Package org.apache.commons.math3.linear

Class RRQRDecomposition.Solver

java.lang.Object

org.apache.commons.math3.linear.RRQRDecomposition.Solver

All Implemented Interfaces:

DecompositionSolver

Enclosing class:

RRQRDecomposition

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

Specialized solver.

Field Summary

Fields

Modifier and Type	Field	Description
private RealMatrix	p	A permutation matrix for the pivots used in the QR decomposition
private DecompositionSolver	upper	Upper level solver.

Constructor Summary

Constructors

Modifier	Constructor	Description
private	Solver(DecompositionSolver upper, RealMatrix p)	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

upper

private final DecompositionSolver upper

Upper level solver.

p

private RealMatrix p

A permutation matrix for the pivots used in the QR decomposition

Constructor Detail

Solver

private Solver(DecompositionSolver upper,
               RealMatrix p)

Build a solver from decomposed matrix.

Parameters:

upper - upper level solver.

p - permutation matrix

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.