uki |ddlZddlmZddlmZddlmZddl m Z m Z d de de de d e d e f d Z d de de de d e d e f d Z y)N)lax)_const)promote_args_inexact)Array ArrayLikexdflocscalereturnc td||||\}}}}t|d}tjtj|||}tj||}tj |t|d}tj tj ||t|tj}tjtjtj |||} tjtj tj|| tj|} tjtj |||} tjtj | 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) rr r r twoscaled_x df_over_twodf_plus_one_over_twonormalize_term_constnormalize_term_tmpnormalize_term quadratics Q/home/cdr/jupyterlab/.venv/lib/python3.12/site-packages/jax/_src/scipy/stats/t.pylogpdfr#s74+:q"c5I!Re1a# WWSWWQ_e ,(C +jC.@A!6 1bee8LMwwswwsww/CR'HI3O773773::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#)rr r r s r"pdfr'?s4 2sE* ++r$)r)numpyrjax._srcrjax._src.lax.laxrrjax._src.numpy.utilrjax._src.typingrrr#r'r$r"r/so 14,$_i$_Y$_Y$_9$_UZ$_N,9,),), ,RW,r$