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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 singular
FieldVector<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 singular
FieldMatrix<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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