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
    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

        ### 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:        
        random.setstate(rndstate)
        
        x_copy1 = np.copy(x) 
        x_copy1[ix] = x_copy1[ix]+h
        f1, grad1 = f(x_copy1)
        
        random.setstate(rndstate)
        
        x_copy2 = np.copy(x) 
        x_copy2[ix] = x_copy2[ix]-h
        f2, grad2 = f(x_copy2)
        numgrad = (f1-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 ""

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
    quad = lambda x: (np.sum(x ** 3 + x ** 2), x * 2 + 3*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 ""

    ### END YOUR CODE

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