339 lines
12 KiB
C
339 lines
12 KiB
C
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// 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) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_SUITESPARSEQRSUPPORT_H
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#define EIGEN_SUITESPARSEQRSUPPORT_H
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namespace Eigen {
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template<typename MatrixType> class SPQR;
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template<typename SPQRType> struct SPQRMatrixQReturnType;
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template<typename SPQRType> struct SPQRMatrixQTransposeReturnType;
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template <typename SPQRType, typename Derived> struct SPQR_QProduct;
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namespace internal {
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template <typename SPQRType> struct traits<SPQRMatrixQReturnType<SPQRType> >
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{
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typedef typename SPQRType::MatrixType ReturnType;
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};
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template <typename SPQRType> struct traits<SPQRMatrixQTransposeReturnType<SPQRType> >
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{
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typedef typename SPQRType::MatrixType ReturnType;
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};
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template <typename SPQRType, typename Derived> struct traits<SPQR_QProduct<SPQRType, Derived> >
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{
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typedef typename Derived::PlainObject ReturnType;
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};
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} // End namespace internal
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/**
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* \ingroup SPQRSupport_Module
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* \class SPQR
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* \brief Sparse QR factorization based on SuiteSparseQR library
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*
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* This class is used to perform a multithreaded and multifrontal rank-revealing QR decomposition
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* of sparse matrices. The result is then used to solve linear leasts_square systems.
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* Clearly, a QR factorization is returned such that A*P = Q*R where :
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*
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* P is the column permutation. Use colsPermutation() to get it.
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*
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* Q is the orthogonal matrix represented as Householder reflectors.
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* Use matrixQ() to get an expression and matrixQ().transpose() to get the transpose.
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* You can then apply it to a vector.
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*
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* R is the sparse triangular factor. Use matrixQR() to get it as SparseMatrix.
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* NOTE : The Index type of R is always SuiteSparse_long. You can get it with SPQR::Index
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*
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* \tparam _MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<>
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* NOTE
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*
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*/
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template<typename _MatrixType>
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class SPQR
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{
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public:
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typedef typename _MatrixType::Scalar Scalar;
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typedef typename _MatrixType::RealScalar RealScalar;
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typedef SuiteSparse_long Index ;
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typedef SparseMatrix<Scalar, ColMajor, Index> MatrixType;
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typedef PermutationMatrix<Dynamic, Dynamic> PermutationType;
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public:
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SPQR()
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: m_isInitialized(false), m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
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{
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cholmod_l_start(&m_cc);
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}
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SPQR(const _MatrixType& matrix)
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: m_isInitialized(false), m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true)
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{
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cholmod_l_start(&m_cc);
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compute(matrix);
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}
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~SPQR()
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{
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SPQR_free();
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cholmod_l_finish(&m_cc);
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}
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void SPQR_free()
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{
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cholmod_l_free_sparse(&m_H, &m_cc);
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cholmod_l_free_sparse(&m_cR, &m_cc);
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cholmod_l_free_dense(&m_HTau, &m_cc);
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std::free(m_E);
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std::free(m_HPinv);
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}
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void compute(const _MatrixType& matrix)
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{
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if(m_isInitialized) SPQR_free();
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MatrixType mat(matrix);
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/* Compute the default threshold as in MatLab, see:
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* Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing
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* Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3
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*/
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RealScalar pivotThreshold = m_tolerance;
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if(m_useDefaultThreshold)
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{
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using std::max;
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RealScalar max2Norm = 0.0;
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for (int j = 0; j < mat.cols(); j++) max2Norm = (max)(max2Norm, mat.col(j).norm());
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if(max2Norm==RealScalar(0))
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max2Norm = RealScalar(1);
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pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon();
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}
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cholmod_sparse A;
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A = viewAsCholmod(mat);
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Index col = matrix.cols();
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m_rank = SuiteSparseQR<Scalar>(m_ordering, pivotThreshold, col, &A,
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&m_cR, &m_E, &m_H, &m_HPinv, &m_HTau, &m_cc);
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if (!m_cR)
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{
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m_info = NumericalIssue;
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m_isInitialized = false;
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return;
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}
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m_info = Success;
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m_isInitialized = true;
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m_isRUpToDate = false;
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}
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/**
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* Get the number of rows of the input matrix and the Q matrix
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*/
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inline Index rows() const {return m_cR->nrow; }
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/**
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* Get the number of columns of the input matrix.
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*/
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inline Index cols() const { return m_cR->ncol; }
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/** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A.
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*
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* \sa compute()
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*/
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template<typename Rhs>
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inline const internal::solve_retval<SPQR, Rhs> solve(const MatrixBase<Rhs>& B) const
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{
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eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
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eigen_assert(this->rows()==B.rows()
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&& "SPQR::solve(): invalid number of rows of the right hand side matrix B");
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return internal::solve_retval<SPQR, Rhs>(*this, B.derived());
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}
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template<typename Rhs, typename Dest>
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void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
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{
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eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
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eigen_assert(b.cols()==1 && "This method is for vectors only");
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//Compute Q^T * b
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typename Dest::PlainObject y, y2;
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y = matrixQ().transpose() * b;
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// Solves with the triangular matrix R
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Index rk = this->rank();
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y2 = y;
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y.resize((std::max)(cols(),Index(y.rows())),y.cols());
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y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y2.topRows(rk));
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// Apply the column permutation
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// colsPermutation() performs a copy of the permutation,
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// so let's apply it manually:
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for(Index i = 0; i < rk; ++i) dest.row(m_E[i]) = y.row(i);
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for(Index i = rk; i < cols(); ++i) dest.row(m_E[i]).setZero();
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// y.bottomRows(y.rows()-rk).setZero();
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// dest = colsPermutation() * y.topRows(cols());
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m_info = Success;
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}
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/** \returns the sparse triangular factor R. It is a sparse matrix
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*/
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const MatrixType matrixR() const
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{
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eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()");
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if(!m_isRUpToDate) {
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m_R = viewAsEigen<Scalar,ColMajor, typename MatrixType::Index>(*m_cR);
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m_isRUpToDate = true;
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}
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return m_R;
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}
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/// Get an expression of the matrix Q
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SPQRMatrixQReturnType<SPQR> matrixQ() const
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{
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return SPQRMatrixQReturnType<SPQR>(*this);
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}
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/// Get the permutation that was applied to columns of A
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PermutationType colsPermutation() const
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{
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eigen_assert(m_isInitialized && "Decomposition is not initialized.");
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Index n = m_cR->ncol;
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PermutationType colsPerm(n);
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for(Index j = 0; j <n; j++) colsPerm.indices()(j) = m_E[j];
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return colsPerm;
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}
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/**
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* Gets the rank of the matrix.
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* It should be equal to matrixQR().cols if the matrix is full-rank
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*/
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Index rank() const
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{
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eigen_assert(m_isInitialized && "Decomposition is not initialized.");
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return m_cc.SPQR_istat[4];
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}
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/// Set the fill-reducing ordering method to be used
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void setSPQROrdering(int ord) { m_ordering = ord;}
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/// Set the tolerance tol to treat columns with 2-norm < =tol as zero
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void setPivotThreshold(const RealScalar& tol)
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{
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m_useDefaultThreshold = false;
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m_tolerance = tol;
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}
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/** \returns a pointer to the SPQR workspace */
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cholmod_common *cholmodCommon() const { return &m_cc; }
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/** \brief Reports whether previous computation was successful.
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*
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* \returns \c Success if computation was succesful,
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* \c NumericalIssue if the sparse QR can not be computed
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*/
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ComputationInfo info() const
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{
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eigen_assert(m_isInitialized && "Decomposition is not initialized.");
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return m_info;
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}
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protected:
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bool m_isInitialized;
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bool m_analysisIsOk;
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bool m_factorizationIsOk;
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mutable bool m_isRUpToDate;
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mutable ComputationInfo m_info;
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int m_ordering; // Ordering method to use, see SPQR's manual
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int m_allow_tol; // Allow to use some tolerance during numerical factorization.
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RealScalar m_tolerance; // treat columns with 2-norm below this tolerance as zero
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mutable cholmod_sparse *m_cR; // The sparse R factor in cholmod format
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mutable MatrixType m_R; // The sparse matrix R in Eigen format
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mutable Index *m_E; // The permutation applied to columns
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mutable cholmod_sparse *m_H; //The householder vectors
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mutable Index *m_HPinv; // The row permutation of H
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mutable cholmod_dense *m_HTau; // The Householder coefficients
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mutable Index m_rank; // The rank of the matrix
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mutable cholmod_common m_cc; // Workspace and parameters
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bool m_useDefaultThreshold; // Use default threshold
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template<typename ,typename > friend struct SPQR_QProduct;
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};
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template <typename SPQRType, typename Derived>
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struct SPQR_QProduct : ReturnByValue<SPQR_QProduct<SPQRType,Derived> >
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{
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typedef typename SPQRType::Scalar Scalar;
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typedef typename SPQRType::Index Index;
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//Define the constructor to get reference to argument types
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SPQR_QProduct(const SPQRType& spqr, const Derived& other, bool transpose) : m_spqr(spqr),m_other(other),m_transpose(transpose) {}
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inline Index rows() const { return m_transpose ? m_spqr.rows() : m_spqr.cols(); }
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inline Index cols() const { return m_other.cols(); }
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// Assign to a vector
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template<typename ResType>
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void evalTo(ResType& res) const
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{
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cholmod_dense y_cd;
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cholmod_dense *x_cd;
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int method = m_transpose ? SPQR_QTX : SPQR_QX;
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cholmod_common *cc = m_spqr.cholmodCommon();
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y_cd = viewAsCholmod(m_other.const_cast_derived());
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x_cd = SuiteSparseQR_qmult<Scalar>(method, m_spqr.m_H, m_spqr.m_HTau, m_spqr.m_HPinv, &y_cd, cc);
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res = Matrix<Scalar,ResType::RowsAtCompileTime,ResType::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x), x_cd->nrow, x_cd->ncol);
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cholmod_l_free_dense(&x_cd, cc);
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}
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const SPQRType& m_spqr;
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const Derived& m_other;
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bool m_transpose;
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};
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template<typename SPQRType>
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struct SPQRMatrixQReturnType{
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SPQRMatrixQReturnType(const SPQRType& spqr) : m_spqr(spqr) {}
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template<typename Derived>
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SPQR_QProduct<SPQRType, Derived> operator*(const MatrixBase<Derived>& other)
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{
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return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(),false);
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}
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SPQRMatrixQTransposeReturnType<SPQRType> adjoint() const
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{
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return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);
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}
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// To use for operations with the transpose of Q
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SPQRMatrixQTransposeReturnType<SPQRType> transpose() const
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{
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return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr);
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}
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const SPQRType& m_spqr;
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};
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template<typename SPQRType>
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struct SPQRMatrixQTransposeReturnType{
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SPQRMatrixQTransposeReturnType(const SPQRType& spqr) : m_spqr(spqr) {}
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template<typename Derived>
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SPQR_QProduct<SPQRType,Derived> operator*(const MatrixBase<Derived>& other)
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{
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return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(), true);
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}
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const SPQRType& m_spqr;
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};
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namespace internal {
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template<typename _MatrixType, typename Rhs>
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struct solve_retval<SPQR<_MatrixType>, Rhs>
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: solve_retval_base<SPQR<_MatrixType>, Rhs>
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{
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typedef SPQR<_MatrixType> Dec;
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EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
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template<typename Dest> void evalTo(Dest& dst) const
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{
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dec()._solve(rhs(),dst);
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}
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};
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} // end namespace internal
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}// End namespace Eigen
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#endif
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