org.apache.commons.math.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 `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.

Since:
2.0
• ### Method Summary

All Methods
Modifier and Type Method and 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.
`T[]` `solve(T[] b)`
Solve the linear equation A × X = B for matrices A.
• ### Method Detail

• #### solve

```T[] solve(T[] b)
throws java.lang.IllegalArgumentException,
InvalidMatrixException```
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:
`java.lang.IllegalArgumentException` - if matrices dimensions don't match
`InvalidMatrixException` - if decomposed matrix is singular
• #### solve

```FieldVector<T> solve(FieldVector<T> b)
throws java.lang.IllegalArgumentException,
InvalidMatrixException```
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:
`java.lang.IllegalArgumentException` - if matrices dimensions don't match
`InvalidMatrixException` - if decomposed matrix is singular
• #### solve

```FieldMatrix<T> solve(FieldMatrix<T> b)
throws java.lang.IllegalArgumentException,
InvalidMatrixException```
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:
`java.lang.IllegalArgumentException` - if matrices dimensions don't match
`InvalidMatrixException` - if 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()
throws InvalidMatrixException```
Get the inverse (or pseudo-inverse) of the decomposed matrix.
Returns:
inverse matrix
Throws:
`InvalidMatrixException` - if decomposed matrix is singular

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