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

Class SVD

java.lang.Object

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

All Implemented Interfaces:

SVDDecomposition, java.io.Serializable

public class SVD
extends java.lang.Object
implements SVDDecomposition

SVD decomposition decomposes a matrix A of dimension m x n, where m >= n, such that U' * A * V = D, or U * D * V' = A.

• U is orthogonal and has the dimension m x n.
• D is diagonal and has the dimension n x n.
• V is orthogonal and has the dimension n x n.

See Also:

Wikipedia: Singular value decomposition, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double	epsilon

Constructor Summary

Constructors

Constructor and Description
SVD(Matrix A, boolean doUV) Run the SVD decomposition on a matrix.
SVD(Matrix A, boolean doUV, double epsilon) Run the SVD decomposition on a matrix.

Method Summary

Modifier and Type	Method and Description
DiagonalMatrix	D() Get the D matrix as in SVD decomposition.
double[]	getSingularValues() Get the normalized, hence positive, singular values.
Matrix	U() Get the U matrix as in SVD decomposition.
Matrix	Ut() Get the transpose of i>U, i.e., U().t().
Matrix	V() Get the V matrix as in SVD decomposition.

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

Constructor Detail

SVD

public SVD(Matrix A,
           boolean doUV,
           double epsilon)

Run the SVD decomposition on a matrix.

Parameters:

A - a matrix

doUV - false if to compute only the singular values but not U and V

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

SVD

public SVD(Matrix A,
           boolean doUV)

Run the SVD decomposition on a matrix.

Parameters:

A - a matrix

doUV - false if to compute only the singular values but not U and V

Method Detail

getSingularValues

public double[] getSingularValues()

Description copied from interface: SVDDecomposition

Get the normalized, hence positive, singular values. They may differ from the values in D if this computation turns off normalization.

Specified by:

getSingularValues in interface SVDDecomposition

Returns:

the singular values

D

public DiagonalMatrix D()

Description copied from interface: SVDDecomposition

Get the D matrix as in SVD decomposition.

Specified by:

D in interface SVDDecomposition

Returns:

D

U

public Matrix U()

Description copied from interface: SVDDecomposition

Get the U matrix as in SVD decomposition.

Specified by:

U in interface SVDDecomposition

Returns:

U

Ut

public Matrix Ut()

Description copied from interface: SVDDecomposition

Get the transpose of i>U, i.e., U().t().

Specified by:

Ut in interface SVDDecomposition

Returns:

U().t()

V

public Matrix V()

Description copied from interface: SVDDecomposition

Get the V matrix as in SVD decomposition.

Specified by:

V in interface SVDDecomposition

Returns:

V