src/PardisoSupport/PardisoSupport.h

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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 Index>
  struct pardiso_run_selector
  {
    static Index run( _MKL_DSS_HANDLE_t pt, Index maxfct, Index mnum, Index type, Index phase, Index n, void *a,
                      Index *ia, Index *ja, Index *perm, Index nrhs, Index *iparm, Index msglvl, void *b, void *x)
    {
      Index 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 Index;
    static Index run( _MKL_DSS_HANDLE_t pt, Index maxfct, Index mnum, Index type, Index phase, Index n, void *a,
                      Index *ia, Index *ja, Index *perm, Index nrhs, Index *iparm, Index msglvl, void *b, void *x)
    {
      Index 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::Index Index;
  };

  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::Index Index;
  };

  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::Index Index;
  };

}

template<class Derived>
class PardisoImpl
{
    typedef internal::pardiso_traits<Derived> Traits;
  public:
    typedef typename Traits::MatrixType MatrixType;
    typedef typename Traits::Scalar Scalar;
    typedef typename Traits::RealScalar RealScalar;
    typedef typename Traits::Index Index;
    typedef SparseMatrix<Scalar,RowMajor,Index> SparseMatrixType;
    typedef Matrix<Scalar,Dynamic,1> VectorType;
    typedef Matrix<Index, 1, MatrixType::ColsAtCompileTime> IntRowVectorType;
    typedef Matrix<Index, MatrixType::RowsAtCompileTime, 1> IntColVectorType;
    enum {
      ScalarIsComplex = NumTraits<Scalar>::IsComplex
    };

    PardisoImpl()
    {
      eigen_assert((sizeof(Index) >= sizeof(_INTEGER_t) && sizeof(Index) <= 8) && "Non-supported index type");
      m_iparm.setZero();
      m_msglvl = 0; // No output
      m_initialized = 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_initialized && "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. */
    Array<Index,64,1>& 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);

    /** \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<PardisoImpl, Rhs>
    solve(const MatrixBase<Rhs>& b) const
    {
      eigen_assert(m_initialized && "Pardiso solver is not initialized.");
      eigen_assert(rows()==b.rows()
                && "PardisoImpl::solve(): invalid number of rows of the right hand side matrix b");
      return internal::solve_retval<PardisoImpl, 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<PardisoImpl, Rhs>
    solve(const SparseMatrixBase<Rhs>& b) const
    {
      eigen_assert(m_initialized && "Pardiso solver is not initialized.");
      eigen_assert(rows()==b.rows()
                && "PardisoImpl::solve(): invalid number of rows of the right hand side matrix b");
      return internal::sparse_solve_retval<PardisoImpl, Rhs>(*this, b.derived());
    }

    Derived& derived()
    {
      return *static_cast<Derived*>(this);
    }
    const Derived& derived() const
    {
      return *static_cast<const Derived*>(this);
    }

    template<typename BDerived, typename XDerived>
    bool _solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& 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_size==b.rows());

      // we process the sparse rhs per block of NbColsAtOnce columns temporarily stored into a dense matrix.
      static const int NbColsAtOnce = 4;
      int rhsCols = b.cols();
      int size = b.rows();
      // Pardiso cannot solve in-place,
      // so we need two temporaries
      Eigen::Matrix<DestScalar,Dynamic,Dynamic,ColMajor> tmp_rhs(size,rhsCols);
      Eigen::Matrix<DestScalar,Dynamic,Dynamic,ColMajor> tmp_res(size,rhsCols);
      for(int k=0; k<rhsCols; k+=NbColsAtOnce)
      {
        int actualCols = std::min<int>(rhsCols-k, NbColsAtOnce);
        tmp_rhs.leftCols(actualCols) = b.middleCols(k,actualCols);
        tmp_res.leftCols(actualCols) = derived().solve(tmp_rhs.leftCols(actualCols));
        dest.middleCols(k,actualCols) = tmp_res.leftCols(actualCols).sparseView();
      }
    }

  protected:
    void pardisoRelease()
    {
      if(m_initialized) // Factorization ran at least once
      {
        internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, -1, m_size, 0, 0, 0, m_perm.data(), 0,
                                                   m_iparm.data(), m_msglvl, 0, 0);
      }
    }

    void pardisoInit(int type)
    {
      m_type = type;
      bool symmetric = abs(m_type) < 10;
      m_iparm[0] = 1;   // No solver default
      m_iparm[1] = 3;   // use Metis for the ordering
      m_iparm[2] = 1;   // 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
      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[59] = 1;  // Automatic switch between In-Core and Out-of-Core modes
    }

  protected:
    // cached data to reduce reallocation, etc.

    void manageErrorCode(Index error)
    {
      switch(error)
      {
        case 0:
          m_info = Success;
          break;
        case -4:
        case -7:
          m_info = NumericalIssue;
          break;
        default:
          m_info = InvalidInput;
      }
    }

    mutable SparseMatrixType m_matrix;
    ComputationInfo m_info;
    bool m_initialized, m_analysisIsOk, m_factorizationIsOk;
    Index m_type, m_msglvl;
    mutable void *m_pt[64];
    mutable Array<Index,64,1> m_iparm;
    mutable IntColVectorType m_perm;
    Index m_size;

  private:
    PardisoImpl(PardisoImpl &) {}
};

template<class Derived>
Derived& PardisoImpl<Derived>::compute(const MatrixType& a)
{
  m_size = a.rows();
  eigen_assert(a.rows() == a.cols());

  pardisoRelease();
  memset(m_pt, 0, sizeof(m_pt));
  m_perm.setZero(m_size);
  derived().getMatrix(a);

  Index error;
  error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 12, 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_initialized = true;
  return derived();
}

template<class Derived>
Derived& PardisoImpl<Derived>::analyzePattern(const MatrixType& a)
{
  m_size = a.rows();
  eigen_assert(m_size == a.cols());

  pardisoRelease();
  memset(m_pt, 0, sizeof(m_pt));
  m_perm.setZero(m_size);
  derived().getMatrix(a);

  Index error;
  error = internal::pardiso_run_selector<Index>::run(m_pt, 1, 1, m_type, 11, 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_initialized = 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<Index>::run(m_pt, 1, 1, m_type, 22, 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 Base>
template<typename BDerived,typename XDerived>
bool PardisoImpl<Base>::_solve(const MatrixBase<BDerived> &b, MatrixBase<XDerived>& x) const
{
  if(m_iparm[0] == 0) // Factorization was not computed
    return false;

  //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<Index>::run(m_pt, 1, 1, m_type, 33, m_size,
                                                     m_matrix.valuePtr(), m_matrix.outerIndexPtr(), m_matrix.innerIndexPtr(),
                                                     m_perm.data(), nrhs, m_iparm.data(), m_msglvl,
                                                     rhs_ptr, x.derived().data());

  return error==0;
}


/** \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.
  *
  * \tparam _MatrixType the type of the sparse matrix A, it must be a SparseMatrix<>
  *
  * \sa \ref TutorialSparseDirectSolvers
  */
template<typename MatrixType>
class PardisoLU : public PardisoImpl< PardisoLU<MatrixType> >
{
  protected:
    typedef PardisoImpl< PardisoLU<MatrixType> > 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);
    }

    PardisoLU(const MatrixType& matrix)
      : Base()
    {
      pardisoInit(Base::ScalarIsComplex ? 13 : 11);
      compute(matrix);
    }
  protected:
    void getMatrix(const MatrixType& matrix)
    {
      m_matrix = matrix;
    }

  private:
    PardisoLU(PardisoLU& ) {}
};

/** \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.
  *
  * \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.
  *
  * \sa \ref TutorialSparseDirectSolvers
  */
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::Index Index;
    typedef typename Base::RealScalar RealScalar;
    using Base::pardisoInit;
    using Base::m_matrix;
    friend class PardisoImpl< PardisoLLT<MatrixType,_UpLo> >;

  public:

    enum { UpLo = _UpLo };
    using Base::compute;
    using Base::solve;

    PardisoLLT()
      : Base()
    {
      pardisoInit(Base::ScalarIsComplex ? 4 : 2);
    }

    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,Index> p_null;
      m_matrix.resize(matrix.rows(), matrix.cols());
      m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
    }

  private:
    PardisoLLT(PardisoLLT& ) {}
};

/** \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.
  *
  * \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.
  *
  * \sa \ref TutorialSparseDirectSolvers
  */
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::Index Index;
    typedef typename Base::RealScalar RealScalar;
    using Base::pardisoInit;
    using Base::m_matrix;
    friend class PardisoImpl< PardisoLDLT<MatrixType,Options> >;

  public:

    using Base::compute;
    using Base::solve;
    enum { UpLo = Options&(Upper|Lower) };

    PardisoLDLT()
      : Base()
    {
      pardisoInit(Base::ScalarIsComplex ? ( bool(Options&Symmetric) ? 6 : -4 ) : -2);
    }

    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,Index> p_null;
      m_matrix.resize(matrix.rows(), matrix.cols());
      m_matrix.template selfadjointView<Upper>() = matrix.template selfadjointView<UpLo>().twistedBy(p_null);
    }

  private:
    PardisoLDLT(PardisoLDLT& ) {}
};

namespace internal {

template<typename _Derived, typename Rhs>
struct solve_retval<PardisoImpl<_Derived>, Rhs>
  : solve_retval_base<PardisoImpl<_Derived>, Rhs>
{
  typedef PardisoImpl<_Derived> Dec;
  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)

  template<typename Dest> void evalTo(Dest& dst) const
  {
    dec()._solve(rhs(),dst);
  }
};

template<typename Derived, typename Rhs>
struct sparse_solve_retval<PardisoImpl<Derived>, Rhs>
  : sparse_solve_retval_base<PardisoImpl<Derived>, Rhs>
{
  typedef PardisoImpl<Derived> Dec;
  EIGEN_MAKE_SPARSE_SOLVE_HELPERS(Dec,Rhs)

  template<typename Dest> void evalTo(Dest& dst) const
  {
    dec().derived()._solve_sparse(rhs(),dst);
  }
};

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_PARDISOSUPPORT_H