cern.colt.matrix.linalg

Class SingularValueDecomposition

java.lang.Object

cern.colt.matrix.linalg.SingularValueDecomposition

All Implemented Interfaces:

java.io.Serializable

public class SingularValueDecomposition
extends java.lang.Object
implements java.io.Serializable

For an m x n matrix A with m >= n, the singular value decomposition is an m x n orthogonal matrix U, an n x n diagonal matrix S, and an n x n orthogonal matrix V so that A = U*S*V'.

The singular values, sigma[k] = S[k][k], are ordered so that sigma[0] >= sigma[1] >= ... >= sigma[n-1].

The singular value decomposition always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
SingularValueDecomposition(DoubleMatrix2D Arg) Constructs and returns a new singular value decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Method Summary

Modifier and Type	Method and Description
double	cond() Returns the two norm condition number, which is max(S) / min(S).
DoubleMatrix2D	getS() Returns the diagonal matrix of singular values.
double[]	getSingularValues() Returns the diagonal of S, which is a one-dimensional array of singular values
DoubleMatrix2D	getU() Returns the left singular vectors U.
DoubleMatrix2D	getV() Returns the right singular vectors V.
double	norm2() Returns the two norm, which is max(S).
int	rank() Returns the effective numerical matrix rank, which is the number of nonnegligible singular values.
java.lang.String	toString() Returns a String with (propertyName, propertyValue) pairs.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

SingularValueDecomposition

public SingularValueDecomposition(DoubleMatrix2D Arg)

Constructs and returns a new singular value decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.

Parameters:

A - A rectangular matrix.

Throws:

java.lang.IllegalArgumentException - if A.rows() < A.columns().

Method Detail

cond

public double cond()

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

getS

public DoubleMatrix2D getS()

Returns the diagonal matrix of singular values.

Returns:

S

getSingularValues

public double[] getSingularValues()

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

Returns:

diagonal of S.

getU

public DoubleMatrix2D getU()

Returns the left singular vectors U.

Returns:

U

getV

public DoubleMatrix2D getV()

Returns the right singular vectors V.

Returns:

V

norm2

public double norm2()

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

rank

public int rank()

Returns the effective numerical matrix rank, which is the number of nonnegligible singular values.

toString

public java.lang.String toString()

Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,

rank          : 3
trace         : 0

Overrides:

toString in class java.lang.Object