ukim ddlZddlmZddlmZddlmZddlm Z ddl m Z m Z ddl mZmZdded ed ed ed ef d Zdded ed ed ed ef dZdded ed ed ed ef dZdded ed ed ed ef dZdded ed ed ed ef dZdded ed ed ed ef dZy)N)lax)numpy)_const)promote_args_inexact)gammainc gammaincc)Array ArrayLikexdflocscalereturnc td||||\}}}}t|d}t|d}tjtj|||}tj||}tjtj tj||tj |tj||}tjtjtj|tjtj tj |||} tjtj| tj ||} tjtj||tj | S)aChi-square log probability distribution function. JAX implementation of :obj:`scipy.stats.chi2` ``logpdf``. The chi-square probability distribution function is given by: .. math:: f(x, k) = \begin{cases} \frac{x^{k/2-1}e^{-x/2}}{2^{k/2}\Gamma(k/2)} & x \ge 0 \\ 0 & \mathrm{otherwise} \end{cases} for :math:`k` degrees of freedom, and where :math:`\Gamma` is the :func:`~jax.scipy.special.gamma` function. JAX follows the scipy convention of using ``df`` to denote degrees of freedom. Args: x: arraylike, value at which to evaluate the PDF df: 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.chi2.cdf` - :func:`jax.scipy.stats.chi2.pdf` - :func:`jax.scipy.stats.chi2.sf` - :func:`jax.scipy.stats.chi2.logcdf` - :func:`jax.scipy.stats.chi2.logsf` z chi2.logpdf)r _lax_constrdivsubmullognegaddlgammajnpwhereltnpinf) r r r ronetwoy df_on_twokernel nrml_cnst log_probss T/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/scipy/stats/chi2.pylogpdfr(s"D+=!ReL!Re1a#1a# ggcggaou%!ggb#) 773773779c2CGGAJ?3 P&ggcggcjj3CGGCGGCGGCLRTBFF7I 66cDtjt||||S)aChi-square probability distribution function. JAX implementation of :obj:`scipy.stats.chi2` ``pdf``. The chi-square probability distribution function is given by: .. math:: f(x, k) = \begin{cases} \frac{x^{k/2-1}e^{-x/2}}{2^{k/2}\Gamma(k/2)} & x \ge 0 \\ 0 & \mathrm{otherwise} \end{cases} for :math:`k` degrees of freedom, and where :math:`\Gamma` is the :func:`~jax.scipy.special.gamma` function. JAX follows the scipy convention of using ``df`` to denote degrees of freedom. Args: x: arraylike, value at which to evaluate the PDF df: 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.chi2.cdf` - :func:`jax.scipy.stats.chi2.sf` - :func:`jax.scipy.stats.chi2.logcdf` - :func:`jax.scipy.stats.chi2.logpdf` - :func:`jax.scipy.stats.chi2.logsf` )rexpr(r r r rs r'pdfr-IsD 2sE* ++r)c htd||||\}}}}t|d}ttj||tj t|dtjtj ||tj||t|tjS)aQChi-square cumulative distribution function. JAX implementation of :obj:`scipy.stats.chi2` ``cdf``. The cdf is defined as .. math:: f_{cdf}(x, k) = \int_{-\infty}^x f_{pdf}(y, k)\mathrm{d}y where :math:`f_{pdf}` is the probability density function, :func:`jax.scipy.stats.chi2.pdf`. JAX follows the scipy convention of using ``df`` to denote degrees of freedom. Args: x: arraylike, value at which to evaluate the CDF df: 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.chi2.pdf` - :func:`jax.scipy.stats.chi2.sf` - :func:`jax.scipy.stats.chi2.logcdf` - :func:`jax.scipy.stats.chi2.logpdf` - :func:`jax.scipy.stats.chi2.logsf` zchi2.cdfrr) rrrrrclamprrrrr r r rr!s r'cdfr1ns>+:q"c5I!Re5!# GGBIIA gg 3 sBFF   r)cDtjt||||S)aWChi-square log cumulative distribution function. JAX implementation of :obj:`scipy.stats.chi2` ``logcdf``. The cdf is defined as .. math:: f_{cdf}(x, k) = \int_{-\infty}^x f_{pdf}(y, k)\mathrm{d}y where :math:`f_{pdf}` is the probability density function, :func:`jax.scipy.stats.chi2.pdf`. JAX follows the scipy convention of using ``df`` to denote degrees of freedom. Args: x: arraylike, value at which to evaluate the CDF df: 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.chi2.cdf` - :func:`jax.scipy.stats.chi2.pdf` - :func:`jax.scipy.stats.chi2.sf` - :func:`jax.scipy.stats.chi2.logpdf` - :func:`jax.scipy.stats.chi2.logsf` )rrr1r,s r'logcdfr3s> QC' ((r)c htd||||\}}}}t|d}ttj||tj t|dtjtj ||tj||t|tjS)a?Chi-square survival function. JAX implementation of :obj:`scipy.stats.chi2` ``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.chi2.cdf`. JAX follows the scipy convention of using ``df`` to denote degrees of freedom. Args: x: arraylike, value at which to evaluate the SF df: 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.chi2.cdf` - :func:`jax.scipy.stats.chi2.pdf` - :func:`jax.scipy.stats.chi2.logcdf` - :func:`jax.scipy.stats.chi2.logpdf` - :func:`jax.scipy.stats.chi2.logsf` zchi2.sfrr) rrrrrr/rrrrr0s r'sfr5s>+9aS%H!Re5!# GGBIIA gg 3 sBFF   r)cDtjt||||S)aFChi-square log survival function. JAX implementation of :obj:`scipy.stats.chi2` ``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.chi2.cdf`. JAX follows the scipy convention of using ``df`` to denote degrees of freedom. Args: x: arraylike, value at which to evaluate the SF df: 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.chi2.cdf` - :func:`jax.scipy.stats.chi2.pdf` - :func:`jax.scipy.stats.chi2.sf` - :func:`jax.scipy.stats.chi2.logcdf` - :func:`jax.scipy.stats.chi2.logpdf` )rrr5r,s r'logsfr7s> Ar3& ''r))rr)rrjax._srcrrjax._src.lax.laxrrjax._src.numpy.utilrjax._src.scipy.specialrrjax._src.typingr r r(r-r1r3r5r7r)r'r>s!146,-7i-7Y-7Y-79-7UZ-7`",9",)",)", ",RW",J+9+)+)+ +RW+\)i)Y)Y)9)UZ)D+)+++y+QV+\(Y(I(I()(TY(r)