newton_cotes.py 文件源码

def __init__(self, index):
        self.points = numpy.linspace(-1.0, 1.0, index+2)[1:-1]
        self.degree = index if (index+1) % 2 == 0 else index - 1
        #
        n = index+1
        self.weights = numpy.empty(n-1)
        t = sympy.Symbol('t')
        for r in range(1, n):
            # Compare with get_weights().
            f = sympy.prod([(t - i) for i in range(1, n) if i != r])
            alpha = 2 * \
                (-1)**(n-r+1) * sympy.integrate(f, (t, 0, n)) \
                / (math.factorial(r-1) * math.factorial(n-1-r)) \
                / n
            self.weights[r-1] = alpha
        return