Function differentiate

maths/dual_number_automatic_differentiation.py:95–128

>>> differentiate(lambda x: x**2, 2, 2) 2 >>> differentiate(lambda x: x**2 * x**4, 9, 2) 196830 >>> differentiate(lambda y: 0.5 * (y + 3) ** 6, 3.5, 4) 7605.0 >>> differentiate(lambda y: y ** 2, 4, 3) 0 >>> differentiate(8, 8, 8) Traceback (most rec

(func, position, order)

def differentiate(func, position, order):
    """
    >>> differentiate(lambda x: x**2, 2, 2)
    2
    >>> differentiate(lambda x: x**2 * x**4, 9, 2)
    196830
    >>> differentiate(lambda y: 0.5 * (y + 3) ** 6, 3.5, 4)
    7605.0
    >>> differentiate(lambda y: y ** 2, 4, 3)
    0
    >>> differentiate(8, 8, 8)
    Traceback (most recent call last):
        ...
    ValueError: differentiate() requires a function as input for func
    >>> differentiate(lambda x: x **2, "", 1)
    Traceback (most recent call last):
        ...
    ValueError: differentiate() requires a float as input for position
    >>> differentiate(lambda x: x**2, 3, "")
    Traceback (most recent call last):
        ...
    ValueError: differentiate() requires an int as input for order
    """
    if not callable(func):
        raise ValueError("differentiate() requires a function as input for func")
    if not isinstance(position, (float, int)):
        raise ValueError("differentiate() requires a float as input for position")
    if not isinstance(order, int):
        raise ValueError("differentiate() requires an int as input for order")
    d = Dual(position, 1)
    result = func(d)
    if order == 0:
        return result.real
    return result.duals[order - 1] * factorial(order)


if __name__ == "__main__":