lucid.hstack

lucid.hstack(arr: tuple[Tensor, ...], /) → Tensor

The hstack function stacks a sequence of tensors horizontally (column-wise) along the second dimension (axis=1 by default).

It concatenates the input tensors along the specified axis, effectively increasing the size of that dimension.

Function Signature

def hstack(arr: tuple[Tensor, ...]) -> Tensor

Parameters

  • arr (tuple[Tensor, …]):

    A sequence of tensors to be horizontally stacked. All tensors must have the same shape except in the dimension corresponding to axis.

Returns

  • Tensor:

    A new tensor resulting from horizontally stacking the input tensors. The resulting tensor has the same number of dimensions as the input tensors, with the size along the horizontal axis (axis=1 by default) being the sum of the sizes of the input tensors along that axis.

Forward Calculation

The hstack operation concatenates the input tensors along the horizontal axis.

\[\mathbf{out} = \text{hstack}(\mathbf{a}_1, \mathbf{a}_2, \dots, \mathbf{a}_n)\]

Backward Gradient Calculation

The gradient for the hstack operation is split and passed to each of the input tensors along the concatenated axis.

\[\frac{\partial \mathbf{out}}{\partial \mathbf{a}_i} = \mathbf{I}_i\]

Example

>>> import lucid
>>> a = Tensor([[1.0, 2.0]], requires_grad=True)
>>> b = Tensor([[3.0, 4.0]], requires_grad=True)
>>> h_stacked = lucid.hstack((a, b))
>>> print(h_stacked)
Tensor([[1. 2. 3. 4.]], grad=None)

>>> c = Tensor([[5.0, 6.0]], requires_grad=True)
>>> h_stacked = lucid.hstack((a, b, c))
>>> print(h_stacked)
Tensor([[1. 2. 3. 4. 5. 6.]], grad=None)

Note

  • All input tensors must have the same shape except in the dimension corresponding to the horizontal axis (axis=1 by default).

  • The hstack operation increases the size of the specified axis by concatenating the input tensors.

  • The resulting tensor will have the same number of dimensions as the input tensors.

  • If any of the input tensors require gradients, the resulting tensor will also require gradients.

  • The horizontal axis can be adjusted by modifying the underlying implementation if necessary.