numerical_derivative.py

def numerical_derivative(func, func_input, respect_to_index=0, h=0.0001):
  """Compute the numerical derivative of a function

  Args:
    func (function): A function
    func_input (list): A list of inputs given to the function
    respect_to_index (int): The index of the value the derivative is calculated with respect to
    h (float): the amount to tweak the function with to compute the gradient

  Returns:
    float: the derivative of the function at the input 
  """
  
  # compute function value
  f0 = func(*func_input)

  # compute inputs with slightly tweaked respective input weight
  new_respect_to_weight = np.add(func_input[respect_to_index], h)
  func_input_h = func_input
  func_input_h[respect_to_index] = new_respect_to_weight

  f0_h = func(*func_input_h)

  # compute the difference, the slope of the function
  delta_f = f0_h - f0
  delta_f_normalized = delta_f/h

  return delta_f_normalized