cern.colt.matrix.tdouble.algo.decomposition

Class DenseDoubleSingularValueDecomposition

java.lang.Object

cern.colt.matrix.tdouble.algo.decomposition.DenseDoubleSingularValueDecomposition

public class DenseDoubleSingularValueDecomposition
extends Object

For an m x n matrix A, the singular value decomposition is an m x m orthogonal matrix U, an m 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[min(m-1,n-1)].

This implementation uses the divide-and-conquer algorithm (dgesdd) from LAPACK.

Author:

Piotr Wendykier (piotr.wendykier@gmail.com)

Constructor Summary

Constructors

Constructor and Description
DenseDoubleSingularValueDecomposition(DoubleMatrix2D A, boolean wantUV, boolean wantWholeUV) 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

Methods

Modifier and Type	Method and Description
double	cond() Returns the two norm condition number, which is max(S) / min(S).
org.netlib.util.intW	getInfo() Returns the output flag
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.
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

DenseDoubleSingularValueDecomposition

public DenseDoubleSingularValueDecomposition(DoubleMatrix2D A,
                                     boolean wantUV,
                                     boolean wantWholeUV)

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 - rectangular matrix

wantUV - if true then all matrices (U, S, V') are computed; otherwise only S is computed

wantWholeUV - if true then all m columns of U and all n rows of V' are computed; otherwise only the first min(m,n) columns of U and the first min(m,n) rows of V' are computed

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

getInfo

public org.netlib.util.intW getInfo()

Returns the output flag

Returns:

0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: process did not converge.

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 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 Object