public class QRDecompositionImpl extends Object implements QRDecomposition
The QR-decomposition of a matrix A consists of two matrices Q and R that satisfy: A = QR, Q is orthogonal (QTQ = I), and R is upper triangular. If A is m×n, Q is m×m and R m×n.
This class compute the decomposition using Householder reflectors.
For efficiency purposes, the decomposition in packed form is transposed. This allows inner loop to iterate inside rows, which is much more cache-efficient in Java.
Modifier and Type | Class and Description |
---|---|
private static class |
QRDecompositionImpl.Solver
Specialized solver.
|
Modifier and Type | Field and Description |
---|---|
private RealMatrix |
cachedH
Cached value of H.
|
private RealMatrix |
cachedQ
Cached value of Q.
|
private RealMatrix |
cachedQT
Cached value of QT.
|
private RealMatrix |
cachedR
Cached value of R.
|
private double[][] |
qrt
A packed TRANSPOSED representation of the QR decomposition.
|
private double[] |
rDiag
The diagonal elements of R.
|
Constructor and Description |
---|
QRDecompositionImpl(RealMatrix matrix)
Calculates the QR-decomposition of the given matrix.
|
Modifier and Type | Method and Description |
---|---|
RealMatrix |
getH()
Returns the Householder reflector vectors.
|
RealMatrix |
getQ()
Returns the matrix Q of the decomposition.
|
RealMatrix |
getQT()
Returns the transpose of the matrix Q of the decomposition.
|
RealMatrix |
getR()
Returns the matrix R of the decomposition.
|
DecompositionSolver |
getSolver()
Get a solver for finding the A × X = B solution in least square sense.
|
private double[][] qrt
The elements BELOW the diagonal are the elements of the UPPER triangular matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors from which an explicit form of Q can be recomputed if desired.
private double[] rDiag
private RealMatrix cachedQ
private RealMatrix cachedQT
private RealMatrix cachedR
private RealMatrix cachedH
public QRDecompositionImpl(RealMatrix matrix)
matrix
- The matrix to decompose.public RealMatrix getR()
R is an upper-triangular matrix
getR
in interface QRDecomposition
public RealMatrix getQ()
Q is an orthogonal matrix
getQ
in interface QRDecomposition
public RealMatrix getQT()
Q is an orthogonal matrix
getQT
in interface QRDecomposition
public RealMatrix getH()
H is a lower trapezoidal matrix whose columns represent each successive Householder reflector vector. This matrix is used to compute Q.
getH
in interface QRDecomposition
public DecompositionSolver getSolver()
getSolver
in interface QRDecomposition
Copyright (c) 2003-2014 Apache Software Foundation