private static class QRDecomposition.Solver extends java.lang.Object implements DecompositionSolver
Modifier and Type | Field and Description |
---|---|
private double[][] |
qrt
A packed TRANSPOSED representation of the QR decomposition.
|
private double[] |
rDiag
The diagonal elements of R.
|
private double |
threshold
Singularity threshold.
|
Modifier | Constructor and Description |
---|---|
private |
QRDecomposition.Solver(double[][] qrt,
double[] rDiag,
double threshold)
Build a solver from decomposed matrix.
|
Modifier and Type | Method and Description |
---|---|
RealMatrix |
getInverse()
Get the pseudo-inverse
of the decomposed matrix.
|
boolean |
isNonSingular()
Check if the decomposed matrix is non-singular.
|
RealMatrix |
solve(RealMatrix b)
Solve the linear equation A × X = B for matrices A.
|
RealVector |
solve(RealVector b)
Solve the linear equation A × X = B for matrices A.
|
private final double[][] qrt
The elements BELOW the diagonal are the elements of the UPPER triangular matrix R, and the rows ABOVE the diagonal are the Householder reflector vectors from which an explicit form of Q can be recomputed if desired.
private final double[] rDiag
private final double threshold
private QRDecomposition.Solver(double[][] qrt, double[] rDiag, double threshold)
qrt
- Packed TRANSPOSED representation of the QR decomposition.rDiag
- Diagonal elements of R.threshold
- Singularity threshold.public boolean isNonSingular()
isNonSingular
in interface DecompositionSolver
public RealVector solve(RealVector b)
The A matrix is implicit, it is provided by the underlying decomposition algorithm.
solve
in interface DecompositionSolver
b
- right-hand side of the equation A × X = Bpublic RealMatrix solve(RealMatrix b)
The A matrix is implicit, it is provided by the underlying decomposition algorithm.
solve
in interface DecompositionSolver
b
- right-hand side of the equation A × X = Bpublic RealMatrix getInverse()
This is equal to the inverse of the decomposed matrix, if such an inverse exists.
If no such inverse exists, then the result has properties that resemble that of an inverse.
In particular, in this case, if the decomposed matrix is A, then the system of equations \( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudo-inverse \( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \| A z - b \right \|_2 \) is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest solution, meaning \( \left \| z \right \|_2 \) is minimized.
Note however that some decompositions cannot compute a pseudo-inverse for all matrices.
For example, the LUDecomposition
is not defined for non-square matrices to begin
with. The QRDecomposition
can operate on non-square matrices, but will throw
SingularMatrixException
if the decomposed matrix is singular. Refer to the javadoc
of specific decomposition implementations for more details.
getInverse
in interface DecompositionSolver
SingularMatrixException
- if the decomposed matrix is singular.Copyright (c) 2003-2014 Apache Software Foundation