rand

→Tensor

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

source

Return a tensor of samples drawn from the continuous uniform distribution.

Each element is drawn independently from $U[0, 1)$ , the uniform distribution on the half-open unit interval:

X_i \sim U[0, 1), \quad f_X(x) = \begin{cases} 1 & 0 \le x < 1 \\ 0 & \text{otherwise} \end{cases}

The distribution has mean $\mathbb{E}[X] = \tfrac{1}{2}$ and variance $\operatorname{Var}[X] = \tfrac{1}{12}$ .

Parameters

*sizeint or tuple[int, ...]

Shape of the output tensor. Accepts varargs rand(2, 3) or a single tuple rand((2, 3)).

dtypelucid.dtype

Floating-point data type. Defaults to the global default (lucid.float32). Integer dtypes are not supported.

devicestr or lucid.device

Target device — "cpu" or "metal".

requires_gradbool

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

generatorlucid._C.engine.Generator

Explicit generator to use. When None (default), the global default generator is used.

Returns

Tensor

Tensor of shape size with values in $[0, 1)$ .

Notes

Internally the engine applies the Philox bijection and converts the raw 32-bit output to a float via the standard IEEE 754 mantissa trick:

\begin{aligned} x = (u \;\&\; \texttt{0x007FFFFF}) \;\big|\; \texttt{0x3F800000} \;\text{(reinterpreted as float32)} \;-\; 1.0 \end{aligned}

yielding $2^{23}$ equally spaced values in $[0, 1)$ with spacing $2^{-23} \approx 1.19 \times 10^{-7}$ .

Examples

>>> import lucid
>>> lucid.manual_seed(0)
>>> x = lucid.rand(3, 4)
>>> x.shape
(3, 4)
>>> float(x.min()) >= 0.0 and float(x.max()) < 1.0
True
Monte-Carlo estimate of $\pi$:
>>> lucid.manual_seed(0)
>>> n = 1_000_000
>>> pts = lucid.rand(n, 2)
>>> inside = ((pts ** 2).sum(dim=-1) < 1.0).float().mean()
>>> float(inside) * 4   # ≈ 3.1416