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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_SPARSETRIANGULARSOLVER_H
#define EIGEN_SPARSETRIANGULARSOLVER_H
namespace Eigen {
namespace internal {
template<typename Lhs, typename Rhs, int Mode,
int UpLo = (Mode & Lower)
? Lower
: (Mode & Upper)
? Upper
: -1,
int StorageOrder = int(traits<Lhs>::Flags) & RowMajorBit>
struct sparse_solve_triangular_selector;
// forward substitution, row-major
template<typename Lhs, typename Rhs, int Mode>
struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,RowMajor>
{
typedef typename Rhs::Scalar Scalar;
typedef typename Lhs::Index Index;
typedef typename evaluator<Lhs>::type LhsEval;
typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
static void run(const Lhs& lhs, Rhs& other)
{
LhsEval lhsEval(lhs);
for(Index col=0 ; col<other.cols() ; ++col)
{
for(Index i=0; i<lhs.rows(); ++i)
{
Scalar tmp = other.coeff(i,col);
Scalar lastVal(0);
Index lastIndex = 0;
for(LhsIterator it(lhsEval, i); it; ++it)
{
lastVal = it.value();
lastIndex = it.index();
if(lastIndex==i)
break;
tmp -= lastVal * other.coeff(lastIndex,col);
}
if (Mode & UnitDiag)
other.coeffRef(i,col) = tmp;
else
{
eigen_assert(lastIndex==i);
other.coeffRef(i,col) = tmp/lastVal;
}
}
}
}
};
// backward substitution, row-major
template<typename Lhs, typename Rhs, int Mode>
struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,RowMajor>
{
typedef typename Rhs::Scalar Scalar;
typedef typename Lhs::Index Index;
typedef typename evaluator<Lhs>::type LhsEval;
typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
static void run(const Lhs& lhs, Rhs& other)
{
LhsEval lhsEval(lhs);
for(Index col=0 ; col<other.cols() ; ++col)
{
for(Index i=lhs.rows()-1 ; i>=0 ; --i)
{
Scalar tmp = other.coeff(i,col);
Scalar l_ii = 0;
LhsIterator it(lhsEval, i);
while(it && it.index()<i)
++it;
if(!(Mode & UnitDiag))
{
eigen_assert(it && it.index()==i);
l_ii = it.value();
++it;
}
else if (it && it.index() == i)
++it;
for(; it; ++it)
{
tmp -= it.value() * other.coeff(it.index(),col);
}
if (Mode & UnitDiag) other.coeffRef(i,col) = tmp;
else other.coeffRef(i,col) = tmp/l_ii;
}
}
}
};
// forward substitution, col-major
template<typename Lhs, typename Rhs, int Mode>
struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Lower,ColMajor>
{
typedef typename Rhs::Scalar Scalar;
typedef typename Lhs::Index Index;
typedef typename evaluator<Lhs>::type LhsEval;
typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
static void run(const Lhs& lhs, Rhs& other)
{
LhsEval lhsEval(lhs);
for(Index col=0 ; col<other.cols() ; ++col)
{
for(Index i=0; i<lhs.cols(); ++i)
{
Scalar& tmp = other.coeffRef(i,col);
if (tmp!=Scalar(0)) // optimization when other is actually sparse
{
LhsIterator it(lhsEval, i);
while(it && it.index()<i)
++it;
if(!(Mode & UnitDiag))
{
eigen_assert(it && it.index()==i);
tmp /= it.value();
}
if (it && it.index()==i)
++it;
for(; it; ++it)
other.coeffRef(it.index(), col) -= tmp * it.value();
}
}
}
}
};
// backward substitution, col-major
template<typename Lhs, typename Rhs, int Mode>
struct sparse_solve_triangular_selector<Lhs,Rhs,Mode,Upper,ColMajor>
{
typedef typename Rhs::Scalar Scalar;
typedef typename Lhs::Index Index;
typedef typename evaluator<Lhs>::type LhsEval;
typedef typename evaluator<Lhs>::InnerIterator LhsIterator;
static void run(const Lhs& lhs, Rhs& other)
{
LhsEval lhsEval(lhs);
for(Index col=0 ; col<other.cols() ; ++col)
{
for(Index i=lhs.cols()-1; i>=0; --i)
{
Scalar& tmp = other.coeffRef(i,col);
if (tmp!=Scalar(0)) // optimization when other is actually sparse
{
if(!(Mode & UnitDiag))
{
// TODO replace this by a binary search. make sure the binary search is safe for partially sorted elements
LhsIterator it(lhsEval, i);
while(it && it.index()!=i)
++it;
eigen_assert(it && it.index()==i);
other.coeffRef(i,col) /= it.value();
}
LhsIterator it(lhsEval, i);
for(; it && it.index()<i; ++it)
other.coeffRef(it.index(), col) -= tmp * it.value();
}
}
}
}
};
} // end namespace internal
template<typename ExpressionType,unsigned int Mode>
template<typename OtherDerived>
void TriangularViewImpl<ExpressionType,Mode,Sparse>::solveInPlace(MatrixBase<OtherDerived>& other) const
{
eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows());
eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };
typedef typename internal::conditional<copy,
typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
OtherCopy otherCopy(other.derived());
internal::sparse_solve_triangular_selector<ExpressionType, typename internal::remove_reference<OtherCopy>::type, Mode>::run(derived().nestedExpression(), otherCopy);
if (copy)
other = otherCopy;
}
// pure sparse path
namespace internal {
template<typename Lhs, typename Rhs, int Mode,
int UpLo = (Mode & Lower)
? Lower
: (Mode & Upper)
? Upper
: -1,
int StorageOrder = int(Lhs::Flags) & (RowMajorBit)>
struct sparse_solve_triangular_sparse_selector;
// forward substitution, col-major
template<typename Lhs, typename Rhs, int Mode, int UpLo>
struct sparse_solve_triangular_sparse_selector<Lhs,Rhs,Mode,UpLo,ColMajor>
{
typedef typename Rhs::Scalar Scalar;
typedef typename promote_index_type<typename traits<Lhs>::Index,
typename traits<Rhs>::Index>::type Index;
static void run(const Lhs& lhs, Rhs& other)
{
const bool IsLower = (UpLo==Lower);
AmbiVector<Scalar,Index> tempVector(other.rows()*2);
tempVector.setBounds(0,other.rows());
Rhs res(other.rows(), other.cols());
res.reserve(other.nonZeros());
for(Index col=0 ; col<other.cols() ; ++col)
{
// FIXME estimate number of non zeros
tempVector.init(.99/*float(other.col(col).nonZeros())/float(other.rows())*/);
tempVector.setZero();
tempVector.restart();
for (typename Rhs::InnerIterator rhsIt(other, col); rhsIt; ++rhsIt)
{
tempVector.coeffRef(rhsIt.index()) = rhsIt.value();
}
for(Index i=IsLower?0:lhs.cols()-1;
IsLower?i<lhs.cols():i>=0;
i+=IsLower?1:-1)
{
tempVector.restart();
Scalar& ci = tempVector.coeffRef(i);
if (ci!=Scalar(0))
{
// find
typename Lhs::InnerIterator it(lhs, i);
if(!(Mode & UnitDiag))
{
if (IsLower)
{
eigen_assert(it.index()==i);
ci /= it.value();
}
else
ci /= lhs.coeff(i,i);
}
tempVector.restart();
if (IsLower)
{
if (it.index()==i)
++it;
for(; it; ++it)
tempVector.coeffRef(it.index()) -= ci * it.value();
}
else
{
for(; it && it.index()<i; ++it)
tempVector.coeffRef(it.index()) -= ci * it.value();
}
}
}
Index count = 0;
// FIXME compute a reference value to filter zeros
for (typename AmbiVector<Scalar,Index>::Iterator it(tempVector/*,1e-12*/); it; ++it)
{
++ count;
// std::cerr << "fill " << it.index() << ", " << col << "\n";
// std::cout << it.value() << " ";
// FIXME use insertBack
res.insert(it.index(), col) = it.value();
}
// std::cout << "tempVector.nonZeros() == " << int(count) << " / " << (other.rows()) << "\n";
}
res.finalize();
other = res.markAsRValue();
}
};
} // end namespace internal
template<typename ExpressionType,unsigned int Mode>
template<typename OtherDerived>
void TriangularViewImpl<ExpressionType,Mode,Sparse>::solveInPlace(SparseMatrixBase<OtherDerived>& other) const
{
eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows());
eigen_assert( (!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
// enum { copy = internal::traits<OtherDerived>::Flags & RowMajorBit };
// typedef typename internal::conditional<copy,
// typename internal::plain_matrix_type_column_major<OtherDerived>::type, OtherDerived&>::type OtherCopy;
// OtherCopy otherCopy(other.derived());
internal::sparse_solve_triangular_sparse_selector<ExpressionType, OtherDerived, Mode>::run(derived().nestedExpression(), other.derived());
// if (copy)
// other = otherCopy;
}
} // end namespace Eigen
#endif // EIGEN_SPARSETRIANGULARSOLVER_H
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