QRDecomposition
Jama

## Class QRDecomposition

• All Implemented Interfaces:
Serializable

```public class QRDecomposition
extends Object
implements 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
• ### Constructor Summary

Constructors
Constructor and Description
`QRDecomposition(Matrix A)`
QR Decomposition, computed by Householder reflections.
• ### Method Summary

Methods
Modifier and Type Method and Description
`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

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### 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.