| 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) 2008 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_SPARSETRIANGULARSOLVER_H
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| 11 | #define EIGEN_SPARSETRIANGULARSOLVER_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | namespace internal {
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| 16 |
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| 17 | template<typename Lhs, typename Rhs, int Mode,
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| 18 | int UpLo = (Mode & Lower)
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| 19 | ? Lower
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| 20 | : (Mode & Upper)
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| 21 | ? Upper
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| 22 | : -1,
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| 23 | int StorageOrder = int(traits<Lhs>::Flags) & RowMajorBit>
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| 24 | struct sparse_solve_triangular_selector;
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| 25 |
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| 26 | // forward substitution, row-major
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| 27 | template<typename Lhs, typename Rhs, int Mode>
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| 28 | struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,RowMajor>
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| 29 | {
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| 30 | typedef typename Rhs::Scalar Scalar;
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| 31 | static void run(const Lhs& lhs, Rhs& other)
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| 32 | {
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| 33 | for(int col=0 ; col<other.cols() ; ++col)
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| 34 | {
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| 35 | for(int i=0; i<lhs.rows(); ++i)
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| 36 | {
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| 37 | Scalar tmp = other.coeff(i,col);
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| 38 | Scalar lastVal(0);
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| 39 | int lastIndex = 0;
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| 40 | for(typename Lhs::InnerIterator it(lhs, i); it; ++it)
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| 41 | {
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| 42 | lastVal = it.value();
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| 43 | lastIndex = it.index();
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| 44 | if(lastIndex==i)
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| 45 | break;
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| 46 | tmp -= lastVal * other.coeff(lastIndex,col);
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| 47 | }
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| 48 | if (Mode & UnitDiag)
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| 49 | other.coeffRef(i,col) = tmp;
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| 50 | else
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| 51 | {
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| 52 | eigen_assert(lastIndex==i);
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| 53 | other.coeffRef(i,col) = tmp/lastVal;
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| 54 | }
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| 55 | }
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| 56 | }
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| 57 | }
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| 58 | };
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| 59 |
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| 60 | // backward substitution, row-major
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| 61 | template<typename Lhs, typename Rhs, int Mode>
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| 62 | struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,RowMajor>
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| 63 | {
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| 64 | typedef typename Rhs::Scalar Scalar;
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| 65 | static void run(const Lhs& lhs, Rhs& other)
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| 66 | {
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| 67 | for(int col=0 ; col<other.cols() ; ++col)
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| 68 | {
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| 69 | for(int i=lhs.rows()-1 ; i>=0 ; --i)
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| 70 | {
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| 71 | Scalar tmp = other.coeff(i,col);
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| 72 | Scalar l_ii(0);
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| 73 | typename Lhs::InnerIterator it(lhs, i);
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| 74 | while(it && it.index()<i)
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| 75 | ++it;
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| 76 | if(!(Mode & UnitDiag))
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| 77 | {
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| 78 | eigen_assert(it && it.index()==i);
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| 79 | l_ii = it.value();
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| 80 | ++it;
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| 81 | }
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| 82 | else if (it && it.index() == i)
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| 83 | ++it;
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| 84 | for(; it; ++it)
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| 85 | {
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| 86 | tmp -= it.value() * other.coeff(it.index(),col);
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| 87 | }
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| 88 |
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| 89 | if (Mode & UnitDiag)
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| 90 | other.coeffRef(i,col) = tmp;
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| 91 | else
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| 92 | other.coeffRef(i,col) = tmp/l_ii;
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| 93 | }
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| 94 | }
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| 95 | }
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| 96 | };
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| 97 |
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| 98 | // forward substitution, col-major
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| 99 | template<typename Lhs, typename Rhs, int Mode>
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| 100 | struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,ColMajor>
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| 101 | {
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| 102 | typedef typename Rhs::Scalar Scalar;
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| 103 | static void run(const Lhs& lhs, Rhs& other)
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| 104 | {
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| 105 | for(int col=0 ; col<other.cols() ; ++col)
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| 106 | {
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| 107 | for(int i=0; i<lhs.cols(); ++i)
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| 108 | {
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| 109 | Scalar& tmp = other.coeffRef(i,col);
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| 110 | if (tmp!=Scalar(0)) // optimization when other is actually sparse
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| 111 | {
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| 112 | typename Lhs::InnerIterator it(lhs, i);
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| 113 | while(it && it.index()<i)
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| 114 | ++it;
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| 115 | if(!(Mode & UnitDiag))
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| 116 | {
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| 117 | eigen_assert(it && it.index()==i);
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| 118 | tmp /= it.value();
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| 119 | }
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| 120 | if (it && it.index()==i)
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| 121 | ++it;
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| 122 | for(; it; ++it)
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| 123 | other.coeffRef(it.index(), col) -= tmp * it.value();
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| 124 | }
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| 125 | }
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| 126 | }
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| 127 | }
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| 128 | };
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| 129 |
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| 130 | // backward substitution, col-major
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| 131 | template<typename Lhs, typename Rhs, int Mode>
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| 132 | struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,ColMajor>
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| 133 | {
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| 134 | typedef typename Rhs::Scalar Scalar;
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| 135 | static void run(const Lhs& lhs, Rhs& other)
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| 136 | {
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| 137 | for(int col=0 ; col<other.cols() ; ++col)
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| 138 | {
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| 139 | for(int i=lhs.cols()-1; i>=0; --i)
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| 140 | {
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| 141 | Scalar& tmp = other.coeffRef(i,col);
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| 142 | if (tmp!=Scalar(0)) // optimization when other is actually sparse
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| 143 | {
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| 144 | if(!(Mode & UnitDiag))
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| 145 | {
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| 146 | // TODO replace this by a binary search. make sure the binary search is safe for partially sorted elements
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| 147 | typename Lhs::ReverseInnerIterator it(lhs, i);
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| 148 | while(it && it.index()!=i)
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| 149 | --it;
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| 150 | eigen_assert(it && it.index()==i);
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| 151 | other.coeffRef(i,col) /= it.value();
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| 152 | }
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| 153 | typename Lhs::InnerIterator it(lhs, i);
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| 154 | for(; it && it.index()<i; ++it)
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| 155 | other.coeffRef(it.index(), col) -= tmp * it.value();
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| 156 | }
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| 157 | }
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| 158 | }
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| 159 | }
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| 160 | };
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| 161 |
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| 162 | } // end namespace internal
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| 163 |
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| 164 | template<typename ExpressionType,int Mode>
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| 165 | template<typename OtherDerived>
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| 166 | void SparseTriangularView<ExpressionType,Mode>::solveInPlace(MatrixBase<OtherDerived>& other) const
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| 167 | {
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| 168 | eigen_assert(m_matrix.cols() == m_matrix.rows() && m_matrix.cols() == other.rows());
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| 169 | eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
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| 170 |
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| 171 | enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };
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| 172 |
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| 173 | typedef typename internal::conditional<copy,
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| 174 | typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
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| 175 | OtherCopy otherCopy(other.derived());
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| 176 |
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| 177 | internal::sparse_solve_triangular_selector<ExpressionType, typename internal::remove_reference<OtherCopy>::type, Mode>::run(m_matrix, otherCopy);
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| 178 |
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| 179 | if (copy)
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| 180 | other = otherCopy;
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| 181 | }
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| 182 |
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| 183 | template<typename ExpressionType,int Mode>
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| 184 | template<typename OtherDerived>
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| 185 | typename internal::plain_matrix_type_column_major<OtherDerived>::type
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| 186 | SparseTriangularView<ExpressionType,Mode>::solve(const MatrixBase<OtherDerived>& other) const
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| 187 | {
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| 188 | typename internal::plain_matrix_type_column_major<OtherDerived>::type res(other);
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| 189 | solveInPlace(res);
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| 190 | return res;
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| 191 | }
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| 192 |
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| 193 | // pure sparse path
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| 194 |
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| 195 | namespace internal {
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| 196 |
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| 197 | template<typename Lhs, typename Rhs, int Mode,
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| 198 | int UpLo = (Mode & Lower)
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| 199 | ? Lower
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| 200 | : (Mode & Upper)
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| 201 | ? Upper
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| 202 | : -1,
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| 203 | int StorageOrder = int(Lhs::Flags) & (RowMajorBit)>
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| 204 | struct sparse_solve_triangular_sparse_selector;
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| 205 |
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| 206 | // forward substitution, col-major
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| 207 | template<typename Lhs, typename Rhs, int Mode, int UpLo>
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| 208 | struct sparse_solve_triangular_sparse_selector<Lhs,Rhs,Mode,UpLo,ColMajor>
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| 209 | {
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| 210 | typedef typename Rhs::Scalar Scalar;
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| 211 | typedef typename promote_index_type<typename traits<Lhs>::Index,
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| 212 | typename traits<Rhs>::Index>::type Index;
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| 213 | static void run(const Lhs& lhs, Rhs& other)
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| 214 | {
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| 215 | const bool IsLower = (UpLo==Lower);
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| 216 | AmbiVector<Scalar,Index> tempVector(other.rows()*2);
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| 217 | tempVector.setBounds(0,other.rows());
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| 218 |
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| 219 | Rhs res(other.rows(), other.cols());
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| 220 | res.reserve(other.nonZeros());
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| 221 |
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| 222 | for(int col=0 ; col<other.cols() ; ++col)
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| 223 | {
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| 224 | // FIXME estimate number of non zeros
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| 225 | tempVector.init(.99/*float(other.col(col).nonZeros())/float(other.rows())*/);
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| 226 | tempVector.setZero();
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| 227 | tempVector.restart();
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| 228 | for (typename Rhs::InnerIterator rhsIt(other, col); rhsIt; ++rhsIt)
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| 229 | {
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| 230 | tempVector.coeffRef(rhsIt.index()) = rhsIt.value();
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| 231 | }
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| 232 |
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| 233 | for(int i=IsLower?0:lhs.cols()-1;
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| 234 | IsLower?i<lhs.cols():i>=0;
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| 235 | i+=IsLower?1:-1)
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| 236 | {
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| 237 | tempVector.restart();
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| 238 | Scalar& ci = tempVector.coeffRef(i);
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| 239 | if (ci!=Scalar(0))
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| 240 | {
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| 241 | // find
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| 242 | typename Lhs::InnerIterator it(lhs, i);
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| 243 | if(!(Mode & UnitDiag))
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| 244 | {
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| 245 | if (IsLower)
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| 246 | {
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| 247 | eigen_assert(it.index()==i);
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| 248 | ci /= it.value();
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| 249 | }
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| 250 | else
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| 251 | ci /= lhs.coeff(i,i);
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| 252 | }
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| 253 | tempVector.restart();
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| 254 | if (IsLower)
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| 255 | {
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| 256 | if (it.index()==i)
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| 257 | ++it;
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| 258 | for(; it; ++it)
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| 259 | tempVector.coeffRef(it.index()) -= ci * it.value();
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| 260 | }
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| 261 | else
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| 262 | {
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| 263 | for(; it && it.index()<i; ++it)
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| 264 | tempVector.coeffRef(it.index()) -= ci * it.value();
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| 265 | }
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| 266 | }
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| 267 | }
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| 268 |
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| 269 |
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| 270 | int count = 0;
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| 271 | // FIXME compute a reference value to filter zeros
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| 272 | for (typename AmbiVector<Scalar,Index>::Iterator it(tempVector/*,1e-12*/); it; ++it)
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| 273 | {
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| 274 | ++ count;
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| 275 | // std::cerr << "fill " << it.index() << ", " << col << "\n";
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| 276 | // std::cout << it.value() << " ";
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| 277 | // FIXME use insertBack
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| 278 | res.insert(it.index(), col) = it.value();
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| 279 | }
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| 280 | // std::cout << "tempVector.nonZeros() == " << int(count) << " / " << (other.rows()) << "\n";
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| 281 | }
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| 282 | res.finalize();
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| 283 | other = res.markAsRValue();
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| 284 | }
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| 285 | };
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| 286 |
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| 287 | } // end namespace internal
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| 288 |
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| 289 | template<typename ExpressionType,int Mode>
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| 290 | template<typename OtherDerived>
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| 291 | void SparseTriangularView<ExpressionType,Mode>::solveInPlace(SparseMatrixBase<OtherDerived>& other) const
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| 292 | {
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| 293 | eigen_assert(m_matrix.cols() == m_matrix.rows() && m_matrix.cols() == other.rows());
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| 294 | eigen_assert( (!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
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| 295 |
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| 296 | // enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };
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| 297 |
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| 298 | // typedef typename internal::conditional<copy,
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| 299 | // typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
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| 300 | // OtherCopy otherCopy(other.derived());
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| 301 |
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| 302 | internal::sparse_solve_triangular_sparse_selector<ExpressionType, OtherDerived, Mode>::run(m_matrix, other.derived());
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| 303 |
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| 304 | // if (copy)
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| 305 | // other = otherCopy;
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| 306 | }
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| 307 |
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| 308 | #ifdef EIGEN2_SUPPORT
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| 309 |
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| 310 | // deprecated stuff:
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| 311 |
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| 312 | /** \deprecated */
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| 313 | template<typename Derived>
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| 314 | template<typename OtherDerived>
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| 315 | void SparseMatrixBase<Derived>::solveTriangularInPlace(MatrixBase<OtherDerived>& other) const
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| 316 | {
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| 317 | this->template triangular<Flags&(Upper|Lower)>().solveInPlace(other);
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| 318 | }
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| 319 |
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| 320 | /** \deprecated */
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| 321 | template<typename Derived>
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| 322 | template<typename OtherDerived>
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| 323 | typename internal::plain_matrix_type_column_major<OtherDerived>::type
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| 324 | SparseMatrixBase<Derived>::solveTriangular(const MatrixBase<OtherDerived>& other) const
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| 325 | {
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| 326 | typename internal::plain_matrix_type_column_major<OtherDerived>::type res(other);
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| 327 | derived().solveTriangularInPlace(res);
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| 328 | return res;
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| 329 | }
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| 330 | #endif // EIGEN2_SUPPORT
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| 331 |
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| 332 | } // end namespace Eigen
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| 333 |
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| 334 | #endif // EIGEN_SPARSETRIANGULARSOLVER_H
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