tensorflow-for-deep-learning-py/Numpy/gradient.py

# compute the gradient numerically:
# a generic function takes a function f, a vector x o evaluate 
# the gradient on, and returns the gradient of f at x:

def eval_numerical_gradient(f, x):
  """ 
  a naive implementation of numerical gradient of f at x 
  - f should be a function that takes a single argument
  - x is the point (numpy array) to evaluate the gradient at
  """ 

  fx = f(x) # evaluate function value at original point
  grad = np.zeros(x.shape)
  h = 0.00001

  # iterate over all indexes in x
  it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
  while not it.finished:

    # evaluate function at x+h
    ix = it.multi_index
    old_value = x[ix]
    x[ix] = old_value + h # increment by h
    fxh = f(x) # evalute f(x + h)
    x[ix] = old_value # restore to previous value (very important!)

    # compute the partial derivative
    grad[ix] = (fxh - fx) / h # the slope
    it.iternext() # step to next dimension

  return grad