mikera.matrixx.solve.impl.qr

Class QRHouseColSolver

java.lang.Object

mikera.matrixx.solve.impl.qr.QRHouseColSolver

public class QRHouseColSolver
extends java.lang.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.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
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

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

Constructor Detail

QRHouseColSolver

public QRHouseColSolver()

Creates a linear solver that uses QR decomposition.

Method Detail

getA

public AMatrix getA()

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.