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Diffstat (limited to 'third_party/eigen3/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h')
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diff --git a/third_party/eigen3/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h b/third_party/eigen3/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h deleted file mode 100644 index b55afc1363..0000000000 --- a/third_party/eigen3/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h +++ /dev/null @@ -1,467 +0,0 @@ -// This file is part of Eigen, a lightweight C++ template library -// for linear algebra. -// -// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@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_INCOMPLETE_LUT_H -#define EIGEN_INCOMPLETE_LUT_H - - -namespace Eigen { - -namespace internal { - -/** \internal - * Compute a quick-sort split of a vector - * On output, the vector row is permuted such that its elements satisfy - * abs(row(i)) >= abs(row(ncut)) if i<ncut - * abs(row(i)) <= abs(row(ncut)) if i>ncut - * \param row The vector of values - * \param ind The array of index for the elements in @p row - * \param ncut The number of largest elements to keep - **/ -template <typename VectorV, typename VectorI, typename Index> -Index QuickSplit(VectorV &row, VectorI &ind, Index ncut) -{ - typedef typename VectorV::RealScalar RealScalar; - using std::swap; - using std::abs; - Index mid; - Index n = row.size(); /* length of the vector */ - Index first, last ; - - ncut--; /* to fit the zero-based indices */ - first = 0; - last = n-1; - if (ncut < first || ncut > last ) return 0; - - do { - mid = first; - RealScalar abskey = abs(row(mid)); - for (Index j = first + 1; j <= last; j++) { - if ( abs(row(j)) > abskey) { - ++mid; - swap(row(mid), row(j)); - swap(ind(mid), ind(j)); - } - } - /* Interchange for the pivot element */ - swap(row(mid), row(first)); - swap(ind(mid), ind(first)); - - if (mid > ncut) last = mid - 1; - else if (mid < ncut ) first = mid + 1; - } while (mid != ncut ); - - return 0; /* mid is equal to ncut */ -} - -}// end namespace internal - -/** \ingroup IterativeLinearSolvers_Module - * \class IncompleteLUT - * \brief Incomplete LU factorization with dual-threshold strategy - * - * During the numerical factorization, two dropping rules are used : - * 1) any element whose magnitude is less than some tolerance is dropped. - * This tolerance is obtained by multiplying the input tolerance @p droptol - * by the average magnitude of all the original elements in the current row. - * 2) After the elimination of the row, only the @p fill largest elements in - * the L part and the @p fill largest elements in the U part are kept - * (in addition to the diagonal element ). Note that @p fill is computed from - * the input parameter @p fillfactor which is used the ratio to control the fill_in - * relatively to the initial number of nonzero elements. - * - * The two extreme cases are when @p droptol=0 (to keep all the @p fill*2 largest elements) - * and when @p fill=n/2 with @p droptol being different to zero. - * - * References : Yousef Saad, ILUT: A dual threshold incomplete LU factorization, - * Numerical Linear Algebra with Applications, 1(4), pp 387-402, 1994. - * - * NOTE : The following implementation is derived from the ILUT implementation - * in the SPARSKIT package, Copyright (C) 2005, the Regents of the University of Minnesota - * released under the terms of the GNU LGPL: - * http://www-users.cs.umn.edu/~saad/software/SPARSKIT/README - * However, Yousef Saad gave us permission to relicense his ILUT code to MPL2. - * See the Eigen mailing list archive, thread: ILUT, date: July 8, 2012: - * http://listengine.tuxfamily.org/lists.tuxfamily.org/eigen/2012/07/msg00064.html - * alternatively, on GMANE: - * http://comments.gmane.org/gmane.comp.lib.eigen/3302 - */ -template <typename _Scalar> -class IncompleteLUT : internal::noncopyable -{ - typedef _Scalar Scalar; - typedef typename NumTraits<Scalar>::Real RealScalar; - typedef Matrix<Scalar,Dynamic,1> Vector; - typedef SparseMatrix<Scalar,RowMajor> FactorType; - typedef SparseMatrix<Scalar,ColMajor> PermutType; - typedef typename FactorType::Index Index; - - public: - typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType; - - IncompleteLUT() - : m_droptol(NumTraits<Scalar>::dummy_precision()), m_fillfactor(10), - m_analysisIsOk(false), m_factorizationIsOk(false), m_isInitialized(false) - {} - - template<typename MatrixType> - IncompleteLUT(const MatrixType& mat, const RealScalar& droptol=NumTraits<Scalar>::dummy_precision(), int fillfactor = 10) - : m_droptol(droptol),m_fillfactor(fillfactor), - m_analysisIsOk(false),m_factorizationIsOk(false),m_isInitialized(false) - { - eigen_assert(fillfactor != 0); - compute(mat); - } - - Index rows() const { return m_lu.rows(); } - - Index cols() const { return m_lu.cols(); } - - /** \brief Reports whether previous computation was successful. - * - * \returns \c Success if computation was succesful, - * \c NumericalIssue if the matrix.appears to be negative. - */ - ComputationInfo info() const - { - eigen_assert(m_isInitialized && "IncompleteLUT is not initialized."); - return m_info; - } - - template<typename MatrixType> - void analyzePattern(const MatrixType& amat); - - template<typename MatrixType> - void factorize(const MatrixType& amat); - - /** - * Compute an incomplete LU factorization with dual threshold on the matrix mat - * No pivoting is done in this version - * - **/ - template<typename MatrixType> - IncompleteLUT<Scalar>& compute(const MatrixType& amat) - { - analyzePattern(amat); - factorize(amat); - m_isInitialized = m_factorizationIsOk; - return *this; - } - - void setDroptol(const RealScalar& droptol); - void setFillfactor(int fillfactor); - - template<typename Rhs, typename Dest> - void _solve(const Rhs& b, Dest& x) const - { - x = m_Pinv * b; - x = m_lu.template triangularView<UnitLower>().solve(x); - x = m_lu.template triangularView<Upper>().solve(x); - x = m_P * x; - } - - template<typename Rhs> inline const internal::solve_retval<IncompleteLUT, Rhs> - solve(const MatrixBase<Rhs>& b) const - { - eigen_assert(m_isInitialized && "IncompleteLUT is not initialized."); - eigen_assert(cols()==b.rows() - && "IncompleteLUT::solve(): invalid number of rows of the right hand side matrix b"); - return internal::solve_retval<IncompleteLUT, Rhs>(*this, b.derived()); - } - -protected: - - /** keeps off-diagonal entries; drops diagonal entries */ - struct keep_diag { - inline bool operator() (const Index& row, const Index& col, const Scalar&) const - { - return row!=col; - } - }; - -protected: - - FactorType m_lu; - RealScalar m_droptol; - int m_fillfactor; - bool m_analysisIsOk; - bool m_factorizationIsOk; - bool m_isInitialized; - ComputationInfo m_info; - PermutationMatrix<Dynamic,Dynamic,Index> m_P; // Fill-reducing permutation - PermutationMatrix<Dynamic,Dynamic,Index> m_Pinv; // Inverse permutation -}; - -/** - * Set control parameter droptol - * \param droptol Drop any element whose magnitude is less than this tolerance - **/ -template<typename Scalar> -void IncompleteLUT<Scalar>::setDroptol(const RealScalar& droptol) -{ - this->m_droptol = droptol; -} - -/** - * Set control parameter fillfactor - * \param fillfactor This is used to compute the number @p fill_in of largest elements to keep on each row. - **/ -template<typename Scalar> -void IncompleteLUT<Scalar>::setFillfactor(int fillfactor) -{ - this->m_fillfactor = fillfactor; -} - -template <typename Scalar> -template<typename _MatrixType> -void IncompleteLUT<Scalar>::analyzePattern(const _MatrixType& amat) -{ - // Compute the Fill-reducing permutation - SparseMatrix<Scalar,ColMajor, Index> mat1 = amat; - SparseMatrix<Scalar,ColMajor, Index> mat2 = amat.transpose(); - // Symmetrize the pattern - // FIXME for a matrix with nearly symmetric pattern, mat2+mat1 is the appropriate choice. - // on the other hand for a really non-symmetric pattern, mat2*mat1 should be prefered... - SparseMatrix<Scalar,ColMajor, Index> AtA = mat2 + mat1; - AtA.prune(keep_diag()); - internal::minimum_degree_ordering<Scalar, Index>(AtA, m_P); // Then compute the AMD ordering... - - m_Pinv = m_P.inverse(); // ... and the inverse permutation - - m_analysisIsOk = true; -} - -template <typename Scalar> -template<typename _MatrixType> -void IncompleteLUT<Scalar>::factorize(const _MatrixType& amat) -{ - using std::sqrt; - using std::swap; - using std::abs; - - eigen_assert((amat.rows() == amat.cols()) && "The factorization should be done on a square matrix"); - Index n = amat.cols(); // Size of the matrix - m_lu.resize(n,n); - // Declare Working vectors and variables - Vector u(n) ; // real values of the row -- maximum size is n -- - VectorXi ju(n); // column position of the values in u -- maximum size is n - VectorXi jr(n); // Indicate the position of the nonzero elements in the vector u -- A zero location is indicated by -1 - - // Apply the fill-reducing permutation - eigen_assert(m_analysisIsOk && "You must first call analyzePattern()"); - SparseMatrix<Scalar,RowMajor, Index> mat; - mat = amat.twistedBy(m_Pinv); - - // Initialization - jr.fill(-1); - ju.fill(0); - u.fill(0); - - // number of largest elements to keep in each row: - Index fill_in = static_cast<Index> (amat.nonZeros()*m_fillfactor)/n+1; - if (fill_in > n) fill_in = n; - - // number of largest nonzero elements to keep in the L and the U part of the current row: - Index nnzL = fill_in/2; - Index nnzU = nnzL; - m_lu.reserve(n * (nnzL + nnzU + 1)); - - // global loop over the rows of the sparse matrix - for (Index ii = 0; ii < n; ii++) - { - // 1 - copy the lower and the upper part of the row i of mat in the working vector u - - Index sizeu = 1; // number of nonzero elements in the upper part of the current row - Index sizel = 0; // number of nonzero elements in the lower part of the current row - ju(ii) = ii; - u(ii) = 0; - jr(ii) = ii; - RealScalar rownorm = 0; - - typename FactorType::InnerIterator j_it(mat, ii); // Iterate through the current row ii - for (; j_it; ++j_it) - { - Index k = j_it.index(); - if (k < ii) - { - // copy the lower part - ju(sizel) = k; - u(sizel) = j_it.value(); - jr(k) = sizel; - ++sizel; - } - else if (k == ii) - { - u(ii) = j_it.value(); - } - else - { - // copy the upper part - Index jpos = ii + sizeu; - ju(jpos) = k; - u(jpos) = j_it.value(); - jr(k) = jpos; - ++sizeu; - } - rownorm += numext::abs2(j_it.value()); - } - - // 2 - detect possible zero row - if(rownorm==0) - { - m_info = NumericalIssue; - return; - } - // Take the 2-norm of the current row as a relative tolerance - rownorm = sqrt(rownorm); - - // 3 - eliminate the previous nonzero rows - Index jj = 0; - Index len = 0; - while (jj < sizel) - { - // In order to eliminate in the correct order, - // we must select first the smallest column index among ju(jj:sizel) - Index k; - Index minrow = ju.segment(jj,sizel-jj).minCoeff(&k); // k is relative to the segment - k += jj; - if (minrow != ju(jj)) - { - // swap the two locations - Index j = ju(jj); - swap(ju(jj), ju(k)); - jr(minrow) = jj; jr(j) = k; - swap(u(jj), u(k)); - } - // Reset this location - jr(minrow) = -1; - - // Start elimination - typename FactorType::InnerIterator ki_it(m_lu, minrow); - while (ki_it && ki_it.index() < minrow) ++ki_it; - eigen_internal_assert(ki_it && ki_it.col()==minrow); - Scalar fact = u(jj) / ki_it.value(); - - // drop too small elements - if(abs(fact) <= m_droptol) - { - jj++; - continue; - } - - // linear combination of the current row ii and the row minrow - ++ki_it; - for (; ki_it; ++ki_it) - { - Scalar prod = fact * ki_it.value(); - Index j = ki_it.index(); - Index jpos = jr(j); - if (jpos == -1) // fill-in element - { - Index newpos; - if (j >= ii) // dealing with the upper part - { - newpos = ii + sizeu; - sizeu++; - eigen_internal_assert(sizeu<=n); - } - else // dealing with the lower part - { - newpos = sizel; - sizel++; - eigen_internal_assert(sizel<=ii); - } - ju(newpos) = j; - u(newpos) = -prod; - jr(j) = newpos; - } - else - u(jpos) -= prod; - } - // store the pivot element - u(len) = fact; - ju(len) = minrow; - ++len; - - jj++; - } // end of the elimination on the row ii - - // reset the upper part of the pointer jr to zero - for(Index k = 0; k <sizeu; k++) jr(ju(ii+k)) = -1; - - // 4 - partially sort and insert the elements in the m_lu matrix - - // sort the L-part of the row - sizel = len; - len = (std::min)(sizel, nnzL); - typename Vector::SegmentReturnType ul(u.segment(0, sizel)); - typename VectorXi::SegmentReturnType jul(ju.segment(0, sizel)); - internal::QuickSplit(ul, jul, len); - - // store the largest m_fill elements of the L part - m_lu.startVec(ii); - for(Index k = 0; k < len; k++) - m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k); - - // store the diagonal element - // apply a shifting rule to avoid zero pivots (we are doing an incomplete factorization) - if (u(ii) == Scalar(0)) - u(ii) = sqrt(m_droptol) * rownorm; - m_lu.insertBackByOuterInnerUnordered(ii, ii) = u(ii); - - // sort the U-part of the row - // apply the dropping rule first - len = 0; - for(Index k = 1; k < sizeu; k++) - { - if(abs(u(ii+k)) > m_droptol * rownorm ) - { - ++len; - u(ii + len) = u(ii + k); - ju(ii + len) = ju(ii + k); - } - } - sizeu = len + 1; // +1 to take into account the diagonal element - len = (std::min)(sizeu, nnzU); - typename Vector::SegmentReturnType uu(u.segment(ii+1, sizeu-1)); - typename VectorXi::SegmentReturnType juu(ju.segment(ii+1, sizeu-1)); - internal::QuickSplit(uu, juu, len); - - // store the largest elements of the U part - for(Index k = ii + 1; k < ii + len; k++) - m_lu.insertBackByOuterInnerUnordered(ii,ju(k)) = u(k); - } - - m_lu.finalize(); - m_lu.makeCompressed(); - - m_factorizationIsOk = true; - m_info = Success; -} - -namespace internal { - -template<typename _MatrixType, typename Rhs> -struct solve_retval<IncompleteLUT<_MatrixType>, Rhs> - : solve_retval_base<IncompleteLUT<_MatrixType>, Rhs> -{ - typedef IncompleteLUT<_MatrixType> Dec; - EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) - - template<typename Dest> void evalTo(Dest& dst) const - { - dec()._solve(rhs(),dst); - } -}; - -} // end namespace internal - -} // end namespace Eigen - -#endif // EIGEN_INCOMPLETE_LUT_H |