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:
        old_xix = x[ix]
        x[ix] = old_xix + h
        random.setstate(rndstate)
        fp = f(x)[0]
        x[ix] = old_xix - h
        random.setstate(rndstate)
        fm = f(x)[0]
        x[ix] = old_xix

        numgrad = (fp - fm)/(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 grad_numerical(f, x, h=1e-4):
    """ 
    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
    - h is the size of the shift for all dimensions
    """ 

    rndstate = random.getstate()
    random.setstate(rndstate)  
    fx, grad = f(x) # Evaluate function value at original point
    num_grad = np.zeros(x.shape)

    # 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:
        old_xix = x[ix]
        x[ix] += 0.5 * h
        random.setstate(rndstate)
        fp = f(x)[0]
        x[ix] -= h
        random.setstate(rndstate)
        fm = f(x)[0]
        x[ix] = old_xix

        num_grad += (fp - fm)/h
        ### END YOUR CODE
        it.iternext() # Step to next dimension
    return num_grad

def eval_numerical_gradient_array(f, x, df, h=1e-5):
  """
  Evaluate a numeric gradient for a function that accepts a numpy
  array and returns a numpy array.
  """
  grad = np.zeros_like(x)
  it = np.nditer(x, flags=['multi_index'], op_flags=['readwrite'])
  while not it.finished:
    ix = it.multi_index
    
    oldval = x[ix]
    x[ix] = oldval + h
    pos = f(x).copy()
    x[ix] = oldval - h
    neg = f(x).copy()
    x[ix] = oldval
    
    grad[ix] = np.sum((pos - neg) * df) / (2 * h)
    it.iternext()
  return grad

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
    print("")
    ### END YOUR CODE

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