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 | #include <alloc.h> //malloc(), embarcadero |
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12 | #include <math.h> //sqrt(), embarcadero |
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13 | |
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14 | |
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15 | double *Create(int nSize) |
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16 | { |
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17 | double *matrix = (double *) malloc(nSize * sizeof (double)); |
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18 | |
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19 | for (int i = 0; i < nSize; i++) |
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20 | { |
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21 | matrix[i] = 0; |
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22 | } |
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23 | |
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24 | return matrix; |
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25 | } |
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26 | |
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27 | double *Multiply(double *&a, double *&b, int nrow, int ncol, double ncol2, double *&toDel, int delSize) |
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28 | { |
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29 | double *c = Create(nrow * ncol2); |
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30 | int i = 0, j = 0, k = 0; |
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31 | |
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32 | for (i = 0; i < nrow; i++) |
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33 | { |
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34 | for (j = 0; j < ncol2; j++) |
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35 | { |
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36 | for (k = 0; k < ncol; k++) |
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37 | c[i * nrow + j] += a[i * nrow + k] * b[k * ncol + j]; |
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38 | } |
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39 | } |
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40 | |
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41 | if (delSize != 0) |
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42 | free(toDel); |
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43 | return c; |
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44 | } |
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45 | |
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46 | double *Power(double *&array, int nrow, int ncol, double pow, double *&toDel, int delSize) |
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47 | { |
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48 | double *m_Power = Create(nrow * ncol); |
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49 | if (pow == 2) |
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50 | { |
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51 | for (int i = 0; i < nrow; i++) |
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52 | { |
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53 | for (int j = 0; j < ncol; j++) |
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54 | { |
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55 | m_Power[i * nrow + j] = array[i * nrow + j] * array[i * nrow + j]; |
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56 | } |
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57 | |
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58 | } |
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59 | } |
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60 | else |
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61 | { |
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62 | for (int i = 0; i < nrow; i++) |
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63 | { |
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64 | for (int j = 0; j < ncol; j++) |
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65 | { |
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66 | m_Power[i * nrow + j] = sqrt(array[i * nrow + j]); |
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67 | } |
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68 | |
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69 | } |
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70 | } |
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71 | |
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72 | if (delSize != 0) |
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73 | free(toDel); |
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74 | |
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75 | return m_Power; |
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76 | } |
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77 | |
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78 | void Print(double *&mat, int nelems) |
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79 | { |
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80 | for (int i = 0; i < nelems; i++) |
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81 | printf("%6.2f ", mat[i]); |
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82 | printf("\n"); |
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83 | |
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84 | } |
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85 | |
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86 | double *Transpose(double *&A, int arow, int acol) |
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87 | { |
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88 | double *result = Create(acol * arow); |
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89 | |
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90 | for (int i = 0; i < acol; i++) |
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91 | for (int j = 0; j < arow; j++) |
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92 | { |
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93 | result[i * arow + j] = A[j * acol + i]; |
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94 | } |
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95 | |
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96 | return result; |
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97 | |
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98 | } |
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99 | |
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100 | /** Computes the SVD of the nSize x nSize distance matrix |
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101 | @param vdEigenvalues [OUT] Vector of doubles. On return holds the eigenvalues of the |
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102 | decomposed distance matrix (or rather, to be strict, of the matrix of scalar products |
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103 | created from the matrix of distances). The vector is assumed to be empty before the function call and |
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104 | all variance percentages are pushed at the end of it. |
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105 | @param nSize size of the matrix of distances. |
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106 | @param pDistances [IN] matrix of distances between parts. |
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107 | @param Coordinates [OUT] array of three dimensional coordinates obtained from SVD of pDistances matrix. |
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108 | */ |
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109 | void MatrixTools::SVD(std::vector<double> &vdEigenvalues, int nSize, double *pDistances, Pt3D *&Coordinates) |
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110 | { |
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111 | // compute squares of elements of this array |
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112 | // compute the matrix B that is the parameter of SVD |
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113 | double *B = Create(nSize * nSize); |
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114 | { |
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115 | // use additional scope to delete temporary matrices |
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116 | double *Ones, *Eye, *Z, *D; |
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117 | |
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118 | D = Create(nSize * nSize); |
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119 | D = Power(pDistances, nSize, nSize, 2.0, D, nSize); |
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120 | |
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121 | Ones = Create(nSize * nSize); |
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122 | for (int i = 0; i < nSize; i++) |
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123 | for (int j = 0; j < nSize; j++) |
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124 | { |
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125 | Ones[i * nSize + j] = 1; |
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126 | } |
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127 | |
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128 | Eye = Create(nSize * nSize); |
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129 | for (int i = 0; i < nSize; i++) |
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130 | { |
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131 | for (int j = 0; j < nSize; j++) |
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132 | { |
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133 | if (i == j) |
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134 | { |
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135 | Eye[i * nSize + j] = 1; |
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136 | } |
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137 | else |
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138 | { |
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139 | Eye[i * nSize + j] = 0; |
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140 | } |
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141 | } |
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142 | } |
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143 | |
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144 | Z = Create(nSize * nSize); |
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145 | for (int i = 0; i < nSize; i++) |
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146 | { |
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147 | for (int j = 0; j < nSize; j++) |
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148 | { |
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149 | Z[i * nSize + j] = 1.0 / ((double) nSize) * Ones[i * nSize + j]; |
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150 | } |
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151 | } |
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152 | |
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153 | for (int i = 0; i < nSize; i++) |
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154 | { |
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155 | for (int j = 0; j < nSize; j++) |
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156 | { |
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157 | Z[i * nSize + j] = Eye[i * nSize + j] - Z[i * nSize + j]; |
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158 | } |
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159 | } |
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160 | |
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161 | for (int i = 0; i < nSize; i++) |
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162 | { |
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163 | for (int j = 0; j < nSize; j++) |
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164 | { |
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165 | B[i * nSize + j] = Z[i * nSize + j] * -0.5; |
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166 | } |
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167 | } |
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168 | |
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169 | B = Multiply(B, D, nSize, nSize, nSize, B, nSize); |
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170 | B = Multiply(B, Z, nSize, nSize, nSize, B, nSize); |
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171 | |
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172 | free(Ones); |
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173 | free(Eye); |
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174 | free(Z); |
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175 | free(D); |
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176 | } |
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177 | |
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178 | double *Eigenvalues = Create(nSize); |
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179 | double *S = Create(nSize * nSize); |
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180 | |
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181 | // call SVD function |
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182 | double *Vt = Create(nSize * nSize); |
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183 | size_t astep = nSize * sizeof (double); |
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184 | Lapack::JacobiSVD(B, astep, Eigenvalues, Vt, astep, nSize, nSize, nSize); |
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185 | |
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186 | double *W = Transpose(Vt, nSize, nSize); |
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187 | |
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188 | free(B); |
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189 | free(Vt); |
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190 | |
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191 | for (int i = 0; i < nSize; i++) |
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192 | for (int j = 0; j < nSize; j++) |
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193 | { |
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194 | if (i == j) |
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195 | S[i * nSize + j] = Eigenvalues[i]; |
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196 | else |
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197 | S[i * nSize + j] = 0; |
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198 | } |
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199 | |
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200 | // compute coordinates of points |
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201 | double *sqS, *dCoordinates; |
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202 | sqS = Power(S, nSize, nSize, 0.5, S, nSize); |
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203 | dCoordinates = Multiply(W, sqS, nSize, nSize, nSize, W, nSize); |
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204 | free(sqS); |
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205 | |
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206 | for (int i = 0; i < nSize; i++) |
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207 | { |
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208 | // set coordinate from the SVD solution |
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209 | Coordinates[ i ].x = dCoordinates[i * nSize]; |
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210 | Coordinates[ i ].y = dCoordinates[i * nSize + 1 ]; |
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211 | if (nSize > 2) |
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212 | Coordinates[ i ].z = dCoordinates[i * nSize + 2 ]; |
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213 | else |
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214 | Coordinates[ i ].z = 0; |
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215 | } |
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216 | |
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217 | // store the eigenvalues in the output vector |
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218 | for (int i = 0; i < nSize; i++) |
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219 | { |
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220 | double dElement = Eigenvalues[i]; |
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221 | vdEigenvalues.push_back(dElement); |
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222 | } |
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223 | |
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224 | free(Eigenvalues); |
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225 | free(dCoordinates); |
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226 | } |
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