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I've defined a function in this way: 

def qfun(par):
    return(par[0]+atan(par[3])*par[1]+atan(par[4])*par[2])

How can I obtain the gradient of this function for only some of the elements (par [0:2]) in a specific point? I only find functions with only one "x", so for those cases it is simple, but when your function has more parameters what should I do?

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Several options:

  • You can use the defintion of the derivative to have an approximation....

    def f(x):
    return x[0]**2 + 3*x[1]**3

def der(f, x, der_index=[]):
    # der_index: variable w.r.t. get gradient

    epsilon = 2.34E-10
    grads = []

   for idx in der_index:
       x_ = x.copy()
       x_[idx]+=epsilon

       grads.append((f(x_) - f(x))/epsilon)

   return grads

print(der(f, np.array([1.,1.]), der_index=[0, 1]))

  • If you can solve it analytically, it is better you write the derivative function by yourself

  • You can also use symbolic programming, like in Matlab, with the library sympy https://towardsdatascience.com/taking-derivatives-in-python-d6229ba72c64

  • Another way to do it is going for the "differentiable programming" paradigm or "software 2.0"

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  • $\begingroup$ Yeah the analytical way is obviously the best one but once you have a lot of parameters and a complex function it becomes a little bit lenghty. I think I will opt for the approximation, thank you! $\endgroup$
    – unter_983
    Commented May 8, 2020 at 13:59

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