Class QRDecomposition.Solver
- All Implemented Interfaces:
DecompositionSolver
- Enclosing class:
QRDecomposition
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Field Summary
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Constructor Summary
ConstructorsModifierConstructorDescriptionprivate
Solver
(double[][] qrt, double[] rDiag, double threshold) Build a solver from decomposed matrix. -
Method Summary
Modifier and TypeMethodDescriptionGet the pseudo-inverse of the decomposed matrix.boolean
Check if the decomposed matrix is non-singular.solve
(RealMatrix b) Solve the linear equation A × X = B for matrices A.solve
(RealVector b) Solve the linear equation A × X = B for matrices A.
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Field Details
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qrt
private final double[][] qrtA packed TRANSPOSED representation of the QR decomposition.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.
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rDiag
private final double[] rDiagThe diagonal elements of R. -
threshold
private final double thresholdSingularity threshold.
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Constructor Details
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Solver
private Solver(double[][] qrt, double[] rDiag, double threshold) Build a solver from decomposed matrix.- Parameters:
qrt
- Packed TRANSPOSED representation of the QR decomposition.rDiag
- Diagonal elements of R.threshold
- Singularity threshold.
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Method Details
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isNonSingular
public boolean isNonSingular()Check if the decomposed matrix is non-singular.- Specified by:
isNonSingular
in interfaceDecompositionSolver
- Returns:
- true if the decomposed matrix is non-singular.
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solve
Solve the linear equation A × X = B for matrices A.The A matrix is implicit, it is provided by the underlying decomposition algorithm.
- Specified by:
solve
in interfaceDecompositionSolver
- Parameters:
b
- right-hand side of the equation A × X = B- Returns:
- a vector X that minimizes the two norm of A × X - B
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solve
Solve the linear equation A × X = B for matrices A.The A matrix is implicit, it is provided by the underlying decomposition algorithm.
- Specified by:
solve
in interfaceDecompositionSolver
- Parameters:
b
- right-hand side of the equation A × X = B- Returns:
- a matrix X that minimizes the two norm of A × X - B
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getInverse
Get the pseudo-inverse of the decomposed matrix.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. TheQRDecomposition
can operate on non-square matrices, but will throwSingularMatrixException
if the decomposed matrix is singular. Refer to the javadoc of specific decomposition implementations for more details.- Specified by:
getInverse
in interfaceDecompositionSolver
- Returns:
- pseudo-inverse matrix (which is the inverse, if it exists), if the decomposition can pseudo-invert the decomposed matrix
- Throws:
SingularMatrixException
- if the decomposed matrix is singular.
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