Question: I'm trying to do it by myself the assignments from Stanford CS231n 2017 CNN course. I'm trying to compute L2 distance using only matrix multiplication and sum broadcasting with Numpy. L2 distance is:  And I think I can do it if I use this formula:  The following code shows three methods to compute L2 distance. If I compare the output from the method compute_distances_two_loops with the output from method compute_distances_one_loop, both are equals. But I compare the output from the method compute_distances_two_loops with the output from the method compute_distances_no_loops, where I have implemented the L2 distance using only matrix multiplication and sum broadcasting, they are different. def compute_distances_two_loops(self, X): """ Compute the distance between each test point in X and each training point in self.X_train using a nested loop over both the training data and the test data. Inputs: - X: A numpy array of shape (num_test, D) containing test data. Returns: - dists: A numpy array of shape (num_test, num_train) where dists[i, j] is the Euclidean distance between the ith test point and the jth training point. """ num_test = X.shape[0] num_train = self.X_train.shape[0] dists = np.zeros((num_test, num_train)) for i in xrange(num_test): for j in xrange(num_train): ##################################################################### # TODO: # # Compute the l2 distance between the ith test point and the jth # # training point, and store the result in dists[i, j]. You should # # not use a loop over dimension. # ##################################################################### #dists[i, j] = np.sqrt(np.sum((X[i, :] - self.X_train[j, :]) ** 2)) dists[i, j] = np.sqrt(np.sum(np.square(X[i, :] - self.X_train[j, :]))) ##################################################################### # END OF YOUR CODE # ##################################################################### return dists def compute_distances_one_loop(self, X): """ Compute the distance between each test point in X and each training point in self.X_train using a single loop over the test data. Input / Output: Same as compute_distances_two_loops """ num_test = X.shape[0] num_train = self.X_train.shape[0] dists = np.zeros((num_test, num_train)) for i in xrange(num_test): ####################################################################### # TODO: # # Compute the l2 distance between the ith test point and all training # # points, and store the result in dists[i, :]. # ####################################################################### dists[i, :] = np.sqrt(np.sum(np.square(self.X_train - X[i, :]), axis = 1)) ####################################################################### # END OF YOUR CODE # ####################################################################### print(dists.shape) return dists def compute_distances_no_loops(self, X): """ Compute the distance between each test point in X and each training point in self.X_train using no explicit loops. Input / Output: Same as compute_distances_two_loops """ num_test = X.shape[0] num_train = self.X_train.shape[0] dists = np.zeros((num_test, num_train)) ######################################################################### # TODO: # # Compute the l2 distance between all test points and all training # # points without using any explicit loops, and store the result in # # dists. # # # # You should implement this function using only basic array operations; # # in particular you should not use functions from scipy. # # # # HINT: Try to formulate the l2 distance using matrix multiplication # # and two broadcast sums. # ######################################################################### dists = np.sqrt(-2 * np.dot(X, self.X_train.T) + np.sum(np.square(self.X_train), axis=1) + np.sum(np.square(X), axis=1)[:, np.newaxis]) print(dists.shape) ######################################################################### # END OF YOUR CODE # ######################################################################### return dists  You can find a full working testable code here. Do you know what am I doing wrong in compute_distances_no_loops, or wherever? UPDATE: The code that throws the error message is: dists_two = classifier.compute_distances_no_loops(X_test) # check that the distance matrix agrees with the one we computed before: difference = np.linalg.norm(dists - dists_two, ord='fro') print('Difference was: %f' % (difference, )) if difference < 0.001: print('Good! The distance matrices are the same') else: print('Uh-oh! The distance matrices are different')  And the error message: Difference was: 372100.327569 Uh-oh! The distance matrices are different 

Answer: Here is how you can compute pairwise distances between rows of X and Y without creating any 3-dimensional matrices: def dist(X, Y): sx = np.sum(X**2, axis=1, keepdims=True) sy = np.sum(Y**2, axis=1, keepdims=True) return np.sqrt(-2 * X.dot(Y.T) + sx + sy.T)