q2_gradcheck.py

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 
    - f should be a function that takes a single argument and outputs the cost and its gradients
    - x is 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
    ##print("fx", fx)
    ##print("grad", grad)
    ##print("x",x)
    h = 1e-4

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

        ### 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:
        
        old_value = x[ix]
        x[ix] = old_value + h # increment by h
        random.setstate(rndstate)
        fxph,_ = f(x) # evaluate f(x + h)
        x[ix] = old_value - h # decrement by h
        random.setstate(rndstate)
        fxnh,_ = f(x) # evaluate f(x - h)
        x[ix] = old_value # restore to previous value (very important)
        # compute the partial derivative
        numgrad = (fxph - fxnh) / (2 * h) # the slope
        ##print("numgrad",numgrad)

        ### END YOUR CODE

        # Compare gradients
        print ("numgrad", numgrad, "ix", ix, "grad[ix]", grad[ix])
        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 ("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 ("")

def your_sanity_checks(): 
    """
    Use this space add any additional sanity checks by running:
        python q2_gradcheck.py 
    This function will not be called by the autograder, nor will
    your additional tests be graded.
    """
    print ("Running your sanity checks...")
    ### YOUR CODE HERE
    #https://github.com/ZhangBanger/cs224d/blob/master/assignment1/q2_gradcheck.py
    foo = lambda x: (np.sum(np.power(x, 2)), 2 * x)
    gradcheck_naive(foo, np.array([300.455, 3.5]))
    bar = lambda x: (np.sum(np.exp(x)), np.exp(x))
    gradcheck_naive(bar, np.array([[5., 2., 1.], [3., 3., 2.]]))

    baz = lambda x: (np.sum(np.exp(x ** 2)), np.exp(x ** 2) * 2 * x)
    gradcheck_naive(baz, np.array([3., 2., 1.]))    ### END YOUR CODE

if __name__ == "__main__":
    sanity_check()
    your_sanity_checks()