PLanczos.h File Reference

Preconditioned Lanczos solver. More...

#include <cmath>
#include <vector>
#include "oops/assimilation/TriDiagSolve.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::PLanczos (VECTOR &xx, const VECTOR &bb, const AMATRIX &A, const PMATRIX &precond, const int maxiter, const double tolerance)

Detailed Description

Preconditioned Lanczos solver.

This algorihtm is based on the standard Preconditioned Lanczos method for solving the linear system Ax = b

A must be square and symmetric.

On entry:

• x = starting point, \( x_0 \).
• b = right hand side.
• A = \( A \).
• precond = preconditioner \( P_k \).

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 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 PLanczos.h.