Class QMRSolver

java.lang.Object

org.ojalgo.matrix.task.iterative.IterativeSolverTask

org.ojalgo.matrix.task.iterative.QMRSolver

All Implemented Interfaces:

MatrixTask<Double>, SolverTask<Double>

public final class QMRSolver
extends IterativeSolverTask

Quasi-Minimal Residual (QMR) solver for general nonsymmetric square systems.

This is a Java port of SciPy's qmr() reference implementation. It is almost a straight line-by-line translation from SciPy. Implemented here with right-preconditioning only (M1 = I, M2 != I), and using ojAlgo's dense MatrixStore operations for matrix–vector products with A and A^T.

Characteristics

• Operates on matrix–vector products with both A and A^T.
• Right-preconditioning is used; both forward and transpose applications of the preconditioner may be invoked.
• Stops when the residual norm is small relative to the RHS norm (or absolutely small when RHS is zero), or when the iteration limit is reached.

When to use

• For nonsymmetric or indefinite problems where SPD-specific methods are inapplicable.
• When a robust Krylov method is preferred over simple stationary iterations.
• If A^T is unavailable or too costly, consider alternatives that avoid explicit transpose products.

References

• Templates for the Solution of Linear Systems, Barrett et al., Figure 2.8.
• Freund invalid input: '&' Nachtigal (1991), QMR: a quasi-minimal residual method for non-Hermitian linear systems.

Nested Class Summary

Nested classes/interfaces inherited from class IterativeSolverTask

IterativeSolverTask.Configurator

Nested classes/interfaces inherited from interface SolverTask

SolverTask.Factory<N>

Field Summary

Fields

Modifier and Type	Field	Description
private R064Store	d
private R064Store	p
private R064Store	ptilde
private R064Store	q
private R064Store	r
private R064Store	s
private R064Store	v
private R064Store	vtilde
private R064Store	wtilde
private R064Store	z

Fields inherited from class IterativeSolverTask

DEFAULT

Fields inherited from interface SolverTask

C128, H256, Q128, R064, R128

Constructor Summary

Constructors

Constructor	Description
QMRSolver()

Method Summary

Modifier and Type	Method	Description
private static void	axpby(double alpha, R064Store src, double beta, R064Store dst)
private static void	axpy(double alpha, R064Store x, Mutate1D.Modifiable<?> y)
private static double	norm2(R064Store a)
double	resolve(List<Equation> equations, PhysicalStore<Double> x)
private static void	scaleCopy(R064Store src, double alpha, R064Store dst)
private static void	scaleInPlace(R064Store x, double alpha)

Methods inherited from class IterativeSolverTask

configurator, debug, getAccuracyContext, getIterationsLimit, getPreconditioner, getRelaxationFactor, isDebugPrinterSet, preallocate, resolve, setAccuracyContext, setDebugPrinter, setIterationsLimit, setPreconditioner, setRelaxationFactor, solve, solve, toListOfRows, worker

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface SolverTask

preallocate, solve, toSolutionProvider

Field Details

r

private R064Store r

vtilde

private R064Store vtilde

wtilde

private R064Store wtilde

v

private R064Store v

z

private R064Store z

p

private R064Store p

q

private R064Store q

ptilde

private R064Store ptilde

d

private R064Store d

s

private R064Store s

Constructor Details

QMRSolver

public QMRSolver()

Method Details

axpby

private static void axpby(double alpha,
 R064Store src,
 double beta,
 R064Store dst)

axpy

private static void axpy(double alpha,
 R064Store x,
 Mutate1D.Modifiable<?> y)

norm2

private static double norm2(R064Store a)

scaleCopy

private static void scaleCopy(R064Store src,
 double alpha,
 R064Store dst)

scaleInPlace

private static void scaleInPlace(R064Store x,
 double alpha)

resolve

public double resolve(List<Equation> equations,
 PhysicalStore<Double> x)

Specified by:

resolve in class IterativeSolverTask