QRDecomposition (patrimoine de base SIRIUS 4.13 API)

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

All Implemented Interfaces:

Decomposition
```
public class QRDecomposition
extends Object
implements Decomposition
```
Calculates the QR-decomposition of a matrix.
The QR-decomposition of a matrix A consists of two matrices Q and R that satisfy: A = QR, Q is orthogonal (Q^TQ = I), and R is upper triangular. If A is m×n, Q is m×m and R m×n.

This class compute the decomposition using Householder reflectors.

For efficiency purposes, the decomposition in packed form is transposed. This allows inner loop to iterate inside rows, which is much more cache-efficient in Java.

This class is based on the class with similar name from the JAMA library, with the following changes:
- a getQT method has been added,
- the solve and isFullRank methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.
This class is up-to-date with commons-math 3.6.1.
Since:

1.2 (changed to concrete class in 3.0)

Version:

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

See Also:

MathWorld, Wikipedia

Constructor Summary

Constructors
Constructor and Description
`QRDecomposition(RealMatrix matrix)` Simple constructor.
`QRDecomposition(RealMatrix matrix, double thresholdIn)` Constructor used to set the singularity threshold.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`static Function<RealMatrix,Decomposition>`	`decompositionBuilder(double thresholdIn)` Builder for decomposition.
`RealMatrix`	`getH()` Returns the Householder reflector vectors.
`RealMatrix`	`getQ()` Returns the matrix Q of the decomposition.
`RealMatrix`	`getQT()` Returns the transpose of the matrix Q of the decomposition.
`RealMatrix`	`getR()` Returns the matrix R of the decomposition.
`RealMatrix`	`getR(boolean compactForm)` Returns the matrix R of the decomposition in its compact form (n × n) or in its full form (m × n).
`DecompositionSolver`	`getSolver()` Gets a solver for finding the A × X = B solution in exact linear sense.
`protected void`	`performHouseholderReflection(int minor)` Perform Householder reflection for a minor A(minor, minor) of A.

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

- Constructor Detail
  - QRDecomposition
```
public QRDecomposition(RealMatrix matrix)
```
    Simple constructor. The singularity threshold defaults to zero.
    The decomposition is directly computed on the input matrix
    
    Parameters:
    
    matrix - The matrix to decompose.
    
    See Also:
    
    QRDecomposition(RealMatrix, double)
  - QRDecomposition
```
public QRDecomposition(RealMatrix matrix,
                       double thresholdIn)
```
    Constructor used to set the singularity threshold.
    The decomposition is directly computed on the input matrix
    
    Parameters:
    
    matrix - The matrix to decompose.
    
    thresholdIn - Singularity threshold.
- Method Detail
  - performHouseholderReflection
```
protected void performHouseholderReflection(int minor)
```
    Perform Householder reflection for a minor A(minor, minor) of A.
    
    Parameters:
    
    minor - minor index
  - getR
```
public RealMatrix getR()
```
    Returns the matrix R of the decomposition. By default, this method returns the full form (n × m) of the matrix R.
    R is an upper-triangular matrix
    
    Returns:
    
    the R matrix
  - getR
```
public RealMatrix getR(boolean compactForm)
```
    Returns the matrix R of the decomposition in its compact form (n × n) or in its full form (m × n).
    R is an upper-triangular matrix
    
    Parameters:
    
    compactForm - if true R dimensions will be n × n, else R dimensions will be m × n
    
    Returns:
    
    the R matrix
  - getQ
```
public RealMatrix getQ()
```
    Returns the matrix Q of the decomposition.
    Q is an orthogonal matrix
    
    Returns:
    
    the Q matrix
  - getQT
```
public RealMatrix getQT()
```
    Returns the transpose of the matrix Q of the decomposition.
    Q is an orthogonal matrix
    
    Returns:
    
    the transpose of the Q matrix, Q^T
  - getH
```
public RealMatrix getH()
```
    Returns the Householder reflector vectors.
    H is a lower trapezoidal matrix whose columns represent each successive Householder reflector vector. This matrix is used to compute Q.
    
    Returns:
    
    a matrix containing the Householder reflector vectors
  - getSolver
```
public DecompositionSolver getSolver()
```
    Gets a solver for finding the A × X = B solution in exact linear sense. Get a solver for finding the A × X = B solution in least square sense.
    Least Square sense means a solver can be computed for an overdetermined system, (i.e. a system with more equations than unknowns, which corresponds to a tall A matrix with more rows than columns). In any case, if the matrix is singular within the tolerance set at construction, an error will be triggered when the solve method will be called.
    
    Specified by:
    
    getSolver in interface Decomposition
    
    Returns:
    
    a solver
  - decompositionBuilder
```
public static Function<RealMatrix,Decomposition> decompositionBuilder(double thresholdIn)
```
    Builder for decomposition.
    
    Parameters:
    
    thresholdIn - Singularity threshold.
    
    Returns:
    
    decomposition

Class QRDecomposition

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

QRDecomposition

QRDecomposition

Method Detail

performHouseholderReflection

getR

getR

getQ

getQT

getH

getSolver

decompositionBuilder