eigen/Eigen/src/Cholesky/LLT_LAPACKE.h

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 ********************************************************************************
 *   Content : Eigen bindings to LAPACKe
 *     LLt decomposition based on LAPACKE_?potrf function.
 ********************************************************************************
*/

#ifndef EIGEN_LLT_LAPACKE_H
#define EIGEN_LLT_LAPACKE_H

#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

namespace lapacke_llt_helpers {

  // -------------------------------------------------------------------------------------------------------------------
  //        Translation from Eigen to Lapacke types
  // -------------------------------------------------------------------------------------------------------------------

  // For complex numbers, the types in Eigen and Lapacke are different, but layout compatible.
  template<typename Scalar> struct translate_type;
  template<> struct translate_type<float> { using type = float; };
  template<> struct translate_type<double> { using type = double; };
  template<> struct translate_type<dcomplex> { using type = lapack_complex_double; };
  template<> struct translate_type<scomplex> { using type = lapack_complex_float; };

  // -------------------------------------------------------------------------------------------------------------------
  //        Dispatch for potrf handling double, float, complex double, complex float types
  // -------------------------------------------------------------------------------------------------------------------

  inline lapack_int potrf(lapack_int matrix_order, char uplo, lapack_int size, double* a, lapack_int lda) {
    return LAPACKE_dpotrf( matrix_order, uplo, size, a, lda );
  }

  inline lapack_int potrf(lapack_int matrix_order, char uplo, lapack_int size, float* a, lapack_int lda) {
    return LAPACKE_spotrf( matrix_order, uplo, size, a, lda );
  }

  inline lapack_int potrf(lapack_int matrix_order, char uplo, lapack_int size, lapack_complex_double* a, lapack_int lda) {
    return LAPACKE_zpotrf( matrix_order, uplo, size, a, lda );
  }

  inline lapack_int potrf(lapack_int matrix_order, char uplo, lapack_int size, lapack_complex_float* a, lapack_int lda) {
    return LAPACKE_cpotrf( matrix_order, uplo, size, a, lda );
  }

  // -------------------------------------------------------------------------------------------------------------------
  //        Dispatch for rank update handling upper and lower parts
  // -------------------------------------------------------------------------------------------------------------------

  template<unsigned Mode>
  struct rank_update {};

  template<>
  struct rank_update<Lower> {
      template<typename MatrixType, typename VectorType>
      static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
        return Eigen::internal::llt_rank_update_lower(mat, vec, sigma);
      }
  };

  template<>
  struct rank_update<Upper> {
      template<typename MatrixType, typename VectorType>
      static Index run(MatrixType &mat, const VectorType &vec, const typename MatrixType::RealScalar &sigma) {
        Transpose<MatrixType> matt(mat);
        return Eigen::internal::llt_rank_update_lower(matt, vec.conjugate(), sigma);
      }
  };

  // -------------------------------------------------------------------------------------------------------------------
  //        Generic lapacke llt implementation that hands of to the dispatches
  // -------------------------------------------------------------------------------------------------------------------

  template<typename Scalar, unsigned Mode>
  struct lapacke_llt {
    using BlasType = typename translate_type<Scalar>::type;
    template<typename MatrixType>
    static Index blocked(MatrixType& m)
    {
      eigen_assert(m.rows() == m.cols());
      if(m.rows() == 0) {
        return -1;
      }

      /* Set up parameters for ?potrf */
      lapack_int size = convert_index<lapack_int>(m.rows());
      lapack_int StorageOrder = MatrixType::Flags&RowMajorBit?RowMajor:ColMajor;
      lapack_int matrix_order = StorageOrder==RowMajor ? LAPACK_ROW_MAJOR : LAPACK_COL_MAJOR;
      Scalar* a = &(m.coeffRef(0,0));
      lapack_int lda = convert_index<lapack_int>(m.outerStride());

      lapack_int info = potrf( matrix_order, Mode == Lower ? 'L' : 'U', size, (BlasType*)a, lda );
      info = (info==0) ? -1 : info>0 ? info-1 : size;
      return info;
    }

    template<typename MatrixType, typename VectorType>
    static Index rankUpdate(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
    {
      return rank_update<Mode>::run(mat, vec, sigma);
    }
  };
}
// end namespace lapacke_llt_helpers

/*
 * Here, we just put the generic implementation from lapacke_llt into a full specialization of the llt_inplace
 * type. By being a full specialization, the versions defined here thus get precedence over the generic implementation
 * in LLT.h for double, float and complex double, complex float types.
 */

#define EIGEN_LAPACKE_LLT(EIGTYPE) \
template<> struct llt_inplace<EIGTYPE, Lower> : public lapacke_llt_helpers::lapacke_llt<EIGTYPE, Lower> {}; \
template<> struct llt_inplace<EIGTYPE, Upper> : public lapacke_llt_helpers::lapacke_llt<EIGTYPE, Upper> {};

EIGEN_LAPACKE_LLT(double)
EIGEN_LAPACKE_LLT(float)
EIGEN_LAPACKE_LLT(dcomplex)
EIGEN_LAPACKE_LLT(scomplex)

#undef EIGEN_LAPACKE_LLT

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_LLT_LAPACKE_H