Package 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

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
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

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

Constructor Details

SingularValueDecompositionImpl

public SingularValueDecompositionImpl(RealMatrix matrix)
                               throws InvalidMatrixException

Calculates the compact Singular Value Decomposition of the given matrix.

Parameters:

matrix - The matrix to decompose.

Throws:

InvalidMatrixException - (wrapping a ConvergenceException if algorithm fails to converge

Method Details

getU

public RealMatrix getU()
                throws InvalidMatrixException

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

Throws:

InvalidMatrixException

See Also:

• SingularValueDecomposition.getUT()

getUT

public RealMatrix getUT()
                 throws InvalidMatrixException

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)

Throws:

InvalidMatrixException

See Also:

• SingularValueDecomposition.getU()

getS

public RealMatrix getS()
                throws InvalidMatrixException

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

Throws:

InvalidMatrixException

getSingularValues

public double[] getSingularValues()
                           throws InvalidMatrixException

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

Throws:

InvalidMatrixException

getV

public RealMatrix getV()
                throws InvalidMatrixException

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)

Throws:

InvalidMatrixException

See Also:

• SingularValueDecomposition.getVT()

getVT

public RealMatrix getVT()
                 throws InvalidMatrixException

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)

Throws:

InvalidMatrixException

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()
               throws InvalidMatrixException

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

Throws:

InvalidMatrixException

getConditionNumber

public double getConditionNumber()
                          throws InvalidMatrixException

Return the condition number of the matrix.

Specified by:

getConditionNumber in interface SingularValueDecomposition

Returns:

condition number of the matrix

Throws:

InvalidMatrixException

getRank

public int getRank()
            throws IllegalStateException

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

Throws:

IllegalStateException

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