org.apache.ignite.ml.math.decompositions

Class SingularValueDecomposition

java.lang.Object

org.apache.ignite.ml.math.decompositions.SingularValueDecomposition

All Implemented Interfaces:

Destroyable

public class SingularValueDecomposition
extends Object
implements Destroyable

Compute a singular value decomposition (SVD) of (l x k) matrix m.

This decomposition can be thought as an extension of EigenDecomposition to rectangular matrices. The factorization we get is following:

m = u * s * v^{*}, where

• u is a real or complex unitary matrix.
• s is a rectangular diagonal matrix with non-negative real numbers on diagonal (these numbers are singular values of m).
• v is a real or complex unitary matrix.

If m is real then u and v are also real.

See also: Wikipedia article on SVD.

Note: complex case is currently not supported.

Constructor Summary

Constructors

Constructor and Description
SingularValueDecomposition(Matrix arg) Singular value decomposition object.

Method Summary

Modifier and Type	Method and Description
double	cond() Gets the two norm condition number, which is max(S) / min(S) .
Matrix	getS()
double[]	getSingularValues() Gets the diagonal of S, which is a one-dimensional array of singular values.
Matrix	getU() Gets the left singular vectors U.
Matrix	getV() Gets the right singular vectors V.
double	norm2() Gets the two norm, which is max(S).
int	rank() Gets effective numerical matrix rank.

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.ignite.ml.math.Destroyable

destroy

Constructor Detail

SingularValueDecomposition

public SingularValueDecomposition(Matrix arg)

Singular value decomposition object.

Parameters:

arg - A rectangular matrix.

Method Detail

cond

public double cond()

Gets the two norm condition number, which is max(S) / min(S) .

getS

public Matrix getS()

Returns:

the diagonal matrix of singular values.

getSingularValues

public double[] getSingularValues()

Gets the diagonal of S, which is a one-dimensional array of singular values.

Returns:

diagonal of S.

getU

public Matrix getU()

Gets the left singular vectors U.

Returns:

U

getV

public Matrix getV()

Gets the right singular vectors V.

Returns:

V

norm2

public double norm2()

Gets the two norm, which is max(S).

rank

public int rank()

Gets effective numerical matrix rank.