Vpf ~ddlZddlmZddlmZddlmZddl m Z m Z dde de d e d e d e f d Z dde de d e d e d e f d Z dS)N)lax)_const)promote_args_inexact)Array ArrayLikexdflocscalereturnc td||||\}}}}t|d}tjtj|||}tj||}tj|t|d}tjtj||t|tj}tjtj tj|||} tjtjtj || tj |} tjtj|||} tj tj| tj|tj | S)aStudent's T log probability distribution function. JAX implementation of :obj:`scipy.stats.t` ``logpdf``. The Student's T probability distribution function is given by .. math:: f(x, \nu) = \frac{\Gamma((\nu + 1)/2)}{\sqrt{\pi\nu}\Gamma(\nu/2)}(1 + x^2/\nu)^{(\nu+1)/2} Where :math:`\Gamma` is the :func:`~jax.scipy.special.gamma` function, and :math:`\nu > 0` is the degrees of freedom (JAX follows the scipy convention of naming this ``df``). 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.t.pdf` zt.logpdfg?) r _lax_constrdivsubaddmulnppiloglgammaneglog1p) r r r r twoscaled_x df_over_twodf_plus_one_over_twonormalize_term_constnormalize_term_tmpnormalize_term quadratics V/var/www/html/nettyfy-visnx/env/lib/python3.11/site-packages/jax/_src/scipy/stats/t.pylogpdfr$sU4+:q"c5II!Re1a# WSWQ__e , ,(C  +jC.@.@AA!6!6 1be8L8LMMwswsw/CR'H'HII3OO7373:k#:#: 0` is the degrees of freedom (JAX follows the scipy convention of naming this ``df``). Args: x: arraylike, value at which to evaluate the PDF df: arraylike, distribution shape parameter loc: arraylike, distribution offset parameter scale: arraylike, distribution scale parameter Returns: array See Also: :func:`jax.scipy.stats.t.logpdf` )rexpr$)r r r r s r#pdfr(?s"4 2sE** + ++r%)rr)numpyrjaxrjax._src.lax.laxrrjax._src.numpy.utilrjax._src.typingrrr$r(r%r#r/s 111111444444,,,,,,,,$_$_i$_Y$_Y$_9$_UZ$_$_$_$_N,,9,),), ,RW,,,,,,r%