Package org.apache.commons.math4.legacy.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

    • 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