public class RRQRDecomposition extends QRDecomposition
The rank-revealing QR-decomposition of a matrix A consists of three matrices Q, R and P such that AP=QR. Q is orthogonal (QTQ = 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 rank-revealing 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 cache-efficient 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getQT method has been added,solve and isFullRank methods have been replaced
by a getSolver method and the equivalent methods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 QR-decomposition of the given matrix.
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RRQRDecomposition(RealMatrix matrix,
double threshold)
Calculates the QR-decomposition of the given matrix.
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| Modifier and Type | Method and Description |
|---|---|
protected void |
decompose(double[][] qrt)
Decompose matrix.
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RealMatrix |
getP()
Returns the pivot matrix, P, used in the QR Decomposition of matrix A such that AP = QR.
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int |
getRank(double dropThreshold)
Return the effective numerical matrix rank.
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DecompositionSolver |
getSolver()
Get a solver for finding the A × X = B solution in least square sense.
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protected void |
performHouseholderReflection(int minor,
double[][] qrt)
Perform Householder reflection for a minor A(minor, minor) of A.
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getH, getQ, getQT, getRpublic 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 QRDecompositionqrt - transposed matrixprotected void performHouseholderReflection(int minor,
double[][] qrt)
performHouseholderReflection in class QRDecompositionminor - minor indexqrt - transposed matrixpublic RealMatrix getP()
public int getRank(double dropThreshold)
The effective numerical rank is the number of non-negligible 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 QRDecompositionCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.