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1 /* |
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2 |
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3 Copyright (C) 2005 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 2, or (at your option) any |
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10 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, write to the Free |
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19 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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20 02110-1301, USA. |
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21 |
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22 */ |
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23 |
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24 #ifdef HAVE_CONFIG_H |
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25 #include <config.h> |
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26 #endif |
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27 |
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28 #include <algorithm> |
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29 |
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30 #include "ov.h" |
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31 #include "defun-dld.h" |
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32 #include "error.h" |
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33 #include "ov-re-mat.h" |
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34 #include "ov-cx-mat.h" |
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35 #include "ov-re-sparse.h" |
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36 #include "ov-cx-sparse.h" |
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37 #include "MatrixType.h" |
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38 |
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39 DEFUN_DLD (matrix_type, args, , |
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40 "-*- texinfo -*-\n\ |
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41 @deftypefn {Loadable Function} {@var{type} =} matrix_type (@var{a})\n\ |
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42 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, @var{type})\n\ |
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43 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'upper', @var{perm})\n\ |
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44 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'lower', @var{perm})\n\ |
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45 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'banded', @var{nl}, @var{nu})\n\ |
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46 Identify the matrix type or mark a matrix as a particular type. This allows rapid\n\ |
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47 for solutions of linear equations involving @var{a} to be performed. Called with a\n\ |
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48 single argument, @code{matrix_type} returns the type of the matrix and caches it for\n\ |
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49 future use. Called with more than one argument, @code{matrix_type} allows the type\n\ |
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50 of the matrix to be defined.\n\ |
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51 \n\ |
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52 The possible matrix types depend on whether the matrix is full or sparse, and can be\n\ |
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53 one of the following\n\ |
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54 \n\ |
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55 @table @asis\n\ |
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56 @item 'unknown'\n\ |
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57 Remove any previously cached matrix type, and mark type as unknown\n\ |
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58 \n\ |
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59 @item 'full'\n\ |
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60 Mark the matrix as full.\n\ |
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61 \n\ |
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62 @item 'positive definite'\n\ |
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63 Full positive definite matrix.\n\ |
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64 \n\ |
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65 @item 'diagonal'\n\ |
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66 Diagonal Matrix. (Sparse matrices only)\n\ |
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67 \n\ |
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68 @item 'permuted diagonal'\n\ |
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69 Permuted Diagonal matrix. The permutation does not need to be specifically\n\ |
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70 indicated, as the structure of the matrix explicitly gives this. (Sparse matrices\n\ |
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71 only)\n\ |
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72 \n\ |
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73 @item 'upper'\n\ |
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74 Upper triangular. If the optional third argument @var{perm} is given, the matrix is\n\ |
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75 assumed to be a permuted upper triangular with the permutations defined by the\n\ |
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76 vector @var{perm}.\n\ |
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77 \n\ |
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78 @item 'lower'\n\ |
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79 Lower triangular. If the optional third argument @var{perm} is given, the matrix is\n\ |
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80 assumed to be a permuted lower triangular with the permutations defined by the\n\ |
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81 vector @var{perm}.\n\ |
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82 \n\ |
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83 @item 'banded'\n\ |
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84 @itemx 'banded positive definite'\n\ |
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85 Banded matrix with the band size of @var{nl} below the diagonal and @var{nu} above\n\ |
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86 it. If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal and treated\n\ |
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87 with specialized code. In addition the matrix can be marked as positive definite\n\ |
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88 (Sparse matrices only)\n\ |
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89 \n\ |
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90 @item 'singular'\n\ |
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91 The matrix is assumed to be singular and will be treated with a minimum norm solution\n\ |
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92 \n\ |
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93 @end table\n\ |
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94 \n\ |
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95 Note that the matrix type will be discovered automatically on the first attempt to\n\ |
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96 solve a linear equation involving @var{a}. Therefore @code{matrix_type} is only\n\ |
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97 useful to give Octave hints of the matrix type. Incorrectly defining the\n\ |
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98 matrix type will result in incorrect results from solutions of linear equations,\n\ |
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99 and so it is entirely the responsibility of the user to correctly indentify the\n\ |
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100 matrix type.\n\ |
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101 @end deftypefn") |
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102 { |
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103 int nargin = args.length (); |
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104 octave_value retval; |
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105 |
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106 if (nargin == 0) |
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107 print_usage (); |
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108 else if (nargin > 4) |
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109 error ("matrix_type: incorrect number of arguments"); |
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110 else |
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111 { |
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112 if (args(0).is_sparse_type ()) |
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113 { |
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114 if (nargin == 1) |
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115 { |
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116 MatrixType mattyp; |
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117 |
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118 if (args(0).type_name () == "sparse complex matrix" ) |
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119 { |
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120 mattyp = args(0).matrix_type (); |
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121 |
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122 if (mattyp.is_unknown ()) |
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123 { |
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124 SparseComplexMatrix m = |
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125 args(0).sparse_complex_matrix_value (); |
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126 if (!error_state) |
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127 { |
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128 mattyp = MatrixType (m); |
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129 args(0).matrix_type (mattyp); |
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130 } |
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131 } |
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132 } |
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133 else |
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134 { |
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135 mattyp = args(0).matrix_type (); |
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136 |
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137 if (mattyp.is_unknown ()) |
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138 { |
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139 SparseMatrix m = args(0).sparse_matrix_value (); |
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140 if (!error_state) |
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141 { |
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142 mattyp = MatrixType (m); |
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143 args(0).matrix_type (mattyp); |
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144 } |
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145 } |
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146 } |
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147 |
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148 int typ = mattyp.type (); |
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149 |
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150 if (typ == MatrixType::Diagonal) |
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151 retval = octave_value ("Diagonal"); |
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152 else if (typ == MatrixType::Permuted_Diagonal) |
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153 retval = octave_value ("Permuted Diagonal"); |
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154 else if (typ == MatrixType::Upper) |
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155 retval = octave_value ("Upper"); |
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156 else if (typ == MatrixType::Permuted_Upper) |
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157 retval = octave_value ("Permuted Upper"); |
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158 else if (typ == MatrixType::Lower) |
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159 retval = octave_value ("Lower"); |
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160 else if (typ == MatrixType::Permuted_Lower) |
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161 retval = octave_value ("Permuted Lower"); |
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162 else if (typ == MatrixType::Banded) |
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163 retval = octave_value ("Banded"); |
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164 else if (typ == MatrixType::Banded_Hermitian) |
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165 retval = octave_value ("Banded Positive Definite"); |
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166 else if (typ == MatrixType::Tridiagonal) |
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167 retval = octave_value ("Tridiagonal"); |
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168 else if (typ == MatrixType::Tridiagonal_Hermitian) |
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169 retval = octave_value ("Tridiagonal Positive Definite"); |
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170 else if (typ == MatrixType::Hermitian) |
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171 retval = octave_value ("Positive Definite"); |
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172 else if (typ == MatrixType::Rectangular) |
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173 { |
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174 if (args(0).rows() == args(0).columns()) |
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175 retval = octave_value ("Singular"); |
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176 else |
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177 retval = octave_value ("Rectangular"); |
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178 } |
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179 else if (typ == MatrixType::Full) |
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180 retval = octave_value ("Full"); |
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181 else |
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182 // This should never happen!!! |
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183 retval = octave_value ("Unknown"); |
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184 } |
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185 else |
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186 { |
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187 // Ok, we're changing the matrix type |
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188 std::string str_typ = args(1).string_value (); |
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189 |
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190 // FIXME -- why do I have to explicitly call the constructor? |
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191 MatrixType mattyp = MatrixType (); |
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192 |
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193 octave_idx_type nl = 0; |
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194 octave_idx_type nu = 0; |
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195 |
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196 if (error_state) |
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197 error ("Matrix type must be a string"); |
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198 else |
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199 { |
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200 // Use STL function to convert to lower case |
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201 std::transform (str_typ.begin (), str_typ.end (), |
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202 str_typ.begin (), tolower); |
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203 |
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204 if (str_typ == "diagonal") |
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205 mattyp.mark_as_diagonal (); |
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206 if (str_typ == "permuted diagonal") |
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207 mattyp.mark_as_permuted_diagonal (); |
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208 else if (str_typ == "upper") |
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209 mattyp.mark_as_upper_triangular (); |
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210 else if (str_typ == "lower") |
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211 mattyp.mark_as_lower_triangular (); |
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212 else if (str_typ == "banded" || str_typ == "banded positive definite") |
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213 { |
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214 if (nargin != 4) |
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215 error ("matrix_type: banded matrix type requires 4 arguments"); |
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216 else |
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217 { |
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218 nl = args(2).nint_value (); |
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219 nu = args(3).nint_value (); |
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220 |
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221 if (error_state) |
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222 error ("matrix_type: band size must be integer"); |
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223 else |
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224 { |
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225 if (nl == 1 && nu == 1) |
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226 mattyp.mark_as_tridiagonal (); |
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227 else |
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228 mattyp.mark_as_banded (nu, nl); |
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229 |
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230 if (str_typ == "banded positive definite") |
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231 mattyp.mark_as_symmetric (); |
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232 } |
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233 } |
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234 } |
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235 else if (str_typ == "positive definite") |
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236 { |
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237 mattyp.mark_as_full (); |
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238 mattyp.mark_as_symmetric (); |
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239 } |
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240 else if (str_typ == "singular") |
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241 mattyp.mark_as_rectangular (); |
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242 else if (str_typ == "full") |
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243 mattyp.mark_as_full (); |
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244 else if (str_typ == "unknown") |
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245 mattyp.invalidate_type (); |
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246 else |
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247 error ("matrix_type: Unknown matrix type %s", str_typ.c_str()); |
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248 |
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249 if (! error_state) |
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250 { |
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251 if (nargin == 3 && (str_typ == "upper" || str_typ == "lower")) |
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252 { |
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253 const ColumnVector perm = |
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254 ColumnVector (args (2).vector_value ()); |
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255 |
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256 if (error_state) |
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257 error ("matrix_type: Invalid permutation vector"); |
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258 else |
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259 { |
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260 octave_idx_type len = perm.length (); |
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261 dim_vector dv = args(0).dims (); |
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262 |
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263 if (len != dv(0)) |
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264 error ("matrix_type: Invalid permutation vector"); |
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265 else |
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266 { |
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267 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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268 |
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269 for (octave_idx_type i = 0; i < len; i++) |
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270 p[i] = static_cast<octave_idx_type> (perm (i)) - 1; |
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271 |
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272 if (str_typ == "upper") |
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273 mattyp.mark_as_permuted (len, p); |
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274 else |
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275 mattyp.mark_as_permuted (len, p); |
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276 } |
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277 } |
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278 } |
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279 else if (nargin != 2 && str_typ != "banded positive definite" && |
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280 str_typ != "banded") |
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281 error ("matrix_type: Invalid number of arguments"); |
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282 |
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283 if (! error_state) |
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284 { |
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285 // Set the matrix type |
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286 if (args(0).type_name () == "sparse complex matrix" ) |
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287 retval = |
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288 octave_value (args(0).sparse_complex_matrix_value (), |
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289 mattyp); |
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290 else |
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291 retval = octave_value (args(0).sparse_matrix_value (), |
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292 mattyp); |
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293 } |
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294 } |
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295 } |
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296 } |
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297 } |
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298 else |
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299 { |
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300 if (nargin == 1) |
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301 { |
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302 MatrixType mattyp; |
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303 |
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304 if (args(0).type_name () == "complex matrix" ) |
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305 { |
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306 mattyp = args(0).matrix_type (); |
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307 |
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308 if (mattyp.is_unknown ()) |
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309 { |
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310 ComplexMatrix m = args(0).complex_matrix_value (); |
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311 if (!error_state) |
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312 { |
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313 mattyp = MatrixType (m); |
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314 args(0).matrix_type (mattyp); |
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315 } |
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316 } |
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317 } |
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318 else |
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319 { |
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320 mattyp = args(0).matrix_type (); |
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321 |
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322 if (mattyp.is_unknown ()) |
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323 { |
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324 Matrix m = args(0).matrix_value (); |
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325 if (!error_state) |
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326 { |
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327 mattyp = MatrixType (m); |
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328 args(0).matrix_type (mattyp); |
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329 } |
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330 } |
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331 } |
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332 |
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333 int typ = mattyp.type (); |
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334 |
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335 if (typ == MatrixType::Upper) |
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336 retval = octave_value ("Upper"); |
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337 else if (typ == MatrixType::Permuted_Upper) |
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338 retval = octave_value ("Permuted Upper"); |
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339 else if (typ == MatrixType::Lower) |
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340 retval = octave_value ("Lower"); |
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341 else if (typ == MatrixType::Permuted_Lower) |
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342 retval = octave_value ("Permuted Lower"); |
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343 else if (typ == MatrixType::Hermitian) |
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344 retval = octave_value ("Positive Definite"); |
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345 else if (typ == MatrixType::Rectangular) |
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346 { |
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347 if (args(0).rows() == args(0).columns()) |
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348 retval = octave_value ("Singular"); |
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349 else |
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350 retval = octave_value ("Rectangular"); |
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351 } |
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352 else if (typ == MatrixType::Full) |
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353 retval = octave_value ("Full"); |
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354 else |
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355 // This should never happen!!! |
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356 retval = octave_value ("Unknown"); |
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357 } |
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358 else |
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359 { |
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360 // Ok, we're changing the matrix type |
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361 std::string str_typ = args(1).string_value (); |
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362 |
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363 // FIXME -- why do I have to explicitly call the constructor? |
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364 MatrixType mattyp = MatrixType (MatrixType::Unknown, true); |
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365 |
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366 if (error_state) |
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367 error ("Matrix type must be a string"); |
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368 else |
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369 { |
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370 // Use STL function to convert to lower case |
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371 std::transform (str_typ.begin (), str_typ.end (), |
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372 str_typ.begin (), tolower); |
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373 |
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374 if (str_typ == "upper") |
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375 mattyp.mark_as_upper_triangular (); |
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376 else if (str_typ == "lower") |
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377 mattyp.mark_as_lower_triangular (); |
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378 else if (str_typ == "positive definite") |
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379 { |
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380 mattyp.mark_as_full (); |
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381 mattyp.mark_as_symmetric (); |
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382 } |
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383 else if (str_typ == "singular") |
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384 mattyp.mark_as_rectangular (); |
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385 else if (str_typ == "full") |
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386 mattyp.mark_as_full (); |
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387 else if (str_typ == "unknown") |
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388 mattyp.invalidate_type (); |
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389 else |
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390 error ("matrix_type: Unknown matrix type %s", str_typ.c_str()); |
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391 |
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392 if (! error_state) |
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393 { |
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394 if (nargin == 3 && (str_typ == "upper" |
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395 || str_typ == "lower")) |
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396 { |
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397 const ColumnVector perm = |
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398 ColumnVector (args (2).vector_value ()); |
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399 |
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400 if (error_state) |
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401 error ("matrix_type: Invalid permutation vector"); |
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402 else |
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403 { |
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404 octave_idx_type len = perm.length (); |
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405 dim_vector dv = args(0).dims (); |
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406 |
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407 if (len != dv(0)) |
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408 error ("matrix_type: Invalid permutation vector"); |
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409 else |
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410 { |
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411 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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412 |
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413 for (octave_idx_type i = 0; i < len; i++) |
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414 p[i] = static_cast<octave_idx_type> (perm (i)) - 1; |
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415 |
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416 if (str_typ == "upper") |
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417 mattyp.mark_as_permuted (len, p); |
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418 else |
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419 mattyp.mark_as_permuted (len, p); |
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420 } |
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421 } |
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422 } |
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423 else if (nargin != 2) |
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424 error ("matrix_type: Invalid number of arguments"); |
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425 |
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426 if (! error_state) |
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427 { |
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428 // Set the matrix type |
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429 if (args(0).type_name () == "complex matrix" ) |
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430 retval = |
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431 octave_value (args(0).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).matrix_value (), |
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|
435 mattyp); |
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436 } |
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437 } |
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438 } |
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439 } |
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440 } |
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5323
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441 } |
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442 |
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443 return retval; |
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444 } |
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445 |
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446 /* |
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5681
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447 |
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5775
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448 ## FIXME |
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5681
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449 ## Disable tests for lower under-determined and upper over-determined |
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5785
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450 ## matrices and this detection is disabled in MatrixType due to issues |
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5681
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451 ## of non minimum norm solution being found. |
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5610
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452 |
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453 %!assert(matrix_type(speye(10,10)),"Diagonal"); |
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454 %!assert(matrix_type(speye(10,10)([2:10,1],:)),"Permuted Diagonal"); |
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455 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]]),"Upper"); |
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456 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]](:,[2,1,3:11])),"Permuted Upper"); |
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457 %!assert(matrix_type([speye(10,10),sparse(10,1);1,sparse(1,9),1]),"Lower"); |
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458 %!assert(matrix_type([speye(10,10),sparse(10,1);1,sparse(1,9),1]([2,1,3:11],:)),"Permuted Lower"); |
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459 %!test |
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460 %! bnd=spparms("bandden"); |
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461 %! spparms("bandden",0.5); |
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462 %! a = spdiags(randn(10,3),[-1,0,1],10,10); |
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463 %! assert(matrix_type(a),"Tridiagonal"); |
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464 %! assert(matrix_type(abs(a')+abs(a)),"Tridiagonal Positive Definite"); |
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465 %! spparms("bandden",bnd); |
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466 %!test |
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467 %! bnd=spparms("bandden"); |
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468 %! spparms("bandden",0.5); |
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469 %! a = spdiags(randn(10,4),[-2:1],10,10); |
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470 %! assert(matrix_type(a),"Banded"); |
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471 %! assert(matrix_type(a'*a),"Banded Positive Definite"); |
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472 %! spparms("bandden",bnd); |
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473 %!test |
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474 %! a=[speye(10,10),[sparse(9,1);1];-1,sparse(1,9),1]; |
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475 %! assert(matrix_type(a),"Full"); |
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476 %! assert(matrix_type(a'*a),"Positive Definite"); |
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5630
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477 %!assert(matrix_type(speye(10,11)),"Diagonal"); |
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478 %!assert(matrix_type(speye(10,11)([2:10,1],:)),"Permuted Diagonal"); |
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479 %!assert(matrix_type(speye(11,10)),"Diagonal"); |
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480 %!assert(matrix_type(speye(11,10)([2:11,1],:)),"Permuted Diagonal"); |
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5681
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481 %#!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]]),"Upper"); |
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482 %#!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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5630
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483 %!assert(matrix_type([speye(11,9),[1;sparse(8,1);1;0]]),"Upper"); |
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484 %!assert(matrix_type([speye(11,9),[1;sparse(8,1);1;0]](:,[2,1,3:10])),"Permuted Upper"); |
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5681
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485 %#!assert(matrix_type([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]),"Lower"); |
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486 %#!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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5630
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487 %!assert(matrix_type([speye(9,11);[1,sparse(1,8),1,0]]),"Lower"); |
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488 %!assert(matrix_type([speye(9,11);[1,sparse(1,8),1,0]]([2,1,3:10],:)),"Permuted Lower"); |
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489 %!assert(matrix_type(spdiags(randn(10,4),[-2:1],10,9)),"Rectangular") |
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5610
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490 |
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491 %!assert(matrix_type(1i*speye(10,10)),"Diagonal"); |
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492 %!assert(matrix_type(1i*speye(10,10)([2:10,1],:)),"Permuted Diagonal"); |
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493 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]]),"Upper"); |
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494 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]](:,[2,1,3:11])),"Permuted Upper"); |
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495 %!assert(matrix_type([speye(10,10),sparse(10,1);1i,sparse(1,9),1]),"Lower"); |
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496 %!assert(matrix_type([speye(10,10),sparse(10,1);1i,sparse(1,9),1]([2,1,3:11],:)),"Permuted Lower"); |
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497 %!test |
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498 %! bnd=spparms("bandden"); |
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499 %! spparms("bandden",0.5); |
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500 %! assert(matrix_type(spdiags(1i*randn(10,3),[-1,0,1],10,10)),"Tridiagonal"); |
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501 %! a = 1i*randn(9,1);a=[[a;0],ones(10,1),[0;-a]]; |
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502 %! assert(matrix_type(spdiags(a,[-1,0,1],10,10)),"Tridiagonal Positive Definite"); |
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503 %! spparms("bandden",bnd); |
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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(10,4),[-2:1],10,10)),"Banded"); |
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508 %! a = 1i*randn(9,2);a=[[a;[0,0]],ones(10,1),[[0;-a(:,2)],[0;0;-a(1:8,1)]]]; |
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509 %! assert(matrix_type(spdiags(a,[-2:2],10,10)),"Banded Positive Definite"); |
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510 %! spparms("bandden",bnd); |
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511 %!test |
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512 %! a=[speye(10,10),[sparse(9,1);1i];-1,sparse(1,9),1]; |
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513 %! assert(matrix_type(a),"Full"); |
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514 %! assert(matrix_type(a'*a),"Positive Definite"); |
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5630
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515 %!assert(matrix_type(1i*speye(10,11)),"Diagonal"); |
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516 %!assert(matrix_type(1i*speye(10,11)([2:10,1],:)),"Permuted Diagonal"); |
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517 %!assert(matrix_type(1i*speye(11,10)),"Diagonal"); |
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518 %!assert(matrix_type(1i*speye(11,10)([2:11,1],:)),"Permuted Diagonal"); |
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5681
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519 %#!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]]),"Upper"); |
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520 %#!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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5630
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521 %!assert(matrix_type([speye(11,9),[1i;sparse(8,1);1i;0]]),"Upper"); |
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522 %!assert(matrix_type([speye(11,9),[1i;sparse(8,1);1i;0]](:,[2,1,3:10])),"Permuted Upper"); |
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5681
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523 %#!assert(matrix_type([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]),"Lower"); |
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524 %#!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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5630
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525 %!assert(matrix_type([speye(9,11);[1i,sparse(1,8),1i,0]]),"Lower"); |
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526 %!assert(matrix_type([speye(9,11);[1i,sparse(1,8),1i,0]]([2,1,3:10],:)),"Permuted Lower"); |
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527 %!assert(matrix_type(1i*spdiags(randn(10,4),[-2:1],10,9)),"Rectangular") |
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5610
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528 |
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529 %!test |
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530 %! a = matrix_type(spdiags(randn(10,3),[-1,0,1],10,10),"Singular"); |
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531 %! assert(matrix_type(a),"Singular"); |
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532 |
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5785
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533 %!assert(matrix_type(triu(ones(10,10))),"Upper"); |
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534 %!assert(matrix_type(triu(ones(10,10),-1)),"Full"); |
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535 %!assert(matrix_type(tril(ones(10,10))),"Lower"); |
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536 %!assert(matrix_type(tril(ones(10,10),1)),"Full"); |
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537 %!assert(matrix_type(10*eye(10,10) + ones(10,10)), "Positive Definite"); |
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538 %!assert(matrix_type(ones(11,10)),"Rectangular") |
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539 %!test |
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540 %! a = matrix_type(ones(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(1i*ones(10,10))),"Upper"); |
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544 %!assert(matrix_type(triu(1i*ones(10,10),-1)),"Full"); |
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545 %!assert(matrix_type(tril(1i*ones(10,10))),"Lower"); |
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546 %!assert(matrix_type(tril(1i*ones(10,10),1)),"Full"); |
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547 %!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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548 %!assert(matrix_type(ones(11,10)),"Rectangular") |
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549 %!test |
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550 %! a = matrix_type(ones(10,10),"Singular"); |
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551 %! assert(matrix_type(a),"Singular"); |
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552 |
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5610
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553 */ |
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554 |
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555 /* |
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5323
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556 ;;; Local Variables: *** |
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557 ;;; mode: C++ *** |
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558 ;;; End: *** |
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559 */ |
