ones

→Tensor

ones(size: _int | tuple[_int, ...] = (), dtype: DTypeLike = None, device: DeviceLike = None, requires_grad: _bool = False)

source

Return a tensor filled with the multiplicative identity element, one.

Allocates a new tensor of the requested shape and fills every element with the scalar value $1$ . Every entry satisfies

O_{i_1, \ldots, i_n} = 1 \quad \forall\; (i_1, \ldots, i_n) \in \prod_k [0, s_k)

One-initialisation is the canonical starting point for multiplicative accumulators, scale parameters in normalisation layers (before any training), and homogeneous coordinate vectors in projective geometry.

Parameters

*sizeint or tuple[int, ...]

Shape of the output tensor. Accepts separate ints ones(2, 3) or a single tuple ones((2, 3)).

dtypelucid.dtype

Scalar data type. Defaults to the global default dtype (lucid.float32 unless overridden).

devicestr or lucid.device

Target device — "cpu" or "metal".

requires_gradbool

If True, downstream operations are tracked by autograd. Default: False.

Returns

Tensor

Tensor of shape size filled with ones.

Notes

The all-ones vector $\mathbf{1} \in \mathbb{R}^n$ plays an important role in matrix algebra: multiplying a matrix $A$ on the right by $\mathbf{1}$ computes its row sums, $A\mathbf{1} = \text{rowsum}(A)$ . This is useful when implementing attention masks, normalisation denominators, and indicator functions.

Examples

>>> import lucid
>>> lucid.ones(4).tolist()
[1.0, 1.0, 1.0, 1.0]
>>> lucid.ones(2, 2, dtype=lucid.int8)
Tensor([[1, 1],
        [1, 1]], dtype=int8)
Row-sum via matrix-vector product:
>>> A = lucid.tensor([[1.0, 2.0], [3.0, 4.0]])
>>> row_sums = A @ lucid.ones(2)
>>> row_sums.tolist()
[3.0, 7.0]