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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 Octave is free software; you can redistribute it and/or modify it |
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6 under the terms of the GNU General Public License as published by the |
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7 Free Software Foundation; either version 2, or (at your option) any |
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8 later version. |
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9 |
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10 Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 for more details. |
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14 |
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15 You should have received a copy of the GNU General Public License |
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16 along with this program; see the file COPYING. If not, write to the Free |
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17 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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18 |
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19 */ |
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20 |
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21 #ifdef HAVE_CONFIG_H |
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22 #include <config.h> |
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23 #endif |
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24 |
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25 #include <algorithm> |
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26 |
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27 #include "ov.h" |
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28 #include "defun-dld.h" |
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29 #include "error.h" |
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30 #include "ov-re-sparse.h" |
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31 #include "ov-cx-sparse.h" |
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32 #include "SparseType.h" |
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33 |
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34 DEFUN_DLD (matrix_type, args, , |
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35 "-*- texinfo -*-\n\ |
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36 @deftypefn {Loadable Function} {@var{type} =} matrix_type (@var{a})\n\ |
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37 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, @var{type})\n\ |
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38 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'upper', @var{perm})\n\ |
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39 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'lower', @var{perm})\n\ |
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40 @deftypefnx {Loadable Function} {@var{a} =} matrix_type (@var{a}, 'banded', @var{nl}, @var{nu})\n\ |
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41 Identify the matrix type or mark a matrix as a particular type. This allows rapid\n\ |
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42 for solutions of linear equations involving @var{a} to be performed. Called with a\n\ |
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43 single argument, @code{matrix_type} returns the type of the matrix and caches it for\n\ |
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44 future use. Called with more than one argument, @code{matrix_type} allows the type\n\ |
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45 of the matrix to be defined.\n\ |
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46 \n\ |
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47 The possible matrix types depend on whether the matrix is full or sparse, and can be\n\ |
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48 one of the following\n\ |
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49 \n\ |
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50 @table @asis\n\ |
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51 @item 'unknown'\n\ |
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52 Remove any previously cached matrix type, and mark type as unknown\n\ |
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53 \n\ |
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54 @item 'full'\n\ |
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55 Mark the matrix as full.\n\ |
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56 \n\ |
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57 @item 'positive definite'\n\ |
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58 Full positive definite matrix.\n\ |
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59 \n\ |
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60 @item 'diagonal'\n\ |
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61 Diagonal Matrix. (Sparse matrices only)\n\ |
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62 \n\ |
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63 @item 'permuted diagonal'\n\ |
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64 Permuted Diagonal matrix. The permutation does not need to be specifically\n\ |
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65 indicated, as the structure of the matrix explicitly gives this. (Sparse matrices\n\ |
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66 only)\n\ |
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67 \n\ |
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68 @item 'upper'\n\ |
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69 Upper triangular. If the optional third argument @var{perm} is given, the matrix is\n\ |
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70 assumed to be a permuted upper triangular with the permutations defined by the\n\ |
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71 vector @var{perm}.\n\ |
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72 \n\ |
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73 @item 'lower'\n\ |
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74 Lower triangular. If the optional third argument @var{perm} is given, the matrix is\n\ |
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75 assumed to be a permuted lower 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 'banded'\n\ |
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79 @itemx 'banded positive definite'\n\ |
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80 Banded matrix with the band size of @var{nl} below the diagonal and @var{nu} above\n\ |
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81 it. If @var{nl} and @var{nu} are 1, then the matrix is tridiagonal and treated\n\ |
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82 with specialized code. In addition the matrix can be marked as positive definite\n\ |
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83 (Sparse matrices only)\n\ |
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84 \n\ |
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85 @item 'singular'\n\ |
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86 The matrix is assumed to be singular and will be treated with a minimum norm solution\n\ |
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87 \n\ |
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88 @end table\n\ |
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89 \n\ |
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90 Note that the matrix type will be discovered automatically on the first attempt to\n\ |
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91 solve a linear equation involving @var{a}. Therefore @code{matrix_type} is only\n\ |
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92 useful to give Octave hints of the matrix type. Incorrectly defining the\n\ |
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93 matrix type will result in incorrect results from solutions of linear equations,\n\ |
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94 and so it is entirely the responsibility of the user to correctly indentify the\n\ |
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95 matrix type.\n\ |
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96 @end deftypefn") |
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97 { |
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98 int nargin = args.length (); |
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99 octave_value retval; |
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100 |
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101 if (nargin == 0) |
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102 print_usage ("matrix_type"); |
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103 else if (nargin > 4) |
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104 error ("matrix_type: incorrect number of arguments"); |
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105 else |
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106 { |
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107 if (args(0).is_sparse_type ()) |
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108 { |
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109 if (nargin == 1) |
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110 { |
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111 SparseType mattyp; |
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112 const octave_value& rep = args(0).get_rep (); |
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113 |
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114 if (args(0).type_name () == "sparse complex matrix" ) |
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115 { |
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116 mattyp = |
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117 ((const octave_sparse_complex_matrix &)rep).sparse_type (); |
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118 |
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119 if (mattyp.is_unknown ()) |
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120 { |
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121 mattyp = SparseType (args(0).sparse_complex_matrix_value ()); |
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122 ((octave_sparse_complex_matrix &)rep).sparse_type (mattyp); |
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123 } |
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124 } |
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125 else |
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126 { |
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127 mattyp = ((const octave_sparse_matrix &)rep).sparse_type (); |
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128 |
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129 if (mattyp.is_unknown ()) |
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130 { |
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131 mattyp = SparseType (args(0).sparse_matrix_value ()); |
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132 ((octave_sparse_matrix &)rep).sparse_type (mattyp); |
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133 } |
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134 } |
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135 |
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136 int typ = mattyp.type (); |
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137 |
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138 if (typ == SparseType::Diagonal) |
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139 retval = octave_value ("Diagonal"); |
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140 else if (typ == SparseType::Permuted_Diagonal) |
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141 retval = octave_value ("Permuted Diagonal"); |
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142 else if (typ == SparseType::Upper) |
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143 retval = octave_value ("Upper"); |
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144 else if (typ == SparseType::Permuted_Upper) |
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145 retval = octave_value ("Permuted Upper"); |
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146 else if (typ == SparseType::Lower) |
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147 retval = octave_value ("Lower"); |
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148 else if (typ == SparseType::Permuted_Lower) |
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149 retval = octave_value ("Permuted Lower"); |
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150 else if (typ == SparseType::Banded) |
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151 retval = octave_value ("Banded"); |
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152 else if (typ == SparseType::Banded_Hermitian) |
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153 retval = octave_value ("Banded Positive Definite"); |
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154 else if (typ == SparseType::Tridiagonal) |
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155 retval = octave_value ("Tridiagonal"); |
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156 else if (typ == SparseType::Tridiagonal_Hermitian) |
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157 retval = octave_value ("Tridiagonal Positive Definite"); |
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158 else if (typ == SparseType::Hermitian) |
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159 retval = octave_value ("Positive Definite"); |
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160 else if (typ == SparseType::Rectangular) |
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161 { |
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162 if (args(0).rows() == args(0).columns()) |
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163 retval = octave_value ("Singular"); |
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164 else |
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165 retval = octave_value ("Rectangular"); |
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166 } |
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167 else if (typ == SparseType::Full) |
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168 retval = octave_value ("Full"); |
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169 else |
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170 // This should never happen!!! |
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171 retval = octave_value ("Unknown"); |
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172 } |
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173 else |
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174 { |
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175 // Ok, we're changing the matrix type |
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176 std::string str_typ = args(1).string_value (); |
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177 |
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178 // XXX FIXME, why do I have to explicitly call the constructor? |
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179 SparseType mattyp = SparseType (); |
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180 |
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181 octave_idx_type nl = 0; |
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182 octave_idx_type nu = 0; |
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183 |
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184 if (error_state) |
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185 error ("Matrix type must be a string"); |
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186 else |
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187 { |
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188 // Use STL function to convert to lower case |
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189 std::transform (str_typ.begin (), str_typ.end (), |
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190 str_typ.begin (), tolower); |
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191 |
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192 if (str_typ == "diagonal") |
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193 mattyp.mark_as_diagonal (); |
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194 if (str_typ == "permuted diagonal") |
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195 mattyp.mark_as_permuted_diagonal (); |
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196 else if (str_typ == "upper") |
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197 mattyp.mark_as_upper_triangular (); |
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198 else if (str_typ == "lower") |
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199 mattyp.mark_as_lower_triangular (); |
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200 else if (str_typ == "banded" || str_typ == "banded positive definite") |
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201 { |
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202 if (nargin != 4) |
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203 error ("matrix_type: banded matrix type requires 4 arguments"); |
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204 else |
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205 { |
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206 nl = args(2).nint_value (); |
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207 nu = args(3).nint_value (); |
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208 |
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209 if (error_state) |
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210 error ("matrix_type: band size must be integer"); |
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211 else |
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212 { |
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213 if (nl == 1 && nu == 1) |
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214 mattyp.mark_as_tridiagonal (); |
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215 else |
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216 mattyp.mark_as_banded (nu, nl); |
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217 |
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218 if (str_typ == "banded positive definite") |
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219 mattyp.mark_as_symmetric (); |
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220 } |
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221 } |
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222 } |
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223 else if (str_typ == "positive definite") |
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224 { |
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225 mattyp.mark_as_full (); |
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226 mattyp.mark_as_symmetric (); |
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227 } |
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228 else if (str_typ == "singular") |
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229 mattyp.mark_as_rectangular (); |
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230 else if (str_typ == "full") |
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231 mattyp.mark_as_full (); |
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232 else if (str_typ == "unknown") |
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233 mattyp.invalidate_type (); |
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234 else |
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235 error ("matrix_type: Unknown matrix type %s", str_typ.c_str()); |
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236 |
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237 if (! error_state) |
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238 { |
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239 if (nargin == 3 && (str_typ == "upper" || str_typ == "lower")) |
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240 { |
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241 const ColumnVector perm = |
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242 ColumnVector (args (2).vector_value ()); |
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243 |
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244 if (error_state) |
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245 error ("matrix_type: Invalid permutation vector"); |
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246 else |
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247 { |
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248 octave_idx_type len = perm.length (); |
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249 dim_vector dv = args(0).dims (); |
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250 |
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251 if (len != dv(0)) |
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252 error ("matrix_type: Invalid permutation vector"); |
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253 else |
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254 { |
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255 OCTAVE_LOCAL_BUFFER (octave_idx_type, p, len); |
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256 |
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257 for (octave_idx_type i = 0; i < len; i++) |
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258 p[i] = (octave_idx_type) (perm (i)) - 1; |
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259 |
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260 if (str_typ == "upper") |
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261 mattyp.mark_as_permuted (len, p); |
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262 else |
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263 mattyp.mark_as_permuted (len, p); |
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264 } |
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265 } |
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266 } |
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267 else if (nargin != 2 && str_typ != "banded positive definite" && |
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268 str_typ != "banded") |
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269 error ("matrix_type: Invalid number of arguments"); |
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270 |
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271 if (! error_state) |
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272 { |
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273 // Set the matrix type |
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274 if (args(0).type_name () == "sparse complex matrix" ) |
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275 retval = |
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276 octave_value (args(0).sparse_complex_matrix_value (), |
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277 mattyp); |
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278 else |
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279 retval = octave_value (args(0).sparse_matrix_value (), |
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280 mattyp); |
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281 } |
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282 } |
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283 } |
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284 } |
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285 } |
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286 else |
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287 error ("matrix_type: Only sparse matrices treated at the moment"); |
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288 } |
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289 |
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290 return retval; |
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291 } |
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292 |
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293 /* |
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294 |
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295 %!assert(matrix_type(speye(10,10)),"Diagonal"); |
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296 %!assert(matrix_type(speye(10,10)([2:10,1],:)),"Permuted Diagonal"); |
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297 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]]),"Upper"); |
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298 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1;sparse(9,1);1]](:,[2,1,3:11])),"Permuted Upper"); |
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299 %!assert(matrix_type([speye(10,10),sparse(10,1);1,sparse(1,9),1]),"Lower"); |
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300 %!assert(matrix_type([speye(10,10),sparse(10,1);1,sparse(1,9),1]([2,1,3:11],:)),"Permuted Lower"); |
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301 %!test |
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302 %! bnd=spparms("bandden"); |
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303 %! spparms("bandden",0.5); |
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304 %! a = spdiags(randn(10,3),[-1,0,1],10,10); |
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305 %! assert(matrix_type(a),"Tridiagonal"); |
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306 %! assert(matrix_type(abs(a')+abs(a)),"Tridiagonal Positive Definite"); |
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307 %! spparms("bandden",bnd); |
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308 %!test |
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309 %! bnd=spparms("bandden"); |
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310 %! spparms("bandden",0.5); |
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311 %! a = spdiags(randn(10,4),[-2:1],10,10); |
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312 %! assert(matrix_type(a),"Banded"); |
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313 %! assert(matrix_type(a'*a),"Banded Positive Definite"); |
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314 %! spparms("bandden",bnd); |
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315 %!test |
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316 %! a=[speye(10,10),[sparse(9,1);1];-1,sparse(1,9),1]; |
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317 %! assert(matrix_type(a),"Full"); |
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318 %! assert(matrix_type(a'*a),"Positive Definite"); |
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319 %!assert(matrix_type(speye(10,11)),"Diagonal"); |
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320 %!assert(matrix_type(speye(10,11)([2:10,1],:)),"Permuted Diagonal"); |
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321 %!assert(matrix_type(speye(11,10)),"Diagonal"); |
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322 %!assert(matrix_type(speye(11,10)([2:11,1],:)),"Permuted Diagonal"); |
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323 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1,1];sparse(9,2);[1,1]]]),"Upper"); |
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324 %!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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325 %!assert(matrix_type([speye(11,9),[1;sparse(8,1);1;0]]),"Upper"); |
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326 %!assert(matrix_type([speye(11,9),[1;sparse(8,1);1;0]](:,[2,1,3:10])),"Permuted Upper"); |
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327 %!assert(matrix_type([speye(10,10),sparse(10,1);[1;1],sparse(2,9),[1;1]]),"Lower"); |
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328 %!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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329 %!assert(matrix_type([speye(9,11);[1,sparse(1,8),1,0]]),"Lower"); |
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330 %!assert(matrix_type([speye(9,11);[1,sparse(1,8),1,0]]([2,1,3:10],:)),"Permuted Lower"); |
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331 %!assert(matrix_type(spdiags(randn(10,4),[-2:1],10,9)),"Rectangular") |
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332 |
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333 %!assert(matrix_type(1i*speye(10,10)),"Diagonal"); |
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334 %!assert(matrix_type(1i*speye(10,10)([2:10,1],:)),"Permuted Diagonal"); |
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335 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]]),"Upper"); |
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336 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[1i;sparse(9,1);1]](:,[2,1,3:11])),"Permuted Upper"); |
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337 %!assert(matrix_type([speye(10,10),sparse(10,1);1i,sparse(1,9),1]),"Lower"); |
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338 %!assert(matrix_type([speye(10,10),sparse(10,1);1i,sparse(1,9),1]([2,1,3:11],:)),"Permuted Lower"); |
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339 %!test |
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340 %! bnd=spparms("bandden"); |
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341 %! spparms("bandden",0.5); |
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342 %! assert(matrix_type(spdiags(1i*randn(10,3),[-1,0,1],10,10)),"Tridiagonal"); |
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343 %! a = 1i*randn(9,1);a=[[a;0],ones(10,1),[0;-a]]; |
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344 %! assert(matrix_type(spdiags(a,[-1,0,1],10,10)),"Tridiagonal Positive Definite"); |
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345 %! spparms("bandden",bnd); |
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346 %!test |
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347 %! bnd=spparms("bandden"); |
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348 %! spparms("bandden",0.5); |
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349 %! assert(matrix_type(spdiags(1i*randn(10,4),[-2:1],10,10)),"Banded"); |
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350 %! 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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351 %! assert(matrix_type(spdiags(a,[-2:2],10,10)),"Banded Positive Definite"); |
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352 %! spparms("bandden",bnd); |
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353 %!test |
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354 %! a=[speye(10,10),[sparse(9,1);1i];-1,sparse(1,9),1]; |
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355 %! assert(matrix_type(a),"Full"); |
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356 %! assert(matrix_type(a'*a),"Positive Definite"); |
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357 %!assert(matrix_type(1i*speye(10,11)),"Diagonal"); |
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358 %!assert(matrix_type(1i*speye(10,11)([2:10,1],:)),"Permuted Diagonal"); |
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359 %!assert(matrix_type(1i*speye(11,10)),"Diagonal"); |
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360 %!assert(matrix_type(1i*speye(11,10)([2:11,1],:)),"Permuted Diagonal"); |
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361 %!assert(matrix_type([[speye(10,10);sparse(1,10)],[[1i,1i];sparse(9,2);[1i,1i]]]),"Upper"); |
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362 %!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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363 %!assert(matrix_type([speye(11,9),[1i;sparse(8,1);1i;0]]),"Upper"); |
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364 %!assert(matrix_type([speye(11,9),[1i;sparse(8,1);1i;0]](:,[2,1,3:10])),"Permuted Upper"); |
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365 %!assert(matrix_type([speye(10,10),sparse(10,1);[1i;1i],sparse(2,9),[1i;1i]]),"Lower"); |
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366 %!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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367 %!assert(matrix_type([speye(9,11);[1i,sparse(1,8),1i,0]]),"Lower"); |
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368 %!assert(matrix_type([speye(9,11);[1i,sparse(1,8),1i,0]]([2,1,3:10],:)),"Permuted Lower"); |
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369 %!assert(matrix_type(1i*spdiags(randn(10,4),[-2:1],10,9)),"Rectangular") |
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5610
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370 |
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371 %!test |
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372 %! a = matrix_type(spdiags(randn(10,3),[-1,0,1],10,10),"Singular"); |
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373 %! assert(matrix_type(a),"Singular"); |
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374 |
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375 */ |
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376 |
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377 /* |
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5323
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378 ;;; Local Variables: *** |
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379 ;;; mode: C++ *** |
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380 ;;; End: *** |
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381 */ |
