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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-sparse.h" |
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34 #include "ov-cx-sparse.h" |
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35 #include "SparseType.h" |
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36 |
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37 DEFUN_DLD (matrix_type, args, , |
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38 "-*- texinfo -*-\n\ |
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39 @deftypefn {Loadable Function} {@var{type} =} matrix_type (@var{a})\n\ |
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40 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, @var{type})\n\ |
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41 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'upper', @var{perm})\n\ |
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42 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'lower', @var{perm})\n\ |
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43 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'banded', @var{nl}, @var{nu})\n\ |
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44 Identify the matrix type or mark a matrix as a particular type. This allows rapid\n\ |
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45 for solutions of linear equations involving @var{a} to be performed. Called with a\n\ |
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46 single argument, @code{matrix_type} returns the type of the matrix and caches it for\n\ |
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47 future use. Called with more than one argument, @code{matrix_type} allows the type\n\ |
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48 of the matrix to be defined.\n\ |
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49 \n\ |
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50 The possible matrix types depend on whether the matrix is full or sparse, and can be\n\ |
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51 one of the following\n\ |
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52 \n\ |
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53 @table @asis\n\ |
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54 @item 'unknown'\n\ |
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55 Remove any previously cached matrix type, and mark type as unknown\n\ |
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56 \n\ |
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57 @item 'full'\n\ |
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58 Mark the matrix as full.\n\ |
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59 \n\ |
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60 @item 'positive definite'\n\ |
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61 Full positive definite matrix.\n\ |
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62 \n\ |
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63 @item 'diagonal'\n\ |
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64 Diagonal Matrix. (Sparse matrices only)\n\ |
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65 \n\ |
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66 @item 'permuted diagonal'\n\ |
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67 Permuted Diagonal matrix. The permutation does not need to be specifically\n\ |
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68 indicated, as the structure of the matrix explicitly gives this. (Sparse matrices\n\ |
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69 only)\n\ |
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70 \n\ |
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71 @item 'upper'\n\ |
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72 Upper triangular. If the optional third argument @var{perm} is given, the matrix is\n\ |
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73 assumed to be a permuted upper triangular with the permutations defined by the\n\ |
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74 vector @var{perm}.\n\ |
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75 \n\ |
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76 @item 'lower'\n\ |
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77 Lower triangular. If the optional third argument @var{perm} is given, the matrix is\n\ |
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78 assumed to be a permuted lower triangular with the permutations defined by the\n\ |
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79 vector @var{perm}.\n\ |
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80 \n\ |
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81 @item 'banded'\n\ |
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82 @itemx 'banded positive definite'\n\ |
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83 Banded matrix with the band size of @var{nl} below the diagonal and @var{nu} above\n\ |
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84 it. If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal and treated\n\ |
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85 with specialized code. In addition the matrix can be marked as positive definite\n\ |
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86 (Sparse matrices only)\n\ |
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87 \n\ |
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88 @item 'singular'\n\ |
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89 The matrix is assumed to be singular and will be treated with a minimum norm solution\n\ |
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90 \n\ |
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91 @end table\n\ |
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92 \n\ |
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93 Note that the matrix type will be discovered automatically on the first attempt to\n\ |
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94 solve a linear equation involving @var{a}. Therefore @code{matrix_type} is only\n\ |
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95 useful to give Octave hints of the matrix type. Incorrectly defining the\n\ |
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96 matrix type will result in incorrect results from solutions of linear equations,\n\ |
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97 and so it is entirely the responsibility of the user to correctly indentify the\n\ |
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98 matrix type.\n\ |
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99 @end deftypefn") |
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100 { |
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101 int nargin = args.length (); |
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102 octave_value retval; |
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103 |
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104 if (nargin == 0) |
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105 print_usage ("matrix_type"); |
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106 else if (nargin > 4) |
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107 error ("matrix_type: incorrect number of arguments"); |
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108 else |
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109 { |
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110 if (args(0).is_sparse_type ()) |
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111 { |
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112 if (nargin == 1) |
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113 { |
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114 SparseType mattyp; |
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115 |
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116 if (args(0).type_name () == "sparse complex matrix" ) |
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117 { |
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118 const octave_sparse_complex_matrix& rep |
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119 = dynamic_cast<const octave_sparse_complex_matrix&> (args(0).get_rep ()); |
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120 |
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121 mattyp = rep.sparse_type (); |
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122 |
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123 if (mattyp.is_unknown ()) |
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124 { |
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125 SparseComplexMatrix m = |
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126 args(0).sparse_complex_matrix_value (); |
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127 if (!error_state) |
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128 { |
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129 mattyp = SparseType (m); |
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130 rep.sparse_type (mattyp); |
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131 } |
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132 } |
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133 } |
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134 else |
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135 { |
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136 const octave_sparse_matrix& rep |
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137 = dynamic_cast<const octave_sparse_matrix&> (args(0).get_rep ()); |
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138 |
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139 mattyp = rep.sparse_type (); |
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140 |
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141 if (mattyp.is_unknown ()) |
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142 { |
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143 SparseMatrix m = args(0).sparse_matrix_value (); |
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144 if (!error_state) |
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145 { |
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146 mattyp = SparseType (m); |
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147 rep.sparse_type (mattyp); |
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148 } |
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149 } |
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150 } |
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151 |
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152 int typ = mattyp.type (); |
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153 |
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154 if (typ == SparseType::Diagonal) |
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155 retval = octave_value ("Diagonal"); |
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156 else if (typ == SparseType::Permuted_Diagonal) |
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157 retval = octave_value ("Permuted Diagonal"); |
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158 else if (typ == SparseType::Upper) |
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159 retval = octave_value ("Upper"); |
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160 else if (typ == SparseType::Permuted_Upper) |
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161 retval = octave_value ("Permuted Upper"); |
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162 else if (typ == SparseType::Lower) |
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163 retval = octave_value ("Lower"); |
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164 else if (typ == SparseType::Permuted_Lower) |
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165 retval = octave_value ("Permuted Lower"); |
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166 else if (typ == SparseType::Banded) |
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167 retval = octave_value ("Banded"); |
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168 else if (typ == SparseType::Banded_Hermitian) |
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169 retval = octave_value ("Banded Positive Definite"); |
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170 else if (typ == SparseType::Tridiagonal) |
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171 retval = octave_value ("Tridiagonal"); |
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172 else if (typ == SparseType::Tridiagonal_Hermitian) |
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173 retval = octave_value ("Tridiagonal Positive Definite"); |
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174 else if (typ == SparseType::Hermitian) |
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175 retval = octave_value ("Positive Definite"); |
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176 else if (typ == SparseType::Rectangular) |
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177 { |
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178 if (args(0).rows() == args(0).columns()) |
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179 retval = octave_value ("Singular"); |
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180 else |
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181 retval = octave_value ("Rectangular"); |
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182 } |
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183 else if (typ == SparseType::Full) |
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184 retval = octave_value ("Full"); |
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185 else |
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186 // This should never happen!!! |
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187 retval = octave_value ("Unknown"); |
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188 } |
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189 else |
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190 { |
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191 // Ok, we're changing the matrix type |
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192 std::string str_typ = args(1).string_value (); |
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193 |
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194 // FIXME -- why do I have to explicitly call the constructor? |
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195 SparseType mattyp = SparseType (); |
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196 |
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197 octave_idx_type nl = 0; |
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198 octave_idx_type nu = 0; |
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199 |
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200 if (error_state) |
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201 error ("Matrix type must be a string"); |
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202 else |
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203 { |
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204 // Use STL function to convert to lower case |
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205 std::transform (str_typ.begin (), str_typ.end (), |
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206 str_typ.begin (), tolower); |
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207 |
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208 if (str_typ == "diagonal") |
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209 mattyp.mark_as_diagonal (); |
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210 if (str_typ == "permuted diagonal") |
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211 mattyp.mark_as_permuted_diagonal (); |
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212 else if (str_typ == "upper") |
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213 mattyp.mark_as_upper_triangular (); |
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214 else if (str_typ == "lower") |
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215 mattyp.mark_as_lower_triangular (); |
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216 else if (str_typ == "banded" || str_typ == "banded positive definite") |
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217 { |
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218 if (nargin != 4) |
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219 error ("matrix_type: banded matrix type requires 4 arguments"); |
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220 else |
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221 { |
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222 nl = args(2).nint_value (); |
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223 nu = args(3).nint_value (); |
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224 |
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225 if (error_state) |
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226 error ("matrix_type: band size must be integer"); |
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227 else |
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228 { |
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229 if (nl == 1 && nu == 1) |
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230 mattyp.mark_as_tridiagonal (); |
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231 else |
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232 mattyp.mark_as_banded (nu, nl); |
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233 |
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234 if (str_typ == "banded positive definite") |
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235 mattyp.mark_as_symmetric (); |
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236 } |
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237 } |
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238 } |
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239 else if (str_typ == "positive definite") |
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240 { |
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241 mattyp.mark_as_full (); |
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242 mattyp.mark_as_symmetric (); |
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243 } |
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244 else if (str_typ == "singular") |
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245 mattyp.mark_as_rectangular (); |
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246 else if (str_typ == "full") |
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247 mattyp.mark_as_full (); |
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248 else if (str_typ == "unknown") |
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249 mattyp.invalidate_type (); |
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250 else |
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251 error ("matrix_type: Unknown matrix type %s", str_typ.c_str()); |
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252 |
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253 if (! error_state) |
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254 { |
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255 if (nargin == 3 && (str_typ == "upper" || str_typ == "lower")) |
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256 { |
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257 const ColumnVector perm = |
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258 ColumnVector (args (2).vector_value ()); |
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259 |
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260 if (error_state) |
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261 error ("matrix_type: Invalid permutation vector"); |
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262 else |
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263 { |
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264 octave_idx_type len = perm.length (); |
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265 dim_vector dv = args(0).dims (); |
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266 |
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267 if (len != dv(0)) |
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268 error ("matrix_type: Invalid permutation vector"); |
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269 else |
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270 { |
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271 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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272 |
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273 for (octave_idx_type i = 0; i < len; i++) |
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274 p[i] = static_cast<octave_idx_type> (perm (i)) - 1; |
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275 |
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276 if (str_typ == "upper") |
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277 mattyp.mark_as_permuted (len, p); |
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278 else |
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279 mattyp.mark_as_permuted (len, p); |
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280 } |
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281 } |
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282 } |
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283 else if (nargin != 2 && str_typ != "banded positive definite" && |
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284 str_typ != "banded") |
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285 error ("matrix_type: Invalid number of arguments"); |
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286 |
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287 if (! error_state) |
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288 { |
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289 // Set the matrix type |
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290 if (args(0).type_name () == "sparse complex matrix" ) |
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291 retval = |
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292 octave_value (args(0).sparse_complex_matrix_value (), |
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293 mattyp); |
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294 else |
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295 retval = octave_value (args(0).sparse_matrix_value (), |
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296 mattyp); |
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297 } |
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298 } |
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299 } |
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300 } |
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301 } |
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302 else |
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303 error ("matrix_type: Only sparse matrices treated at the moment"); |
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304 } |
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305 |
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306 return retval; |
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307 } |
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308 |
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309 /* |
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310 |
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311 ## FIXME |
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312 ## Disable tests for lower under-determined and upper over-determined |
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313 ## matrices and this detection is disabled in SparseType due to issues |
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314 ## of non minimum norm solution being found. |
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315 |
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316 %!assert(matrix_type(speye(10,10)),"Diagonal"); |
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317 %!assert(matrix_type(speye(10,10)([2:10,1],:)),"Permuted Diagonal"); |
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318 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]]),"Upper"); |
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319 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]](:,[2,1,3:11])),"Permuted Upper"); |
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320 %!assert(matrix_type([speye(10,10),sparse(10,1);1,sparse(1,9),1]),"Lower"); |
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321 %!assert(matrix_type([speye(10,10),sparse(10,1);1,sparse(1,9),1]([2,1,3:11],:)),"Permuted Lower"); |
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322 %!test |
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323 %! bnd=spparms("bandden"); |
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324 %! spparms("bandden",0.5); |
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325 %! a = spdiags(randn(10,3),[-1,0,1],10,10); |
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326 %! assert(matrix_type(a),"Tridiagonal"); |
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327 %! assert(matrix_type(abs(a')+abs(a)),"Tridiagonal Positive Definite"); |
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328 %! spparms("bandden",bnd); |
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329 %!test |
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330 %! bnd=spparms("bandden"); |
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331 %! spparms("bandden",0.5); |
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332 %! a = spdiags(randn(10,4),[-2:1],10,10); |
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333 %! assert(matrix_type(a),"Banded"); |
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334 %! assert(matrix_type(a'*a),"Banded Positive Definite"); |
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335 %! spparms("bandden",bnd); |
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336 %!test |
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337 %! a=[speye(10,10),[sparse(9,1);1];-1,sparse(1,9),1]; |
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338 %! assert(matrix_type(a),"Full"); |
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339 %! assert(matrix_type(a'*a),"Positive Definite"); |
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340 %!assert(matrix_type(speye(10,11)),"Diagonal"); |
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341 %!assert(matrix_type(speye(10,11)([2:10,1],:)),"Permuted Diagonal"); |
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342 %!assert(matrix_type(speye(11,10)),"Diagonal"); |
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343 %!assert(matrix_type(speye(11,10)([2:11,1],:)),"Permuted Diagonal"); |
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344 %#!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]]),"Upper"); |
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345 %#!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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346 %!assert(matrix_type([speye(11,9),[1;sparse(8,1);1;0]]),"Upper"); |
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347 %!assert(matrix_type([speye(11,9),[1;sparse(8,1);1;0]](:,[2,1,3:10])),"Permuted Upper"); |
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348 %#!assert(matrix_type([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]),"Lower"); |
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349 %#!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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350 %!assert(matrix_type([speye(9,11);[1,sparse(1,8),1,0]]),"Lower"); |
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351 %!assert(matrix_type([speye(9,11);[1,sparse(1,8),1,0]]([2,1,3:10],:)),"Permuted Lower"); |
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352 %!assert(matrix_type(spdiags(randn(10,4),[-2:1],10,9)),"Rectangular") |
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353 |
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354 %!assert(matrix_type(1i*speye(10,10)),"Diagonal"); |
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355 %!assert(matrix_type(1i*speye(10,10)([2:10,1],:)),"Permuted Diagonal"); |
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356 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]]),"Upper"); |
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357 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]](:,[2,1,3:11])),"Permuted Upper"); |
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358 %!assert(matrix_type([speye(10,10),sparse(10,1);1i,sparse(1,9),1]),"Lower"); |
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359 %!assert(matrix_type([speye(10,10),sparse(10,1);1i,sparse(1,9),1]([2,1,3:11],:)),"Permuted Lower"); |
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360 %!test |
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361 %! bnd=spparms("bandden"); |
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362 %! spparms("bandden",0.5); |
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363 %! assert(matrix_type(spdiags(1i*randn(10,3),[-1,0,1],10,10)),"Tridiagonal"); |
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364 %! a = 1i*randn(9,1);a=[[a;0],ones(10,1),[0;-a]]; |
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365 %! assert(matrix_type(spdiags(a,[-1,0,1],10,10)),"Tridiagonal Positive Definite"); |
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366 %! spparms("bandden",bnd); |
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367 %!test |
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368 %! bnd=spparms("bandden"); |
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369 %! spparms("bandden",0.5); |
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370 %! assert(matrix_type(spdiags(1i*randn(10,4),[-2:1],10,10)),"Banded"); |
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371 %! 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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372 %! assert(matrix_type(spdiags(a,[-2:2],10,10)),"Banded Positive Definite"); |
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373 %! spparms("bandden",bnd); |
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374 %!test |
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375 %! a=[speye(10,10),[sparse(9,1);1i];-1,sparse(1,9),1]; |
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376 %! assert(matrix_type(a),"Full"); |
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377 %! assert(matrix_type(a'*a),"Positive Definite"); |
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378 %!assert(matrix_type(1i*speye(10,11)),"Diagonal"); |
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379 %!assert(matrix_type(1i*speye(10,11)([2:10,1],:)),"Permuted Diagonal"); |
|
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380 %!assert(matrix_type(1i*speye(11,10)),"Diagonal"); |
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381 %!assert(matrix_type(1i*speye(11,10)([2:11,1],:)),"Permuted Diagonal"); |
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5681
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382 %#!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]]),"Upper"); |
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383 %#!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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384 %!assert(matrix_type([speye(11,9),[1i;sparse(8,1);1i;0]]),"Upper"); |
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385 %!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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386 %#!assert(matrix_type([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]),"Lower"); |
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387 %#!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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388 %!assert(matrix_type([speye(9,11);[1i,sparse(1,8),1i,0]]),"Lower"); |
|
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389 %!assert(matrix_type([speye(9,11);[1i,sparse(1,8),1i,0]]([2,1,3:10],:)),"Permuted Lower"); |
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390 %!assert(matrix_type(1i*spdiags(randn(10,4),[-2:1],10,9)),"Rectangular") |
|
5610
|
391 |
|
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392 %!test |
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393 %! a = matrix_type(spdiags(randn(10,3),[-1,0,1],10,10),"Singular"); |
|
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394 %! assert(matrix_type(a),"Singular"); |
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395 |
|
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396 */ |
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397 |
|
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398 /* |
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5323
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399 ;;; Local Variables: *** |
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400 ;;; mode: C++ *** |
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401 ;;; End: *** |
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402 */ |
