pypomp.random.fast_gamma

pypomp.random.fast_gamma(key: Array, alpha: Array, dtype: dtype | None = None, adjustment_size: int = 3, newton_steps: int = 3) → Array[source]

Sample Gamma random variates using a GPU-optimized inverse CDF algorithm.

Generates Gamma(alpha, 1)-distributed samples using an approximate inverse CDF method based on Temme (1992) [1]. A multi-step adjustment trick extends accuracy to alpha values less than 2. Results are very close to exact but not guaranteed to be identical to a reference sampler.

Parameters:

  • key (jax.Array) – JAX PRNG key.

  • alpha (jax.Array) – Shape parameter(s) for the Gamma(alpha, 1) distribution. Must be positive.

  • dtype (np.dtype or None, optional) – Floating-point output dtype. Defaults to float64 if jax_enable_x64=True, otherwise float32.

  • adjustment_size (int, optional) – Number of uniform adjustments to apply for small-alpha accuracy. Defaults to 3.

  • newton_steps (int, optional) – Number of Newton-Raphson refinement steps. Defaults to 3.

Returns:

Gamma samples with the same shape as alpha.

Return type:

jax.Array

Notes

For speed and accuracy metrics, see the Quant Tests.

Examples

>>> import jax
>>> import jax.numpy as jnp
>>> from pypomp.random import fast_gamma
>>> fast_gamma(jax.random.key(0), alpha=jnp.array(2.0))
Array(1.8..., dtype=float32)

References