org.apache.commons.math.linear

## Class QRDecompositionImpl

• java.lang.Object
• org.apache.commons.math.linear.QRDecompositionImpl
• All Implemented Interfaces:
QRDecomposition

```public class QRDecompositionImpl
extends java.lang.Object
implements QRDecomposition```
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.

Since:
1.2
MathWorld, Wikipedia
• ### Constructor Summary

Constructors
Constructor and Description
`QRDecompositionImpl(RealMatrix matrix)`
Calculates the QR-decomposition of the given matrix.
• ### Method Summary

All 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

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### QRDecompositionImpl

`public QRDecompositionImpl(RealMatrix matrix)`
Calculates the QR-decomposition of the given matrix.
Parameters:
`matrix` - The matrix to decompose.
• ### Method Detail

• #### getR

`public RealMatrix getR()`
Returns the matrix R of the decomposition.

R is an upper-triangular matrix

Specified by:
`getR` in interface `QRDecomposition`
Returns:
the R matrix
• #### getQ

`public RealMatrix getQ()`
Returns the matrix Q of the decomposition.

Q is an orthogonal matrix

Specified by:
`getQ` in interface `QRDecomposition`
Returns:
the Q matrix
• #### getQT

`public RealMatrix getQT()`
Returns the transpose of the matrix Q of the decomposition.

Q is an orthogonal matrix

Specified by:
`getQT` in interface `QRDecomposition`
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.

Specified by:
`getH` in interface `QRDecomposition`
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.
Specified by:
`getSolver` in interface `QRDecomposition`
Returns:
a solver