## org.apache.commons.math3.linear Interface FieldDecompositionSolver<T extends FieldElement<T>>

Type Parameters:
`T` - the type of the field elements

`public 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 `FieldLUDecomposition` 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.

Since:
2.0
Version:
\$Id: FieldDecompositionSolver.java 1416643 2012-12-03 19:37:14Z tn \$

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.

Method Detail

### solve

`FieldVector<T> solve(FieldVector<T> b)`
Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Parameters:
`b` - right-hand side of the equation A × X = B
Returns:
a vector X that minimizes the two norm of A × X - B
Throws:
`DimensionMismatchException` - if the matrices dimensions do not match.
`SingularMatrixException` - if the decomposed matrix is singular.

### solve

`FieldMatrix<T> solve(FieldMatrix<T> b)`
Solve the linear equation A × X = B for matrices A.

The A matrix is implicit, it is provided by the underlying decomposition algorithm.

Parameters:
`b` - right-hand side of the equation A × X = B
Returns:
a matrix X that minimizes the two norm of A × X - B
Throws:
`DimensionMismatchException` - if the matrices dimensions do not match.
`SingularMatrixException` - if the decomposed matrix is singular.

### isNonSingular

`boolean isNonSingular()`
Check if the decomposed matrix is non-singular.

Returns:
true if the decomposed matrix is non-singular

### getInverse

`FieldMatrix<T> getInverse()`
Get the inverse (or pseudo-inverse) of the decomposed matrix.

Returns:
inverse matrix
Throws:
`SingularMatrixException` - if the decomposed matrix is singular.

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