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annotate liboctave/numeric/oct-norm.cc @ 31608:23664317f0d3

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maint: merge stable to default
author Rik <rik@octave.org>
date Thu, 01 Dec 2022 20:05:44 -0800
parents dfa5d9c3ae72 aac27ad79be6
children 5f11de0e7440
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1 ////////////////////////////////////////////////////////////////////////
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2 //
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3 // Copyright (C) 2008-2022 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 <cmath>
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31
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32 #include <algorithm>
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33 #include <limits>
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34 #include <vector>
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35
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36 #include "Array.h"
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37 #include "CColVector.h"
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38 #include "CMatrix.h"
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39 #include "CRowVector.h"
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40 #include "CSparse.h"
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41 #include "MArray.h"
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42 #include "dColVector.h"
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43 #include "dDiagMatrix.h"
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44 #include "dMatrix.h"
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45 #include "dRowVector.h"
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46 #include "dSparse.h"
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47 #include "fCColVector.h"
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48 #include "fCMatrix.h"
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49 #include "fCRowVector.h"
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50 #include "fColVector.h"
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51 #include "fDiagMatrix.h"
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52 #include "fMatrix.h"
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53 #include "fRowVector.h"
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54 #include "lo-error.h"
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55 #include "lo-ieee.h"
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56 #include "lo-mappers.h"
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57 #include "mx-cm-s.h"
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58 #include "mx-fcm-fs.h"
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59 #include "mx-fs-fcm.h"
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60 #include "mx-s-cm.h"
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61 #include "oct-cmplx.h"
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62 #include "oct-norm.h"
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63 #include "quit.h"
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64 #include "svd.h"
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65
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66 OCTAVE_BEGIN_NAMESPACE(octave)
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67
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68 // Theory: norm accumulator is an object that has an accum method able
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69 // to handle both real and complex element, and a cast operator
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70 // returning the intermediate norm. Reference: Higham, N. "Estimating
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71 // the Matrix p-Norm." Numer. Math. 62, 539-555, 1992.
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72
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73 // norm accumulator for the p-norm
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74 template <typename R>
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75 class norm_accumulator_p
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76 {
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77 public:
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78 norm_accumulator_p () { } // we need this one for Array
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79 norm_accumulator_p (R pp) : m_p(pp), m_scl(0), m_sum(1) { }
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80
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81 template <typename U>
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82 void accum (U val)
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83 {
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84 octave_quit ();
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85 R t = std::abs (val);
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86 if (m_scl == t) // we need this to handle Infs properly
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87 m_sum += 1;
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88 else if (m_scl < t)
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89 {
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90 m_sum *= std::pow (m_scl/t, m_p);
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91 m_sum += 1;
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92 m_scl = t;
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93 }
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94 else if (t != 0)
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95 m_sum += std::pow (t/m_scl, m_p);
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96 }
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97
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98 operator R () { return m_scl * std::pow (m_sum, 1/m_p); }
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99
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100 private:
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101 R m_p, m_scl, m_sum;
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102 };
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103
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104 // norm accumulator for the minus p-pseudonorm
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105 template <typename R>
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106 class norm_accumulator_mp
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107 {
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108 public:
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109 norm_accumulator_mp () { } // we need this one for Array
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110 norm_accumulator_mp (R pp) : m_p(pp), m_scl(0), m_sum(1) { }
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111
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112 template <typename U>
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113 void accum (U val)
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114 {
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115 octave_quit ();
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116 R t = 1 / std::abs (val);
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117 if (m_scl == t)
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118 m_sum += 1;
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119 else if (m_scl < t)
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120 {
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121 m_sum *= std::pow (m_scl/t, m_p);
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122 m_sum += 1;
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123 m_scl = t;
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124 }
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125 else if (t != 0)
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126 m_sum += std::pow (t/m_scl, m_p);
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127 }
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128
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129 operator R () { return m_scl * std::pow (m_sum, -1/m_p); }
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130
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131 private:
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132 R m_p, m_scl, m_sum;
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133 };
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134
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135 // norm accumulator for the 2-norm (euclidean)
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136 template <typename R>
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137 class norm_accumulator_2
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138 {
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139 public:
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140 norm_accumulator_2 () : m_scl(0), m_sum(1) { }
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141
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142 void accum (R val)
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143 {
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144 R t = std::abs (val);
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145 if (m_scl == t)
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146 m_sum += 1;
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147 else if (m_scl < t)
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148 {
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149 m_sum *= pow2 (m_scl/t);
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150 m_sum += 1;
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151 m_scl = t;
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152 }
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153 else if (t != 0)
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154 m_sum += pow2 (t/m_scl);
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155 }
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156
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157 void accum (std::complex<R> val)
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158 {
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159 accum (val.real ());
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160 accum (val.imag ());
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161 }
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162
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163 operator R () { return m_scl * std::sqrt (m_sum); }
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164
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165 private:
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166 static inline R pow2 (R x) { return x*x; }
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167
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168 //--------
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169
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170 R m_scl, m_sum;
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171 };
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172
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173 // norm accumulator for the 1-norm (city metric)
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174 template <typename R>
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175 class norm_accumulator_1
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176 {
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177 public:
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178 norm_accumulator_1 () : m_sum (0) { }
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179 template <typename U>
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180 void accum (U val)
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181 {
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182 m_sum += std::abs (val);
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183 }
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184
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185 operator R () { return m_sum; }
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186
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187 private:
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188 R m_sum;
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189 };
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190
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191 // norm accumulator for the inf-norm (max metric)
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192 template <typename R>
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193 class norm_accumulator_inf
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194 {
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195 public:
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196 norm_accumulator_inf () : m_max (0) { }
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197 template <typename U>
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198 void accum (U val)
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199 {
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200 if (math::isnan (val))
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201 m_max = numeric_limits<R>::NaN ();
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202 else
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203 m_max = std::max (m_max, std::abs (val));
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204 }
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205
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206 operator R () { return m_max; }
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207
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208 private:
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209 R m_max;
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210 };
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211
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212 // norm accumulator for the -inf pseudonorm (min abs value)
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213 template <typename R>
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214 class norm_accumulator_minf
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215 {
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216 public:
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217 norm_accumulator_minf () : m_min (numeric_limits<R>::Inf ()) { }
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218 template <typename U>
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219 void accum (U val)
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220 {
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221 if (math::isnan (val))
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222 m_min = numeric_limits<R>::NaN ();
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223 else
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224 m_min = std::min (m_min, std::abs (val));
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225 }
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226
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227 operator R () { return m_min; }
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228
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229 private:
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230 R m_min;
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231 };
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232
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233 // norm accumulator for the 0-pseudonorm (hamming distance)
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234 template <typename R>
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235 class norm_accumulator_0
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236 {
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237 public:
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238 norm_accumulator_0 () : m_num (0) { }
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239 template <typename U>
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240 void accum (U val)
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241 {
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242 if (val != static_cast<U> (0)) ++m_num;
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243 }
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244
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245 operator R () { return m_num; }
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246
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247 private:
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248 unsigned int m_num;
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249 };
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250
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251 // OK, we're armed :) Now let's go for the fun
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252
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253 template <typename T, typename R, typename ACC>
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254 inline void vector_norm (const Array<T>& v, R& res, ACC acc)
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255 {
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256 for (octave_idx_type i = 0; i < v.numel (); i++)
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257 acc.accum (v(i));
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258
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259 res = acc;
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260 }
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261
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262 // dense versions
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263 template <typename T, typename R, typename ACC>
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264 void column_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
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265 {
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266 res = MArray<R> (dim_vector (1, m.columns ()));
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267 for (octave_idx_type j = 0; j < m.columns (); j++)
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268 {
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269 ACC accj = acc;
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270 for (octave_idx_type i = 0; i < m.rows (); i++)
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271 accj.accum (m(i, j));
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272
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273 res.xelem (j) = accj;
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274 }
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275 }
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276
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277 template <typename T, typename R, typename ACC>
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278 void row_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
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279 {
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280 res = MArray<R> (dim_vector (m.rows (), 1));
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281 std::vector<ACC> acci (m.rows (), acc);
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282 for (octave_idx_type j = 0; j < m.columns (); j++)
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283 {
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284 for (octave_idx_type i = 0; i < m.rows (); i++)
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285 acci[i].accum (m(i, j));
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286 }
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287
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288 for (octave_idx_type i = 0; i < m.rows (); i++)
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289 res.xelem (i) = acci[i];
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290 }
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291
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292 // sparse versions
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293 template <typename T, typename R, typename ACC>
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294 void column_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
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295 {
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296 res = MArray<R> (dim_vector (1, m.columns ()));
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297 for (octave_idx_type j = 0; j < m.columns (); j++)
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298 {
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299 ACC accj = acc;
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300 for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
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301 accj.accum (m.data (k));
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302
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303 res.xelem (j) = accj;
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304 }
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305 }
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306
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307 template <typename T, typename R, typename ACC>
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308 void row_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
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309 {
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310 res = MArray<R> (dim_vector (m.rows (), 1));
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311 std::vector<ACC> acci (m.rows (), acc);
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312 for (octave_idx_type j = 0; j < m.columns (); j++)
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313 {
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314 for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
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315 acci[m.ridx (k)].accum (m.data (k));
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316 }
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317
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318 for (octave_idx_type i = 0; i < m.rows (); i++)
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319 res.xelem (i) = acci[i];
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320 }
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321
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322 // now the dispatchers
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323 #define DEFINE_DISPATCHER(FCN_NAME, ARG_TYPE, RES_TYPE) \
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324 template <typename T, typename R> \
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325 RES_TYPE FCN_NAME (const ARG_TYPE& v, R p) \
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326 { \
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327 RES_TYPE res; \
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328 if (p == 2) \
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329 FCN_NAME (v, res, norm_accumulator_2<R> ()); \
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330 else if (p == 1) \
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331 FCN_NAME (v, res, norm_accumulator_1<R> ()); \
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332 else if (lo_ieee_isinf (p)) \
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333 { \
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334 if (p > 0) \
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335 FCN_NAME (v, res, norm_accumulator_inf<R> ()); \
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336 else \
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337 FCN_NAME (v, res, norm_accumulator_minf<R> ()); \
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338 } \
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339 else if (p == 0) \
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340 FCN_NAME (v, res, norm_accumulator_0<R> ()); \
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341 else if (p > 0) \
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342 FCN_NAME (v, res, norm_accumulator_p<R> (p)); \
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343 else \
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344 FCN_NAME (v, res, norm_accumulator_mp<R> (p)); \
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345 return res; \
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346 }
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347
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348 DEFINE_DISPATCHER (vector_norm, MArray<T>, R)
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349 DEFINE_DISPATCHER (column_norms, MArray<T>, MArray<R>)
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350 DEFINE_DISPATCHER (row_norms, MArray<T>, MArray<R>)
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351 DEFINE_DISPATCHER (column_norms, MSparse<T>, MArray<R>)
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352 DEFINE_DISPATCHER (row_norms, MSparse<T>, MArray<R>)
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353
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354 // The approximate subproblem in Higham's method. Find lambda and mu such
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355 // that norm ([lambda, mu], p) == 1 and norm (y*lambda + col*mu, p) is
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356 // maximized.
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357 // Real version. As in Higham's paper.
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358 template <typename ColVectorT, typename R>
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diff changeset
359 static void
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360 higham_subp (const ColVectorT& y, const ColVectorT& col,
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diff changeset
361 octave_idx_type nsamp, R p, R& lambda, R& mu)
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diff changeset
362 {
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diff changeset
363 R nrm = 0;
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diff changeset
364 for (octave_idx_type i = 0; i < nsamp; i++)
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diff changeset
365 {
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366 octave_quit ();
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367 R fi = i * static_cast<R> (M_PI) / nsamp;
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368 R lambda1 = cos (fi);
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369 R mu1 = sin (fi);
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370 R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
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diff changeset
371 std::pow (std::abs (mu1), p), 1/p);
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diff changeset
372 lambda1 /= lmnr; mu1 /= lmnr;
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diff changeset
373 R nrm1 = vector_norm (lambda1 * y + mu1 * col, p);
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374 if (nrm1 > nrm)
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diff changeset
375 {
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diff changeset
376 lambda = lambda1;
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diff changeset
377 mu = mu1;
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378 nrm = nrm1;
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379 }
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diff changeset
380 }
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diff changeset
381 }
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382
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383 // Complex version. Higham's paper does not deal with complex case, so we
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diff changeset
384 // use a simple extension. First, guess the magnitudes as in real version,
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diff changeset
385 // then try to rotate lambda to improve further.
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diff changeset
386 template <typename ColVectorT, typename R>
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diff changeset
387 static void
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diff changeset
388 higham_subp (const ColVectorT& y, const ColVectorT& col,
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diff changeset
389 octave_idx_type nsamp, R p,
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diff changeset
390 std::complex<R>& lambda, std::complex<R>& mu)
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diff changeset
391 {
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392 typedef std::complex<R> CR;
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393 R nrm = 0;
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diff changeset
394 lambda = 1.0;
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395 CR lamcu = lambda / std::abs (lambda);
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diff changeset
396 // Probe magnitudes
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diff changeset
397 for (octave_idx_type i = 0; i < nsamp; i++)
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diff changeset
398 {
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diff changeset
399 octave_quit ();
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diff changeset
400 R fi = i * static_cast<R> (M_PI) / nsamp;
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diff changeset
401 R lambda1 = cos (fi);
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diff changeset
402 R mu1 = sin (fi);
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diff changeset
403 R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
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diff changeset
404 std::pow (std::abs (mu1), p), 1/p);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
405 lambda1 /= lmnr; mu1 /= lmnr;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
406 R nrm1 = vector_norm (lambda1 * lamcu * y + mu1 * col, p);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
407 if (nrm1 > nrm)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
408 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
409 lambda = lambda1 * lamcu;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
410 mu = mu1;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
411 nrm = nrm1;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
412 }
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
413 }
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
414 R lama = std::abs (lambda);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
415 // Probe orientation
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
416 for (octave_idx_type i = 0; i < nsamp; i++)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
417 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
418 octave_quit ();
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
419 R fi = i * static_cast<R> (M_PI) / nsamp;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
420 lamcu = CR (cos (fi), sin (fi));
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
421 R nrm1 = vector_norm (lama * lamcu * y + mu * col, p);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
422 if (nrm1 > nrm)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
423 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
424 lambda = lama * lamcu;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
425 nrm = nrm1;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
426 }
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
427 }
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
428 }
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
429
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
430 // the p-dual element (should work for both real and complex)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
431 template <typename T, typename R>
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
432 inline T elem_dual_p (T x, R p)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
433 {
29950
6549fa7558ba eliminate some unnecessary octave:: namespace tags
John W. Eaton <jwe@octave.org>
parents: 29874
diff changeset
434 return math::signum (x) * std::pow (std::abs (x), p-1);
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
435 }
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
436
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
437 // the VectorT is used for vectors, but actually it has to be
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
438 // a Matrix type to allow all the operations. For instance SparseMatrix
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
439 // does not support multiplication with column/row vectors.
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
440 // the dual vector
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
441 template <typename VectorT, typename R>
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
442 VectorT dual_p (const VectorT& x, R p, R q)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
443 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
444 VectorT res (x.dims ());
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
445 for (octave_idx_type i = 0; i < x.numel (); i++)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
446 res.xelem (i) = elem_dual_p (x(i), p);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
447 return res / vector_norm (res, q);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
448 }
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
449
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
450 // Higham's hybrid method
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
451 template <typename MatrixT, typename VectorT, typename R>
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
452 R higham (const MatrixT& m, R p, R tol, int maxiter,
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
453 VectorT& x)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
454 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
455 x.resize (m.columns (), 1);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
456 // the OSE part
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
457 VectorT y(m.rows (), 1, 0), z(m.rows (), 1);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
458 typedef typename VectorT::element_type RR;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
459 RR lambda = 0;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
460 RR mu = 1;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
461 for (octave_idx_type k = 0; k < m.columns (); k++)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
462 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
463 octave_quit ();
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
464 VectorT col (m.column (k));
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
465 if (k > 0)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
466 higham_subp (y, col, 4*k, p, lambda, mu);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
467 for (octave_idx_type i = 0; i < k; i++)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
468 x(i) *= lambda;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
469 x(k) = mu;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
470 y = lambda * y + mu * col;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
471 }
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
472
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
473 // the PM part
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
474 x = x / vector_norm (x, p);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
475 R q = p/(p-1);
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
476
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
477 R gamma = 0, gamma1;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
478 int iter = 0;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
479 while (iter < maxiter)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
480 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
481 octave_quit ();
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
482 y = m*x;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
483 gamma1 = gamma;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
484 gamma = vector_norm (y, p);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
485 z = dual_p (y, p, q);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
486 z = z.hermitian ();
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
487 z = z * m;
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
488
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
489 if (iter > 0 && (vector_norm (z, q) <= gamma
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
490 || (gamma - gamma1) <= tol*gamma))
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
491 break;
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
492
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
493 z = z.hermitian ();
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
494 x = dual_p (z, q, p);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
495 iter++;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
496 }
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
497
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
498 return gamma;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
499 }
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
500
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
501 // derive column vector and SVD types
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
502
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
503 static const char *p_less1_gripe = "xnorm: p must be >= 1";
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
504
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
505 // Static constant to control the maximum number of iterations. 100 seems to
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
506 // be a good value. Eventually, we can provide a means to change this
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
507 // constant from Octave.
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
508 static int max_norm_iter = 100;
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
509
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
510 // version with SVD for dense matrices
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
511 template <typename MatrixT, typename VectorT, typename R>
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
512 R svd_matrix_norm (const MatrixT& m, R p, VectorT)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
513 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
514 R res = 0;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
515 if (p == 2)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
516 {
29950
6549fa7558ba eliminate some unnecessary octave:: namespace tags
John W. Eaton <jwe@octave.org>
parents: 29874
diff changeset
517 math::svd<MatrixT> fact (m, math::svd<MatrixT>::Type::sigma_only);
30394
f3f3e3793fb5 maint: style check C++ files in liboctave/ ahead of 7.1 release.
Rik <rik@octave.org>
parents: 30114
diff changeset
518 res = fact.singular_values () (0, 0);
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
519 }
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
520 else if (p == 1)
31457
a96f68a48e9e maint: Remove more deprecated code from Octave 9.
Rik <rik@octave.org>
parents: 30898
diff changeset
521 res = xcolnorms (m, static_cast<R> (1)).max ();
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
522 else if (lo_ieee_isinf (p) && p > 1)
31457
a96f68a48e9e maint: Remove more deprecated code from Octave 9.
Rik <rik@octave.org>
parents: 30898
diff changeset
523 res = xrownorms (m, static_cast<R> (1)).max ();
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
524 else if (p > 1)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
525 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
526 VectorT x;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
527 const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
528 res = higham (m, p, sqrteps, max_norm_iter, x);
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
529 }
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
530 else
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
531 (*current_liboctave_error_handler) ("%s", p_less1_gripe);
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
532
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
533 return res;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
534 }
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
535
29874
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
536 // SVD-free version for sparse matrices
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
537 template <typename MatrixT, typename VectorT, typename R>
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
538 R matrix_norm (const MatrixT& m, R p, VectorT)
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
539 {
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
540 R res = 0;
92662b17ef7e move liboctave xnorm functions inside octave namespace
John W. Eaton <jwe@octave.org>
parents: 29358
diff changeset
541 if (p == 1)
31457
a96f68a48e9e maint: Remove more deprecated code from Octave 9.
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542 res = xcolnorms (m, static_cast<R> (1)).max ();
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543 else if (lo_ieee_isinf (p) && p > 1)
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544 res = xrownorms (m, static_cast<R> (1)).max ();
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545 else if (p > 1)
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546 {
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547 VectorT x;
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548 const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
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549 res = higham (m, p, sqrteps, max_norm_iter, x);
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550 }
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551 else
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552 (*current_liboctave_error_handler) ("%s", p_less1_gripe);
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553
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554 return res;
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555 }
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556
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557 // and finally, here's what we've promised in the header file
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558
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diff changeset
559 #define DEFINE_XNORM_FCNS(PREFIX, RTYPE) \
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560 RTYPE xnorm (const PREFIX##ColumnVector& x, RTYPE p) \
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561 { \
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562 return vector_norm (x, p); \
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563 } \
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564 RTYPE xnorm (const PREFIX##RowVector& x, RTYPE p) \
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565 { \
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566 return vector_norm (x, p); \
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567 } \
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568 RTYPE xnorm (const PREFIX##Matrix& x, RTYPE p) \
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569 { \
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570 return svd_matrix_norm (x, p, PREFIX##Matrix ()); \
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571 } \
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572 RTYPE xfrobnorm (const PREFIX##Matrix& x) \
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573 { \
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574 return vector_norm (x, static_cast<RTYPE> (2)); \
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575 }
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576
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577 DEFINE_XNORM_FCNS(, double)
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diff changeset
578 DEFINE_XNORM_FCNS(Complex, double)
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diff changeset
579 DEFINE_XNORM_FCNS(Float, float)
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580 DEFINE_XNORM_FCNS(FloatComplex, float)
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581
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582 // this is needed to avoid copying the sparse matrix for xfrobnorm
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583 template <typename T, typename R>
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584 inline void array_norm_2 (const T *v, octave_idx_type n, R& res)
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585 {
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586 norm_accumulator_2<R> acc;
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587 for (octave_idx_type i = 0; i < n; i++)
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diff changeset
588 acc.accum (v[i]);
8303
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589
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590 res = acc;
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591 }
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592
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Rik <rik@octave.org>
parents: 30564
diff changeset
593 #define DEFINE_XNORM_SPARSE_FCNS(PREFIX, RTYPE) \
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594 RTYPE xnorm (const Sparse##PREFIX##Matrix& x, RTYPE p) \
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595 { \
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596 return matrix_norm (x, p, PREFIX##Matrix ()); \
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597 } \
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598 RTYPE xfrobnorm (const Sparse##PREFIX##Matrix& x) \
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599 { \
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600 RTYPE res; \
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601 array_norm_2 (x.data (), x.nnz (), res); \
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602 return res; \
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603 }
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604
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Rik <rik@octave.org>
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605 DEFINE_XNORM_SPARSE_FCNS(, double)
51a3d3a69193 maint: Use "fcn" as preferred abbreviation for "function" in liboctave/.
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diff changeset
606 DEFINE_XNORM_SPARSE_FCNS(Complex, double)
8303
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607
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diff changeset
608 #define DEFINE_COLROW_NORM_FCNS(PREFIX, RPREFIX, RTYPE) \
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diff changeset
609 RPREFIX##RowVector \
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diff changeset
610 xcolnorms (const PREFIX##Matrix& m, RTYPE p) \
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diff changeset
611 { \
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diff changeset
612 return column_norms (m, p); \
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diff changeset
613 } \
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diff changeset
614 RPREFIX##ColumnVector \
22197
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diff changeset
615 xrownorms (const PREFIX##Matrix& m, RTYPE p) \
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diff changeset
616 { \
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diff changeset
617 return row_norms (m, p); \
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618 } \
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diff changeset
619
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diff changeset
620 DEFINE_COLROW_NORM_FCNS(, , double)
51a3d3a69193 maint: Use "fcn" as preferred abbreviation for "function" in liboctave/.
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diff changeset
621 DEFINE_COLROW_NORM_FCNS(Complex, , double)
51a3d3a69193 maint: Use "fcn" as preferred abbreviation for "function" in liboctave/.
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diff changeset
622 DEFINE_COLROW_NORM_FCNS(Float, Float, float)
51a3d3a69193 maint: Use "fcn" as preferred abbreviation for "function" in liboctave/.
Rik <rik@octave.org>
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diff changeset
623 DEFINE_COLROW_NORM_FCNS(FloatComplex, Float, float)
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diff changeset
624
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Rik <rik@octave.org>
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diff changeset
625 DEFINE_COLROW_NORM_FCNS(Sparse, , double)
51a3d3a69193 maint: Use "fcn" as preferred abbreviation for "function" in liboctave/.
Rik <rik@octave.org>
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diff changeset
626 DEFINE_COLROW_NORM_FCNS(SparseComplex, , double)
31605
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Rik <rik@octave.org>
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diff changeset
627
e88a07dec498 maint: Use macros to begin/end C++ namespaces.
Rik <rik@octave.org>
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diff changeset
628 OCTAVE_END_NAMESPACE(octave)