1// This file is part of Eigen, a lightweight C++ template library 2// for linear algebra. 3// 4// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr> 5// Copyright (C) 2012 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 12#ifndef EIGEN_SPARSE_LU_H 13#define EIGEN_SPARSE_LU_H 14 15namespace Eigen { 16 17template <typename _MatrixType, typename _OrderingType = COLAMDOrdering<typename _MatrixType::Index> > class SparseLU; 18template <typename MappedSparseMatrixType> struct SparseLUMatrixLReturnType; 19template <typename MatrixLType, typename MatrixUType> struct SparseLUMatrixUReturnType; 20 21/** \ingroup SparseLU_Module 22 * \class SparseLU 23 * 24 * \brief Sparse supernodal LU factorization for general matrices 25 * 26 * This class implements the supernodal LU factorization for general matrices. 27 * It uses the main techniques from the sequential SuperLU package 28 * (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real 29 * and complex arithmetics with single and double precision, depending on the 30 * scalar type of your input matrix. 31 * The code has been optimized to provide BLAS-3 operations during supernode-panel updates. 32 * It benefits directly from the built-in high-performant Eigen BLAS routines. 33 * Moreover, when the size of a supernode is very small, the BLAS calls are avoided to 34 * enable a better optimization from the compiler. For best performance, 35 * you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors. 36 * 37 * An important parameter of this class is the ordering method. It is used to reorder the columns 38 * (and eventually the rows) of the matrix to reduce the number of new elements that are created during 39 * numerical factorization. The cheapest method available is COLAMD. 40 * See \link OrderingMethods_Module the OrderingMethods module \endlink for the list of 41 * built-in and external ordering methods. 42 * 43 * Simple example with key steps 44 * \code 45 * VectorXd x(n), b(n); 46 * SparseMatrix<double, ColMajor> A; 47 * SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<Index> > solver; 48 * // fill A and b; 49 * // Compute the ordering permutation vector from the structural pattern of A 50 * solver.analyzePattern(A); 51 * // Compute the numerical factorization 52 * solver.factorize(A); 53 * //Use the factors to solve the linear system 54 * x = solver.solve(b); 55 * \endcode 56 * 57 * \warning The input matrix A should be in a \b compressed and \b column-major form. 58 * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix. 59 * 60 * \note Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix. 61 * For badly scaled matrices, this step can be useful to reduce the pivoting during factorization. 62 * If this is the case for your matrices, you can try the basic scaling method at 63 * "unsupported/Eigen/src/IterativeSolvers/Scaling.h" 64 * 65 * \tparam _MatrixType The type of the sparse matrix. It must be a column-major SparseMatrix<> 66 * \tparam _OrderingType The ordering method to use, either AMD, COLAMD or METIS. Default is COLMAD 67 * 68 * 69 * \sa \ref TutorialSparseDirectSolvers 70 * \sa \ref OrderingMethods_Module 71 */ 72template <typename _MatrixType, typename _OrderingType> 73class SparseLU : public internal::SparseLUImpl<typename _MatrixType::Scalar, typename _MatrixType::Index> 74{ 75 public: 76 typedef _MatrixType MatrixType; 77 typedef _OrderingType OrderingType; 78 typedef typename MatrixType::Scalar Scalar; 79 typedef typename MatrixType::RealScalar RealScalar; 80 typedef typename MatrixType::Index Index; 81 typedef SparseMatrix<Scalar,ColMajor,Index> NCMatrix; 82 typedef internal::MappedSuperNodalMatrix<Scalar, Index> SCMatrix; 83 typedef Matrix<Scalar,Dynamic,1> ScalarVector; 84 typedef Matrix<Index,Dynamic,1> IndexVector; 85 typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType; 86 typedef internal::SparseLUImpl<Scalar, Index> Base; 87 88 public: 89 SparseLU():m_isInitialized(true),m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1) 90 { 91 initperfvalues(); 92 } 93 SparseLU(const MatrixType& matrix):m_isInitialized(true),m_lastError(""),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0),m_detPermR(1) 94 { 95 initperfvalues(); 96 compute(matrix); 97 } 98 99 ~SparseLU() 100 { 101 // Free all explicit dynamic pointers 102 } 103 104 void analyzePattern (const MatrixType& matrix); 105 void factorize (const MatrixType& matrix); 106 void simplicialfactorize(const MatrixType& matrix); 107 108 /** 109 * Compute the symbolic and numeric factorization of the input sparse matrix. 110 * The input matrix should be in column-major storage. 111 */ 112 void compute (const MatrixType& matrix) 113 { 114 // Analyze 115 analyzePattern(matrix); 116 //Factorize 117 factorize(matrix); 118 } 119 120 inline Index rows() const { return m_mat.rows(); } 121 inline Index cols() const { return m_mat.cols(); } 122 /** Indicate that the pattern of the input matrix is symmetric */ 123 void isSymmetric(bool sym) 124 { 125 m_symmetricmode = sym; 126 } 127 128 /** \returns an expression of the matrix L, internally stored as supernodes 129 * The only operation available with this expression is the triangular solve 130 * \code 131 * y = b; matrixL().solveInPlace(y); 132 * \endcode 133 */ 134 SparseLUMatrixLReturnType<SCMatrix> matrixL() const 135 { 136 return SparseLUMatrixLReturnType<SCMatrix>(m_Lstore); 137 } 138 /** \returns an expression of the matrix U, 139 * The only operation available with this expression is the triangular solve 140 * \code 141 * y = b; matrixU().solveInPlace(y); 142 * \endcode 143 */ 144 SparseLUMatrixUReturnType<SCMatrix,MappedSparseMatrix<Scalar,ColMajor,Index> > matrixU() const 145 { 146 return SparseLUMatrixUReturnType<SCMatrix, MappedSparseMatrix<Scalar,ColMajor,Index> >(m_Lstore, m_Ustore); 147 } 148 149 /** 150 * \returns a reference to the row matrix permutation \f$ P_r \f$ such that \f$P_r A P_c^T = L U\f$ 151 * \sa colsPermutation() 152 */ 153 inline const PermutationType& rowsPermutation() const 154 { 155 return m_perm_r; 156 } 157 /** 158 * \returns a reference to the column matrix permutation\f$ P_c^T \f$ such that \f$P_r A P_c^T = L U\f$ 159 * \sa rowsPermutation() 160 */ 161 inline const PermutationType& colsPermutation() const 162 { 163 return m_perm_c; 164 } 165 /** Set the threshold used for a diagonal entry to be an acceptable pivot. */ 166 void setPivotThreshold(const RealScalar& thresh) 167 { 168 m_diagpivotthresh = thresh; 169 } 170 171 /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A. 172 * 173 * \warning the destination matrix X in X = this->solve(B) must be colmun-major. 174 * 175 * \sa compute() 176 */ 177 template<typename Rhs> 178 inline const internal::solve_retval<SparseLU, Rhs> solve(const MatrixBase<Rhs>& B) const 179 { 180 eigen_assert(m_factorizationIsOk && "SparseLU is not initialized."); 181 eigen_assert(rows()==B.rows() 182 && "SparseLU::solve(): invalid number of rows of the right hand side matrix B"); 183 return internal::solve_retval<SparseLU, Rhs>(*this, B.derived()); 184 } 185 186 /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A. 187 * 188 * \sa compute() 189 */ 190 template<typename Rhs> 191 inline const internal::sparse_solve_retval<SparseLU, Rhs> solve(const SparseMatrixBase<Rhs>& B) const 192 { 193 eigen_assert(m_factorizationIsOk && "SparseLU is not initialized."); 194 eigen_assert(rows()==B.rows() 195 && "SparseLU::solve(): invalid number of rows of the right hand side matrix B"); 196 return internal::sparse_solve_retval<SparseLU, Rhs>(*this, B.derived()); 197 } 198 199 /** \brief Reports whether previous computation was successful. 200 * 201 * \returns \c Success if computation was succesful, 202 * \c NumericalIssue if the LU factorization reports a problem, zero diagonal for instance 203 * \c InvalidInput if the input matrix is invalid 204 * 205 * \sa iparm() 206 */ 207 ComputationInfo info() const 208 { 209 eigen_assert(m_isInitialized && "Decomposition is not initialized."); 210 return m_info; 211 } 212 213 /** 214 * \returns A string describing the type of error 215 */ 216 std::string lastErrorMessage() const 217 { 218 return m_lastError; 219 } 220 221 template<typename Rhs, typename Dest> 222 bool _solve(const MatrixBase<Rhs> &B, MatrixBase<Dest> &X_base) const 223 { 224 Dest& X(X_base.derived()); 225 eigen_assert(m_factorizationIsOk && "The matrix should be factorized first"); 226 EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0, 227 THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES); 228 229 // Permute the right hand side to form X = Pr*B 230 // on return, X is overwritten by the computed solution 231 X.resize(B.rows(),B.cols()); 232 233 // this ugly const_cast_derived() helps to detect aliasing when applying the permutations 234 for(Index j = 0; j < B.cols(); ++j) 235 X.col(j) = rowsPermutation() * B.const_cast_derived().col(j); 236 237 //Forward substitution with L 238 this->matrixL().solveInPlace(X); 239 this->matrixU().solveInPlace(X); 240 241 // Permute back the solution 242 for (Index j = 0; j < B.cols(); ++j) 243 X.col(j) = colsPermutation().inverse() * X.col(j); 244 245 return true; 246 } 247 248 /** 249 * \returns the absolute value of the determinant of the matrix of which 250 * *this is the QR decomposition. 251 * 252 * \warning a determinant can be very big or small, so for matrices 253 * of large enough dimension, there is a risk of overflow/underflow. 254 * One way to work around that is to use logAbsDeterminant() instead. 255 * 256 * \sa logAbsDeterminant(), signDeterminant() 257 */ 258 Scalar absDeterminant() 259 { 260 eigen_assert(m_factorizationIsOk && "The matrix should be factorized first."); 261 // Initialize with the determinant of the row matrix 262 Scalar det = Scalar(1.); 263 // Note that the diagonal blocks of U are stored in supernodes, 264 // which are available in the L part :) 265 for (Index j = 0; j < this->cols(); ++j) 266 { 267 for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it) 268 { 269 if(it.index() == j) 270 { 271 det *= (std::abs)(it.value()); 272 break; 273 } 274 } 275 } 276 return det; 277 } 278 279 /** \returns the natural log of the absolute value of the determinant of the matrix 280 * of which **this is the QR decomposition 281 * 282 * \note This method is useful to work around the risk of overflow/underflow that's 283 * inherent to the determinant computation. 284 * 285 * \sa absDeterminant(), signDeterminant() 286 */ 287 Scalar logAbsDeterminant() const 288 { 289 eigen_assert(m_factorizationIsOk && "The matrix should be factorized first."); 290 Scalar det = Scalar(0.); 291 for (Index j = 0; j < this->cols(); ++j) 292 { 293 for (typename SCMatrix::InnerIterator it(m_Lstore, j); it; ++it) 294 { 295 if(it.row() < j) continue; 296 if(it.row() == j) 297 { 298 det += (std::log)((std::abs)(it.value())); 299 break; 300 } 301 } 302 } 303 return det; 304 } 305 306 /** \returns A number representing the sign of the determinant 307 * 308 * \sa absDeterminant(), logAbsDeterminant() 309 */ 310 Scalar signDeterminant() 311 { 312 eigen_assert(m_factorizationIsOk && "The matrix should be factorized first."); 313 return Scalar(m_detPermR); 314 } 315 316 protected: 317 // Functions 318 void initperfvalues() 319 { 320 m_perfv.panel_size = 1; 321 m_perfv.relax = 1; 322 m_perfv.maxsuper = 128; 323 m_perfv.rowblk = 16; 324 m_perfv.colblk = 8; 325 m_perfv.fillfactor = 20; 326 } 327 328 // Variables 329 mutable ComputationInfo m_info; 330 bool m_isInitialized; 331 bool m_factorizationIsOk; 332 bool m_analysisIsOk; 333 std::string m_lastError; 334 NCMatrix m_mat; // The input (permuted ) matrix 335 SCMatrix m_Lstore; // The lower triangular matrix (supernodal) 336 MappedSparseMatrix<Scalar,ColMajor,Index> m_Ustore; // The upper triangular matrix 337 PermutationType m_perm_c; // Column permutation 338 PermutationType m_perm_r ; // Row permutation 339 IndexVector m_etree; // Column elimination tree 340 341 typename Base::GlobalLU_t m_glu; 342 343 // SparseLU options 344 bool m_symmetricmode; 345 // values for performance 346 internal::perfvalues<Index> m_perfv; 347 RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot 348 Index m_nnzL, m_nnzU; // Nonzeros in L and U factors 349 Index m_detPermR; // Determinant of the coefficient matrix 350 private: 351 // Disable copy constructor 352 SparseLU (const SparseLU& ); 353 354}; // End class SparseLU 355 356 357 358// Functions needed by the anaysis phase 359/** 360 * Compute the column permutation to minimize the fill-in 361 * 362 * - Apply this permutation to the input matrix - 363 * 364 * - Compute the column elimination tree on the permuted matrix 365 * 366 * - Postorder the elimination tree and the column permutation 367 * 368 */ 369template <typename MatrixType, typename OrderingType> 370void SparseLU<MatrixType, OrderingType>::analyzePattern(const MatrixType& mat) 371{ 372 373 //TODO It is possible as in SuperLU to compute row and columns scaling vectors to equilibrate the matrix mat. 374 375 OrderingType ord; 376 ord(mat,m_perm_c); 377 378 // Apply the permutation to the column of the input matrix 379 //First copy the whole input matrix. 380 m_mat = mat; 381 if (m_perm_c.size()) { 382 m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. FIXME : This vector is filled but not subsequently used. 383 //Then, permute only the column pointers 384 const Index * outerIndexPtr; 385 if (mat.isCompressed()) outerIndexPtr = mat.outerIndexPtr(); 386 else 387 { 388 Index *outerIndexPtr_t = new Index[mat.cols()+1]; 389 for(Index i = 0; i <= mat.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i]; 390 outerIndexPtr = outerIndexPtr_t; 391 } 392 for (Index i = 0; i < mat.cols(); i++) 393 { 394 m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i]; 395 m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i]; 396 } 397 if(!mat.isCompressed()) delete[] outerIndexPtr; 398 } 399 // Compute the column elimination tree of the permuted matrix 400 IndexVector firstRowElt; 401 internal::coletree(m_mat, m_etree,firstRowElt); 402 403 // In symmetric mode, do not do postorder here 404 if (!m_symmetricmode) { 405 IndexVector post, iwork; 406 // Post order etree 407 internal::treePostorder(m_mat.cols(), m_etree, post); 408 409 410 // Renumber etree in postorder 411 Index m = m_mat.cols(); 412 iwork.resize(m+1); 413 for (Index i = 0; i < m; ++i) iwork(post(i)) = post(m_etree(i)); 414 m_etree = iwork; 415 416 // Postmultiply A*Pc by post, i.e reorder the matrix according to the postorder of the etree 417 PermutationType post_perm(m); 418 for (Index i = 0; i < m; i++) 419 post_perm.indices()(i) = post(i); 420 421 // Combine the two permutations : postorder the permutation for future use 422 if(m_perm_c.size()) { 423 m_perm_c = post_perm * m_perm_c; 424 } 425 426 } // end postordering 427 428 m_analysisIsOk = true; 429} 430 431// Functions needed by the numerical factorization phase 432 433 434/** 435 * - Numerical factorization 436 * - Interleaved with the symbolic factorization 437 * On exit, info is 438 * 439 * = 0: successful factorization 440 * 441 * > 0: if info = i, and i is 442 * 443 * <= A->ncol: U(i,i) is exactly zero. The factorization has 444 * been completed, but the factor U is exactly singular, 445 * and division by zero will occur if it is used to solve a 446 * system of equations. 447 * 448 * > A->ncol: number of bytes allocated when memory allocation 449 * failure occurred, plus A->ncol. If lwork = -1, it is 450 * the estimated amount of space needed, plus A->ncol. 451 */ 452template <typename MatrixType, typename OrderingType> 453void SparseLU<MatrixType, OrderingType>::factorize(const MatrixType& matrix) 454{ 455 using internal::emptyIdxLU; 456 eigen_assert(m_analysisIsOk && "analyzePattern() should be called first"); 457 eigen_assert((matrix.rows() == matrix.cols()) && "Only for squared matrices"); 458 459 typedef typename IndexVector::Scalar Index; 460 461 462 // Apply the column permutation computed in analyzepattern() 463 // m_mat = matrix * m_perm_c.inverse(); 464 m_mat = matrix; 465 if (m_perm_c.size()) 466 { 467 m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. 468 //Then, permute only the column pointers 469 const Index * outerIndexPtr; 470 if (matrix.isCompressed()) outerIndexPtr = matrix.outerIndexPtr(); 471 else 472 { 473 Index* outerIndexPtr_t = new Index[matrix.cols()+1]; 474 for(Index i = 0; i <= matrix.cols(); i++) outerIndexPtr_t[i] = m_mat.outerIndexPtr()[i]; 475 outerIndexPtr = outerIndexPtr_t; 476 } 477 for (Index i = 0; i < matrix.cols(); i++) 478 { 479 m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i]; 480 m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = outerIndexPtr[i+1] - outerIndexPtr[i]; 481 } 482 if(!matrix.isCompressed()) delete[] outerIndexPtr; 483 } 484 else 485 { //FIXME This should not be needed if the empty permutation is handled transparently 486 m_perm_c.resize(matrix.cols()); 487 for(Index i = 0; i < matrix.cols(); ++i) m_perm_c.indices()(i) = i; 488 } 489 490 Index m = m_mat.rows(); 491 Index n = m_mat.cols(); 492 Index nnz = m_mat.nonZeros(); 493 Index maxpanel = m_perfv.panel_size * m; 494 // Allocate working storage common to the factor routines 495 Index lwork = 0; 496 Index info = Base::memInit(m, n, nnz, lwork, m_perfv.fillfactor, m_perfv.panel_size, m_glu); 497 if (info) 498 { 499 m_lastError = "UNABLE TO ALLOCATE WORKING MEMORY\n\n" ; 500 m_factorizationIsOk = false; 501 return ; 502 } 503 504 // Set up pointers for integer working arrays 505 IndexVector segrep(m); segrep.setZero(); 506 IndexVector parent(m); parent.setZero(); 507 IndexVector xplore(m); xplore.setZero(); 508 IndexVector repfnz(maxpanel); 509 IndexVector panel_lsub(maxpanel); 510 IndexVector xprune(n); xprune.setZero(); 511 IndexVector marker(m*internal::LUNoMarker); marker.setZero(); 512 513 repfnz.setConstant(-1); 514 panel_lsub.setConstant(-1); 515 516 // Set up pointers for scalar working arrays 517 ScalarVector dense; 518 dense.setZero(maxpanel); 519 ScalarVector tempv; 520 tempv.setZero(internal::LUnumTempV(m, m_perfv.panel_size, m_perfv.maxsuper, /*m_perfv.rowblk*/m) ); 521 522 // Compute the inverse of perm_c 523 PermutationType iperm_c(m_perm_c.inverse()); 524 525 // Identify initial relaxed snodes 526 IndexVector relax_end(n); 527 if ( m_symmetricmode == true ) 528 Base::heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end); 529 else 530 Base::relax_snode(n, m_etree, m_perfv.relax, marker, relax_end); 531 532 533 m_perm_r.resize(m); 534 m_perm_r.indices().setConstant(-1); 535 marker.setConstant(-1); 536 m_detPermR = 1; // Record the determinant of the row permutation 537 538 m_glu.supno(0) = emptyIdxLU; m_glu.xsup.setConstant(0); 539 m_glu.xsup(0) = m_glu.xlsub(0) = m_glu.xusub(0) = m_glu.xlusup(0) = Index(0); 540 541 // Work on one 'panel' at a time. A panel is one of the following : 542 // (a) a relaxed supernode at the bottom of the etree, or 543 // (b) panel_size contiguous columns, <panel_size> defined by the user 544 Index jcol; 545 IndexVector panel_histo(n); 546 Index pivrow; // Pivotal row number in the original row matrix 547 Index nseg1; // Number of segments in U-column above panel row jcol 548 Index nseg; // Number of segments in each U-column 549 Index irep; 550 Index i, k, jj; 551 for (jcol = 0; jcol < n; ) 552 { 553 // Adjust panel size so that a panel won't overlap with the next relaxed snode. 554 Index panel_size = m_perfv.panel_size; // upper bound on panel width 555 for (k = jcol + 1; k < (std::min)(jcol+panel_size, n); k++) 556 { 557 if (relax_end(k) != emptyIdxLU) 558 { 559 panel_size = k - jcol; 560 break; 561 } 562 } 563 if (k == n) 564 panel_size = n - jcol; 565 566 // Symbolic outer factorization on a panel of columns 567 Base::panel_dfs(m, panel_size, jcol, m_mat, m_perm_r.indices(), nseg1, dense, panel_lsub, segrep, repfnz, xprune, marker, parent, xplore, m_glu); 568 569 // Numeric sup-panel updates in topological order 570 Base::panel_bmod(m, panel_size, jcol, nseg1, dense, tempv, segrep, repfnz, m_glu); 571 572 // Sparse LU within the panel, and below the panel diagonal 573 for ( jj = jcol; jj< jcol + panel_size; jj++) 574 { 575 k = (jj - jcol) * m; // Column index for w-wide arrays 576 577 nseg = nseg1; // begin after all the panel segments 578 //Depth-first-search for the current column 579 VectorBlock<IndexVector> panel_lsubk(panel_lsub, k, m); 580 VectorBlock<IndexVector> repfnz_k(repfnz, k, m); 581 info = Base::column_dfs(m, jj, m_perm_r.indices(), m_perfv.maxsuper, nseg, panel_lsubk, segrep, repfnz_k, xprune, marker, parent, xplore, m_glu); 582 if ( info ) 583 { 584 m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_DFS() "; 585 m_info = NumericalIssue; 586 m_factorizationIsOk = false; 587 return; 588 } 589 // Numeric updates to this column 590 VectorBlock<ScalarVector> dense_k(dense, k, m); 591 VectorBlock<IndexVector> segrep_k(segrep, nseg1, m-nseg1); 592 info = Base::column_bmod(jj, (nseg - nseg1), dense_k, tempv, segrep_k, repfnz_k, jcol, m_glu); 593 if ( info ) 594 { 595 m_lastError = "UNABLE TO EXPAND MEMORY IN COLUMN_BMOD() "; 596 m_info = NumericalIssue; 597 m_factorizationIsOk = false; 598 return; 599 } 600 601 // Copy the U-segments to ucol(*) 602 info = Base::copy_to_ucol(jj, nseg, segrep, repfnz_k ,m_perm_r.indices(), dense_k, m_glu); 603 if ( info ) 604 { 605 m_lastError = "UNABLE TO EXPAND MEMORY IN COPY_TO_UCOL() "; 606 m_info = NumericalIssue; 607 m_factorizationIsOk = false; 608 return; 609 } 610 611 // Form the L-segment 612 info = Base::pivotL(jj, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu); 613 if ( info ) 614 { 615 m_lastError = "THE MATRIX IS STRUCTURALLY SINGULAR ... ZERO COLUMN AT "; 616 std::ostringstream returnInfo; 617 returnInfo << info; 618 m_lastError += returnInfo.str(); 619 m_info = NumericalIssue; 620 m_factorizationIsOk = false; 621 return; 622 } 623 624 // Update the determinant of the row permutation matrix 625 if (pivrow != jj) m_detPermR *= -1; 626 627 // Prune columns (0:jj-1) using column jj 628 Base::pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu); 629 630 // Reset repfnz for this column 631 for (i = 0; i < nseg; i++) 632 { 633 irep = segrep(i); 634 repfnz_k(irep) = emptyIdxLU; 635 } 636 } // end SparseLU within the panel 637 jcol += panel_size; // Move to the next panel 638 } // end for -- end elimination 639 640 // Count the number of nonzeros in factors 641 Base::countnz(n, m_nnzL, m_nnzU, m_glu); 642 // Apply permutation to the L subscripts 643 Base::fixupL(n, m_perm_r.indices(), m_glu); 644 645 // Create supernode matrix L 646 m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup); 647 // Create the column major upper sparse matrix U; 648 new (&m_Ustore) MappedSparseMatrix<Scalar, ColMajor, Index> ( m, n, m_nnzU, m_glu.xusub.data(), m_glu.usub.data(), m_glu.ucol.data() ); 649 650 m_info = Success; 651 m_factorizationIsOk = true; 652} 653 654template<typename MappedSupernodalType> 655struct SparseLUMatrixLReturnType : internal::no_assignment_operator 656{ 657 typedef typename MappedSupernodalType::Index Index; 658 typedef typename MappedSupernodalType::Scalar Scalar; 659 SparseLUMatrixLReturnType(const MappedSupernodalType& mapL) : m_mapL(mapL) 660 { } 661 Index rows() { return m_mapL.rows(); } 662 Index cols() { return m_mapL.cols(); } 663 template<typename Dest> 664 void solveInPlace( MatrixBase<Dest> &X) const 665 { 666 m_mapL.solveInPlace(X); 667 } 668 const MappedSupernodalType& m_mapL; 669}; 670 671template<typename MatrixLType, typename MatrixUType> 672struct SparseLUMatrixUReturnType : internal::no_assignment_operator 673{ 674 typedef typename MatrixLType::Index Index; 675 typedef typename MatrixLType::Scalar Scalar; 676 SparseLUMatrixUReturnType(const MatrixLType& mapL, const MatrixUType& mapU) 677 : m_mapL(mapL),m_mapU(mapU) 678 { } 679 Index rows() { return m_mapL.rows(); } 680 Index cols() { return m_mapL.cols(); } 681 682 template<typename Dest> void solveInPlace(MatrixBase<Dest> &X) const 683 { 684 Index nrhs = X.cols(); 685 Index n = X.rows(); 686 // Backward solve with U 687 for (Index k = m_mapL.nsuper(); k >= 0; k--) 688 { 689 Index fsupc = m_mapL.supToCol()[k]; 690 Index lda = m_mapL.colIndexPtr()[fsupc+1] - m_mapL.colIndexPtr()[fsupc]; // leading dimension 691 Index nsupc = m_mapL.supToCol()[k+1] - fsupc; 692 Index luptr = m_mapL.colIndexPtr()[fsupc]; 693 694 if (nsupc == 1) 695 { 696 for (Index j = 0; j < nrhs; j++) 697 { 698 X(fsupc, j) /= m_mapL.valuePtr()[luptr]; 699 } 700 } 701 else 702 { 703 Map<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(m_mapL.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(lda) ); 704 Map< Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) ); 705 U = A.template triangularView<Upper>().solve(U); 706 } 707 708 for (Index j = 0; j < nrhs; ++j) 709 { 710 for (Index jcol = fsupc; jcol < fsupc + nsupc; jcol++) 711 { 712 typename MatrixUType::InnerIterator it(m_mapU, jcol); 713 for ( ; it; ++it) 714 { 715 Index irow = it.index(); 716 X(irow, j) -= X(jcol, j) * it.value(); 717 } 718 } 719 } 720 } // End For U-solve 721 } 722 const MatrixLType& m_mapL; 723 const MatrixUType& m_mapU; 724}; 725 726namespace internal { 727 728template<typename _MatrixType, typename Derived, typename Rhs> 729struct solve_retval<SparseLU<_MatrixType,Derived>, Rhs> 730 : solve_retval_base<SparseLU<_MatrixType,Derived>, Rhs> 731{ 732 typedef SparseLU<_MatrixType,Derived> Dec; 733 EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) 734 735 template<typename Dest> void evalTo(Dest& dst) const 736 { 737 dec()._solve(rhs(),dst); 738 } 739}; 740 741template<typename _MatrixType, typename Derived, typename Rhs> 742struct sparse_solve_retval<SparseLU<_MatrixType,Derived>, Rhs> 743 : sparse_solve_retval_base<SparseLU<_MatrixType,Derived>, Rhs> 744{ 745 typedef SparseLU<_MatrixType,Derived> Dec; 746 EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs) 747 748 template<typename Dest> void evalTo(Dest& dst) const 749 { 750 this->defaultEvalTo(dst); 751 } 752}; 753} // end namespace internal 754 755} // End namespace Eigen 756 757#endif 758