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

Class GloubKahanSVD

java.lang.Object

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

All Implemented Interfaces:

SVDDecomposition, java.io.Serializable

public class GloubKahanSVD
extends java.lang.Object
implements SVDDecomposition

Gloub-Kahan algorithm does the SVD decomposition of a tall matrix in two stages.

1. First, it reduces the matrix to a bidiagonal matrix using a sequence of Householder transformations.
2. Second, it reduces the super-diagonal of the bidiagonal matrix to 0s, using a sequence of Givens transformations.

See Also:

"G. H. Golub, C. F. van Loan, "Algorithm 8.6.2," Matrix Computations, 3rd edition.", Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double	epsilon

Constructor Summary

Constructors

Constructor and Description
GloubKahanSVD(Matrix A, boolean doUV, boolean normalize, double epsilon) Run the Gloub-Kahan SVD decomposition on a tall 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

GloubKahanSVD

public GloubKahanSVD(Matrix A,
                     boolean doUV,
                     boolean normalize,
                     double epsilon)

Run the Gloub-Kahan SVD decomposition on a tall matrix.

Parameters:

A - a tall matrix

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

normalize - true if to sort the singular values in descending order and make them positive

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

Throws:

java.lang.IllegalArgumentException - if A is not tall

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