Python: partial that takes three arguments

Question

I'm trying to learn Python by reading the book Data Science from Scratch by Joel Grus, and on page 94 they describe how to approximate a derivative of f = x^2 using the following code

def difference_quotient(f, x, h):
    return (f(x + h) - f(x)) / h

def square(x):
    return x * x

def derivative(x):
    return 2 * x

derivative_estimate = partial(difference_quotient, square, h=0.00001)

# plot to show they're basically the same
import matplotlib.pyplot as plt
x = range(-10,10)
plt.title("Actual Derivatives vs. Estimates")
plt.plot(x, map(derivative, x), 'rx', label='Actual')
plt.plot(x, map(derivative_estimate, x), 'b+', label='Estimate')
plt.legend(loc=9)
plt.show()

Everything works fine, but when I change the line derivative_estimate = partial(difference_quotient, square, h=0.00001) to derivative_estimate = partial(difference_quotient, f=square, h=0.00001) (because I think that is clearer to read), then I get the following error

Traceback (most recent call last):
  File "page_93.py", line 37, in <module>
    plt.plot(x, map(derivative_estimate, x), 'b+', label='Estimate')
TypeError: difference_quotient() got multiple values for keyword argument 'f'

What is going on here?

Answer 1

It was answered and perfectly explained in this topic:

• functools.partial wants to use a positional argument as a keyword argument

Which in your case implies that you should pass x as a keyword argument:

plt.plot(x, [derivative_estimate(x=item) for item in x], 'b+', label='Estimate')