**'jhplot.math.QRDecomposition'**Java class

jhplot.math

## Class QRDecomposition

- java.lang.Object
- jhplot.math.QRDecomposition

public class QRDecompositionextends Object

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.

### Constructor Summary

Constructors Constructor and Description **QRDecomposition**(double[][] A)QR Decomposition, computed by Householder reflections.

### Method Summary

Methods Modifier and Type Method and Description `double[][]`

**getH**()Return the Householder vectors`double[][]`

**getQ**()Generate and return the (economy-sized) orthogonal factor`double[][]`

**getR**()Return the upper triangular factor`boolean`

**isFullRank**()Is the matrix full rank?`double[][]`

**solve**(double[][] B)Least squares solution of A*X = B

### Constructor Detail

#### QRDecomposition

public QRDecomposition(double[][] 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 double[][] getH()

Return the Householder vectors- Returns:
- Lower trapezoidal matrix whose columns define the reflections

#### getR

public double[][] getR()

Return the upper triangular factor- Returns:
- R

#### getQ

public double[][] getQ()

Generate and return the (economy-sized) orthogonal factor- Returns:
- Q

#### solve

public double[][] solve(double[][] 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.

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