QRDecomposition (patrius 4.5.1 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- the solve and isFullRank methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.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()` Simple constructor.
`QRDecomposition(double thresholdIn)` Constructor used to set the singularity threshold.
`QRDecomposition(RealMatrix matrix)` Simple constructor.
`QRDecomposition(RealMatrix matrix, double thresholdIn)` Constructor used to set the singularity threshold.

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.
`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, double[][] matrix)` 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()
```
    Simple constructor. The singularity threshold defaults to zero.
    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.
    
    See Also:
    
    QRDecomposition(double)
  - QRDecomposition
```
public QRDecomposition(double thresholdIn)
```
    Constructor used to set the singularity threshold.
    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.
    
    Parameters:
    
    thresholdIn - Singularity threshold.
  - QRDecomposition
```
public QRDecomposition(RealMatrix matrix)
```
    Simple constructor. The singularity threshold defaults to zero.
    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.
    
    See Also:
    
    QRDecomposition(double)
  - QRDecomposition
```
public QRDecomposition(RealMatrix matrix,
                       double thresholdIn)
```
    Constructor used to set the singularity threshold.
    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.
    
    thresholdIn - Singularity threshold.
- Method Detail
  - decompose
```
public void decompose(RealMatrix matrix)
```
    Run the decomposition process on the input matrix.
    Calculates the QR-decomposition of the given matrix.
    
    The QR decomposition of a matrix A is calculated using Householder reflectors by repeating the following operations to each minor A(minor,minor) of A.
    
    Specified by:
    
    decompose in interface Decomposition
    
    Parameters:
    
    matrix - The matrix to decompose.
  - performHouseholderReflection
```
protected void performHouseholderReflection(int minor,
                                            double[][] matrix)
```
    Perform Householder reflection for a minor A(minor, minor) of A.
    
    Parameters:
    
    minor - minor index
    
    matrix - transposed matrix
  - 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
  - checkDecompositionPerformed
```
public void checkDecompositionPerformed()
```
    Check decomposition has been performed.
    
    Throws:
    
    ArithmeticException - thrown if decomposition has not been performed yet

Class QRDecomposition

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

QRDecomposition

QRDecomposition

QRDecomposition

QRDecomposition

Method Detail

decompose

performHouseholderReflection

getR

getR

getQ

getQT

getH

getSolver

checkDecompositionPerformed