org.apache.commons.math3.linear
public class RRQRDecomposition extends QRDecomposition
The rankrevealing QRdecomposition of a matrix A consists of three matrices Q, R and P such that AP=QR. Q is orthogonal (Q^{T}Q = I), and R is upper triangular. If A is m×n, Q is m×m and R is m×n and P is n×n.
QR decomposition with column pivoting produces a rankrevealing QR
decomposition and the getRank(double)
method may be used to return the rank of the
input matrix A.
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methods have been replaced
by a getSolver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 

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

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

Modifier and Type  Method and Description 

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

RealMatrix 
getP()
Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.

int 
getRank(double dropThreshold)
Return the effective numerical matrix rank.

DecompositionSolver 
getSolver()
Get a solver for finding the A × X = B solution in least square sense.

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

getH, getQ, getQT, getR
public RRQRDecomposition(RealMatrix matrix)
matrix
 The matrix to decompose.RRQRDecomposition(RealMatrix, double)
public RRQRDecomposition(RealMatrix matrix, double threshold)
matrix
 The matrix to decompose.threshold
 Singularity threshold.RRQRDecomposition(RealMatrix)
protected void decompose(double[][] qrt)
decompose
in class QRDecomposition
qrt
 transposed matrixprotected void performHouseholderReflection(int minor, double[][] qrt)
performHouseholderReflection
in class QRDecomposition
minor
 minor indexqrt
 transposed matrixpublic RealMatrix getP()
public int getRank(double dropThreshold)
The effective numerical rank is the number of nonnegligible singular values.
This implementation looks at Frobenius norms of the sequence of bottom right submatrices. When a large fall in norm is seen, the rank is returned. The drop is computed as:
(thisNorm/lastNorm) * rNorm < dropThreshold
where thisNorm is the Frobenius norm of the current submatrix, lastNorm is the Frobenius norm of the previous submatrix, rNorm is is the Frobenius norm of the complete matrix
dropThreshold
 threshold triggering rank computationpublic 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.
getSolver
in class QRDecomposition
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