def test_broadcasted_scalar_add(self) -> None:
""" In this test t2 is a scalar"""
t1 = Tensor([[1, 2, 3], [4, 5, 6]], requires_grad=True)
t2 = Tensor(1, requires_grad=True)
t3 = t1 + t2
assert t3.data.tolist() == [[2, 3, 4], [5, 6, 7]]
t3.backward(np.asarray([[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]))
assert t1.grad.tolist() == [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
# The gradient of t2 should be doubled since all it's values are
# broadcasted to two places.
assert t2.grad.tolist() == 6.0
# Also try the reverse direction
t1.zero_grad(), t2.zero_grad()
t4 = t2 + t1
assert t4.data.tolist() == [[2, 3, 4], [5, 6, 7]]
t4.backward(np.asarray([[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]))
assert t1.grad.tolist() == [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]
# The gradient of t2 should be doubled since all it's values are
# broadcasted to two places.
assert t2.grad.tolist() == 6.0
def test_axis_sum(self) -> None:
t1 = Tensor([[1.0, 2.0, 3.0], [1.0, 2.0, 3.0]], requires_grad=True)
# First axis
t2 = t1.sum(0)
assert t2.data.tolist() == [2, 4, 6]
t2.backward(np.asarray([1.0, 2.0, 3.0]))
assert t1.grad.tolist() == [[1.0, 2.0, 3.0], [1.0, 2.0, 3.0]]
# Second axis
t1.zero_grad()
t3 = t1.sum(1)
assert t3.data.tolist() == [6, 6]
t3.backward(np.asarray([1.0, 2.0]))
assert t1.grad.tolist() == [[1.0, 1.0, 1.0], [2.0, 2.0, 2.0]]
def test_simple_sum(self) -> None:
t1 = Tensor([1, 2, 3], requires_grad=True)
t2 = t1.sum()
assert t2.data.tolist() == 6
assert t2.requires_grad
t2.backward()
assert t1.grad.tolist() == [1.0, 1.0, 1.0]
# Also try with a specified grad
t1.zero_grad()
t3 = t1.sum()
assert t3.data.tolist() == 6
t2.backward(2)
assert t1.grad.tolist() == [2.0, 2.0, 2.0]
def test_broadcasted_scalar_mul(self) -> None:
""" In this test t2 is a scalar"""
t1 = Tensor([[1, 2, 3], [4, 5, 6]], requires_grad=True)
t2 = Tensor(2, requires_grad=True)
t3 = t1 * t2
assert t3.data.tolist() == [[2, 4, 6], [8, 10, 12]]
t3.backward(np.asarray([[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]))
assert t1.grad.tolist() == [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]
assert t2.grad.tolist() == 21.0
# Also try the reverse direction
t1.zero_grad(), t2.zero_grad()
t4 = t2 * t1
assert t4.data.tolist() == [[2, 4, 6], [8, 10, 12]]
t4.backward(np.asarray([[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]))
assert t1.grad.tolist() == [[2.0, 2.0, 2.0], [2.0, 2.0, 2.0]]
assert t2.grad.tolist() == 21.0
bias = 2
y = x @ coefs + bias
# Our model
w = Tensor(np.random.randn(3), requires_grad=True)
b = Tensor(np.random.rand(), requires_grad=True)
# Train the model
lr = 0.001
batch_size = 25
for _ in range(1000):
# Train in batches
idx = np.arange(x.shape[0])
np.random.shuffle(idx)
w.zero_grad(), b.zero_grad()
for start in range(0, x.shape[0], batch_size):
batch_idx = idx[start:start + batch_size]
pred = x[batch_idx] @ w + b
errors = y[batch_idx] - pred
mse_loss = (errors * errors).sum()
mse_loss.backward()
print(mse_loss.data)
# Gradient Descent
w.data -= lr * w.grad
b.data -= lr * b.grad
print(f"Target function: coefficients={coefs.data}, bias={bias}")