gmm_iter_solvers.h

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// Copyright (C) 2002-2008 Yves Renard
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/**@file gmm_iter_solvers.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date October 13, 2002.
   @brief Include standard gmm iterative solvers (cg, gmres, ...)
*/
#ifndef GMM_ITER_SOLVERS_H__
#define GMM_ITER_SOLVERS_H__

#include "gmm_iter.h"


namespace gmm {

  /** mixed method to find a zero of a real function G, a priori 
   * between a and b. If the zero is not between a and b, iterations
   * of secant are applied. When a convenient interval is found,
   * iterations of dichotomie and regula falsi are applied.
   */
  template <typename FUNC, typename T>
  T find_root(const FUNC &G, T a = T(0), T b = T(1),
	      T tol = gmm::default_tol(T())) {
    T c, Ga = G(a), Gb = G(b), Gc, d;
    d = gmm::abs(b - a);
#if 0
    for (int i = 0; i < 4; i++) { /* secant iterations.                   */
      if (d < tol) return (b + a) / 2.0;
      c = b - Gb * (b - a) / (Gb - Ga); Gc = G(c);
      a = b; b = c; Ga = Gb; Gb = Gc;
      d = gmm::abs(b - a);
    }
#endif
    while (Ga * Gb > 0.0) { /* secant iterations.                         */
      if (d < tol) return (b + a) / 2.0;
      c = b - Gb * (b - a) / (Gb - Ga); Gc = G(c);
      a = b; b = c; Ga = Gb; Gb = Gc;
      d = gmm::abs(b - a);
    }
    
    c = std::max(a, b); a = std::min(a, b); b = c;
    while (d > tol) {
      c = b - (b - a) * (Gb / (Gb - Ga)); /* regula falsi.     */
      if (c > b) c = b; if (c < a) c = a; 
      Gc = G(c);
      if (Gc*Gb > 0) { b = c; Gb = Gc; } else { a = c; Ga = Gc; }
      c = (b + a) / 2.0 ; Gc = G(c); /* Dichotomie.                       */
      if (Gc*Gb > 0) { b = c; Gb = Gc; } else { a = c; Ga = Gc; }
      d = gmm::abs(b - a); c = (b + a) / 2.0; if ((c == a) || (c == b)) d = 0.0;
    }
    return (b + a) / 2.0;
  }
  
}

#include "gmm_precond_diagonal.h"
#include "gmm_precond_ildlt.h"
#include "gmm_precond_ildltt.h"
#include "gmm_precond_mr_approx_inverse.h"
#include "gmm_precond_ilu.h"
#include "gmm_precond_ilut.h"
#include "gmm_precond_ilutp.h"



#include "gmm_solver_cg.h"
#include "gmm_solver_bicgstab.h"
#include "gmm_solver_qmr.h"
#include "gmm_solver_constrained_cg.h"
#include "gmm_solver_Schwarz_additive.h"
#include "gmm_modified_gram_schmidt.h"
#include "gmm_tri_solve.h"
#include "gmm_solver_gmres.h"
#include "gmm_solver_bfgs.h"
#include "gmm_least_squares_cg.h"

// #include "gmm_solver_idgmres.h"



#endif //  GMM_ITER_SOLVERS_H__