def subtract(left: Tensor, right: Tensor):
left, right = coalesce(left, right)
return Tensor.from_numpy(
data=left.data - right.data,
backward=lambda gradient: Gradients.accumulate(
Gradient(tensor=left, gradient=gradient),
Gradient(tensor=right, gradient=-gradient),
),
)
def divide(left: Tensor, right: Tensor):
left, right = coalesce(left, right)
return Tensor.from_numpy(
data=left.data / right.data,
backward=lambda gradient: Gradients.accumulate(
Gradient(tensor=left, gradient=gradient / right.data),
Gradient(
tensor=right,
gradient=-gradient * left.data / np.square(right.data),
),
),
)
def matrix_multiply(left: Tensor, right: Tensor):
left = coalesce(left)
right = coalesce(right)
assert len(left.shape) == 2
assert len(right.shape) == 2
assert left.shape[1] == right.shape[0]
return Tensor.from_numpy(
data=np.matmul(left.data, right.data),
backward=lambda gradient: Gradients.accumulate(
Gradient(tensor=left, gradient=np.matmul(gradient, right.data.T)),
Gradient(tensor=right, gradient=np.matmul(left.data.T, gradient)),
),
)
def negate(tensor: Tensor):
tensor = coalesce(tensor)
return Tensor.from_numpy(
data=-tensor.data,
backward=lambda gradient: Gradients.accumulate(
Gradient(tensor=tensor, gradient=-gradient)),
)
def exp(tensor: Tensor):
tensor = coalesce(tensor)
return Tensor.from_numpy(
data=np.exp(tensor.data),
backward=lambda gradient: Gradients.accumulate(
Gradient(tensor=tensor, gradient=gradient * np.exp(tensor.data))),
)
def squeeze(tensor: Tensor, axes: Union[None, int, Tuple[int]] = None):
tensor = coalesce(tensor)
axes = () if axes is None else tuplify(axes)
return Tensor.from_numpy(
data=np.squeeze(tensor.data, axes),
backward=lambda gradient: Gradients.accumulate(
Gradient(tensor=tensor, gradient=np.expand_dims(gradient, axes))),
)
def sum(tensor: Tensor, axes=None):
tensor = coalesce(tensor)
axes = tuplify(range(len(tensor.shape)) if axes is None else axes)
return Tensor.from_numpy(
data=tensor.data.sum(axes),
backward=lambda gradient: Gradients.accumulate(
Gradient(
tensor=tensor,
gradient=np.tile(
np.expand_dims(gradient, axes),
[
dim if idx in axes or idx - len(tensor.shape) in axes else 1
for idx, dim in enumerate(tensor.shape)
],
),
)
),
)
def tile(tensor: Tensor, tiling: Tuple[int]):
tensor = coalesce(tensor)
tiling = tuple(tiling)
assert len(tensor.shape) == len(tiling)
return Tensor.from_numpy(
data=np.tile(tensor.data, tiling),
backward=lambda gradient: Gradients.accumulate(
Gradient(
tensor=tensor,
gradient=np.reshape(
gradient,
[
value for idx, dim in enumerate(tensor.shape)
for value in [tiling[idx], dim]
],
).sum(tuple(range(0,
len(tiling) * 2, 2))),
)),
)
def backward(gradient: np.ndarray):
result = gradient.copy()
result[(tensor.data < low.data) | (tensor.data > high.data)] = 0
return Gradients.accumulate(Gradient(tensor=tensor, gradient=result))