17.1 Multivariable functions in code

It’s been a long time since we put theory into code. So, let’s take a look at multivariable functions!

Last time, we built a Function base class with two main methods: one for computing the derivative (Function.prime) and one for getting the dictionary of parameters (Function.parameters).

This won’t be much of a surprise: the multivariate function base class is not much different. For clarity, we’ll appropriately rename the prime method to grad.

class MultivariableFunction: 
    def __init__(self): 
        pass 
 
    def __call__(self, *args, **kwargs): 
        pass 
 
    def grad(self): 
        pass 
 
    def parameters(self): 
        return dict()

Let’s see a few examples right away. The simplest one is the squared Euclidean norm f(x) = ∥x∥², a close relative to the mean squared error function. Its gradient is given by

thus everything is ready to implement it. As we’ve used...