gmm_precond_ilutp.h

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/**@file gmm_precond_ilutp.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date October 14, 2004.
   @brief ILUTP: Incomplete LU with threshold and K fill-in Preconditioner and
   column pivoting.

   
*/
#ifndef GMM_PRECOND_ILUTP_H
#define GMM_PRECOND_ILUTP_H

#include "gmm_precond_ilut.h"

namespace gmm {

  /**
     ILUTP: Incomplete LU with threshold and K fill-in Preconditioner and
     column pivoting.
   
     See Yousef Saad, Iterative Methods for
     sparse linear systems, PWS Publishing Company, section 10.4.4

      TODO : store the permutation by cycles to avoid the temporary vector
  */
  template <typename Matrix>
  class ilutp_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;
    typedef col_matrix<_wsvector> CLU_Matrix;

    bool invert;
    LU_Matrix L, U;
    gmm::unsorted_sub_index indperm;
    gmm::unsorted_sub_index indperminv;
    mutable std::vector<value_type> temporary;

  protected:
    size_type K;
    double eps;

    template<typename M> void do_ilutp(const M&, row_major);
    void do_ilutp(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_ilutp(A, typename principal_orientation_type<typename
              linalg_traits<Matrix>::sub_orientation>::potype());
    }
    ilutp_precond(const Matrix& A, size_type k_, double eps_) 
      : L(mat_nrows(A), mat_ncols(A)), U(mat_nrows(A), mat_ncols(A)),
        K(k_), eps(eps_) { build_with(A); }
    ilutp_precond(int k_, double eps_) :  K(k_), eps(eps_) {}
    ilutp_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 ilutp_precond<Matrix>::do_ilutp(const M& A, row_major) {
    typedef value_type T;
    typedef typename number_traits<T>::magnitude_type R;

    size_type n = mat_nrows(A);
    CLU_Matrix CU(n,n);
    if (n == 0) return;
    std::vector<T> indiag(n);
    temporary.resize(n);
    std::vector<size_type> ipvt(n), ipvtinv(n);
    for (size_type i = 0; i < n; ++i) ipvt[i] = ipvtinv[i] = i;
    indperm = unsorted_sub_index(ipvt);
    indperminv = unsorted_sub_index(ipvtinv);
    _wsvector w(mat_ncols(A));
    _rsvector ww(mat_ncols(A));
    
    T tmp = T(0);
    gmm::clear(L); gmm::clear(U);
    R prec = default_tol(R()); 
    R max_pivot = gmm::abs(A(0,0)) * prec;

    for (size_type i = 0; i < n; ++i) {

      copy(sub_vector(mat_const_row(A, i), indperm), w);
      double norm_row = gmm::vect_norm2(mat_const_row(A, i)); 

      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; }
      }

      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 ip = size_type(-1);

      for (; wit != wite; ++wit)
        if (wit->c >= i) { ip = wit->c; tmp = wit->e; break; }
      if (ip == size_type(-1) || gmm::abs(tmp) <= max_pivot)
        { GMM_WARNING2("pivot " << i << " too small"); ip=i; ww[i]=tmp=T(1); }
      max_pivot = std::max(max_pivot, std::min(gmm::abs(tmp) * prec, R(1)));
      indiag[i] = T(1) / tmp;
      wit = ww.begin();

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

      if (ip != i) {
        typename _wsvector::const_iterator iti = CU.col(i).begin();
        typename _wsvector::const_iterator itie = CU.col(i).end();
        typename _wsvector::const_iterator itp = CU.col(ip).begin();
        typename _wsvector::const_iterator itpe = CU.col(ip).end();
        
        while (iti != itie && itp != itpe) {
          if (iti->first < itp->first)
            { U.row(iti->first).swap_indices(i, ip); ++iti; }
          else if (iti->first > itp->first)
            { U.row(itp->first).swap_indices(i,ip);++itp; }
          else
            { U.row(iti->first).swap_indices(i, ip); ++iti; ++itp; }
        }
        
        for( ; iti != itie; ++iti) U.row(iti->first).swap_indices(i, ip);
        for( ; itp != itpe; ++itp) U.row(itp->first).swap_indices(i, ip);

        CU.swap_col(i, ip);
        
        indperm.swap(i, ip);
        indperminv.swap(ipvt[i], ipvt[ip]);
        std::swap(ipvtinv[ipvt[i]], ipvtinv[ipvt[ip]]);
        std::swap(ipvt[i], ipvt[ip]);
      }
    }
  }

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

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

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

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

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

}

#endif