[136] | 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 Gael Guennebaud <gael.guennebaud@inria.fr>
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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_SELFADJOINTMATRIX_H
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| 11 | #define EIGEN_SELFADJOINTMATRIX_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | /** \class SelfAdjointView
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| 16 | * \ingroup Core_Module
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| 17 | *
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| 18 | *
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| 19 | * \brief Expression of a selfadjoint matrix from a triangular part of a dense matrix
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| 20 | *
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| 21 | * \param MatrixType the type of the dense matrix storing the coefficients
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| 22 | * \param TriangularPart can be either \c #Lower or \c #Upper
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| 23 | *
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| 24 | * This class is an expression of a sefladjoint matrix from a triangular part of a matrix
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| 25 | * with given dense storage of the coefficients. It is the return type of MatrixBase::selfadjointView()
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| 26 | * and most of the time this is the only way that it is used.
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| 27 | *
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| 28 | * \sa class TriangularBase, MatrixBase::selfadjointView()
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| 29 | */
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| 30 |
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| 31 | namespace internal {
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| 32 | template<typename MatrixType, unsigned int UpLo>
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| 33 | struct traits<SelfAdjointView<MatrixType, UpLo> > : traits<MatrixType>
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| 34 | {
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| 35 | typedef typename nested<MatrixType>::type MatrixTypeNested;
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| 36 | typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
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| 37 | typedef MatrixType ExpressionType;
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| 38 | typedef typename MatrixType::PlainObject DenseMatrixType;
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| 39 | enum {
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| 40 | Mode = UpLo | SelfAdjoint,
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| 41 | Flags = MatrixTypeNestedCleaned::Flags & (HereditaryBits)
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| 42 | & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)), // FIXME these flags should be preserved
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| 43 | CoeffReadCost = MatrixTypeNestedCleaned::CoeffReadCost
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| 44 | };
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| 45 | };
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| 46 | }
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| 47 |
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| 48 | template <typename Lhs, int LhsMode, bool LhsIsVector,
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| 49 | typename Rhs, int RhsMode, bool RhsIsVector>
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| 50 | struct SelfadjointProductMatrix;
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| 51 |
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| 52 | // FIXME could also be called SelfAdjointWrapper to be consistent with DiagonalWrapper ??
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| 53 | template<typename MatrixType, unsigned int UpLo> class SelfAdjointView
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| 54 | : public TriangularBase<SelfAdjointView<MatrixType, UpLo> >
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| 55 | {
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| 56 | public:
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| 57 |
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| 58 | typedef TriangularBase<SelfAdjointView> Base;
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| 59 | typedef typename internal::traits<SelfAdjointView>::MatrixTypeNested MatrixTypeNested;
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| 60 | typedef typename internal::traits<SelfAdjointView>::MatrixTypeNestedCleaned MatrixTypeNestedCleaned;
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| 61 |
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| 62 | /** \brief The type of coefficients in this matrix */
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| 63 | typedef typename internal::traits<SelfAdjointView>::Scalar Scalar;
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| 64 |
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| 65 | typedef typename MatrixType::Index Index;
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| 66 |
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| 67 | enum {
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| 68 | Mode = internal::traits<SelfAdjointView>::Mode
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| 69 | };
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| 70 | typedef typename MatrixType::PlainObject PlainObject;
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| 71 |
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| 72 | inline SelfAdjointView(MatrixType& matrix) : m_matrix(matrix)
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| 73 | {}
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| 74 |
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| 75 | inline Index rows() const { return m_matrix.rows(); }
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| 76 | inline Index cols() const { return m_matrix.cols(); }
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| 77 | inline Index outerStride() const { return m_matrix.outerStride(); }
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| 78 | inline Index innerStride() const { return m_matrix.innerStride(); }
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| 79 |
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| 80 | /** \sa MatrixBase::coeff()
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| 81 | * \warning the coordinates must fit into the referenced triangular part
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| 82 | */
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| 83 | inline Scalar coeff(Index row, Index col) const
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| 84 | {
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| 85 | Base::check_coordinates_internal(row, col);
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| 86 | return m_matrix.coeff(row, col);
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| 87 | }
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| 88 |
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| 89 | /** \sa MatrixBase::coeffRef()
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| 90 | * \warning the coordinates must fit into the referenced triangular part
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| 91 | */
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| 92 | inline Scalar& coeffRef(Index row, Index col)
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| 93 | {
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| 94 | Base::check_coordinates_internal(row, col);
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| 95 | return m_matrix.const_cast_derived().coeffRef(row, col);
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| 96 | }
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| 97 |
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| 98 | /** \internal */
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| 99 | const MatrixTypeNestedCleaned& _expression() const { return m_matrix; }
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| 100 |
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| 101 | const MatrixTypeNestedCleaned& nestedExpression() const { return m_matrix; }
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| 102 | MatrixTypeNestedCleaned& nestedExpression() { return *const_cast<MatrixTypeNestedCleaned*>(&m_matrix); }
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| 103 |
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| 104 | /** Efficient self-adjoint matrix times vector/matrix product */
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| 105 | template<typename OtherDerived>
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| 106 | SelfadjointProductMatrix<MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
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| 107 | operator*(const MatrixBase<OtherDerived>& rhs) const
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| 108 | {
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| 109 | return SelfadjointProductMatrix
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| 110 | <MatrixType,Mode,false,OtherDerived,0,OtherDerived::IsVectorAtCompileTime>
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| 111 | (m_matrix, rhs.derived());
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| 112 | }
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| 113 |
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| 114 | /** Efficient vector/matrix times self-adjoint matrix product */
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| 115 | template<typename OtherDerived> friend
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| 116 | SelfadjointProductMatrix<OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
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| 117 | operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView& rhs)
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| 118 | {
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| 119 | return SelfadjointProductMatrix
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| 120 | <OtherDerived,0,OtherDerived::IsVectorAtCompileTime,MatrixType,Mode,false>
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| 121 | (lhs.derived(),rhs.m_matrix);
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| 122 | }
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| 123 |
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| 124 | /** Perform a symmetric rank 2 update of the selfadjoint matrix \c *this:
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| 125 | * \f$ this = this + \alpha u v^* + conj(\alpha) v u^* \f$
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| 126 | * \returns a reference to \c *this
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| 127 | *
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| 128 | * The vectors \a u and \c v \b must be column vectors, however they can be
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| 129 | * a adjoint expression without any overhead. Only the meaningful triangular
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| 130 | * part of the matrix is updated, the rest is left unchanged.
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| 131 | *
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| 132 | * \sa rankUpdate(const MatrixBase<DerivedU>&, Scalar)
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| 133 | */
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| 134 | template<typename DerivedU, typename DerivedV>
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| 135 | SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const MatrixBase<DerivedV>& v, const Scalar& alpha = Scalar(1));
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| 136 |
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| 137 | /** Perform a symmetric rank K update of the selfadjoint matrix \c *this:
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| 138 | * \f$ this = this + \alpha ( u u^* ) \f$ where \a u is a vector or matrix.
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| 139 | *
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| 140 | * \returns a reference to \c *this
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| 141 | *
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| 142 | * Note that to perform \f$ this = this + \alpha ( u^* u ) \f$ you can simply
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| 143 | * call this function with u.adjoint().
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| 144 | *
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| 145 | * \sa rankUpdate(const MatrixBase<DerivedU>&, const MatrixBase<DerivedV>&, Scalar)
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| 146 | */
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| 147 | template<typename DerivedU>
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| 148 | SelfAdjointView& rankUpdate(const MatrixBase<DerivedU>& u, const Scalar& alpha = Scalar(1));
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| 149 |
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| 150 | /////////// Cholesky module ///////////
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| 151 |
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| 152 | const LLT<PlainObject, UpLo> llt() const;
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| 153 | const LDLT<PlainObject, UpLo> ldlt() const;
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| 154 |
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| 155 | /////////// Eigenvalue module ///////////
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| 156 |
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| 157 | /** Real part of #Scalar */
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| 158 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 159 | /** Return type of eigenvalues() */
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| 160 | typedef Matrix<RealScalar, internal::traits<MatrixType>::ColsAtCompileTime, 1> EigenvaluesReturnType;
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| 161 |
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| 162 | EigenvaluesReturnType eigenvalues() const;
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| 163 | RealScalar operatorNorm() const;
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| 164 |
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| 165 | #ifdef EIGEN2_SUPPORT
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| 166 | template<typename OtherDerived>
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| 167 | SelfAdjointView& operator=(const MatrixBase<OtherDerived>& other)
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| 168 | {
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| 169 | enum {
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| 170 | OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
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| 171 | };
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| 172 | m_matrix.const_cast_derived().template triangularView<UpLo>() = other;
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| 173 | m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.adjoint();
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| 174 | return *this;
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| 175 | }
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| 176 | template<typename OtherMatrixType, unsigned int OtherMode>
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| 177 | SelfAdjointView& operator=(const TriangularView<OtherMatrixType, OtherMode>& other)
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| 178 | {
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| 179 | enum {
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| 180 | OtherPart = UpLo == Upper ? StrictlyLower : StrictlyUpper
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| 181 | };
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| 182 | m_matrix.const_cast_derived().template triangularView<UpLo>() = other.toDenseMatrix();
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| 183 | m_matrix.const_cast_derived().template triangularView<OtherPart>() = other.toDenseMatrix().adjoint();
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| 184 | return *this;
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| 185 | }
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| 186 | #endif
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| 187 |
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| 188 | protected:
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| 189 | MatrixTypeNested m_matrix;
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| 190 | };
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| 191 |
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| 192 |
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| 193 | // template<typename OtherDerived, typename MatrixType, unsigned int UpLo>
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| 194 | // internal::selfadjoint_matrix_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >
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| 195 | // operator*(const MatrixBase<OtherDerived>& lhs, const SelfAdjointView<MatrixType,UpLo>& rhs)
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| 196 | // {
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| 197 | // return internal::matrix_selfadjoint_product_returntype<OtherDerived,SelfAdjointView<MatrixType,UpLo> >(lhs.derived(),rhs);
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| 198 | // }
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| 199 |
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| 200 | // selfadjoint to dense matrix
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| 201 |
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| 202 | namespace internal {
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| 203 |
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| 204 | template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
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| 205 | struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount, ClearOpposite>
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| 206 | {
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| 207 | enum {
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| 208 | col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
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| 209 | row = (UnrollCount-1) % Derived1::RowsAtCompileTime
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| 210 | };
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| 211 |
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| 212 | static inline void run(Derived1 &dst, const Derived2 &src)
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| 213 | {
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| 214 | triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Upper), UnrollCount-1, ClearOpposite>::run(dst, src);
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| 215 |
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| 216 | if(row == col)
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| 217 | dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
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| 218 | else if(row < col)
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| 219 | dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
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| 220 | }
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| 221 | };
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| 222 |
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| 223 | template<typename Derived1, typename Derived2, bool ClearOpposite>
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| 224 | struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, 0, ClearOpposite>
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| 225 | {
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| 226 | static inline void run(Derived1 &, const Derived2 &) {}
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| 227 | };
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| 228 |
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| 229 | template<typename Derived1, typename Derived2, int UnrollCount, bool ClearOpposite>
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| 230 | struct triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount, ClearOpposite>
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| 231 | {
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| 232 | enum {
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| 233 | col = (UnrollCount-1) / Derived1::RowsAtCompileTime,
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| 234 | row = (UnrollCount-1) % Derived1::RowsAtCompileTime
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| 235 | };
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| 236 |
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| 237 | static inline void run(Derived1 &dst, const Derived2 &src)
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| 238 | {
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| 239 | triangular_assignment_selector<Derived1, Derived2, (SelfAdjoint|Lower), UnrollCount-1, ClearOpposite>::run(dst, src);
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| 240 |
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| 241 | if(row == col)
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| 242 | dst.coeffRef(row, col) = numext::real(src.coeff(row, col));
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| 243 | else if(row > col)
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| 244 | dst.coeffRef(col, row) = numext::conj(dst.coeffRef(row, col) = src.coeff(row, col));
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| 245 | }
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| 246 | };
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| 247 |
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| 248 | template<typename Derived1, typename Derived2, bool ClearOpposite>
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| 249 | struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, 0, ClearOpposite>
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| 250 | {
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| 251 | static inline void run(Derived1 &, const Derived2 &) {}
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| 252 | };
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| 253 |
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| 254 | template<typename Derived1, typename Derived2, bool ClearOpposite>
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| 255 | struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Upper, Dynamic, ClearOpposite>
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| 256 | {
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| 257 | typedef typename Derived1::Index Index;
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| 258 | static inline void run(Derived1 &dst, const Derived2 &src)
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| 259 | {
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| 260 | for(Index j = 0; j < dst.cols(); ++j)
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| 261 | {
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| 262 | for(Index i = 0; i < j; ++i)
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| 263 | {
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| 264 | dst.copyCoeff(i, j, src);
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| 265 | dst.coeffRef(j,i) = numext::conj(dst.coeff(i,j));
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| 266 | }
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| 267 | dst.copyCoeff(j, j, src);
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| 268 | }
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| 269 | }
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| 270 | };
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| 271 |
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| 272 | template<typename Derived1, typename Derived2, bool ClearOpposite>
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| 273 | struct triangular_assignment_selector<Derived1, Derived2, SelfAdjoint|Lower, Dynamic, ClearOpposite>
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| 274 | {
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| 275 | static inline void run(Derived1 &dst, const Derived2 &src)
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| 276 | {
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| 277 | typedef typename Derived1::Index Index;
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| 278 | for(Index i = 0; i < dst.rows(); ++i)
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| 279 | {
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| 280 | for(Index j = 0; j < i; ++j)
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| 281 | {
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| 282 | dst.copyCoeff(i, j, src);
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| 283 | dst.coeffRef(j,i) = numext::conj(dst.coeff(i,j));
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| 284 | }
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| 285 | dst.copyCoeff(i, i, src);
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| 286 | }
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| 287 | }
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| 288 | };
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| 289 |
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| 290 | } // end namespace internal
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| 291 |
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| 292 | /***************************************************************************
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| 293 | * Implementation of MatrixBase methods
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| 294 | ***************************************************************************/
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| 295 |
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| 296 | template<typename Derived>
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| 297 | template<unsigned int UpLo>
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| 298 | typename MatrixBase<Derived>::template ConstSelfAdjointViewReturnType<UpLo>::Type
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| 299 | MatrixBase<Derived>::selfadjointView() const
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| 300 | {
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| 301 | return derived();
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| 302 | }
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| 303 |
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| 304 | template<typename Derived>
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| 305 | template<unsigned int UpLo>
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| 306 | typename MatrixBase<Derived>::template SelfAdjointViewReturnType<UpLo>::Type
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| 307 | MatrixBase<Derived>::selfadjointView()
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| 308 | {
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| 309 | return derived();
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| 310 | }
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| 311 |
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| 312 | } // end namespace Eigen
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| 313 |
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| 314 | #endif // EIGEN_SELFADJOINTMATRIX_H
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