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 range(num_test):
# Note axis=1 computes norm along rows
dists[i] = np.linalg.norm(X[i]-self.X_train, axis=1)
return dists
Difference was: 0.000000
Good! The distance matrices are the samedef 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 range(num_test):
for j in range(num_train):
dists[i, j] = np.linalg.norm(X[i]-self.X_train[j])
return dists
(500, 5000)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]
# Expand ||x - y||**2 = ||x||**2 - 2 x.T ⋅y + ||y||**2,
# where ||x||**2 = sum(x**2) (element-wise on matrix rows)
# The final result is a (num_test, num_train) matrix
# so the x**2 and y**2 intermediates must be reshaped appropriately
x2 = np.sum(X**2, axis=1).reshape((num_test, 1))
y2 = np.sum(self.X_train**2, axis=1).reshape((1, num_train))
xy = -2*np.matmul(X, self.X_train.T)
dists = np.sqrt(x2 + xy + y2)
return dists
Difference was: 0.000000
Good! The distance matrices are the same