FullGMRES.h File Reference

FullGMRES solver for Ax=b. More...

#include <cmath>
#include <iostream>
#include <vector>
#include "oops/assimilation/rotmat.h"
#include "oops/assimilation/UpTriSolve.h"
#include "oops/util/dot_product.h"
#include "oops/util/formats.h"
#include "oops/util/Logger.h"

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Namespaces
	oops
	The namespace for the main oops code.

Functions
template<typename VECTOR , typename AMATRIX , typename PMATRIX >
double	oops::FullGMRES (VECTOR &xx, const VECTOR &bb, const AMATRIX &A, const PMATRIX &precond, const int maxiter, const double tolerance, std::vector< VECTOR > &pqVEC, std::vector< VECTOR > &xyVEC)

Detailed Description

FullGMRES solver for Ax=b.

GMRES solver for Ax=b.(based on implementation following Saad-Schultz and C. T. Kelley, July 10, 1994)

A must be square, but need not be symmetric. 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 \( F_k \approx (A)^{-1} \).
• maxiter = maximum number of iterations
• tol = error tolerance

On exit, x will contain the solution. The return value is the achieved reduction in residual norm.

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

VECTOR must implement:

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

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 FullGMRES.h.