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********************************************************************************
* Content : Eigen bindings to Intel(R) MKL PARDISO
********************************************************************************
*/
#ifndef EIGEN_PARDISOSUPPORT_H
#define EIGEN_PARDISOSUPPORT_H
namespace Eigen {
template<typename _MatrixType> class PardisoLU;
template<typename _MatrixType, int Options=Upper> class PardisoLLT;
template<typename _MatrixType, int Options=Upper> class PardisoLDLT;
namespace internal
{
template<typename IndexType>
struct pardiso_run_selector
{
static IndexType run( _MKL_DSS_HANDLE_t pt, IndexType maxfct, IndexType mnum, IndexType type, IndexType phase, IndexType n, void *a,
IndexType *ia, IndexType *ja, IndexType *perm, IndexType nrhs, IndexType *iparm, IndexType msglvl, void *b, void *x)
{
IndexType error = 0;
::pardiso(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);
return error;
}
};
template<>
struct pardiso_run_selector<long long int>
{
typedef long long int IndexType;
static IndexType run( _MKL_DSS_HANDLE_t pt, IndexType maxfct, IndexType mnum, IndexType type, IndexType phase, IndexType n, void *a,
IndexType *ia, IndexType *ja, IndexType *perm, IndexType nrhs, IndexType *iparm, IndexType msglvl, void *b, void *x)
{
IndexType error = 0;
::pardiso_64(pt, &maxfct, &mnum, &type, &phase, &n, a, ia, ja, perm, &nrhs, iparm, &msglvl, b, x, &error);
return error;
}
};
template<class Pardiso> struct pardiso_traits;
template<typename _MatrixType>
struct pardiso_traits< PardisoLU<_MatrixType> >
{
typedef _MatrixType MatrixType;
typedef typename _MatrixType::Scalar Scalar;
typedef typename _MatrixType::RealScalar RealScalar;
typedef typename _MatrixType::StorageIndex StorageIndex;
};
template<typename _MatrixType, int Options>
struct pardiso_traits< PardisoLLT<_MatrixType, Options> >
{
typedef _MatrixType MatrixType;
typedef typename _MatrixType::Scalar Scalar;
typedef typename _MatrixType::RealScalar RealScalar;
typedef typename _MatrixType::StorageIndex StorageIndex;
};
template<typename _MatrixType, int Options>
struct pardiso_traits< PardisoLDLT<_MatrixType, Options> >
{
typedef _MatrixType MatrixType;
typedef typename _MatrixType::Scalar Scalar;
typedef typename _MatrixType::RealScalar RealScalar;
typedef typename _MatrixType::StorageIndex StorageIndex;
};
} // end namespace internal
template<class Derived>
class PardisoImpl : public SparseSolverBase<Derived>
{
protected:
typedef SparseSolverBase<Derived> Base;
using Base::derived;
using Base::m_isInitialized;
typedef internal::pardiso_traits<Derived> Traits;
public:
using Base::_solve_impl;
typedef typename Traits::MatrixType MatrixType;
typedef typename Traits::Scalar Scalar;
typedef typename Traits::RealScalar RealScalar;
typedef typename Traits::StorageIndex StorageIndex;
typedef SparseMatrix<Scalar,RowMajor,StorageIndex> SparseMatrixType;
typedef Matrix<Scalar,Dynamic,1> VectorType;
typedef Matrix<StorageIndex, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
typedef Matrix<StorageIndex, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
typedef Array<StorageIndex,64,1,DontAlign> ParameterType;
enum {
ScalarIsComplex = NumTraits<Scalar>::IsComplex,
ColsAtCompileTime = Dynamic,
MaxColsAtCompileTime = Dynamic
};
PardisoImpl()
{
eigen_assert((sizeof(StorageIndex) >= sizeof(_INTEGER_t) && sizeof(StorageIndex) <= 8) && "Non-supported index type");
m_iparm.setZero();
m_msglvl = 0; // No output
m_isInitialized = false;
}
~PardisoImpl()
{
pardisoRelease();
}
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 matrix appears to be negative.
*/
ComputationInfo info() const
{
eigen_assert(m_isInitialized && "Decomposition is not initialized.");
return m_info;
}
/** \warning for advanced usage only.
* \returns a reference to the parameter array controlling PARDISO.
* See the PARDISO manual to know how to use it. */
ParameterType& pardisoParameterArray()
{
return m_iparm;
}
/** Performs a symbolic decomposition on the sparcity of \a matrix.
*
* This function is particularly useful when solving for several problems having the same structure.
*
* \sa factorize()
*/
Derived& analyzePattern(const MatrixType& matrix);
/** Performs a numeric decomposition of \a matrix
*
* The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.
*
* \sa analyzePattern()
*/
Derived& factorize(const MatrixType& matrix);
Derived& compute(const MatrixType& matrix);
template<typename Rhs,typename Dest>
void _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &dest) const;
protected:
void pardisoRelease()
{
if(m_isInitialized) // Factorization ran at least once
{
internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, -1, internal::convert_index<StorageIndex>(m_size),0, 0, 0, m_perm.data(), 0,
m_iparm.data(), m_msglvl, NULL, NULL);
m_isInitialized = false;
}
}
void pardisoInit(int type)
{
m_type = type;
bool symmetric = std::abs(m_type) < 10;
m_iparm[0] = 1; // No solver default
m_iparm[1] = 2; // use Metis for the ordering
m_iparm[2] = 0; // Reserved. Set to zero. (??Numbers of processors, value of OMP_NUM_THREADS??)
m_iparm[3] = 0; // No iterative-direct algorithm
m_iparm[4] = 0; // No user fill-in reducing permutation
m_iparm[5] = 0; // Write solution into x, b is left unchanged
m_iparm[6] = 0; // Not in use
m_iparm[7] = 2; // Max numbers of iterative refinement steps
m_iparm[8] = 0; // Not in use
m_iparm[9] = 13; // Perturb the pivot elements with 1E-13
m_iparm[10] = symmetric ? 0 : 1; // Use nonsymmetric permutation and scaling MPS
m_iparm[11] = 0; // Not in use
m_iparm[12] = symmetric ? 0 : 1; // Maximum weighted matching algorithm is switched-off (default for symmetric).
// Try m_iparm[12] = 1 in case of inappropriate accuracy
m_iparm[13] = 0; // Output: Number of perturbed pivots
m_iparm[14] = 0; // Not in use
m_iparm[15] = 0; // Not in use
m_iparm[16] = 0; // Not in use
m_iparm[17] = -1; // Output: Number of nonzeros in the factor LU
m_iparm[18] = -1; // Output: Mflops for LU factorization
m_iparm[19] = 0; // Output: Numbers of CG Iterations
m_iparm[20] = 0; // 1x1 pivoting
m_iparm[26] = 0; // No matrix checker
m_iparm[27] = (sizeof(RealScalar) == 4) ? 1 : 0;
m_iparm[34] = 1; // C indexing
m_iparm[36] = 0; // CSR
m_iparm[59] = 0; // 0 - In-Core ; 1 - Automatic switch between In-Core and Out-of-Core modes ; 2 - Out-of-Core
memset(m_pt, 0, sizeof(m_pt));
}
protected:
// cached data to reduce reallocation, etc.
void manageErrorCode(Index error) const
{
switch(error)
{
case 0:
m_info = Success;
break;
case -4:
case -7:
m_info = NumericalIssue;
break;
default:
m_info = InvalidInput;
}
}
mutable SparseMatrixType m_matrix;
mutable ComputationInfo m_info;
bool m_analysisIsOk, m_factorizationIsOk;
StorageIndex m_type, m_msglvl;
mutable void *m_pt[64];
mutable ParameterType m_iparm;
mutable IntColVectorType m_perm;
Index m_size;
};
template<class Derived>
Derived& PardisoImpl<Derived>::compute(const MatrixType& a)
{
m_size = a.rows();
eigen_assert(a.rows() == a.cols());
pardisoRelease();
m_perm.setZero(m_size);
derived().getMatrix(a);
Index error;
error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 12, internal::convert_index<StorageIndex>(m_size),
m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
manageErrorCode(error);
m_analysisIsOk = true;
m_factorizationIsOk = true;
m_isInitialized = true;
return derived();
}
template<class Derived>
Derived& PardisoImpl<Derived>::analyzePattern(const MatrixType& a)
{
m_size = a.rows();
eigen_assert(m_size == a.cols());
pardisoRelease();
m_perm.setZero(m_size);
derived().getMatrix(a);
Index error;
error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 11, internal::convert_index<StorageIndex>(m_size),
m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
manageErrorCode(error);
m_analysisIsOk = true;
m_factorizationIsOk = false;
m_isInitialized = true;
return derived();
}
template<class Derived>
Derived& PardisoImpl<Derived>::factorize(const MatrixType& a)
{
eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
eigen_assert(m_size == a.rows() && m_size == a.cols());
derived().getMatrix(a);
Index error;
error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 22, internal::convert_index<StorageIndex>(m_size),
m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
m_perm.data(), 0, m_iparm.data(), m_msglvl, NULL, NULL);
manageErrorCode(error);
m_factorizationIsOk = true;
return derived();
}
template<class Derived>
template<typename BDerived,typename XDerived>
void PardisoImpl<Derived>::_solve_impl(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& x) const
{
if(m_iparm[0] == 0) // Factorization was not computed
{
m_info = InvalidInput;
return;
}
//Index n = m_matrix.rows();
Index nrhs = Index(b.cols());
eigen_assert(m_size==b.rows());
eigen_assert(((MatrixBase<BDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && "Row-major right hand sides are not supported");
eigen_assert(((MatrixBase<XDerived>::Flags & RowMajorBit) == 0 || nrhs == 1) && "Row-major matrices of unknowns are not supported");
eigen_assert(((nrhs == 1) || b.outerStride() == b.rows()));
// switch (transposed) {
// case SvNoTrans : m_iparm[11] = 0 ; break;
// case SvTranspose : m_iparm[11] = 2 ; break;
// case SvAdjoint : m_iparm[11] = 1 ; break;
// default:
// //std::cerr << "Eigen: transposition option \"" << transposed << "\" not supported by the PARDISO backend\n";
// m_iparm[11] = 0;
// }
Scalar* rhs_ptr = const_cast<Scalar*>(b.derived().data());
Matrix<Scalar,Dynamic,Dynamic,ColMajor> tmp;
// Pardiso cannot solve in-place
if(rhs_ptr == x.derived().data())
{
tmp = b;
rhs_ptr = tmp.data();
}
Index error;
error = internal::pardiso_run_selector<StorageIndex>::run(m_pt, 1, 1, m_type, 33, internal::convert_index<StorageIndex>(m_size),
m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
m_perm.data(), internal::convert_index<StorageIndex>(nrhs), m_iparm.data(), m_msglvl,
rhs_ptr, x.derived().data());
manageErrorCode(error);
}
/** \ingroup PardisoSupport_Module
* \class PardisoLU
* \brief A sparse direct LU factorization and solver based on the PARDISO library
*
* This class allows to solve for A.X = B sparse linear problems via a direct LU factorization
* using the Intel MKL PARDISO library. The sparse matrix A must be squared and invertible.
* The vectors or matrices X and B can be either dense or sparse.
*
* By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
* \code solver.pardisoParameterArray()[59] = 1; \endcode
*
* \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
*
* \implsparsesolverconcept
*
* \sa \ref TutorialSparseSolverConcept, class SparseLU
*/
template<typename MatrixType>
class PardisoLU : public PardisoImpl< PardisoLU<MatrixType> >
{
protected:
typedef PardisoImpl<PardisoLU> Base;
typedef typename Base::Scalar Scalar;
typedef typename Base::RealScalar RealScalar;
using Base::pardisoInit;
using Base::m_matrix;
friend class PardisoImpl< PardisoLU<MatrixType> >;
public:
using Base::compute;
using Base::solve;
PardisoLU()
: Base()
{
pardisoInit(Base::ScalarIsComplex ? 13 : 11);
}
explicit PardisoLU(const MatrixType& matrix)
: Base()
{
pardisoInit(Base::ScalarIsComplex ? 13 : 11);
compute(matrix);
}
protected:
void getMatrix(const MatrixType& matrix)
{
m_matrix = matrix;
m_matrix.makeCompressed();
}
};
/** \ingroup PardisoSupport_Module
* \class PardisoLLT
* \brief A sparse direct Cholesky (LLT) factorization and solver based on the PARDISO library
*
* This class allows to solve for A.X = B sparse linear problems via a LL^T Cholesky factorization
* using the Intel MKL PARDISO library. The sparse matrix A must be selfajoint and positive definite.
* The vectors or matrices X and B can be either dense or sparse.
*
* By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
* \code solver.pardisoParameterArray()[59] = 1; \endcode
*
* \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \tparam UpLo can be any bitwise combination of Upper, Lower. The default is Upper, meaning only the upper triangular part has to be used.
* Upper|Lower can be used to tell both triangular parts can be used as input.
*
* \implsparsesolverconcept
*
* \sa \ref TutorialSparseSolverConcept, class SimplicialLLT
*/
template<typename MatrixType, int _UpLo>
class PardisoLLT : public PardisoImpl< PardisoLLT<MatrixType,_UpLo> >
{
protected:
typedef PardisoImpl< PardisoLLT<MatrixType,_UpLo> > Base;
typedef typename Base::Scalar Scalar;
typedef typename Base::RealScalar RealScalar;
using Base::pardisoInit;
using Base::m_matrix;
friend class PardisoImpl< PardisoLLT<MatrixType,_UpLo> >;
public:
typedef typename Base::StorageIndex StorageIndex;
enum { UpLo = _UpLo };
using Base::compute;
PardisoLLT()
: Base()
{
pardisoInit(Base::ScalarIsComplex ? 4 : 2);
}
explicit PardisoLLT(const MatrixType& matrix)
: Base()
{
pardisoInit(Base::ScalarIsComplex ? 4 : 2);
compute(matrix);
}
protected:
void getMatrix(const MatrixType& matrix)
{
// PARDISO supports only upper, row-major matrices
PermutationMatrix<Dynamic,Dynamic,StorageIndex> p_null;
m_matrix.resize(matrix.rows(), matrix.cols());
m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
m_matrix.makeCompressed();
}
};
/** \ingroup PardisoSupport_Module
* \class PardisoLDLT
* \brief A sparse direct Cholesky (LDLT) factorization and solver based on the PARDISO library
*
* This class allows to solve for A.X = B sparse linear problems via a LDL^T Cholesky factorization
* using the Intel MKL PARDISO library. The sparse matrix A is assumed to be selfajoint and positive definite.
* For complex matrices, A can also be symmetric only, see the \a Options template parameter.
* The vectors or matrices X and B can be either dense or sparse.
*
* By default, it runs in in-core mode. To enable PARDISO's out-of-core feature, set:
* \code solver.pardisoParameterArray()[59] = 1; \endcode
*
* \tparam MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
* \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.
* Symmetric can be used for symmetric, non-selfadjoint complex matrices, the default being to assume a selfadjoint matrix.
* Upper|Lower can be used to tell both triangular parts can be used as input.
*
* \implsparsesolverconcept
*
* \sa \ref TutorialSparseSolverConcept, class SimplicialLDLT
*/
template<typename MatrixType, int Options>
class PardisoLDLT : public PardisoImpl< PardisoLDLT<MatrixType,Options> >
{
protected:
typedef PardisoImpl< PardisoLDLT<MatrixType,Options> > Base;
typedef typename Base::Scalar Scalar;
typedef typename Base::RealScalar RealScalar;
using Base::pardisoInit;
using Base::m_matrix;
friend class PardisoImpl< PardisoLDLT<MatrixType,Options> >;
public:
typedef typename Base::StorageIndex StorageIndex;
using Base::compute;
enum { UpLo = Options&(Upper|Lower) };
PardisoLDLT()
: Base()
{
pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
}
explicit PardisoLDLT(const MatrixType& matrix)
: Base()
{
pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
compute(matrix);
}
void getMatrix(const MatrixType& matrix)
{
// PARDISO supports only upper, row-major matrices
PermutationMatrix<Dynamic,Dynamic,StorageIndex> p_null;
m_matrix.resize(matrix.rows(), matrix.cols());
m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
m_matrix.makeCompressed();
}
};
} // end namespace Eigen
#endif // EIGEN_PARDISOSUPPORT_H