org.apache.commons.math3.linear
public class QRDecomposition extends Object
The QRdecomposition of a matrix A consists of two matrices Q and R that satisfy: A = QR, Q is orthogonal (Q^{T}Q = 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 cacheefficient in Java.
This class is based on the class with similar name from the JAMA library, with the following changes:
getQT
method has been added,solve
and isFullRank
methods have been replaced
by a getSolver
method and the equivalent methods
provided by the returned DecompositionSolver
.Constructor and Description 

QRDecomposition(RealMatrix matrix)
Calculates the QRdecomposition of the given matrix.

QRDecomposition(RealMatrix matrix,
double threshold)
Calculates the QRdecomposition of the given matrix.

Modifier and Type  Method and Description 

protected void 
decompose(double[][] matrix)
Decompose matrix.

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.

protected void 
performHouseholderReflection(int minor,
double[][] matrix)
Perform Householder reflection for a minor A(minor, minor) of A.

public QRDecomposition(RealMatrix matrix)
matrix
 The matrix to decompose.QRDecomposition(RealMatrix,double)
public QRDecomposition(RealMatrix matrix, double threshold)
matrix
 The matrix to decompose.threshold
 Singularity threshold.protected void decompose(double[][] matrix)
matrix
 transposed matrixprotected void performHouseholderReflection(int minor, double[][] matrix)
minor
 minor indexmatrix
 transposed matrixpublic RealMatrix getR()
R is an uppertriangular matrix
public RealMatrix getQ()
Q is an orthogonal matrix
public RealMatrix getQT()
Q is an orthogonal matrix
public RealMatrix getH()
H is a lower trapezoidal matrix whose columns represent each successive Householder reflector vector. This matrix is used to compute Q.
public DecompositionSolver getSolver()
Least Square sense means a solver can be computed for an overdetermined system,
(i.e. a system with more equations than unknowns, which corresponds to a tall A
matrix with more rows than columns). In any case, if the matrix is singular
within the tolerance set at construction
, an error will be triggered when
the solve
method will be called.
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