1 | // This file is a part of Framsticks SDK. http://www.framsticks.com/ |
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2 | // Copyright (C) 1999-2015 Maciej Komosinski and Szymon Ulatowski. |
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3 | // See LICENSE.txt for details. |
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4 | |
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5 | |
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6 | #include "matrix_tools.h" |
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7 | #include "lapack.h" |
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8 | #include <cstdlib> |
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9 | #include <cmath> |
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10 | #include <cstdio> |
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11 | |
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12 | double *Create(int nSize) |
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13 | { |
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14 | double *matrix = (double *) malloc(nSize * sizeof (double)); |
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15 | |
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16 | for (int i = 0; i < nSize; i++) |
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17 | { |
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18 | matrix[i] = 0; |
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19 | } |
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20 | |
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21 | return matrix; |
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22 | } |
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23 | |
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24 | double *Multiply(double *&a, double *&b, int nrow, int ncol, double ncol2, double *&toDel, int delSize) |
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25 | { |
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26 | double *c = Create(nrow * ncol2); |
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27 | int i = 0, j = 0, k = 0; |
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28 | |
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29 | for (i = 0; i < nrow; i++) |
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30 | { |
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31 | for (j = 0; j < ncol2; j++) |
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32 | { |
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33 | for (k = 0; k < ncol; k++) |
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34 | c[i * nrow + j] += a[i * nrow + k] * b[k * ncol + j]; |
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35 | } |
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36 | } |
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37 | |
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38 | if (delSize != 0) |
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39 | free(toDel); |
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40 | return c; |
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41 | } |
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42 | |
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43 | double *Power(double *&array, int nrow, int ncol, double pow, double *&toDel, int delSize) |
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44 | { |
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45 | double *m_Power = Create(nrow * ncol); |
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46 | if (pow == 2) |
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47 | { |
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48 | for (int i = 0; i < nrow; i++) |
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49 | { |
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50 | for (int j = 0; j < ncol; j++) |
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51 | { |
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52 | m_Power[i * nrow + j] = array[i * nrow + j] * array[i * nrow + j]; |
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53 | } |
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54 | |
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55 | } |
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56 | } |
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57 | else |
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58 | { |
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59 | for (int i = 0; i < nrow; i++) |
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60 | { |
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61 | for (int j = 0; j < ncol; j++) |
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62 | { |
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63 | m_Power[i * nrow + j] = sqrt(array[i * nrow + j]); |
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64 | } |
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65 | |
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66 | } |
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67 | } |
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68 | |
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69 | if (delSize != 0) |
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70 | free(toDel); |
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71 | |
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72 | return m_Power; |
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73 | } |
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74 | |
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75 | void Print(double *&mat, int nelems) |
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76 | { |
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77 | for (int i = 0; i < nelems; i++) |
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78 | printf("%6.2f ", mat[i]); |
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79 | printf("\n"); |
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80 | |
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81 | } |
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82 | |
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83 | double *Transpose(double *&A, int arow, int acol) |
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84 | { |
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85 | double *result = Create(acol * arow); |
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86 | |
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87 | for (int i = 0; i < acol; i++) |
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88 | for (int j = 0; j < arow; j++) |
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89 | { |
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90 | result[i * arow + j] = A[j * acol + i]; |
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91 | } |
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92 | |
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93 | return result; |
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94 | |
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95 | } |
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96 | |
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97 | /** Computes the SVD of the nSize x nSize distance matrix |
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98 | @param vdEigenvalues [OUT] Vector of doubles. On return holds the eigenvalues of the |
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99 | decomposed distance matrix (or rather, to be strict, of the matrix of scalar products |
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100 | created from the matrix of distances). The vector is assumed to be empty before the function call and |
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101 | all variance percentages are pushed at the end of it. |
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102 | @param nSize size of the matrix of distances. |
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103 | @param pDistances [IN] matrix of distances between parts. |
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104 | @param Coordinates [OUT] array of three dimensional coordinates obtained from SVD of pDistances matrix. |
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105 | */ |
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106 | void MatrixTools::SVD(std::vector<double> &vdEigenvalues, int nSize, double *pDistances, Pt3D *&Coordinates) |
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107 | { |
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108 | // compute squares of elements of this array |
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109 | // compute the matrix B that is the parameter of SVD |
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110 | double *B = Create(nSize * nSize); |
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111 | { |
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112 | // use additional scope to delete temporary matrices |
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113 | double *Ones, *Eye, *Z, *D; |
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114 | |
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115 | D = Create(nSize * nSize); |
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116 | D = Power(pDistances, nSize, nSize, 2.0, D, nSize); |
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117 | |
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118 | Ones = Create(nSize * nSize); |
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119 | for (int i = 0; i < nSize; i++) |
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120 | for (int j = 0; j < nSize; j++) |
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121 | { |
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122 | Ones[i * nSize + j] = 1; |
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123 | } |
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124 | |
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125 | Eye = Create(nSize * nSize); |
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126 | for (int i = 0; i < nSize; i++) |
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127 | { |
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128 | for (int j = 0; j < nSize; j++) |
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129 | { |
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130 | if (i == j) |
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131 | { |
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132 | Eye[i * nSize + j] = 1; |
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133 | } |
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134 | else |
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135 | { |
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136 | Eye[i * nSize + j] = 0; |
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137 | } |
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138 | } |
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139 | } |
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140 | |
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141 | Z = Create(nSize * nSize); |
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142 | for (int i = 0; i < nSize; i++) |
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143 | { |
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144 | for (int j = 0; j < nSize; j++) |
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145 | { |
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146 | Z[i * nSize + j] = 1.0 / ((double) nSize) * Ones[i * nSize + j]; |
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147 | } |
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148 | } |
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149 | |
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150 | for (int i = 0; i < nSize; i++) |
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151 | { |
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152 | for (int j = 0; j < nSize; j++) |
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153 | { |
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154 | Z[i * nSize + j] = Eye[i * nSize + j] - Z[i * nSize + j]; |
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155 | } |
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156 | } |
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157 | |
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158 | for (int i = 0; i < nSize; i++) |
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159 | { |
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160 | for (int j = 0; j < nSize; j++) |
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161 | { |
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162 | B[i * nSize + j] = Z[i * nSize + j] * -0.5; |
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163 | } |
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164 | } |
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165 | |
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166 | B = Multiply(B, D, nSize, nSize, nSize, B, nSize); |
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167 | B = Multiply(B, Z, nSize, nSize, nSize, B, nSize); |
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168 | |
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169 | free(Ones); |
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170 | free(Eye); |
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171 | free(Z); |
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172 | free(D); |
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173 | } |
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174 | |
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175 | double *Eigenvalues = Create(nSize); |
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176 | double *S = Create(nSize * nSize); |
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177 | |
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178 | // call SVD function |
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179 | double *Vt = Create(nSize * nSize); |
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180 | size_t astep = nSize * sizeof (double); |
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181 | Lapack::JacobiSVD(B, astep, Eigenvalues, Vt, astep, nSize, nSize, nSize); |
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182 | |
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183 | double *W = Transpose(Vt, nSize, nSize); |
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184 | |
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185 | free(B); |
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186 | free(Vt); |
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187 | |
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188 | for (int i = 0; i < nSize; i++) |
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189 | for (int j = 0; j < nSize; j++) |
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190 | { |
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191 | if (i == j) |
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192 | S[i * nSize + j] = Eigenvalues[i]; |
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193 | else |
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194 | S[i * nSize + j] = 0; |
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195 | } |
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196 | |
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197 | // compute coordinates of points |
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198 | double *sqS, *dCoordinates; |
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199 | sqS = Power(S, nSize, nSize, 0.5, S, nSize); |
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200 | dCoordinates = Multiply(W, sqS, nSize, nSize, nSize, W, nSize); |
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201 | free(sqS); |
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202 | |
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203 | for (int i = 0; i < nSize; i++) |
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204 | { |
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205 | // set coordinate from the SVD solution |
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206 | Coordinates[ i ].x = dCoordinates[i * nSize]; |
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207 | Coordinates[ i ].y = dCoordinates[i * nSize + 1 ]; |
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208 | if (nSize > 2) |
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209 | Coordinates[ i ].z = dCoordinates[i * nSize + 2 ]; |
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210 | else |
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211 | Coordinates[ i ].z = 0; |
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212 | } |
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213 | |
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214 | // store the eigenvalues in the output vector |
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215 | for (int i = 0; i < nSize; i++) |
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216 | { |
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217 | double dElement = Eigenvalues[i]; |
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218 | vdEigenvalues.push_back(dElement); |
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219 | } |
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220 | |
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221 | free(Eigenvalues); |
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222 | free(dCoordinates); |
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223 | } |
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