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maint: merge stable to default.
author John W. Eaton <jwe@octave.org>
date Wed, 10 Feb 2021 10:10:40 -0500
parents 06c8e0877864 0a5b15007766
children 32c3a5805893
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 1996-2021 The Octave Project Developers
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4 //
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5 // See the file COPYRIGHT.md in the top-level directory of this
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6 // distribution or <https://octave.org/copyright/>.
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7 //
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8 // This file is part of Octave.
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9 //
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10 // Octave is free software: you can redistribute it and/or modify it
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11 // under the terms of the GNU General Public License as published by
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12 // the Free Software Foundation, either version 3 of the License, or
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13 // (at your option) any later version.
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14 //
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15 // Octave is distributed in the hope that it will be useful, but
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 // GNU General Public License for more details.
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19 //
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20 // You should have received a copy of the GNU General Public License
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21 // along with Octave; see the file COPYING. If not, see
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22 // <https://www.gnu.org/licenses/>.
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23 //
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24 ////////////////////////////////////////////////////////////////////////
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25
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26 #if defined (HAVE_CONFIG_H)
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27 # include "config.h"
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28 #endif
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29
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30 #include "DET.h"
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31
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32 #include "defun.h"
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33 #include "error.h"
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34 #include "errwarn.h"
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35 #include "ovl.h"
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36 #include "ops.h"
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37
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38 #include "ov-re-mat.h"
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39 #include "ov-cx-mat.h"
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40 #include "ov-flt-re-mat.h"
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41 #include "ov-flt-cx-mat.h"
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42 #include "ov-re-diag.h"
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43 #include "ov-cx-diag.h"
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44 #include "ov-flt-re-diag.h"
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45 #include "ov-flt-cx-diag.h"
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46 #include "ov-perm.h"
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47
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48 #define MAYBE_CAST(VAR, CLASS) \
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49 const CLASS *VAR = (arg.type_id () == CLASS::static_type_id () \
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50 ? dynamic_cast<const CLASS *> (&arg.get_rep ()) \
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51 : nullptr)
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52
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53 DEFUN (det, args, nargout,
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54 doc: /* -*- texinfo -*-
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55 @deftypefn {} {} det (@var{A})
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56 @deftypefnx {} {[@var{d}, @var{rcond}] =} det (@var{A})
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57 Compute the determinant of @var{A}.
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58
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59 Return an estimate of the reciprocal condition number if requested.
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60
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61 Programming Notes: Routines from @sc{lapack} are used for full matrices and
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62 code from @sc{umfpack} is used for sparse matrices.
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63
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64 The determinant should not be used to check a matrix for singularity.
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65 For that, use any of the condition number functions: @code{cond},
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66 @code{condest}, @code{rcond}.
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67 @seealso{cond, condest, rcond}
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68 @end deftypefn */)
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69 {
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70 if (args.length () != 1)
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71 print_usage ();
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72
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73 octave_value arg = args(0);
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74
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75 if (arg.isempty ())
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76 return ovl (1.0);
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77
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78 if (arg.rows () != arg.columns ())
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79 err_square_matrix_required ("det", "A");
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80
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81 octave_value_list retval (2);
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82
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83 bool isfloat = arg.is_single_type ();
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84
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85 if (arg.is_diag_matrix ())
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86 {
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87 if (nargout <= 1)
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88 retval.resize (1);
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89
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90 if (arg.iscomplex ())
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91 {
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92 if (isfloat)
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93 {
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94 retval(0) = arg.float_complex_diag_matrix_value ()
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95 .determinant ().value ();
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96 if (nargout > 1)
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97 retval(1) = arg.float_complex_diag_matrix_value ().rcond ();
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98 }
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99 else
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100 {
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101 retval(0) = arg.complex_diag_matrix_value ()
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102 .determinant ().value ();
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103 if (nargout > 1)
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104 retval(1) = arg.complex_diag_matrix_value ().rcond ();
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105 }
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106 }
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107 else
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108 {
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109 if (isfloat)
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110 {
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111 retval(0) = arg.float_diag_matrix_value ()
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112 .determinant ().value ();
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113 if (nargout > 1)
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114 retval(1) = arg.float_diag_matrix_value ().rcond ();
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115 }
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116 else
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117 {
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118 retval(0) = arg.diag_matrix_value ().determinant ().value ();
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119 if (nargout > 1)
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120 retval(1) = arg.diag_matrix_value ().rcond ();
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121 }
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122 }
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123 }
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124 else if (arg.is_perm_matrix ())
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125 {
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126 if (nargout <= 1)
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127 retval.resize (1);
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128
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129 retval(0) = static_cast<double> (arg.perm_matrix_value ().determinant ());
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130 if (nargout > 1)
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131 retval(1) = 1.0;
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132 }
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133 else if (arg.is_single_type ())
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134 {
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135 if (arg.isreal ())
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136 {
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137 octave_idx_type info;
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138 float rcond = 0.0;
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139 // Always compute rcond, so we can detect singular matrices.
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140 FloatMatrix m = arg.float_matrix_value ();
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141
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142 MAYBE_CAST (rep, octave_float_matrix);
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143 MatrixType mtype = (rep ? rep -> matrix_type () : MatrixType ());
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144 FloatDET det = m.determinant (mtype, info, rcond);
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145 retval(0) = (info == -1 ? 0.0f : det.value ());
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146 retval(1) = rcond;
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147 if (rep)
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148 rep->matrix_type (mtype);
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149 }
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150 else if (arg.iscomplex ())
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151 {
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152 octave_idx_type info;
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153 float rcond = 0.0;
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154 // Always compute rcond, so we can detect singular matrices.
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155 FloatComplexMatrix m = arg.float_complex_matrix_value ();
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156
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157 MAYBE_CAST (rep, octave_float_complex_matrix);
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158 MatrixType mtype = (rep ? rep -> matrix_type () : MatrixType ());
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159 FloatComplexDET det = m.determinant (mtype, info, rcond);
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160 retval(0) = (info == -1 ? FloatComplex (0.0) : det.value ());
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161 retval(1) = rcond;
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162 if (rep)
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163 rep->matrix_type (mtype);
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164 }
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165 }
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166 else
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167 {
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168 if (arg.isreal ())
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169 {
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170 octave_idx_type info;
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171 double rcond = 0.0;
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172 // Always compute rcond, so we can detect singular matrices.
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173 if (arg.issparse ())
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174 {
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175 SparseMatrix m = arg.sparse_matrix_value ();
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176
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177 DET det = m.determinant (info, rcond);
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178 retval(0) = (info == -1 ? 0.0 : det.value ());
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179 retval(1) = rcond;
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180 }
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181 else
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182 {
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183 Matrix m = arg.matrix_value ();
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184
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185 MAYBE_CAST (rep, octave_matrix);
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186 MatrixType mtype = (rep ? rep -> matrix_type ()
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187 : MatrixType ());
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188 DET det = m.determinant (mtype, info, rcond);
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189 retval(0) = (info == -1 ? 0.0 : det.value ());
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190 retval(1) = rcond;
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191 if (rep)
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192 rep->matrix_type (mtype);
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193 }
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194 }
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195 else if (arg.iscomplex ())
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196 {
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197 octave_idx_type info;
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198 double rcond = 0.0;
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199 // Always compute rcond, so we can detect singular matrices.
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200 if (arg.issparse ())
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201 {
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202 SparseComplexMatrix m = arg.sparse_complex_matrix_value ();
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203
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204 ComplexDET det = m.determinant (info, rcond);
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205 retval(0) = (info == -1 ? Complex (0.0) : det.value ());
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206 retval(1) = rcond;
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207 }
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208 else
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209 {
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210 ComplexMatrix m = arg.complex_matrix_value ();
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211
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212 MAYBE_CAST (rep, octave_complex_matrix);
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213 MatrixType mtype = (rep ? rep -> matrix_type ()
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214 : MatrixType ());
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215 ComplexDET det = m.determinant (mtype, info, rcond);
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216 retval(0) = (info == -1 ? Complex (0.0) : det.value ());
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217 retval(1) = rcond;
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218 if (rep)
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219 rep->matrix_type (mtype);
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220 }
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221 }
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222 else
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223 err_wrong_type_arg ("det", arg);
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224 }
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225
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226 return retval;
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227 }
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228
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229 /*
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230 %!assert (det ([1, 2; 3, 4]), -2, 10*eps)
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231 %!assert (det (single ([1, 2; 3, 4])), single (-2), 10*eps ("single"))
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232 %!assert (det (eye (2000)), 1)
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233 %!error det ()
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234 %!error det (1, 2)
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235 %!error <must be a square matrix> det ([1, 2; 3, 4; 5, 6])
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236 */