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

Interface SVDDecomposition

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

GloubKahanSVD, SVD

public interface SVDDecomposition
extends java.io.Serializable

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

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.

Method Detail

getSingularValues

double[] getSingularValues()

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

Returns:

the singular values

D

DiagonalMatrix D()

Get the D matrix as in SVD decomposition.

Returns:

D

U

Matrix U()

Get the U matrix as in SVD decomposition.

Returns:

U

Ut

Matrix Ut()

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

Returns:

U().t()

V

Matrix V()

Get the V matrix as in SVD decomposition.

Returns:

V