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// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008 Gael Guennebaud // // 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 // IWYU pragma: private #include "./InternalHeaderCheck.h" namespace Eigen { namespace internal { template ::Flags) & RowMajorBit> struct sparse_solve_triangular_selector; // forward substitution, row-major template struct sparse_solve_triangular_selector { typedef typename Rhs::Scalar Scalar; typedef evaluator LhsEval; typedef typename evaluator::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 = numext::madd(-lastVal, other.coeff(lastIndex, col), tmp); } if (Mode & UnitDiag) other.coeffRef(i, col) = tmp; else { eigen_assert(lastIndex == i); other.coeffRef(i, col) = tmp / lastVal; } } } } }; // backward substitution, row-major template struct sparse_solve_triangular_selector { typedef typename Rhs::Scalar Scalar; typedef evaluator LhsEval; typedef typename evaluator::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 = numext::madd(-it.value(), other.coeff(it.index(), col), tmp); } if (Mode & UnitDiag) other.coeffRef(i, col) = tmp; else other.coeffRef(i, col) = tmp / l_ii; } } } }; // forward substitution, col-major template struct sparse_solve_triangular_selector { typedef typename Rhs::Scalar Scalar; typedef evaluator LhsEval; typedef typename evaluator::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 (!numext::is_exactly_zero(tmp)) // 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) = numext::madd(-tmp, it.value(), other.coeffRef(it.index(), col)); } } } } } }; // backward substitution, col-major template struct sparse_solve_triangular_selector { typedef typename Rhs::Scalar Scalar; typedef evaluator LhsEval; typedef typename evaluator::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 (!numext::is_exactly_zero(tmp)) // 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) = numext::madd(-tmp, it.value(), other.coeffRef(it.index(), col)); } } } } } }; } // end namespace internal #ifndef EIGEN_PARSED_BY_DOXYGEN template template void TriangularViewImpl::solveInPlace(MatrixBase& other) const { eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows()); eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper | Lower))); enum { copy = internal::traits::Flags & RowMajorBit }; typedef std::conditional_t::type, OtherDerived&> OtherCopy; OtherCopy otherCopy(other.derived()); internal::sparse_solve_triangular_selector, Mode>::run( derived().nestedExpression(), otherCopy); if (copy) other = otherCopy; } #endif // pure sparse path namespace internal { template struct sparse_solve_triangular_sparse_selector; // forward substitution, col-major template struct sparse_solve_triangular_sparse_selector { typedef typename Rhs::Scalar Scalar; typedef typename promote_index_type::StorageIndex, typename traits::StorageIndex>::type StorageIndex; static void run(const Lhs& lhs, Rhs& other) { const bool IsLower = (UpLo == Lower); AmbiVector 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 (!numext::is_exactly_zero(ci)) { // 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()) = numext::madd(-ci, it.value(), tempVector.coeffRef(it.index())); } } else { for (; it && it.index() < i; ++it) { tempVector.coeffRef(it.index()) = numext::madd(-ci, it.value(), tempVector.coeffRef(it.index())); } } } } // Index count = 0; // FIXME compute a reference value to filter zeros for (typename AmbiVector::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 #ifndef EIGEN_PARSED_BY_DOXYGEN template template void TriangularViewImpl::solveInPlace(SparseMatrixBase& other) const { eigen_assert(derived().cols() == derived().rows() && derived().cols() == other.rows()); eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper | Lower))); // enum { copy = internal::traits::Flags & RowMajorBit }; // typedef std::conditional_t::type, OtherDerived&> OtherCopy; // OtherCopy otherCopy(other.derived()); internal::sparse_solve_triangular_sparse_selector::run( derived().nestedExpression(), other.derived()); // if (copy) // other = otherCopy; } #endif } // end namespace Eigen #endif // EIGEN_SPARSETRIANGULARSOLVER_H