QRDecomposition (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.linear.QRDecomposition

Direct Known Subclasses:

RRQRDecomposition
```
public class QRDecomposition
extends Object
```
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- the solve and isFullRank methods have been replaced by a getSolver method and the equivalent methods provided by the returned DecompositionSolver.
Since:

1.2 (changed to concrete class in 3.0)

See Also:
MathWorld, Wikipedia

Constructor Summary

Constructors
Constructor and Description
`QRDecomposition(RealMatrix matrix)` Calculates the QR-decomposition of the given matrix.
`QRDecomposition(RealMatrix matrix, double threshold)` Calculates the QR-decomposition of the given matrix.

Method Summary

Methods
Modifier and Type	Method and Description
`protected void`	`decompose(double[][] matrix)` Decompose 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.
`DecompositionSolver`	`getSolver()` Get a solver for finding the A × X = B solution in least square 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(RealMatrix matrix)
```
    Calculates the QR-decomposition of the given matrix. The singularity threshold defaults to zero.
    
    Parameters:
    matrix - The matrix to decompose.
    See Also:
    QRDecomposition(RealMatrix,double)
  - QRDecomposition
```
public QRDecomposition(RealMatrix matrix,
               double threshold)
```
    Calculates the QR-decomposition of the given matrix.
    
    Parameters:
    matrix - The matrix to decompose.
    threshold - Singularity threshold.
- Method Detail
  - decompose
```
protected void decompose(double[][] matrix)
```
    Decompose matrix.
    
    Parameters:
    matrix - transposed matrix
    Since:
    
    3.2
  - 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
    Since:
    
    3.2
  - getR
```
public RealMatrix getR()
```
    Returns the matrix R of the decomposition.
    R is an upper-triangular matrix
    
    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()
```
    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.
    
    Returns:
    a solver

Class QRDecomposition

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

QRDecomposition

QRDecomposition

Method Detail

decompose

performHouseholderReflection

getR

getQ

getQT

getH

getSolver