private static class RRQRDecomposition.Solver extends java.lang.Object implements DecompositionSolver
Modifier and Type | Field and Description |
---|---|
private RealMatrix |
p
A permutation matrix for the pivots used in the QR decomposition
|
private DecompositionSolver |
upper
Upper level solver.
|
Modifier | Constructor and Description |
---|---|
private |
Solver(DecompositionSolver upper,
RealMatrix p)
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 DecompositionSolver upper
private RealMatrix p
private Solver(DecompositionSolver upper, RealMatrix p)
upper
- upper level solver.p
- permutation matrixpublic 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) 2003-2016 Apache Software Foundation