Mercurial > octave
annotate liboctave/numeric/svd.cc @ 29359:7854d5752dd2
maint: merge stable to default.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 10 Feb 2021 10:10:40 -0500 |
parents | 5c14f81e0937 0a5b15007766 |
children | 9b6bf68ea663 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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3 // Copyright (C) 1994-2021 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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26 #if defined (HAVE_CONFIG_H) |
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27 # include "config.h" |
457 | 28 #endif |
29 | |
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30 #include <cassert> |
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31 |
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32 #include <algorithm> |
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34 #include "CMatrix.h" |
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35 #include "dDiagMatrix.h" |
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36 #include "dMatrix.h" |
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37 #include "fCMatrix.h" |
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38 #include "fDiagMatrix.h" |
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39 #include "fMatrix.h" |
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40 #include "lo-error.h" |
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41 #include "lo-lapack-proto.h" |
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42 #include "svd.h" |
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44 namespace octave |
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45 { |
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46 namespace math |
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47 { |
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48 template <typename T> |
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49 T |
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50 svd<T>::left_singular_matrix (void) const |
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51 { |
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52 if (m_type == svd::Type::sigma_only) |
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53 (*current_liboctave_error_handler) |
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54 ("svd: U not computed because type == svd::sigma_only"); |
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55 |
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56 return left_sm; |
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57 } |
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59 template <typename T> |
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60 T |
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61 svd<T>::right_singular_matrix (void) const |
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62 { |
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63 if (m_type == svd::Type::sigma_only) |
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64 (*current_liboctave_error_handler) |
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65 ("svd: V not computed because type == svd::sigma_only"); |
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66 |
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67 return right_sm; |
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68 } |
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70 // GESVD specializations |
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71 |
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72 #define GESVD_REAL_STEP(f, F) \ |
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73 F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&jobu, 1), \ |
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74 F77_CONST_CHAR_ARG2 (&jobv, 1), \ |
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75 m, n, tmp_data, m1, s_vec, u, m1, vt, \ |
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76 nrow_vt1, work.data (), lwork, info \ |
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77 F77_CHAR_ARG_LEN (1) \ |
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78 F77_CHAR_ARG_LEN (1))) |
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79 |
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80 #define GESVD_COMPLEX_STEP(f, F, CMPLX_ARG) \ |
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81 F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&jobu, 1), \ |
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82 F77_CONST_CHAR_ARG2 (&jobv, 1), \ |
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83 m, n, CMPLX_ARG (tmp_data), \ |
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84 m1, s_vec, CMPLX_ARG (u), m1, \ |
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85 CMPLX_ARG (vt), nrow_vt1, \ |
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86 CMPLX_ARG (work.data ()), \ |
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87 lwork, rwork.data (), info \ |
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88 F77_CHAR_ARG_LEN (1) \ |
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89 F77_CHAR_ARG_LEN (1))) |
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90 |
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91 // DGESVD |
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92 template<> |
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93 OCTAVE_API void |
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94 svd<Matrix>::gesvd (char& jobu, char& jobv, F77_INT m, F77_INT n, |
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95 double *tmp_data, F77_INT m1, double *s_vec, |
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96 double *u, double *vt, F77_INT nrow_vt1, |
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97 std::vector<double>& work, F77_INT& lwork, |
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98 F77_INT& info) |
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99 { |
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100 GESVD_REAL_STEP (dgesvd, DGESVD); |
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101 |
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102 lwork = static_cast<F77_INT> (work[0]); |
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103 work.reserve (lwork); |
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104 |
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105 GESVD_REAL_STEP (dgesvd, DGESVD); |
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106 } |
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107 |
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108 // SGESVD |
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109 template<> |
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110 OCTAVE_API void |
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111 svd<FloatMatrix>::gesvd (char& jobu, char& jobv, F77_INT m, F77_INT n, |
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112 float *tmp_data, F77_INT m1, float *s_vec, |
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113 float *u, float *vt, F77_INT nrow_vt1, |
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114 std::vector<float>& work, F77_INT& lwork, |
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115 F77_INT& info) |
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116 { |
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117 GESVD_REAL_STEP (sgesvd, SGESVD); |
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118 |
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119 lwork = static_cast<F77_INT> (work[0]); |
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120 work.reserve (lwork); |
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121 |
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122 GESVD_REAL_STEP (sgesvd, SGESVD); |
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123 } |
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124 |
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125 // ZGESVD |
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126 template<> |
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127 OCTAVE_API void |
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128 svd<ComplexMatrix>::gesvd (char& jobu, char& jobv, F77_INT m, F77_INT n, |
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129 Complex *tmp_data, F77_INT m1, double *s_vec, |
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130 Complex *u, Complex *vt, F77_INT nrow_vt1, |
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131 std::vector<Complex>& work, F77_INT& lwork, |
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132 F77_INT& info) |
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133 { |
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134 std::vector<double> rwork (5 * std::max (m, n)); |
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135 |
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136 GESVD_COMPLEX_STEP (zgesvd, ZGESVD, F77_DBLE_CMPLX_ARG); |
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137 |
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138 lwork = static_cast<F77_INT> (work[0].real ()); |
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139 work.reserve (lwork); |
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140 |
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141 GESVD_COMPLEX_STEP (zgesvd, ZGESVD, F77_DBLE_CMPLX_ARG); |
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142 } |
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143 |
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144 // CGESVD |
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145 template<> |
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146 OCTAVE_API void |
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147 svd<FloatComplexMatrix>::gesvd (char& jobu, char& jobv, F77_INT m, |
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148 F77_INT n, FloatComplex *tmp_data, |
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149 F77_INT m1, float *s_vec, FloatComplex *u, |
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150 FloatComplex *vt, F77_INT nrow_vt1, |
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151 std::vector<FloatComplex>& work, |
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152 F77_INT& lwork, F77_INT& info) |
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153 { |
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154 std::vector<float> rwork (5 * std::max (m, n)); |
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155 |
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156 GESVD_COMPLEX_STEP (cgesvd, CGESVD, F77_CMPLX_ARG); |
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157 |
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158 lwork = static_cast<F77_INT> (work[0].real ()); |
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159 work.reserve (lwork); |
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160 |
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161 GESVD_COMPLEX_STEP (cgesvd, CGESVD, F77_CMPLX_ARG); |
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162 } |
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163 |
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164 #undef GESVD_REAL_STEP |
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165 #undef GESVD_COMPLEX_STEP |
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166 |
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167 // GESDD specializations |
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168 |
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169 #define GESDD_REAL_STEP(f, F) \ |
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170 F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&jobz, 1), \ |
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171 m, n, tmp_data, m1, s_vec, u, m1, vt, nrow_vt1, \ |
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172 work.data (), lwork, iwork, info \ |
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173 F77_CHAR_ARG_LEN (1))) |
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174 |
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175 #define GESDD_COMPLEX_STEP(f, F, CMPLX_ARG) \ |
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176 F77_XFCN (f, F, (F77_CONST_CHAR_ARG2 (&jobz, 1), m, n, \ |
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177 CMPLX_ARG (tmp_data), m1, \ |
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178 s_vec, CMPLX_ARG (u), m1, \ |
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179 CMPLX_ARG (vt), nrow_vt1, \ |
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180 CMPLX_ARG (work.data ()), lwork, \ |
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181 rwork.data (), iwork, info \ |
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182 F77_CHAR_ARG_LEN (1))) |
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183 |
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184 // DGESDD |
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185 template<> |
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186 OCTAVE_API void |
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187 svd<Matrix>::gesdd (char& jobz, F77_INT m, F77_INT n, double *tmp_data, |
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188 F77_INT m1, double *s_vec, double *u, double *vt, |
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189 F77_INT nrow_vt1, std::vector<double>& work, |
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190 F77_INT& lwork, F77_INT *iwork, F77_INT& info) |
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191 { |
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192 GESDD_REAL_STEP (dgesdd, DGESDD); |
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193 |
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194 lwork = static_cast<F77_INT> (work[0]); |
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195 work.reserve (lwork); |
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196 |
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197 GESDD_REAL_STEP (dgesdd, DGESDD); |
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198 } |
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199 |
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200 // SGESDD |
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201 template<> |
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202 OCTAVE_API void |
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203 svd<FloatMatrix>::gesdd (char& jobz, F77_INT m, F77_INT n, float *tmp_data, |
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204 F77_INT m1, float *s_vec, float *u, float *vt, |
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205 F77_INT nrow_vt1, std::vector<float>& work, |
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206 F77_INT& lwork, F77_INT* iwork, F77_INT& info) |
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207 { |
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208 GESDD_REAL_STEP (sgesdd, SGESDD); |
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209 |
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210 lwork = static_cast<F77_INT> (work[0]); |
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211 work.reserve (lwork); |
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212 |
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213 GESDD_REAL_STEP (sgesdd, SGESDD); |
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214 } |
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215 |
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216 // ZGESDD |
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217 template<> |
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218 OCTAVE_API void |
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219 svd<ComplexMatrix>::gesdd (char& jobz, F77_INT m, F77_INT n, |
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220 Complex *tmp_data, F77_INT m1, double *s_vec, |
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221 Complex *u, Complex *vt, F77_INT nrow_vt1, |
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222 std::vector<Complex>& work, F77_INT& lwork, |
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223 F77_INT *iwork, F77_INT& info) |
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224 { |
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225 |
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226 F77_INT min_mn = std::min (m, n); |
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227 F77_INT max_mn = std::max (m, n); |
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228 |
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229 F77_INT lrwork; |
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230 if (jobz == 'N') |
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231 lrwork = 7*min_mn; |
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232 else |
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233 lrwork = min_mn * std::max (5*min_mn+5, 2*max_mn+2*min_mn+1); |
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234 |
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235 std::vector<double> rwork (lrwork); |
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236 |
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237 GESDD_COMPLEX_STEP (zgesdd, ZGESDD, F77_DBLE_CMPLX_ARG); |
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238 |
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239 lwork = static_cast<F77_INT> (work[0].real ()); |
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240 work.reserve (lwork); |
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241 |
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242 GESDD_COMPLEX_STEP (zgesdd, ZGESDD, F77_DBLE_CMPLX_ARG); |
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243 } |
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244 |
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245 // CGESDD |
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246 template<> |
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247 OCTAVE_API void |
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248 svd<FloatComplexMatrix>::gesdd (char& jobz, F77_INT m, F77_INT n, |
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249 FloatComplex *tmp_data, F77_INT m1, |
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250 float *s_vec, FloatComplex *u, |
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251 FloatComplex *vt, F77_INT nrow_vt1, |
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252 std::vector<FloatComplex>& work, |
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253 F77_INT& lwork, F77_INT *iwork, |
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254 F77_INT& info) |
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255 { |
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256 F77_INT min_mn = std::min (m, n); |
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257 F77_INT max_mn = std::max (m, n); |
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258 |
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259 F77_INT lrwork; |
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260 if (jobz == 'N') |
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261 lrwork = 7*min_mn; |
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262 else |
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263 lrwork = min_mn * std::max (5*min_mn+5, 2*max_mn+2*min_mn+1); |
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264 std::vector<float> rwork (lrwork); |
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265 |
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266 GESDD_COMPLEX_STEP (cgesdd, CGESDD, F77_CMPLX_ARG); |
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267 |
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268 lwork = static_cast<F77_INT> (work[0].real ()); |
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269 work.reserve (lwork); |
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270 |
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271 GESDD_COMPLEX_STEP (cgesdd, CGESDD, F77_CMPLX_ARG); |
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272 } |
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273 |
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274 #undef GESDD_REAL_STEP |
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275 #undef GESDD_COMPLEX_STEP |
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276 |
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277 template<typename T> |
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278 svd<T>::svd (const T& a, svd::Type type, |
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279 svd::Driver driver) |
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280 : m_type (type), m_driver (driver), left_sm (), sigma (), right_sm () |
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281 { |
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282 F77_INT info; |
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283 |
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284 F77_INT m = to_f77_int (a.rows ()); |
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285 F77_INT n = to_f77_int (a.cols ()); |
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286 |
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287 if (m == 0 || n == 0) |
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288 { |
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289 switch (m_type) |
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290 { |
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291 case svd::Type::std: |
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292 left_sm = T (m, m, 0); |
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293 for (F77_INT i = 0; i < m; i++) |
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294 left_sm.xelem (i, i) = 1; |
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295 sigma = DM_T (m, n); |
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296 right_sm = T (n, n, 0); |
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297 for (F77_INT i = 0; i < n; i++) |
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298 right_sm.xelem (i, i) = 1; |
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299 break; |
457 | 300 |
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301 case svd::Type::economy: |
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302 left_sm = T (m, 0, 0); |
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303 sigma = DM_T (0, 0); |
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304 right_sm = T (0, n, 0); |
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305 break; |
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306 |
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307 case svd::Type::sigma_only: |
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308 default: |
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309 sigma = DM_T (0, 1); |
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310 break; |
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311 } |
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312 return; |
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313 } |
457 | 314 |
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315 T atmp = a; |
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316 P *tmp_data = atmp.fortran_vec (); |
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317 |
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318 F77_INT min_mn = (m < n ? m : n); |
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319 |
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320 char jobu = 'A'; |
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321 char jobv = 'A'; |
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322 |
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323 F77_INT ncol_u = m; |
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324 F77_INT nrow_vt = n; |
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325 F77_INT nrow_s = m; |
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326 F77_INT ncol_s = n; |
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327 |
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328 switch (m_type) |
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329 { |
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330 case svd::Type::economy: |
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331 jobu = jobv = 'S'; |
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332 ncol_u = nrow_vt = nrow_s = ncol_s = min_mn; |
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333 break; |
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334 |
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335 case svd::Type::sigma_only: |
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336 |
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337 // Note: for this case, both jobu and jobv should be 'N', but there |
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338 // seems to be a bug in dgesvd from Lapack V2.0. To demonstrate the |
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339 // bug, set both jobu and jobv to 'N' and find the singular values of |
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340 // [eye(3), eye(3)]. The result is [-sqrt(2), -sqrt(2), -sqrt(2)]. |
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341 // |
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342 // For Lapack 3.0, this problem seems to be fixed. |
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343 |
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344 jobu = jobv = 'N'; |
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345 ncol_u = nrow_vt = 1; |
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346 break; |
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347 |
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348 default: |
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349 break; |
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350 } |
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351 |
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352 if (! (jobu == 'N' || jobu == 'O')) |
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353 left_sm.resize (m, ncol_u); |
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354 |
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355 P *u = left_sm.fortran_vec (); |
457 | 356 |
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357 sigma.resize (nrow_s, ncol_s); |
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358 DM_P *s_vec = sigma.fortran_vec (); |
457 | 359 |
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360 if (! (jobv == 'N' || jobv == 'O')) |
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361 right_sm.resize (nrow_vt, n); |
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362 |
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363 P *vt = right_sm.fortran_vec (); |
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365 // Query _GESVD for the correct dimension of WORK. |
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366 |
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367 F77_INT lwork = -1; |
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368 |
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369 std::vector<P> work (1); |
537 | 370 |
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371 F77_INT m1 = std::max (m, static_cast<F77_INT> (1)); |
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372 F77_INT nrow_vt1 = std::max (nrow_vt, static_cast<F77_INT> (1)); |
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373 |
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374 if (m_driver == svd::Driver::GESVD) |
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375 gesvd (jobu, jobv, m, n, tmp_data, m1, s_vec, u, vt, nrow_vt1, |
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376 work, lwork, info); |
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377 else if (m_driver == svd::Driver::GESDD) |
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378 { |
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379 assert (jobu == jobv); |
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380 char jobz = jobu; |
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381 |
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382 std::vector<F77_INT> iwork (8 * std::min (m, n)); |
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383 |
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384 gesdd (jobz, m, n, tmp_data, m1, s_vec, u, vt, nrow_vt1, |
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385 work, lwork, iwork.data (), info); |
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386 } |
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387 else |
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388 (*current_liboctave_error_handler) ("svd: unknown driver"); |
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389 |
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390 // LAPACK can return -0 which is a small problem (bug #55710). |
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391 for (octave_idx_type i = 0; i < sigma.diag_length (); i++) |
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392 { |
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393 if (! sigma.dgxelem (i)) |
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394 sigma.dgxelem (i) = DM_P (0); |
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395 } |
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396 |
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397 if (! (jobv == 'N' || jobv == 'O')) |
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398 right_sm = right_sm.hermitian (); |
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399 } |
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400 |
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401 // Instantiations we need. |
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402 |
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403 template class svd<Matrix>; |
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404 |
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405 template class svd<FloatMatrix>; |
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406 |
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407 template class svd<ComplexMatrix>; |
3336 | 408 |
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409 template class svd<FloatComplexMatrix>; |
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410 } |
457 | 411 } |