SingularValueDecomposition (patrius 4.5.1 API)

java.lang.Object
- fr.cnes.sirius.patrius.math.linear.SingularValueDecomposition

All Implemented Interfaces:

Decomposition
```
public class SingularValueDecomposition
extends Object
implements Decomposition
```
Calculates the compact Singular Value Decomposition of a matrix.
The Singular Value Decomposition of matrix A is a set of three matrices: U, Σ and V such that A = U × Σ × V^T. Let A be a m × n matrix, then U is a m × p orthogonal matrix, Σ is a p × p diagonal matrix with positive or null elements, V is a p × n orthogonal matrix (hence V^T is also orthogonal) where p=min(m,n).

This class is similar to the class with similar name from the JAMA library, with the following changes:
- the norm2 method which has been renamed as getNorm,
- the cond method which has been renamed as getConditionNumber,
- the rank method which has been renamed as getRank,
- a getUT method has been added,
- a getVT method has been added,
- a getSolver method has been added,
- a getCovariance method has been added.
This class is up-to-date with commons-math 3.6.1.
Since:

2.0 (changed to concrete class in 3.0)

Version:

$Id: SingularValueDecomposition.java 18108 2017-10-04 06:45:27Z bignon $

See Also:

MathWorld, Wikipedia

Constructor Summary

Constructors
Constructor and Description

SingularValueDecomposition()
Simple constructor.

SingularValueDecomposition(RealMatrix matrix)
Simple constructor.

Constructors
Constructor and Description
`SingularValueDecomposition()` Simple constructor.
`SingularValueDecomposition(RealMatrix matrix)` Simple constructor.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`void`	`checkDecompositionPerformed()` Check decomposition has been performed.
`void`	`decompose(RealMatrix matrix)` Run the decomposition process on the input matrix.
`double`	`getConditionNumber()` Return the condition number of the matrix.
`RealMatrix`	`getCovariance(double minSingularValue)` Returns the n × n covariance matrix.
`double`	`getInverseConditionNumber()` Computes the inverse of the condition number.
`double`	`getNorm()` Returns the L₂ norm of the matrix.
`int`	`getRank()` Return the effective numerical matrix rank.
`RealMatrix`	`getS()` Returns the diagonal matrix Σ of the decomposition.
`double[]`	`getSingularValues()` Returns the diagonal elements of the matrix Σ of the decomposition.
`DecompositionSolver`	`getSolver()` Gets a solver for finding the A × X = B solution in exact linear sense.
`RealMatrix`	`getU()` Returns the matrix U of the decomposition.
`RealMatrix`	`getUT()` Returns the transpose of the matrix U of the decomposition.
`RealMatrix`	`getV()` Returns the matrix V of the decomposition.
`RealMatrix`	`getVT()` Returns the transpose of the matrix V of the decomposition.

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

- Constructor Detail
  - SingularValueDecomposition
```
public SingularValueDecomposition()
```
    Simple constructor.
    Once the decomposition object is built, the method decompose(RealMatrix) needs to be called on the expected matrix to run the decomposition process before calling any others methods. Otherwise the data won't be initialize.
  - SingularValueDecomposition
```
public SingularValueDecomposition(RealMatrix matrix)
```
    Simple constructor.
    The decomposition is directly computed on the input matrix. There is no need to run the method decompose(RealMatrix) separately.
    
    Parameters:
    
    matrix - The matrix to decompose.
- Method Detail
  - decompose
```
public void decompose(RealMatrix matrix)
```
    Run the decomposition process on the input matrix.
    Calculates the compact Singular Value Decomposition of the given matrix.
    
    Specified by:
    
    decompose in interface Decomposition
    
    Parameters:
    
    matrix - The matrix to decompose.
  - getU
```
public RealMatrix getU()
```
    Returns the matrix U of the decomposition.
    U is an orthogonal matrix, i.e. its transpose is also its inverse.
    
    Returns:
    
    the U matrix
    
    See Also:
    
    getUT()
  - getUT
```
public RealMatrix getUT()
```
    Returns the transpose of the matrix U of the decomposition.
    U is an orthogonal matrix, i.e. its transpose is also its inverse.
    
    Returns:
    
    the transpose of the U matrix
    
    See Also:
    
    getU()
  - getS
```
public RealMatrix getS()
```
    Returns the diagonal matrix Σ of the decomposition.
    Σ is a diagonal matrix. The singular values are provided in non-increasing order, for compatibility with Jama.
    
    Returns:
    
    the Σ matrix
  - getSingularValues
```
public double[] getSingularValues()
```
    Returns the diagonal elements of the matrix Σ of the decomposition.
    The singular values are provided in non-increasing order, for compatibility with Jama.
    
    Returns:
    
    the diagonal elements of the Σ matrix
  - getV
```
public RealMatrix getV()
```
    Returns the matrix V of the decomposition.
    V is an orthogonal matrix, i.e. its transpose is also its inverse.
    
    Returns:
    
    the V matrix (or null if decomposed matrix is singular)
    
    See Also:
    
    getVT()
  - getVT
```
public RealMatrix getVT()
```
    Returns the transpose of the matrix V of the decomposition.
    V is an orthogonal matrix, i.e. its transpose is also its inverse.
    
    Returns:
    
    the V matrix
    
    See Also:
    
    getV()
  - getCovariance
```
public RealMatrix getCovariance(double minSingularValue)
```
    Returns the n × n covariance matrix.
    The covariance matrix is V × J × V^T where J is the diagonal matrix of the inverse of the squares of the singular values.
    
    Parameters:
    
    minSingularValue - value below which singular values are ignored (a 0 or negative value implies all singular value will be used)
    
    Returns:
    
    covariance matrix
    
    Throws:
    
    IllegalArgumentException - if minSingularValue is larger than the largest singular value, meaning all singular values are ignored
  - getNorm
```
public double getNorm()
```
    Returns the L₂ norm of the matrix.
    The L₂ norm is max(|A × u|₂ / |u|₂), where |.|₂ denotes the vectorial 2-norm (i.e. the traditional euclidian norm).
    
    Returns:
    
    norm
  - getConditionNumber
```
public double getConditionNumber()
```
    Return the condition number of the matrix.
    
    Returns:
    
    condition number of the matrix
  - getInverseConditionNumber
```
public double getInverseConditionNumber()
```
    Computes the inverse of the condition number. In cases of rank deficiency, the condition number will become undefined.
    
    Returns:
    
    the inverse of the condition number.
  - getRank
```
public int getRank()
```
    Return the effective numerical matrix rank.
    The effective numerical rank is the number of non-negligible singular values. The threshold used to identify non-negligible terms is max(m,n) × ulp(s₁) where ulp(s₁) is the least significant bit of the largest singular value.
    
    Returns:
    
    effective numerical matrix rank
  - getSolver
```
public DecompositionSolver getSolver()
```
    Gets a solver for finding the A × X = B solution in exact linear sense.
    
    Specified by:
    
    getSolver in interface Decomposition
    
    Returns:
    
    the decomposition solver.
  - checkDecompositionPerformed
```
public void checkDecompositionPerformed()
```
    Check decomposition has been performed.
    
    Throws:
    
    ArithmeticException - thrown if decomposition has not been performed yet

Class SingularValueDecomposition

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

SingularValueDecomposition

SingularValueDecomposition

Method Detail

decompose

getU

getUT

getS

getSingularValues

getV

getVT

getCovariance

getNorm

getConditionNumber

getInverseConditionNumber

getRank

getSolver

checkDecompositionPerformed