Eigen/src/PardisoSupport/PardisoSupport.h

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 ********************************************************************************
 *   Content : Eigen bindings to Intel(R) MKL PARDISO
 ********************************************************************************
*/

#ifndef EIGEN_PARDISOSUPPORT_H
#define EIGEN_PARDISOSUPPORT_H

// IWYU pragma: private
#include "./InternalHeaderCheck.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() : m_analysisIsOk(false), m_factorizationIsOk(false) {
    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 successful,
   *          \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 = m_info == Eigen::Success;
  m_factorizationIsOk = m_info == Eigen::Success;
  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 = m_info == Eigen::Success;
  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 = m_info == Eigen::Success;
  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;
  using Base::m_matrix;
  using Base::pardisoInit;
  friend class PardisoImpl<PardisoLU<MatrixType> >;

 public:
  typedef typename Base::Scalar Scalar;
  typedef typename Base::RealScalar RealScalar;

  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;
  using Base::m_matrix;
  using Base::pardisoInit;
  friend class PardisoImpl<PardisoLLT<MatrixType, UpLo_> >;

 public:
  typedef typename Base::Scalar Scalar;
  typedef typename Base::RealScalar RealScalar;
  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;
  using Base::m_matrix;
  using Base::pardisoInit;
  friend class PardisoImpl<PardisoLDLT<MatrixType, Options> >;

 public:
  typedef typename Base::Scalar Scalar;
  typedef typename Base::RealScalar RealScalar;
  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