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annotate liboctave/numeric/oct-norm.cc @ 21723:bae585228161

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use namespace for numeric_limits * lo-ieee.h (octave_numeric_limits): Rename to numeric_limits and define inside octave namespace. * Canvas.cc, data.cc, graphics.cc, graphics.in.h, oct-handle.h, oct-stream.cc, quadcc.cc, sparse-xdiv.cc, str2double.cc, variables.h, __glpk__.cc, __init_fltk__.cc, __voronoi__.cc, octave.cc, CMatrix.cc, CNDArray.cc, CSparse.cc, Sparse-C.cc, dDiagMatrix.cc, dMatrix.cc, dSparse.cc, fCMatrix.cc, fCNDArray.cc, fDiagMatrix.cc, fMatrix.cc, Faddeeva.cc, eigs-base.cc, lo-mappers.cc, lo-mappers.h, lo-specfun.cc, oct-norm.cc, oct-rand.cc, oct-rand.h, oct-spparms.cc, randgamma.cc, randpoisson.cc, lo-utils.cc: Change all uses of octave_numeric_limits to octave::numeric_limits.
author John W. Eaton <jwe@octave.org>
date Tue, 17 May 2016 11:32:53 -0400
parents bcc30b45a225
children aba2e6293dd8
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1 /*
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2
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3 Copyright (C) 2008-2015 VZLU Prague, a.s.
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 // author: Jaroslav Hajek <highegg@gmail.com>
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24
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25 #ifdef HAVE_CONFIG_H
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26 # include "config.h"
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27 #endif
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28
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29 #include <cassert>
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30 #include <cfloat>
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31 #include <cmath>
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32
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33 #include <iostream>
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34 #include <vector>
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35
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36 #include "Array-util.h"
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37 #include "Array.h"
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38 #include "CColVector.h"
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39 #include "CMatrix.h"
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40 #include "CRowVector.h"
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41 #include "CSparse.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 "mx-cm-s.h"
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57 #include "mx-fcm-fs.h"
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58 #include "mx-fs-fcm.h"
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59 #include "mx-s-cm.h"
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60 #include "oct-cmplx.h"
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61 #include "svd.h"
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62
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63 // Theory: norm accumulator is an object that has an accum method able
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64 // to handle both real and complex element, and a cast operator
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65 // returning the intermediate norm. Reference: Higham, N. "Estimating
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66 // the Matrix p-Norm." Numer. Math. 62, 539-555, 1992.
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67
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68 // norm accumulator for the p-norm
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69 template <typename R>
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70 class norm_accumulator_p
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71 {
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72 R p,scl,sum;
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73 public:
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74 norm_accumulator_p () {} // we need this one for Array
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75 norm_accumulator_p (R pp) : p(pp), scl(0), sum(1) {}
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76
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77 template <typename U>
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78 void accum (U val)
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79 {
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80 octave_quit ();
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81 R t = std::abs (val);
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82 if (scl == t) // we need this to handle Infs properly
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83 sum += 1;
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84 else if (scl < t)
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85 {
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86 sum *= std::pow (scl/t, p);
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87 sum += 1;
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88 scl = t;
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89 }
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90 else if (t != 0)
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91 sum += std::pow (t/scl, p);
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92 }
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93 operator R () { return scl * std::pow (sum, 1/p); }
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94 };
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95
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96 // norm accumulator for the minus p-pseudonorm
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97 template <typename R>
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98 class norm_accumulator_mp
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99 {
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100 R p,scl,sum;
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101 public:
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102 norm_accumulator_mp () {} // we need this one for Array
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103 norm_accumulator_mp (R pp) : p(pp), scl(0), sum(1) {}
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104
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105 template <typename U>
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106 void accum (U val)
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107 {
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108 octave_quit ();
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109 R t = 1 / std::abs (val);
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110 if (scl == t)
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111 sum += 1;
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112 else if (scl < t)
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113 {
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114 sum *= std::pow (scl/t, p);
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115 sum += 1;
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116 scl = t;
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117 }
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118 else if (t != 0)
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119 sum += std::pow (t/scl, p);
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120 }
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121 operator R () { return scl * std::pow (sum, -1/p); }
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122 };
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123
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124 // norm accumulator for the 2-norm (euclidean)
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125 template <typename R>
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126 class norm_accumulator_2
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127 {
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128 R scl,sum;
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129 static R pow2 (R x) { return x*x; }
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130 public:
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131 norm_accumulator_2 () : scl(0), sum(1) {}
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132
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133 void accum (R val)
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134 {
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135 R t = std::abs (val);
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136 if (scl == t)
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137 sum += 1;
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138 else if (scl < t)
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139 {
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140 sum *= pow2 (scl/t);
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141 sum += 1;
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142 scl = t;
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143 }
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144 else if (t != 0)
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145 sum += pow2 (t/scl);
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146 }
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147
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148 void accum (std::complex<R> val)
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149 {
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150 accum (val.real ());
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151 accum (val.imag ());
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152 }
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153
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154 operator R () { return scl * std::sqrt (sum); }
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155 };
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156
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157 // norm accumulator for the 1-norm (city metric)
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158 template <typename R>
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159 class norm_accumulator_1
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160 {
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161 R sum;
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162 public:
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163 norm_accumulator_1 () : sum (0) {}
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164 template <typename U>
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165 void accum (U val)
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166 {
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167 sum += std::abs (val);
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168 }
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169 operator R () { return sum; }
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170 };
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171
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172 // norm accumulator for the inf-norm (max metric)
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173 template <typename R>
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174 class norm_accumulator_inf
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175 {
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176 R max;
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177 public:
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178 norm_accumulator_inf () : max (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 if (xisnan (val))
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183 max = octave::numeric_limits<R>::NaN ();
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184 else
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185 max = std::max (max, std::abs (val));
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186 }
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187 operator R () { return max; }
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188 };
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189
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190 // norm accumulator for the -inf pseudonorm (min abs value)
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191 template <typename R>
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192 class norm_accumulator_minf
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193 {
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194 R min;
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195 public:
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196 norm_accumulator_minf () : min (octave::numeric_limits<R>::Inf ()) {}
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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 (xisnan (val))
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201 min = octave::numeric_limits<R>::NaN ();
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202 else
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203 min = std::min (min, std::abs (val));
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204 }
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205 operator R () { return min; }
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206 };
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207
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208 // norm accumulator for the 0-pseudonorm (hamming distance)
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209 template <typename R>
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210 class norm_accumulator_0
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211 {
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212 unsigned int num;
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213 public:
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214 norm_accumulator_0 () : num (0) {}
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215 template <typename U>
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216 void accum (U val)
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217 {
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218 if (val != static_cast<U> (0)) ++num;
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219 }
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220 operator R () { return num; }
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221 };
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222
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223
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224 // OK, we're armed :) Now let's go for the fun
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225
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226 template <typename T, typename R, typename ACC>
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227 inline void vector_norm (const Array<T>& v, R& res, ACC acc)
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228 {
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229 for (octave_idx_type i = 0; i < v.numel (); i++)
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230 acc.accum (v(i));
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231
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232 res = acc;
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233 }
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234
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235 // dense versions
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236 template <typename T, typename R, typename ACC>
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237 void column_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
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238 {
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239 res = MArray<R> (dim_vector (1, m.columns ()));
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240 for (octave_idx_type j = 0; j < m.columns (); j++)
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241 {
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242 ACC accj = acc;
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243 for (octave_idx_type i = 0; i < m.rows (); i++)
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244 accj.accum (m(i, j));
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245
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246 res.xelem (j) = accj;
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247 }
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248 }
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249
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250 template <typename T, typename R, typename ACC>
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251 void row_norms (const MArray<T>& m, MArray<R>& res, ACC acc)
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252 {
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253 res = MArray<R> (dim_vector (m.rows (), 1));
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254 std::vector<ACC> acci (m.rows (), acc);
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255 for (octave_idx_type j = 0; j < m.columns (); j++)
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256 {
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257 for (octave_idx_type i = 0; i < m.rows (); i++)
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258 acci[i].accum (m(i, j));
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259 }
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260
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261 for (octave_idx_type i = 0; i < m.rows (); i++)
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262 res.xelem (i) = acci[i];
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263 }
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264
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265 // sparse versions
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266 template <typename T, typename R, typename ACC>
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267 void column_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
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268 {
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269 res = MArray<R> (dim_vector (1, m.columns ()));
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270 for (octave_idx_type j = 0; j < m.columns (); j++)
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271 {
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272 ACC accj = acc;
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273 for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
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274 accj.accum (m.data (k));
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275
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276 res.xelem (j) = accj;
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277 }
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278 }
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279
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280 template <typename T, typename R, typename ACC>
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281 void row_norms (const MSparse<T>& m, MArray<R>& res, ACC acc)
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282 {
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283 res = MArray<R> (dim_vector (m.rows (), 1));
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284 std::vector<ACC> acci (m.rows (), acc);
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285 for (octave_idx_type j = 0; j < m.columns (); j++)
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286 {
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287 for (octave_idx_type k = m.cidx (j); k < m.cidx (j+1); k++)
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288 acci[m.ridx (k)].accum (m.data (k));
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289 }
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290
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291 for (octave_idx_type i = 0; i < m.rows (); i++)
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292 res.xelem (i) = acci[i];
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293 }
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294
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295 // now the dispatchers
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296 #define DEFINE_DISPATCHER(FUNC_NAME, ARG_TYPE, RES_TYPE) \
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297 template <typename T, typename R> \
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298 RES_TYPE FUNC_NAME (const ARG_TYPE& v, R p) \
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299 { \
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300 RES_TYPE res; \
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301 if (p == 2) \
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302 FUNC_NAME (v, res, norm_accumulator_2<R> ()); \
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303 else if (p == 1) \
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304 FUNC_NAME (v, res, norm_accumulator_1<R> ()); \
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305 else if (lo_ieee_isinf (p)) \
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306 { \
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307 if (p > 0) \
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308 FUNC_NAME (v, res, norm_accumulator_inf<R> ()); \
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309 else \
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310 FUNC_NAME (v, res, norm_accumulator_minf<R> ()); \
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311 } \
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312 else if (p == 0) \
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313 FUNC_NAME (v, res, norm_accumulator_0<R> ()); \
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314 else if (p > 0) \
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315 FUNC_NAME (v, res, norm_accumulator_p<R> (p)); \
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316 else \
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317 FUNC_NAME (v, res, norm_accumulator_mp<R> (p)); \
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318 return res; \
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319 }
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320
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321 DEFINE_DISPATCHER (vector_norm, MArray<T>, R)
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322 DEFINE_DISPATCHER (column_norms, MArray<T>, MArray<R>)
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323 DEFINE_DISPATCHER (row_norms, MArray<T>, MArray<R>)
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324 DEFINE_DISPATCHER (column_norms, MSparse<T>, MArray<R>)
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325 DEFINE_DISPATCHER (row_norms, MSparse<T>, MArray<R>)
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326
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327 // The approximate subproblem in Higham's method. Find lambda and mu such that
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328 // norm ([lambda, mu], p) == 1 and norm (y*lambda + col*mu, p) is maximized.
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329 // Real version. As in Higham's paper.
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330 template <typename ColVectorT, typename R>
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331 static void
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332 higham_subp (const ColVectorT& y, const ColVectorT& col,
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333 octave_idx_type nsamp, R p, R& lambda, R& mu)
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334 {
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335 R nrm = 0;
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336 for (octave_idx_type i = 0; i < nsamp; i++)
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337 {
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338 octave_quit ();
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339 R fi = i * static_cast<R> (M_PI) / nsamp;
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340 R lambda1 = cos (fi);
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341 R mu1 = sin (fi);
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342 R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
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343 std::pow (std::abs (mu1), p), 1/p);
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344 lambda1 /= lmnr; mu1 /= lmnr;
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345 R nrm1 = vector_norm (lambda1 * y + mu1 * col, p);
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346 if (nrm1 > nrm)
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347 {
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348 lambda = lambda1;
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349 mu = mu1;
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350 nrm = nrm1;
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351 }
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352 }
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353 }
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354
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355 // Complex version. Higham's paper does not deal with complex case, so we use a
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356 // simple extension. First, guess the magnitudes as in real version, then try
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357 // to rotate lambda to improve further.
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358 template <typename ColVectorT, typename R>
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359 static void
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360 higham_subp (const ColVectorT& y, const ColVectorT& col,
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361 octave_idx_type nsamp, R p,
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362 std::complex<R>& lambda, std::complex<R>& mu)
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363 {
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364 typedef std::complex<R> CR;
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365 R nrm = 0;
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366 lambda = 1.0;
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367 CR lamcu = lambda / std::abs (lambda);
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368 // Probe magnitudes
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369 for (octave_idx_type i = 0; i < nsamp; i++)
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370 {
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371 octave_quit ();
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372 R fi = i * static_cast<R> (M_PI) / nsamp;
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373 R lambda1 = cos (fi);
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374 R mu1 = sin (fi);
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375 R lmnr = std::pow (std::pow (std::abs (lambda1), p) +
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376 std::pow (std::abs (mu1), p), 1/p);
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377 lambda1 /= lmnr; mu1 /= lmnr;
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378 R nrm1 = vector_norm (lambda1 * lamcu * y + mu1 * col, p);
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379 if (nrm1 > nrm)
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380 {
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381 lambda = lambda1 * lamcu;
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382 mu = mu1;
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383 nrm = nrm1;
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384 }
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385 }
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386 R lama = std::abs (lambda);
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387 // Probe orientation
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388 for (octave_idx_type i = 0; i < nsamp; i++)
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389 {
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390 octave_quit ();
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391 R fi = i * static_cast<R> (M_PI) / nsamp;
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392 lamcu = CR (cos (fi), sin (fi));
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393 R nrm1 = vector_norm (lama * lamcu * y + mu * col, p);
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394 if (nrm1 > nrm)
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395 {
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396 lambda = lama * lamcu;
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397 nrm = nrm1;
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398 }
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399 }
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400 }
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401
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402 // the p-dual element (should work for both real and complex)
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403 template <typename T, typename R>
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404 inline T elem_dual_p (T x, R p)
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405 {
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406 return signum (x) * std::pow (std::abs (x), p-1);
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407 }
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408
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409 // the VectorT is used for vectors, but actually it has to be
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410 // a Matrix type to allow all the operations. For instance SparseMatrix
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411 // does not support multiplication with column/row vectors.
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412 // the dual vector
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413 template <typename VectorT, typename R>
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414 VectorT dual_p (const VectorT& x, R p, R q)
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415 {
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diff changeset
416 VectorT res (x.dims ());
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417 for (octave_idx_type i = 0; i < x.numel (); i++)
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418 res.xelem (i) = elem_dual_p (x(i), p);
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419 return res / vector_norm (res, q);
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420 }
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421
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422 // Higham's hybrid method
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423 template <typename MatrixT, typename VectorT, typename R>
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424 R higham (const MatrixT& m, R p, R tol, int maxiter,
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425 VectorT& x)
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426 {
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diff changeset
427 x.resize (m.columns (), 1);
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428 // the OSE part
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429 VectorT y(m.rows (), 1, 0), z(m.rows (), 1);
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430 typedef typename VectorT::element_type RR;
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431 RR lambda = 0;
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432 RR mu = 1;
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433 for (octave_idx_type k = 0; k < m.columns (); k++)
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434 {
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435 octave_quit ();
8303
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diff changeset
436 VectorT col (m.column (k));
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diff changeset
437 if (k > 0)
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diff changeset
438 higham_subp (y, col, 4*k, p, lambda, mu);
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439 for (octave_idx_type i = 0; i < k; i++)
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diff changeset
440 x(i) *= lambda;
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diff changeset
441 x(k) = mu;
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442 y = lambda * y + mu * col;
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443 }
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444
8303
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445 // the PM part
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
446 x = x / vector_norm (x, p);
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
447 R q = p/(p-1);
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
448
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
449 R gamma = 0, gamma1;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
450 int iter = 0;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
451 while (iter < maxiter)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
452 {
10142
829e69ec3110 make OCTAVE_QUIT a function
Jaroslav Hajek <highegg@gmail.com>
parents: 9245
diff changeset
453 octave_quit ();
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
454 y = m*x;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
455 gamma1 = gamma;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
456 gamma = vector_norm (y, p);
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
457 z = dual_p (y, p, q);
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
458 z = z.hermitian ();
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
459 z = z * m;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
460
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
461 if (iter > 0 && (vector_norm (z, q) <= gamma
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
462 || (gamma - gamma1) <= tol*gamma))
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
463 break;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
464
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
465 z = z.hermitian ();
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
466 x = dual_p (z, q, p);
20714
7b6d8c19dab0 Cuddle increment (++) and decrement (--) operators with variable in question.
Rik <rik@octave.org>
parents: 19924
diff changeset
467 iter++;
8303
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
468 }
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
469
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
470 return gamma;
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
471 }
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
472
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11570
diff changeset
473 // derive column vector and SVD types
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
474
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
475 static const char *p_less1_gripe = "xnorm: p must be at least 1";
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
476
17769
49a5a4be04a1 maint: Use GNU style coding conventions for code in liboctave/
Rik <rik@octave.org>
parents: 17744
diff changeset
477 // Static constant to control the maximum number of iterations. 100 seems to
49a5a4be04a1 maint: Use GNU style coding conventions for code in liboctave/
Rik <rik@octave.org>
parents: 17744
diff changeset
478 // be a good value. Eventually, we can provide a means to change this
49a5a4be04a1 maint: Use GNU style coding conventions for code in liboctave/
Rik <rik@octave.org>
parents: 17744
diff changeset
479 // constant from Octave.
8303
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parents:
diff changeset
480 static int max_norm_iter = 100;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
481
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
482 // version with SVD for dense matrices
21273
cbced1c09916 better use of templates for svd classes
John W. Eaton <jwe@octave.org>
parents: 21202
diff changeset
483 template <typename MatrixT, typename VectorT, typename R>
cbced1c09916 better use of templates for svd classes
John W. Eaton <jwe@octave.org>
parents: 21202
diff changeset
484 R svd_matrix_norm (const MatrixT& m, R p, VectorT)
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
485 {
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
486 R res = 0;
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
487 if (p == 2)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
488 {
21273
cbced1c09916 better use of templates for svd classes
John W. Eaton <jwe@octave.org>
parents: 21202
diff changeset
489 svd<MatrixT> fact (m, svd<MatrixT>::sigma_only);
cbced1c09916 better use of templates for svd classes
John W. Eaton <jwe@octave.org>
parents: 21202
diff changeset
490 res = fact.singular_values () (0,0);
8303
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
491 }
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
492 else if (p == 1)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
493 res = xcolnorms (m, 1).max ();
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
494 else if (lo_ieee_isinf (p))
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
495 res = xrownorms (m, 1).max ();
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
496 else if (p > 1)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
497 {
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parents:
diff changeset
498 VectorT x;
8995
1b097d86a61a remove a TODO in oct-norm.cc
Jaroslav Hajek <highegg@gmail.com>
parents: 8319
diff changeset
499 const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
1b097d86a61a remove a TODO in oct-norm.cc
Jaroslav Hajek <highegg@gmail.com>
parents: 8319
diff changeset
500 res = higham (m, p, sqrteps, max_norm_iter, x);
8303
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parents:
diff changeset
501 }
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
502 else
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11570
diff changeset
503 (*current_liboctave_error_handler) (p_less1_gripe);
8303
b11c31849b44 improve norm computation capabilities
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parents:
diff changeset
504
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
505 return res;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
506 }
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
507
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
508 // SVD-free version for sparse matrices
21139
538b57866b90 consistently use "typename" intead of "class" in template declarations
John W. Eaton <jwe@octave.org>
parents: 20714
diff changeset
509 template <typename MatrixT, typename VectorT, typename R>
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
510 R matrix_norm (const MatrixT& m, R p, VectorT)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
511 {
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
512 R res = 0;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
513 if (p == 1)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
514 res = xcolnorms (m, 1).max ();
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
515 else if (lo_ieee_isinf (p))
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
516 res = xrownorms (m, 1).max ();
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
517 else if (p > 1)
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Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
518 {
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
519 VectorT x;
8995
1b097d86a61a remove a TODO in oct-norm.cc
Jaroslav Hajek <highegg@gmail.com>
parents: 8319
diff changeset
520 const R sqrteps = std::sqrt (std::numeric_limits<R>::epsilon ());
1b097d86a61a remove a TODO in oct-norm.cc
Jaroslav Hajek <highegg@gmail.com>
parents: 8319
diff changeset
521 res = higham (m, p, sqrteps, max_norm_iter, x);
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
522 }
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
523 else
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11570
diff changeset
524 (*current_liboctave_error_handler) (p_less1_gripe);
8303
b11c31849b44 improve norm computation capabilities
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parents:
diff changeset
525
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
526 return res;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
527 }
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
528
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
529 // and finally, here's what we've promised in the header file
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
530
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
531 #define DEFINE_XNORM_FUNCS(PREFIX, RTYPE) \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
532 OCTAVE_API RTYPE xnorm (const PREFIX##ColumnVector& x, RTYPE p) \
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
533 { return vector_norm (x, p); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
534 OCTAVE_API RTYPE xnorm (const PREFIX##RowVector& x, RTYPE p) \
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
535 { return vector_norm (x, p); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
536 OCTAVE_API RTYPE xnorm (const PREFIX##Matrix& x, RTYPE p) \
21273
cbced1c09916 better use of templates for svd classes
John W. Eaton <jwe@octave.org>
parents: 21202
diff changeset
537 { return svd_matrix_norm (x, p, PREFIX##Matrix ()); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
538 OCTAVE_API RTYPE xfrobnorm (const PREFIX##Matrix& x) \
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
539 { return vector_norm (x, static_cast<RTYPE> (2)); }
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
540
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
541 DEFINE_XNORM_FUNCS(, double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
542 DEFINE_XNORM_FUNCS(Complex, double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
543 DEFINE_XNORM_FUNCS(Float, float)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
544 DEFINE_XNORM_FUNCS(FloatComplex, float)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
545
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
546 // this is needed to avoid copying the sparse matrix for xfrobnorm
21139
538b57866b90 consistently use "typename" intead of "class" in template declarations
John W. Eaton <jwe@octave.org>
parents: 20714
diff changeset
547 template <typename T, typename R>
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
548 inline void array_norm_2 (const T* v, octave_idx_type n, R& res)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
549 {
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
550 norm_accumulator_2<R> acc;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
551 for (octave_idx_type i = 0; i < n; i++)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
552 acc.accum (v[i]);
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
553
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
554 res = acc;
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
555 }
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
556
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
557 #define DEFINE_XNORM_SPARSE_FUNCS(PREFIX, RTYPE) \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
558 OCTAVE_API RTYPE xnorm (const Sparse##PREFIX##Matrix& x, RTYPE p) \
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
559 { return matrix_norm (x, p, PREFIX##Matrix ()); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
560 OCTAVE_API RTYPE xfrobnorm (const Sparse##PREFIX##Matrix& x) \
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
561 { \
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
562 RTYPE res; \
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
563 array_norm_2 (x.data (), x.nnz (), res); \
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
564 return res; \
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
565 }
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
566
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
567 DEFINE_XNORM_SPARSE_FUNCS(, double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
568 DEFINE_XNORM_SPARSE_FUNCS(Complex, double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
569
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
570 #define DEFINE_COLROW_NORM_FUNCS(PREFIX, RPREFIX, RTYPE) \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
571 extern OCTAVE_API RPREFIX##RowVector xcolnorms (const PREFIX##Matrix& m, RTYPE p) \
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
572 { return column_norms (m, p); } \
8319
c374691576f6 Fix for MSVC compilation
Michael Goffioul <michael.goffioul@gmail.com>
parents: 8309
diff changeset
573 extern OCTAVE_API RPREFIX##ColumnVector xrownorms (const PREFIX##Matrix& m, RTYPE p) \
8303
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
574 { return row_norms (m, p); } \
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
575
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
576 DEFINE_COLROW_NORM_FUNCS(, , double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
577 DEFINE_COLROW_NORM_FUNCS(Complex, , double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
578 DEFINE_COLROW_NORM_FUNCS(Float, Float, float)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
579 DEFINE_COLROW_NORM_FUNCS(FloatComplex, Float, float)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
580
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
581 DEFINE_COLROW_NORM_FUNCS(Sparse, , double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
582 DEFINE_COLROW_NORM_FUNCS(SparseComplex, , double)
b11c31849b44 improve norm computation capabilities
Jaroslav Hajek <highegg@gmail.com>
parents:
diff changeset
583