org.apache.commons.math.linear
Class SingularValueDecompositionImpl

java.lang.Object
  org.apache.commons.math.linear.SingularValueDecompositionImpl

All Implemented Interfaces:

SingularValueDecomposition

public class SingularValueDecompositionImpl
extends Object
implements SingularValueDecomposition

Calculates the compact Singular Value Decomposition of a matrix.

The Singular Value Decomposition of matrix A is a set of three matrices: U, Σ and V such that A = U × Σ × V^T. Let A be a m × n matrix, then U is a m × p orthogonal matrix, Σ is a p × p diagonal matrix with positive or null elements, V is a p × n orthogonal matrix (hence V^T is also orthogonal) where p=min(m,n).

Since:

2.0

Version:

$Id: SingularValueDecompositionImpl.java 1131229 2011-06-03 20:49:25Z luc $

Constructor Summary

SingularValueDecompositionImpl(RealMatrix matrix)
Calculates the compact Singular Value Decomposition of the given matrix.

Method Summary

double	getConditionNumber() Return the condition number of the matrix.
RealMatrix	getCovariance(double minSingularValue) Returns the n × n covariance matrix.
double	getNorm() Returns the L2 norm of the matrix.
int	getRank() Return the effective numerical matrix rank.
RealMatrix	getS() Returns the diagonal matrix Σ of the decomposition.
double[]	getSingularValues() Returns the diagonal elements of the matrix Σ of the decomposition.
DecompositionSolver	getSolver() Get a solver for finding the A × X = B solution in least square sense.
RealMatrix	getU() Returns the matrix U of the decomposition.
RealMatrix	getUT() Returns the transpose of the matrix U of the decomposition.
RealMatrix	getV() Returns the matrix V of the decomposition.
RealMatrix	getVT() Returns the transpose of the matrix V of the decomposition.

Methods inherited from class java.lang.Object

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

Constructor Detail

SingularValueDecompositionImpl

public SingularValueDecompositionImpl(RealMatrix matrix)

Calculates the compact Singular Value Decomposition of the given matrix.

Parameters:

matrix - Matrix to decompose.

Method Detail

getU

public RealMatrix getU()

Returns the matrix U of the decomposition.

U is an orthogonal matrix, i.e. its transpose is also its inverse.

Specified by:

getU in interface SingularValueDecomposition

Returns:

the U matrix

See Also:

SingularValueDecomposition.getUT()

getUT

public RealMatrix getUT()

Returns the transpose of the matrix U of the decomposition.

U is an orthogonal matrix, i.e. its transpose is also its inverse.

Specified by:

getUT in interface SingularValueDecomposition

Returns:

the U matrix (or null if decomposed matrix is singular)

See Also:

SingularValueDecomposition.getU()

getS

public RealMatrix getS()

Returns the diagonal matrix Σ of the decomposition.

Σ is a diagonal matrix. The singular values are provided in non-increasing order, for compatibility with Jama.

Specified by:

getS in interface SingularValueDecomposition

Returns:

the Σ matrix

getSingularValues

public double[] getSingularValues()

Returns the diagonal elements of the matrix Σ of the decomposition.

The singular values are provided in non-increasing order, for compatibility with Jama.

Specified by:

getSingularValues in interface SingularValueDecomposition

Returns:

the diagonal elements of the Σ matrix

getV

public RealMatrix getV()

Returns the matrix V of the decomposition.

V is an orthogonal matrix, i.e. its transpose is also its inverse.

Specified by:

getV in interface SingularValueDecomposition

Returns:

the V matrix (or null if decomposed matrix is singular)

See Also:

SingularValueDecomposition.getVT()

getVT

public RealMatrix getVT()

Returns the transpose of the matrix V of the decomposition.

V is an orthogonal matrix, i.e. its transpose is also its inverse.

Specified by:

getVT in interface SingularValueDecomposition

Returns:

the V matrix (or null if decomposed matrix is singular)

See Also:

SingularValueDecomposition.getV()

getCovariance

public RealMatrix getCovariance(double minSingularValue)

Returns the n × n covariance matrix.

The covariance matrix is V × J × V^T where J is the diagonal matrix of the inverse of the squares of the singular values.

Specified by:

getCovariance in interface SingularValueDecomposition

Parameters:

minSingularValue - value below which singular values are ignored (a 0 or negative value implies all singular value will be used)

Returns:

covariance matrix

getNorm

public double getNorm()

Returns the L₂ norm of the matrix.

The L₂ norm is max(|A × u|₂ / |u|₂), where |.|₂ denotes the vectorial 2-norm (i.e. the traditional euclidian norm).

Specified by:

getNorm in interface SingularValueDecomposition

Returns:

norm

getConditionNumber

public double getConditionNumber()

Return the condition number of the matrix.

Specified by:

getConditionNumber in interface SingularValueDecomposition

Returns:

condition number of the matrix

getRank

public int getRank()

Return the effective numerical matrix rank.

The effective numerical rank is the number of non-negligible singular values. The threshold used to identify non-negligible terms is max(m,n) × ulp(s₁) where ulp(s₁) is the least significant bit of the largest singular value.

Specified by:

getRank in interface SingularValueDecomposition

Returns:

effective numerical matrix rank

getSolver

public DecompositionSolver getSolver()

Get a solver for finding the A × X = B solution in least square sense.

Specified by:

getSolver in interface SingularValueDecomposition

Returns:

a solver