1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2009-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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5 | //
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6 | // Copyright (C) 2013 Gauthier Brun <brun.gauthier@gmail.com>
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7 | // Copyright (C) 2013 Nicolas Carre <nicolas.carre@ensimag.fr>
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8 | // Copyright (C) 2013 Jean Ceccato <jean.ceccato@ensimag.fr>
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9 | // Copyright (C) 2013 Pierre Zoppitelli <pierre.zoppitelli@ensimag.fr>
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10 | //
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11 | // This Source Code Form is subject to the terms of the Mozilla
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12 | // Public License v. 2.0. If a copy of the MPL was not distributed
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13 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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14 |
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15 | #ifndef EIGEN_SVD_H
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16 | #define EIGEN_SVD_H
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17 |
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18 | namespace Eigen {
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19 | /** \ingroup SVD_Module
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20 | *
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21 | *
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22 | * \class SVDBase
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23 | *
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24 | * \brief Mother class of SVD classes algorithms
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25 | *
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26 | * \param MatrixType the type of the matrix of which we are computing the SVD decomposition
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27 | * SVD decomposition consists in decomposing any n-by-p matrix \a A as a product
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28 | * \f[ A = U S V^* \f]
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29 | * where \a U is a n-by-n unitary, \a V is a p-by-p unitary, and \a S is a n-by-p real positive matrix which is zero outside of its main diagonal;
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30 | * the diagonal entries of S are known as the \em singular \em values of \a A and the columns of \a U and \a V are known as the left
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31 | * and right \em singular \em vectors of \a A respectively.
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32 | *
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33 | * Singular values are always sorted in decreasing order.
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34 | *
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35 | *
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36 | * You can ask for only \em thin \a U or \a V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting \a m be the
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37 | * smaller value among \a n and \a p, there are only \a m singular vectors; the remaining columns of \a U and \a V do not correspond to actual
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38 | * singular vectors. Asking for \em thin \a U or \a V means asking for only their \a m first columns to be formed. So \a U is then a n-by-m matrix,
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39 | * and \a V is then a p-by-m matrix. Notice that thin \a U and \a V are all you need for (least squares) solving.
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40 | *
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41 | * If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to
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42 | * terminate in finite (and reasonable) time.
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43 | * \sa MatrixBase::genericSvd()
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44 | */
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45 | template<typename _MatrixType>
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46 | class SVDBase
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47 | {
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48 |
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49 | public:
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50 | typedef _MatrixType MatrixType;
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51 | typedef typename MatrixType::Scalar Scalar;
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52 | typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
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53 | typedef typename MatrixType::Index Index;
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54 | enum {
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55 | RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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56 | ColsAtCompileTime = MatrixType::ColsAtCompileTime,
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57 | DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime),
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58 | MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
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59 | MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,
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60 | MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime),
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61 | MatrixOptions = MatrixType::Options
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62 | };
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63 |
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64 | typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime,
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65 | MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTime>
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66 | MatrixUType;
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67 | typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime,
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68 | MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTime>
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69 | MatrixVType;
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70 | typedef typename internal::plain_diag_type<MatrixType, RealScalar>::type SingularValuesType;
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71 | typedef typename internal::plain_row_type<MatrixType>::type RowType;
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72 | typedef typename internal::plain_col_type<MatrixType>::type ColType;
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73 | typedef Matrix<Scalar, DiagSizeAtCompileTime, DiagSizeAtCompileTime,
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74 | MatrixOptions, MaxDiagSizeAtCompileTime, MaxDiagSizeAtCompileTime>
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75 | WorkMatrixType;
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76 |
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77 |
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78 |
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79 |
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80 | /** \brief Method performing the decomposition of given matrix using custom options.
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81 | *
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82 | * \param matrix the matrix to decompose
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83 | * \param computationOptions optional parameter allowing to specify if you want full or thin U or V unitaries to be computed.
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84 | * By default, none is computed. This is a bit-field, the possible bits are #ComputeFullU, #ComputeThinU,
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85 | * #ComputeFullV, #ComputeThinV.
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86 | *
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87 | * Thin unitaries are only available if your matrix type has a Dynamic number of columns (for example MatrixXf). They also are not
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88 | * available with the (non-default) FullPivHouseholderQR preconditioner.
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89 | */
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90 | SVDBase& compute(const MatrixType& matrix, unsigned int computationOptions);
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91 |
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92 | /** \brief Method performing the decomposition of given matrix using current options.
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93 | *
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94 | * \param matrix the matrix to decompose
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95 | *
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96 | * This method uses the current \a computationOptions, as already passed to the constructor or to compute(const MatrixType&, unsigned int).
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97 | */
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98 | //virtual SVDBase& compute(const MatrixType& matrix) = 0;
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99 | SVDBase& compute(const MatrixType& matrix);
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100 |
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101 | /** \returns the \a U matrix.
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102 | *
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103 | * For the SVDBase decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
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104 | * the U matrix is n-by-n if you asked for #ComputeFullU, and is n-by-m if you asked for #ComputeThinU.
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105 | *
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106 | * The \a m first columns of \a U are the left singular vectors of the matrix being decomposed.
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107 | *
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108 | * This method asserts that you asked for \a U to be computed.
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109 | */
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110 | const MatrixUType& matrixU() const
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111 | {
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112 | eigen_assert(m_isInitialized && "SVD is not initialized.");
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113 | eigen_assert(computeU() && "This SVD decomposition didn't compute U. Did you ask for it?");
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114 | return m_matrixU;
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115 | }
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116 |
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117 | /** \returns the \a V matrix.
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118 | *
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119 | * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p,
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120 | * the V matrix is p-by-p if you asked for #ComputeFullV, and is p-by-m if you asked for ComputeThinV.
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121 | *
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122 | * The \a m first columns of \a V are the right singular vectors of the matrix being decomposed.
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123 | *
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124 | * This method asserts that you asked for \a V to be computed.
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125 | */
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126 | const MatrixVType& matrixV() const
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127 | {
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128 | eigen_assert(m_isInitialized && "SVD is not initialized.");
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129 | eigen_assert(computeV() && "This SVD decomposition didn't compute V. Did you ask for it?");
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130 | return m_matrixV;
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131 | }
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132 |
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133 | /** \returns the vector of singular values.
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134 | *
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135 | * For the SVD decomposition of a n-by-p matrix, letting \a m be the minimum of \a n and \a p, the
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136 | * returned vector has size \a m. Singular values are always sorted in decreasing order.
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137 | */
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138 | const SingularValuesType& singularValues() const
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139 | {
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140 | eigen_assert(m_isInitialized && "SVD is not initialized.");
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141 | return m_singularValues;
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142 | }
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143 |
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144 |
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145 |
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146 | /** \returns the number of singular values that are not exactly 0 */
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147 | Index nonzeroSingularValues() const
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148 | {
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149 | eigen_assert(m_isInitialized && "SVD is not initialized.");
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150 | return m_nonzeroSingularValues;
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151 | }
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152 |
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153 |
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154 | /** \returns true if \a U (full or thin) is asked for in this SVD decomposition */
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155 | inline bool computeU() const { return m_computeFullU || m_computeThinU; }
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156 | /** \returns true if \a V (full or thin) is asked for in this SVD decomposition */
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157 | inline bool computeV() const { return m_computeFullV || m_computeThinV; }
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158 |
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159 |
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160 | inline Index rows() const { return m_rows; }
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161 | inline Index cols() const { return m_cols; }
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162 |
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163 |
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164 | protected:
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165 | // return true if already allocated
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166 | bool allocate(Index rows, Index cols, unsigned int computationOptions) ;
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167 |
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168 | MatrixUType m_matrixU;
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169 | MatrixVType m_matrixV;
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170 | SingularValuesType m_singularValues;
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171 | bool m_isInitialized, m_isAllocated;
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172 | bool m_computeFullU, m_computeThinU;
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173 | bool m_computeFullV, m_computeThinV;
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174 | unsigned int m_computationOptions;
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175 | Index m_nonzeroSingularValues, m_rows, m_cols, m_diagSize;
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176 |
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177 |
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178 | /** \brief Default Constructor.
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179 | *
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180 | * Default constructor of SVDBase
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181 | */
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182 | SVDBase()
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183 | : m_isInitialized(false),
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184 | m_isAllocated(false),
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185 | m_computationOptions(0),
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186 | m_rows(-1), m_cols(-1)
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187 | {}
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188 |
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189 |
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190 | };
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191 |
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192 |
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193 | template<typename MatrixType>
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194 | bool SVDBase<MatrixType>::allocate(Index rows, Index cols, unsigned int computationOptions)
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195 | {
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196 | eigen_assert(rows >= 0 && cols >= 0);
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197 |
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198 | if (m_isAllocated &&
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199 | rows == m_rows &&
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200 | cols == m_cols &&
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201 | computationOptions == m_computationOptions)
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202 | {
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203 | return true;
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204 | }
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205 |
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206 | m_rows = rows;
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207 | m_cols = cols;
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208 | m_isInitialized = false;
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209 | m_isAllocated = true;
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210 | m_computationOptions = computationOptions;
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211 | m_computeFullU = (computationOptions & ComputeFullU) != 0;
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212 | m_computeThinU = (computationOptions & ComputeThinU) != 0;
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213 | m_computeFullV = (computationOptions & ComputeFullV) != 0;
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214 | m_computeThinV = (computationOptions & ComputeThinV) != 0;
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215 | eigen_assert(!(m_computeFullU && m_computeThinU) && "SVDBase: you can't ask for both full and thin U");
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216 | eigen_assert(!(m_computeFullV && m_computeThinV) && "SVDBase: you can't ask for both full and thin V");
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217 | eigen_assert(EIGEN_IMPLIES(m_computeThinU || m_computeThinV, MatrixType::ColsAtCompileTime==Dynamic) &&
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218 | "SVDBase: thin U and V are only available when your matrix has a dynamic number of columns.");
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219 |
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220 | m_diagSize = (std::min)(m_rows, m_cols);
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221 | m_singularValues.resize(m_diagSize);
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222 | if(RowsAtCompileTime==Dynamic)
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223 | m_matrixU.resize(m_rows, m_computeFullU ? m_rows
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224 | : m_computeThinU ? m_diagSize
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225 | : 0);
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226 | if(ColsAtCompileTime==Dynamic)
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227 | m_matrixV.resize(m_cols, m_computeFullV ? m_cols
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228 | : m_computeThinV ? m_diagSize
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229 | : 0);
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230 |
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231 | return false;
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232 | }
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233 |
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234 | }// end namespace
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235 |
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236 | #endif // EIGEN_SVD_H
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