(alpha, beta, int_1, xr)
return x, w
From <http://www.scientificpython.net/pyblog/radau-quadrature>:
    Compute the Radau nodes and weights with the preassigned node xr.

    Based on the section 7 of the paper

        Some modified matrix eigenvalue problems,
        Gene Golub,
        SIAM Review Vol 15, No. 2, April 1973, pp.318--334.
From <http://www.scientificpython.net/pyblog/radau-quadrature>:
    Compute the Radau nodes and weights with the preassigned node xr.
From <http : // www . scientificpython . net / pyblog / radau - quadrature > : Compute the Radau nodes and weights with the preassigned node xr .
def _radau(alpha, beta, int_1, xr):
    """From <http://www.scientificpython.net/pyblog/radau-quadrature>:
    Compute the Radau nodes and weights with the preassigned node xr.

    Based on the section 7 of the paper

        Some modified matrix eigenvalue problems,
        Gene Golub,
        SIAM Review Vol 15, No. 2, April 1973, pp.318--334.
    """
    from scipy.linalg import solve_banded

    beta[0] = int_1

    n = len(alpha) - 1
    f = np.zeros(n)
    f[-1] = beta[-1]
    A = np.vstack((np.sqrt(beta), alpha - xr))
    J = np.vstack((A[:, 0:-1], A[0, 1:]))
    delta = solve_banded((1, 1), J, f)
    alphar = alpha.copy()
    alphar[-1] = xr + delta[-1]
    x, w = scheme_from_rc(alphar, beta, int_1, mode="numpy")
    return x, w
def _radau ( alpha , beta , int_1 , xr ) : from scipy . linalg import solve_banded beta [ 0 ] = int_1 n = len ( alpha ) - 1 f = np . zeros ( n ) f [ - 1 ] = beta [ - 1 ] A = np . vstack ( ( np . sqrt ( beta ) , alpha - xr ) ) J = np . vstack ( ( A [ : , 0 : - 1 ] , A [ 0 , 1 : ] ) ) delta = solve_banded ( ( 1 , 1 ) , J , f ) alphar = alpha . copy ( ) alphar [ - 1 ] = xr + delta [ - 1 ] x , w = scheme_from_rc ( alphar , beta , int_1 , mode = "numpy" ) return x , w