AbstractSingularValueDecomposition (Cognitive Foundry)

java.lang.Object
- gov.sandia.cognition.math.matrix.decomposition.AbstractSingularValueDecomposition

All Implemented Interfaces:: SingularValueDecomposition

Direct Known Subclasses:: SingularValueDecompositionMTJ

@CodeReview(reviewer="Jonathan McClain",
            date="2006-05-16",
            changesNeeded=false,
            comments={"Made very minor changes.","Otherwise, looks fine."})
public abstract class AbstractSingularValueDecomposition
extends java.lang.Object
implements SingularValueDecomposition

Abstract container class that stores the matrices for a Singular Value Decomposition (SVD) and related operations but does not actually perform a singular value decomposition

Since:: 1.0
Author:: Kevin R. Dixon

Constructor Summary

Constructors
Constructor and Description
`AbstractSingularValueDecomposition()` Default constructor that nulls out all matrices
`AbstractSingularValueDecomposition(Matrix U, Matrix S, Matrix Vtranspose)` Creates a new instance of AbstractSingularValueDecomposition where USVtranspose = original_matrix

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`conditionNumber()` Returns the condition number of the underlying matrix, which is simply the ratio of the largest to smallest singular value
`int`	`effectiveRank(double effectiveZero)` Returns the effective rank of the underlying matrix by counting the number of singular values whose values are larger than effectiveZero
`Matrix`	`getS()` Gets the PSD diagonal matrix containing the sorted singular values
`Matrix`	`getU()` Gets the orthonormal matrix containing the left singular vectors of the underlying matrix
`Matrix`	`getVtranspose()` Gets the transpose of the orthonormal matrix containing the right singular vectors of the underlying matrix
`double`	`norm2()` Returns the associated 2-norm (spectral norm) of the underlying matrix, which is simply the largest singular value
`Matrix`	`pseudoInverse()` Computes the Least Squares pseudoinverse of the underlying matrix
`Matrix`	`pseudoInverse(double effectiveZero)` Computes the Least Squares pseudoinverse of the underlying matrix, while clipping the singular values at effectiveZero
`int`	`rank()` Returns the rank of the underlying matrix by calling this.effectiveRank with an effectiveZero = 0.0
`protected void`	`setS(Matrix S)` setter for the singular values matrix
`protected void`	`setU(Matrix U)` setter for left singular vectors
`protected void`	`setVtranspose(Matrix Vtranspose)` sets the transpose of the right singular vectors matrix

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

- Constructor Detail
  - AbstractSingularValueDecomposition
```
public AbstractSingularValueDecomposition()
```
    Default constructor that nulls out all matrices
  - AbstractSingularValueDecomposition
```
public AbstractSingularValueDecomposition(Matrix U,
                                          Matrix S,
                                          Matrix Vtranspose)
```
    Creates a new instance of AbstractSingularValueDecomposition where U*S*Vtranspose = original_matrix
    
    Parameters:
    
    U - orthonormal matrix of left singular vectors
    
    S - PSD diagonal matrix of singular values, sorted in descending order
    
    Vtranspose - transpose of the orthonormal matrix of the right singular vectors
- Method Detail
  - getU
```
public Matrix getU()
```
    Description copied from interface: SingularValueDecomposition
    
    Gets the orthonormal matrix containing the left singular vectors of the underlying matrix
    
    Specified by:
    
    getU in interface SingularValueDecomposition
    
    Returns:
    
    U
  - setU
```
protected void setU(Matrix U)
```
    setter for left singular vectors
    
    Parameters:
    
    U - left singular vectors
  - getS
```
public Matrix getS()
```
    Description copied from interface: SingularValueDecomposition
    
    Gets the PSD diagonal matrix containing the sorted singular values
    
    Specified by:
    
    getS in interface SingularValueDecomposition
    
    Returns:
    
    S
  - setS
```
protected void setS(Matrix S)
```
    setter for the singular values matrix
    
    Parameters:
    
    S - singular values matrix
  - getVtranspose
```
public Matrix getVtranspose()
```
    Description copied from interface: SingularValueDecomposition
    
    Gets the transpose of the orthonormal matrix containing the right singular vectors of the underlying matrix
    
    Specified by:
    
    getVtranspose in interface SingularValueDecomposition
    
    Returns:
    
    Vtranspose
  - setVtranspose
```
protected void setVtranspose(Matrix Vtranspose)
```
    sets the transpose of the right singular vectors matrix
    
    Parameters:
    
    Vtranspose - transpose of the right singular vectors matrix
  - norm2
```
public double norm2()
```
    Description copied from interface: SingularValueDecomposition
    
    Returns the associated 2-norm (spectral norm) of the underlying matrix, which is simply the largest singular value
    
    Specified by:
    
    norm2 in interface SingularValueDecomposition
    
    Returns:
    
    Largest singular value on the interval [0.0, inf)
  - conditionNumber
```
public double conditionNumber()
```
    Description copied from interface: SingularValueDecomposition
    
    Returns the condition number of the underlying matrix, which is simply the ratio of the largest to smallest singular value
    
    Specified by:
    
    conditionNumber in interface SingularValueDecomposition
    
    Returns:
    
    Condition number on the interval [1.0, inf]
  - rank
```
public int rank()
```
    Description copied from interface: SingularValueDecomposition
    
    Returns the rank of the underlying matrix by calling this.effectiveRank with an effectiveZero = 0.0
    
    Specified by:
    
    rank in interface SingularValueDecomposition
    
    Returns:
    
    rank of the underlying matrix
  - effectiveRank
```
public int effectiveRank(double effectiveZero)
```
    Description copied from interface: SingularValueDecomposition
    
    Returns the effective rank of the underlying matrix by counting the number of singular values whose values are larger than effectiveZero
    
    Specified by:
    
    effectiveRank in interface SingularValueDecomposition
    
    Parameters:
    
    effectiveZero - threshold for considering a singular value to be zero
    
    Returns:
    
    effective rank of the underlying matrix
  - pseudoInverse
```
public Matrix pseudoInverse()
```
    Description copied from interface: SingularValueDecomposition
    
    Computes the Least Squares pseudoinverse of the underlying matrix
    
    Specified by:
    
    pseudoInverse in interface SingularValueDecomposition
    
    Returns:
    
    pseudoinverse of the underlying matrix: V * pinv(S) * U'
  - pseudoInverse
```
public Matrix pseudoInverse(double effectiveZero)
```
    Description copied from interface: SingularValueDecomposition
    
    Computes the Least Squares pseudoinverse of the underlying matrix, while clipping the singular values at effectiveZero
    
    Specified by:
    
    pseudoInverse in interface SingularValueDecomposition
    
    Parameters:
    
    effectiveZero - value below which to consider the singular values zero
    
    Returns:
    
    pseudoinverse of the underlying matrix: V * pinv(S,effectiveZero) * U'

Class AbstractSingularValueDecomposition

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

AbstractSingularValueDecomposition

AbstractSingularValueDecomposition

Method Detail

getU

setU

getS

setS

getVtranspose

setVtranspose

norm2

conditionNumber

rank

effectiveRank

pseudoInverse

pseudoInverse