SingularValueDecomposition (math 8.0.4 API)

java.lang.Object
- de.gsi.math.matrix.SingularValueDecomposition

```
public class SingularValueDecomposition
extends Object
```
computes IN = U*S*V^T. With diag(S)={fEigenValues(0), fEigenValues(1),..,fEigenValues(n)} and V the fEigenVector matrix of IN
algorithm according to Golub and Reinsch G. Golub and C. Reinsch, "Handbook for Automatic Computation II, Linear Algebra". Springer, NY, 1971. numerically checked but... TODO: code clean up necessary... code as been translated from FORTRAN -> C -> C++ -> Java ;-)

Author:

rstein

Constructor Summary

Constructors
Constructor and Description

SingularValueDecomposition()
default constructor.

SingularValueDecomposition(MatrixD inputMatrix)
default constructor.

Constructors
Constructor and Description
`SingularValueDecomposition()` default constructor.
`SingularValueDecomposition(MatrixD inputMatrix)` default constructor.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`double`	`cond()` Two norm condition number
`boolean`	`decompose()` Perform the singular value decomposition.
`boolean`	`decompose(boolean useSquareMatrix)` Perform the singular value decomposition.
`MatrixD`	`getEigenSolution(int eigen)`
`MatrixD`	`getEigenValues()`
`MatrixD`	`getEigenVector(int eigen)`
`MatrixD`	`getEigenVectorMatrixU()`
`MatrixD`	`getEigenVectorMatrixV()`
`MatrixD`	`getInverse()`
`MatrixD`	`getInverse(boolean timer, int nEigenValues)`
`MatrixD`	`getMatrix()`
`MatrixD`	`getPseudoInverseEigenvalues()`
`double[]`	`getSingularValues()`
`double`	`getThreshold()`
`double`	`getTol()`
`MatrixD`	`getU()`
`MatrixD`	`getV()`
`static void`	`main(String[] argc)` some small test routines to check SVD matrix computation.
`double`	`norm2()` Deprecated. used only in old implementation
`int`	`rank()` Effective numerical matrix rank
`void`	`setMatrix(MatrixD inputMatrix)` Sets the input matrix to be decomposed.
`void`	`setThreshold(double val)`
`void`	`setTol(double val)`
`boolean`	`testInvert()` Test of 'inputMatrix'*'pseudo-inverse SVD matrix' == 1.
`boolean`	`testInvert(double threshold)` Test of 'inputMatrix'*'pseudo-inverse SVD matrix' == '1' matrix.
`boolean`	`testSVD()` Tests whether 'inputMatrix' == 'SVD decomposed matrix'.
`boolean`	`testSVD(double threshold)` Tests whether 'inputMatrix' == 'SVD decomposed matrix'.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - SingularValueDecomposition
```
public SingularValueDecomposition()
```
    default constructor.
  - SingularValueDecomposition
```
public SingularValueDecomposition(MatrixD inputMatrix)
```
    default constructor.
    
    Parameters:
    
    inputMatrix - the preset input matrix to be decomposed
- Method Detail
  - setThreshold
```
public void setThreshold(double val)
```
  - getThreshold
```
public double getThreshold()
```
  - setTol
```
public void setTol(double val)
```
  - getTol
```
public double getTol()
```
  - getEigenValues
```
public MatrixD getEigenValues()
```
  - getSingularValues
```
public double[] getSingularValues()
```
  - getPseudoInverseEigenvalues
```
public MatrixD getPseudoInverseEigenvalues()
```
  - getEigenVectorMatrixV
```
public MatrixD getEigenVectorMatrixV()
```
    Returns:
    
    the eigenvector matrix V (n x n)
  - getV
```
public MatrixD getV()
```
    Returns:
    
    the eigenvector matrix V (n x n)
  - getEigenVectorMatrixU
```
public MatrixD getEigenVectorMatrixU()
```
    Returns:
    
    the eigenvector matrix U (m x n)
  - getU
```
public MatrixD getU()
```
    Returns:
    
    the eigenvector matrix U (n x n)
  - setMatrix
```
public void setMatrix(MatrixD inputMatrix)
```
    Sets the input matrix to be decomposed.
    
    Parameters:
    
    inputMatrix - the input matrix
  - decompose
```
public boolean decompose()
```
    Perform the singular value decomposition. (does not use intermediate square matrices)
    
    Returns:
    
    true if operation was successful, false otherwise
  - decompose
```
public boolean decompose(boolean useSquareMatrix)
```
    Perform the singular value decomposition.
    
    Parameters:
    
    useSquareMatrix - whether to use intermediate step of transforming the input matrix to a square one.
    
    Returns:
    
    true if operation was successful, false otherwise
  - getMatrix
```
public MatrixD getMatrix()
```
  - getInverse
```
public MatrixD getInverse()
```
  - getInverse
```
public MatrixD getInverse(boolean timer,
                          int nEigenValues)
```
  - getEigenVector
```
public MatrixD getEigenVector(int eigen)
```
  - getEigenSolution
```
public MatrixD getEigenSolution(int eigen)
```
  - norm2
```
@Deprecated
public double norm2()
```
    Deprecated. used only in old implementation
    
    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 non-negligible singular values.
  - testSVD
```
public boolean testSVD()
```
    Tests whether 'inputMatrix' == 'SVD decomposed matrix'. assumes default numerical precision threshold,
    
    Returns:
    
    true if test successful, false otherwise
    
    See Also:
    
    for more info
  - testSVD
```
public boolean testSVD(double threshold)
```
    Tests whether 'inputMatrix' == 'SVD decomposed matrix'.
    
    Parameters:
    
    threshold - the numerical threshold for the test
    
    Returns:
    
    true if test successful, false otherwise
  - testInvert
```
public boolean testInvert()
```
    Test of 'inputMatrix'*'pseudo-inverse SVD matrix' == 1. only works for non-singular matrices
    
    Returns:
    
    true if test successful, false otherwise
    
    See Also:
    
    for more info
  - testInvert
```
public boolean testInvert(double threshold)
```
    Test of 'inputMatrix'*'pseudo-inverse SVD matrix' == '1' matrix. only works for non-singular matrices
    
    Parameters:
    
    threshold - the numerical threshold for the test
    
    Returns:
    
    true if test successful, false otherwise
  - main
```
public static void main(String[] argc)
```
    some small test routines to check SVD matrix computation.
    
    Parameters:
    
    argc - the input parameter (unused)

Class SingularValueDecomposition

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

SingularValueDecomposition

SingularValueDecomposition

Method Detail

setThreshold

getThreshold

setTol

getTol

getEigenValues

getSingularValues

getPseudoInverseEigenvalues

getEigenVectorMatrixV

getV

getEigenVectorMatrixU

getU

setMatrix

decompose

decompose

getMatrix

getInverse

getInverse

getEigenVector

getEigenSolution

norm2

cond

rank

testSVD

testSVD

testInvert

testInvert

main