Fill in the implementation for the rectified linear layer activation function and its gradient.

import numpy as np

def relu(x): """ Compute the relu function for the input here.

Arguments: x -- A scalar or numpy array.

Return: s -- relu(x) """ #################### # your answer here ####################

raise NotImplementedError # END YOUR CODE

return s

def relu_grad(s): """ Compute the gradient for the relu function here. Note that for this implementation, the input s should be the relu function value of your original input x.

Arguments: s -- A scalar or numpy array.

Return: ds -- Your computed gradient. """ #################### # your answer here ####################

raise NotImplementedError # END YOUR CODE

return ds

def test_relu_basic(): """ Some simple tests to get you started. Warning: these are not exhaustive. """ print "Running basic tests..." x = np.array([[1, 2], [-1, -2]]) f = relu(x) g = relu_grad(f) print f f_ans = np.array([ [1, 2], [0, 0]]) assert np.allclose(f, f_ans, rtol=1e-05, atol=1e-06) print g g_ans = np.array([ [1, 1], [0, 0]]) assert np.allclose(g, g_ans, rtol=1e-05, atol=1e-06) print "You should verify these results by hand! "

def test_relu(): """ Use this space to test your relu implementation by running: python q2_relu.py This function will not be called by the autograder, nor will your tests be graded. """ #################### # your answer here #################### print "Running your tests..."

# END YOUR CODE

if __name__ == "__main__": test_relu_basic() test_relu()