gmm_precond_ilu.h

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/**@file gmm_precond_ilu.h
   @author Andrew Lumsdaine <[email protected]>
   @author Lie-Quan Lee <[email protected]>
   @author Yves Renard <[email protected]>
   @date June 5, 2003.
   @brief Incomplete LU without fill-in Preconditioner.
*/
 
#ifndef GMM_PRECOND_ILU_H
#define GMM_PRECOND_ILU_H
 
//
// Notes: The idea under a concrete Preconditioner such 
//        as Incomplete LU is to create a Preconditioner
//        object to use in iterative methods. 
//
 
#include "gmm_precond.h"
 
namespace gmm {
  /** Incomplete LU without fill-in Preconditioner. */
  template <typename Matrix>
  class ilu_precond {
 
  public :
    typedef typename linalg_traits<Matrix>::value_type value_type;
    typedef csr_matrix_ref<value_type *, size_type *, size_type *, 0> tm_type;
 
    tm_type U, L;
    bool invert;
  protected :
    std::vector<value_type> L_val, U_val;
    std::vector<size_type> L_ind, U_ind, L_ptr, U_ptr;
 
    template<typename M> void do_ilu(const M& A, row_major);
    void do_ilu(const Matrix& A, col_major);
 
  public:
    
    size_type nrows(void) const { return mat_nrows(L); }
    size_type ncols(void) const { return mat_ncols(U); }
    
    void build_with(const Matrix& A) {
      invert = false;
       L_ptr.resize(mat_nrows(A)+1);
       U_ptr.resize(mat_nrows(A)+1);
       do_ilu(A, typename principal_orientation_type<typename
              linalg_traits<Matrix>::sub_orientation>::potype());
    }
    ilu_precond(const Matrix& A) { build_with(A); }
    ilu_precond(void) {}
    size_type memsize() const { 
      return sizeof(*this) + 
        (L_val.size()+U_val.size()) * sizeof(value_type) + 
        (L_ind.size()+L_ptr.size()) * sizeof(size_type) +
        (U_ind.size()+U_ptr.size()) * sizeof(size_type); 
    }
  };
 
  template <typename Matrix> template <typename M>
  void ilu_precond<Matrix>::do_ilu(const M& A, row_major) {
    typedef typename linalg_traits<Matrix>::storage_type store_type;
    typedef value_type T;
    typedef typename number_traits<T>::magnitude_type R;
 
    size_type L_loc = 0, U_loc = 0, n = mat_nrows(A), i, j, k;
    if (n == 0) return;
    L_ptr[0] = 0; U_ptr[0] = 0;
    R prec = default_tol(R());
    R max_pivot = gmm::abs(A(0,0)) * prec;
 
 
    for (int count = 0; count < 2; ++count) {
      if (count) { 
        L_val.resize(L_loc); L_ind.resize(L_loc);
        U_val.resize(U_loc); U_ind.resize(U_loc);
      }
      L_loc = U_loc = 0;
      for (i = 0; i < n; ++i) {
        typedef typename linalg_traits<M>::const_sub_row_type row_type;
        row_type row = mat_const_row(A, i);
        typename linalg_traits<typename org_type<row_type>::t>::const_iterator
          it = vect_const_begin(row), ite = vect_const_end(row);
        
        if (count) { U_val[U_loc] = T(0); U_ind[U_loc] = i; }
        ++U_loc; // diagonal element
        
        for (k = 0; it != ite && k < 1000; ++it, ++k) {
          // if a plain row is present, retains only the 1000 firsts
          // nonzero elements. ---> a sort should be done.
          j = index_of_it(it, k, store_type());
          if (j < i) {
            if (count) { L_val[L_loc] = *it; L_ind[L_loc] = j; }
            L_loc++;
          }
          else if (i == j) {
            if (count) U_val[U_loc-1] = *it;
          }
          else {
            if (count) { U_val[U_loc] = *it; U_ind[U_loc] = j; }
            U_loc++;
          }
        }
        L_ptr[i+1] = L_loc; U_ptr[i+1] = U_loc;
      }
    }
    
    if (A(0,0) == T(0)) {
      U_val[U_ptr[0]] = T(1);
      GMM_WARNING2("pivot 0 is too small");
    }
 
    size_type qn, pn, rn;
    for (i = 1; i < n; i++) {
 
      pn = U_ptr[i];
      if (gmm::abs(U_val[pn]) <= max_pivot) {
        U_val[pn] = T(1);
        GMM_WARNING2("pivot " << i << " is too small");
      }
      max_pivot = std::max(max_pivot,
                           std::min(gmm::abs(U_val[pn]) * prec, R(1)));
 
      for (j = L_ptr[i]; j < L_ptr[i+1]; j++) {
        pn = U_ptr[L_ind[j]];
        
        T multiplier = (L_val[j] /= U_val[pn]);
        
        qn = j + 1;
        rn = U_ptr[i];
        
        for (pn++; pn < U_ptr[L_ind[j]+1] && U_ind[pn] < i; pn++) {
          while (qn < L_ptr[i+1] && L_ind[qn] < U_ind[pn])
            qn++;
          if (qn < L_ptr[i+1] && U_ind[pn] == L_ind[qn])
            L_val[qn] -= multiplier * U_val[pn];
        }
        for (; pn < U_ptr[L_ind[j]+1]; pn++) {
          while (rn < U_ptr[i+1] && U_ind[rn] < U_ind[pn])
            rn++;
          if (rn < U_ptr[i+1] && U_ind[pn] == U_ind[rn])
            U_val[rn] -= multiplier * U_val[pn];
        }
      }
    }
 
    L = tm_type(&(L_val[0]), &(L_ind[0]), &(L_ptr[0]), n, mat_ncols(A));
    U = tm_type(&(U_val[0]), &(U_ind[0]), &(U_ptr[0]), n, mat_ncols(A));
  }
  
  template <typename Matrix>
  void ilu_precond<Matrix>::do_ilu(const Matrix& A, col_major) {
    do_ilu(gmm::transposed(A), row_major());
    invert = true;
  }
 
  template <typename Matrix, typename V1, typename V2> inline
  void mult(const ilu_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 ilu_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 ilu_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 ilu_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 ilu_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 ilu_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