com.numericalmethod.suanshu.matrix.doubles.factorization.svd
Class SVD

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.factorization.svd.SVD

All Implemented Interfaces:

SVDDecomposition

public class SVD
extends java.lang.Object
implements SVDDecomposition

The SVD decomposition of a matrix.

Given a tall matrix A of dimension m x n, where m >= n we find orthogonal matrices U and V such that

U' %*% A %*% V = D

Alternatively,

U %*% D %*% V' = A

• U is orthogonal and has dimension m x n.
• V is orthogonal and has dimension n x n.
• D is a diagonal matrix of dimension n x n.

See Also:

Wikipedia: Singular value decomposition

Nested Class Summary

static class

SVD.Method the methods available to compute eigenvalues and eigenvectors

Field Summary

double

epsilon a precision parameter: when a number |x| ≤ ε, it is considered 0

Constructor Summary

SVD(Matrix A, boolean doUV)
Construct an instance of the SVD decomposition.

SVD(Matrix A, boolean doUV, SVD.Method method, double epsilon)
Construct an instance of the SVD decomposition.

Method Summary

DiagonalMatrix	D() Get a copy of D as in U' %*% A %*% V = D U %*% D %*% V' = A
double[]	singularValues() Get an array of the normalized, hence positive, singular values.
Matrix	U() Get a copy of U as in U' %*% A %*% V = D U %*% D %*% V' = A
Matrix	Ut() Get a copy of U.t() as in U.t() %*% A %*% V = D U %*% D %*% V' = A
Matrix	V() Get a copy of V as in U' %*% A %*% V = D U %*% D %*% V' = A

Methods inherited from class java.lang.Object

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

Field Detail

epsilon

public final double epsilon

a precision parameter: when a number |x| ≤ ε, it is considered 0

Constructor Detail

SVD

public SVD(Matrix A,
           boolean doUV,
           SVD.Method method,
           double epsilon)

Construct an instance of the SVD decomposition.

Parameters:

A - a matrix

doUV - true if only the singular values are wanted; U and V are not computed

method - choose one of the algorithms in SVD.Method

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

SVD

public SVD(Matrix A,
           boolean doUV)

Construct an instance of the SVD decomposition.

Parameters:

A - a matrix

doUV - true if only the singular values are wanted; U and V are not computed

Method Detail

singularValues

public double[] singularValues()

Description copied from interface: SVDDecomposition

Get an array of the normalized, hence positive, singular values. It may differ from D if this class is constructed with normalization off.

Specified by:

singularValues in interface SVDDecomposition

Returns:

the singular values

D

public DiagonalMatrix D()

Description copied from interface: SVDDecomposition

Get a copy of D as in

 U' %*% A %*% V = D
 U %*% D %*% V' = A
 

Specified by:

D in interface SVDDecomposition

Returns:

a copy of D

U

public Matrix U()

Description copied from interface: SVDDecomposition

Get a copy of U as in

 U' %*% A %*% V = D
 U %*% D %*% V' = A
 

Specified by:

U in interface SVDDecomposition

Returns:

a copy of U

Ut

public Matrix Ut()

Description copied from interface: SVDDecomposition

Get a copy of U.t() as in

 U.t() %*% A %*% V = D
 U %*% D %*% V' = A
 

Specified by:

Ut in interface SVDDecomposition

Returns:

a copy of U.t()

V

public Matrix V()

Description copied from interface: SVDDecomposition

Get a copy of V as in

 U' %*% A %*% V = D
 U %*% D %*% V' = A
 

Specified by:

V in interface SVDDecomposition

Returns:

a copy of V