org.apache.commons.math3.linear

## Class QRDecomposition

• ```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 (QTQ = 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:

Since:
1.2 (changed to concrete class in 3.0)
Version:
\$Id: QRDecomposition.java 1244107 2012-02-14 16:17:55Z erans \$
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
`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.
• ### 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.
`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

• #### 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 Q matrix
• #### 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.
Returns:
a solver