newton_cotes.py 文件源码

def __init__(self, index):
        self.points = numpy.linspace(-1.0, 1.0, index+1)
        self.degree = index + 1 if index % 2 == 0 else index

        # Formula (26) from
        # <http://mathworld.wolfram.com/Newton-CotesFormulas.html>.
        # Note that Sympy carries out all operations in rationals, i.e.,
        # _exactly_. Only at the end, the rational is converted into a float.
        n = index
        self.weights = numpy.empty(n+1)
        t = sympy.Symbol('t')
        for r in range(n+1):
            # Compare with get_weights().
            f = sympy.prod([(t - i) for i in range(n+1) if i != r])
            alpha = 2 * \
                (-1)**(n-r) * sympy.integrate(f, (t, 0, n)) \
                / (math.factorial(r) * math.factorial(n-r)) \
                / index
            self.weights[r] = alpha
        return