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java.lang.Objectorg.apache.commons.math3.linear.QRDecomposition
org.apache.commons.math3.linear.RRQRDecomposition
public class RRQRDecomposition
Calculates the rank-revealing QR-decomposition of a matrix, with column pivoting.
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methods have been replaced
by a getSolver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
.
Nested Class Summary | |
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private static class |
RRQRDecomposition.Solver
Specialized solver. |
Field Summary | |
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private RealMatrix |
cachedP
Cached value of P. |
private int[] |
p
An array to record the column pivoting for later creation of P. |
Constructor Summary | |
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RRQRDecomposition(RealMatrix matrix)
Calculates the QR-decomposition of the given matrix. |
|
RRQRDecomposition(RealMatrix matrix,
double threshold)
Calculates the QR-decomposition of the given matrix. |
Method Summary | |
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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.math3.linear.QRDecomposition |
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getH, getQ, getQT, getR |
Methods inherited from class java.lang.Object |
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clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
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private int[] p
private RealMatrix cachedP
Constructor Detail |
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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)
Method Detail |
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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 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 computation
public DecompositionSolver getSolver()
getSolver
in class QRDecomposition
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