[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
|
---|
| 2 | // for linear algebra.
|
---|
| 3 | //
|
---|
| 4 | // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
|
---|
| 5 | //
|
---|
| 6 | // This Source Code Form is subject to the terms of the Mozilla
|
---|
| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
|
---|
| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
|
---|
| 9 |
|
---|
| 10 | #ifndef EIGEN_SOLVETRIANGULAR_H
|
---|
| 11 | #define EIGEN_SOLVETRIANGULAR_H
|
---|
| 12 |
|
---|
| 13 | namespace Eigen {
|
---|
| 14 |
|
---|
| 15 | namespace internal {
|
---|
| 16 |
|
---|
| 17 | // Forward declarations:
|
---|
| 18 | // The following two routines are implemented in the products/TriangularSolver*.h files
|
---|
| 19 | template<typename LhsScalar, typename RhsScalar, typename Index, int Side, int Mode, bool Conjugate, int StorageOrder>
|
---|
| 20 | struct triangular_solve_vector;
|
---|
| 21 |
|
---|
| 22 | template <typename Scalar, typename Index, int Side, int Mode, bool Conjugate, int TriStorageOrder, int OtherStorageOrder>
|
---|
| 23 | struct triangular_solve_matrix;
|
---|
| 24 |
|
---|
| 25 | // small helper struct extracting some traits on the underlying solver operation
|
---|
| 26 | template<typename Lhs, typename Rhs, int Side>
|
---|
| 27 | class trsolve_traits
|
---|
| 28 | {
|
---|
| 29 | private:
|
---|
| 30 | enum {
|
---|
| 31 | RhsIsVectorAtCompileTime = (Side==OnTheLeft ? Rhs::ColsAtCompileTime : Rhs::RowsAtCompileTime)==1
|
---|
| 32 | };
|
---|
| 33 | public:
|
---|
| 34 | enum {
|
---|
| 35 | Unrolling = (RhsIsVectorAtCompileTime && Rhs::SizeAtCompileTime != Dynamic && Rhs::SizeAtCompileTime <= 8)
|
---|
| 36 | ? CompleteUnrolling : NoUnrolling,
|
---|
| 37 | RhsVectors = RhsIsVectorAtCompileTime ? 1 : Dynamic
|
---|
| 38 | };
|
---|
| 39 | };
|
---|
| 40 |
|
---|
| 41 | template<typename Lhs, typename Rhs,
|
---|
| 42 | int Side, // can be OnTheLeft/OnTheRight
|
---|
| 43 | int Mode, // can be Upper/Lower | UnitDiag
|
---|
| 44 | int Unrolling = trsolve_traits<Lhs,Rhs,Side>::Unrolling,
|
---|
| 45 | int RhsVectors = trsolve_traits<Lhs,Rhs,Side>::RhsVectors
|
---|
| 46 | >
|
---|
| 47 | struct triangular_solver_selector;
|
---|
| 48 |
|
---|
| 49 | template<typename Lhs, typename Rhs, int Side, int Mode>
|
---|
| 50 | struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,1>
|
---|
| 51 | {
|
---|
| 52 | typedef typename Lhs::Scalar LhsScalar;
|
---|
| 53 | typedef typename Rhs::Scalar RhsScalar;
|
---|
| 54 | typedef blas_traits<Lhs> LhsProductTraits;
|
---|
| 55 | typedef typename LhsProductTraits::ExtractType ActualLhsType;
|
---|
| 56 | typedef Map<Matrix<RhsScalar,Dynamic,1>, Aligned> MappedRhs;
|
---|
| 57 | static void run(const Lhs& lhs, Rhs& rhs)
|
---|
| 58 | {
|
---|
| 59 | ActualLhsType actualLhs = LhsProductTraits::extract(lhs);
|
---|
| 60 |
|
---|
| 61 | // FIXME find a way to allow an inner stride if packet_traits<Scalar>::size==1
|
---|
| 62 |
|
---|
| 63 | bool useRhsDirectly = Rhs::InnerStrideAtCompileTime==1 || rhs.innerStride()==1;
|
---|
| 64 |
|
---|
| 65 | ei_declare_aligned_stack_constructed_variable(RhsScalar,actualRhs,rhs.size(),
|
---|
| 66 | (useRhsDirectly ? rhs.data() : 0));
|
---|
| 67 |
|
---|
| 68 | if(!useRhsDirectly)
|
---|
| 69 | MappedRhs(actualRhs,rhs.size()) = rhs;
|
---|
| 70 |
|
---|
| 71 | triangular_solve_vector<LhsScalar, RhsScalar, typename Lhs::Index, Side, Mode, LhsProductTraits::NeedToConjugate,
|
---|
| 72 | (int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor>
|
---|
| 73 | ::run(actualLhs.cols(), actualLhs.data(), actualLhs.outerStride(), actualRhs);
|
---|
| 74 |
|
---|
| 75 | if(!useRhsDirectly)
|
---|
| 76 | rhs = MappedRhs(actualRhs, rhs.size());
|
---|
| 77 | }
|
---|
| 78 | };
|
---|
| 79 |
|
---|
| 80 | // the rhs is a matrix
|
---|
| 81 | template<typename Lhs, typename Rhs, int Side, int Mode>
|
---|
| 82 | struct triangular_solver_selector<Lhs,Rhs,Side,Mode,NoUnrolling,Dynamic>
|
---|
| 83 | {
|
---|
| 84 | typedef typename Rhs::Scalar Scalar;
|
---|
| 85 | typedef typename Rhs::Index Index;
|
---|
| 86 | typedef blas_traits<Lhs> LhsProductTraits;
|
---|
| 87 | typedef typename LhsProductTraits::DirectLinearAccessType ActualLhsType;
|
---|
| 88 |
|
---|
| 89 | static void run(const Lhs& lhs, Rhs& rhs)
|
---|
| 90 | {
|
---|
| 91 | typename internal::add_const_on_value_type<ActualLhsType>::type actualLhs = LhsProductTraits::extract(lhs);
|
---|
| 92 |
|
---|
| 93 | const Index size = lhs.rows();
|
---|
| 94 | const Index othersize = Side==OnTheLeft? rhs.cols() : rhs.rows();
|
---|
| 95 |
|
---|
| 96 | typedef internal::gemm_blocking_space<(Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor,Scalar,Scalar,
|
---|
| 97 | Rhs::MaxRowsAtCompileTime, Rhs::MaxColsAtCompileTime, Lhs::MaxRowsAtCompileTime,4> BlockingType;
|
---|
| 98 |
|
---|
| 99 | BlockingType blocking(rhs.rows(), rhs.cols(), size);
|
---|
| 100 |
|
---|
| 101 | triangular_solve_matrix<Scalar,Index,Side,Mode,LhsProductTraits::NeedToConjugate,(int(Lhs::Flags) & RowMajorBit) ? RowMajor : ColMajor,
|
---|
| 102 | (Rhs::Flags&RowMajorBit) ? RowMajor : ColMajor>
|
---|
| 103 | ::run(size, othersize, &actualLhs.coeffRef(0,0), actualLhs.outerStride(), &rhs.coeffRef(0,0), rhs.outerStride(), blocking);
|
---|
| 104 | }
|
---|
| 105 | };
|
---|
| 106 |
|
---|
| 107 | /***************************************************************************
|
---|
| 108 | * meta-unrolling implementation
|
---|
| 109 | ***************************************************************************/
|
---|
| 110 |
|
---|
| 111 | template<typename Lhs, typename Rhs, int Mode, int Index, int Size,
|
---|
| 112 | bool Stop = Index==Size>
|
---|
| 113 | struct triangular_solver_unroller;
|
---|
| 114 |
|
---|
| 115 | template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
|
---|
| 116 | struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,false> {
|
---|
| 117 | enum {
|
---|
| 118 | IsLower = ((Mode&Lower)==Lower),
|
---|
| 119 | RowIndex = IsLower ? Index : Size - Index - 1,
|
---|
| 120 | S = IsLower ? 0 : RowIndex+1
|
---|
| 121 | };
|
---|
| 122 | static void run(const Lhs& lhs, Rhs& rhs)
|
---|
| 123 | {
|
---|
| 124 | if (Index>0)
|
---|
| 125 | rhs.coeffRef(RowIndex) -= lhs.row(RowIndex).template segment<Index>(S).transpose()
|
---|
| 126 | .cwiseProduct(rhs.template segment<Index>(S)).sum();
|
---|
| 127 |
|
---|
| 128 | if(!(Mode & UnitDiag))
|
---|
| 129 | rhs.coeffRef(RowIndex) /= lhs.coeff(RowIndex,RowIndex);
|
---|
| 130 |
|
---|
| 131 | triangular_solver_unroller<Lhs,Rhs,Mode,Index+1,Size>::run(lhs,rhs);
|
---|
| 132 | }
|
---|
| 133 | };
|
---|
| 134 |
|
---|
| 135 | template<typename Lhs, typename Rhs, int Mode, int Index, int Size>
|
---|
| 136 | struct triangular_solver_unroller<Lhs,Rhs,Mode,Index,Size,true> {
|
---|
| 137 | static void run(const Lhs&, Rhs&) {}
|
---|
| 138 | };
|
---|
| 139 |
|
---|
| 140 | template<typename Lhs, typename Rhs, int Mode>
|
---|
| 141 | struct triangular_solver_selector<Lhs,Rhs,OnTheLeft,Mode,CompleteUnrolling,1> {
|
---|
| 142 | static void run(const Lhs& lhs, Rhs& rhs)
|
---|
| 143 | { triangular_solver_unroller<Lhs,Rhs,Mode,0,Rhs::SizeAtCompileTime>::run(lhs,rhs); }
|
---|
| 144 | };
|
---|
| 145 |
|
---|
| 146 | template<typename Lhs, typename Rhs, int Mode>
|
---|
| 147 | struct triangular_solver_selector<Lhs,Rhs,OnTheRight,Mode,CompleteUnrolling,1> {
|
---|
| 148 | static void run(const Lhs& lhs, Rhs& rhs)
|
---|
| 149 | {
|
---|
| 150 | Transpose<const Lhs> trLhs(lhs);
|
---|
| 151 | Transpose<Rhs> trRhs(rhs);
|
---|
| 152 |
|
---|
| 153 | triangular_solver_unroller<Transpose<const Lhs>,Transpose<Rhs>,
|
---|
| 154 | ((Mode&Upper)==Upper ? Lower : Upper) | (Mode&UnitDiag),
|
---|
| 155 | 0,Rhs::SizeAtCompileTime>::run(trLhs,trRhs);
|
---|
| 156 | }
|
---|
| 157 | };
|
---|
| 158 |
|
---|
| 159 | } // end namespace internal
|
---|
| 160 |
|
---|
| 161 | /***************************************************************************
|
---|
| 162 | * TriangularView methods
|
---|
| 163 | ***************************************************************************/
|
---|
| 164 |
|
---|
| 165 | /** "in-place" version of TriangularView::solve() where the result is written in \a other
|
---|
| 166 | *
|
---|
| 167 | * \warning The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here.
|
---|
| 168 | * This function will const_cast it, so constness isn't honored here.
|
---|
| 169 | *
|
---|
| 170 | * See TriangularView:solve() for the details.
|
---|
| 171 | */
|
---|
| 172 | template<typename MatrixType, unsigned int Mode>
|
---|
| 173 | template<int Side, typename OtherDerived>
|
---|
| 174 | void TriangularView<MatrixType,Mode>::solveInPlace(const MatrixBase<OtherDerived>& _other) const
|
---|
| 175 | {
|
---|
| 176 | OtherDerived& other = _other.const_cast_derived();
|
---|
| 177 | eigen_assert( cols() == rows() && ((Side==OnTheLeft && cols() == other.rows()) || (Side==OnTheRight && cols() == other.cols())) );
|
---|
| 178 | eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
|
---|
| 179 |
|
---|
| 180 | enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit && OtherDerived::IsVectorAtCompileTime };
|
---|
| 181 | typedef typename internal::conditional<copy,
|
---|
| 182 | typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
|
---|
| 183 | OtherCopy otherCopy(other);
|
---|
| 184 |
|
---|
| 185 | internal::triangular_solver_selector<MatrixType, typename internal::remove_reference<OtherCopy>::type,
|
---|
| 186 | Side, Mode>::run(nestedExpression(), otherCopy);
|
---|
| 187 |
|
---|
| 188 | if (copy)
|
---|
| 189 | other = otherCopy;
|
---|
| 190 | }
|
---|
| 191 |
|
---|
| 192 | /** \returns the product of the inverse of \c *this with \a other, \a *this being triangular.
|
---|
| 193 | *
|
---|
| 194 | * This function computes the inverse-matrix matrix product inverse(\c *this) * \a other if
|
---|
| 195 | * \a Side==OnTheLeft (the default), or the right-inverse-multiply \a other * inverse(\c *this) if
|
---|
| 196 | * \a Side==OnTheRight.
|
---|
| 197 | *
|
---|
| 198 | * The matrix \c *this must be triangular and invertible (i.e., all the coefficients of the
|
---|
| 199 | * diagonal must be non zero). It works as a forward (resp. backward) substitution if \c *this
|
---|
| 200 | * is an upper (resp. lower) triangular matrix.
|
---|
| 201 | *
|
---|
| 202 | * Example: \include MatrixBase_marked.cpp
|
---|
| 203 | * Output: \verbinclude MatrixBase_marked.out
|
---|
| 204 | *
|
---|
| 205 | * This function returns an expression of the inverse-multiply and can works in-place if it is assigned
|
---|
| 206 | * to the same matrix or vector \a other.
|
---|
| 207 | *
|
---|
| 208 | * For users coming from BLAS, this function (and more specifically solveInPlace()) offer
|
---|
| 209 | * all the operations supported by the \c *TRSV and \c *TRSM BLAS routines.
|
---|
| 210 | *
|
---|
| 211 | * \sa TriangularView::solveInPlace()
|
---|
| 212 | */
|
---|
| 213 | template<typename Derived, unsigned int Mode>
|
---|
| 214 | template<int Side, typename Other>
|
---|
| 215 | const internal::triangular_solve_retval<Side,TriangularView<Derived,Mode>,Other>
|
---|
| 216 | TriangularView<Derived,Mode>::solve(const MatrixBase<Other>& other) const
|
---|
| 217 | {
|
---|
| 218 | return internal::triangular_solve_retval<Side,TriangularView,Other>(*this, other.derived());
|
---|
| 219 | }
|
---|
| 220 |
|
---|
| 221 | namespace internal {
|
---|
| 222 |
|
---|
| 223 |
|
---|
| 224 | template<int Side, typename TriangularType, typename Rhs>
|
---|
| 225 | struct traits<triangular_solve_retval<Side, TriangularType, Rhs> >
|
---|
| 226 | {
|
---|
| 227 | typedef typename internal::plain_matrix_type_column_major<Rhs>::type ReturnType;
|
---|
| 228 | };
|
---|
| 229 |
|
---|
| 230 | template<int Side, typename TriangularType, typename Rhs> struct triangular_solve_retval
|
---|
| 231 | : public ReturnByValue<triangular_solve_retval<Side, TriangularType, Rhs> >
|
---|
| 232 | {
|
---|
| 233 | typedef typename remove_all<typename Rhs::Nested>::type RhsNestedCleaned;
|
---|
| 234 | typedef ReturnByValue<triangular_solve_retval> Base;
|
---|
| 235 | typedef typename Base::Index Index;
|
---|
| 236 |
|
---|
| 237 | triangular_solve_retval(const TriangularType& tri, const Rhs& rhs)
|
---|
| 238 | : m_triangularMatrix(tri), m_rhs(rhs)
|
---|
| 239 | {}
|
---|
| 240 |
|
---|
| 241 | inline Index rows() const { return m_rhs.rows(); }
|
---|
| 242 | inline Index cols() const { return m_rhs.cols(); }
|
---|
| 243 |
|
---|
| 244 | template<typename Dest> inline void evalTo(Dest& dst) const
|
---|
| 245 | {
|
---|
| 246 | const typename Dest::Scalar *dst_data = internal::extract_data(dst);
|
---|
| 247 | if(!(is_same<RhsNestedCleaned,Dest>::value && dst_data!=0 && extract_data(dst) == extract_data(m_rhs)))
|
---|
| 248 | dst = m_rhs;
|
---|
| 249 | m_triangularMatrix.template solveInPlace<Side>(dst);
|
---|
| 250 | }
|
---|
| 251 |
|
---|
| 252 | protected:
|
---|
| 253 | const TriangularType& m_triangularMatrix;
|
---|
| 254 | typename Rhs::Nested m_rhs;
|
---|
| 255 | };
|
---|
| 256 |
|
---|
| 257 | } // namespace internal
|
---|
| 258 |
|
---|
| 259 | } // end namespace Eigen
|
---|
| 260 |
|
---|
| 261 | #endif // EIGEN_SOLVETRIANGULAR_H
|
---|