Function gradient

recipes/Python/580610_Auto_differentiation/recipe-580610.py:194–205

Vector of the partial derivatives of a scalar field >>> func = lambda x, y: x*y + sin(x) >>> point = (2.5, 3.5) >>> gradient(func, point) (2.6988563844530664, 2.5) See: https://www.wolframalpha.com/input/?lk=3&i=grad(x*y+%2B+sin(x))

(func, point)

    return d(func(*[Num(x, i==index) for i, x in enumerate(point)]))

def gradient(func, point):
    ''' Vector of the partial derivatives of a scalar field

        >>> func = lambda x, y:  x*y + sin(x)
        >>> point = (2.5, 3.5)
        >>> gradient(func, point)
        (2.6988563844530664, 2.5)

        See:  https://www.wolframalpha.com/input/?lk=3&i=grad(x*y+%2B+sin(x))

    '''
    return tuple(partial(func, point, index) for index in range(len(point)))

def directional_derivative(func, point, direction):
    ''' The dot product of the gradient and a direction vector.