gmm_least_squares_cg.h

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/**@file gmm_leastsquares_cg.h
   @author Benjamin Schleimer <bensch128  (at) yahoo (dot) com>
   @date January 23, 2007.
   @brief Conjugate gradient least squares algorithm. 
   Algorithm taken from http://www.stat.washington.edu/wxs/Stat538-w05/Notes/conjugate-gradients.pdf page 6
*/
#ifndef GMM_LEAST_SQUARES_CG_H__
#define GMM_LEAST_SQUARES_CG_H__

#include "gmm_kernel.h"
#include "gmm_iter.h"
#include "gmm_conjugated.h"

namespace gmm {

  template <typename Matrix, typename Vector1, typename Vector2>
  void least_squares_cg(const Matrix& C, Vector1& x, const Vector2& y,
                        iteration &iter) {

    typedef typename temporary_dense_vector<Vector1>::vector_type temp_vector;
    typedef typename linalg_traits<Vector1>::value_type T;

    T rho, rho_1(0), a;
    temp_vector p(vect_size(x)), q(vect_size(y)), g(vect_size(x));
    temp_vector r(vect_size(y));
    iter.set_rhsnorm(gmm::sqrt(gmm::abs(vect_hp(y, y))));

    if (iter.get_rhsnorm() == 0.0)
      clear(x);
    else {
      mult(C, scaled(x, T(-1)), y, r);
      mult(conjugated(C), r, g);
      rho = vect_hp(g, g);
      copy(g, p);

      while (!iter.finished_vect(g)) {

        if (!iter.first()) { 
          rho = vect_hp(g, g);
          add(g, scaled(p, rho / rho_1), p);
        }

        mult(C, p, q);

        a = rho / vect_hp(q, q);        
        add(scaled(p, a), x);
        add(scaled(q, -a), r);
        // NOTE: how do we minimize the impact to the transpose?
        mult(conjugated(C), r, g);
        rho_1 = rho;

        ++iter;
      }
    }
  }

  template <typename Matrix, typename Precond, 
            typename Vector1, typename Vector2> inline 
  void least_squares_cg(const Matrix& C, const Vector1& x, const Vector2& y,
                        iteration &iter)
  { least_squares_cg(C, linalg_const_cast(x), y, iter); }
}


#endif //  GMM_SOLVER_CG_H__