## org.apache.commons.math3.linear Class QRDecomposition

```java.lang.Object
org.apache.commons.math3.linear.QRDecomposition
```
Direct Known Subclasses:
RRQRDecomposition

`public class QRDecompositionextends 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 1462423 2013-03-29 07:25:18Z luc \$
See Also:
MathWorld, Wikipedia

Constructor Summary
`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
`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, QT

### 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

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