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annotate Framework/Toolbox/LinearAlgebra.cpp @ 164:432b1f812d14 wasm

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inversion of general matrices
author Sebastien Jodogne <s.jodogne@gmail.com>
date Wed, 14 Feb 2018 16:49:43 +0100
parents 8c5b24892ed2
children 8d50e6be565d
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1 /**
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2 * Stone of Orthanc
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3 * Copyright (C) 2012-2016 Sebastien Jodogne, Medical Physics
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4 * Department, University Hospital of Liege, Belgium
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5 * Copyright (C) 2017-2018 Osimis S.A., Belgium
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6 *
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7 * This program is free software: you can redistribute it and/or
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8 * modify it under the terms of the GNU Affero General Public License
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9 * as published by the Free Software Foundation, either version 3 of
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10 * the License, or (at your option) any later version.
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11 *
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12 * This program is distributed in the hope that it will be useful, but
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13 * WITHOUT ANY WARRANTY; without even the implied warranty of
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14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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15 * Affero General Public License for more details.
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16 *
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17 * You should have received a copy of the GNU Affero General Public License
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18 * along with this program. If not, see <http://www.gnu.org/licenses/>.
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19 **/
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20
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21
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22 #include "LinearAlgebra.h"
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23
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24 #include <Core/Logging.h>
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25 #include <Core/OrthancException.h>
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26 #include <Core/Toolbox.h>
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27
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28 #include <stdio.h>
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29 #include <boost/lexical_cast.hpp>
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30 #include <boost/numeric/ublas/lu.hpp>
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31
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32 namespace OrthancStone
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33 {
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34 namespace LinearAlgebra
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35 {
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36 void Print(const Vector& v)
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37 {
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38 for (size_t i = 0; i < v.size(); i++)
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39 {
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40 printf("%g\n", v[i]);
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41 //printf("%8.2f\n", v[i]);
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42 }
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43 printf("\n");
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44 }
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45
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46
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47 void Print(const Matrix& m)
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48 {
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49 for (size_t i = 0; i < m.size1(); i++)
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50 {
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51 for (size_t j = 0; j < m.size2(); j++)
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52 {
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53 printf("%g ", m(i,j));
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54 //printf("%8.2f ", m(i,j));
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55 }
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56 printf("\n");
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57 }
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58 printf("\n");
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59 }
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60
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61
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62 bool ParseVector(Vector& target,
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63 const std::string& value)
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64 {
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65 std::vector<std::string> items;
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66 Orthanc::Toolbox::TokenizeString(items, value, '\\');
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67
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68 target.resize(items.size());
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69
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70 for (size_t i = 0; i < items.size(); i++)
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71 {
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72 try
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73 {
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74 target[i] = boost::lexical_cast<double>(Orthanc::Toolbox::StripSpaces(items[i]));
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75 }
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76 catch (boost::bad_lexical_cast&)
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77 {
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78 target.clear();
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79 return false;
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80 }
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81 }
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82
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83 return true;
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84 }
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85
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86
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87 bool ParseVector(Vector& target,
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88 const Orthanc::DicomMap& dataset,
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89 const Orthanc::DicomTag& tag)
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90 {
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91 std::string value;
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92 return (dataset.CopyToString(value, tag, false) &&
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93 ParseVector(target, value));
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94 }
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95
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96
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97 void AssignVector(Vector& v,
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98 double v1,
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99 double v2)
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100 {
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101 v.resize(2);
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102 v[0] = v1;
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103 v[1] = v2;
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104 }
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105
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106
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107 void AssignVector(Vector& v,
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108 double v1,
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109 double v2,
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110 double v3)
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111 {
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112 v.resize(3);
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113 v[0] = v1;
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114 v[1] = v2;
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115 v[2] = v3;
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116 }
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117
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118
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119 void AssignVector(Vector& v,
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120 double v1,
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121 double v2,
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122 double v3,
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123 double v4)
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124 {
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125 v.resize(4);
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126 v[0] = v1;
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127 v[1] = v2;
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128 v[2] = v3;
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129 v[3] = v4;
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130 }
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131
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132
158
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133 bool IsNear(double x,
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134 double y)
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135 {
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136 // As most input is read as single-precision numbers, we take the
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137 // epsilon machine for float32 into consideration to compare numbers
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138 return IsNear(x, y, 10.0 * std::numeric_limits<float>::epsilon());
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139 }
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140
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141
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142 void NormalizeVector(Vector& u)
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143 {
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144 double norm = boost::numeric::ublas::norm_2(u);
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145 if (!IsCloseToZero(norm))
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146 {
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147 u = u / norm;
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148 }
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149 }
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150
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151
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152 void CrossProduct(Vector& result,
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153 const Vector& u,
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154 const Vector& v)
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155 {
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156 if (u.size() != 3 ||
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157 v.size() != 3)
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158 {
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159 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
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160 }
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161
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162 result.resize(3);
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163
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164 result[0] = u[1] * v[2] - u[2] * v[1];
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165 result[1] = u[2] * v[0] - u[0] * v[2];
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166 result[2] = u[0] * v[1] - u[1] * v[0];
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167 }
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168
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169
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170 void FillMatrix(Matrix& target,
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171 size_t rows,
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172 size_t columns,
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173 const double values[])
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174 {
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175 target.resize(rows, columns);
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176
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177 size_t index = 0;
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178
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179 for (size_t y = 0; y < rows; y++)
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180 {
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181 for (size_t x = 0; x < columns; x++, index++)
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182 {
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183 target(y, x) = values[index];
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184 }
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185 }
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186 }
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187
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188
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189 void FillVector(Vector& target,
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190 size_t size,
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191 const double values[])
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192 {
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193 target.resize(size);
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194
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195 for (size_t i = 0; i < size; i++)
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196 {
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197 target[i] = values[i];
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198 }
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199 }
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200
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201
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202 void Convert(Matrix& target,
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203 const Vector& source)
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204 {
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205 const size_t n = source.size();
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206
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207 target.resize(n, 1);
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208
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209 for (size_t i = 0; i < n; i++)
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210 {
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211 target(i, 0) = source[i];
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212 }
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213 }
159
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214
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215
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216 double ComputeDeterminant(const Matrix& a)
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217 {
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218 if (a.size1() != a.size2())
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219 {
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220 LOG(ERROR) << "Determinant only exists for square matrices";
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221 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
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222 }
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223
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224 // https://en.wikipedia.org/wiki/Rule_of_Sarrus
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225 if (a.size1() == 1)
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226 {
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227 return a(0,0);
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228 }
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229 else if (a.size1() == 2)
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230 {
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231 return a(0,0) * a(1,1) - a(0,1) * a(1,0);
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232 }
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233 else if (a.size1() == 3)
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234 {
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235 return (a(0,0) * a(1,1) * a(2,2) +
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236 a(0,1) * a(1,2) * a(2,0) +
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237 a(0,2) * a(1,0) * a(2,1) -
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238 a(2,0) * a(1,1) * a(0,2) -
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239 a(2,1) * a(1,2) * a(0,0) -
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240 a(2,2) * a(1,0) * a(0,1));
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241 }
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242 else
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243 {
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244 throw Orthanc::OrthancException(Orthanc::ErrorCode_NotImplemented);
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245 }
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246 }
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247
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248
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249 bool IsOrthogonalMatrix(const Matrix& q,
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250 double threshold)
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251 {
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252 // https://en.wikipedia.org/wiki/Orthogonal_matrix
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253
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254 using namespace boost::numeric::ublas;
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255
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256 const Matrix check = prod(trans(q), q) - identity_matrix<double>(3);
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257
160
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258 type_traits<double>::real_type norm = norm_inf(check);
159
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259
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260 return (norm <= threshold);
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261 }
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262
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263
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264 bool IsOrthogonalMatrix(const Matrix& q)
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265 {
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266 return IsOrthogonalMatrix(q, 10.0 * std::numeric_limits<float>::epsilon());
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267 }
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268
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269
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270 bool IsRotationMatrix(const Matrix& r,
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271 double threshold)
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272 {
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273 return (IsOrthogonalMatrix(r, threshold) &&
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274 IsNear(ComputeDeterminant(r), 1.0, threshold));
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275 }
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276
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277
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278 bool IsRotationMatrix(const Matrix& r)
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279 {
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280 return IsRotationMatrix(r, 10.0 * std::numeric_limits<float>::epsilon());
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281 }
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282
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283
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284 void InvertUpperTriangularMatrix(Matrix& output,
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285 const Matrix& k)
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286 {
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287 if (k.size1() != k.size2())
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diff changeset
288 {
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289 LOG(ERROR) << "Determinant only exists for square matrices";
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diff changeset
290 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
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291 }
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diff changeset
292
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diff changeset
293 output.resize(k.size1(), k.size2());
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diff changeset
294
0a73d76333db populating LinearAlgebra
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diff changeset
295 for (size_t i = 1; i < k.size1(); i++)
0a73d76333db populating LinearAlgebra
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diff changeset
296 {
0a73d76333db populating LinearAlgebra
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diff changeset
297 for (size_t j = 0; j < i; j++)
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diff changeset
298 {
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
299 if (!IsCloseToZero(k(i, j)))
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parents: 158
diff changeset
300 {
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
301 LOG(ERROR) << "Not an upper triangular matrix";
0a73d76333db populating LinearAlgebra
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diff changeset
302 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
0a73d76333db populating LinearAlgebra
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diff changeset
303 }
0a73d76333db populating LinearAlgebra
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diff changeset
304
0a73d76333db populating LinearAlgebra
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diff changeset
305 output(i, j) = 0; // The output is also upper triangular
0a73d76333db populating LinearAlgebra
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diff changeset
306 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
307 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
308
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
309 if (k.size1() == 3)
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
310 {
0a73d76333db populating LinearAlgebra
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311 // https://math.stackexchange.com/a/1004181
0a73d76333db populating LinearAlgebra
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diff changeset
312 double a = k(0, 0);
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diff changeset
313 double b = k(0, 1);
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diff changeset
314 double c = k(0, 2);
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diff changeset
315 double d = k(1, 1);
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diff changeset
316 double e = k(1, 2);
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diff changeset
317 double f = k(2, 2);
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diff changeset
318
0a73d76333db populating LinearAlgebra
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diff changeset
319 if (IsCloseToZero(a) ||
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diff changeset
320 IsCloseToZero(d) ||
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diff changeset
321 IsCloseToZero(f))
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parents: 158
diff changeset
322 {
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diff changeset
323 LOG(ERROR) << "Singular upper triangular matrix";
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diff changeset
324 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
0a73d76333db populating LinearAlgebra
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diff changeset
325 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
326 else
0a73d76333db populating LinearAlgebra
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diff changeset
327 {
0a73d76333db populating LinearAlgebra
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diff changeset
328 output(0, 0) = 1.0 / a;
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329 output(0, 1) = -b / (a * d);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
330 output(0, 2) = (b * e - c * d) / (a * f * d);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
331 output(1, 1) = 1.0 / d;
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
332 output(1, 2) = -e / (f * d);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
333 output(2, 2) = 1.0 / f;
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
334 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
335 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
336 else
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
337 {
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
338 throw Orthanc::OrthancException(Orthanc::ErrorCode_NotImplemented);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
339 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
340 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
341
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
342
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
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diff changeset
343 static void GetGivensComponent(double& c,
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344 double& s,
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345 const Matrix& a,
0a73d76333db populating LinearAlgebra
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diff changeset
346 size_t i,
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diff changeset
347 size_t j)
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
348 {
0a73d76333db populating LinearAlgebra
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diff changeset
349 assert(i < 3 && j < 3);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
350
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
351 double x = a(i, i);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
352 double y = a(i, j);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
353 double n = sqrt(x * x + y * y);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
354
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
355 if (IsCloseToZero(n))
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Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
356 {
0a73d76333db populating LinearAlgebra
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diff changeset
357 c = 1;
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diff changeset
358 s = 0;
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parents: 158
diff changeset
359 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
360 else
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
361 {
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
362 c = x / n;
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parents: 158
diff changeset
363 s = -y / n;
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
364 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
365 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
366
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
367
0a73d76333db populating LinearAlgebra
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diff changeset
368 /**
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diff changeset
369 * This function computes the RQ decomposition of a 3x3 matrix,
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
370 * using Givens rotations. Reference: Algorithm A4.1 (page 579) of
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parents: 158
diff changeset
371 * "Multiple View Geometry in Computer Vision" (2nd edition). The
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
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diff changeset
372 * output matrix "Q" is a rotation matrix, and "R" is upper
0a73d76333db populating LinearAlgebra
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diff changeset
373 * triangular.
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diff changeset
374 **/
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diff changeset
375 void RQDecomposition3x3(Matrix& r,
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Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
376 Matrix& q,
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Sebastien Jodogne <s.jodogne@gmail.com>
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diff changeset
377 const Matrix& a)
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diff changeset
378 {
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
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diff changeset
379 using namespace boost::numeric::ublas;
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diff changeset
380
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
381 if (a.size1() != 3 ||
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
382 a.size2() != 3)
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
383 {
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
384 LOG(ERROR) << "Only applicable to a 3x3 matrix";
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Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
385 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
386 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
387
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
388 r.resize(3, 3);
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parents: 158
diff changeset
389 q.resize(3, 3);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
390
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
391 r = a;
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Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
392 q = identity_matrix<double>(3);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
393
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
394 {
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
395 // Set A(2,1) to zero
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
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diff changeset
396 double c, s;
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
397 GetGivensComponent(c, s, r, 2, 1);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
398
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
399 double v[9] = { 1, 0, 0,
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
400 0, c, -s,
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
401 0, s, c };
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
402
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
403 Matrix g;
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
404 FillMatrix(g, 3, 3, v);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
405
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
406 r = prod(r, g);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
407 q = prod(trans(g), q);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
408 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
409
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
410
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
411 {
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
412 // Set A(2,0) to zero
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Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
413 double c, s;
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parents: 158
diff changeset
414 GetGivensComponent(c, s, r, 2, 0);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
415
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
416 double v[9] = { c, 0, -s,
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parents: 158
diff changeset
417 0, 1, 0,
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parents: 158
diff changeset
418 s, 0, c };
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parents: 158
diff changeset
419
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
420 Matrix g;
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
421 FillMatrix(g, 3, 3, v);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
422
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
423 r = prod(r, g);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
424 q = prod(trans(g), q);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
425 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
426
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
427
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
428 {
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
429 // Set A(1,0) to zero
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
430 double c, s;
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parents: 158
diff changeset
431 GetGivensComponent(c, s, r, 1, 0);
0a73d76333db populating LinearAlgebra
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parents: 158
diff changeset
432
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Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
433 double v[9] = { c, -s, 0,
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parents: 158
diff changeset
434 s, c, 0,
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
435 0, 0, 1 };
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parents: 158
diff changeset
436
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
437 Matrix g;
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
438 FillMatrix(g, 3, 3, v);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
439
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
440 r = prod(r, g);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
441 q = prod(trans(g), q);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
442 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
443
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
444 if (!IsCloseToZero(norm_inf(prod(r, q) - a)) ||
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
445 !IsRotationMatrix(q) ||
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
446 !IsCloseToZero(r(1, 0)) ||
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
447 !IsCloseToZero(r(2, 0)) ||
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
448 !IsCloseToZero(r(2, 1)))
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
449 {
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
450 throw Orthanc::OrthancException(Orthanc::ErrorCode_InternalError);
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
451 }
0a73d76333db populating LinearAlgebra
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 158
diff changeset
452 }
163
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
453
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
454
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
455 void InvertMatrix(Matrix& target,
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
456 const Matrix& source)
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
457 {
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
458 if (source.size1() != source.size2())
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
459 {
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
460 LOG(ERROR) << "Inverse only exists for square matrices";
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
461 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
462 }
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
463
164
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
464 if (source.size1() < 4)
163
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
465 {
164
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
466 // For matrices with size below 4, use direct computations
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
467 // instead of LU decomposition
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
468
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
469 if (source.size1() == 0)
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
470 {
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
471 // By convention, the inverse of the empty matrix, is itself the empty matrix
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
472 target.resize(0, 0);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
473 return;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
474 }
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
475
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
476 double determinant = ComputeDeterminant(source);
432b1f812d14 inversion of general matrices
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parents: 163
diff changeset
477
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
478 if (IsCloseToZero(determinant))
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
479 {
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
480 LOG(ERROR) << "Cannot invert singular matrix";
432b1f812d14 inversion of general matrices
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parents: 163
diff changeset
481 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
432b1f812d14 inversion of general matrices
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parents: 163
diff changeset
482 }
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
483
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
484 double denominator = 1.0 / determinant;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
485
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
486 target.resize(source.size1(), source.size2());
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
487
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
488 if (source.size1() == 1)
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
489 {
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
490 target(0, 0) = denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
491 }
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
492 else if (source.size1() == 2)
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
493 {
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
494 // https://en.wikipedia.org/wiki/Invertible_matrix#Inversion_of_2_%C3%97_2_matrices
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
495 target(0, 0) = source(1, 1) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
496 target(0, 1) = -source(0, 1) * denominator;
432b1f812d14 inversion of general matrices
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parents: 163
diff changeset
497 target(1, 0) = -source(1, 0) * denominator;
432b1f812d14 inversion of general matrices
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parents: 163
diff changeset
498 target(1, 1) = source(0, 0) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
499 }
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
500 else if (source.size1() == 3)
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
501 {
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
502 // https://en.wikipedia.org/wiki/Invertible_matrix#Inversion_of_3_%C3%97_3_matrices
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
503 const double a = source(0, 0);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
504 const double b = source(0, 1);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
505 const double c = source(0, 2);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
506 const double d = source(1, 0);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
507 const double e = source(1, 1);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
508 const double f = source(1, 2);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
509 const double g = source(2, 0);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
510 const double h = source(2, 1);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
511 const double i = source(2, 2);
163
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
512
164
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
513 target(0, 0) = (e * i - f * h) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
514 target(0, 1) = -(b * i - c * h) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
515 target(0, 2) = (b * f - c * e) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
516 target(1, 0) = -(d * i - f * g) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
517 target(1, 1) = (a * i - c * g) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
518 target(1, 2) = -(a * f - c * d) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
519 target(2, 0) = (d * h - e * g) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
520 target(2, 1) = -(a * h - b * g) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
521 target(2, 2) = (a * e - b * d) * denominator;
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
522 }
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
523 else
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
524 {
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
525 throw Orthanc::OrthancException(Orthanc::ErrorCode_InternalError);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
526 }
163
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
527 }
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
528 else
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
529 {
164
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
530 // General case, using LU decomposition
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
531
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
532 Matrix a = source; // Copy the source matrix, as "lu_factorize()" modifies it
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
533
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
534 boost::numeric::ublas::permutation_matrix<size_t> permutation(source.size1());
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
535
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
536 if (boost::numeric::ublas::lu_factorize(a, permutation) != 0)
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
537 {
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
538 LOG(ERROR) << "Cannot invert singular matrix";
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
539 throw Orthanc::OrthancException(Orthanc::ErrorCode_ParameterOutOfRange);
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
540 }
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
541
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
542 target = boost::numeric::ublas::identity_matrix<double>(source.size1());
432b1f812d14 inversion of general matrices
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 163
diff changeset
543 lu_substitute(a, permutation, target);
163
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
544 }
8c5b24892ed2 LinearAlgebra::InvertMatrix
Sebastien Jodogne <s.jodogne@gmail.com>
parents: 161
diff changeset
545 }
158
a053ca7fa5c6 LinearAlgebra toolbox
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
diff changeset
546 }
a053ca7fa5c6 LinearAlgebra toolbox
Sebastien Jodogne <s.jodogne@gmail.com>
parents:
diff changeset
547 }