Gradient of a function in Python

Question

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?

Answer 1

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"