/usr/include/eigen3/Eigen/src/CholmodSupport/CholmodSupport.h is in libeigen3-dev 3.2.2-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 | // This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_CHOLMODSUPPORT_H
#define EIGEN_CHOLMODSUPPORT_H
namespace Eigen {
namespace internal {
template<typename Scalar, typename CholmodType>
void cholmod_configure_matrix(CholmodType& mat)
{
if (internal::is_same<Scalar,float>::value)
{
mat.xtype = CHOLMOD_REAL;
mat.dtype = CHOLMOD_SINGLE;
}
else if (internal::is_same<Scalar,double>::value)
{
mat.xtype = CHOLMOD_REAL;
mat.dtype = CHOLMOD_DOUBLE;
}
else if (internal::is_same<Scalar,std::complex<float> >::value)
{
mat.xtype = CHOLMOD_COMPLEX;
mat.dtype = CHOLMOD_SINGLE;
}
else if (internal::is_same<Scalar,std::complex<double> >::value)
{
mat.xtype = CHOLMOD_COMPLEX;
mat.dtype = CHOLMOD_DOUBLE;
}
else
{
eigen_assert(false && "Scalar type not supported by CHOLMOD");
}
}
} // namespace internal
/** Wraps the Eigen sparse matrix \a mat into a Cholmod sparse matrix object.
* Note that the data are shared.
*/
template<typename _Scalar, int _Options, typename _Index>
cholmod_sparse viewAsCholmod(SparseMatrix<_Scalar,_Options,_Index>& mat)
{
cholmod_sparse res;
res.nzmax = mat.nonZeros();
res.nrow = mat.rows();;
res.ncol = mat.cols();
res.p = mat.outerIndexPtr();
res.i = mat.innerIndexPtr();
res.x = mat.valuePtr();
res.z = 0;
res.sorted = 1;
if(mat.isCompressed())
{
res.packed = 1;
res.nz = 0;
}
else
{
res.packed = 0;
res.nz = mat.innerNonZeroPtr();
}
res.dtype = 0;
res.stype = -1;
if (internal::is_same<_Index,int>::value)
{
res.itype = CHOLMOD_INT;
}
else if (internal::is_same<_Index,UF_long>::value)
{
res.itype = CHOLMOD_LONG;
}
else
{
eigen_assert(false && "Index type not supported yet");
}
// setup res.xtype
internal::cholmod_configure_matrix<_Scalar>(res);
res.stype = 0;
return res;
}
template<typename _Scalar, int _Options, typename _Index>
const cholmod_sparse viewAsCholmod(const SparseMatrix<_Scalar,_Options,_Index>& mat)
{
cholmod_sparse res = viewAsCholmod(mat.const_cast_derived());
return res;
}
/** Returns a view of the Eigen sparse matrix \a mat as Cholmod sparse matrix.
* The data are not copied but shared. */
template<typename _Scalar, int _Options, typename _Index, unsigned int UpLo>
cholmod_sparse viewAsCholmod(const SparseSelfAdjointView<SparseMatrix<_Scalar,_Options,_Index>, UpLo>& mat)
{
cholmod_sparse res = viewAsCholmod(mat.matrix().const_cast_derived());
if(UpLo==Upper) res.stype = 1;
if(UpLo==Lower) res.stype = -1;
return res;
}
/** Returns a view of the Eigen \b dense matrix \a mat as Cholmod dense matrix.
* The data are not copied but shared. */
template<typename Derived>
cholmod_dense viewAsCholmod(MatrixBase<Derived>& mat)
{
EIGEN_STATIC_ASSERT((internal::traits<Derived>::Flags&RowMajorBit)==0,THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
typedef typename Derived::Scalar Scalar;
cholmod_dense res;
res.nrow = mat.rows();
res.ncol = mat.cols();
res.nzmax = res.nrow * res.ncol;
res.d = Derived::IsVectorAtCompileTime ? mat.derived().size() : mat.derived().outerStride();
res.x = (void*)(mat.derived().data());
res.z = 0;
internal::cholmod_configure_matrix<Scalar>(res);
return res;
}
/** Returns a view of the Cholmod sparse matrix \a cm as an Eigen sparse matrix.
* The data are not copied but shared. */
template<typename Scalar, int Flags, typename Index>
MappedSparseMatrix<Scalar,Flags,Index> viewAsEigen(cholmod_sparse& cm)
{
return MappedSparseMatrix<Scalar,Flags,Index>
(cm.nrow, cm.ncol, static_cast<Index*>(cm.p)[cm.ncol],
static_cast<Index*>(cm.p), static_cast<Index*>(cm.i),static_cast<Scalar*>(cm.x) );
}
enum CholmodMode {
CholmodAuto, CholmodSimplicialLLt, CholmodSupernodalLLt, CholmodLDLt
};
/** \ingroup CholmodSupport_Module
* \class CholmodBase
* \brief The base class for the direct Cholesky factorization of Cholmod
* \sa class CholmodSupernodalLLT, class CholmodSimplicialLDLT, class CholmodSimplicialLLT
*/
template<typename _MatrixType, int _UpLo, typename Derived>
class CholmodBase : internal::noncopyable
{
public:
typedef _MatrixType MatrixType;
enum { UpLo = _UpLo };
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef MatrixType CholMatrixType;
typedef typename MatrixType::Index Index;
public:
CholmodBase()
: m_cholmodFactor(0), m_info(Success), m_isInitialized(false)
{
m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0);
cholmod_start(&m_cholmod);
}
CholmodBase(const MatrixType& matrix)
: m_cholmodFactor(0), m_info(Success), m_isInitialized(false)
{
m_shiftOffset[0] = m_shiftOffset[1] = RealScalar(0.0);
cholmod_start(&m_cholmod);
compute(matrix);
}
~CholmodBase()
{
if(m_cholmodFactor)
cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
cholmod_finish(&m_cholmod);
}
inline Index cols() const { return m_cholmodFactor->n; }
inline Index rows() const { return m_cholmodFactor->n; }
Derived& derived() { return *static_cast<Derived*>(this); }
const Derived& derived() const { return *static_cast<const Derived*>(this); }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was succesful,
* \c NumericalIssue if the matrix.appears to be negative.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
return m_info;
}
/** Computes the sparse Cholesky decomposition of \a matrix */
Derived& compute(const MatrixType& matrix)
{
analyzePattern(matrix);
factorize(matrix);
return derived();
}
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* \sa compute()
*/
template<typename Rhs>
inline const internal::solve_retval<CholmodBase, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(rows()==b.rows()
&& "CholmodDecomposition::solve(): invalid number of rows of the right hand side matrix b");
return internal::solve_retval<CholmodBase, Rhs>(*this, b.derived());
}
/** \returns the solution x of \f$ A x = b \f$ using the current decomposition of A.
*
* \sa compute()
*/
template<typename Rhs>
inline const internal::sparse_solve_retval<CholmodBase, Rhs>
solve(const SparseMatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "LLT is not initialized.");
eigen_assert(rows()==b.rows()
&& "CholmodDecomposition::solve(): invalid number of rows of the right hand side matrix b");
return internal::sparse_solve_retval<CholmodBase, Rhs>(*this, b.derived());
}
/** Performs a symbolic decomposition on the sparsity pattern of \a matrix.
*
* This function is particularly useful when solving for several problems having the same structure.
*
* \sa factorize()
*/
void analyzePattern(const MatrixType& matrix)
{
if(m_cholmodFactor)
{
cholmod_free_factor(&m_cholmodFactor, &m_cholmod);
m_cholmodFactor = 0;
}
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
m_cholmodFactor = cholmod_analyze(&A, &m_cholmod);
this->m_isInitialized = true;
this->m_info = Success;
m_analysisIsOk = true;
m_factorizationIsOk = false;
}
/** Performs a numeric decomposition of \a matrix
*
* The given matrix must have the same sparsity pattern as the matrix on which the symbolic decomposition has been performed.
*
* \sa analyzePattern()
*/
void factorize(const MatrixType& matrix)
{
eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
cholmod_sparse A = viewAsCholmod(matrix.template selfadjointView<UpLo>());
cholmod_factorize_p(&A, m_shiftOffset, 0, 0, m_cholmodFactor, &m_cholmod);
// If the factorization failed, minor is the column at which it did. On success minor == n.
this->m_info = (m_cholmodFactor->minor == m_cholmodFactor->n ? Success : NumericalIssue);
m_factorizationIsOk = true;
}
/** Returns a reference to the Cholmod's configuration structure to get a full control over the performed operations.
* See the Cholmod user guide for details. */
cholmod_common& cholmod() { return m_cholmod; }
#ifndef EIGEN_PARSED_BY_DOXYGEN
/** \internal */
template<typename Rhs,typename Dest>
void _solve(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const
{
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
const Index size = m_cholmodFactor->n;
EIGEN_UNUSED_VARIABLE(size);
eigen_assert(size==b.rows());
// note: cd stands for Cholmod Dense
Rhs& b_ref(b.const_cast_derived());
cholmod_dense b_cd = viewAsCholmod(b_ref);
cholmod_dense* x_cd = cholmod_solve(CHOLMOD_A, m_cholmodFactor, &b_cd, &m_cholmod);
if(!x_cd)
{
this->m_info = NumericalIssue;
}
// TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
dest = Matrix<Scalar,Dest::RowsAtCompileTime,Dest::ColsAtCompileTime>::Map(reinterpret_cast<Scalar*>(x_cd->x),b.rows(),b.cols());
cholmod_free_dense(&x_cd, &m_cholmod);
}
/** \internal */
template<typename RhsScalar, int RhsOptions, typename RhsIndex, typename DestScalar, int DestOptions, typename DestIndex>
void _solve(const SparseMatrix<RhsScalar,RhsOptions,RhsIndex> &b, SparseMatrix<DestScalar,DestOptions,DestIndex> &dest) const
{
eigen_assert(m_factorizationIsOk && "The decomposition is not in a valid state for solving, you must first call either compute() or symbolic()/numeric()");
const Index size = m_cholmodFactor->n;
EIGEN_UNUSED_VARIABLE(size);
eigen_assert(size==b.rows());
// note: cs stands for Cholmod Sparse
cholmod_sparse b_cs = viewAsCholmod(b);
cholmod_sparse* x_cs = cholmod_spsolve(CHOLMOD_A, m_cholmodFactor, &b_cs, &m_cholmod);
if(!x_cs)
{
this->m_info = NumericalIssue;
}
// TODO optimize this copy by swapping when possible (be careful with alignment, etc.)
dest = viewAsEigen<DestScalar,DestOptions,DestIndex>(*x_cs);
cholmod_free_sparse(&x_cs, &m_cholmod);
}
#endif // EIGEN_PARSED_BY_DOXYGEN
/** Sets the shift parameter that will be used to adjust the diagonal coefficients during the numerical factorization.
*
* During the numerical factorization, an offset term is added to the diagonal coefficients:\n
* \c d_ii = \a offset + \c d_ii
*
* The default is \a offset=0.
*
* \returns a reference to \c *this.
*/
Derived& setShift(const RealScalar& offset)
{
m_shiftOffset[0] = offset;
return derived();
}
template<typename Stream>
void dumpMemory(Stream& /*s*/)
{}
protected:
mutable cholmod_common m_cholmod;
cholmod_factor* m_cholmodFactor;
RealScalar m_shiftOffset[2];
mutable ComputationInfo m_info;
bool m_isInitialized;
int m_factorizationIsOk;
int m_analysisIsOk;
};
/** \ingroup CholmodSupport_Module
* \class CholmodSimplicialLLT
* \brief A simplicial direct Cholesky (LLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a simplicial LL^T Cholesky factorization
* using the Cholmod library.
* This simplicial variant is equivalent to Eigen's built-in SimplicialLLT class. Therefore, it has little practical interest.
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLLT
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSimplicialLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSimplicialLLT() : Base() { init(); }
CholmodSimplicialLLT(const MatrixType& matrix) : Base()
{
init();
compute(matrix);
}
~CholmodSimplicialLLT() {}
protected:
void init()
{
m_cholmod.final_asis = 0;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
m_cholmod.final_ll = 1;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodSimplicialLDLT
* \brief A simplicial direct Cholesky (LDLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a simplicial LDL^T Cholesky factorization
* using the Cholmod library.
* This simplicial variant is equivalent to Eigen's built-in SimplicialLDLT class. Therefore, it has little practical interest.
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \sa \ref TutorialSparseDirectSolvers, class CholmodSupernodalLLT, class SimplicialLDLT
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSimplicialLDLT : public CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSimplicialLDLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSimplicialLDLT() : Base() { init(); }
CholmodSimplicialLDLT(const MatrixType& matrix) : Base()
{
init();
compute(matrix);
}
~CholmodSimplicialLDLT() {}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodSupernodalLLT
* \brief A supernodal Cholesky (LLT) factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a supernodal LL^T Cholesky factorization
* using the Cholmod library.
* This supernodal variant performs best on dense enough problems, e.g., 3D FEM, or very high order 2D FEM.
* The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \sa \ref TutorialSparseDirectSolvers
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodSupernodalLLT : public CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodSupernodalLLT> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodSupernodalLLT() : Base() { init(); }
CholmodSupernodalLLT(const MatrixType& matrix) : Base()
{
init();
compute(matrix);
}
~CholmodSupernodalLLT() {}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
}
};
/** \ingroup CholmodSupport_Module
* \class CholmodDecomposition
* \brief A general Cholesky factorization and solver based on Cholmod
*
* This class allows to solve for A.X = B sparse linear problems via a LL^T or LDL^T Cholesky factorization
* using the Cholmod library. The sparse matrix A must be selfadjoint and positive definite. The vectors or matrices
* X and B can be either dense or sparse.
*
* This variant permits to change the underlying Cholesky method at runtime.
* On the other hand, it does not provide access to the result of the factorization.
* The default is to let Cholmod automatically choose between a simplicial and supernodal factorization.
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam _UpLo the triangular part that will be used for the computations. It can be Lower
* or Upper. Default is Lower.
*
* This class supports all kind of SparseMatrix<>: row or column major; upper, lower, or both; compressed or non compressed.
*
* \sa \ref TutorialSparseDirectSolvers
*/
template<typename _MatrixType, int _UpLo = Lower>
class CholmodDecomposition : public CholmodBase<_MatrixType, _UpLo, CholmodDecomposition<_MatrixType, _UpLo> >
{
typedef CholmodBase<_MatrixType, _UpLo, CholmodDecomposition> Base;
using Base::m_cholmod;
public:
typedef _MatrixType MatrixType;
CholmodDecomposition() : Base() { init(); }
CholmodDecomposition(const MatrixType& matrix) : Base()
{
init();
compute(matrix);
}
~CholmodDecomposition() {}
void setMode(CholmodMode mode)
{
switch(mode)
{
case CholmodAuto:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_AUTO;
break;
case CholmodSimplicialLLt:
m_cholmod.final_asis = 0;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
m_cholmod.final_ll = 1;
break;
case CholmodSupernodalLLt:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SUPERNODAL;
break;
case CholmodLDLt:
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_SIMPLICIAL;
break;
default:
break;
}
}
protected:
void init()
{
m_cholmod.final_asis = 1;
m_cholmod.supernodal = CHOLMOD_AUTO;
}
};
namespace internal {
template<typename _MatrixType, int _UpLo, typename Derived, typename Rhs>
struct solve_retval<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
: solve_retval_base<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
{
typedef CholmodBase<_MatrixType,_UpLo,Derived> Dec;
EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve(rhs(),dst);
}
};
template<typename _MatrixType, int _UpLo, typename Derived, typename Rhs>
struct sparse_solve_retval<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
: sparse_solve_retval_base<CholmodBase<_MatrixType,_UpLo,Derived>, Rhs>
{
typedef CholmodBase<_MatrixType,_UpLo,Derived> Dec;
EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve(rhs(),dst);
}
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_CHOLMODSUPPORT_H
|