mikera.matrixx.solve.impl.qr

Class QRHouseColSolver

java.lang.Object

mikera.matrixx.solve.impl.qr.QRHouseColSolver

public class QRHouseColSolver
extends Object

QR decomposition can be used to solve for systems. However, this is not as computationally efficient as LU decomposition and costs about 3n² flops.

It solve for x by first multiplying b by the transpose of Q then solving for the result.
QRx=b
Rx=Q^T b

A column major decomposition is used in this solver.

Author:

Peter Abeles

Field Summary

Fields

Modifier and Type	Field and Description
protected AMatrix	A
protected int	maxCols
protected int	maxRows
protected int	numCols
protected int	numRows

Constructor Summary

Constructors

Constructor and Description
QRHouseColSolver() Creates a linear solver that uses QR decomposition.

Method Summary

Modifier and Type	Method and Description
protected void	_setA(AMatrix A)
AMatrix	getA()
double	quality()
static double	qualityTriangular(boolean upper, AMatrix T) Computes the quality of a triangular matrix.
boolean	setA(AMatrix A) Performs QR decomposition on A
void	setMaxSize(int maxRows, int maxCols)
AMatrix	solve(AMatrix B) Solves for X using the QR decomposition.

Methods inherited from class java.lang.Object

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

Field Detail

A

protected AMatrix A

numRows

protected int numRows

numCols

protected int numCols

maxRows

protected int maxRows

maxCols

protected int maxCols

Constructor Detail

QRHouseColSolver

public QRHouseColSolver()

Creates a linear solver that uses QR decomposition.

Method Detail

getA

public AMatrix getA()

_setA

protected void _setA(AMatrix A)

setMaxSize

public void setMaxSize(int maxRows,
                       int maxCols)

setA

public boolean setA(AMatrix A)

Performs QR decomposition on A

Parameters:

A - not modified.

quality

public double quality()

solve

public AMatrix solve(AMatrix B)

Solves for X using the QR decomposition.

Parameters:

B - A matrix that is n by m. Not modified.

qualityTriangular

public static double qualityTriangular(boolean upper,
                                       AMatrix T)

Computes the quality of a triangular matrix. In this situation the quality is the absolute value of the product of each diagonal element divided by the magnitude of the largest diagonal element. If all diagonal elements are zero then zero is returned.

Parameters:

upper - if it is upper triangular or not.

T - A matrix. @return product of the diagonal elements.

Returns:

the quality of the system.