the matrix. |
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123 @end deftypefn */) |
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125 int nargin = args.length (); | |
126 | |
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127 if (nargin == 0 || nargin > 4) |
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129 |
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130 bool autocomp = true; |
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131 if (nargin == 2 && args(1).is_string () |
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132 && args(1).string_value () == "nocompute") |
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133 { |
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134 nargin = 1; |
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135 autocomp = false; |
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136 } |
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137 |
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138 octave_value retval; |
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139 |
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140 if (args(0).is_scalar_type ()) |
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141 { |
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142 if (nargin == 1) |
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143 retval = octave_value ("Diagonal"); |
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144 else |
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145 retval = args(0); |
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146 } |
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147 else if (args(0).issparse ()) |
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148 { |
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149 if (nargin == 1) |
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150 { |
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151 MatrixType mattyp; |
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152 |
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153 if (args(0).iscomplex ()) |
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154 { |
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155 mattyp = args(0).matrix_type (); |
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156 |
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157 if (mattyp.is_unknown () && autocomp) |
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158 { |
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159 SparseComplexMatrix m |
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160 = args(0).sparse_complex_matrix_value (); |
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161 |
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162 mattyp = MatrixType (m); |
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163 args(0).matrix_type (mattyp); |
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164 } |
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165 } |
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166 else |
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167 { |
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168 mattyp = args(0).matrix_type (); |
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169 |
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170 if (mattyp.is_unknown () && autocomp) |
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171 { |
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172 SparseMatrix m = args(0).sparse_matrix_value (); |
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173 |
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174 mattyp = MatrixType (m); |
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175 args(0).matrix_type (mattyp); |
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176 } |
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177 } |
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178 |
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179 int typ = mattyp.type (); |
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180 |
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181 if (typ == MatrixType::Diagonal) |
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182 retval = octave_value ("Diagonal"); |
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183 else if (typ == MatrixType::Permuted_Diagonal) |
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184 retval = octave_value ("Permuted Diagonal"); |
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185 else if (typ == MatrixType::Upper) |
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186 retval = octave_value ("Upper"); |
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187 else if (typ == MatrixType::Permuted_Upper) |
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188 retval = octave_value ("Permuted Upper"); |
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189 else if (typ == MatrixType::Lower) |
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190 retval = octave_value ("Lower"); |
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191 else if (typ == MatrixType::Permuted_Lower) |
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192 retval = octave_value ("Permuted Lower"); |
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193 else if (typ == MatrixType::Banded) |
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194 retval = octave_value ("Banded"); |
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195 else if (typ == MatrixType::Banded_Hermitian) |
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196 retval = octave_value ("Banded Positive Definite"); |
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197 else if (typ == MatrixType::Tridiagonal) |
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198 retval = octave_value ("Tridiagonal"); |
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199 else if (typ == MatrixType::Tridiagonal_Hermitian) |
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200 retval = octave_value ("Tridiagonal Positive Definite"); |
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201 else if (typ == MatrixType::Hermitian) |
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202 retval = octave_value ("Positive Definite"); |
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203 else if (typ == MatrixType::Rectangular) |
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204 { |
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205 if (args(0).rows () == args(0).columns ()) |
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206 retval = octave_value ("Singular"); |
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207 else |
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208 retval = octave_value ("Rectangular"); |
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209 } |
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210 else if (typ == MatrixType::Full) |
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211 retval = octave_value ("Full"); |
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212 else |
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213 retval = octave_value ("Unknown"); |
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214 } |
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215 else |
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216 { |
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217 // Ok, we're changing the matrix type |
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218 std::string str_typ = args(1).xstring_value ("matrix_type: TYPE must be a string"); |
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219 |
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220 // FIXME: why do I have to explicitly call the constructor? |
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221 MatrixType mattyp = MatrixType (); |
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222 |
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223 octave_idx_type nl = 0; |
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224 octave_idx_type nu = 0; |
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225 |
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226 // Use STL function to convert to lower case |
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227 std::transform (str_typ.begin (), str_typ.end (), |
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228 str_typ.begin (), tolower); |
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229 |
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230 if (str_typ == "diagonal") |
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231 mattyp.mark_as_diagonal (); |
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232 if (str_typ == "permuted diagonal") |
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233 mattyp.mark_as_permuted_diagonal (); |
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234 else if (str_typ == "upper") |
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235 mattyp.mark_as_upper_triangular (); |
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236 else if (str_typ == "lower") |
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237 mattyp.mark_as_lower_triangular (); |
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238 else if (str_typ == "banded" |
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239 || str_typ == "banded positive definite") |
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240 { |
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241 if (nargin != 4) |
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242 error ("matrix_type: banded matrix type requires 4 arguments"); |
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243 |
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244 nl = args(2).xnint_value ("matrix_type: band size NL, NU must be integers"); |
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245 nu = args(3).xnint_value ("matrix_type: band size NL, NU must be integers"); |
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246 |
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247 if (nl == 1 && nu == 1) |
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248 mattyp.mark_as_tridiagonal (); |
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249 else |
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250 mattyp.mark_as_banded (nu, nl); |
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251 |
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252 if (str_typ == "banded positive definite") |
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253 mattyp.mark_as_symmetric (); |
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254 } |
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255 else if (str_typ == "positive definite") |
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256 { |
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257 mattyp.mark_as_full (); |
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258 mattyp.mark_as_symmetric (); |
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259 } |
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260 else if (str_typ == "singular") |
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261 mattyp.mark_as_rectangular (); |
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262 else if (str_typ == "full") |
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263 mattyp.mark_as_full (); |
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264 else if (str_typ == "unknown") |
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265 mattyp.invalidate_type (); |
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266 else |
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267 error ("matrix_type: Unknown matrix type %s", str_typ.c_str ()); |
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268 |
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269 if (nargin == 3 |
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270 && (str_typ == "upper" || str_typ == "lower")) |
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271 { |
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272 const ColumnVector perm = args(2).xvector_value ("matrix_type: Invalid permutation vector PERM"); |
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273 |
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274 octave_idx_type len = perm.numel (); |
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275 dim_vector dv = args(0).dims (); |
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276 |
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277 if (len != dv(0)) |
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278 error ("matrix_type: Invalid permutation vector PERM"); |
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279 |
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280 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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281 |
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282 for (octave_idx_type i = 0; i < len; i++) |
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283 p[i] = static_cast<octave_idx_type> (perm (i)) - 1; |
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284 |
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285 mattyp.mark_as_permuted (len, p); |
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286 } |
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287 else if (nargin != 2 |
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288 && str_typ != "banded positive definite" |
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289 && str_typ != "banded") |
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290 error ("matrix_type: Invalid number of arguments"); |
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291 |
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292 // Set the matrix type |
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293 if (args(0).iscomplex ()) |
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294 retval = octave_value (args(0).sparse_complex_matrix_value (), |
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295 mattyp); |
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296 else |
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297 retval = octave_value (args(0).sparse_matrix_value (), |
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298 mattyp); |
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299 } |
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300 } |
5323 | 301 else |
302 { | |
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303 if (nargin == 1) |
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304 { |
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305 MatrixType mattyp; |
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306 |
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307 if (args(0).iscomplex ()) |
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308 { |
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309 mattyp = args(0).matrix_type (); |
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311 if (mattyp.is_unknown () && autocomp) |
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312 { |
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313 if (args(0).is_single_type ()) |
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314 { |
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315 FloatComplexMatrix m; |
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316 m = args(0).float_complex_matrix_value (); |
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317 |
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318 mattyp = MatrixType (m); |
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319 args(0).matrix_type (mattyp); |
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320 } |
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321 else |
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322 { |
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323 ComplexMatrix m = args(0).complex_matrix_value (); |
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324 |
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325 mattyp = MatrixType (m); |
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326 args(0).matrix_type (mattyp); |
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327 } |
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328 } |
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329 } |
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330 else |
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331 { |
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332 mattyp = args(0).matrix_type (); |
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333 |
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334 if (mattyp.is_unknown () && autocomp) |
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335 { |
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336 if (args(0).is_single_type ()) |
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337 { |
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338 FloatMatrix m = args(0).float_matrix_value (); |
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339 |
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340 mattyp = MatrixType (m); |
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341 args(0).matrix_type (mattyp); |
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342 } |
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343 else |
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344 { |
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345 Matrix m = args(0).matrix_value (); |
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347 mattyp = MatrixType (m); |
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348 args(0).matrix_type (mattyp); |
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349 } |
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350 } |
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351 } |
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352 |
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353 int typ = mattyp.type (); |
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354 |
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355 if (typ == MatrixType::Upper) |
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356 retval = octave_value ("Upper"); |
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357 else if (typ == MatrixType::Permuted_Upper) |
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358 retval = octave_value ("Permuted Upper"); |
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359 else if (typ == MatrixType::Lower) |
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360 retval = octave_value ("Lower"); |
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361 else if (typ == MatrixType::Permuted_Lower) |
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362 retval = octave_value ("Permuted Lower"); |
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363 else if (typ == MatrixType::Hermitian) |
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364 retval = octave_value ("Positive Definite"); |
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365 else if (typ == MatrixType::Rectangular) |
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366 { |
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367 if (args(0).rows () == args(0).columns ()) |
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368 retval = octave_value ("Singular"); |
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369 else |
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370 retval = octave_value ("Rectangular"); |
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371 } |
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372 else if (typ == MatrixType::Full) |
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373 retval = octave_value ("Full"); |
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374 else |
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375 retval = octave_value ("Unknown"); |
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376 } |
5323 | 377 else |
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378 { |
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379 // Ok, we're changing the matrix type |
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380 std::string str_typ = args(1).xstring_value ("matrix_type: TYPE must be a string"); |
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382 // FIXME: why do I have to explicitly call the constructor? |
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383 MatrixType mattyp = MatrixType (MatrixType::Unknown, true); |
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384 |
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385 // Use STL function to convert to lower case |
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386 std::transform (str_typ.begin (), str_typ.end (), |
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387 str_typ.begin (), tolower); |
5785 | 388 |
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389 if (str_typ == "upper") |
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390 mattyp.mark_as_upper_triangular (); |
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391 else if (str_typ == "lower") |
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392 mattyp.mark_as_lower_triangular (); |
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393 else if (str_typ == "positive definite") |
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394 { |
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395 mattyp.mark_as_full (); |
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396 mattyp.mark_as_symmetric (); |
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397 } |
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398 else if (str_typ == "singular") |
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399 mattyp.mark_as_rectangular (); |
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400 else if (str_typ == "full") |
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401 mattyp.mark_as_full (); |
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402 else if (str_typ == "unknown") |
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403 mattyp.invalidate_type (); |
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404 else |
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405 error ("matrix_type: Unknown matrix type %s", str_typ.c_str ()); |
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406 |
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407 if (nargin == 3 && (str_typ == "upper" || str_typ == "lower")) |
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408 { |
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409 const ColumnVector perm = args(2).xvector_value ("matrix_type: Invalid permutation vector PERM"); |
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410 |
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411 octave_idx_type len = perm.numel (); |
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412 dim_vector dv = args(0).dims (); |
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413 |
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414 if (len != dv(0)) |
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415 error ("matrix_type: Invalid permutation vector PERM"); |
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416 |
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417 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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418 |
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419 for (octave_idx_type i = 0; i < len; i++) |
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420 p[i] = static_cast<octave_idx_type> (perm (i)) - 1; |
5785 | 421 |
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422 mattyp.mark_as_permuted (len, p); |
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423 } |
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424 else if (nargin != 2) |
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425 error ("matrix_type: Invalid number of arguments"); |
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427 // Set the matrix type |
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428 if (args(0).is_single_type ()) |
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429 { |
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430 if (args(0).iscomplex ()) |
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431 retval = octave_value (args(0).float_complex_matrix_value (), |
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432 mattyp); |
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433 else |
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434 retval = octave_value (args(0).float_matrix_value (), |
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435 mattyp); |
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436 } |
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437 else |
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438 { |
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439 if (args(0).iscomplex ()) |
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440 retval = octave_value (args(0).complex_matrix_value (), |
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441 mattyp); |
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442 else |
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443 retval = octave_value (args(0).matrix_value (), mattyp); |
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444 } |
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445 } |
5323 | 446 } |
447 | |
448 return retval; | |
449 } | |
450 | |
451 /* | |
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452 ## FIXME: |
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453 ## Disable tests for lower under-determined and upper over-determined |
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454 ## matrices as this detection is disabled in MatrixType due to issues |
5681 | 455 ## of non minimum norm solution being found. |
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456 |
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457 %!assert (matrix_type (speye (10,10)), "Diagonal") |
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458 %!assert (matrix_type (speye (10,10)([2:10,1],:)), "Permuted Diagonal") |
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459 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]]), "Upper") |
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460 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]](:,[2,1,3:11])), "Permuted Upper") |
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461 %!assert (matrix_type ([speye(10,10),sparse(10,1);1,sparse(1,9),1]), "Lower") |
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462 %!assert (matrix_type ([speye(10,10),sparse(10,1);1,sparse(1,9),1]([2,1,3:11],:)), "Permuted Lower") |
5610 | 463 |
464 %!test | |
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465 %! bnd = spparms ("bandden"); |
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466 %! spparms ("bandden", 0.5); |
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467 %! a = spdiags (rand (10,3)-0.5,[-1,0,1],10,10); |
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468 %! assert (matrix_type (a), "Tridiagonal"); |
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469 %! assert (matrix_type (a'+a+2*speye (10)), "Tridiagonal Positive Definite"); |
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470 %! spparms ("bandden", bnd); |
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471 %!test |
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472 %! bnd=spparms ("bandden"); |
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473 %! spparms ("bandden", 0.5); |
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474 %! a = spdiags (randn (10,4),[-2:1],10,10); |
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475 %! assert (matrix_type (a), "Banded"); |
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476 %! assert (matrix_type (a'*a), "Banded Positive Definite"); |
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477 %! spparms ("bandden", bnd); |
5610 | 478 %!test |
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479 %! a = [speye(10,10),[sparse(9,1);1];-1,sparse(1,9),1]; |
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480 %! assert (matrix_type (a), "Full"); |
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481 %! assert (matrix_type (a'*a), "Positive Definite"); |
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482 |
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483 %!assert (matrix_type (speye (10,11)), "Diagonal") |
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484 %!assert (matrix_type (speye (10,11)([2:10,1],:)), "Permuted Diagonal") |
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485 %!assert (matrix_type (speye (11,10)), "Diagonal") |
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486 %!assert (matrix_type (speye (11,10)([2:11,1],:)), "Permuted Diagonal") |
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487 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]]), "Upper") |
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488 %#!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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489 %!assert (matrix_type ([speye(11,9),[1;sparse(8,1);1;0]]), "Upper") |
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490 %!assert (matrix_type ([speye(11,9),[1;sparse(8,1);1;0]](:,[2,1,3:10])), "Permuted Upper") |
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491 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]), "Lower") |
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492 %#!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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493 %!assert (matrix_type ([speye(9,11);[1,sparse(1,8),1,0]]), "Lower") |
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494 %!assert (matrix_type ([speye(9,11);[1,sparse(1,8),1,0]]([2,1,3:10],:)), "Permuted Lower") |
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495 %!assert (matrix_type (spdiags (randn (10,4),[-2:1],10,9)), "Rectangular") |
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496 |
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497 %!assert (matrix_type (1i*speye (10,10)), "Diagonal") |
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498 %!assert (matrix_type (1i*speye (10,10)([2:10,1],:)), "Permuted Diagonal") |
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499 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]]), "Upper") |
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500 %!assert (matrix_type ([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]](:,[2,1,3:11])), "Permuted Upper") |
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501 %!assert (matrix_type ([speye(10,10),sparse(10,1);1i,sparse(1,9),1]), "Lower") |
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502 %!assert (matrix_type ([speye(10,10),sparse(10,1);1i,sparse(1,9),1]([2,1,3:11],:)), "Permuted Lower") |
5610 | 503 |
504 %!test | |
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505 %! bnd = spparms ("bandden"); |
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506 %! spparms ("bandden", 0.5); |
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507 %! assert (matrix_type (spdiags (1i*randn (10,3),[-1,0,1],10,10)), "Tridiagonal"); |
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508 %! a = 1i*(rand (9,1)-0.5); |
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509 %! a = [[a;0],ones(10,1),[0;-a]]; |
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510 %! assert (matrix_type (spdiags (a,[-1,0,1],10,10)), "Tridiagonal Positive Definite"); |
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511 %! spparms ("bandden", bnd); |
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512 %!test |
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513 %! bnd = spparms ("bandden"); |
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514 %! spparms ("bandden", 0.5); |
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515 %! assert (matrix_type (spdiags (1i*randn (10,4),[-2:1],10,10)), "Banded"); |
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516 %! a = 1i*(rand (9,2)-0.5); |
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517 %! a = [[a;[0,0]],ones(10,1),[[0;-a(:,2)],[0;0;-a(1:8,1)]]]; |
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518 %! assert (matrix_type (spdiags (a,[-2:2],10,10)), "Banded Positive Definite"); |
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519 %! spparms ("bandden", bnd); |
5785 | 520 %!test |
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521 %! a = [speye(10,10),[sparse(9,1);1i];-1,sparse(1,9),1]; |
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522 %! assert (matrix_type (a), "Full"); |
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523 %! assert (matrix_type (a'*a), "Positive Definite"); |
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524 |
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525 %!assert (matrix_type (1i*speye (10,11)), "Diagonal") |
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526 %!assert (matrix_type (1i*speye (10,11)([2:10,1],:)), "Permuted Diagonal") |
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527 %!assert (matrix_type (1i*speye (11,10)), "Diagonal") |
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528 %!assert (matrix_type (1i*speye (11,10)([2:11,1],:)), "Permuted Diagonal") |
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529 %#!assert (matrix_type ([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]]), "Upper") |
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530 %#!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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531 %!assert (matrix_type ([speye(11,9),[1i;sparse(8,1);1i;0]]), "Upper") |
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532 %!assert (matrix_type ([speye(11,9),[1i;sparse(8,1);1i;0]](:,[2,1,3:10])), "Permuted Upper") |
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533 %#!assert (matrix_type ([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]), "Lower") |
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534 %#!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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535 %!assert (matrix_type ([speye(9,11);[1i,sparse(1,8),1i,0]]), "Lower") |
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536 %!assert (matrix_type ([speye(9,11);[1i,sparse(1,8),1i,0]]([2,1,3:10],:)), "Permuted Lower") |
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537 %!assert (matrix_type (1i*spdiags(randn(10,4),[-2:1],10,9)), "Rectangular") |
5785 | 538 |
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539 %!test |
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540 %! a = matrix_type (spdiags (randn (10,3),[-1,0,1],10,10), "Singular"); |
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541 %! assert (matrix_type (a), "Singular"); |
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542 |
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543 %!assert (matrix_type (triu (ones (10,10))), "Upper") |
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544 %!assert (matrix_type (triu (ones (10,10),-1)), "Full") |
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545 %!assert (matrix_type (tril (ones (10,10))), "Lower") |
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546 %!assert (matrix_type (tril (ones (10,10),1)), "Full") |
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547 %!assert (matrix_type (10*eye (10,10) + ones (10,10)), "Positive Definite") |
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548 %!assert (matrix_type (ones (11,10)), "Rectangular") |
5785 | 549 %!test |
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550 %! a = matrix_type (ones (10,10), "Singular"); |
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551 %! assert (matrix_type (a), "Singular"); |
5785 | 552 |
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553 %!assert (matrix_type (triu (1i*ones (10,10))), "Upper") |
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554 %!assert (matrix_type (triu (1i*ones (10,10),-1)), "Full") |
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555 %!assert (matrix_type (tril (1i*ones (10,10))), "Lower") |
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556 %!assert (matrix_type (tril (1i*ones (10,10),1)), "Full") |
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557 %!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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558 %!assert (matrix_type (ones (11,10)), "Rectangular") |
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559 %!test |
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560 %! a = matrix_type (ones (10,10), "Singular"); |
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561 %! assert (matrix_type (a), "Singular"); |
5610 | 562 */ |