QRDecomposition (math 11.1.5 API)

java.lang.Object
- de.gsi.math.matrix.QRDecomposition

All Implemented Interfaces:

java.io.Serializable
```
public class QRDecomposition
extends java.lang.Object
implements java.io.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 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 nonsquare systems of simultaneous linear equations. This will fail if isFullRank() returns false.

See Also:

Serialized Form

Constructor Summary

Constructors
Constructor Description

QRDecomposition(MatrixD A)
QR Decomposition, computed by Householder reflections.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`MatrixD`	`getH()`	Return the Householder vectors
`MatrixD`	`getQ()`	Generate and return the (economy-sized) orthogonal factor
`MatrixD`	`getR()`	Return the upper triangular factor
`boolean`	`isFullRank()`	Is the matrix full rank?
`MatrixD`	`solve(MatrixD 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

- Constructor Detail
  - QRDecomposition
```
public QRDecomposition(MatrixD A)
```
    QR Decomposition, computed by Householder reflections.
    
    Parameters:
    
    A - Rectangular matrix Structure to access R and the Householder vectors and compute Q.
- Method Detail
  - getH
```
public MatrixD getH()
```
    Return the Householder vectors
    
    Returns:
    
    Lower trapezoidal matrix whose columns define the reflections
  - getQ
```
public MatrixD getQ()
```
    Generate and return the (economy-sized) orthogonal factor
    
    Returns:
    
    Q
  - getR
```
public MatrixD getR()
```
    Return the upper triangular factor
    
    Returns:
    
    R
  - isFullRank
```
public boolean isFullRank()
```
    Is the matrix full rank?
    
    Returns:
    
    true if R, and hence A, has full rank.
  - solve
```
public MatrixD solve(MatrixD 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:
    
    java.lang.IllegalArgumentException - Matrix row dimensions must agree.
    
    java.lang.RuntimeException - Matrix is rank deficient.