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1 /* |
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2 |
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3 Copyright (C) 2005, 2006, 2007 David Bateman |
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4 |
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5 This file is part of Octave. |
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6 |
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7 Octave is free software; you can redistribute it and/or modify it |
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8 under the terms of the GNU General Public License as published by the |
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9 Free Software Foundation; either version 3 of the License, or (at your |
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10 option) any later version. |
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11 |
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12 Octave is distributed in the hope that it will be useful, but WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 for more details. |
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16 |
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17 You should have received a copy of the GNU General Public License |
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18 along with Octave; see the file COPYING. If not, see |
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19 <http://www.gnu.org/licenses/>. |
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20 |
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21 */ |
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22 |
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23 #ifdef HAVE_CONFIG_H |
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24 #include <config.h> |
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25 #endif |
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26 |
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27 #include <algorithm> |
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28 |
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29 #include "ov.h" |
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30 #include "defun-dld.h" |
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31 #include "error.h" |
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32 #include "ov-re-mat.h" |
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33 #include "ov-cx-mat.h" |
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34 #include "ov-re-sparse.h" |
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35 #include "ov-cx-sparse.h" |
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36 #include "MatrixType.h" |
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37 |
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38 DEFUN_DLD (matrix_type, args, , |
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39 "-*- texinfo -*-\n\ |
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40 @deftypefn {Loadable Function} {@var{type} =} matrix_type (@var{a})\n\ |
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41 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, @var{type})\n\ |
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42 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'upper', @var{perm})\n\ |
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43 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'lower', @var{perm})\n\ |
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44 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'banded', @var{nl}, @var{nu})\n\ |
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45 Identify the matrix type or mark a matrix as a particular type. This allows rapid\n\ |
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46 for solutions of linear equations involving @var{a} to be performed. Called with a\n\ |
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47 single argument, @code{matrix_type} returns the type of the matrix and caches it for\n\ |
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48 future use. Called with more than one argument, @code{matrix_type} allows the type\n\ |
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49 of the matrix to be defined.\n\ |
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50 \n\ |
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51 The possible matrix types depend on whether the matrix is full or sparse, and can be\n\ |
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52 one of the following\n\ |
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53 \n\ |
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54 @table @asis\n\ |
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55 @item 'unknown'\n\ |
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56 Remove any previously cached matrix type, and mark type as unknown\n\ |
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57 \n\ |
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58 @item 'full'\n\ |
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59 Mark the matrix as full.\n\ |
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60 \n\ |
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61 @item 'positive definite'\n\ |
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62 Full positive definite matrix.\n\ |
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63 \n\ |
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64 @item 'diagonal'\n\ |
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65 Diagonal Matrix. (Sparse matrices only)\n\ |
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66 \n\ |
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67 @item 'permuted diagonal'\n\ |
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68 Permuted Diagonal matrix. The permutation does not need to be specifically\n\ |
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69 indicated, as the structure of the matrix explicitly gives this. (Sparse matrices\n\ |
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70 only)\n\ |
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71 \n\ |
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72 @item 'upper'\n\ |
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73 Upper triangular. If the optional third argument @var{perm} is given, the matrix is\n\ |
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74 assumed to be a permuted upper triangular with the permutations defined by the\n\ |
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75 vector @var{perm}.\n\ |
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76 \n\ |
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77 @item 'lower'\n\ |
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78 Lower triangular. If the optional third argument @var{perm} is given, the matrix is\n\ |
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79 assumed to be a permuted lower triangular with the permutations defined by the\n\ |
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80 vector @var{perm}.\n\ |
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81 \n\ |
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82 @item 'banded'\n\ |
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83 @itemx 'banded positive definite'\n\ |
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84 Banded matrix with the band size of @var{nl} below the diagonal and @var{nu} above\n\ |
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85 it. If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal and treated\n\ |
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86 with specialized code. In addition the matrix can be marked as positive definite\n\ |
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87 (Sparse matrices only)\n\ |
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88 \n\ |
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89 @item 'singular'\n\ |
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90 The matrix is assumed to be singular and will be treated with a minimum norm solution\n\ |
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91 \n\ |
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92 @end table\n\ |
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93 \n\ |
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94 Note that the matrix type will be discovered automatically on the first attempt to\n\ |
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95 solve a linear equation involving @var{a}. Therefore @code{matrix_type} is only\n\ |
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96 useful to give Octave hints of the matrix type. Incorrectly defining the\n\ |
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97 matrix type will result in incorrect results from solutions of linear equations,\n\ |
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98 and so it is entirely the responsibility of the user to correctly identify the\n\ |
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99 matrix type.\n\ |
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100 @end deftypefn") |
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101 { |
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102 int nargin = args.length (); |
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103 octave_value retval; |
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104 |
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105 if (nargin == 0) |
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106 print_usage (); |
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107 else if (nargin > 4) |
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108 error ("matrix_type: incorrect number of arguments"); |
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109 else |
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110 { |
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111 if (args(0).is_scalar_type()) |
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112 { |
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113 if (nargin == 1) |
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114 retval = octave_value ("Full"); |
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115 else |
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116 retval = args(0); |
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117 } |
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118 else if (args(0).is_sparse_type ()) |
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119 { |
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120 if (nargin == 1) |
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121 { |
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122 MatrixType mattyp; |
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123 |
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124 if (args(0).is_complex_type ()) |
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125 { |
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126 mattyp = args(0).matrix_type (); |
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127 |
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128 if (mattyp.is_unknown ()) |
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129 { |
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130 SparseComplexMatrix m = |
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131 args(0).sparse_complex_matrix_value (); |
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132 if (!error_state) |
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133 { |
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134 mattyp = MatrixType (m); |
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135 args(0).matrix_type (mattyp); |
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136 } |
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137 } |
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138 } |
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139 else |
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140 { |
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141 mattyp = args(0).matrix_type (); |
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142 |
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143 if (mattyp.is_unknown ()) |
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144 { |
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145 SparseMatrix m = args(0).sparse_matrix_value (); |
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146 if (!error_state) |
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147 { |
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148 mattyp = MatrixType (m); |
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149 args(0).matrix_type (mattyp); |
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150 } |
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151 } |
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152 } |
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153 |
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154 int typ = mattyp.type (); |
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155 |
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156 if (typ == MatrixType::Diagonal) |
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157 retval = octave_value ("Diagonal"); |
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158 else if (typ == MatrixType::Permuted_Diagonal) |
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159 retval = octave_value ("Permuted Diagonal"); |
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160 else if (typ == MatrixType::Upper) |
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161 retval = octave_value ("Upper"); |
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162 else if (typ == MatrixType::Permuted_Upper) |
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163 retval = octave_value ("Permuted Upper"); |
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164 else if (typ == MatrixType::Lower) |
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165 retval = octave_value ("Lower"); |
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166 else if (typ == MatrixType::Permuted_Lower) |
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167 retval = octave_value ("Permuted Lower"); |
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168 else if (typ == MatrixType::Banded) |
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169 retval = octave_value ("Banded"); |
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170 else if (typ == MatrixType::Banded_Hermitian) |
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171 retval = octave_value ("Banded Positive Definite"); |
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172 else if (typ == MatrixType::Tridiagonal) |
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173 retval = octave_value ("Tridiagonal"); |
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174 else if (typ == MatrixType::Tridiagonal_Hermitian) |
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175 retval = octave_value ("Tridiagonal Positive Definite"); |
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176 else if (typ == MatrixType::Hermitian) |
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177 retval = octave_value ("Positive Definite"); |
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178 else if (typ == MatrixType::Rectangular) |
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179 { |
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180 if (args(0).rows() == args(0).columns()) |
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181 retval = octave_value ("Singular"); |
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182 else |
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183 retval = octave_value ("Rectangular"); |
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184 } |
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185 else if (typ == MatrixType::Full) |
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186 retval = octave_value ("Full"); |
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187 else |
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188 // This should never happen!!! |
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189 retval = octave_value ("Unknown"); |
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190 } |
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191 else |
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192 { |
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193 // Ok, we're changing the matrix type |
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194 std::string str_typ = args(1).string_value (); |
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195 |
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196 // FIXME -- why do I have to explicitly call the constructor? |
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197 MatrixType mattyp = MatrixType (); |
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198 |
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199 octave_idx_type nl = 0; |
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200 octave_idx_type nu = 0; |
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201 |
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202 if (error_state) |
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203 error ("Matrix type must be a string"); |
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204 else |
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205 { |
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206 // Use STL function to convert to lower case |
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207 std::transform (str_typ.begin (), str_typ.end (), |
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208 str_typ.begin (), tolower); |
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209 |
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210 if (str_typ == "diagonal") |
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211 mattyp.mark_as_diagonal (); |
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212 if (str_typ == "permuted diagonal") |
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213 mattyp.mark_as_permuted_diagonal (); |
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214 else if (str_typ == "upper") |
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215 mattyp.mark_as_upper_triangular (); |
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216 else if (str_typ == "lower") |
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217 mattyp.mark_as_lower_triangular (); |
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218 else if (str_typ == "banded" || str_typ == "banded positive definite") |
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219 { |
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220 if (nargin != 4) |
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221 error ("matrix_type: banded matrix type requires 4 arguments"); |
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222 else |
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223 { |
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224 nl = args(2).nint_value (); |
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225 nu = args(3).nint_value (); |
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226 |
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227 if (error_state) |
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228 error ("matrix_type: band size must be integer"); |
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229 else |
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230 { |
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231 if (nl == 1 && nu == 1) |
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232 mattyp.mark_as_tridiagonal (); |
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233 else |
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234 mattyp.mark_as_banded (nu, nl); |
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235 |
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236 if (str_typ == "banded positive definite") |
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237 mattyp.mark_as_symmetric (); |
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238 } |
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239 } |
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240 } |
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241 else if (str_typ == "positive definite") |
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242 { |
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243 mattyp.mark_as_full (); |
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244 mattyp.mark_as_symmetric (); |
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245 } |
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246 else if (str_typ == "singular") |
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247 mattyp.mark_as_rectangular (); |
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248 else if (str_typ == "full") |
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249 mattyp.mark_as_full (); |
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250 else if (str_typ == "unknown") |
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251 mattyp.invalidate_type (); |
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252 else |
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253 error ("matrix_type: Unknown matrix type %s", str_typ.c_str()); |
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254 |
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255 if (! error_state) |
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256 { |
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257 if (nargin == 3 && (str_typ == "upper" || str_typ == "lower")) |
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258 { |
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259 const ColumnVector perm = |
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260 ColumnVector (args (2).vector_value ()); |
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261 |
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262 if (error_state) |
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263 error ("matrix_type: Invalid permutation vector"); |
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264 else |
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265 { |
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266 octave_idx_type len = perm.length (); |
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267 dim_vector dv = args(0).dims (); |
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268 |
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269 if (len != dv(0)) |
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270 error ("matrix_type: Invalid permutation vector"); |
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271 else |
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272 { |
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273 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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274 |
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275 for (octave_idx_type i = 0; i < len; i++) |
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276 p[i] = static_cast<octave_idx_type> (perm (i)) - 1; |
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277 |
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278 if (str_typ == "upper") |
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279 mattyp.mark_as_permuted (len, p); |
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280 else |
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281 mattyp.mark_as_permuted (len, p); |
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282 } |
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283 } |
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284 } |
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285 else if (nargin != 2 && str_typ != "banded positive definite" && |
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286 str_typ != "banded") |
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287 error ("matrix_type: Invalid number of arguments"); |
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288 |
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289 if (! error_state) |
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290 { |
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291 // Set the matrix type |
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292 if (args(0).is_complex_type ()) |
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293 retval = |
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294 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 } |
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301 } |
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302 } |
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303 } |
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304 else |
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305 { |
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306 if (nargin == 1) |
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307 { |
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308 MatrixType mattyp; |
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309 |
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310 if (args(0).is_complex_type ()) |
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311 { |
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312 mattyp = args(0).matrix_type (); |
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313 |
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314 if (mattyp.is_unknown ()) |
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315 { |
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316 ComplexMatrix m = args(0).complex_matrix_value (); |
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317 if (!error_state) |
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318 { |
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319 mattyp = MatrixType (m); |
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320 args(0).matrix_type (mattyp); |
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321 } |
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322 } |
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323 } |
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324 else |
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325 { |
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326 mattyp = args(0).matrix_type (); |
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327 |
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328 if (mattyp.is_unknown ()) |
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329 { |
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330 Matrix m = args(0).matrix_value (); |
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331 if (!error_state) |
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332 { |
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333 mattyp = MatrixType (m); |
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334 args(0).matrix_type (mattyp); |
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335 } |
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336 } |
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337 } |
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338 |
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339 int typ = mattyp.type (); |
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340 |
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341 if (typ == MatrixType::Upper) |
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342 retval = octave_value ("Upper"); |
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343 else if (typ == MatrixType::Permuted_Upper) |
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344 retval = octave_value ("Permuted Upper"); |
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345 else if (typ == MatrixType::Lower) |
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346 retval = octave_value ("Lower"); |
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347 else if (typ == MatrixType::Permuted_Lower) |
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348 retval = octave_value ("Permuted Lower"); |
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349 else if (typ == MatrixType::Hermitian) |
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350 retval = octave_value ("Positive Definite"); |
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351 else if (typ == MatrixType::Rectangular) |
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352 { |
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353 if (args(0).rows() == args(0).columns()) |
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354 retval = octave_value ("Singular"); |
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355 else |
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356 retval = octave_value ("Rectangular"); |
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357 } |
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358 else if (typ == MatrixType::Full) |
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359 retval = octave_value ("Full"); |
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360 else |
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361 // This should never happen!!! |
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362 retval = octave_value ("Unknown"); |
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363 } |
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364 else |
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365 { |
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366 // Ok, we're changing the matrix type |
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367 std::string str_typ = args(1).string_value (); |
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368 |
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369 // FIXME -- why do I have to explicitly call the constructor? |
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370 MatrixType mattyp = MatrixType (MatrixType::Unknown, true); |
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371 |
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372 if (error_state) |
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373 error ("Matrix type must be a string"); |
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374 else |
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375 { |
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376 // Use STL function to convert to lower case |
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377 std::transform (str_typ.begin (), str_typ.end (), |
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378 str_typ.begin (), tolower); |
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379 |
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380 if (str_typ == "upper") |
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381 mattyp.mark_as_upper_triangular (); |
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382 else if (str_typ == "lower") |
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383 mattyp.mark_as_lower_triangular (); |
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384 else if (str_typ == "positive definite") |
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385 { |
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386 mattyp.mark_as_full (); |
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387 mattyp.mark_as_symmetric (); |
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388 } |
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389 else if (str_typ == "singular") |
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390 mattyp.mark_as_rectangular (); |
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391 else if (str_typ == "full") |
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392 mattyp.mark_as_full (); |
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393 else if (str_typ == "unknown") |
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394 mattyp.invalidate_type (); |
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395 else |
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396 error ("matrix_type: Unknown matrix type %s", str_typ.c_str()); |
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397 |
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398 if (! error_state) |
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399 { |
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400 if (nargin == 3 && (str_typ == "upper" |
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401 || str_typ == "lower")) |
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402 { |
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403 const ColumnVector perm = |
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404 ColumnVector (args (2).vector_value ()); |
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405 |
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406 if (error_state) |
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407 error ("matrix_type: Invalid permutation vector"); |
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408 else |
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409 { |
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410 octave_idx_type len = perm.length (); |
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411 dim_vector dv = args(0).dims (); |
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412 |
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413 if (len != dv(0)) |
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414 error ("matrix_type: Invalid permutation vector"); |
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415 else |
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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; |
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421 |
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422 if (str_typ == "upper") |
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423 mattyp.mark_as_permuted (len, p); |
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424 else |
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425 mattyp.mark_as_permuted (len, p); |
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426 } |
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427 } |
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428 } |
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429 else if (nargin != 2) |
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430 error ("matrix_type: Invalid number of arguments"); |
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431 |
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432 if (! error_state) |
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433 { |
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434 // Set the matrix type |
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6371
|
435 if (args(0).is_complex_type()) |
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5785
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436 retval = |
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437 octave_value (args(0).complex_matrix_value (), |
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438 mattyp); |
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439 else |
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440 retval = octave_value (args(0).matrix_value (), |
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441 mattyp); |
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442 } |
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443 } |
|
|
444 } |
|
|
445 } |
|
|
446 } |
|
5323
|
447 } |
|
|
448 |
|
|
449 return retval; |
|
|
450 } |
|
|
451 |
|
|
452 /* |
|
5681
|
453 |
|
5775
|
454 ## FIXME |
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5681
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455 ## Disable tests for lower under-determined and upper over-determined |
|
5785
|
456 ## matrices and this detection is disabled in MatrixType due to issues |
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5681
|
457 ## of non minimum norm solution being found. |
|
5610
|
458 |
|
|
459 %!assert(matrix_type(speye(10,10)),"Diagonal"); |
|
|
460 %!assert(matrix_type(speye(10,10)([2:10,1],:)),"Permuted Diagonal"); |
|
|
461 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]]),"Upper"); |
|
|
462 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]](:,[2,1,3:11])),"Permuted Upper"); |
|
|
463 %!assert(matrix_type([speye(10,10),sparse(10,1);1,sparse(1,9),1]),"Lower"); |
|
|
464 %!assert(matrix_type([speye(10,10),sparse(10,1);1,sparse(1,9),1]([2,1,3:11],:)),"Permuted Lower"); |
|
|
465 %!test |
|
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466 %! bnd=spparms("bandden"); |
|
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467 %! spparms("bandden",0.5); |
|
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468 %! a = spdiags(randn(10,3),[-1,0,1],10,10); |
|
|
469 %! assert(matrix_type(a),"Tridiagonal"); |
|
|
470 %! assert(matrix_type(abs(a')+abs(a)),"Tridiagonal Positive Definite"); |
|
|
471 %! spparms("bandden",bnd); |
|
|
472 %!test |
|
|
473 %! bnd=spparms("bandden"); |
|
|
474 %! spparms("bandden",0.5); |
|
|
475 %! a = spdiags(randn(10,4),[-2:1],10,10); |
|
|
476 %! assert(matrix_type(a),"Banded"); |
|
|
477 %! assert(matrix_type(a'*a),"Banded Positive Definite"); |
|
|
478 %! spparms("bandden",bnd); |
|
|
479 %!test |
|
|
480 %! a=[speye(10,10),[sparse(9,1);1];-1,sparse(1,9),1]; |
|
|
481 %! assert(matrix_type(a),"Full"); |
|
|
482 %! assert(matrix_type(a'*a),"Positive Definite"); |
|
5630
|
483 %!assert(matrix_type(speye(10,11)),"Diagonal"); |
|
|
484 %!assert(matrix_type(speye(10,11)([2:10,1],:)),"Permuted Diagonal"); |
|
|
485 %!assert(matrix_type(speye(11,10)),"Diagonal"); |
|
|
486 %!assert(matrix_type(speye(11,10)([2:11,1],:)),"Permuted Diagonal"); |
|
5681
|
487 %#!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]]),"Upper"); |
|
|
488 %#!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]](:,[2,1,3:12])),"Permuted Upper"); |
|
5630
|
489 %!assert(matrix_type([speye(11,9),[1;sparse(8,1);1;0]]),"Upper"); |
|
|
490 %!assert(matrix_type([speye(11,9),[1;sparse(8,1);1;0]](:,[2,1,3:10])),"Permuted Upper"); |
|
5681
|
491 %#!assert(matrix_type([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]),"Lower"); |
|
|
492 %#!assert(matrix_type([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]([2,1,3:12],:)),"Permuted Lower"); |
|
5630
|
493 %!assert(matrix_type([speye(9,11);[1,sparse(1,8),1,0]]),"Lower"); |
|
|
494 %!assert(matrix_type([speye(9,11);[1,sparse(1,8),1,0]]([2,1,3:10],:)),"Permuted Lower"); |
|
|
495 %!assert(matrix_type(spdiags(randn(10,4),[-2:1],10,9)),"Rectangular") |
|
5610
|
496 |
|
|
497 %!assert(matrix_type(1i*speye(10,10)),"Diagonal"); |
|
|
498 %!assert(matrix_type(1i*speye(10,10)([2:10,1],:)),"Permuted Diagonal"); |
|
|
499 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]]),"Upper"); |
|
|
500 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]](:,[2,1,3:11])),"Permuted Upper"); |
|
|
501 %!assert(matrix_type([speye(10,10),sparse(10,1);1i,sparse(1,9),1]),"Lower"); |
|
|
502 %!assert(matrix_type([speye(10,10),sparse(10,1);1i,sparse(1,9),1]([2,1,3:11],:)),"Permuted Lower"); |
|
|
503 %!test |
|
|
504 %! bnd=spparms("bandden"); |
|
|
505 %! spparms("bandden",0.5); |
|
|
506 %! assert(matrix_type(spdiags(1i*randn(10,3),[-1,0,1],10,10)),"Tridiagonal"); |
|
|
507 %! a = 1i*randn(9,1);a=[[a;0],ones(10,1),[0;-a]]; |
|
|
508 %! assert(matrix_type(spdiags(a,[-1,0,1],10,10)),"Tridiagonal Positive Definite"); |
|
|
509 %! spparms("bandden",bnd); |
|
|
510 %!test |
|
|
511 %! bnd=spparms("bandden"); |
|
|
512 %! spparms("bandden",0.5); |
|
|
513 %! assert(matrix_type(spdiags(1i*randn(10,4),[-2:1],10,10)),"Banded"); |
|
|
514 %! a = 1i*randn(9,2);a=[[a;[0,0]],ones(10,1),[[0;-a(:,2)],[0;0;-a(1:8,1)]]]; |
|
|
515 %! assert(matrix_type(spdiags(a,[-2:2],10,10)),"Banded Positive Definite"); |
|
|
516 %! spparms("bandden",bnd); |
|
|
517 %!test |
|
|
518 %! a=[speye(10,10),[sparse(9,1);1i];-1,sparse(1,9),1]; |
|
|
519 %! assert(matrix_type(a),"Full"); |
|
|
520 %! assert(matrix_type(a'*a),"Positive Definite"); |
|
5630
|
521 %!assert(matrix_type(1i*speye(10,11)),"Diagonal"); |
|
|
522 %!assert(matrix_type(1i*speye(10,11)([2:10,1],:)),"Permuted Diagonal"); |
|
|
523 %!assert(matrix_type(1i*speye(11,10)),"Diagonal"); |
|
|
524 %!assert(matrix_type(1i*speye(11,10)([2:11,1],:)),"Permuted Diagonal"); |
|
5681
|
525 %#!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]]),"Upper"); |
|
|
526 %#!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]](:,[2,1,3:12])),"Permuted Upper"); |
|
5630
|
527 %!assert(matrix_type([speye(11,9),[1i;sparse(8,1);1i;0]]),"Upper"); |
|
|
528 %!assert(matrix_type([speye(11,9),[1i;sparse(8,1);1i;0]](:,[2,1,3:10])),"Permuted Upper"); |
|
5681
|
529 %#!assert(matrix_type([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]),"Lower"); |
|
|
530 %#!assert(matrix_type([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]([2,1,3:12],:)),"Permuted Lower"); |
|
5630
|
531 %!assert(matrix_type([speye(9,11);[1i,sparse(1,8),1i,0]]),"Lower"); |
|
|
532 %!assert(matrix_type([speye(9,11);[1i,sparse(1,8),1i,0]]([2,1,3:10],:)),"Permuted Lower"); |
|
|
533 %!assert(matrix_type(1i*spdiags(randn(10,4),[-2:1],10,9)),"Rectangular") |
|
5610
|
534 |
|
|
535 %!test |
|
|
536 %! a = matrix_type(spdiags(randn(10,3),[-1,0,1],10,10),"Singular"); |
|
|
537 %! assert(matrix_type(a),"Singular"); |
|
|
538 |
|
5785
|
539 %!assert(matrix_type(triu(ones(10,10))),"Upper"); |
|
|
540 %!assert(matrix_type(triu(ones(10,10),-1)),"Full"); |
|
|
541 %!assert(matrix_type(tril(ones(10,10))),"Lower"); |
|
|
542 %!assert(matrix_type(tril(ones(10,10),1)),"Full"); |
|
|
543 %!assert(matrix_type(10*eye(10,10) + ones(10,10)), "Positive Definite"); |
|
|
544 %!assert(matrix_type(ones(11,10)),"Rectangular") |
|
|
545 %!test |
|
|
546 %! a = matrix_type(ones(10,10),"Singular"); |
|
|
547 %! assert(matrix_type(a),"Singular"); |
|
|
548 |
|
|
549 %!assert(matrix_type(triu(1i*ones(10,10))),"Upper"); |
|
|
550 %!assert(matrix_type(triu(1i*ones(10,10),-1)),"Full"); |
|
|
551 %!assert(matrix_type(tril(1i*ones(10,10))),"Lower"); |
|
|
552 %!assert(matrix_type(tril(1i*ones(10,10),1)),"Full"); |
|
|
553 %!assert(matrix_type(10*eye(10,10) + 1i*triu(ones(10,10),1) -1i*tril(ones(10,10),-1)), "Positive Definite"); |
|
|
554 %!assert(matrix_type(ones(11,10)),"Rectangular") |
|
|
555 %!test |
|
|
556 %! a = matrix_type(ones(10,10),"Singular"); |
|
|
557 %! assert(matrix_type(a),"Singular"); |
|
|
558 |
|
5610
|
559 */ |
|
|
560 |
|
|
561 /* |
|
5323
|
562 ;;; Local Variables: *** |
|
|
563 ;;; mode: C++ *** |
|
|
564 ;;; End: *** |
|
|
565 */ |
