Ë ñuki¤ã ó—ddlZddlmZddlmZddlmZddlm Z ddl m Z m Z m Z mZddlmZmZdded ed ed ed ef d „Zdded ed ed ed ef d„Zdded ed ed ed ef d„Zdded ed ed ed ef d„Zdded ed ed ed ef d„Zdded ed ed ed ef d„Zy)éN)Úlax)Únumpy)Ú_const)Úpromote_args_inexact)ÚgammalnÚxlogyÚgammaincÚ gammaincc)ÚArrayÚ ArrayLikeÚxÚaÚlocÚscaleÚreturnc ó0—td||||«\}}}}tj||«}t|d«}t j |tj tj||«|«|«}tjttj||«|«|«}tjt|«tj|««}tj||«} t j || tj «S)a4Gamma log probability distribution function. JAX implementation of :obj:`scipy.stats.gamma` ``logpdf``. The Gamma probability distribution is given by .. math:: f(x, a) = \frac{1}{\Gamma(a)}x^{a-1}e^{-x} Where :math:`\Gamma(a)` is the :func:`~jax.scipy.special.gamma` function. It is defined for :math:`x \ge 0` and :math:`a > 0`. Args: x: arraylike, value at which to evaluate the PDF a: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logpdf values. See Also: - :func:`jax.scipy.stats.gamma.cdf` - :func:`jax.scipy.stats.gamma.pdf` - :func:`jax.scipy.stats.gamma.sf` - :func:`jax.scipy.stats.gamma.logcdf` - :func:`jax.scipy.stats.gamma.logsf` z gamma.logpdfé)rrÚgeÚ _lax_constÚjnpÚwhereÚdivÚsubrÚaddrÚlogÚnpÚinf) r rrrÚokÚoneÚyÚlog_linear_termÚ shape_termsÚ log_probss úU/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/scipy/stats/gamma.pyÚlogpdfr%sÇ€ô<*¨.¸!¸QÀÀUÓKÑ€!€QˆˆUÜ ‡vvˆaƒ~€"Ü1aÓ€#Ü ‡ii”C—G‘GœCŸG™G A s›O¨UÓ3°SÓ9€!Ü—G‘GœE¤#§'¡'¨!¨S£/°1Ó5°qÓ9€/Ü—‘œ › ¤C§G¡G¨E£NÓ3€+Üg‰go {Ó3€)Ü ‰2y¤2§6¡6 'Ó *Ð*ócóD—tjt||||««S)a-Gamma probability distribution function. JAX implementation of :obj:`scipy.stats.gamma` ``pdf``. The Gamma probability distribution is given by .. math:: f(x, a) = \frac{1}{\Gamma(a)}x^{a-1}e^{-x} Where :math:`\Gamma(a)` is the :func:`~jax.scipy.special.gamma` function. It is defined for :math:`x \ge 0` and :math:`a > 0`. Args: x: arraylike, value at which to evaluate the PDF a: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of pdf values. See Also: - :func:`jax.scipy.stats.gamma.cdf` - :func:`jax.scipy.stats.gamma.sf` - :func:`jax.scipy.stats.gamma.logcdf` - :func:`jax.scipy.stats.gamma.logpdf` - :func:`jax.scipy.stats.gamma.logsf` )rÚexpr%©r rrrs r$Úpdfr*As€ô< ‰”˜˜1˜c 5Ó)Ó *Ð*r&c ó—td||||«\}}}}t|tjt |d«tj tj ||«|«t |tj«««S)aGamma cumulative distribution function. JAX implementation of :obj:`scipy.stats.gamma` ``cdf``. The cdf is defined as .. math:: f_{cdf}(x, a) = \int_{-\infty}^x f_{pdf}(y, a)\mathrm{d}y where :math:`f_{pdf}` is the probability density function, :func:`jax.scipy.stats.gamma.pdf`. Args: x: arraylike, value at which to evaluate the CDF a: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of cdf values. See Also: - :func:`jax.scipy.stats.gamma.pdf` - :func:`jax.scipy.stats.gamma.sf` - :func:`jax.scipy.stats.gamma.logcdf` - :func:`jax.scipy.stats.gamma.logpdf` - :func:`jax.scipy.stats.gamma.logsf` z gamma.cdfr) rr rÚclamprrrrrr)s r$Úcdfr-bsk€ô<*¨+°q¸!¸SÀ%ÓHÑ€!€QˆˆUÜ Ø܇IIÜAÓÜ ‡ggŒcg‰ga˜‹o˜uÓ%Ü”B—F‘FÓóó ðr&cóD—tjt||||««S)aGamma log cumulative distribution function. JAX implementation of :obj:`scipy.stats.gamma` ``logcdf``. The cdf is defined as .. math:: f_{cdf}(x, a) = \int_{-\infty}^x f_{pdf}(y, a)\mathrm{d}y where :math:`f_{pdf}` is the probability density function, :func:`jax.scipy.stats.gamma.pdf`. Args: x: arraylike, value at which to evaluate the CDF a: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logcdf values. See Also: - :func:`jax.scipy.stats.gamma.cdf` - :func:`jax.scipy.stats.gamma.pdf` - :func:`jax.scipy.stats.gamma.sf` - :func:`jax.scipy.stats.gamma.logpdf` - :func:`jax.scipy.stats.gamma.logsf` )rrr-r)s r$Úlogcdfr/‹s€ô< ‰”Q˜˜3 Ó&Ó 'Ð'r&c óü—td||||«\}}}}tjtj||«|«}t j tj |t|d««dt||««S)aïGamma survival function. JAX implementation of :obj:`scipy.stats.gamma` ``sf``. The survival function is defined as .. math:: f_{sf}(x, k) = 1 - f_{cdf}(x, k) where :math:`f_{cdf}(x, k)` is the cumulative distribution function, :func:`jax.scipy.stats.gamma.cdf`. Args: x: arraylike, value at which to evaluate the SF a: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of sf values. See Also: - :func:`jax.scipy.stats.gamma.cdf` - :func:`jax.scipy.stats.gamma.pdf` - :func:`jax.scipy.stats.gamma.logcdf` - :func:`jax.scipy.stats.gamma.logpdf` - :func:`jax.scipy.stats.gamma.logsf` zgamma.sfrr) rrrrrrÚltrr )r rrrr s r$Úsfr2¬sd€ô<*¨*°a¸¸CÀÓGÑ€!€QˆˆUÜ ‡ggŒcg‰ga˜‹o˜uÓ%€!Ü ‰”3—6‘6˜!œZ¨¨1Ó-Ó.°´9¸QÀ³?Ó CÐCr&cóD—tjt||||««S)aöGamma log survival function. JAX implementation of :obj:`scipy.stats.gamma` ``logsf``. The survival function is defined as .. math:: f_{sf}(x, k) = 1 - f_{cdf}(x, k) where :math:`f_{cdf}(x, k)` is the cumulative distribution function, :func:`jax.scipy.stats.gamma.cdf`. Args: x: arraylike, value at which to evaluate the SF a: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logsf values. See Also: - :func:`jax.scipy.stats.gamma.cdf` - :func:`jax.scipy.stats.gamma.pdf` - :func:`jax.scipy.stats.gamma.sf` - :func:`jax.scipy.stats.gamma.logcdf` - :func:`jax.scipy.stats.gamma.logpdf` )rrr2r)s r$Úlogsfr4Ïs€ô< ‰”Aq˜#˜uÓ%Ó &Ð&r&)rr)rrÚjax._srcrrÚjax._src.lax.laxrrÚjax._src.numpy.utilrÚjax._src.scipy.specialrrr r Újax._src.typingr r r%r*r-r/r2r4©r&r$úr;s ðóåÝ!Ý1Ý4ßFÓFß,ñ%+ˆið%+˜Ið%+¨Ið%+À)ð%+ÐTYó%+ñP+ˆ9ð+˜ð+¨ð+¸yð+ÐQVó+ñB&ˆ9ð&˜ð&¨ð&¸yð&ÐQVó&ñR(ˆið(˜Ið(¨Ið(À)ð(ÐTYó(ñB Dˆ)ð D˜ ð D¨ ð D¸ið DÐPUó DñF'ˆYð'˜9ð'¨9ð'Àð'ÐSXô'r&