Vpf" ddlZddlmZddlmZddlmZddl m Z ddl m Z m Z dde d e d e d e fd Zdde d e d e d e fd Zdde d e d e d e fdZdde d e d e d e fdZdde d e d e d e fdZdde d e d e d e fdZdde d e d e d e fdZdde d e d e d e fdZdS)N)lax)_const)promote_args_inexact)arctan)Array ArrayLikexlocscalereturnc td|||\}}}t|tj}t jt j|||}t jt j||}t j t j |t j t j||S)aCauchy log probability distribution function. JAX implementation of :obj:`scipy.stats.cauchy` ``logpdf``. The Cauchy probability distribution function is .. math:: f(x) = \frac{1}{\pi(1 + x^2)} Args: x: arraylike, value at which to evaluate the PDF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logpdf values See Also: - :func:`jax.scipy.stats.cauchy.cdf` - :func:`jax.scipy.stats.cauchy.pdf` - :func:`jax.scipy.stats.cauchy.sf` - :func:`jax.scipy.stats.cauchy.logcdf` - :func:`jax.scipy.stats.cauchy.logsf` - :func:`jax.scipy.stats.cauchy.isf` - :func:`jax.scipy.stats.cauchy.ppf` z cauchy.logpdf) r _lax_constnppirdivsublogmulnegaddlog1p)r r r rscaled_xnormalize_terms [/var/www/html/nettyfy-visnx/env/lib/python3.11/site-packages/jax/_src/scipy/stats/cauchy.pylogpdfrs8'3FF-!S%!RU" WSWQ__e , ,(7372u--... 378X3N3N)O)OPP Q QQcHtjt|||S)aCauchy probability distribution function. JAX implementation of :obj:`scipy.stats.cauchy` ``pdf``. The Cauchy probability distribution function is .. math:: f(x) = \frac{1}{\pi(1 + x^2)} Args: x: arraylike, value at which to evaluate the PDF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of pdf values See Also: - :func:`jax.scipy.stats.cauchy.cdf` - :func:`jax.scipy.stats.cauchy.sf` - :func:`jax.scipy.stats.cauchy.logcdf` - :func:`jax.scipy.stats.cauchy.logpdf` - :func:`jax.scipy.stats.cauchy.logsf` - :func:`jax.scipy.stats.cauchy.isf` - :func:`jax.scipy.stats.cauchy.ppf` )rexprr r r s rpdfr!<s 8 3&& ' ''rc ztd|||\}}}t|tj}t jt j|||}t jt|dt jt jt|d|t|S)a5Cauchy cumulative distribution function. JAX implementation of :obj:`scipy.stats.cauchy` ``cdf``. The cdf is defined as .. math:: f_{cdf} = \int_{-\infty}^x f_{pdf}(y) \mathrm{d}y where here :math:`f_{pdf}` is the Cauchy probability distribution function, :func:`jax.scipy.stats.cauchy.pdf`. Args: x: arraylike, value at which to evaluate the CDF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of cdf values. See Also: - :func:`jax.scipy.stats.cauchy.pdf` - :func:`jax.scipy.stats.cauchy.sf` - :func:`jax.scipy.stats.cauchy.logcdf` - :func:`jax.scipy.stats.cauchy.logpdf` - :func:`jax.scipy.stats.cauchy.logsf` - :func:`jax.scipy.stats.cauchy.isf` - :func:`jax.scipy.stats.cauchy.ppf` z cauchy.cdfg?g?) rrrrrrrrrr)r r r rrs rcdfr#[s>'|QUCC-!S%!RU" WSWQ__e , ,( As##SWSWZ25F5F-K-KVT\M]M]%^%^ _ __rcHtjt|||S)a;Cauchy log cumulative distribution function. JAX implementation of :obj:`scipy.stats.cauchy` ``logcdf`` The cdf is defined as .. math:: f_{cdf} = \int_{-\infty}^x f_{pdf}(y) \mathrm{d}y where here :math:`f_{pdf}` is the Cauchy probability distribution function, :func:`jax.scipy.stats.cauchy.pdf`. Args: x: arraylike, value at which to evaluate the CDF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logcdf values. See Also: - :func:`jax.scipy.stats.cauchy.cdf` - :func:`jax.scipy.stats.cauchy.pdf` - :func:`jax.scipy.stats.cauchy.sf` - :func:`jax.scipy.stats.cauchy.logpdf` - :func:`jax.scipy.stats.cauchy.logsf` - :func:`jax.scipy.stats.cauchy.isf` - :func:`jax.scipy.stats.cauchy.ppf` )rrr#r s rlogcdfr%s > QU## $ $$rcTtd|||\}}}t| | |S)a!Cauchy distribution log survival function. JAX implementation of :obj:`scipy.stats.cauchy` ``sf``. The survival function is defined as .. math:: f_{sf}(x) = 1 - f_{cdf}(x) where :math:`f_{cdf}(x)` is the cumulative distribution function, :func:`jax.scipy.stats.cauchy.cdf`. Args: x: arraylike, value at which to evaluate the SF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of sf values See Also: - :func:`jax.scipy.stats.cauchy.cdf` - :func:`jax.scipy.stats.cauchy.pdf` - :func:`jax.scipy.stats.cauchy.logcdf` - :func:`jax.scipy.stats.cauchy.logpdf` - :func:`jax.scipy.stats.cauchy.logsf` - :func:`jax.scipy.stats.cauchy.isf` - :func:`jax.scipy.stats.cauchy.ppf` z cauchy.sf)rr#r s rsfr's3>'{AsEBB-!S% aR#u  rcTtd|||\}}}t| | |S)a$Cauchy distribution log survival function. JAX implementation of :obj:`scipy.stats.cauchy` ``logsf`` The survival function is defined as .. math:: f_{sf}(x) = 1 - f_{cdf}(x) where :math:`f_{cdf}(x)` is the cumulative distribution function, :func:`jax.scipy.stats.cauchy.cdf`. Args: x: arraylike, value at which to evaluate the SF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logsf values. See Also: - :func:`jax.scipy.stats.cauchy.cdf` - :func:`jax.scipy.stats.cauchy.pdf` - :func:`jax.scipy.stats.cauchy.sf` - :func:`jax.scipy.stats.cauchy.logcdf` - :func:`jax.scipy.stats.cauchy.logpdf` - :func:`jax.scipy.stats.cauchy.isf` - :func:`jax.scipy.stats.cauchy.ppf` z cauchy.logsf)rr%r s rlogsfr)s3>'~q#uEE-!S% SD%  rqc `td|||\}}}t|tj}t|tjdz }t jt j|t j||}t jt j|||S)aCauchy distribution inverse survival function. JAX implementation of :obj:`scipy.stats.cauchy` ``isf``. Returns the inverse of the survival function, :func:`jax.scipy.stats.cauchy.sf`. Args: q: arraylike, value at which to evaluate the ISF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of isf values. See Also: - :func:`jax.scipy.stats.cauchy.cdf` - :func:`jax.scipy.stats.cauchy.pdf` - :func:`jax.scipy.stats.cauchy.sf` - :func:`jax.scipy.stats.cauchy.logcdf` - :func:`jax.scipy.stats.cauchy.logpdf` - :func:`jax.scipy.stats.cauchy.logsf` - :func:`jax.scipy.stats.cauchy.ppf` z cauchy.isf rrrrrtanrrrr*r r rhalf_piunscaleds risfr2s2'|QUCC-!S%!RU" q"%!) $ $' WSWWcgb!nn55 6 6( 5))3 / //rc`td|||\}}}t|tj}t|tjdz }t jt jt j|||}t jt j|||S)aCauchy distribution percent point function. JAX implementation of :obj:`scipy.stats.cauchy` ``ppf``. The percent point function is defined as the inverse of the cumulative distribution function, :func:`jax.scipy.stats.cauchy.cdf`. Args: q: arraylike, value at which to evaluate the PPF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of ppf values. See Also: - :func:`jax.scipy.stats.cauchy.cdf` - :func:`jax.scipy.stats.cauchy.pdf` - :func:`jax.scipy.stats.cauchy.sf` - :func:`jax.scipy.stats.cauchy.logcdf` - :func:`jax.scipy.stats.cauchy.logpdf` - :func:`jax.scipy.stats.cauchy.logsf` - :func:`jax.scipy.stats.cauchy.isf` z cauchy.ppfr,r-r/s rppfr4s2'|QUCC-!S%!RU" q"%!) $ $' WSWSWR^^W55 6 6( 5))3 / //r)rr )numpyrjaxrjax._src.lax.laxrrjax._src.numpy.utilr jax.numpyrjax._src.typingrrrr!r#r%r'r)r2r4rrr<s= 111111444444,,,,,,,, R Ri Ri RI Re R R R RF((9(9((5((((>"`"`9"`9"`"`5"`"`"`"`J%%i%i%I%e%%%%D  ) )  %    F ! !Y !Y !9 !U ! ! ! !F009090050000@00909005000000r