// Copyright (C) 2016 National ICT Australia (NICTA)
//
// 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/.
// -------------------------------------------------------------------
//
// Written by Yixuan Qiu
// Written by Conrad Sanderson - http://conradsanderson.id.au


namespace newarp
{


template<typename eT>
inline
UpperHessenbergEigen<eT>::UpperHessenbergEigen()
  : n(0)
  , computed(false)
  {
  arma_extra_debug_sigprint();
  }



template<typename eT>
inline
UpperHessenbergEigen<eT>::UpperHessenbergEigen(const Mat<eT>& mat_obj)
  : n(mat_obj.n_rows)
  , computed(false)
  {
  arma_extra_debug_sigprint();
  
  compute(mat_obj);
  }



template<typename eT>
inline
void
UpperHessenbergEigen<eT>::compute(const Mat<eT>& mat_obj)
  {
  arma_extra_debug_sigprint();
  
  arma_debug_check( (mat_obj.is_square() == false), "newarp::UpperHessenbergEigen::compute(): matrix must be square" );
  
  n = blas_int(mat_obj.n_rows);
  
  mat_Z.set_size(n, n);
  mat_T.set_size(n, n);
  evals.set_size(n);
  
  mat_Z.eye();
  mat_T = mat_obj;
  
  blas_int want_T = blas_int(1);
  blas_int want_Z = blas_int(1);
  
  blas_int ilo  = blas_int(1);
  blas_int ihi  = blas_int(n);
  blas_int iloz = blas_int(1);
  blas_int ihiz = blas_int(n);
  
  blas_int info = blas_int(0);
  
  podarray<eT> wr(static_cast<uword>(n));
  podarray<eT> wi(static_cast<uword>(n));
  
  
  lapack::lahqr(&want_T, &want_Z, &n, &ilo, &ihi, mat_T.memptr(), &n, wr.memptr(), wi.memptr(), &iloz, &ihiz, mat_Z.memptr(), &n, &info);
  
  for(blas_int i = 0; i < n; i++)
    {
    evals(i) = std::complex<eT>(wr[i], wi[i]);
    }
  
  if(info > 0)  { arma_stop_runtime_error("lapack::lahqr(): failed to compute all eigenvalues"); return; }
  
  char     side   = 'R';
  char     howmny = 'B';
  blas_int m      = blas_int(0);
  
  podarray<eT> work(static_cast<uword>(3 * n));
  
  lapack::trevc(&side, &howmny, (blas_int*) NULL, &n, mat_T.memptr(), &n, (eT*) NULL, &n, mat_Z.memptr(), &n, &n, &m, work.memptr(), &info);
  
  if(info < 0)  { arma_stop_logic_error("lapack::trevc(): illegal value"); return; }
  
  computed = true;
  }



template<typename eT>
inline
Col< std::complex<eT> >
UpperHessenbergEigen<eT>::eigenvalues()
  {
  arma_extra_debug_sigprint();
  
  arma_debug_check( (computed == false), "newarp::UpperHessenbergEigen::eigenvalues(): need to call compute() first" );

  return evals;
  }



template<typename eT>
inline
Mat< std::complex<eT> >
UpperHessenbergEigen<eT>::eigenvectors()
  {
  arma_extra_debug_sigprint();
  
  arma_debug_check( (computed == false), "newarp::UpperHessenbergEigen::eigenvectors(): need to call compute() first" );

  // in fact Lapack will set the imaginary parts of real eigenvalues to be exact zero
  // here we just use a small value
  eT prec = std::numeric_limits<eT>::epsilon();
  
  Mat< std::complex<eT> > evecs(n, n);
  
  std::complex<eT>* col_ptr = evecs.memptr();
  
  for(blas_int i = 0; i < n; i++)
    {
    if(cx_attrib::is_real(evals(i), prec))
      {
      // for real eigenvector, normalise and copy
      eT z_norm = norm(mat_Z.col(i));
      
      for(blas_int j = 0; j < n; j++)
        {
        col_ptr[j] = std::complex<eT>(mat_Z(j, i) / z_norm, 0);
        }

      col_ptr += n;
      }
    else
      {
      // complex eigenvectors are stored in consecutive columns
      eT r2 = dot(mat_Z.col(i), mat_Z.col(i));
      eT i2 = dot(mat_Z.col(i + 1), mat_Z.col(i + 1));
      
      eT  z_norm = std::sqrt(r2 + i2);
      eT* z_ptr  = mat_Z.colptr(i);
      
      for(blas_int j = 0; j < n; j++)
        {
        col_ptr[j    ] = std::complex<eT>(z_ptr[j] / z_norm, z_ptr[j + n] / z_norm);
        col_ptr[j + n] = std::conj(col_ptr[j]);
        }

      i++;
      col_ptr += 2 * n;
      }
    }

  return evecs;
  }


}  // namespace newarp
