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Adding an interface to PaStiX, the multithreaded and distributed linear solver

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Desire NUENTSA 2012-03-08 18:59:08 +01:00
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Eigen/src/PaStiXSupport/CMakeLists.txt Normal file
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FILE(GLOB Eigen_PastixSupport_SRCS "*.h")
INSTALL(FILES
${Eigen_PastixSupport_SRCS}
DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/PastixSupport COMPONENT Devel
)

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Eigen/src/PaStiXSupport/PaStiXSupport.h Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef EIGEN_PASTIXSUPPORT_H
#define EIGEN_PASTIXSUPPORT_H
/** \ingroup PaStiXSupport_Module
* \brief Interface to the PaStix solver
*
* This class is used to solve the linear systems A.X = B via the PaStix library.
* The matrix can be either real or complex, symmetric or not.
*
* \sa TutorialSparseDirectSolvers
*/
template<typename _MatrixType, bool IsStrSym = false> class PastixLU;
template<typename _MatrixType, int Options> class PastixLLT;
template<typename _MatrixType, int Options> class PastixLDLT;
namespace internal
{
template<class Pastix> struct pastix_traits;
template<typename _MatrixType>
struct pastix_traits< PastixLU<_MatrixType> >
{
typedef _MatrixType MatrixType;
typedef typename _MatrixType::Scalar Scalar;
typedef typename _MatrixType::RealScalar RealScalar;
typedef typename _MatrixType::Index Index;
};
template<typename _MatrixType, int Options>
struct pastix_traits< PastixLLT<_MatrixType,Options> >
{
typedef _MatrixType MatrixType;
typedef typename _MatrixType::Scalar Scalar;
typedef typename _MatrixType::RealScalar RealScalar;
typedef typename _MatrixType::Index Index;
};
template<typename _MatrixType, int Options>
struct pastix_traits< PastixLDLT<_MatrixType,Options> >
{
typedef _MatrixType MatrixType;
typedef typename _MatrixType::Scalar Scalar;
typedef typename _MatrixType::RealScalar RealScalar;
typedef typename _MatrixType::Index Index;
};
void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, float *vals, int *perm, int * invp, float *x, int nbrhs, int *iparm, double *dparm)
{
if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
if (nbrhs == 0) x = NULL;
s_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
}
void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, double *vals, int *perm, int * invp, double *x, int nbrhs, int *iparm, double *dparm)
{
if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
if (nbrhs == 0) x = NULL;
d_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
}
void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<float> *vals, int *perm, int * invp, std::complex<float> *x, int nbrhs, int *iparm, double *dparm)
{
c_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<COMPLEX*>(vals), perm, invp, reinterpret_cast<COMPLEX*>(x), nbrhs, iparm, dparm);
}
void eigen_pastix(pastix_data_t **pastix_data, int pastix_comm, int n, int *ptr, int *idx, std::complex<double> *vals, int *perm, int * invp, std::complex<double> *x, int nbrhs, int *iparm, double *dparm)
{
if (n == 0) { ptr = NULL; idx = NULL; vals = NULL; }
if (nbrhs == 0) x = NULL;
z_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<DCOMPLEX*>(vals), perm, invp, reinterpret_cast<DCOMPLEX*>(x), nbrhs, iparm, dparm);
}
// Convert the matrix to Fortran-style Numbering
template <typename MatrixType>
void EigenToFortranNumbering (MatrixType& mat)
{
if ( !(mat.outerIndexPtr()[0]) )
{
int i;
for(i = 0; i <= mat.rows(); ++i)
++mat.outerIndexPtr()[i];
for(i = 0; i < mat.nonZeros(); ++i)
++mat.innerIndexPtr()[i];
}
}
// Convert to C-style Numbering
template <typename MatrixType>
void EigenToCNumbering (MatrixType& mat)
{
// Check the Numbering
if ( mat.outerIndexPtr()[0] == 1 )
{ // Convert to C-style numbering
int i;
for(i = 0; i <= mat.rows(); ++i)
--mat.outerIndexPtr()[i];
for(i = 0; i < mat.nonZeros(); ++i)
--mat.innerIndexPtr()[i];
}
}
// Symmetrize the graph of the input matrix
// In : The Input matrix to symmetrize the pattern
// Out : The output matrix
// StrMatTrans : The structural pattern of the transpose of In; It is
// used to optimize the future symmetrization with the same matrix pattern
// WARNING It is assumed here that successive calls to this routine are done
// with matrices having the same pattern.
template <typename MatrixType>
void EigenSymmetrizeMatrixGraph (const MatrixType& In, MatrixType& Out, MatrixType& StrMatTrans)
{
eigen_assert(In.cols()==In.rows() && " Can only symmetrize the graph of a square matrix");
if (StrMatTrans.outerSize() == 0)
{ //First call to this routine, need to compute the structural pattern of In^T
StrMatTrans = In.transpose();
// Set the elements of the matrix to zero
for (int i = 0; i < StrMatTrans.rows(); i++)
{
for (typename MatrixType::InnerIterator it(StrMatTrans, i); it; ++it)
it.valueRef() = 0.0;
}
}
Out = (StrMatTrans + In).eval();
}
}
// This is the base class to interface with PaStiX functions.
// Users should not used this class directly.
template <class Derived>
class PastixBase
{
public:
typedef typename internal::pastix_traits<Derived>::MatrixType _MatrixType;
typedef _MatrixType MatrixType;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::Index Index;
typedef Matrix<Scalar,Dynamic,1> Vector;
public:
PastixBase():m_initisOk(false),m_analysisIsOk(false),m_factorizationIsOk(false),m_isInitialized(false)
{
m_pastixdata = 0;
PastixInit();
}
~PastixBase()
{
PastixDestroy();
}
// Initialize the Pastix data structure, check the matrix
void PastixInit();
// Compute the ordering and the symbolic factorization
Derived& analyzePattern (MatrixType& mat);
// Compute the numerical factorization
Derived& factorize (MatrixType& mat);
/** \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<PastixBase, Rhs>
solve(const MatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "Pastix solver is not initialized.");
eigen_assert(rows()==b.rows()
&& "PastixBase::solve(): invalid number of rows of the right hand side matrix b");
return internal::solve_retval<PastixBase, Rhs>(*this, b.derived());
}
template<typename Rhs,typename Dest>
bool _solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const;
/** \internal */
template<typename Rhs, typename DestScalar, int DestOptions, typename DestIndex>
void _solve_sparse(const Rhs& 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()");
eigen_assert(rows()==b.rows());
// we process the sparse rhs per block of NbColsAtOnce columns temporarily stored into a dense matrix.
static const int NbColsAtOnce = 1;
int rhsCols = b.cols();
int size = b.rows();
Eigen::Matrix<DestScalar,Dynamic,Dynamic> tmp(size,rhsCols);
for(int k=0; k<rhsCols; k+=NbColsAtOnce)
{
int actualCols = std::min<int>(rhsCols-k, NbColsAtOnce);
tmp.leftCols(actualCols) = b.middleCols(k,actualCols);
tmp.leftCols(actualCols) = derived().solve(tmp.leftCols(actualCols));
dest.middleCols(k,actualCols) = tmp.leftCols(actualCols).sparseView();
}
}
Derived& derived()
{
return *static_cast<Derived*>(this);
}
const Derived& derived() const
{
return *static_cast<const Derived*>(this);
}
/** Returns a reference to the integer vector IPARM of PaStiX parameters
* to modify the default parameters.
* The statistics related to the different phases of factorization and solve are saved here as well
* \sa analyzePattern() factorize()
*/
Array<Index,IPARM_SIZE,1>& iparm()
{
return m_iparm;
}
/** Returns a reference to the double vector DPARM of PaStiX parameters
* The statistics related to the different phases of factorization and solve are saved here as well
* \sa analyzePattern() factorize()
*/
Array<RealScalar,IPARM_SIZE,1>& dparm()
{
return m_dparm;
}
inline Index cols() const { return m_size; }
inline Index rows() const { return m_size; }
/** \brief Reports whether previous computation was successful.
*
* \returns \c Success if computation was succesful,
* \c NumericalIssue if the PaStiX reports a problem
* \c InvalidInput if the input matrix is invalid
*
* \sa iparm()
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
return m_info;
}
/** \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<PastixBase, Rhs>
solve(const SparseMatrixBase<Rhs>& b) const
{
eigen_assert(m_isInitialized && "Pastix LU, LLT or LDLT is not initialized.");
eigen_assert(rows()==b.rows()
&& "PastixBase::solve(): invalid number of rows of the right hand side matrix b");
return internal::sparse_solve_retval<PastixBase, Rhs>(*this, b.derived());
}
protected:
// Free all the data allocated by Pastix
void PastixDestroy()
{
eigen_assert(m_initisOk && "The Pastix structure should be allocated first");
m_iparm(IPARM_START_TASK) = API_TASK_CLEAN;
m_iparm(IPARM_END_TASK) = API_TASK_CLEAN;
internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, m_mat_null.outerIndexPtr(), m_mat_null.innerIndexPtr(),
m_mat_null.valuePtr(), m_perm.data(), m_invp.data(), m_vec_null.data(), 1, m_iparm.data(), m_dparm.data());
}
Derived& compute (MatrixType& mat);
int m_initisOk;
int m_analysisIsOk;
int m_factorizationIsOk;
bool m_isInitialized;
ComputationInfo m_info;
mutable pastix_data_t *m_pastixdata; // Data structure for pastix
mutable SparseMatrix<Scalar, ColMajor> m_mat_null; // An input null matrix
mutable Matrix<Scalar, Dynamic,1> m_vec_null; // An input null vector
mutable SparseMatrix<Scalar, ColMajor> m_StrMatTrans; // The transpose pattern of the input matrix
mutable int m_comm; // The MPI communicator identifier
mutable Matrix<Index,IPARM_SIZE,1> m_iparm; // integer vector for the input parameters
mutable Matrix<double,DPARM_SIZE,1> m_dparm; // Scalar vector for the input parameters
mutable Matrix<Index,Dynamic,1> m_perm; // Permutation vector
mutable Matrix<Index,Dynamic,1> m_invp; // Inverse permutation vector
mutable int m_ordering; // ordering method to use
mutable int m_amalgamation; // level of amalgamation
mutable int m_size; // Size of the matrix
};
/** Initialize the PaStiX data structure.
*A first call to this function fills iparm and dparm with the default PaStiX parameters
* \sa iparm() dparm()
*/
template <class Derived>
void PastixBase<Derived>::PastixInit()
{
m_size = 0;
m_iparm.resize(IPARM_SIZE);
m_dparm.resize(DPARM_SIZE);
m_iparm(IPARM_MODIFY_PARAMETER) = API_NO;
if(m_pastixdata)
{ // This trick is used to reset the Pastix internal data between successive
// calls with (structural) different matrices
PastixDestroy();
m_pastixdata = 0;
m_iparm(IPARM_MODIFY_PARAMETER) = API_YES;
}
m_iparm(IPARM_START_TASK) = API_TASK_INIT;
m_iparm(IPARM_END_TASK) = API_TASK_INIT;
m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, m_mat_null.outerIndexPtr(), m_mat_null.innerIndexPtr(),
m_mat_null.valuePtr(), m_perm.data(), m_invp.data(), m_vec_null.data(), 1, m_iparm.data(), m_dparm.data());
m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
// Check the returned error
if(m_iparm(IPARM_ERROR_NUMBER)) {
m_info = InvalidInput;
m_initisOk = false;
}
else {
m_info = Success;
m_initisOk = true;
}
}
template <class Derived>
Derived& PastixBase<Derived>::compute(MatrixType& mat)
{
eigen_assert(mat.rows() == mat.cols() && "The input matrix should be squared");
typedef typename MatrixType::Scalar Scalar;
// Save the size of the current matrix
m_size = mat.rows();
// Convert the matrix in fortran-style numbering
internal::EigenToFortranNumbering(mat);
analyzePattern(mat);
factorize(mat);
m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
if (m_factorizationIsOk) m_isInitialized = true;
//Convert back the matrix -- Is it really necessary here
internal::EigenToCNumbering(mat);
return derived();
}
template <class Derived>
Derived& PastixBase<Derived>::analyzePattern(MatrixType& mat)
{
eigen_assert(m_initisOk && "PastixInit should be called first to set the default parameters");
m_size = mat.rows();
m_perm.resize(m_size);
m_invp.resize(m_size);
// Convert the matrix in fortran-style numbering
internal::EigenToFortranNumbering(mat);
m_iparm(IPARM_START_TASK) = API_TASK_ORDERING;
m_iparm(IPARM_END_TASK) = API_TASK_ANALYSE;
internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
mat.valuePtr(), m_perm.data(), m_invp.data(), m_vec_null.data(), 0, m_iparm.data(), m_dparm.data());
// Check the returned error
if(m_iparm(IPARM_ERROR_NUMBER)) {
m_info = NumericalIssue;
m_analysisIsOk = false;
}
else {
m_info = Success;
m_analysisIsOk = true;
}
return derived();
}
template <class Derived>
Derived& PastixBase<Derived>::factorize(MatrixType& mat)
{
eigen_assert(m_analysisIsOk && "The analysis phase should be called before the factorization phase");
m_iparm(IPARM_START_TASK) = API_TASK_NUMFACT;
m_iparm(IPARM_END_TASK) = API_TASK_NUMFACT;
m_size = mat.rows();
// Convert the matrix in fortran-style numbering
internal::EigenToFortranNumbering(mat);
internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
mat.valuePtr(), m_perm.data(), m_invp.data(), m_vec_null.data(), 0, m_iparm.data(), m_dparm.data());
// Check the returned error
if(m_iparm(IPARM_ERROR_NUMBER)) {
m_info = NumericalIssue;
m_factorizationIsOk = false;
m_isInitialized = false;
}
else {
m_info = Success;
m_factorizationIsOk = true;
m_isInitialized = true;
}
std::cout << "IPARM " << m_iparm(IPARM_ERROR_NUMBER) << " \n";
return derived();
}
/* Solve the system */
template<typename Base>
template<typename Rhs,typename Dest>
bool PastixBase<Base>::_solve (const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const
{
eigen_assert(m_isInitialized && "The matrix should be factorized first");
EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0,
THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES);
int rhs = 1;
x = b; /* on return, x is overwritten by the computed solution */
for (int i = 0; i < b.cols(); i++){
m_iparm(IPARM_START_TASK) = API_TASK_SOLVE;
m_iparm(IPARM_END_TASK) = API_TASK_REFINE;
m_iparm(IPARM_RHS_MAKING) = API_RHS_B;
internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, x.rows(), m_mat_null.outerIndexPtr(), m_mat_null.innerIndexPtr(),
m_mat_null.valuePtr(), m_perm.data(), m_invp.data(), &x(0, i), rhs, m_iparm.data(), m_dparm.data());
}
// Check the returned error
if(m_iparm(IPARM_ERROR_NUMBER)) {
m_info = NumericalIssue;
return false;
}
else {
return true;
}
}
/** \ingroup PaStiXSupport_Module
* \class PastixLU
* \brief Sparse direct LU solver based on PaStiX library
*
* This class is used to solve the linear systems A.X = B with a supernodal LU
* factorization in the PaStiX library. The matrix A should be squared and nonsingular
* PaStiX requires that the matrix A has a symmetric structural pattern.
* This interface can symmetrize the input matrix otherwise.
* 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 IsStrSym Indicates if the input matrix has a symmetric pattern, default is false
* NOTE : Note that if the analysis and factorization phase are called separately,
* the input matrix will be symmetrized at each call, hence it is advised to
* symmetrize the matrix in a end-user program and set \p IsStrSym to true
*
* \sa \ref TutorialSparseDirectSolvers
*
*/
template<typename _MatrixType, bool IsStrSym>
class PastixLU : public PastixBase< PastixLU<_MatrixType> >
{
public:
typedef _MatrixType MatrixType;
typedef PastixBase<PastixLU<MatrixType> > Base;
typedef typename MatrixType::Scalar Scalar;
typedef SparseMatrix<Scalar, ColMajor> PaStiXType;
public:
PastixLU():Base() {}
PastixLU(const MatrixType& matrix):Base()
{
compute(matrix);
}
/** Compute the LU supernodal factorization of \p matrix.
* iparm and dparm can be used to tune the PaStiX parameters.
* see the PaStiX user's manual
* \sa analyzePattern() factorize()
*/
void compute (const MatrixType& matrix)
{
// Pastix supports only column-major matrices with a symmetric pattern
Base::PastixInit();
PaStiXType temp(matrix.rows(), matrix.cols());
// Symmetrize the graph of the matrix
if (IsStrSym)
temp = matrix;
else
{
internal::EigenSymmetrizeMatrixGraph<PaStiXType>(matrix, temp, m_StrMatTrans);
}
m_iparm[IPARM_SYM] = API_SYM_NO;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;
Base::compute(temp);
}
/** Compute the LU symbolic factorization of \p matrix using its sparsity pattern.
* Several ordering methods can be used at this step. See the PaStiX user's manual.
* The result of this operation can be used with successive matrices having the same pattern as \p matrix
* \sa factorize()
*/
void analyzePattern(const MatrixType& matrix)
{
Base::PastixInit();
/* Pastix supports only column-major matrices with symmetrized patterns */
SparseMatrix<Scalar, ColMajor> temp(matrix.rows(), matrix.cols());
// Symmetrize the graph of the matrix
if (IsStrSym)
temp = matrix;
else
{
internal::EigenSymmetrizeMatrixGraph<PaStiXType>(matrix, temp, m_StrMatTrans);
}
m_iparm(IPARM_SYM) = API_SYM_NO;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;
Base::analyzePattern(temp);
}
/** Compute the LU supernodal factorization of \p matrix
* WARNING The matrix \p matrix should have the same structural pattern
* as the same used in the analysis phase.
* \sa analyzePattern()
*/
void factorize(const MatrixType& matrix)
{
/* Pastix supports only column-major matrices with symmetrized patterns */
SparseMatrix<Scalar, ColMajor> temp(matrix.rows(), matrix.cols());
// Symmetrize the graph of the matrix
if (IsStrSym)
temp = matrix;
else
{
internal::EigenSymmetrizeMatrixGraph<PaStiXType>(matrix, temp, m_StrMatTrans);
}
m_iparm(IPARM_SYM) = API_SYM_NO;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;
Base::factorize(temp);
}
protected:
using Base::m_iparm;
using Base::m_dparm;
using Base::m_StrMatTrans;
};
/** \ingroup PaStiXSupport_Module
* \class PastixLLT
* \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
*
* This class is used to solve the linear systems A.X = B via a LL^T supernodal Cholesky factorization
* available in the PaStiX library. The matrix A should be symmetric and positive definite
* WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
* 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 part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
*
* \sa \ref TutorialSparseDirectSolvers
*/
template<typename _MatrixType, int _UpLo>
class PastixLLT : public PastixBase< PastixLLT<_MatrixType, _UpLo> >
{
public:
typedef _MatrixType MatrixType;
typedef PastixBase<PastixLLT<MatrixType, _UpLo> > Base;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::Index Index;
public:
enum { UpLo = _UpLo };
PastixLLT():Base() {}
PastixLLT(const MatrixType& matrix):Base()
{
compute(matrix);
}
/** Compute the L factor of the LL^T supernodal factorization of \p matrix
* \sa analyzePattern() factorize()
*/
void compute (const MatrixType& matrix)
{
// Pastix supports only lower, column-major matrices
Base::PastixInit(); // This is necessary to let PaStiX initialize its data structure between successive calls to compute
SparseMatrix<Scalar, ColMajor> temp(matrix.rows(), matrix.cols());
PermutationMatrix<Dynamic,Dynamic,Index> pnull;
temp.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>().twistedBy(pnull);
m_iparm(IPARM_SYM) = API_SYM_YES;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;
Base::compute(temp);
}
/** Compute the LL^T symbolic factorization of \p matrix using its sparsity pattern
* The result of this operation can be used with successive matrices having the same pattern as \p matrix
* \sa factorize()
*/
void analyzePattern(const MatrixType& matrix)
{
Base::PastixInit();
// Pastix supports only lower, column-major matrices
SparseMatrix<Scalar, ColMajor> temp(matrix.rows(), matrix.cols());
PermutationMatrix<Dynamic,Dynamic,Index> pnull;
temp.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>().twistedBy(pnull);
m_iparm(IPARM_SYM) = API_SYM_YES;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;
Base::analyzePattern(temp);
}
/** Compute the LL^T supernodal numerical factorization of \p matrix
* \sa analyzePattern()
*/
void factorize(const MatrixType& matrix)
{
// Pastix supports only lower, column-major matrices
SparseMatrix<Scalar, ColMajor> temp(matrix.rows(), matrix.cols());
PermutationMatrix<Dynamic,Dynamic,Index> pnull;
temp.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>().twistedBy(pnull);
m_iparm(IPARM_SYM) = API_SYM_YES;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;
Base::factorize(temp);
}
protected:
using Base::m_iparm;
};
/** \ingroup PaStiXSupport_Module
* \class PastixLDLT
* \brief A sparse direct supernodal Cholesky (LLT) factorization and solver based on the PaStiX library
*
* This class is used to solve the linear systems A.X = B via a LDL^T supernodal Cholesky factorization
* available in the PaStiX library. The matrix A should be symmetric and positive definite
* WARNING Selfadjoint complex matrices are not supported in the current version of PaStiX
* 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 part of the matrix to use : Lower or Upper. The default is Lower as required by PaStiX
*
* \sa \ref TutorialSparseDirectSolvers
*/
template<typename _MatrixType, int _UpLo>
class PastixLDLT : public PastixBase< PastixLDLT<_MatrixType, _UpLo> >
{
public:
typedef _MatrixType MatrixType;
typedef PastixBase<PastixLDLT<MatrixType, _UpLo> > Base;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::Index Index;
public:
enum { UpLo = _UpLo };
PastixLDLT():Base() {}
PastixLDLT(const MatrixType& matrix):Base()
{
compute(matrix);
}
/** Compute the L and D factors of the LDL^T factorization of \p matrix
* \sa analyzePattern() factorize()
*/
void compute (const MatrixType& matrix)
{
Base::PastixInit();
// Pastix supports only lower, column-major matrices
SparseMatrix<Scalar, ColMajor> temp(matrix.rows(), matrix.cols());
PermutationMatrix<Dynamic,Dynamic,Index> pnull;
temp.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>().twistedBy(pnull);
m_iparm(IPARM_SYM) = API_SYM_YES;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;
Base::compute(temp);
}
/** Compute the LDL^T symbolic factorization of \p matrix using its sparsity pattern
* The result of this operation can be used with successive matrices having the same pattern as \p matrix
* \sa factorize()
*/
void analyzePattern(const MatrixType& matrix)
{
Base::PastixInit();
// Pastix supports only lower, column-major matrices
SparseMatrix<Scalar, ColMajor> temp(matrix.rows(), matrix.cols());
PermutationMatrix<Dynamic,Dynamic,Index> pnull;
temp.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>().twistedBy(pnull);
m_iparm(IPARM_SYM) = API_SYM_YES;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;
Base::analyzePattern(temp);
}
/** Compute the LDL^T supernodal numerical factorization of \p matrix
*
*/
void factorize(const MatrixType& matrix)
{
// Pastix supports only lower, column-major matrices
SparseMatrix<Scalar, ColMajor> temp(matrix.rows(), matrix.cols());
PermutationMatrix<Dynamic,Dynamic,Index> pnull;
temp.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>().twistedBy(pnull);
m_iparm(IPARM_SYM) = API_SYM_YES;
m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;
Base::factorize(temp);
}
protected:
using Base::m_iparm;
};
namespace internal {
template<typename _MatrixType, typename Rhs>
struct solve_retval<PastixBase<_MatrixType>, Rhs>
: solve_retval_base<PastixBase<_MatrixType>, Rhs>
{
typedef PastixBase<_MatrixType> Dec;
EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve(rhs(),dst);
}
};
template<typename _MatrixType, typename Rhs>
struct sparse_solve_retval<PastixBase<_MatrixType>, Rhs>
: sparse_solve_retval_base<PastixBase<_MatrixType>, Rhs>
{
typedef PastixBase<_MatrixType> Dec;
EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve_sparse(rhs(),dst);
}
};
}
#endif

24
cmake/FindMetis.cmake Normal file
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@ -0,0 +1,24 @@
# Pastix requires METIS or METIS (partitioning and reordering tools)
if (METIS_INCLUDES AND METIS_LIBRARIES)
set(METIS_FIND_QUIETLY TRUE)
endif (METIS_INCLUDES AND METIS_LIBRARIES)
find_path(METIS_INCLUDES
NAMES
metis.h
PATHS
$ENV{METISDIR}
${INCLUDE_INSTALL_DIR}
PATH_SUFFIXES
metis
)
find_library(METIS_LIBRARIES metis PATHS $ENV{METISDIR} ${LIB_INSTALL_DIR})
include(FindPackageHandleStandardArgs)
find_package_handle_standard_args(METIS DEFAULT_MSG
METIS_INCLUDES METIS_LIBRARIES)
mark_as_advanced(METIS_INCLUDES METIS_LIBRARIES)

25
cmake/FindPastix.cmake Normal file
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@ -0,0 +1,25 @@
# Pastix lib requires linking to a blas library.
# It is up to the user of this module to find a BLAS and link to it.
# Pastix requires SCOTCH or METIS (partitioning and reordering tools) as well
if (PASTIX_INCLUDES AND PASTIX_LIBRARIES)
set(PASTIX_FIND_QUIETLY TRUE)
endif (PASTIX_INCLUDES AND PASTIX_LIBRARIES)
find_path(PASTIX_INCLUDES
NAMES
pastix_nompi.h
PATHS
$ENV{PASTIXDIR}
${INCLUDE_INSTALL_DIR}
)
find_library(PASTIX_LIBRARIES pastix PATHS $ENV{PASTIXDIR} ${LIB_INSTALL_DIR})
include(FindPackageHandleStandardArgs)
find_package_handle_standard_args(PASTIX DEFAULT_MSG
PASTIX_INCLUDES PASTIX_LIBRARIES)
mark_as_advanced(PASTIX_INCLUDES PASTIX_LIBRARIES)

24
cmake/FindScotch.cmake Normal file
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@ -0,0 +1,24 @@
# Pastix requires SCOTCH or METIS (partitioning and reordering tools)
if (SCOTCH_INCLUDES AND SCOTCH_LIBRARIES)
set(SCOTCH_FIND_QUIETLY TRUE)
endif (SCOTCH_INCLUDES AND SCOTCH_LIBRARIES)
find_path(SCOTCH_INCLUDES
NAMES
scotch.h
PATHS
$ENV{SCOTCHDIR}
${INCLUDE_INSTALL_DIR}
PATH_SUFFIXES
scotch
)
find_library(SCOTCH_LIBRARIES scotch PATHS $ENV{SCOTCHDIR} ${LIB_INSTALL_DIR})
include(FindPackageHandleStandardArgs)
find_package_handle_standard_args(SCOTCH DEFAULT_MSG
SCOTCH_INCLUDES SCOTCH_LIBRARIES)
mark_as_advanced(SCOTCH_INCLUDES SCOTCH_LIBRARIES)

28
test/CMakeLists.txt
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@ -53,6 +53,29 @@ else()
ei_add_property(EIGEN_MISSING_BACKENDS "SuperLU, ")
endif()
find_package(Pastix)
find_package(Scotch)
find_package(Metis)
if(PASTIX_FOUND AND BLAS_FOUND)
add_definitions("-DEIGEN_PASTIX_SUPPORT")
include_directories(${PASTIX_INCLUDES})
if(SCOTCH_FOUND)
include_directories(${SCOTCH_INCLUDES})
set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${SCOTCH_LIBRARIES})
elseif(METIS_FOUND)
include_directories(${METIS_INCLUDES})
set(PASTIX_LIBRARIES ${PASTIX_LIBRARIES} ${METIS_LIBRARIES})
else(SCOTCH_FOUND)
ei_add_property(EIGEN_MISSING_BACKENDS "PaStiX, ")
endif(SCOTCH_FOUND)
set(SPARSE_LIBS ${SPARSE_LIBS} ${PASTIX_LIBRARIES} ${ORDERING_LIBRARIES} ${BLAS_LIBRARIES})
set(PASTIX_ALL_LIBS ${PASTIX_LIBRARIES} ${BLAS_LIBRARIES})
ei_add_property(EIGEN_TESTED_BACKENDS "PaStiX, ")
else()
ei_add_property(EIGEN_MISSING_BACKENDS "PaStiX, ")
endif()
option(EIGEN_TEST_NOQT "Disable Qt support in unit tests" OFF)
if(NOT EIGEN_TEST_NOQT)
find_package(Qt4)
@ -170,6 +193,7 @@ ei_add_test(simplicial_cholesky)
ei_add_test(conjugate_gradient)
ei_add_test(bicgstab)
if(UMFPACK_FOUND)
ei_add_test(umfpack_support "" "${UMFPACK_ALL_LIBS}")
endif()
@ -186,6 +210,10 @@ if(PARDISO_FOUND)
ei_add_test(pardiso_support "" "${PARDISO_ALL_LIBS}")
endif()
if(PASTIX_FOUND AND (SCOTCH_FOUND OR METIS_FOUND))
ei_add_test(pastix_support "" "${PASTIX_ALL_LIBS}")
endif()
string(TOLOWER "${CMAKE_CXX_COMPILER}" cmake_cxx_compiler_tolower)
if(cmake_cxx_compiler_tolower MATCHES "qcc")
set(CXX_IS_QCC "ON")

61
test/pastix_support.cpp Normal file
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@ -0,0 +1,61 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "sparse_solver.h"
#include <Eigen/PaStiXSupport>
#include <unsupported/Eigen/SparseExtra>
template<typename T> void test_pastix_T()
{
PastixLLT< SparseMatrix<T, ColMajor>, Eigen::Lower > pastix_llt_lower;
PastixLDLT< SparseMatrix<T, ColMajor>, Eigen::Lower > pastix_ldlt_lower;
PastixLLT< SparseMatrix<T, ColMajor>, Eigen::Upper > pastix_llt_upper;
PastixLDLT< SparseMatrix<T, ColMajor>, Eigen::Upper > pastix_ldlt_upper;
PastixLU< SparseMatrix<T, ColMajor> > pastix_lu;
check_sparse_spd_solving(pastix_llt_lower);
check_sparse_spd_solving(pastix_ldlt_lower);
check_sparse_spd_solving(pastix_llt_upper);
check_sparse_spd_solving(pastix_ldlt_upper);
check_sparse_square_solving(pastix_lu);
}
// There is no support for selfadjoint matrices with PaStiX.
// Complex symmetric matrices should pass though
template<typename T> void test_pastix_T_LU()
{
PastixLU< SparseMatrix<T, ColMajor> > pastix_lu;
check_sparse_square_solving(pastix_lu);
}
void test_pastix_support()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(test_pastix_T<float>());
CALL_SUBTEST_2(test_pastix_T<double>());
CALL_SUBTEST_3( (test_pastix_T_LU<std::complex<float> >()) );
CALL_SUBTEST_4(test_pastix_T_LU<std::complex<double> >());
}
}