Class RRQRDecomposition.Solver

    • Field Detail

      • p

        private RealMatrix p
        A permutation matrix for the pivots used in the QR decomposition
    • Constructor Detail

      • Solver

        private Solver​(DecompositionSolver upper,
                       RealMatrix p)
        Build a solver from decomposed matrix.
        Parameters:
        upper - upper level solver.
        p - permutation matrix
    • Method Detail

      • isNonSingular

        public boolean isNonSingular()
        Check if the decomposed matrix is non-singular.
        Specified by:
        isNonSingular in interface DecompositionSolver
        Returns:
        true if the decomposed matrix is non-singular.
      • solve

        public RealVector solve​(RealVector b)
        Solve the linear equation A × X = B for matrices A.

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

        Specified by:
        solve in interface DecompositionSolver
        Parameters:
        b - right-hand side of the equation A × X = B
        Returns:
        a vector X that minimizes the two norm of A × X - B
      • solve

        public RealMatrix solve​(RealMatrix b)
        Solve the linear equation A × X = B for matrices A.

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

        Specified by:
        solve in interface DecompositionSolver
        Parameters:
        b - right-hand side of the equation A × X = B
        Returns:
        a matrix X that minimizes the two norm of A × X - B
      • getInverse

        public RealMatrix getInverse()
        Get the pseudo-inverse of the decomposed matrix.

        This is equal to the inverse of the decomposed matrix, if such an inverse exists.

        If no such inverse exists, then the result has properties that resemble that of an inverse.

        In particular, in this case, if the decomposed matrix is A, then the system of equations \( A x = b \) may have no solutions, or many. If it has no solutions, then the pseudo-inverse \( A^+ \) gives the "closest" solution \( z = A^+ b \), meaning \( \left \| A z - b \right \|_2 \) is minimized. If there are many solutions, then \( z = A^+ b \) is the smallest solution, meaning \( \left \| z \right \|_2 \) is minimized.

        Note however that some decompositions cannot compute a pseudo-inverse for all matrices. For example, the LUDecomposition is not defined for non-square matrices to begin with. The QRDecomposition can operate on non-square matrices, but will throw SingularMatrixException if the decomposed matrix is singular. Refer to the javadoc of specific decomposition implementations for more details.

        Specified by:
        getInverse in interface DecompositionSolver
        Returns:
        pseudo-inverse matrix (which is the inverse, if it exists), if the decomposition can pseudo-invert the decomposed matrix
        Throws:
        SingularMatrixException - if the decomposed matrix is singular.