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) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | #ifndef EIGEN_BIDIAGONALIZATION_H
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11 | #define EIGEN_BIDIAGONALIZATION_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | namespace internal {
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16 | // UpperBidiagonalization will probably be replaced by a Bidiagonalization class, don't want to make it stable API.
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17 | // At the same time, it's useful to keep for now as it's about the only thing that is testing the BandMatrix class.
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18 |
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19 | template<typename _MatrixType> class UpperBidiagonalization
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20 | {
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21 | public:
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22 |
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23 | typedef _MatrixType MatrixType;
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24 | enum {
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25 | RowsAtCompileTime = MatrixType::RowsAtCompileTime,
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26 | ColsAtCompileTime = MatrixType::ColsAtCompileTime,
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27 | ColsAtCompileTimeMinusOne = internal::decrement_size<ColsAtCompileTime>::ret
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28 | };
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29 | typedef typename MatrixType::Scalar Scalar;
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30 | typedef typename MatrixType::RealScalar RealScalar;
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31 | typedef typename MatrixType::Index Index;
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32 | typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
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33 | typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
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34 | typedef BandMatrix<RealScalar, ColsAtCompileTime, ColsAtCompileTime, 1, 0> BidiagonalType;
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35 | typedef Matrix<Scalar, ColsAtCompileTime, 1> DiagVectorType;
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36 | typedef Matrix<Scalar, ColsAtCompileTimeMinusOne, 1> SuperDiagVectorType;
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37 | typedef HouseholderSequence<
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38 | const MatrixType,
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39 | CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>, const Diagonal<const MatrixType,0> >
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40 | > HouseholderUSequenceType;
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41 | typedef HouseholderSequence<
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42 | const typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type,
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43 | Diagonal<const MatrixType,1>,
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44 | OnTheRight
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45 | > HouseholderVSequenceType;
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46 |
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47 | /**
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48 | * \brief Default Constructor.
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49 | *
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50 | * The default constructor is useful in cases in which the user intends to
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51 | * perform decompositions via Bidiagonalization::compute(const MatrixType&).
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52 | */
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53 | UpperBidiagonalization() : m_householder(), m_bidiagonal(), m_isInitialized(false) {}
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54 |
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55 | UpperBidiagonalization(const MatrixType& matrix)
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56 | : m_householder(matrix.rows(), matrix.cols()),
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57 | m_bidiagonal(matrix.cols(), matrix.cols()),
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58 | m_isInitialized(false)
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59 | {
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60 | compute(matrix);
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61 | }
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62 |
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63 | UpperBidiagonalization& compute(const MatrixType& matrix);
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64 |
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65 | const MatrixType& householder() const { return m_householder; }
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66 | const BidiagonalType& bidiagonal() const { return m_bidiagonal; }
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67 |
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68 | const HouseholderUSequenceType householderU() const
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69 | {
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70 | eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
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71 | return HouseholderUSequenceType(m_householder, m_householder.diagonal().conjugate());
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72 | }
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73 |
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74 | const HouseholderVSequenceType householderV() // const here gives nasty errors and i'm lazy
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75 | {
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76 | eigen_assert(m_isInitialized && "UpperBidiagonalization is not initialized.");
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77 | return HouseholderVSequenceType(m_householder.conjugate(), m_householder.const_derived().template diagonal<1>())
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78 | .setLength(m_householder.cols()-1)
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79 | .setShift(1);
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80 | }
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81 |
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82 | protected:
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83 | MatrixType m_householder;
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84 | BidiagonalType m_bidiagonal;
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85 | bool m_isInitialized;
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86 | };
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87 |
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88 | template<typename _MatrixType>
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89 | UpperBidiagonalization<_MatrixType>& UpperBidiagonalization<_MatrixType>::compute(const _MatrixType& matrix)
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90 | {
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91 | Index rows = matrix.rows();
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92 | Index cols = matrix.cols();
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93 |
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94 | eigen_assert(rows >= cols && "UpperBidiagonalization is only for matrices satisfying rows>=cols.");
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95 |
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96 | m_householder = matrix;
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97 |
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98 | ColVectorType temp(rows);
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99 |
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100 | for (Index k = 0; /* breaks at k==cols-1 below */ ; ++k)
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101 | {
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102 | Index remainingRows = rows - k;
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103 | Index remainingCols = cols - k - 1;
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104 |
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105 | // construct left householder transform in-place in m_householder
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106 | m_householder.col(k).tail(remainingRows)
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107 | .makeHouseholderInPlace(m_householder.coeffRef(k,k),
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108 | m_bidiagonal.template diagonal<0>().coeffRef(k));
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109 | // apply householder transform to remaining part of m_householder on the left
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110 | m_householder.bottomRightCorner(remainingRows, remainingCols)
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111 | .applyHouseholderOnTheLeft(m_householder.col(k).tail(remainingRows-1),
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112 | m_householder.coeff(k,k),
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113 | temp.data());
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114 |
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115 | if(k == cols-1) break;
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116 |
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117 | // construct right householder transform in-place in m_householder
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118 | m_householder.row(k).tail(remainingCols)
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119 | .makeHouseholderInPlace(m_householder.coeffRef(k,k+1),
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120 | m_bidiagonal.template diagonal<1>().coeffRef(k));
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121 | // apply householder transform to remaining part of m_householder on the left
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122 | m_householder.bottomRightCorner(remainingRows-1, remainingCols)
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123 | .applyHouseholderOnTheRight(m_householder.row(k).tail(remainingCols-1).transpose(),
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124 | m_householder.coeff(k,k+1),
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125 | temp.data());
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126 | }
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127 | m_isInitialized = true;
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128 | return *this;
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129 | }
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130 |
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131 | #if 0
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132 | /** \return the Householder QR decomposition of \c *this.
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133 | *
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134 | * \sa class Bidiagonalization
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135 | */
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136 | template<typename Derived>
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137 | const UpperBidiagonalization<typename MatrixBase<Derived>::PlainObject>
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138 | MatrixBase<Derived>::bidiagonalization() const
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139 | {
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140 | return UpperBidiagonalization<PlainObject>(eval());
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141 | }
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142 | #endif
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143 |
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144 | } // end namespace internal
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145 |
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146 | } // end namespace Eigen
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147 |
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148 | #endif // EIGEN_BIDIAGONALIZATION_H
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