poisson

→Tensor

poisson(input: Tensor, generator: _C_engine.Generator | None = None)

Sample element-wise from $\mathrm{Poisson}(\text{rate} = \text{input}[i])$ .

inputTensor

Non-negative rates

\lambda_i

per output position. Any shape.

generatorengine.Generator= None

Override Lucid's default Philox generator with an isolated stream. When None (default), draws are controlled by manual_seed.

Tensor

int64 tensor with the same shape as input. Zero rates always return zero.

ValueError

If any element of input is negative.

Two-branch implementation:

Knuth's multiplication method for rate < 30 — exact but runtime grows with the rate.
Normal approximation $\mathrm{Pois}(\lambda) \approx \lfloor \mathcal{N}(\lambda, \sqrt{\lambda}) + 0.5 \rfloor$ for rate >= 30 — bias < 0.05 standard deviations, orders of magnitude faster than Knuth in the tail.