Class RRQRDecomposition
 java.lang.Object

 org.apache.commons.math4.legacy.linear.QRDecomposition

 org.apache.commons.math4.legacy.linear.RRQRDecomposition

public class RRQRDecomposition extends QRDecomposition
Calculates the rankrevealing QRdecomposition of a matrix, with column pivoting.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:
 a
getQT
method has been added,  the
solve
andisFullRank
methods have been replaced by agetSolver
method and the equivalent methods provided by the returnedDecompositionSolver
.
 a


Constructor Summary
Constructors Constructor Description RRQRDecomposition(RealMatrix matrix)
Calculates the QRdecomposition of the given matrix.RRQRDecomposition(RealMatrix matrix, double threshold)
Calculates the QRdecomposition of the given matrix.

Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method 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.
Methods inherited from class org.apache.commons.math4.legacy.linear.QRDecomposition
getH, getQ, getQT, getR




Constructor Detail

RRQRDecomposition
public RRQRDecomposition(RealMatrix matrix)
Calculates the QRdecomposition of the given matrix. The singularity threshold defaults to zero. Parameters:
matrix
 The matrix to decompose. See Also:
RRQRDecomposition(RealMatrix, double)

RRQRDecomposition
public RRQRDecomposition(RealMatrix matrix, double threshold)
Calculates the QRdecomposition of the given matrix. Parameters:
matrix
 The matrix to decompose.threshold
 Singularity threshold. See Also:
RRQRDecomposition(RealMatrix)


Method Detail

decompose
protected void decompose(double[][] qrt)
Decompose matrix. Overrides:
decompose
in classQRDecomposition
 Parameters:
qrt
 transposed matrix

performHouseholderReflection
protected void performHouseholderReflection(int minor, double[][] qrt)
Perform Householder reflection for a minor A(minor, minor) of A. Overrides:
performHouseholderReflection
in classQRDecomposition
 Parameters:
minor
 minor indexqrt
 transposed matrix

getP
public RealMatrix getP()
Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR. If no pivoting is used in this decomposition then P is equal to the identity matrix. Returns:
 a permutation matrix.

getRank
public int getRank(double dropThreshold)
Return the effective numerical matrix rank.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
 Parameters:
dropThreshold
 threshold triggering rank computation Returns:
 effective numerical matrix rank

getSolver
public DecompositionSolver getSolver()
Get a solver for finding the A × X = B solution in least square sense.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 thesolve
method will be called. Overrides:
getSolver
in classQRDecomposition
 Returns:
 a solver

