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T
- the type of the field elementspublic interface FieldDecompositionSolver<T extends FieldElement<T>>
Interface handling decomposition algorithms that can solve A × X = B.
Decomposition algorithms decompose an A matrix has a product of several specific matrices from which they can solve A × X = B in least squares sense: they find X such that ||A × X - B|| is minimal.
Some solvers like LUDecomposition
can only find the solution for
square matrices and when the solution is an exact linear solution, i.e. when
||A × X - B|| is exactly 0. Other solvers can also find solutions
with non-square matrix A and with non-null minimal norm. If an exact linear
solution exists it is also the minimal norm solution.
Method Summary | |
---|---|
FieldMatrix<T> |
getInverse()
Get the inverse (or pseudo-inverse) of the decomposed matrix. |
boolean |
isNonSingular()
Check if the decomposed matrix is non-singular. |
FieldMatrix<T> |
solve(FieldMatrix<T> b)
Solve the linear equation A × X = B for matrices A. |
FieldVector<T> |
solve(FieldVector<T> b)
Solve the linear equation A × X = B for matrices A. |
T[] |
solve(T[] b)
Solve the linear equation A × X = B for matrices A. |
Method Detail |
---|
T[] solve(T[] b) throws IllegalArgumentException, InvalidMatrixException
The A matrix is implicit, it is provided by the underlying decomposition algorithm.
b
- right-hand side of the equation A × X = B
IllegalArgumentException
- if matrices dimensions don't match
InvalidMatrixException
- if decomposed matrix is singularFieldVector<T> solve(FieldVector<T> b) throws IllegalArgumentException, InvalidMatrixException
The A matrix is implicit, it is provided by the underlying decomposition algorithm.
b
- right-hand side of the equation A × X = B
IllegalArgumentException
- if matrices dimensions don't match
InvalidMatrixException
- if decomposed matrix is singularFieldMatrix<T> solve(FieldMatrix<T> b) throws IllegalArgumentException, InvalidMatrixException
The A matrix is implicit, it is provided by the underlying decomposition algorithm.
b
- right-hand side of the equation A × X = B
IllegalArgumentException
- if matrices dimensions don't match
InvalidMatrixException
- if decomposed matrix is singularboolean isNonSingular()
FieldMatrix<T> getInverse() throws InvalidMatrixException
InvalidMatrixException
- if decomposed matrix is singular
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