Documentation API of the 'jhplot.math.SingularValueDecomposition' Java class
SingularValueDecomposition
jhplot.math

## Class SingularValueDecomposition

• `public class SingularValueDecompositionextends Object`
Singular Value Decomposition.

For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-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 decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.

• ### Constructor Summary

Constructors
Constructor and Description
`SingularValueDecomposition(double[][] Arg)`
Construct the singular value decomposition
• ### Method Summary

All Methods
Modifier and TypeMethod and Description
`double``cond()`
Two norm condition number
`double[][]``getS()`
Return the diagonal matrix of singular values
`double[]``getSingularValues()`
Return the one-dimensional array of singular values
`double[][]``getU()`
Return the left singular vectors
`double[][]``getV()`
Return the right singular vectors
`double``norm2()`
Two norm
`int``rank()`
Effective numerical matrix rank
• ### Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### SingularValueDecomposition

`public SingularValueDecomposition(double[][] Arg)`
Construct the singular value decomposition
Parameters:
`Arg` - Rectangular matrix
• ### Method Detail

• #### getU

`public double[][] getU()`
Return the left singular vectors
Returns:
U
• #### getV

`public double[][] getV()`
Return the right singular vectors
Returns:
V
• #### getSingularValues

`public double[] getSingularValues()`
Return the one-dimensional array of singular values
Returns:
diagonal of S.
• #### getS

`public double[][] getS()`
Return the diagonal matrix of singular values
Returns:
S
• #### norm2

`public double norm2()`
Two norm
Returns:
max(S)
• #### cond

`public double cond()`
Two norm condition number
Returns:
max(S)/min(S)
• #### rank

`public int rank()`
Effective numerical matrix rank
Returns:
Number of nonnegligible singular values.

DMelt 1.2 © DataMelt by jWork.ORG

SingularValueDecomposition
jhplot.math

## Class SingularValueDecomposition

• `public class SingularValueDecompositionextends Object`
Singular Value Decomposition.

For an m-by-n matrix A with m >= n, the singular value decomposition is an m-by-n orthogonal matrix U, an n-by-n diagonal matrix S, and an n-by-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 decompostion always exists, so the constructor will never fail. The matrix condition number and the effective numerical rank can be computed from this decomposition.

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