Package org.apache.commons.math3.linear

Class QRDecomposition.Solver

java.lang.Object

org.apache.commons.math3.linear.QRDecomposition.Solver

All Implemented Interfaces:

DecompositionSolver

Enclosing class:

QRDecomposition

private static class QRDecomposition.Solver
extends java.lang.Object
implements DecompositionSolver

Specialized solver.

Field Summary

Fields

Modifier and Type	Field	Description
private double[][]	qrt	A packed TRANSPOSED representation of the QR decomposition.
private double[]	rDiag	The diagonal elements of R.
private double	threshold	Singularity threshold.

Constructor Summary

Constructors

Modifier	Constructor	Description
private	Solver(double[][] qrt, double[] rDiag, double threshold)	Build a solver from decomposed matrix.

Method Summary

Modifier and Type	Method	Description
RealMatrix	getInverse()	Get the pseudo-inverse of the decomposed matrix.
boolean	isNonSingular()	Check if the decomposed matrix is non-singular.
RealMatrix	solve(RealMatrix b)	Solve the linear equation A × X = B for matrices A.
RealVector	solve(RealVector b)	Solve the linear equation A × X = B for matrices A.

Methods inherited from class java.lang.Object

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

Field Detail

qrt

private final double[][] qrt

A packed TRANSPOSED representation of the QR decomposition.

The elements BELOW the diagonal are the elements of the UPPER triangular matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors from which an explicit form of Q can be recomputed if desired.

rDiag

private final double[] rDiag

The diagonal elements of R.

threshold

private final double threshold

Singularity threshold.

Constructor Detail

Solver

private Solver(double[][] qrt,
               double[] rDiag,
               double threshold)

Build a solver from decomposed matrix.

Parameters:

qrt - Packed TRANSPOSED representation of the QR decomposition.

rDiag - Diagonal elements of R.

threshold - Singularity threshold.

Method Detail

isNonSingular

public boolean isNonSingular()

Check if the decomposed matrix is non-singular.

Specified by:

isNonSingular in interface DecompositionSolver

Returns:

true if the decomposed matrix is non-singular.

solve

public RealVector solve(RealVector b)

Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Specified by:

solve in interface DecompositionSolver

Parameters:

b - right-hand side of the equation A × X = B

Returns:

a vector X that minimizes the two norm of A × X - B

solve

public RealMatrix solve(RealMatrix b)

Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Specified by:

solve in interface DecompositionSolver

Parameters:

b - right-hand side of the equation A × X = B

Returns:

a matrix X that minimizes the two norm of A × X - B

getInverse

public RealMatrix getInverse()

Get the pseudo-inverse of the decomposed matrix.

This is equal to the inverse of the decomposed matrix, if such an inverse exists.

If no such inverse exists, then the result has properties that resemble that of an inverse.

In particular, in this case, if the decomposed matrix is A, then the system of equations \( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudo-inverse \( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \| A z - b \right \|_2 \) is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest solution, meaning \( \left \| z \right \|_2 \) is minimized.

Note however that some decompositions cannot compute a pseudo-inverse for all matrices. For example, the LUDecomposition is not defined for non-square matrices to begin with. The QRDecomposition can operate on non-square matrices, but will throw SingularMatrixException if the decomposed matrix is singular. Refer to the javadoc of specific decomposition implementations for more details.

Specified by:

getInverse in interface DecompositionSolver

Returns:

pseudo-inverse matrix (which is the inverse, if it exists), if the decomposition can pseudo-invert the decomposed matrix

Throws:

SingularMatrixException - if the decomposed matrix is singular.