PCG.h File Reference

Preconditioned Conjugate Gradients solver. More...

#include <cmath>
#include <vector>
#include "oops/util/dot_product.h"
#include "oops/util/formats.h"
#include "oops/util/Logger.h"

Include dependency graph for PCG.h:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Namespaces
	oops
	The namespace for the main oops code.

Functions
template<typename VECTOR , typename AMATRIX , typename PMATRIX >
double	oops::PCG (VECTOR &x, const VECTOR &b, const AMATRIX &A, const PMATRIX &precond, const int maxiter, const double tolerance)

Detailed Description

Preconditioned Conjugate Gradients solver.

This solver is based on the standard Preconditioned Conjugate Gradients solver for Ax=b

A must be square, symmetric, positive definite. A preconditioner must be supplied that, given a vector q, returns an approximate solution of Ap=q.

On entry:

• x = starting point, \( x_0 \).
• b = right hand side.
• A = \( A \).
• precond = preconditioner \( P \approx (A)^{-1} \).

On exit, x will contain the solution \( x \)

The return value is the achieved reduction in preconditioned residual norm.

Iteration will stop if the maximum iteration limit "maxiter" is reached or if the preconditioned residual norm reduces by a factor of "tolerance".

VECTOR must implement:

• dot_product
• operator(=)
• operator(+=),
• operator(-=)
• operator(*=) [double * VECTOR],
• axpy

Each of AMATRIX and PMATRIX must implement a method:

• void multiply(const VECTOR&, VECTOR&) const

which applies the matrix to the first argument, and returns the matrix-vector product in the second. (Note: the const is optional, but recommended.)

Definition in file PCG.h.