1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2012 Desire Nuentsa <desire.nuentsa_wakam@inria.fr> 5 // Copyright (C) 2014 Gael Guennebaud <gael.guennebaud@inria.fr> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #ifndef EIGEN_SUITESPARSEQRSUPPORT_H 12 #define EIGEN_SUITESPARSEQRSUPPORT_H 13 14 namespace Eigen { 15 16 template<typename MatrixType> class SPQR; 17 template<typename SPQRType> struct SPQRMatrixQReturnType; 18 template<typename SPQRType> struct SPQRMatrixQTransposeReturnType; 19 template <typename SPQRType, typename Derived> struct SPQR_QProduct; 20 namespace internal { 21 template <typename SPQRType> struct traits<SPQRMatrixQReturnType<SPQRType> > 22 { 23 typedef typename SPQRType::MatrixType ReturnType; 24 }; 25 template <typename SPQRType> struct traits<SPQRMatrixQTransposeReturnType<SPQRType> > 26 { 27 typedef typename SPQRType::MatrixType ReturnType; 28 }; 29 template <typename SPQRType, typename Derived> struct traits<SPQR_QProduct<SPQRType, Derived> > 30 { 31 typedef typename Derived::PlainObject ReturnType; 32 }; 33 } // End namespace internal 34 35 /** 36 * \ingroup SPQRSupport_Module 37 * \class SPQR 38 * \brief Sparse QR factorization based on SuiteSparseQR library 39 * 40 * This class is used to perform a multithreaded and multifrontal rank-revealing QR decomposition 41 * of sparse matrices. The result is then used to solve linear leasts_square systems. 42 * Clearly, a QR factorization is returned such that A*P = Q*R where : 43 * 44 * P is the column permutation. Use colsPermutation() to get it. 45 * 46 * Q is the orthogonal matrix represented as Householder reflectors. 47 * Use matrixQ() to get an expression and matrixQ().transpose() to get the transpose. 48 * You can then apply it to a vector. 49 * 50 * R is the sparse triangular factor. Use matrixQR() to get it as SparseMatrix. 51 * NOTE : The Index type of R is always SuiteSparse_long. You can get it with SPQR::Index 52 * 53 * \tparam _MatrixType The type of the sparse matrix A, must be a column-major SparseMatrix<> 54 * 55 * \implsparsesolverconcept 56 * 57 * 58 */ 59 template<typename _MatrixType> 60 class SPQR : public SparseSolverBase<SPQR<_MatrixType> > 61 { 62 protected: 63 typedef SparseSolverBase<SPQR<_MatrixType> > Base; 64 using Base::m_isInitialized; 65 public: 66 typedef typename _MatrixType::Scalar Scalar; 67 typedef typename _MatrixType::RealScalar RealScalar; 68 typedef SuiteSparse_long StorageIndex ; 69 typedef SparseMatrix<Scalar, ColMajor, StorageIndex> MatrixType; 70 typedef Map<PermutationMatrix<Dynamic, Dynamic, StorageIndex> > PermutationType; 71 enum { 72 ColsAtCompileTime = Dynamic, 73 MaxColsAtCompileTime = Dynamic 74 }; 75 public: 76 SPQR() 77 : m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true) 78 { 79 cholmod_l_start(&m_cc); 80 } 81 82 explicit SPQR(const _MatrixType& matrix) 83 : m_ordering(SPQR_ORDERING_DEFAULT), m_allow_tol(SPQR_DEFAULT_TOL), m_tolerance (NumTraits<Scalar>::epsilon()), m_useDefaultThreshold(true) 84 { 85 cholmod_l_start(&m_cc); 86 compute(matrix); 87 } 88 89 ~SPQR() 90 { 91 SPQR_free(); 92 cholmod_l_finish(&m_cc); 93 } 94 void SPQR_free() 95 { 96 cholmod_l_free_sparse(&m_H, &m_cc); 97 cholmod_l_free_sparse(&m_cR, &m_cc); 98 cholmod_l_free_dense(&m_HTau, &m_cc); 99 std::free(m_E); 100 std::free(m_HPinv); 101 } 102 103 void compute(const _MatrixType& matrix) 104 { 105 if(m_isInitialized) SPQR_free(); 106 107 MatrixType mat(matrix); 108 109 /* Compute the default threshold as in MatLab, see: 110 * Tim Davis, "Algorithm 915, SuiteSparseQR: Multifrontal Multithreaded Rank-Revealing 111 * Sparse QR Factorization, ACM Trans. on Math. Soft. 38(1), 2011, Page 8:3 112 */ 113 RealScalar pivotThreshold = m_tolerance; 114 if(m_useDefaultThreshold) 115 { 116 RealScalar max2Norm = 0.0; 117 for (int j = 0; j < mat.cols(); j++) max2Norm = numext::maxi(max2Norm, mat.col(j).norm()); 118 if(max2Norm==RealScalar(0)) 119 max2Norm = RealScalar(1); 120 pivotThreshold = 20 * (mat.rows() + mat.cols()) * max2Norm * NumTraits<RealScalar>::epsilon(); 121 } 122 cholmod_sparse A; 123 A = viewAsCholmod(mat); 124 m_rows = matrix.rows(); 125 Index col = matrix.cols(); 126 m_rank = SuiteSparseQR<Scalar>(m_ordering, pivotThreshold, col, &A, 127 &m_cR, &m_E, &m_H, &m_HPinv, &m_HTau, &m_cc); 128 129 if (!m_cR) 130 { 131 m_info = NumericalIssue; 132 m_isInitialized = false; 133 return; 134 } 135 m_info = Success; 136 m_isInitialized = true; 137 m_isRUpToDate = false; 138 } 139 /** 140 * Get the number of rows of the input matrix and the Q matrix 141 */ 142 inline Index rows() const {return m_rows; } 143 144 /** 145 * Get the number of columns of the input matrix. 146 */ 147 inline Index cols() const { return m_cR->ncol; } 148 149 template<typename Rhs, typename Dest> 150 void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const 151 { 152 eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()"); 153 eigen_assert(b.cols()==1 && "This method is for vectors only"); 154 155 //Compute Q^T * b 156 typename Dest::PlainObject y, y2; 157 y = matrixQ().transpose() * b; 158 159 // Solves with the triangular matrix R 160 Index rk = this->rank(); 161 y2 = y; 162 y.resize((std::max)(cols(),Index(y.rows())),y.cols()); 163 y.topRows(rk) = this->matrixR().topLeftCorner(rk, rk).template triangularView<Upper>().solve(y2.topRows(rk)); 164 165 // Apply the column permutation 166 // colsPermutation() performs a copy of the permutation, 167 // so let's apply it manually: 168 for(Index i = 0; i < rk; ++i) dest.row(m_E[i]) = y.row(i); 169 for(Index i = rk; i < cols(); ++i) dest.row(m_E[i]).setZero(); 170 171 // y.bottomRows(y.rows()-rk).setZero(); 172 // dest = colsPermutation() * y.topRows(cols()); 173 174 m_info = Success; 175 } 176 177 /** \returns the sparse triangular factor R. It is a sparse matrix 178 */ 179 const MatrixType matrixR() const 180 { 181 eigen_assert(m_isInitialized && " The QR factorization should be computed first, call compute()"); 182 if(!m_isRUpToDate) { 183 m_R = viewAsEigen<Scalar,ColMajor, typename MatrixType::StorageIndex>(*m_cR); 184 m_isRUpToDate = true; 185 } 186 return m_R; 187 } 188 /// Get an expression of the matrix Q 189 SPQRMatrixQReturnType<SPQR> matrixQ() const 190 { 191 return SPQRMatrixQReturnType<SPQR>(*this); 192 } 193 /// Get the permutation that was applied to columns of A 194 PermutationType colsPermutation() const 195 { 196 eigen_assert(m_isInitialized && "Decomposition is not initialized."); 197 return PermutationType(m_E, m_cR->ncol); 198 } 199 /** 200 * Gets the rank of the matrix. 201 * It should be equal to matrixQR().cols if the matrix is full-rank 202 */ 203 Index rank() const 204 { 205 eigen_assert(m_isInitialized && "Decomposition is not initialized."); 206 return m_cc.SPQR_istat[4]; 207 } 208 /// Set the fill-reducing ordering method to be used 209 void setSPQROrdering(int ord) { m_ordering = ord;} 210 /// Set the tolerance tol to treat columns with 2-norm < =tol as zero 211 void setPivotThreshold(const RealScalar& tol) 212 { 213 m_useDefaultThreshold = false; 214 m_tolerance = tol; 215 } 216 217 /** \returns a pointer to the SPQR workspace */ 218 cholmod_common *cholmodCommon() const { return &m_cc; } 219 220 221 /** \brief Reports whether previous computation was successful. 222 * 223 * \returns \c Success if computation was succesful, 224 * \c NumericalIssue if the sparse QR can not be computed 225 */ 226 ComputationInfo info() const 227 { 228 eigen_assert(m_isInitialized && "Decomposition is not initialized."); 229 return m_info; 230 } 231 protected: 232 bool m_analysisIsOk; 233 bool m_factorizationIsOk; 234 mutable bool m_isRUpToDate; 235 mutable ComputationInfo m_info; 236 int m_ordering; // Ordering method to use, see SPQR's manual 237 int m_allow_tol; // Allow to use some tolerance during numerical factorization. 238 RealScalar m_tolerance; // treat columns with 2-norm below this tolerance as zero 239 mutable cholmod_sparse *m_cR; // The sparse R factor in cholmod format 240 mutable MatrixType m_R; // The sparse matrix R in Eigen format 241 mutable StorageIndex *m_E; // The permutation applied to columns 242 mutable cholmod_sparse *m_H; //The householder vectors 243 mutable StorageIndex *m_HPinv; // The row permutation of H 244 mutable cholmod_dense *m_HTau; // The Householder coefficients 245 mutable Index m_rank; // The rank of the matrix 246 mutable cholmod_common m_cc; // Workspace and parameters 247 bool m_useDefaultThreshold; // Use default threshold 248 Index m_rows; 249 template<typename ,typename > friend struct SPQR_QProduct; 250 }; 251 252 template <typename SPQRType, typename Derived> 253 struct SPQR_QProduct : ReturnByValue<SPQR_QProduct<SPQRType,Derived> > 254 { 255 typedef typename SPQRType::Scalar Scalar; 256 typedef typename SPQRType::StorageIndex StorageIndex; 257 //Define the constructor to get reference to argument types 258 SPQR_QProduct(const SPQRType& spqr, const Derived& other, bool transpose) : m_spqr(spqr),m_other(other),m_transpose(transpose) {} 259 260 inline Index rows() const { return m_transpose ? m_spqr.rows() : m_spqr.cols(); } 261 inline Index cols() const { return m_other.cols(); } 262 // Assign to a vector 263 template<typename ResType> 264 void evalTo(ResType& res) const 265 { 266 cholmod_dense y_cd; 267 cholmod_dense *x_cd; 268 int method = m_transpose ? SPQR_QTX : SPQR_QX; 269 cholmod_common *cc = m_spqr.cholmodCommon(); 270 y_cd = viewAsCholmod(m_other.const_cast_derived()); 271 x_cd = SuiteSparseQR_qmult<Scalar>(method, m_spqr.m_H, m_spqr.m_HTau, m_spqr.m_HPinv, &y_cd, cc); 272 res = Matrix<Scalar,ResType::RowsAtCompileTime,ResType::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x), x_cd->nrow, x_cd->ncol); 273 cholmod_l_free_dense(&x_cd, cc); 274 } 275 const SPQRType& m_spqr; 276 const Derived& m_other; 277 bool m_transpose; 278 279 }; 280 template<typename SPQRType> 281 struct SPQRMatrixQReturnType{ 282 283 SPQRMatrixQReturnType(const SPQRType& spqr) : m_spqr(spqr) {} 284 template<typename Derived> 285 SPQR_QProduct<SPQRType, Derived> operator*(const MatrixBase<Derived>& other) 286 { 287 return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(),false); 288 } 289 SPQRMatrixQTransposeReturnType<SPQRType> adjoint() const 290 { 291 return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr); 292 } 293 // To use for operations with the transpose of Q 294 SPQRMatrixQTransposeReturnType<SPQRType> transpose() const 295 { 296 return SPQRMatrixQTransposeReturnType<SPQRType>(m_spqr); 297 } 298 const SPQRType& m_spqr; 299 }; 300 301 template<typename SPQRType> 302 struct SPQRMatrixQTransposeReturnType{ 303 SPQRMatrixQTransposeReturnType(const SPQRType& spqr) : m_spqr(spqr) {} 304 template<typename Derived> 305 SPQR_QProduct<SPQRType,Derived> operator*(const MatrixBase<Derived>& other) 306 { 307 return SPQR_QProduct<SPQRType,Derived>(m_spqr,other.derived(), true); 308 } 309 const SPQRType& m_spqr; 310 }; 311 312 }// End namespace Eigen 313 #endif 314