Class RRQRDecomposition.Solver
- All Implemented Interfaces:
DecompositionSolver
- Enclosing class:
RRQRDecomposition
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate RealMatrix
A permutation matrix for the pivots used in the QR decompositionprivate final DecompositionSolver
Upper level solver. -
Constructor Summary
ConstructorsModifierConstructorDescriptionprivate
Solver
(DecompositionSolver upper, RealMatrix p) 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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upper
Upper level solver. -
p
A permutation matrix for the pivots used in the QR decomposition
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Constructor Details
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Solver
Build a solver from decomposed matrix.- Parameters:
upper
- upper level solver.p
- permutation matrix
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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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