[136] | 1 | /*
|
---|
| 2 | Copyright (c) 2011, Intel Corporation. All rights reserved.
|
---|
| 3 |
|
---|
| 4 | Redistribution and use in source and binary forms, with or without modification,
|
---|
| 5 | are permitted provided that the following conditions are met:
|
---|
| 6 |
|
---|
| 7 | * Redistributions of source code must retain the above copyright notice, this
|
---|
| 8 | list of conditions and the following disclaimer.
|
---|
| 9 | * Redistributions in binary form must reproduce the above copyright notice,
|
---|
| 10 | this list of conditions and the following disclaimer in the documentation
|
---|
| 11 | and/or other materials provided with the distribution.
|
---|
| 12 | * Neither the name of Intel Corporation nor the names of its contributors may
|
---|
| 13 | be used to endorse or promote products derived from this software without
|
---|
| 14 | specific prior written permission.
|
---|
| 15 |
|
---|
| 16 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
---|
| 17 | ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
---|
| 18 | WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
---|
| 19 | DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
|
---|
| 20 | ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
---|
| 21 | (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
---|
| 22 | LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
|
---|
| 23 | ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
---|
| 24 | (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
---|
| 25 | SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
---|
| 26 |
|
---|
| 27 | ********************************************************************************
|
---|
| 28 | * Content : Eigen bindings to Intel(R) MKL PARDISO
|
---|
| 29 | ********************************************************************************
|
---|
| 30 | */
|
---|
| 31 |
|
---|
| 32 | #ifndef EIGEN_PARDISOSUPPORT_H
|
---|
| 33 | #define EIGEN_PARDISOSUPPORT_H
|
---|
| 34 |
|
---|
| 35 | namespace Eigen {
|
---|
| 36 |
|
---|
| 37 | template<typename _MatrixType> class PardisoLU;
|
---|
| 38 | template<typename _MatrixType, int Options=Upper> class PardisoLLT;
|
---|
| 39 | template<typename _MatrixType, int Options=Upper> class PardisoLDLT;
|
---|
| 40 |
|
---|
| 41 | namespace internal
|
---|
| 42 | {
|
---|
| 43 | template<typename Index>
|
---|
| 44 | struct pardiso_run_selector
|
---|
| 45 | {
|
---|
| 46 | static Index run( _MKL_DSS_HANDLE_t pt, Index maxfct, Index mnum, Index type, Index phase, Index n, void *a,
|
---|
| 47 | Index *ia, Index *ja, Index *perm, Index nrhs, Index *iparm, Index msglvl, void *b, void *x)
|
---|
| 48 | {
|
---|
| 49 | Index error = 0;
|
---|
| 50 | ::pardiso(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);
|
---|
| 51 | return error;
|
---|
| 52 | }
|
---|
| 53 | };
|
---|
| 54 | template<>
|
---|
| 55 | struct pardiso_run_selector<long long int>
|
---|
| 56 | {
|
---|
| 57 | typedef long long int Index;
|
---|
| 58 | static Index run( _MKL_DSS_HANDLE_t pt, Index maxfct, Index mnum, Index type, Index phase, Index n, void *a,
|
---|
| 59 | Index *ia, Index *ja, Index *perm, Index nrhs, Index *iparm, Index msglvl, void *b, void *x)
|
---|
| 60 | {
|
---|
| 61 | Index error = 0;
|
---|
| 62 | ::pardiso_64(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);
|
---|
| 63 | return error;
|
---|
| 64 | }
|
---|
| 65 | };
|
---|
| 66 |
|
---|
| 67 | template<class Pardiso> struct pardiso_traits;
|
---|
| 68 |
|
---|
| 69 | template<typename _MatrixType>
|
---|
| 70 | struct pardiso_traits< PardisoLU<_MatrixType> >
|
---|
| 71 | {
|
---|
| 72 | typedef _MatrixType MatrixType;
|
---|
| 73 | typedef typename _MatrixType::Scalar Scalar;
|
---|
| 74 | typedef typename _MatrixType::RealScalar RealScalar;
|
---|
| 75 | typedef typename _MatrixType::Index Index;
|
---|
| 76 | };
|
---|
| 77 |
|
---|
| 78 | template<typename _MatrixType, int Options>
|
---|
| 79 | struct pardiso_traits< PardisoLLT<_MatrixType, Options> >
|
---|
| 80 | {
|
---|
| 81 | typedef _MatrixType MatrixType;
|
---|
| 82 | typedef typename _MatrixType::Scalar Scalar;
|
---|
| 83 | typedef typename _MatrixType::RealScalar RealScalar;
|
---|
| 84 | typedef typename _MatrixType::Index Index;
|
---|
| 85 | };
|
---|
| 86 |
|
---|
| 87 | template<typename _MatrixType, int Options>
|
---|
| 88 | struct pardiso_traits< PardisoLDLT<_MatrixType, Options> >
|
---|
| 89 | {
|
---|
| 90 | typedef _MatrixType MatrixType;
|
---|
| 91 | typedef typename _MatrixType::Scalar Scalar;
|
---|
| 92 | typedef typename _MatrixType::RealScalar RealScalar;
|
---|
| 93 | typedef typename _MatrixType::Index Index;
|
---|
| 94 | };
|
---|
| 95 |
|
---|
| 96 | }
|
---|
| 97 |
|
---|
| 98 | template<class Derived>
|
---|
| 99 | class PardisoImpl
|
---|
| 100 | {
|
---|
| 101 | typedef internal::pardiso_traits<Derived> Traits;
|
---|
| 102 | public:
|
---|
| 103 | typedef typename Traits::MatrixType MatrixType;
|
---|
| 104 | typedef typename Traits::Scalar Scalar;
|
---|
| 105 | typedef typename Traits::RealScalar RealScalar;
|
---|
| 106 | typedef typename Traits::Index Index;
|
---|
| 107 | typedef SparseMatrix<Scalar,RowMajor,Index> SparseMatrixType;
|
---|
| 108 | typedef Matrix<Scalar,Dynamic,1> VectorType;
|
---|
| 109 | typedef Matrix<Index, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
|
---|
| 110 | typedef Matrix<Index, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
|
---|
| 111 | typedef Array<Index,64,1,DontAlign> ParameterType;
|
---|
| 112 | enum {
|
---|
| 113 | ScalarIsComplex = NumTraits<Scalar>::IsComplex
|
---|
| 114 | };
|
---|
| 115 |
|
---|
| 116 | PardisoImpl()
|
---|
| 117 | {
|
---|
| 118 | eigen_assert((sizeof(Index) >= sizeof(_INTEGER_t) && sizeof(Index) <= 8) && "Non-supported index type");
|
---|
| 119 | m_iparm.setZero();
|
---|
| 120 | m_msglvl = 0; // No output
|
---|
| 121 | m_initialized = false;
|
---|
| 122 | }
|
---|
| 123 |
|
---|
| 124 | ~PardisoImpl()
|
---|
| 125 | {
|
---|
| 126 | pardisoRelease();
|
---|
| 127 | }
|
---|
| 128 |
|
---|
| 129 | inline Index cols() const { return m_size; }
|
---|
| 130 | inline Index rows() const { return m_size; }
|
---|
| 131 |
|
---|
| 132 | /** \brief Reports whether previous computation was successful.
|
---|
| 133 | *
|
---|
| 134 | * \returns \c Success if computation was succesful,
|
---|
| 135 | * \c NumericalIssue if the matrix appears to be negative.
|
---|
| 136 | */
|
---|
| 137 | ComputationInfo info() const
|
---|
| 138 | {
|
---|
| 139 | eigen_assert(m_initialized && "Decomposition is not initialized.");
|
---|
| 140 | return m_info;
|
---|
| 141 | }
|
---|
| 142 |
|
---|
| 143 | /** \warning for advanced usage only.
|
---|
| 144 | * \returns a reference to the parameter array controlling PARDISO.
|
---|
| 145 | * See the PARDISO manual to know how to use it. */
|
---|
| 146 | ParameterType& pardisoParameterArray()
|
---|
| 147 | {
|
---|
| 148 | return m_iparm;
|
---|
| 149 | }
|
---|
| 150 |
|
---|
| 151 | /** Performs a symbolic decomposition on the sparcity of \a matrix.
|
---|
| 152 | *
|
---|
| 153 | * This function is particularly useful when solving for several problems having the same structure.
|
---|
| 154 | *
|
---|
| 155 | * \sa factorize()
|
---|
| 156 | */
|
---|
| 157 | Derived& analyzePattern(const MatrixType& matrix);
|
---|
| 158 |
|
---|
| 159 | /** Performs a numeric decomposition of \a matrix
|
---|
| 160 | *
|
---|
| 161 | * The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
|
---|
| 162 | *
|
---|
| 163 | * \sa analyzePattern()
|
---|
| 164 | */
|
---|
| 165 | Derived& factorize(const MatrixType& matrix);
|
---|
| 166 |
|
---|
| 167 | Derived& compute(const MatrixType& matrix);
|
---|
| 168 |
|
---|
| 169 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
|
---|
| 170 | *
|
---|
| 171 | * \sa compute()
|
---|
| 172 | */
|
---|
| 173 | template<typename Rhs>
|
---|
| 174 | inline const internal::solve_retval<PardisoImpl, Rhs>
|
---|
| 175 | solve(const MatrixBase<Rhs>& b) const
|
---|
| 176 | {
|
---|
| 177 | eigen_assert(m_initialized && "Pardiso solver is not initialized.");
|
---|
| 178 | eigen_assert(rows()==b.rows()
|
---|
| 179 | && "PardisoImpl::solve(): invalid number of rows of the right hand side matrix b");
|
---|
| 180 | return internal::solve_retval<PardisoImpl, Rhs>(*this, b.derived());
|
---|
| 181 | }
|
---|
| 182 |
|
---|
| 183 | /** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
|
---|
| 184 | *
|
---|
| 185 | * \sa compute()
|
---|
| 186 | */
|
---|
| 187 | template<typename Rhs>
|
---|
| 188 | inline const internal::sparse_solve_retval<PardisoImpl, Rhs>
|
---|
| 189 | solve(const SparseMatrixBase<Rhs>& b) const
|
---|
| 190 | {
|
---|
| 191 | eigen_assert(m_initialized && "Pardiso solver is not initialized.");
|
---|
| 192 | eigen_assert(rows()==b.rows()
|
---|
| 193 | && "PardisoImpl::solve(): invalid number of rows of the right hand side matrix b");
|
---|
| 194 | return internal::sparse_solve_retval<PardisoImpl, Rhs>(*this, b.derived());
|
---|
| 195 | }
|
---|
| 196 |
|
---|
| 197 | Derived& derived()
|
---|
| 198 | {
|
---|
| 199 | return *static_cast<Derived*>(this);
|
---|
| 200 | }
|
---|
| 201 | const Derived& derived() const
|
---|
| 202 | {
|
---|
| 203 | return *static_cast<const Derived*>(this);
|
---|
| 204 | }
|
---|
| 205 |
|
---|
| 206 | template<typename BDerived, typename XDerived>
|
---|
| 207 | bool _solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& x) const;
|
---|
| 208 |
|
---|
| 209 | protected:
|
---|
| 210 | void pardisoRelease()
|
---|
| 211 | {
|
---|
| 212 | if(m_initialized) // Factorization ran at least once
|
---|
| 213 | {
|
---|
| 214 | internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, -1, m_size, 0, 0, 0, m_perm.data(), 0,
|
---|
| 215 | m_iparm.data(), m_msglvl, 0, 0);
|
---|
| 216 | }
|
---|
| 217 | }
|
---|
| 218 |
|
---|
| 219 | void pardisoInit(int type)
|
---|
| 220 | {
|
---|
| 221 | m_type = type;
|
---|
| 222 | bool symmetric = std::abs(m_type) < 10;
|
---|
| 223 | m_iparm[0] = 1; // No solver default
|
---|
| 224 | m_iparm[1] = 2; // use Metis for the ordering
|
---|
| 225 | m_iparm[2] = 0; // Reserved. Set to zero. (??Numbers of processors, value of OMP_NUM_THREADS??)
|
---|
| 226 | m_iparm[3] = 0; // No iterative-direct algorithm
|
---|
| 227 | m_iparm[4] = 0; // No user fill-in reducing permutation
|
---|
| 228 | m_iparm[5] = 0; // Write solution into x, b is left unchanged
|
---|
| 229 | m_iparm[6] = 0; // Not in use
|
---|
| 230 | m_iparm[7] = 2; // Max numbers of iterative refinement steps
|
---|
| 231 | m_iparm[8] = 0; // Not in use
|
---|
| 232 | m_iparm[9] = 13; // Perturb the pivot elements with 1E-13
|
---|
| 233 | m_iparm[10] = symmetric ? 0 : 1; // Use nonsymmetric permutation and scaling MPS
|
---|
| 234 | m_iparm[11] = 0; // Not in use
|
---|
| 235 | m_iparm[12] = symmetric ? 0 : 1; // Maximum weighted matching algorithm is switched-off (default for symmetric).
|
---|
| 236 | // Try m_iparm[12] = 1 in case of inappropriate accuracy
|
---|
| 237 | m_iparm[13] = 0; // Output: Number of perturbed pivots
|
---|
| 238 | m_iparm[14] = 0; // Not in use
|
---|
| 239 | m_iparm[15] = 0; // Not in use
|
---|
| 240 | m_iparm[16] = 0; // Not in use
|
---|
| 241 | m_iparm[17] = -1; // Output: Number of nonzeros in the factor LU
|
---|
| 242 | m_iparm[18] = -1; // Output: Mflops for LU factorization
|
---|
| 243 | m_iparm[19] = 0; // Output: Numbers of CG Iterations
|
---|
| 244 |
|
---|
| 245 | m_iparm[20] = 0; // 1x1 pivoting
|
---|
| 246 | m_iparm[26] = 0; // No matrix checker
|
---|
| 247 | m_iparm[27] = (sizeof(RealScalar) == 4) ? 1 : 0;
|
---|
| 248 | m_iparm[34] = 1; // C indexing
|
---|
| 249 | m_iparm[36] = 0; // CSR
|
---|
| 250 | m_iparm[59] = 0; // 0 - In-Core ; 1 - Automatic switch between In-Core and Out-of-Core modes ; 2 - Out-of-Core
|
---|
| 251 |
|
---|
| 252 | memset(m_pt, 0, sizeof(m_pt));
|
---|
| 253 | }
|
---|
| 254 |
|
---|
| 255 | protected:
|
---|
| 256 | // cached data to reduce reallocation, etc.
|
---|
| 257 |
|
---|
| 258 | void manageErrorCode(Index error)
|
---|
| 259 | {
|
---|
| 260 | switch(error)
|
---|
| 261 | {
|
---|
| 262 | case 0:
|
---|
| 263 | m_info = Success;
|
---|
| 264 | break;
|
---|
| 265 | case -4:
|
---|
| 266 | case -7:
|
---|
| 267 | m_info = NumericalIssue;
|
---|
| 268 | break;
|
---|
| 269 | default:
|
---|
| 270 | m_info = InvalidInput;
|
---|
| 271 | }
|
---|
| 272 | }
|
---|
| 273 |
|
---|
| 274 | mutable SparseMatrixType m_matrix;
|
---|
| 275 | ComputationInfo m_info;
|
---|
| 276 | bool m_initialized, m_analysisIsOk, m_factorizationIsOk;
|
---|
| 277 | Index m_type, m_msglvl;
|
---|
| 278 | mutable void *m_pt[64];
|
---|
| 279 | mutable ParameterType m_iparm;
|
---|
| 280 | mutable IntColVectorType m_perm;
|
---|
| 281 | Index m_size;
|
---|
| 282 |
|
---|
| 283 | private:
|
---|
| 284 | PardisoImpl(PardisoImpl &) {}
|
---|
| 285 | };
|
---|
| 286 |
|
---|
| 287 | template<class Derived>
|
---|
| 288 | Derived& PardisoImpl<Derived>::compute(const MatrixType& a)
|
---|
| 289 | {
|
---|
| 290 | m_size = a.rows();
|
---|
| 291 | eigen_assert(a.rows() == a.cols());
|
---|
| 292 |
|
---|
| 293 | pardisoRelease();
|
---|
| 294 | memset(m_pt, 0, sizeof(m_pt));
|
---|
| 295 | m_perm.setZero(m_size);
|
---|
| 296 | derived().getMatrix(a);
|
---|
| 297 |
|
---|
| 298 | Index error;
|
---|
| 299 | error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 12, m_size,
|
---|
| 300 | m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
|
---|
| 301 | m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
|
---|
| 302 |
|
---|
| 303 | manageErrorCode(error);
|
---|
| 304 | m_analysisIsOk = true;
|
---|
| 305 | m_factorizationIsOk = true;
|
---|
| 306 | m_initialized = true;
|
---|
| 307 | return derived();
|
---|
| 308 | }
|
---|
| 309 |
|
---|
| 310 | template<class Derived>
|
---|
| 311 | Derived& PardisoImpl<Derived>::analyzePattern(const MatrixType& a)
|
---|
| 312 | {
|
---|
| 313 | m_size = a.rows();
|
---|
| 314 | eigen_assert(m_size == a.cols());
|
---|
| 315 |
|
---|
| 316 | pardisoRelease();
|
---|
| 317 | memset(m_pt, 0, sizeof(m_pt));
|
---|
| 318 | m_perm.setZero(m_size);
|
---|
| 319 | derived().getMatrix(a);
|
---|
| 320 |
|
---|
| 321 | Index error;
|
---|
| 322 | error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 11, m_size,
|
---|
| 323 | m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
|
---|
| 324 | m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
|
---|
| 325 |
|
---|
| 326 | manageErrorCode(error);
|
---|
| 327 | m_analysisIsOk = true;
|
---|
| 328 | m_factorizationIsOk = false;
|
---|
| 329 | m_initialized = true;
|
---|
| 330 | return derived();
|
---|
| 331 | }
|
---|
| 332 |
|
---|
| 333 | template<class Derived>
|
---|
| 334 | Derived& PardisoImpl<Derived>::factorize(const MatrixType& a)
|
---|
| 335 | {
|
---|
| 336 | eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
|
---|
| 337 | eigen_assert(m_size == a.rows() && m_size == a.cols());
|
---|
| 338 |
|
---|
| 339 | derived().getMatrix(a);
|
---|
| 340 |
|
---|
| 341 | Index error;
|
---|
| 342 | error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 22, m_size,
|
---|
| 343 | m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
|
---|
| 344 | m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
|
---|
| 345 |
|
---|
| 346 | manageErrorCode(error);
|
---|
| 347 | m_factorizationIsOk = true;
|
---|
| 348 | return derived();
|
---|
| 349 | }
|
---|
| 350 |
|
---|
| 351 | template<class Base>
|
---|
| 352 | template<typename BDerived,typename XDerived>
|
---|
| 353 | bool PardisoImpl<Base>::_solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& x) const
|
---|
| 354 | {
|
---|
| 355 | if(m_iparm[0] == 0) // Factorization was not computed
|
---|
| 356 | return false;
|
---|
| 357 |
|
---|
| 358 | //Index n = m_matrix.rows();
|
---|
| 359 | Index nrhs = Index(b.cols());
|
---|
| 360 | eigen_assert(m_size==b.rows());
|
---|
| 361 | eigen_assert(((MatrixBase<BDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && "Row-major right hand sides are not supported");
|
---|
| 362 | eigen_assert(((MatrixBase<XDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && "Row-major matrices of unknowns are not supported");
|
---|
| 363 | eigen_assert(((nrhs == 1) || b.outerStride() == b.rows()));
|
---|
| 364 |
|
---|
| 365 |
|
---|
| 366 | // switch (transposed) {
|
---|
| 367 | // case SvNoTrans : m_iparm[11] = 0 ; break;
|
---|
| 368 | // case SvTranspose : m_iparm[11] = 2 ; break;
|
---|
| 369 | // case SvAdjoint : m_iparm[11] = 1 ; break;
|
---|
| 370 | // default:
|
---|
| 371 | // //std::cerr << "Eigen: transposition option \"" << transposed << "\" not supported by the PARDISO backend\n";
|
---|
| 372 | // m_iparm[11] = 0;
|
---|
| 373 | // }
|
---|
| 374 |
|
---|
| 375 | Scalar* rhs_ptr = const_cast<Scalar*>(b.derived().data());
|
---|
| 376 | Matrix<Scalar,Dynamic,Dynamic,ColMajor> tmp;
|
---|
| 377 |
|
---|
| 378 | // Pardiso cannot solve in-place
|
---|
| 379 | if(rhs_ptr == x.derived().data())
|
---|
| 380 | {
|
---|
| 381 | tmp = b;
|
---|
| 382 | rhs_ptr = tmp.data();
|
---|
| 383 | }
|
---|
| 384 |
|
---|
| 385 | Index error;
|
---|
| 386 | error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 33, m_size,
|
---|
| 387 | m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
|
---|
| 388 | m_perm.data(), nrhs, m_iparm.data(), m_msglvl,
|
---|
| 389 | rhs_ptr, x.derived().data());
|
---|
| 390 | return error==0;
|
---|
| 391 | }
|
---|
| 392 |
|
---|
| 393 |
|
---|
| 394 | /** \ingroup PardisoSupport_Module
|
---|
| 395 | * \class PardisoLU
|
---|
| 396 | * \brief A sparse direct LU factorization and solver based on the PARDISO library
|
---|
| 397 | *
|
---|
| 398 | * This class allows to solve for A.X = B sparse linear problems via a direct LU factorization
|
---|
| 399 | * using the Intel MKL PARDISO library. The sparse matrix A must be squared and invertible.
|
---|
| 400 | * The vectors or matrices X and B can be either dense or sparse.
|
---|
| 401 | *
|
---|
| 402 | * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
|
---|
| 403 | * \code solver.pardisoParameterArray()[59] = 1; \endcode
|
---|
| 404 | *
|
---|
| 405 | * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
---|
| 406 | *
|
---|
| 407 | * \sa \ref TutorialSparseDirectSolvers
|
---|
| 408 | */
|
---|
| 409 | template<typename MatrixType>
|
---|
| 410 | class PardisoLU : public PardisoImpl< PardisoLU<MatrixType> >
|
---|
| 411 | {
|
---|
| 412 | protected:
|
---|
| 413 | typedef PardisoImpl< PardisoLU<MatrixType> > Base;
|
---|
| 414 | typedef typename Base::Scalar Scalar;
|
---|
| 415 | typedef typename Base::RealScalar RealScalar;
|
---|
| 416 | using Base::pardisoInit;
|
---|
| 417 | using Base::m_matrix;
|
---|
| 418 | friend class PardisoImpl< PardisoLU<MatrixType> >;
|
---|
| 419 |
|
---|
| 420 | public:
|
---|
| 421 |
|
---|
| 422 | using Base::compute;
|
---|
| 423 | using Base::solve;
|
---|
| 424 |
|
---|
| 425 | PardisoLU()
|
---|
| 426 | : Base()
|
---|
| 427 | {
|
---|
| 428 | pardisoInit(Base::ScalarIsComplex ? 13 : 11);
|
---|
| 429 | }
|
---|
| 430 |
|
---|
| 431 | PardisoLU(const MatrixType& matrix)
|
---|
| 432 | : Base()
|
---|
| 433 | {
|
---|
| 434 | pardisoInit(Base::ScalarIsComplex ? 13 : 11);
|
---|
| 435 | compute(matrix);
|
---|
| 436 | }
|
---|
| 437 | protected:
|
---|
| 438 | void getMatrix(const MatrixType& matrix)
|
---|
| 439 | {
|
---|
| 440 | m_matrix = matrix;
|
---|
| 441 | }
|
---|
| 442 |
|
---|
| 443 | private:
|
---|
| 444 | PardisoLU(PardisoLU& ) {}
|
---|
| 445 | };
|
---|
| 446 |
|
---|
| 447 | /** \ingroup PardisoSupport_Module
|
---|
| 448 | * \class PardisoLLT
|
---|
| 449 | * \brief A sparse direct Cholesky (LLT) factorization and solver based on the PARDISO library
|
---|
| 450 | *
|
---|
| 451 | * This class allows to solve for A.X = B sparse linear problems via a LL^T Cholesky factorization
|
---|
| 452 | * using the Intel MKL PARDISO library. The sparse matrix A must be selfajoint and positive definite.
|
---|
| 453 | * The vectors or matrices X and B can be either dense or sparse.
|
---|
| 454 | *
|
---|
| 455 | * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
|
---|
| 456 | * \code solver.pardisoParameterArray()[59] = 1; \endcode
|
---|
| 457 | *
|
---|
| 458 | * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
---|
| 459 | * \tparam UpLo can be any bitwise combination of Upper, Lower. The default is Upper, meaning only the upper triangular part has to be used.
|
---|
| 460 | * Upper|Lower can be used to tell both triangular parts can be used as input.
|
---|
| 461 | *
|
---|
| 462 | * \sa \ref TutorialSparseDirectSolvers
|
---|
| 463 | */
|
---|
| 464 | template<typename MatrixType, int _UpLo>
|
---|
| 465 | class PardisoLLT : public PardisoImpl< PardisoLLT<MatrixType,_UpLo> >
|
---|
| 466 | {
|
---|
| 467 | protected:
|
---|
| 468 | typedef PardisoImpl< PardisoLLT<MatrixType,_UpLo> > Base;
|
---|
| 469 | typedef typename Base::Scalar Scalar;
|
---|
| 470 | typedef typename Base::Index Index;
|
---|
| 471 | typedef typename Base::RealScalar RealScalar;
|
---|
| 472 | using Base::pardisoInit;
|
---|
| 473 | using Base::m_matrix;
|
---|
| 474 | friend class PardisoImpl< PardisoLLT<MatrixType,_UpLo> >;
|
---|
| 475 |
|
---|
| 476 | public:
|
---|
| 477 |
|
---|
| 478 | enum { UpLo = _UpLo };
|
---|
| 479 | using Base::compute;
|
---|
| 480 | using Base::solve;
|
---|
| 481 |
|
---|
| 482 | PardisoLLT()
|
---|
| 483 | : Base()
|
---|
| 484 | {
|
---|
| 485 | pardisoInit(Base::ScalarIsComplex ? 4 : 2);
|
---|
| 486 | }
|
---|
| 487 |
|
---|
| 488 | PardisoLLT(const MatrixType& matrix)
|
---|
| 489 | : Base()
|
---|
| 490 | {
|
---|
| 491 | pardisoInit(Base::ScalarIsComplex ? 4 : 2);
|
---|
| 492 | compute(matrix);
|
---|
| 493 | }
|
---|
| 494 |
|
---|
| 495 | protected:
|
---|
| 496 |
|
---|
| 497 | void getMatrix(const MatrixType& matrix)
|
---|
| 498 | {
|
---|
| 499 | // PARDISO supports only upper, row-major matrices
|
---|
| 500 | PermutationMatrix<Dynamic,Dynamic,Index> p_null;
|
---|
| 501 | m_matrix.resize(matrix.rows(), matrix.cols());
|
---|
| 502 | m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
|
---|
| 503 | }
|
---|
| 504 |
|
---|
| 505 | private:
|
---|
| 506 | PardisoLLT(PardisoLLT& ) {}
|
---|
| 507 | };
|
---|
| 508 |
|
---|
| 509 | /** \ingroup PardisoSupport_Module
|
---|
| 510 | * \class PardisoLDLT
|
---|
| 511 | * \brief A sparse direct Cholesky (LDLT) factorization and solver based on the PARDISO library
|
---|
| 512 | *
|
---|
| 513 | * This class allows to solve for A.X = B sparse linear problems via a LDL^T Cholesky factorization
|
---|
| 514 | * using the Intel MKL PARDISO library. The sparse matrix A is assumed to be selfajoint and positive definite.
|
---|
| 515 | * For complex matrices, A can also be symmetric only, see the \a Options template parameter.
|
---|
| 516 | * The vectors or matrices X and B can be either dense or sparse.
|
---|
| 517 | *
|
---|
| 518 | * By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
|
---|
| 519 | * \code solver.pardisoParameterArray()[59] = 1; \endcode
|
---|
| 520 | *
|
---|
| 521 | * \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
|
---|
| 522 | * \tparam Options can be any bitwise combination of Upper, Lower, and Symmetric. The default is Upper, meaning only the upper triangular part has to be used.
|
---|
| 523 | * Symmetric can be used for symmetric, non-selfadjoint complex matrices, the default being to assume a selfadjoint matrix.
|
---|
| 524 | * Upper|Lower can be used to tell both triangular parts can be used as input.
|
---|
| 525 | *
|
---|
| 526 | * \sa \ref TutorialSparseDirectSolvers
|
---|
| 527 | */
|
---|
| 528 | template<typename MatrixType, int Options>
|
---|
| 529 | class PardisoLDLT : public PardisoImpl< PardisoLDLT<MatrixType,Options> >
|
---|
| 530 | {
|
---|
| 531 | protected:
|
---|
| 532 | typedef PardisoImpl< PardisoLDLT<MatrixType,Options> > Base;
|
---|
| 533 | typedef typename Base::Scalar Scalar;
|
---|
| 534 | typedef typename Base::Index Index;
|
---|
| 535 | typedef typename Base::RealScalar RealScalar;
|
---|
| 536 | using Base::pardisoInit;
|
---|
| 537 | using Base::m_matrix;
|
---|
| 538 | friend class PardisoImpl< PardisoLDLT<MatrixType,Options> >;
|
---|
| 539 |
|
---|
| 540 | public:
|
---|
| 541 |
|
---|
| 542 | using Base::compute;
|
---|
| 543 | using Base::solve;
|
---|
| 544 | enum { UpLo = Options&(Upper|Lower) };
|
---|
| 545 |
|
---|
| 546 | PardisoLDLT()
|
---|
| 547 | : Base()
|
---|
| 548 | {
|
---|
| 549 | pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
|
---|
| 550 | }
|
---|
| 551 |
|
---|
| 552 | PardisoLDLT(const MatrixType& matrix)
|
---|
| 553 | : Base()
|
---|
| 554 | {
|
---|
| 555 | pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
|
---|
| 556 | compute(matrix);
|
---|
| 557 | }
|
---|
| 558 |
|
---|
| 559 | void getMatrix(const MatrixType& matrix)
|
---|
| 560 | {
|
---|
| 561 | // PARDISO supports only upper, row-major matrices
|
---|
| 562 | PermutationMatrix<Dynamic,Dynamic,Index> p_null;
|
---|
| 563 | m_matrix.resize(matrix.rows(), matrix.cols());
|
---|
| 564 | m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
|
---|
| 565 | }
|
---|
| 566 |
|
---|
| 567 | private:
|
---|
| 568 | PardisoLDLT(PardisoLDLT& ) {}
|
---|
| 569 | };
|
---|
| 570 |
|
---|
| 571 | namespace internal {
|
---|
| 572 |
|
---|
| 573 | template<typename _Derived, typename Rhs>
|
---|
| 574 | struct solve_retval<PardisoImpl<_Derived>, Rhs>
|
---|
| 575 | : solve_retval_base<PardisoImpl<_Derived>, Rhs>
|
---|
| 576 | {
|
---|
| 577 | typedef PardisoImpl<_Derived> Dec;
|
---|
| 578 | EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
|
---|
| 579 |
|
---|
| 580 | template<typename Dest> void evalTo(Dest& dst) const
|
---|
| 581 | {
|
---|
| 582 | dec()._solve(rhs(),dst);
|
---|
| 583 | }
|
---|
| 584 | };
|
---|
| 585 |
|
---|
| 586 | template<typename Derived, typename Rhs>
|
---|
| 587 | struct sparse_solve_retval<PardisoImpl<Derived>, Rhs>
|
---|
| 588 | : sparse_solve_retval_base<PardisoImpl<Derived>, Rhs>
|
---|
| 589 | {
|
---|
| 590 | typedef PardisoImpl<Derived> Dec;
|
---|
| 591 | EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
|
---|
| 592 |
|
---|
| 593 | template<typename Dest> void evalTo(Dest& dst) const
|
---|
| 594 | {
|
---|
| 595 | this->defaultEvalTo(dst);
|
---|
| 596 | }
|
---|
| 597 | };
|
---|
| 598 |
|
---|
| 599 | } // end namespace internal
|
---|
| 600 |
|
---|
| 601 | } // end namespace Eigen
|
---|
| 602 |
|
---|
| 603 | #endif // EIGEN_PARDISOSUPPORT_H
|
---|