FieldDecompositionSolver (Hipparchus 1.4 API)

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.

Method Summary

All Methods Instance Methods Abstract Methods
Modifier and Type	Method	Description
`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:
    
    MathIllegalArgumentException - if the matrices dimensions do not match or 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:
    
    MathIllegalArgumentException - if the matrices dimensions do not match or 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:
    
    MathIllegalArgumentException - if the decomposed matrix is singular.