Package org.apache.commons.math4.legacy.field.linalg

Interface FieldDecompositionSolver<T>

  • Type Parameters:
    T - Type of the field elements.
    public interface FieldDecompositionSolver<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 the above system of equations in a least-squares sense: 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-zero minimal norm. If an exact linear solution exists it is also the minimal norm solution.

    Since:
    4.0

    • Method Detail

      • solve

        FieldDenseMatrix<T> solve​(FieldDenseMatrix<T> b)
        Solves the linear equation A X = B.

        Matrix A is implicit: It is provided by the underlying decomposition algorithm.

        Parameters:
        b - Right-hand side of the equation.
        Returns:
        the matrix X that minimizes ||A X - B||.
        Throws:
        IllegalArgumentException - if the dimensions do not match.