cg.h File Reference

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Functions
template<class Matrix , class Vector , class Preconditioner , class Real >
int	CG (const Matrix &A, Vector &x, const Vector &b, const Preconditioner &M, int &max_iter, Real &tol)

Function Documentation

template<class Matrix , class Vector , class Preconditioner , class Real >

int CG	(	const Matrix &	A,
		Vector &	x,
		const Vector &	b,
		const Preconditioner &	M,
		int &	max_iter,
		Real &	tol
	)

Definition at line 24 of file cg.h.

{
  Real resid;
  Vector p, z, q;
  Vector alpha(1), beta(1), rho(1), rho_1(1);

  Real normb = norm(b);
  Vector r = b - A*x;

  if (normb == 0.0) 
    normb = 1;
  
  if ((resid = norm(r) / normb) <= tol) {
    tol = resid;
    max_iter = 0;
    return 0;
  }

  for (int i = 1; i <= max_iter; i++) {
    z = M.solve(r);
    rho(0) = dot(r, z);
    
    if (i == 1)
      p = z;
    else {
      beta(0) = rho(0) / rho_1(0);
      p = z + beta(0) * p;
    }
    
    q = A*p;
    alpha(0) = rho(0) / dot(p, q);
    
    x += alpha(0) * p;
    r -= alpha(0) * q;
    
    if ((resid = norm(r) / normb) <= tol) {
      tol = resid;
      max_iter = i;
      return 0;     
    }

    rho_1(0) = rho(0);
  }
  
  tol = resid;
  return 1;
}

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