org.apache.mahout.math

## Class QRDecomposition

• All Implemented Interfaces:
QR

```public class QRDecomposition
extends Object
implements QR```
For an m x n matrix A with `m >= n`, the QR decomposition is an m x n orthogonal matrix Q and an n x n upper triangular matrix R so that A = Q*R.

The QR decomposition 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 non-square systems of simultaneous linear equations. This will fail if isFullRank() returns false.

• ### Constructor Summary

Constructors
Constructor and Description
`QRDecomposition(Matrix a)`
Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
• ### Method Summary

All Methods
Modifier and Type Method and Description
`Matrix` `getQ()`
Generates and returns the (economy-sized) orthogonal factor Q.
`Matrix` `getR()`
Returns the upper triangular factor, R.
`boolean` `hasFullRank()`
Returns whether the matrix A has full rank.
`Matrix` `solve(Matrix B)`
Least squares solution of A*X = B; returns X.
`String` `toString()`
Returns a rough string rendition of a QR.
• ### Methods inherited from class java.lang.Object

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

• #### QRDecomposition

`public QRDecomposition(Matrix a)`
Constructs and returns a new QR decomposition object; computed by Householder reflections; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
Parameters:
`a` - A rectangular matrix.
Throws:
`IllegalArgumentException` - if `A.rows() < A.columns()`.
• ### Method Detail

• #### getQ

`public Matrix getQ()`
Generates and returns the (economy-sized) orthogonal factor Q.
Specified by:
`getQ` in interface `QR`
Returns:
Q
• #### getR

`public Matrix getR()`
Returns the upper triangular factor, R.
Specified by:
`getR` in interface `QR`
Returns:
R
• #### hasFullRank

`public boolean hasFullRank()`
Returns whether the matrix A has full rank.
Specified by:
`hasFullRank` in interface `QR`
Returns:
true if R, and hence A, has full rank.
• #### solve

`public Matrix solve(Matrix B)`
Least squares solution of A*X = B; returns X.
Specified by:
`solve` in interface `QR`
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` - if B.rows() != A.rows().
• #### toString

`public String toString()`
Returns a rough string rendition of a QR.
Overrides:
`toString` in class `Object`