inv_rel_cg2.cc

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/*! \file
 *  \brief Conjugate-Gradient algorithm for a generic Linear Operator
 */
 
#include "chromabase.h"
#include "actions/ferm/invert/inv_rel_cg2.h"
 
namespace Chroma {
 
//! Conjugate-Gradient (CGNE) algorithm for a generic Linear Operator
/*! \ingroup invert
 * This subroutine uses the Conjugate Gradient (CG) algorithm to find
 * the solution of the set of linear equations
 *
 *          Chi  =  A . Psi
 *
 * where       A = M^dag . M
 *
 * Algorithm:
 
 *  Psi[0]  :=  initial guess;                 Linear interpolation (argument)
 *  r[0]    :=  Chi - M^dag . M . Psi[0] ;     Initial residual
 *  p[1]    :=  r[0] ;                         Initial direction
 *  IF |r[0]| <= RsdCG |Chi| THEN RETURN;      Converged?
 *  FOR k FROM 1 TO MaxCG DO                   CG iterations
 *      a[k] := |r[k-1]|**2 / <Mp[k],Mp[k]> ;
 *      Psi[k] += a[k] p[k] ;                  New solution std::vector
 *      r[k] -= a[k] M^dag . M . p[k] ;        New residual
 *      IF |r[k]| <= RsdCG |Chi| THEN RETURN;  Converged?
 *      b[k+1] := |r[k]|**2 / |r[k-1]|**2 ;
 *      p[k+1] := r[k] + b[k+1] p[k];          New direction
 *
 * Arguments:
 *
 *  \param M       Linear Operator             (Read)
 *  \param chi     Source                      (Read)
 *  \param psi     Solution                    (Modify)
 *  \param RsdCG   CG residual accuracy        (Read)
 *  \param MaxCG   Maximum CG iterations       (Read)
 *  \param n_count Number of CG iteration      (Write)
 *
 * Local Variables:
 *
 *  p                  Direction std::vector
 *  r                  Residual std::vector
 *  cp                 | r[k] |**2
 *  c                  | r[k-1] |**2
 *  k                  CG iteration counter
 *  a                  a[k]
 *  b                  b[k+1]
 *  d                  < p[k], A.p[k] >
 *  Mp                 Temporary for  M.p
 *
 * Subroutines:
 *                             +               
 *  A       Apply matrix M or M  to std::vector
 *
 * Operations:
 *
 *  2 A + 2 Nc Ns + N_Count ( 2 A + 10 Nc Ns )
 */
 
template<typename T>
void InvRelCG2_a(const LinearOperator<T>& M,
                 const T& chi,
                 T& psi,
                 const Real& RsdCG, 
                 int MaxCG, 
                 int& n_count)
{
  const Subset& s = M.subset();
  
  //  Real rsd_sq = (RsdCG * RsdCG) * Real(norm2(chi,s));
  Real chi_sq =  Real(norm2(chi,s));
 
  QDPIO::cout << "chi_norm = " << sqrt(chi_sq) << std::endl;
  Real rsd_sq = (RsdCG * RsdCG) * chi_sq;
 
  //                                            +
  //  r[0]  :=  Chi - A . Psi[0]    where  A = M  . M
    
  //                      +
  //  r  :=  [ Chi  -  M(u)  . M(u) . psi ]
  T  r, mp, mmp;
  psi[s] = zero;
 
  r[s] = chi;
  //  p[1]  :=  r[0]
  T p;
  p = zero;
  p[s] = r;
  
  //  Cp = |r[0]|^2
  Double c = norm2(r, s);                  /* 2 Nc Ns  flops */
  Double cp = c;
 
  Double zeta = Double(1)/c;
 
  QDPIO::cout << "InvRelCG2: k = 0  c = " << cp << "  rsd_sq = " << rsd_sq << std::endl;
 
  //  IF |r[0]| <= RsdCG |Chi| THEN RETURN;
  if ( toBool(c  <=  rsd_sq) )
  {
    n_count = 0;
    return;
  }
 
  //
  //  FOR k FROM 1 TO MaxCG DO
  //
  Real a;
  Double d;
  
  for(int k = 1; k <= MaxCG; ++k)
  {
    // Inner tolerance = epsilon || chi || || p || sqrt(zeta) / 2
    //
    // The || p || part is taken care of the fact that we are using 
    // relative residua in the inner solve. The factor of 2 is because
    // we apply the operator twice...
    Real inner_tol = sqrt(rsd_sq)*sqrt(zeta)/Real(2);
 
    // Compute M^{dag} M p
    M(mp, p, PLUS, inner_tol);
    M(mmp, mp, MINUS, inner_tol);
 
    //  d = < M^{dag} M p, p>
    d = innerProductReal(mmp, p, s);    /* 2 Nc Ns  flops */
 
    //  a[k] := | r |**2 / < p[k], Ap[k] > ;
    a = Real(c)/Real(d);
 
    //  Psi[k] += a[k] p[k]
    psi[s] += a * p;    /* 2 Nc Ns  flops */
 
    //  r[k] -= a[k] M^{dag}M. p[k] ;
    r[s] -= a * mmp;
 
    //  IF |r[k]| <= RsdCG |Chi| THEN RETURN;
 
    //  cp  =  | r[k] |**2
    c = norm2(r, s);                    /* 2 Nc Ns  flops */
 
    // update relaxation factor
    zeta += Double(1)/c;
 
    // Update p as:
    // p[k+1] := r[k] + c/cp * p
    //
    // we put c/cp into b
    //
    //  b[k+1] := |r[k]|**2 / |r[k-1]|**2
    Real b = Real(c) / Real(cp);
 
    //  p[k+1] := r[k] + b[k+1] p[k]
    p[s] = r + b*p;     /* Nc Ns  flops */
 
    cp = c;
 
    QDPIO::cout << "InvCG: k = " << k << "  cp = " << cp << std::endl;
 
    if ( toBool(cp  <=  rsd_sq) )
    {
      n_count = k;
      return;
    }
  }
  n_count = MaxCG;
  QDPIO::cerr << "Nonconvergence Warning n_count = " << n_count << std::endl;
}
 
 
// Fix here for now
template<>
void InvRelCG2(const LinearOperator<LatticeFermion>& M,
               const LatticeFermion& chi,
               LatticeFermion& psi,
               const Real& RsdCG, 
               int MaxCG, 
               int& n_count)
{
  InvRelCG2_a(M, chi, psi, RsdCG, MaxCG, n_count);
}
 
}  // end namespace Chroma