ukiy ddlZddlmZddlmZddlmZddlm Z m Z m Z ddl m Z mZmZmZddlmZmZdded ed ed efd Zdded ed ed efd Zdded ed ed efdZdd ed ed efdZd ed efdZd ed efdZd ed efdZy)N)lax)numpy)_const)promote_args_inexactpromote_dtypes_inexactensure_arraylike)xlogyentrgammaln gammaincc)Array ArrayLikekmulocreturnc td|||\}}}t|d}tj||}t ||t |dzz |z }t jt jtj||tjt j||tj |S)a7Poisson log probability mass function. JAX implementation of :obj:`scipy.stats.poisson` ``logpmf``. The Poisson probability mass function is given by .. math:: f(k) = e^{-\mu}\frac{\mu^k}{k!} and is defined for :math:`k \ge 0` and :math:`\mu \ge 0`. Args: k: arraylike, value at which to evaluate the PMF mu: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter Returns: array of logpmf values. See Also: - :func:`jax.scipy.stats.poisson.cdf` - :func:`jax.scipy.stats.poisson.pmf` poisson.logpmfr)r _lax_constrsubr r jnpwhere logical_orltneroundnpinf)rrrzerox log_probss W/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/scipy/stats/poisson.pylogpmfr$s2$$4aSA*!R Aq $ ggao!ArlWQU^+b0) 3>>#&&D/"%&&1q"9;=?VVGY PPcBtjt|||S)a0Poisson probability mass function. JAX implementation of :obj:`scipy.stats.poisson` ``pmf``. The Poisson probability mass function is given by .. math:: f(k) = e^{-\mu}\frac{\mu^k}{k!} and is defined for :math:`k \ge 0` and :math:`\mu \ge 0`. Args: k: arraylike, value at which to evaluate the PMF mu: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter Returns: array of pmf values. See Also: - :func:`jax.scipy.stats.poisson.cdf` - :func:`jax.scipy.stats.poisson.logpmf` )rexpr$)rrrs r#pmfr(:s2 2s# $$r%ctd|||\}}}t|d}tj||}t t j d|z|}t jtj||||S)anPoisson cumulative distribution function. JAX implementation of :obj:`scipy.stats.poisson` ``cdf``. The cumulative distribution function is defined as: .. math:: f_{cdf}(k, p) = \sum_{i=0}^k f_{pmf}(k, p) where :math:`f_{pmf}(k, p)` is the probability mass function :func:`jax.scipy.stats.poisson.pmf`. Args: k: arraylike, value at which to evaluate the CDF mu: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter Returns: array of cdf values. See Also: - :func:`jax.scipy.stats.poisson.pmf` - :func:`jax.scipy.stats.poisson.logpmf` rrr) rrrrr rfloorrr)rrrr r!ps r#cdfr,Vsl4$$4aSA*!R Aq $ ggao! !a% "%! 366!T?D! ,,r%ctd||\}}t||\}}tj|j|j}tj |}tj |}tj|dk(|tj|dkt|tj|dkt|t|}tj||j}tj||S)amShannon entropy of the Poisson distribution. JAX implementation of :obj:`scipy.stats.poisson` ``entropy``. The entropy :math:`H(X)` of a Poisson random variable :math:`X \sim \text{Poisson}(\mu)` is defined as: .. math:: H(X) = -\sum_{k=0}^\infty p(k) \log p(k) where :math:`p(k) = e^{-\mu} \mu^k / k!` for :math:`k \geq \max(0, \lfloor \text{loc} \rfloor)`. This implementation uses **regime switching** for numerical stability and performance: - **Small** :math:`\mu < 10`: Direct summation over PMF with adaptive upper bound :math:`k \leq \mu + 20` - **Medium** :math:`10 \leq \mu < 100`: Summation with bound :math:`k \leq \mu + 10\sqrt{\mu} + 20` - **Large** :math:`\mu \geq 100`: Asymptotic Stirling approximation: :math:`H(\mu) \approx \frac{1}{2} \log(2\pi e \mu) - \frac{1}{12\mu}` Matches SciPy to relative error :math:`< 10^{-5}` across all regimes. Args: mu: arraylike, mean parameter of the Poisson distribution. Must be ``> 0``. loc: arraylike, optional location parameter (default: 0). Accepted for API compatibility with scipy but does not affect the entropy Returns: Array of entropy values with shape broadcast from ``mu`` and ``loc``. Returns ``NaN`` for ``mu <= 0``. Examples: >>> from jax.scipy.stats import poisson >>> poisson.entropy(5.0) Array(2.204394, dtype=float32) >>> poisson.entropy(jax.numpy.array([1, 10, 100])) Array([1.3048419, 2.5614073, 3.7206903], dtype=float32) See Also: - :func:`jax.scipy.stats.poisson.pmf` - :func:`jax.scipy.stats.poisson.logpmf` - :obj:`scipy.stats.poisson` zpoisson.entropyr d) rrrbroadcast_shapesshaperavel zeros_liker_entropy_small_mu_entropy_medium_mu_entropy_large_mureshape broadcast_to) rr promoted_mu promoted_loc result_shapemu_flat zero_resultresultresult_mu_shapes r#entropyr@vsd .C 8'"c4R=+|%%, IIk "'w'+ 99 qLII l  ii# 7#'" &KK (9(9:/  /< 88r%cXd}tj||jdddf}t||d}tj|dzj |j}||dddfk}tj ||d}tjt|dS)uEntropy via direct PMF summation for small μ (< 10). Uses adaptive upper bound k ≤ μ + 20 to capture >99.999% of mass. #dtypeNraxis) rarangerDr(ceilastypersumr rmax_krprobs upper_boundsmask probs_maskeds r#r4r4s % jjbhh'40! aQ-%"r'"))!''2, \$' " "$4,, l#! ,,r%cd}tj||jdddf}t||d}tj|dtj |zzdzj |j}||dddfk}tj||d}tjt|dS) uEntropy for medium mu (10-100): Adaptive bounds based on std dev. Bounds: k ≤ μ + 10√μ + 20. Caps at k=250 for JIT compatibility. rCNrr.rErFrG) rrIrDr(rJsqrtrKrrLr rMs r#r5r5s % jjbhh'40! aQ-%"rCHHRL00256==aggF, \$' " "$4,, l#! ,,r%cdtjdtjztjz|zzdd|zz z S)uwEntropy for large mu (>= 100): Asymptotic approximation. Formula: H(λ) ≈ 0.5*log(2πeλ) - 1/(12λ) + O(λ^-2) g?g? )rlogrpie)rs r#r6r6s; swwq255y244'",- -rBw ??r%)r)rrjax._srcrrjax._src.lax.laxrrjax._src.numpy.utilrrrjax._src.scipy.specialr r r r jax._src.typingr rr$r(r,r@r4r5r6r%r#rbs!1^^BB,PiPYPYPuPB%9%)%)%E%8-9-)-)-E-@R9 R9 R9%R9h-%-E- -5-U- @%@E@r%