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## de.lmu.ifi.dbs.elki.math.linearalgebra Class QRDecomposition

```java.lang.Object
de.lmu.ifi.dbs.elki.math.linearalgebra.QRDecomposition
```
All Implemented Interfaces:
Serializable

`public class QRDecompositionextends Objectimplements Serializable`

QR Decomposition.

For an m-by-n matrix A with m >= n, the QR decomposition is an m-by-n orthogonal matrix Q and an n-by-n upper triangular matrix R so that A = Q*R.

The QR decompostion always exists, even if the matrix does not have full rank, so the constructor will never fail. The primary use of the QR decomposition is in the least squares solution of nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.

Serialized Form

Field Summary
`private  int` `m`
Row and column dimensions.
`private  int` `n`
Row and column dimensions.
`private  double[][]` `QR`
Array for internal storage of decomposition.
`private  double[]` `Rdiag`
Array for internal storage of diagonal of R.

Constructor Summary
`QRDecomposition(Matrix A)`
QR Decomposition, computed by Householder reflections.

Method Summary
` Matrix` `getH()`
Return the Householder vectors
` Matrix` `getQ()`
Generate and return the (economy-sized) orthogonal factor
` Matrix` `getR()`
Return the upper triangular factor
` boolean` `isFullRank()`
Is the matrix full rank?
` Matrix` `solve(Matrix B)`
Least squares solution of A*X = B

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Field Detail

### QR

`private double[][] QR`
Array for internal storage of decomposition.

### m

`private int m`
Row and column dimensions.

### n

`private int n`
Row and column dimensions.

### Rdiag

`private double[] Rdiag`
Array for internal storage of diagonal of R.

Constructor Detail

### QRDecomposition

`public QRDecomposition(Matrix A)`
QR Decomposition, computed by Householder reflections.

Parameters:
`A` - Rectangular matrix
Method Detail

### isFullRank

`public boolean isFullRank()`
Is the matrix full rank?

Returns:
true if R, and hence A, has full rank.

### getH

`public Matrix getH()`
Return the Householder vectors

Returns:
Lower trapezoidal matrix whose columns define the reflections

### getR

`public Matrix getR()`
Return the upper triangular factor

Returns:
R

### getQ

`public Matrix getQ()`
Generate and return the (economy-sized) orthogonal factor

Returns:
Q

### solve

`public Matrix solve(Matrix B)`
Least squares solution of A*X = B

Parameters:
`B` - A Matrix with as many rows as A and any number of columns.
Returns:
X that minimizes the two norm of Q*R*X-B.
Throws:
`IllegalArgumentException` - Matrix row dimensions must agree.
`RuntimeException` - Matrix is rank deficient.

 Release 0.2 (2009-07-06_1820)