gmm_precond_ildltt.h

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/**@file gmm_precond_ildltt.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date June 30, 2003.
   @brief incomplete LDL^t (cholesky) preconditioner with fill-in and threshold.
*/

#ifndef GMM_PRECOND_ILDLTT_H
#define GMM_PRECOND_ILDLTT_H

// Store U = LT and D in indiag. On each line, the fill-in is the number
// of non-zero elements on the line of the original matrix plus K, except if
// the matrix is dense. In this case the fill-in is K on each line.

#include "gmm_precond_ilut.h"

namespace gmm {
  /** incomplete LDL^t (cholesky) preconditioner with fill-in and
      threshold. */
  template <typename Matrix>
  class ildltt_precond  {
  public :
    typedef typename linalg_traits<Matrix>::value_type value_type;
    typedef typename number_traits<value_type>::magnitude_type magnitude_type;
    
    typedef rsvector<value_type> svector;

    row_matrix<svector> U;
    std::vector<magnitude_type> indiag;

  protected:
    size_type K;
    double eps;    

    template<typename M> void do_ildltt(const M&, row_major);
    void do_ildltt(const Matrix&, col_major);

  public:
    void build_with(const Matrix& A, int k_ = -1, double eps_ = double(-1)) {
      if (k_ >= 0) K = k_;
      if (eps_ >= double(0)) eps = eps_;
      gmm::resize(U, mat_nrows(A), mat_ncols(A));
      indiag.resize(std::min(mat_nrows(A), mat_ncols(A)));
      do_ildltt(A, typename principal_orientation_type<typename
                linalg_traits<Matrix>::sub_orientation>::potype());
    }
    ildltt_precond(const Matrix& A, int k_, double eps_) 
      : U(mat_nrows(A),mat_ncols(A)), K(k_), eps(eps_) { build_with(A); }
    ildltt_precond(void) { K=10; eps = 1E-7; }
    ildltt_precond(size_type k_, double eps_) :  K(k_), eps(eps_) {}
    size_type memsize() const { 
      return sizeof(*this) + nnz(U)*sizeof(value_type) + indiag.size() * sizeof(magnitude_type);
    }    
  };

  template<typename Matrix> template<typename M> 
  void ildltt_precond<Matrix>::do_ildltt(const M& A,row_major) {
    typedef value_type T;
    typedef typename number_traits<T>::magnitude_type R;

    size_type n = mat_nrows(A);
    if (n == 0) return;
    svector w(n);
    T tmp;
    R prec = default_tol(R()), max_pivot = gmm::abs(A(0,0)) * prec;

    gmm::clear(U);
    for (size_type i = 0; i < n; ++i) {
      gmm::copy(mat_const_row(A, i), w);
      double norm_row = gmm::vect_norm2(w);

      for (size_type krow = 0, k; krow < w.nb_stored(); ++krow) {
        typename svector::iterator wk = w.begin() + krow;
        if ((k = wk->c) >= i) break;
        if (gmm::is_complex(wk->e)) {
          tmp = gmm::conj(U(k, i))/indiag[k]; // not completely satisfactory ..
          gmm::add(scaled(mat_row(U, k), -tmp), w);
        }
        else {
          tmp = wk->e;
          if (gmm::abs(tmp) < eps * norm_row) { w.sup(k); --krow; } 
          else { wk->e += tmp; gmm::add(scaled(mat_row(U, k), -tmp), w); }
        }
      }
      tmp = w[i];

      if (gmm::abs(gmm::real(tmp)) <= max_pivot)
        { GMM_WARNING2("pivot " << i << " is too small"); tmp = T(1); }

      max_pivot = std::max(max_pivot, std::min(gmm::abs(tmp) * prec, R(1)));
      indiag[i] = R(1) / gmm::real(tmp);
      gmm::clean(w, eps * norm_row);
      gmm::scale(w, T(indiag[i]));
      std::sort(w.begin(), w.end(), elt_rsvector_value_less_<T>());
      typename svector::const_iterator wit = w.begin(), wite = w.end();
      for (size_type nnu = 0; wit != wite; ++wit)  // copy to be optimized ...
        if (wit->c > i) { if (nnu < K) { U(i, wit->c) = wit->e; ++nnu; } }
    }
  }

  template<typename Matrix> 
  void ildltt_precond<Matrix>::do_ildltt(const Matrix& A, col_major)
  { do_ildltt(gmm::conjugated(A), row_major()); }

  template <typename Matrix, typename V1, typename V2> inline
  void mult(const ildltt_precond<Matrix>& P, const V1 &v1, V2 &v2) {
    gmm::copy(v1, v2);
    gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true);
    for (size_type i = 0; i < P.indiag.size(); ++i) v2[i] *= P.indiag[i];
    gmm::upper_tri_solve(P.U, v2, true);
  }

  template <typename Matrix, typename V1, typename V2> inline
  void transposed_mult(const ildltt_precond<Matrix>& P,const V1 &v1, V2 &v2)
  { mult(P, v1, v2); }

  template <typename Matrix, typename V1, typename V2> inline
  void left_mult(const ildltt_precond<Matrix>& P, const V1 &v1, V2 &v2) {
    copy(v1, v2);
    gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true);
    for (size_type i = 0; i < P.indiag.size(); ++i) v2[i] *= P.indiag[i];
  }

  template <typename Matrix, typename V1, typename V2> inline
  void right_mult(const ildltt_precond<Matrix>& P, const V1 &v1, V2 &v2)
  { copy(v1, v2); gmm::upper_tri_solve(P.U, v2, true); }

  template <typename Matrix, typename V1, typename V2> inline
  void transposed_left_mult(const ildltt_precond<Matrix>& P, const V1 &v1,
                            V2 &v2) {
    copy(v1, v2);
    gmm::upper_tri_solve(P.U, v2, true);
    for (size_type i = 0; i < P.indiag.size(); ++i) v2[i] *= P.indiag[i];
  }

  template <typename Matrix, typename V1, typename V2> inline
  void transposed_right_mult(const ildltt_precond<Matrix>& P, const V1 &v1,
                             V2 &v2)
  { copy(v1, v2); gmm::lower_tri_solve(gmm::conjugated(P.U), v2, true); }

}

#endif