/*
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 ********************************************************************************
 *   Content : Eigen bindings to LAPACKe
 *    Complex Schur needed to complex unsymmetrical eigenvalues/eigenvectors.
 ********************************************************************************
*/

#ifndef EIGEN_COMPLEX_SCHUR_LAPACKE_H
#define EIGEN_COMPLEX_SCHUR_LAPACKE_H

namespace Eigen {

/** \internal Specialization for the data types supported by LAPACKe */

#define EIGEN_LAPACKE_SCHUR_COMPLEX(EIGTYPE, LAPACKE_TYPE, LAPACKE_PREFIX, LAPACKE_PREFIX_U, EIGCOLROW, LAPACKE_COLROW) \
template<> template<typename InputType> inline \
ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >& \
ComplexSchur<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> >::compute(const EigenBase<InputType>& matrix, bool computeU) \
{ \
  typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW> MatrixType; \
  typedef MatrixType::RealScalar RealScalar; \
  typedef std::complex<RealScalar> ComplexScalar; \
\
  eigen_assert(matrix.cols() == matrix.rows()); \
\
  m_matUisUptodate = false; \
  if(matrix.cols() == 1) \
  { \
    m_matT = matrix.derived().template cast<ComplexScalar>(); \
    if(computeU)  m_matU = ComplexMatrixType::Identity(1,1); \
      m_info = Success; \
      m_isInitialized = true; \
      m_matUisUptodate = computeU; \
      return *this; \
  } \
  lapack_int n = internal::convert_index<lapack_int>(matrix.cols()), sdim, info; \
  lapack_int matrix_order = LAPACKE_COLROW; \
  char jobvs, sort='N'; \
  LAPACK_##LAPACKE_PREFIX_U##_SELECT1 select = 0; \
  jobvs = (computeU) ? 'V' : 'N'; \
  m_matU.resize(n, n); \
  lapack_int ldvs  = internal::convert_index<lapack_int>(m_matU.outerStride()); \
  m_matT = matrix; \
  lapack_int lda = internal::convert_index<lapack_int>(m_matT.outerStride()); \
  Matrix<EIGTYPE, Dynamic, Dynamic> w; \
  w.resize(n, 1);\
  info = LAPACKE_##LAPACKE_PREFIX##gees( matrix_order, jobvs, sort, select, n, (LAPACKE_TYPE*)m_matT.data(), lda, &sdim, (LAPACKE_TYPE*)w.data(), (LAPACKE_TYPE*)m_matU.data(), ldvs ); \
  if(info == 0) \
    m_info = Success; \
  else \
    m_info = NoConvergence; \
\
  m_isInitialized = true; \
  m_matUisUptodate = computeU; \
  return *this; \
\
}

EIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, ColMajor, LAPACK_COL_MAJOR)
EIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float,  c, C, ColMajor, LAPACK_COL_MAJOR)
EIGEN_LAPACKE_SCHUR_COMPLEX(dcomplex, lapack_complex_double, z, Z, RowMajor, LAPACK_ROW_MAJOR)
EIGEN_LAPACKE_SCHUR_COMPLEX(scomplex, lapack_complex_float,  c, C, RowMajor, LAPACK_ROW_MAJOR)

} // end namespace Eigen

#endif // EIGEN_COMPLEX_SCHUR_LAPACKE_H
