gmm_precond_ilut.h

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// This file is a modified version of ilut.h from ITL.
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#ifndef GMM_PRECOND_ILUT_H
#define GMM_PRECOND_ILUT_H

/**@file gmm_precond_ilut.h
   @author  Andrew Lumsdaine <lums@osl.iu.edu>, Lie-Quan Lee <llee@osl.iu.edu>
   @date June 5, 2003.
   @brief ILUT:  Incomplete LU with threshold and K fill-in Preconditioner.
*/

/*
  Performane comparing for SSOR, ILU and ILUT based on sherman 5 matrix 
  in Harwell-Boeing collection on Sun Ultra 30 UPA/PCI (UltraSPARC-II 296MHz)
  Preconditioner & Factorization time  &  Number of Iteration \\ \hline
  SSOR        &   0.010577  & 41 \\
  ILU         &   0.019336  & 32 \\
  ILUT with 0 fill-in and threshold of 1.0e-6 & 0.343612 &  23 \\
  ILUT with 5 fill-in and threshold of 1.0e-6 & 0.343612 &  18 \\ \hline
*/

#include "gmm_precond.h"

namespace gmm {

  template<typename T> struct elt_rsvector_value_less_ {
    inline bool operator()(const elt_rsvector_<T>& a, 
                           const elt_rsvector_<T>& b) const
    { return (gmm::abs(a.e) > gmm::abs(b.e)); }
  };

  /** Incomplete LU with threshold and K fill-in Preconditioner.

  The algorithm of ILUT(A, 0, 1.0e-6) is slower than ILU(A). If No
  fill-in is arrowed, you can use ILU instead of ILUT.

  Notes: The idea under a concrete Preconditioner such as ilut is to
  create a Preconditioner object to use in iterative methods.
  */
  template <typename Matrix>
  class ilut_precond  {
  public :
    typedef typename linalg_traits<Matrix>::value_type value_type;
    typedef wsvector<value_type> _wsvector;
    typedef rsvector<value_type> _rsvector;
    typedef row_matrix<_rsvector> LU_Matrix;

    bool invert;
    LU_Matrix L, U;

  protected:
    size_type K;
    double eps;    

    template<typename M> void do_ilut(const M&, row_major);
    void do_ilut(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_;
      invert = false;
      gmm::resize(L, mat_nrows(A), mat_ncols(A));
      gmm::resize(U, mat_nrows(A), mat_ncols(A));
      do_ilut(A, typename principal_orientation_type<typename
              linalg_traits<Matrix>::sub_orientation>::potype());
    }
    ilut_precond(const Matrix& A, int k_, double eps_) 
      : L(mat_nrows(A), mat_ncols(A)), U(mat_nrows(A), mat_ncols(A)),
        K(k_), eps(eps_) { build_with(A); }
    ilut_precond(size_type k_, double eps_) :  K(k_), eps(eps_) {}
    ilut_precond(void) { K = 10; eps = 1E-7; }
    size_type memsize() const { 
      return sizeof(*this) + (nnz(U)+nnz(L))*sizeof(value_type);
    }
  };

  template<typename Matrix> template<typename M> 
  void ilut_precond<Matrix>::do_ilut(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;
    std::vector<T> indiag(n);
    _wsvector w(mat_ncols(A));
    _rsvector ww(mat_ncols(A)), wL(mat_ncols(A)), wU(mat_ncols(A));
    T tmp;
    gmm::clear(U); gmm::clear(L);
    R prec = default_tol(R()); 
    R max_pivot = gmm::abs(A(0,0)) * prec;

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

      typename _wsvector::iterator wkold = w.end();
      for (typename _wsvector::iterator wk = w.begin();
           wk != w.end() && wk->first < i; ) {
        size_type k = wk->first;
        tmp = (wk->second) * indiag[k];
        if (gmm::abs(tmp) < eps * norm_row) w.erase(k);
        else { wk->second += tmp; gmm::add(scaled(mat_row(U, k), -tmp), w); }
        if (wkold == w.end()) wk = w.begin(); else { wk = wkold; ++wk; }
        if (wk != w.end() && wk->first == k)
          { if (wkold == w.end()) wkold = w.begin(); else ++wkold; ++wk; }
      }
      tmp = w[i];

      if (gmm::abs(tmp) <= max_pivot) {
        GMM_WARNING2("pivot " << i << " too small. try with ilutp ?");
        w[i] = tmp = T(1);
      }

      max_pivot = std::max(max_pivot, std::min(gmm::abs(tmp) * prec, R(1)));
      indiag[i] = T(1) / tmp;
      gmm::clean(w, eps * norm_row);
      gmm::copy(w, ww);
      std::sort(ww.begin(), ww.end(), elt_rsvector_value_less_<T>());
      typename _rsvector::const_iterator wit = ww.begin(), wite = ww.end();

      size_type nnl = 0, nnu = 0;    
      wL.base_resize(K); wU.base_resize(K+1);
      typename _rsvector::iterator witL = wL.begin(), witU = wU.begin();
      for (; wit != wite; ++wit) 
        if (wit->c < i) { if (nnl < K) { *witL++ = *wit; ++nnl; } }
        else { if (nnu < K  || wit->c == i) { *witU++ = *wit; ++nnu; } }
      wL.base_resize(nnl); wU.base_resize(nnu);
      std::sort(wL.begin(), wL.end());
      std::sort(wU.begin(), wU.end());
      gmm::copy(wL, L.row(i));
      gmm::copy(wU, U.row(i));
    }

  }

  template<typename Matrix> 
  void ilut_precond<Matrix>::do_ilut(const Matrix& A, col_major) {
    do_ilut(gmm::transposed(A), row_major());
    invert = true;
  }

  template <typename Matrix, typename V1, typename V2> inline
  void mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
    gmm::copy(v1, v2);
    if (P.invert) {
      gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
      gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
    }
    else {
      gmm::lower_tri_solve(P.L, v2, true);
      gmm::upper_tri_solve(P.U, v2, false);
    }
  }

  template <typename Matrix, typename V1, typename V2> inline
  void transposed_mult(const ilut_precond<Matrix>& P,const V1 &v1,V2 &v2) {
    gmm::copy(v1, v2);
    if (P.invert) {
      gmm::lower_tri_solve(P.L, v2, true);
      gmm::upper_tri_solve(P.U, v2, false);
    }
    else {
      gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
      gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
    }
  }

  template <typename Matrix, typename V1, typename V2> inline
  void left_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
    copy(v1, v2);
    if (P.invert) gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
    else gmm::lower_tri_solve(P.L, v2, true);
  }

  template <typename Matrix, typename V1, typename V2> inline
  void right_mult(const ilut_precond<Matrix>& P, const V1 &v1, V2 &v2) {
    copy(v1, v2);
    if (P.invert) gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
    else gmm::upper_tri_solve(P.U, v2, false);
  }

  template <typename Matrix, typename V1, typename V2> inline
  void transposed_left_mult(const ilut_precond<Matrix>& P, const V1 &v1,
                            V2 &v2) {
    copy(v1, v2);
    if (P.invert) gmm::upper_tri_solve(P.U, v2, false);
    else gmm::upper_tri_solve(gmm::transposed(P.L), v2, true);
  }

  template <typename Matrix, typename V1, typename V2> inline
  void transposed_right_mult(const ilut_precond<Matrix>& P, const V1 &v1,
                             V2 &v2) {
    copy(v1, v2);
    if (P.invert) gmm::lower_tri_solve(P.L, v2, true);
    else gmm::lower_tri_solve(gmm::transposed(P.U), v2, false);
  }

}

#endif