trapz_adapt.py 文件源码

def trapz(fun, a, b, tol=1e-4, *args, **kwargs):
    """
    Compute the area under the curve defined by
    y = fun(x), for x between a and b

    :param fun: the function to evaluate
    :type fun: a function that takes teh vule to be integrated over as
               its first argument. Any arguments can be passed in at the end.

    :param a: the start point for the integration
    :type a: a numeric value

    :param b: the end point for the integration
    :type b: a numeric value

    :param tol=1e-4: accuracy expected.

    any other arguments will be passed through to fun.
    """
    # compute the range

    # loop to try varying step sizes until desired accuracey is achieved

    prev_s = None
    n = 2  # start with only two steps
    while True:  # break out when desired accuracy is reached
        vals = frange(a, b, n)
        s = sum([fun(x, *args, **kwargs) for x in vals[1:-1]])
        s += (fun(a, *args, **kwargs) + fun(b, *args, **kwargs)) / 2
        s *= (b-a) / n
        if prev_s is not None:
            # check if we're close enough
            # abs_tol is for comparison to zero
            if isclose(s, prev_s, rel_tol=tol, abs_tol=tol):
                return s
        n *= 2
        prev_s = s
        # this could be a more sophisticated criterion
        if n >= 2**22:  # it's not going to work (about half the precision of a double)
            raise ValueError("Solution didn't converge")