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https://gitlab.com/libeigen/eigen.git
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91b3039013
The previous "Scalar" semantic was obsolete since we allow for different scalar types in the source and destination expressions. On can still specialize on scalar types through SFINAE and/or assignment functor.
973 lines
36 KiB
C++
973 lines
36 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_TRIANGULARMATRIX_H
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#define EIGEN_TRIANGULARMATRIX_H
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namespace Eigen {
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namespace internal {
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template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval;
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}
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/** \class TriangularBase
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* \ingroup Core_Module
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*
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* \brief Base class for triangular part in a matrix
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*/
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template<typename Derived> class TriangularBase : public EigenBase<Derived>
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{
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public:
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enum {
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Mode = internal::traits<Derived>::Mode,
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RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
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ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
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MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
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MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
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SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
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internal::traits<Derived>::ColsAtCompileTime>::ret),
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/**< This is equal to the number of coefficients, i.e. the number of
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* rows times the number of columns, or to \a Dynamic if this is not
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* known at compile-time. \sa RowsAtCompileTime, ColsAtCompileTime */
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MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
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internal::traits<Derived>::MaxColsAtCompileTime>::ret)
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};
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typedef typename internal::traits<Derived>::Scalar Scalar;
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typedef typename internal::traits<Derived>::StorageKind StorageKind;
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typedef typename internal::traits<Derived>::StorageIndex StorageIndex;
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typedef typename internal::traits<Derived>::FullMatrixType DenseMatrixType;
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typedef DenseMatrixType DenseType;
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typedef Derived const& Nested;
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EIGEN_DEVICE_FUNC
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inline TriangularBase() { eigen_assert(!((Mode&UnitDiag) && (Mode&ZeroDiag))); }
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EIGEN_DEVICE_FUNC
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inline Index rows() const { return derived().rows(); }
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EIGEN_DEVICE_FUNC
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inline Index cols() const { return derived().cols(); }
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EIGEN_DEVICE_FUNC
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inline Index outerStride() const { return derived().outerStride(); }
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EIGEN_DEVICE_FUNC
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inline Index innerStride() const { return derived().innerStride(); }
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// dummy resize function
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void resize(Index rows, Index cols)
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{
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EIGEN_UNUSED_VARIABLE(rows);
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EIGEN_UNUSED_VARIABLE(cols);
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eigen_assert(rows==this->rows() && cols==this->cols());
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}
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EIGEN_DEVICE_FUNC
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inline Scalar coeff(Index row, Index col) const { return derived().coeff(row,col); }
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EIGEN_DEVICE_FUNC
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inline Scalar& coeffRef(Index row, Index col) { return derived().coeffRef(row,col); }
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/** \see MatrixBase::copyCoeff(row,col)
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*/
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template<typename Other>
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EIGEN_DEVICE_FUNC
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EIGEN_STRONG_INLINE void copyCoeff(Index row, Index col, Other& other)
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{
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derived().coeffRef(row, col) = other.coeff(row, col);
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}
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EIGEN_DEVICE_FUNC
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inline Scalar operator()(Index row, Index col) const
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{
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check_coordinates(row, col);
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return coeff(row,col);
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}
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EIGEN_DEVICE_FUNC
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inline Scalar& operator()(Index row, Index col)
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{
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check_coordinates(row, col);
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return coeffRef(row,col);
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}
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#ifndef EIGEN_PARSED_BY_DOXYGEN
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EIGEN_DEVICE_FUNC
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inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
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EIGEN_DEVICE_FUNC
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inline Derived& derived() { return *static_cast<Derived*>(this); }
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#endif // not EIGEN_PARSED_BY_DOXYGEN
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template<typename DenseDerived>
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EIGEN_DEVICE_FUNC
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void evalTo(MatrixBase<DenseDerived> &other) const;
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template<typename DenseDerived>
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EIGEN_DEVICE_FUNC
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void evalToLazy(MatrixBase<DenseDerived> &other) const;
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EIGEN_DEVICE_FUNC
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DenseMatrixType toDenseMatrix() const
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{
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DenseMatrixType res(rows(), cols());
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evalToLazy(res);
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return res;
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}
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protected:
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void check_coordinates(Index row, Index col) const
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{
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EIGEN_ONLY_USED_FOR_DEBUG(row);
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EIGEN_ONLY_USED_FOR_DEBUG(col);
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eigen_assert(col>=0 && col<cols() && row>=0 && row<rows());
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const int mode = int(Mode) & ~SelfAdjoint;
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EIGEN_ONLY_USED_FOR_DEBUG(mode);
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eigen_assert((mode==Upper && col>=row)
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|| (mode==Lower && col<=row)
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|| ((mode==StrictlyUpper || mode==UnitUpper) && col>row)
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|| ((mode==StrictlyLower || mode==UnitLower) && col<row));
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}
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#ifdef EIGEN_INTERNAL_DEBUGGING
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void check_coordinates_internal(Index row, Index col) const
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{
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check_coordinates(row, col);
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}
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#else
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void check_coordinates_internal(Index , Index ) const {}
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#endif
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};
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/** \class TriangularView
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* \ingroup Core_Module
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*
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* \brief Expression of a triangular part in a matrix
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*
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* \param MatrixType the type of the object in which we are taking the triangular part
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* \param Mode the kind of triangular matrix expression to construct. Can be #Upper,
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* #Lower, #UnitUpper, #UnitLower, #StrictlyUpper, or #StrictlyLower.
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* This is in fact a bit field; it must have either #Upper or #Lower,
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* and additionally it may have #UnitDiag or #ZeroDiag or neither.
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*
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* This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular
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* matrices one should speak of "trapezoid" parts. This class is the return type
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* of MatrixBase::triangularView() and SparseMatrixBase::triangularView(), and most of the time this is the only way it is used.
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*
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* \sa MatrixBase::triangularView()
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*/
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namespace internal {
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template<typename MatrixType, unsigned int _Mode>
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struct traits<TriangularView<MatrixType, _Mode> > : traits<MatrixType>
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{
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typedef typename ref_selector<MatrixType>::non_const_type MatrixTypeNested;
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typedef typename remove_reference<MatrixTypeNested>::type MatrixTypeNestedNonRef;
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typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
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typedef typename MatrixType::PlainObject FullMatrixType;
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typedef MatrixType ExpressionType;
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enum {
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Mode = _Mode,
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FlagsLvalueBit = is_lvalue<MatrixType>::value ? LvalueBit : 0,
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Flags = (MatrixTypeNestedCleaned::Flags & (HereditaryBits | FlagsLvalueBit) & (~(PacketAccessBit | DirectAccessBit | LinearAccessBit)))
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};
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};
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}
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template<typename _MatrixType, unsigned int _Mode, typename StorageKind> class TriangularViewImpl;
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template<typename _MatrixType, unsigned int _Mode> class TriangularView
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: public TriangularViewImpl<_MatrixType, _Mode, typename internal::traits<_MatrixType>::StorageKind >
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{
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public:
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typedef TriangularViewImpl<_MatrixType, _Mode, typename internal::traits<_MatrixType>::StorageKind > Base;
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typedef typename internal::traits<TriangularView>::Scalar Scalar;
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typedef _MatrixType MatrixType;
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protected:
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typedef typename internal::traits<TriangularView>::MatrixTypeNested MatrixTypeNested;
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typedef typename internal::traits<TriangularView>::MatrixTypeNestedNonRef MatrixTypeNestedNonRef;
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typedef typename internal::remove_all<typename MatrixType::ConjugateReturnType>::type MatrixConjugateReturnType;
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public:
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typedef typename internal::traits<TriangularView>::StorageKind StorageKind;
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typedef typename internal::traits<TriangularView>::MatrixTypeNestedCleaned NestedExpression;
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enum {
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Mode = _Mode,
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Flags = internal::traits<TriangularView>::Flags,
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TransposeMode = (Mode & Upper ? Lower : 0)
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| (Mode & Lower ? Upper : 0)
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| (Mode & (UnitDiag))
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| (Mode & (ZeroDiag)),
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IsVectorAtCompileTime = false
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};
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EIGEN_DEVICE_FUNC
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explicit inline TriangularView(MatrixType& matrix) : m_matrix(matrix)
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{}
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using Base::operator=;
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TriangularView& operator=(const TriangularView &other)
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{ return Base::operator=(other); }
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/** \copydoc EigenBase::rows() */
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EIGEN_DEVICE_FUNC
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inline Index rows() const { return m_matrix.rows(); }
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/** \copydoc EigenBase::cols() */
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EIGEN_DEVICE_FUNC
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inline Index cols() const { return m_matrix.cols(); }
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/** \returns a const reference to the nested expression */
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EIGEN_DEVICE_FUNC
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const NestedExpression& nestedExpression() const { return m_matrix; }
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/** \returns a reference to the nested expression */
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EIGEN_DEVICE_FUNC
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NestedExpression& nestedExpression() { return m_matrix; }
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typedef TriangularView<const MatrixConjugateReturnType,Mode> ConjugateReturnType;
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/** \sa MatrixBase::conjugate() const */
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EIGEN_DEVICE_FUNC
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inline const ConjugateReturnType conjugate() const
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{ return ConjugateReturnType(m_matrix.conjugate()); }
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typedef TriangularView<const typename MatrixType::AdjointReturnType,TransposeMode> AdjointReturnType;
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/** \sa MatrixBase::adjoint() const */
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EIGEN_DEVICE_FUNC
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inline const AdjointReturnType adjoint() const
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{ return AdjointReturnType(m_matrix.adjoint()); }
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typedef TriangularView<typename MatrixType::TransposeReturnType,TransposeMode> TransposeReturnType;
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/** \sa MatrixBase::transpose() */
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EIGEN_DEVICE_FUNC
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inline TransposeReturnType transpose()
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{
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EIGEN_STATIC_ASSERT_LVALUE(MatrixType)
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typename MatrixType::TransposeReturnType tmp(m_matrix);
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return TransposeReturnType(tmp);
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}
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typedef TriangularView<const typename MatrixType::ConstTransposeReturnType,TransposeMode> ConstTransposeReturnType;
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/** \sa MatrixBase::transpose() const */
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EIGEN_DEVICE_FUNC
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inline const ConstTransposeReturnType transpose() const
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{
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return ConstTransposeReturnType(m_matrix.transpose());
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}
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template<typename Other>
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EIGEN_DEVICE_FUNC
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inline const Solve<TriangularView, Other>
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solve(const MatrixBase<Other>& other) const
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{ return Solve<TriangularView, Other>(*this, other.derived()); }
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// workaround MSVC ICE
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#if EIGEN_COMP_MSVC
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template<int Side, typename Other>
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EIGEN_DEVICE_FUNC
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inline const internal::triangular_solve_retval<Side,TriangularView, Other>
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solve(const MatrixBase<Other>& other) const
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{ return Base::template solve<Side>(other); }
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#else
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using Base::solve;
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#endif
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/** \returns a selfadjoint view of the referenced triangular part which must be either \c #Upper or \c #Lower.
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*
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* This is a shortcut for \code this->nestedExpression().selfadjointView<(*this)::Mode>() \endcode
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* \sa MatrixBase::selfadjointView() */
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EIGEN_DEVICE_FUNC
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SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView()
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{
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EIGEN_STATIC_ASSERT((Mode&(UnitDiag|ZeroDiag))==0,PROGRAMMING_ERROR);
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return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
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}
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/** This is the const version of selfadjointView() */
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EIGEN_DEVICE_FUNC
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const SelfAdjointView<MatrixTypeNestedNonRef,Mode> selfadjointView() const
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{
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EIGEN_STATIC_ASSERT((Mode&(UnitDiag|ZeroDiag))==0,PROGRAMMING_ERROR);
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return SelfAdjointView<MatrixTypeNestedNonRef,Mode>(m_matrix);
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}
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/** \returns the determinant of the triangular matrix
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* \sa MatrixBase::determinant() */
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EIGEN_DEVICE_FUNC
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Scalar determinant() const
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{
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if (Mode & UnitDiag)
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return 1;
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else if (Mode & ZeroDiag)
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return 0;
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else
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return m_matrix.diagonal().prod();
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}
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protected:
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MatrixTypeNested m_matrix;
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};
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/** \ingroup Core_Module
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*
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* \brief Base class for a triangular part in a \b dense matrix
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*
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* This class is an abstract base class of class TriangularView, and objects of type TriangularViewImpl cannot be instantiated.
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* It extends class TriangularView with additional methods which available for dense expressions only.
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*
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* \sa class TriangularView, MatrixBase::triangularView()
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*/
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template<typename _MatrixType, unsigned int _Mode> class TriangularViewImpl<_MatrixType,_Mode,Dense>
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: public TriangularBase<TriangularView<_MatrixType, _Mode> >
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{
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public:
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typedef TriangularView<_MatrixType, _Mode> TriangularViewType;
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typedef TriangularBase<TriangularViewType> Base;
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typedef typename internal::traits<TriangularViewType>::Scalar Scalar;
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typedef _MatrixType MatrixType;
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typedef typename MatrixType::PlainObject DenseMatrixType;
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typedef DenseMatrixType PlainObject;
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public:
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using Base::evalToLazy;
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using Base::derived;
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typedef typename internal::traits<TriangularViewType>::StorageKind StorageKind;
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enum {
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Mode = _Mode,
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Flags = internal::traits<TriangularViewType>::Flags
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};
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/** \returns the outer-stride of the underlying dense matrix
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* \sa DenseCoeffsBase::outerStride() */
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EIGEN_DEVICE_FUNC
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inline Index outerStride() const { return derived().nestedExpression().outerStride(); }
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/** \returns the inner-stride of the underlying dense matrix
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* \sa DenseCoeffsBase::innerStride() */
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EIGEN_DEVICE_FUNC
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inline Index innerStride() const { return derived().nestedExpression().innerStride(); }
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/** \sa MatrixBase::operator+=() */
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template<typename Other>
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EIGEN_DEVICE_FUNC
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TriangularViewType& operator+=(const DenseBase<Other>& other) {
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internal::call_assignment_no_alias(derived(), other.derived(), internal::add_assign_op<Scalar,typename Other::Scalar>());
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return derived();
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}
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/** \sa MatrixBase::operator-=() */
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template<typename Other>
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EIGEN_DEVICE_FUNC
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TriangularViewType& operator-=(const DenseBase<Other>& other) {
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internal::call_assignment_no_alias(derived(), other.derived(), internal::sub_assign_op<Scalar,typename Other::Scalar>());
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return derived();
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}
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/** \sa MatrixBase::operator*=() */
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EIGEN_DEVICE_FUNC
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TriangularViewType& operator*=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = derived().nestedExpression() * other; }
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/** \sa DenseBase::operator/=() */
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EIGEN_DEVICE_FUNC
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TriangularViewType& operator/=(const typename internal::traits<MatrixType>::Scalar& other) { return *this = derived().nestedExpression() / other; }
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/** \sa MatrixBase::fill() */
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EIGEN_DEVICE_FUNC
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void fill(const Scalar& value) { setConstant(value); }
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/** \sa MatrixBase::setConstant() */
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EIGEN_DEVICE_FUNC
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TriangularViewType& setConstant(const Scalar& value)
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{ return *this = MatrixType::Constant(derived().rows(), derived().cols(), value); }
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/** \sa MatrixBase::setZero() */
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EIGEN_DEVICE_FUNC
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TriangularViewType& setZero() { return setConstant(Scalar(0)); }
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/** \sa MatrixBase::setOnes() */
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EIGEN_DEVICE_FUNC
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TriangularViewType& setOnes() { return setConstant(Scalar(1)); }
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/** \sa MatrixBase::coeff()
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* \warning the coordinates must fit into the referenced triangular part
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*/
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EIGEN_DEVICE_FUNC
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inline Scalar coeff(Index row, Index col) const
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{
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Base::check_coordinates_internal(row, col);
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return derived().nestedExpression().coeff(row, col);
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}
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/** \sa MatrixBase::coeffRef()
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* \warning the coordinates must fit into the referenced triangular part
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*/
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EIGEN_DEVICE_FUNC
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inline Scalar& coeffRef(Index row, Index col)
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{
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EIGEN_STATIC_ASSERT_LVALUE(TriangularViewType);
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Base::check_coordinates_internal(row, col);
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return derived().nestedExpression().coeffRef(row, col);
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}
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/** Assigns a triangular matrix to a triangular part of a dense matrix */
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC
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TriangularViewType& operator=(const TriangularBase<OtherDerived>& other);
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/** Shortcut for\code *this = other.other.triangularView<(*this)::Mode>() \endcode */
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC
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TriangularViewType& operator=(const MatrixBase<OtherDerived>& other);
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#ifndef EIGEN_PARSED_BY_DOXYGEN
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EIGEN_DEVICE_FUNC
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TriangularViewType& operator=(const TriangularViewImpl& other)
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{ return *this = other.derived().nestedExpression(); }
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/** \deprecated */
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC
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void lazyAssign(const TriangularBase<OtherDerived>& other);
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/** \deprecated */
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC
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void lazyAssign(const MatrixBase<OtherDerived>& other);
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#endif
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/** Efficient triangular matrix times vector/matrix product */
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template<typename OtherDerived>
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EIGEN_DEVICE_FUNC
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const Product<TriangularViewType,OtherDerived>
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operator*(const MatrixBase<OtherDerived>& rhs) const
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{
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return Product<TriangularViewType,OtherDerived>(derived(), rhs.derived());
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}
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/** Efficient vector/matrix times triangular matrix product */
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template<typename OtherDerived> friend
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EIGEN_DEVICE_FUNC
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const Product<OtherDerived,TriangularViewType>
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operator*(const MatrixBase<OtherDerived>& lhs, const TriangularViewImpl& rhs)
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{
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return Product<OtherDerived,TriangularViewType>(lhs.derived(),rhs.derived());
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}
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/** \returns the product of the inverse of \c *this with \a other, \a *this being triangular.
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*
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* This function computes the inverse-matrix matrix product inverse(\c *this) * \a other if
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* \a Side==OnTheLeft (the default), or the right-inverse-multiply \a other * inverse(\c *this) if
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* \a Side==OnTheRight.
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*
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* The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the
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* diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this
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* is an upper (resp. lower) triangular matrix.
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*
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* Example: \include Triangular_solve.cpp
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* Output: \verbinclude Triangular_solve.out
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*
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* This function returns an expression of the inverse-multiply and can works in-place if it is assigned
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* to the same matrix or vector \a other.
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*
|
|
* For users coming from BLAS, this function (and more specifically solveInPlace()) offer
|
|
* all the operations supported by the \c *TRSV and \c *TRSM BLAS routines.
|
|
*
|
|
* \sa TriangularView::solveInPlace()
|
|
*/
|
|
template<int Side, typename Other>
|
|
EIGEN_DEVICE_FUNC
|
|
inline const internal::triangular_solve_retval<Side,TriangularViewType, Other>
|
|
solve(const MatrixBase<Other>& other) const;
|
|
|
|
/** "in-place" version of TriangularView::solve() where the result is written in \a other
|
|
*
|
|
* \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
|
|
* This function will const_cast it, so constness isn't honored here.
|
|
*
|
|
* See TriangularView:solve() for the details.
|
|
*/
|
|
template<int Side, typename OtherDerived>
|
|
EIGEN_DEVICE_FUNC
|
|
void solveInPlace(const MatrixBase<OtherDerived>& other) const;
|
|
|
|
template<typename OtherDerived>
|
|
EIGEN_DEVICE_FUNC
|
|
void solveInPlace(const MatrixBase<OtherDerived>& other) const
|
|
{ return solveInPlace<OnTheLeft>(other); }
|
|
|
|
/** Swaps the coefficients of the common triangular parts of two matrices */
|
|
template<typename OtherDerived>
|
|
EIGEN_DEVICE_FUNC
|
|
#ifdef EIGEN_PARSED_BY_DOXYGEN
|
|
void swap(TriangularBase<OtherDerived> &other)
|
|
#else
|
|
void swap(TriangularBase<OtherDerived> const & other)
|
|
#endif
|
|
{
|
|
EIGEN_STATIC_ASSERT_LVALUE(OtherDerived);
|
|
call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
|
|
}
|
|
|
|
/** \deprecated
|
|
* Shortcut for \code (*this).swap(other.triangularView<(*this)::Mode>()) \endcode */
|
|
template<typename OtherDerived>
|
|
EIGEN_DEVICE_FUNC
|
|
void swap(MatrixBase<OtherDerived> const & other)
|
|
{
|
|
EIGEN_STATIC_ASSERT_LVALUE(OtherDerived);
|
|
call_assignment(derived(), other.const_cast_derived(), internal::swap_assign_op<Scalar>());
|
|
}
|
|
|
|
template<typename RhsType, typename DstType>
|
|
EIGEN_DEVICE_FUNC
|
|
EIGEN_STRONG_INLINE void _solve_impl(const RhsType &rhs, DstType &dst) const {
|
|
if(!internal::is_same_dense(dst,rhs))
|
|
dst = rhs;
|
|
this->solveInPlace(dst);
|
|
}
|
|
|
|
template<typename ProductType>
|
|
EIGEN_DEVICE_FUNC
|
|
EIGEN_STRONG_INLINE TriangularViewType& _assignProduct(const ProductType& prod, const Scalar& alpha);
|
|
};
|
|
|
|
/***************************************************************************
|
|
* Implementation of triangular evaluation/assignment
|
|
***************************************************************************/
|
|
|
|
// FIXME should we keep that possibility
|
|
template<typename MatrixType, unsigned int Mode>
|
|
template<typename OtherDerived>
|
|
inline TriangularView<MatrixType, Mode>&
|
|
TriangularViewImpl<MatrixType, Mode, Dense>::operator=(const MatrixBase<OtherDerived>& other)
|
|
{
|
|
internal::call_assignment_no_alias(derived(), other.derived(), internal::assign_op<Scalar,typename OtherDerived::Scalar>());
|
|
return derived();
|
|
}
|
|
|
|
// FIXME should we keep that possibility
|
|
template<typename MatrixType, unsigned int Mode>
|
|
template<typename OtherDerived>
|
|
void TriangularViewImpl<MatrixType, Mode, Dense>::lazyAssign(const MatrixBase<OtherDerived>& other)
|
|
{
|
|
internal::call_assignment_no_alias(derived(), other.template triangularView<Mode>());
|
|
}
|
|
|
|
|
|
|
|
template<typename MatrixType, unsigned int Mode>
|
|
template<typename OtherDerived>
|
|
inline TriangularView<MatrixType, Mode>&
|
|
TriangularViewImpl<MatrixType, Mode, Dense>::operator=(const TriangularBase<OtherDerived>& other)
|
|
{
|
|
eigen_assert(Mode == int(OtherDerived::Mode));
|
|
internal::call_assignment(derived(), other.derived());
|
|
return derived();
|
|
}
|
|
|
|
template<typename MatrixType, unsigned int Mode>
|
|
template<typename OtherDerived>
|
|
void TriangularViewImpl<MatrixType, Mode, Dense>::lazyAssign(const TriangularBase<OtherDerived>& other)
|
|
{
|
|
eigen_assert(Mode == int(OtherDerived::Mode));
|
|
internal::call_assignment_no_alias(derived(), other.derived());
|
|
}
|
|
|
|
/***************************************************************************
|
|
* Implementation of TriangularBase methods
|
|
***************************************************************************/
|
|
|
|
/** Assigns a triangular or selfadjoint matrix to a dense matrix.
|
|
* If the matrix is triangular, the opposite part is set to zero. */
|
|
template<typename Derived>
|
|
template<typename DenseDerived>
|
|
void TriangularBase<Derived>::evalTo(MatrixBase<DenseDerived> &other) const
|
|
{
|
|
evalToLazy(other.derived());
|
|
}
|
|
|
|
/***************************************************************************
|
|
* Implementation of TriangularView methods
|
|
***************************************************************************/
|
|
|
|
/***************************************************************************
|
|
* Implementation of MatrixBase methods
|
|
***************************************************************************/
|
|
|
|
/**
|
|
* \returns an expression of a triangular view extracted from the current matrix
|
|
*
|
|
* The parameter \a Mode can have the following values: \c #Upper, \c #StrictlyUpper, \c #UnitUpper,
|
|
* \c #Lower, \c #StrictlyLower, \c #UnitLower.
|
|
*
|
|
* Example: \include MatrixBase_triangularView.cpp
|
|
* Output: \verbinclude MatrixBase_triangularView.out
|
|
*
|
|
* \sa class TriangularView
|
|
*/
|
|
template<typename Derived>
|
|
template<unsigned int Mode>
|
|
typename MatrixBase<Derived>::template TriangularViewReturnType<Mode>::Type
|
|
MatrixBase<Derived>::triangularView()
|
|
{
|
|
return typename TriangularViewReturnType<Mode>::Type(derived());
|
|
}
|
|
|
|
/** This is the const version of MatrixBase::triangularView() */
|
|
template<typename Derived>
|
|
template<unsigned int Mode>
|
|
typename MatrixBase<Derived>::template ConstTriangularViewReturnType<Mode>::Type
|
|
MatrixBase<Derived>::triangularView() const
|
|
{
|
|
return typename ConstTriangularViewReturnType<Mode>::Type(derived());
|
|
}
|
|
|
|
/** \returns true if *this is approximately equal to an upper triangular matrix,
|
|
* within the precision given by \a prec.
|
|
*
|
|
* \sa isLowerTriangular()
|
|
*/
|
|
template<typename Derived>
|
|
bool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const
|
|
{
|
|
using std::abs;
|
|
RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
|
|
for(Index j = 0; j < cols(); ++j)
|
|
{
|
|
Index maxi = (std::min)(j, rows()-1);
|
|
for(Index i = 0; i <= maxi; ++i)
|
|
{
|
|
RealScalar absValue = abs(coeff(i,j));
|
|
if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
|
|
}
|
|
}
|
|
RealScalar threshold = maxAbsOnUpperPart * prec;
|
|
for(Index j = 0; j < cols(); ++j)
|
|
for(Index i = j+1; i < rows(); ++i)
|
|
if(abs(coeff(i, j)) > threshold) return false;
|
|
return true;
|
|
}
|
|
|
|
/** \returns true if *this is approximately equal to a lower triangular matrix,
|
|
* within the precision given by \a prec.
|
|
*
|
|
* \sa isUpperTriangular()
|
|
*/
|
|
template<typename Derived>
|
|
bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const
|
|
{
|
|
using std::abs;
|
|
RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
|
|
for(Index j = 0; j < cols(); ++j)
|
|
for(Index i = j; i < rows(); ++i)
|
|
{
|
|
RealScalar absValue = abs(coeff(i,j));
|
|
if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
|
|
}
|
|
RealScalar threshold = maxAbsOnLowerPart * prec;
|
|
for(Index j = 1; j < cols(); ++j)
|
|
{
|
|
Index maxi = (std::min)(j, rows()-1);
|
|
for(Index i = 0; i < maxi; ++i)
|
|
if(abs(coeff(i, j)) > threshold) return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
|
|
/***************************************************************************
|
|
****************************************************************************
|
|
* Evaluators and Assignment of triangular expressions
|
|
***************************************************************************
|
|
***************************************************************************/
|
|
|
|
namespace internal {
|
|
|
|
|
|
// TODO currently a triangular expression has the form TriangularView<.,.>
|
|
// in the future triangular-ness should be defined by the expression traits
|
|
// such that Transpose<TriangularView<.,.> > is valid. (currently TriangularBase::transpose() is overloaded to make it work)
|
|
template<typename MatrixType, unsigned int Mode>
|
|
struct evaluator_traits<TriangularView<MatrixType,Mode> >
|
|
{
|
|
typedef typename storage_kind_to_evaluator_kind<typename MatrixType::StorageKind>::Kind Kind;
|
|
typedef typename glue_shapes<typename evaluator_traits<MatrixType>::Shape, TriangularShape>::type Shape;
|
|
};
|
|
|
|
template<typename MatrixType, unsigned int Mode>
|
|
struct unary_evaluator<TriangularView<MatrixType,Mode>, IndexBased>
|
|
: evaluator<typename internal::remove_all<MatrixType>::type>
|
|
{
|
|
typedef TriangularView<MatrixType,Mode> XprType;
|
|
typedef evaluator<typename internal::remove_all<MatrixType>::type> Base;
|
|
unary_evaluator(const XprType &xpr) : Base(xpr.nestedExpression()) {}
|
|
};
|
|
|
|
// Additional assignment kinds:
|
|
struct Triangular2Triangular {};
|
|
struct Triangular2Dense {};
|
|
struct Dense2Triangular {};
|
|
|
|
|
|
template<typename Kernel, unsigned int Mode, int UnrollCount, bool ClearOpposite> struct triangular_assignment_loop;
|
|
|
|
|
|
/** \internal Specialization of the dense assignment kernel for triangular matrices.
|
|
* The main difference is that the triangular, diagonal, and opposite parts are processed through three different functions.
|
|
* \tparam UpLo must be either Lower or Upper
|
|
* \tparam Mode must be either 0, UnitDiag, ZeroDiag, or SelfAdjoint
|
|
*/
|
|
template<int UpLo, int Mode, int SetOpposite, typename DstEvaluatorTypeT, typename SrcEvaluatorTypeT, typename Functor, int Version = Specialized>
|
|
class triangular_dense_assignment_kernel : public generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version>
|
|
{
|
|
protected:
|
|
typedef generic_dense_assignment_kernel<DstEvaluatorTypeT, SrcEvaluatorTypeT, Functor, Version> Base;
|
|
typedef typename Base::DstXprType DstXprType;
|
|
typedef typename Base::SrcXprType SrcXprType;
|
|
using Base::m_dst;
|
|
using Base::m_src;
|
|
using Base::m_functor;
|
|
public:
|
|
|
|
typedef typename Base::DstEvaluatorType DstEvaluatorType;
|
|
typedef typename Base::SrcEvaluatorType SrcEvaluatorType;
|
|
typedef typename Base::Scalar Scalar;
|
|
typedef typename Base::AssignmentTraits AssignmentTraits;
|
|
|
|
|
|
EIGEN_DEVICE_FUNC triangular_dense_assignment_kernel(DstEvaluatorType &dst, const SrcEvaluatorType &src, const Functor &func, DstXprType& dstExpr)
|
|
: Base(dst, src, func, dstExpr)
|
|
{}
|
|
|
|
#ifdef EIGEN_INTERNAL_DEBUGGING
|
|
EIGEN_DEVICE_FUNC void assignCoeff(Index row, Index col)
|
|
{
|
|
eigen_internal_assert(row!=col);
|
|
Base::assignCoeff(row,col);
|
|
}
|
|
#else
|
|
using Base::assignCoeff;
|
|
#endif
|
|
|
|
EIGEN_DEVICE_FUNC void assignDiagonalCoeff(Index id)
|
|
{
|
|
if(Mode==UnitDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(1));
|
|
else if(Mode==ZeroDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(0));
|
|
else if(Mode==0) Base::assignCoeff(id,id);
|
|
}
|
|
|
|
EIGEN_DEVICE_FUNC void assignOppositeCoeff(Index row, Index col)
|
|
{
|
|
eigen_internal_assert(row!=col);
|
|
if(SetOpposite)
|
|
m_functor.assignCoeff(m_dst.coeffRef(row,col), Scalar(0));
|
|
}
|
|
};
|
|
|
|
template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType, typename Functor>
|
|
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
|
|
void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& src, const Functor &func)
|
|
{
|
|
eigen_assert(dst.rows() == src.rows() && dst.cols() == src.cols());
|
|
|
|
typedef evaluator<DstXprType> DstEvaluatorType;
|
|
typedef evaluator<SrcXprType> SrcEvaluatorType;
|
|
|
|
DstEvaluatorType dstEvaluator(dst);
|
|
SrcEvaluatorType srcEvaluator(src);
|
|
|
|
typedef triangular_dense_assignment_kernel< Mode&(Lower|Upper),Mode&(UnitDiag|ZeroDiag|SelfAdjoint),SetOpposite,
|
|
DstEvaluatorType,SrcEvaluatorType,Functor> Kernel;
|
|
Kernel kernel(dstEvaluator, srcEvaluator, func, dst.const_cast_derived());
|
|
|
|
enum {
|
|
unroll = DstXprType::SizeAtCompileTime != Dynamic
|
|
&& SrcEvaluatorType::CoeffReadCost < HugeCost
|
|
&& DstXprType::SizeAtCompileTime * (DstEvaluatorType::CoeffReadCost+SrcEvaluatorType::CoeffReadCost) / 2 <= EIGEN_UNROLLING_LIMIT
|
|
};
|
|
|
|
triangular_assignment_loop<Kernel, Mode, unroll ? int(DstXprType::SizeAtCompileTime) : Dynamic, SetOpposite>::run(kernel);
|
|
}
|
|
|
|
template<int Mode, bool SetOpposite, typename DstXprType, typename SrcXprType>
|
|
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
|
|
void call_triangular_assignment_loop(const DstXprType& dst, const SrcXprType& src)
|
|
{
|
|
call_triangular_assignment_loop<Mode,SetOpposite>(dst, src, internal::assign_op<typename DstXprType::Scalar,typename SrcXprType::Scalar>());
|
|
}
|
|
|
|
template<> struct AssignmentKind<TriangularShape,TriangularShape> { typedef Triangular2Triangular Kind; };
|
|
template<> struct AssignmentKind<DenseShape,TriangularShape> { typedef Triangular2Dense Kind; };
|
|
template<> struct AssignmentKind<TriangularShape,DenseShape> { typedef Dense2Triangular Kind; };
|
|
|
|
|
|
template< typename DstXprType, typename SrcXprType, typename Functor>
|
|
struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Triangular>
|
|
{
|
|
EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
|
|
{
|
|
eigen_assert(int(DstXprType::Mode) == int(SrcXprType::Mode));
|
|
|
|
call_triangular_assignment_loop<DstXprType::Mode, false>(dst, src, func);
|
|
}
|
|
};
|
|
|
|
template< typename DstXprType, typename SrcXprType, typename Functor>
|
|
struct Assignment<DstXprType, SrcXprType, Functor, Triangular2Dense>
|
|
{
|
|
EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
|
|
{
|
|
call_triangular_assignment_loop<SrcXprType::Mode, (SrcXprType::Mode&SelfAdjoint)==0>(dst, src, func);
|
|
}
|
|
};
|
|
|
|
template< typename DstXprType, typename SrcXprType, typename Functor>
|
|
struct Assignment<DstXprType, SrcXprType, Functor, Dense2Triangular>
|
|
{
|
|
EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const Functor &func)
|
|
{
|
|
call_triangular_assignment_loop<DstXprType::Mode, false>(dst, src, func);
|
|
}
|
|
};
|
|
|
|
|
|
template<typename Kernel, unsigned int Mode, int UnrollCount, bool SetOpposite>
|
|
struct triangular_assignment_loop
|
|
{
|
|
// FIXME: this is not very clean, perhaps this information should be provided by the kernel?
|
|
typedef typename Kernel::DstEvaluatorType DstEvaluatorType;
|
|
typedef typename DstEvaluatorType::XprType DstXprType;
|
|
|
|
enum {
|
|
col = (UnrollCount-1) / DstXprType::RowsAtCompileTime,
|
|
row = (UnrollCount-1) % DstXprType::RowsAtCompileTime
|
|
};
|
|
|
|
typedef typename Kernel::Scalar Scalar;
|
|
|
|
EIGEN_DEVICE_FUNC
|
|
static inline void run(Kernel &kernel)
|
|
{
|
|
triangular_assignment_loop<Kernel, Mode, UnrollCount-1, SetOpposite>::run(kernel);
|
|
|
|
if(row==col)
|
|
kernel.assignDiagonalCoeff(row);
|
|
else if( ((Mode&Lower) && row>col) || ((Mode&Upper) && row<col) )
|
|
kernel.assignCoeff(row,col);
|
|
else if(SetOpposite)
|
|
kernel.assignOppositeCoeff(row,col);
|
|
}
|
|
};
|
|
|
|
// prevent buggy user code from causing an infinite recursion
|
|
template<typename Kernel, unsigned int Mode, bool SetOpposite>
|
|
struct triangular_assignment_loop<Kernel, Mode, 0, SetOpposite>
|
|
{
|
|
EIGEN_DEVICE_FUNC
|
|
static inline void run(Kernel &) {}
|
|
};
|
|
|
|
|
|
|
|
// TODO: experiment with a recursive assignment procedure splitting the current
|
|
// triangular part into one rectangular and two triangular parts.
|
|
|
|
|
|
template<typename Kernel, unsigned int Mode, bool SetOpposite>
|
|
struct triangular_assignment_loop<Kernel, Mode, Dynamic, SetOpposite>
|
|
{
|
|
typedef typename Kernel::Scalar Scalar;
|
|
EIGEN_DEVICE_FUNC
|
|
static inline void run(Kernel &kernel)
|
|
{
|
|
for(Index j = 0; j < kernel.cols(); ++j)
|
|
{
|
|
Index maxi = (std::min)(j, kernel.rows());
|
|
Index i = 0;
|
|
if (((Mode&Lower) && SetOpposite) || (Mode&Upper))
|
|
{
|
|
for(; i < maxi; ++i)
|
|
if(Mode&Upper) kernel.assignCoeff(i, j);
|
|
else kernel.assignOppositeCoeff(i, j);
|
|
}
|
|
else
|
|
i = maxi;
|
|
|
|
if(i<kernel.rows()) // then i==j
|
|
kernel.assignDiagonalCoeff(i++);
|
|
|
|
if (((Mode&Upper) && SetOpposite) || (Mode&Lower))
|
|
{
|
|
for(; i < kernel.rows(); ++i)
|
|
if(Mode&Lower) kernel.assignCoeff(i, j);
|
|
else kernel.assignOppositeCoeff(i, j);
|
|
}
|
|
}
|
|
}
|
|
};
|
|
|
|
} // end namespace internal
|
|
|
|
/** Assigns a triangular or selfadjoint matrix to a dense matrix.
|
|
* If the matrix is triangular, the opposite part is set to zero. */
|
|
template<typename Derived>
|
|
template<typename DenseDerived>
|
|
void TriangularBase<Derived>::evalToLazy(MatrixBase<DenseDerived> &other) const
|
|
{
|
|
other.derived().resize(this->rows(), this->cols());
|
|
internal::call_triangular_assignment_loop<Derived::Mode,(Derived::Mode&SelfAdjoint)==0 /* SetOpposite */>(other.derived(), derived().nestedExpression());
|
|
}
|
|
|
|
namespace internal {
|
|
|
|
// Triangular = Product
|
|
template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
|
|
struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>
|
|
{
|
|
typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
|
|
static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename SrcXprType::Scalar> &)
|
|
{
|
|
dst.setZero();
|
|
dst._assignProduct(src, 1);
|
|
}
|
|
};
|
|
|
|
// Triangular += Product
|
|
template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
|
|
struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::add_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>
|
|
{
|
|
typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
|
|
static void run(DstXprType &dst, const SrcXprType &src, const internal::add_assign_op<Scalar,typename SrcXprType::Scalar> &)
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|
{
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|
dst._assignProduct(src, 1);
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}
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};
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// Triangular -= Product
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template< typename DstXprType, typename Lhs, typename Rhs, typename Scalar>
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struct Assignment<DstXprType, Product<Lhs,Rhs,DefaultProduct>, internal::sub_assign_op<Scalar,typename Product<Lhs,Rhs,DefaultProduct>::Scalar>, Dense2Triangular>
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|
{
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|
typedef Product<Lhs,Rhs,DefaultProduct> SrcXprType;
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|
static void run(DstXprType &dst, const SrcXprType &src, const internal::sub_assign_op<Scalar,typename SrcXprType::Scalar> &)
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|
{
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dst._assignProduct(src, -1);
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}
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|
};
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|
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} // end namespace internal
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|
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} // end namespace Eigen
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|
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#endif // EIGEN_TRIANGULARMATRIX_H
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