lucid.vstack¶

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

The vstack function stacks a sequence of tensors vertically (row-wise) along the first dimension (axis=0 by default).

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

Function Signature¶

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

Parameters¶

arr (tuple[Tensor, …]):
A sequence of tensors to be vertically stacked. All tensors must have the same shape except in the dimension corresponding to axis.

Returns¶

Tensor:
A new tensor resulting from vertically stacking the input tensors. The resulting tensor has the same number of dimensions as the input tensors, with the size along the vertical axis (axis=0 by default) being the sum of the sizes of the input tensors along that axis.

Forward Calculation¶

The vstack operation concatenates the input tensors along the vertical axis.

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

Backward Gradient Calculation¶

The gradient for the vstack 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)
>>> v_stacked = lucid.vstack((a, b))
>>> print(v_stacked)
Tensor([[1. 2.],
        [3. 4.]], grad=None)

>>> c = Tensor([[5.0, 6.0]], requires_grad=True)
>>> v_stacked = lucid.vstack((a, b, c))
>>> print(v_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 vertical axis (axis=0 by default).
The vstack 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 vertical axis can be adjusted by modifying the underlying implementation if necessary.