uki" ddlZddlmZddlmZddlmZddl m Z ddl m Z m Z dde de d e d e fd Zdde de d e d e fd Zdde de d e d e fd Zdde de d e d e fdZdde de d e d e fdZdde de d e d e fdZdde de d e d e fdZdde de d e d e fdZy)N)lax)_const)arctan)promote_args_inexact)Array ArrayLikexlocscalereturnc td|||\}}}t|tj}t j t j |||}t jt j||}t jt j|t jt 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 V/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/scipy/stats/cauchy.pylogpdfrs8'3F-!S%!RUU" WWSWWQ_e ,(773772u-.. 3778X3N)OP QQcBtjt|||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 <s8 3& ''rc dtd|||\}}}t|tj}t j t j |||}t jt|dt jt j t|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>'|QUC-!S%!RUU" WWSWWQ_e ,( As#SWWSWWZ25F-KVT\M]%^ __rcBtjt|||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"rs rlogcdfr$s> QU# $$rcDtd|||\}}}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"rs rsfr&s->'{AsEB-!S% aR#u rcDtd|||\}}}t| | |S)a$Cauchy distribution log survival function. JAX implementation of :obj:`scipy.stats.cauchy` ``logsf`` The survival function is defined as .. math:: f_{sf}(x) = 1 - f_{cdf}(x) where :math:`f_{cdf}(x)` is the cumulative distribution function, :func:`jax.scipy.stats.cauchy.cdf`. Args: x: arraylike, value at which to evaluate the SF loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array of logsf values. See Also: - :func:`jax.scipy.stats.cauchy.cdf` - :func:`jax.scipy.stats.cauchy.pdf` - :func:`jax.scipy.stats.cauchy.sf` - :func:`jax.scipy.stats.cauchy.logcdf` - :func:`jax.scipy.stats.cauchy.logpdf` - :func:`jax.scipy.stats.cauchy.isf` - :func:`jax.scipy.stats.cauchy.ppf` z cauchy.logsf)rr$rs rlogsfr(s->'~q#uE-!S% SD%  rqc btd|||\}}}t|tj}t|tjdz }t j t 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 risfr1s}2'|QUC-!S%!RUU" q"%%!) $' WWSWWWcggb!n5 6( 5)3 //rcbtd|||\}}}t|tj}t|tjdz }t j t j t 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 rppfr3s}2'|QUC-!S%!RUU" q"%%!) $' WWSWWSWWR^W5 6( 5)3 //r)r)numpyrjax._srcrjax._src.lax.laxrrjax._src.numpy.ufuncsrjax._src.numpy.utilrjax._src.typingrrrr r"r$r&r(r1r3rrr<s1 1(4, Ri Ri RI Re RF(9(9((5(>"`9"`9"`"`5"`J%i%i%I%e%D ) )  % F !Y !Y !9 !U !F09090050@09090050r