import numpy as np
import random
# First implement a gradient checker by filling in the following functions
def gradcheck_naive(f, x):
""" Gradient check for a function f.
Arguments:
f -- a function that takes a single argument and outputs the
cost and its gradients
x -- the point (numpy array) to check the gradient at
"""
rndstate = random.getstate()
random.setstate(rndstate)
fx, grad = f(x) # Evaluate function value at original point
h = 1e-4 # Do not change this!
# Iterate over all indexes in x
it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
while not it.finished:
ix = it.multi_index
# Try modifying x[ix] with h defined above to compute
# numerical gradients. Make sure you call random.setstate(rndstate)
# before calling f(x) each time. This will make it possible
# to test cost functions with built in randomness later.
### YOUR CODE HERE:
x[ix] += h
random.setstate(rndstate)
new_f1 = f(x)[0]
x[ix] -= 2*h
random.setstate(rndstate)
new_f2 = f(x)[0]
x[ix] += h
numgrad = (new_f1 - new_f2) / (2 * h)
### END YOUR CODE
# Compare gradients
reldiff = abs(numgrad - grad[ix]) / max(1, abs(numgrad), abs(grad[ix]))
if reldiff > 1e-5:
print("Gradient check failed.")
print("First gradient error found at index %s" % str(ix))
print("Your gradient: %f \t Numerical gradient: %f" % (
grad[ix], numgrad))
return
it.iternext() # Step to next dimension
print("Gradient check passed!")
def sanity_check():
"""
Some basic sanity checks.
"""
quad = lambda x: (np.sum(x ** 2), x * 2)
print("Running sanity checks...")
gradcheck_naive(quad, np.array(123.456)) # scalar test
gradcheck_naive(quad, np.random.randn(3,)) # 1-D test
gradcheck_naive(quad, np.random.randn(4,5)) # 2-D test
print("")
if __name__ == "__main__":
sanity_check()
Running sanity checks... Gradient check passed! Gradient check passed! Gradient check passed!