eigen/Eigen/src/PaStiXSupport/PaStiXSupport.h

// 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>
//
// 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_PASTIXSUPPORT_H
#define EIGEN_PASTIXSUPPORT_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

#if defined(DCOMPLEX)
#define PASTIX_COMPLEX COMPLEX
#define PASTIX_DCOMPLEX DCOMPLEX
#else
#define PASTIX_COMPLEX std::complex<float>
#define PASTIX_DCOMPLEX std::complex<double>
#endif

/** \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_::StorageIndex StorageIndex;
};

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_::StorageIndex StorageIndex;
};

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_::StorageIndex StorageIndex;
};

inline 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;
    nbrhs = 1;
  }
  s_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
}

inline 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;
    nbrhs = 1;
  }
  d_pastix(pastix_data, pastix_comm, n, ptr, idx, vals, perm, invp, x, nbrhs, iparm, dparm);
}

inline 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) {
  if (n == 0) {
    ptr = NULL;
    idx = NULL;
    vals = NULL;
  }
  if (nbrhs == 0) {
    x = NULL;
    nbrhs = 1;
  }
  c_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_COMPLEX *>(vals), perm, invp,
           reinterpret_cast<PASTIX_COMPLEX *>(x), nbrhs, iparm, dparm);
}

inline 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;
    nbrhs = 1;
  }
  z_pastix(pastix_data, pastix_comm, n, ptr, idx, reinterpret_cast<PASTIX_DCOMPLEX *>(vals), perm, invp,
           reinterpret_cast<PASTIX_DCOMPLEX *>(x), nbrhs, iparm, dparm);
}

// Convert the matrix  to Fortran-style Numbering
template <typename MatrixType>
void c_to_fortran_numbering(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 fortran_to_c_numbering(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];
  }
}
}  // namespace internal

// This is the base class to interface with PaStiX functions.
// Users should not used this class directly.
template <class Derived>
class PastixBase : public SparseSolverBase<Derived> {
 protected:
  typedef SparseSolverBase<Derived> Base;
  using Base::derived;
  using Base::m_isInitialized;

 public:
  using Base::_solve_impl;

  typedef typename internal::pastix_traits<Derived>::MatrixType MatrixType_;
  typedef MatrixType_ MatrixType;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename MatrixType::RealScalar RealScalar;
  typedef typename MatrixType::StorageIndex StorageIndex;
  typedef Matrix<Scalar, Dynamic, 1> Vector;
  typedef SparseMatrix<Scalar, ColMajor> ColSpMatrix;
  enum { ColsAtCompileTime = MatrixType::ColsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };

 public:
  PastixBase() : m_initisOk(false), m_analysisIsOk(false), m_factorizationIsOk(false), m_pastixdata(0), m_size(0) {
    init();
  }

  ~PastixBase() { clean(); }

  template <typename Rhs, typename Dest>
  bool _solve_impl(const MatrixBase<Rhs> &b, MatrixBase<Dest> &x) const;

  /** 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<StorageIndex, IPARM_SIZE, 1> &iparm() { return m_iparm; }

  /** Return a reference to a particular index parameter of the IPARM vector
   * \sa iparm()
   */

  int &iparm(int idxparam) { return m_iparm(idxparam); }

  /** 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<double, DPARM_SIZE, 1> &dparm() { return m_dparm; }

  /** Return a reference to a particular index parameter of the DPARM vector
   * \sa dparm()
   */
  double &dparm(int idxparam) { return m_dparm(idxparam); }

  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 successful,
   *          \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;
  }

 protected:
  // Initialize the Pastix data structure, check the matrix
  void init();

  // Compute the ordering and the symbolic factorization
  void analyzePattern(ColSpMatrix &mat);

  // Compute the numerical factorization
  void factorize(ColSpMatrix &mat);

  // Free all the data allocated by Pastix
  void clean() {
    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, 0, 0, (Scalar *)0, m_perm.data(), m_invp.data(), 0, 0,
                           m_iparm.data(), m_dparm.data());
  }

  void compute(ColSpMatrix &mat);

  int m_initisOk;
  int m_analysisIsOk;
  int m_factorizationIsOk;
  mutable ComputationInfo m_info;
  mutable pastix_data_t *m_pastixdata;              // Data structure for pastix
  mutable int m_comm;                               // The MPI communicator identifier
  mutable Array<int, IPARM_SIZE, 1> m_iparm;        // integer vector for the input parameters
  mutable Array<double, DPARM_SIZE, 1> m_dparm;     // Scalar vector for the input parameters
  mutable Matrix<StorageIndex, Dynamic, 1> m_perm;  // Permutation vector
  mutable Matrix<StorageIndex, Dynamic, 1> m_invp;  // Inverse permutation vector
  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>::init() {
  m_size = 0;
  m_iparm.setZero(IPARM_SIZE);
  m_dparm.setZero(DPARM_SIZE);

  m_iparm(IPARM_MODIFY_PARAMETER) = API_NO;
  pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, 0, 0, 0, 0, 1, m_iparm.data(), m_dparm.data());

  m_iparm[IPARM_MATRIX_VERIFICATION] = API_NO;
  m_iparm[IPARM_VERBOSE] = API_VERBOSE_NOT;
  m_iparm[IPARM_ORDERING] = API_ORDER_SCOTCH;
  m_iparm[IPARM_INCOMPLETE] = API_NO;
  m_iparm[IPARM_OOC_LIMIT] = 2000;
  m_iparm[IPARM_RHS_MAKING] = API_RHS_B;
  m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;

  m_iparm(IPARM_START_TASK) = API_TASK_INIT;
  m_iparm(IPARM_END_TASK) = API_TASK_INIT;
  internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, 0, 0, 0, (Scalar *)0, 0, 0, 0, 0, m_iparm.data(),
                         m_dparm.data());

  // 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>
void PastixBase<Derived>::compute(ColSpMatrix &mat) {
  eigen_assert(mat.rows() == mat.cols() && "The input matrix should be squared");

  analyzePattern(mat);
  factorize(mat);

  m_iparm(IPARM_MATRIX_VERIFICATION) = API_NO;
}

template <class Derived>
void PastixBase<Derived>::analyzePattern(ColSpMatrix &mat) {
  eigen_assert(m_initisOk && "The initialization of PaSTiX failed");

  // clean previous calls
  if (m_size > 0) clean();

  m_size = internal::convert_index<int>(mat.rows());
  m_perm.resize(m_size);
  m_invp.resize(m_size);

  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(), 0, 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;
  }
}

template <class Derived>
void PastixBase<Derived>::factorize(ColSpMatrix &mat) {
  //   if(&m_cpyMat != &mat) m_cpyMat = 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 = internal::convert_index<int>(mat.rows());

  internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, m_size, mat.outerIndexPtr(), mat.innerIndexPtr(),
                         mat.valuePtr(), m_perm.data(), m_invp.data(), 0, 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;
  }
}

/* Solve the system */
template <typename Base>
template <typename Rhs, typename Dest>
bool PastixBase<Base>::_solve_impl(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;

    internal::eigen_pastix(&m_pastixdata, MPI_COMM_WORLD, internal::convert_index<int>(x.rows()), 0, 0, 0,
                           m_perm.data(), m_invp.data(), &x(0, i), rhs, m_iparm.data(), m_dparm.data());
  }

  // Check the returned error
  m_info = m_iparm(IPARM_ERROR_NUMBER) == 0 ? Success : NumericalIssue;

  return m_iparm(IPARM_ERROR_NUMBER) == 0;
}

/** \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
 *
 * \implsparsesolverconcept
 *
 * \sa \ref TutorialSparseSolverConcept, class SparseLU
 *
 */
template <typename MatrixType_, bool IsStrSym>
class PastixLU : public PastixBase<PastixLU<MatrixType_> > {
 public:
  typedef MatrixType_ MatrixType;
  typedef PastixBase<PastixLU<MatrixType> > Base;
  typedef typename Base::ColSpMatrix ColSpMatrix;
  typedef typename MatrixType::StorageIndex StorageIndex;

 public:
  PastixLU() : Base() { init(); }

  explicit PastixLU(const MatrixType &matrix) : Base() {
    init();
    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) {
    m_structureIsUptodate = false;
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    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) {
    m_structureIsUptodate = false;
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    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) {
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    Base::factorize(temp);
  }

 protected:
  void init() {
    m_structureIsUptodate = false;
    m_iparm(IPARM_SYM) = API_SYM_NO;
    m_iparm(IPARM_FACTORIZATION) = API_FACT_LU;
  }

  void grabMatrix(const MatrixType &matrix, ColSpMatrix &out) {
    if (IsStrSym)
      out = matrix;
    else {
      if (!m_structureIsUptodate) {
        // update the transposed structure
        m_transposedStructure = matrix.transpose();

        // Set the elements of the matrix to zero
        for (Index j = 0; j < m_transposedStructure.outerSize(); ++j)
          for (typename ColSpMatrix::InnerIterator it(m_transposedStructure, j); it; ++it) it.valueRef() = 0.0;

        m_structureIsUptodate = true;
      }

      out = m_transposedStructure + matrix;
    }
    internal::c_to_fortran_numbering(out);
  }

  using Base::m_dparm;
  using Base::m_iparm;

  ColSpMatrix m_transposedStructure;
  bool m_structureIsUptodate;
};

/** \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
 *
 * \implsparsesolverconcept
 *
 * \sa \ref TutorialSparseSolverConcept, class SimplicialLLT
 */
template <typename MatrixType_, int UpLo_>
class PastixLLT : public PastixBase<PastixLLT<MatrixType_, UpLo_> > {
 public:
  typedef MatrixType_ MatrixType;
  typedef PastixBase<PastixLLT<MatrixType, UpLo_> > Base;
  typedef typename Base::ColSpMatrix ColSpMatrix;

 public:
  enum { UpLo = UpLo_ };
  PastixLLT() : Base() { init(); }

  explicit PastixLLT(const MatrixType &matrix) : Base() {
    init();
    compute(matrix);
  }

  /** Compute the L factor of the LL^T supernodal factorization of \p matrix
   * \sa analyzePattern() factorize()
   */
  void compute(const MatrixType &matrix) {
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    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) {
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    Base::analyzePattern(temp);
  }
  /** Compute the LL^T supernodal numerical factorization of \p matrix
   * \sa analyzePattern()
   */
  void factorize(const MatrixType &matrix) {
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    Base::factorize(temp);
  }

 protected:
  using Base::m_iparm;

  void init() {
    m_iparm(IPARM_SYM) = API_SYM_YES;
    m_iparm(IPARM_FACTORIZATION) = API_FACT_LLT;
  }

  void grabMatrix(const MatrixType &matrix, ColSpMatrix &out) {
    out.resize(matrix.rows(), matrix.cols());
    // Pastix supports only lower, column-major matrices
    out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
    internal::c_to_fortran_numbering(out);
  }
};

/** \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
 *
 * \implsparsesolverconcept
 *
 * \sa \ref TutorialSparseSolverConcept, class SimplicialLDLT
 */
template <typename MatrixType_, int UpLo_>
class PastixLDLT : public PastixBase<PastixLDLT<MatrixType_, UpLo_> > {
 public:
  typedef MatrixType_ MatrixType;
  typedef PastixBase<PastixLDLT<MatrixType, UpLo_> > Base;
  typedef typename Base::ColSpMatrix ColSpMatrix;

 public:
  enum { UpLo = UpLo_ };
  PastixLDLT() : Base() { init(); }

  explicit PastixLDLT(const MatrixType &matrix) : Base() {
    init();
    compute(matrix);
  }

  /** Compute the L and D factors of the LDL^T factorization of \p matrix
   * \sa analyzePattern() factorize()
   */
  void compute(const MatrixType &matrix) {
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    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) {
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    Base::analyzePattern(temp);
  }
  /** Compute the LDL^T supernodal numerical factorization of \p matrix
   *
   */
  void factorize(const MatrixType &matrix) {
    ColSpMatrix temp;
    grabMatrix(matrix, temp);
    Base::factorize(temp);
  }

 protected:
  using Base::m_iparm;

  void init() {
    m_iparm(IPARM_SYM) = API_SYM_YES;
    m_iparm(IPARM_FACTORIZATION) = API_FACT_LDLT;
  }

  void grabMatrix(const MatrixType &matrix, ColSpMatrix &out) {
    // Pastix supports only lower, column-major matrices
    out.resize(matrix.rows(), matrix.cols());
    out.template selfadjointView<Lower>() = matrix.template selfadjointView<UpLo>();
    internal::c_to_fortran_numbering(out);
  }
};

}  // end namespace Eigen

#endif