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330 lines
10 KiB
C++
330 lines
10 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 Gael Guennebaud <g.gael@free.fr>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_SPARSETRIANGULARSOLVER_H
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#define EIGEN_SPARSETRIANGULARSOLVER_H
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template<typename Lhs, typename Rhs, int Mode,
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int UpLo = (Mode & LowerTriangularBit)
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? LowerTriangular
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: (Mode & UpperTriangularBit)
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? UpperTriangular
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: -1,
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int StorageOrder = int(ei_traits<Lhs>::Flags) & RowMajorBit>
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struct ei_sparse_solve_triangular_selector;
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// forward substitution, row-major
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template<typename Lhs, typename Rhs, int Mode>
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struct ei_sparse_solve_triangular_selector<Lhs,Rhs,Mode,LowerTriangular,RowMajor>
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{
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typedef typename Rhs::Scalar Scalar;
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static void run(const Lhs& lhs, Rhs& other)
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{
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for(int col=0 ; col<other.cols() ; ++col)
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{
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for(int i=0; i<lhs.rows(); ++i)
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{
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Scalar tmp = other.coeff(i,col);
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Scalar lastVal = 0;
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int lastIndex = 0;
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for(typename Lhs::InnerIterator it(lhs, i); it; ++it)
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{
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lastVal = it.value();
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lastIndex = it.index();
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if(lastIndex==i)
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break;
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tmp -= lastVal * other.coeff(lastIndex,col);
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}
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if (Mode & UnitDiagBit)
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other.coeffRef(i,col) = tmp;
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else
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{
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ei_assert(lastIndex==i);
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other.coeffRef(i,col) = tmp/lastVal;
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}
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}
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}
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}
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};
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// backward substitution, row-major
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template<typename Lhs, typename Rhs, int Mode>
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struct ei_sparse_solve_triangular_selector<Lhs,Rhs,Mode,UpperTriangular,RowMajor>
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{
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typedef typename Rhs::Scalar Scalar;
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static void run(const Lhs& lhs, Rhs& other)
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{
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for(int col=0 ; col<other.cols() ; ++col)
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{
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for(int i=lhs.rows()-1 ; i>=0 ; --i)
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{
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Scalar tmp = other.coeff(i,col);
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typename Lhs::InnerIterator it(lhs, i);
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if (it && it.index() == i)
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++it;
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for(; it; ++it)
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{
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tmp -= it.value() * other.coeff(it.index(),col);
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}
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if (Mode & UnitDiagBit)
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other.coeffRef(i,col) = tmp;
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else
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{
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typename Lhs::InnerIterator it(lhs, i);
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ei_assert(it && it.index() == i);
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other.coeffRef(i,col) = tmp/it.value();
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}
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}
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}
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}
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};
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// forward substitution, col-major
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template<typename Lhs, typename Rhs, int Mode>
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struct ei_sparse_solve_triangular_selector<Lhs,Rhs,Mode,LowerTriangular,ColMajor>
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{
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typedef typename Rhs::Scalar Scalar;
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static void run(const Lhs& lhs, Rhs& other)
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{
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for(int col=0 ; col<other.cols() ; ++col)
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{
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for(int i=0; i<lhs.cols(); ++i)
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{
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Scalar& tmp = other.coeffRef(i,col);
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if (tmp!=Scalar(0)) // optimization when other is actually sparse
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{
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typename Lhs::InnerIterator it(lhs, i);
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if(!(Mode & UnitDiagBit))
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{
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ei_assert(it.index()==i);
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tmp /= it.value();
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}
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if (it && it.index()==i)
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++it;
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for(; it; ++it)
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other.coeffRef(it.index(), col) -= tmp * it.value();
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}
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}
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}
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}
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};
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// backward substitution, col-major
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template<typename Lhs, typename Rhs, int Mode>
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struct ei_sparse_solve_triangular_selector<Lhs,Rhs,Mode,UpperTriangular,ColMajor>
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{
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typedef typename Rhs::Scalar Scalar;
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static void run(const Lhs& lhs, Rhs& other)
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{
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for(int col=0 ; col<other.cols() ; ++col)
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{
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for(int i=lhs.cols()-1; i>=0; --i)
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{
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Scalar& tmp = other.coeffRef(i,col);
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if (tmp!=Scalar(0)) // optimization when other is actually sparse
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{
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if(!(Mode & UnitDiagBit))
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{
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// FIXME lhs.coeff(i,i) might not be always efficient while it must simply be the
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// last element of the column !
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other.coeffRef(i,col) /= lhs.innerVector(i).lastCoeff();
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}
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typename Lhs::InnerIterator it(lhs, i);
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for(; it && it.index()<i; ++it)
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other.coeffRef(it.index(), col) -= tmp * it.value();
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}
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}
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}
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}
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};
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template<typename ExpressionType,int Mode>
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template<typename OtherDerived>
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void SparseTriangularView<ExpressionType,Mode>::solveInPlace(MatrixBase<OtherDerived>& other) const
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{
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ei_assert(m_matrix.cols() == m_matrix.rows());
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ei_assert(m_matrix.cols() == other.rows());
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ei_assert(!(Mode & ZeroDiagBit));
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ei_assert(Mode & (UpperTriangularBit|LowerTriangularBit));
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enum { copy = ei_traits<OtherDerived>::Flags & RowMajorBit };
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typedef typename ei_meta_if<copy,
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typename ei_plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::ret OtherCopy;
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OtherCopy otherCopy(other.derived());
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ei_sparse_solve_triangular_selector<ExpressionType, typename ei_unref<OtherCopy>::type, Mode>::run(m_matrix, otherCopy);
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if (copy)
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other = otherCopy;
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}
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template<typename ExpressionType,int Mode>
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template<typename OtherDerived>
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typename ei_plain_matrix_type_column_major<OtherDerived>::type
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SparseTriangularView<ExpressionType,Mode>::solve(const MatrixBase<OtherDerived>& other) const
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{
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typename ei_plain_matrix_type_column_major<OtherDerived>::type res(other);
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solveInPlace(res);
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return res;
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}
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// pure sparse path
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template<typename Lhs, typename Rhs, int Mode,
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int UpLo = (Mode & LowerTriangularBit)
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? LowerTriangular
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: (Mode & UpperTriangularBit)
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? UpperTriangular
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: -1,
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int StorageOrder = int(Lhs::Flags) & (RowMajorBit)>
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struct ei_sparse_solve_triangular_sparse_selector;
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// forward substitution, col-major
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template<typename Lhs, typename Rhs, int Mode, int UpLo>
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struct ei_sparse_solve_triangular_sparse_selector<Lhs,Rhs,Mode,UpLo,ColMajor>
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{
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typedef typename Rhs::Scalar Scalar;
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static void run(const Lhs& lhs, Rhs& other)
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{
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const bool IsLowerTriangular = (UpLo==LowerTriangular);
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AmbiVector<Scalar> tempVector(other.rows()*2);
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tempVector.setBounds(0,other.rows());
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Rhs res(other.rows(), other.cols());
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res.reserve(other.nonZeros());
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for(int col=0 ; col<other.cols() ; ++col)
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{
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// FIXME estimate number of non zeros
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tempVector.init(.99/*float(other.col(col).nonZeros())/float(other.rows())*/);
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tempVector.setZero();
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tempVector.restart();
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for (typename Rhs::InnerIterator rhsIt(other, col); rhsIt; ++rhsIt)
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{
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tempVector.coeffRef(rhsIt.index()) = rhsIt.value();
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}
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for(int i=IsLowerTriangular?0:lhs.cols()-1;
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IsLowerTriangular?i<lhs.cols():i>=0;
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i+=IsLowerTriangular?1:-1)
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{
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tempVector.restart();
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Scalar& ci = tempVector.coeffRef(i);
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if (ci!=Scalar(0))
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{
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// find
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typename Lhs::InnerIterator it(lhs, i);
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if(!(Mode & UnitDiagBit))
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{
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if (IsLowerTriangular)
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{
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ei_assert(it.index()==i);
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ci /= it.value();
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}
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else
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ci /= lhs.coeff(i,i);
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}
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tempVector.restart();
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if (IsLowerTriangular)
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{
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if (it.index()==i)
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++it;
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for(; it; ++it)
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tempVector.coeffRef(it.index()) -= ci * it.value();
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}
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else
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{
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for(; it && it.index()<i; ++it)
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tempVector.coeffRef(it.index()) -= ci * it.value();
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}
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}
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}
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int count = 0;
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// FIXME compute a reference value to filter zeros
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for (typename AmbiVector<Scalar>::Iterator it(tempVector/*,1e-12*/); it; ++it)
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{
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++ count;
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// std::cerr << "fill " << it.index() << ", " << col << "\n";
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// std::cout << it.value() << " ";
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// FIXME use insertBack
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res.insert(it.index(), col) = it.value();
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}
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// std::cout << "tempVector.nonZeros() == " << int(count) << " / " << (other.rows()) << "\n";
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}
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res.finalize();
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other = res.markAsRValue();
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}
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};
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template<typename ExpressionType,int Mode>
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template<typename OtherDerived>
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void SparseTriangularView<ExpressionType,Mode>::solveInPlace(SparseMatrixBase<OtherDerived>& other) const
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{
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ei_assert(m_matrix.cols() == m_matrix.rows());
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ei_assert(m_matrix.cols() == other.rows());
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ei_assert(!(Mode & ZeroDiagBit));
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ei_assert(Mode & (UpperTriangularBit|LowerTriangularBit));
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// enum { copy = ei_traits<OtherDerived>::Flags & RowMajorBit };
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// typedef typename ei_meta_if<copy,
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// typename ei_plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::ret OtherCopy;
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// OtherCopy otherCopy(other.derived());
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ei_sparse_solve_triangular_sparse_selector<ExpressionType, OtherDerived, Mode>::run(m_matrix, other.derived());
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// if (copy)
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// other = otherCopy;
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}
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#ifdef EIGEN2_SUPPORT
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// deprecated stuff:
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/** \deprecated */
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template<typename Derived>
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template<typename OtherDerived>
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void SparseMatrixBase<Derived>::solveTriangularInPlace(MatrixBase<OtherDerived>& other) const
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{
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this->template triangular<Flags&(UpperTriangularBit|LowerTriangularBit)>().solveInPlace(other);
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}
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/** \deprecated */
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template<typename Derived>
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template<typename OtherDerived>
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typename ei_plain_matrix_type_column_major<OtherDerived>::type
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SparseMatrixBase<Derived>::solveTriangular(const MatrixBase<OtherDerived>& other) const
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{
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typename ei_plain_matrix_type_column_major<OtherDerived>::type res(other);
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derived().solveTriangularInPlace(res);
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return res;
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}
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#endif // EIGEN2_SUPPORT
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#endif // EIGEN_SPARSETRIANGULARSOLVER_H
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