B z‹d*ã@sTddlmZmZmZmZddddgZddlZdd„Zd d d„Z dd d„Z d d„Z dS)é)ÚdivisionÚprint_functionÚabsolute_importÚunicode_literalsÚ_ladderÚget_acfÚget_integrated_actÚ&thermodynamic_integration_log_evidenceNcCs t |¡}|ddd… ¡|S)zM Convert an arbitrary iterable of floats into a sorted numpy array. Néÿÿÿÿ)ÚnpÚarrayÚsort)Úbetas©rúY/work/yifan.wang/ringdown/master-ringdown-env/lib/python3.7/site-packages/ptemcee/util.pyr s FcCsÌt |¡}tdƒgt|jƒ}|rTtdt t |j|¡¡ƒ}td|ƒ||<|}n |j|}tjj|tj ||dd||d}td|ƒ||<tjj |t  |¡|dt |ƒj }d||<||t |ƒS)a÷ Estimate the autocorrelation function of a time series using the FFT. :param x: The time series. If multidimensional, set the time axis using the ``axis`` keyword argument and the function will be computed for every other axis. :param axis: (optional) The time axis of ``x``. Assumed to be the first axis if not specified. :param fast: (optional) If ``True``, only use the largest ``2^n`` entries for efficiency. (default: False) Nér)Úaxis)Únr)r Z atleast_1dÚsliceÚlenÚshapeÚintÚfloorÚlog2ZfftZmeanZifftÚ conjugateÚtupleÚreal)ÚxrÚfastÚmrÚfZacfrrrrs  $$é2cCszt|||d}t|jƒdkr6ddt |d|…¡Stdƒgt|jƒ}td|ƒ||<ddtj|t|ƒ|d}|S)aË Estimate the integrated autocorrelation time of a time series. See `Sokal's notes `_ on MCMC and sample estimators for autocorrelation times. :param x: The time series. If multidimensional, set the time axis using the ``axis`` keyword argument and the function will be computed for every other axis. :param axis: (optional) The time axis of ``x``. Assumed to be the first axis if not specified. :param window: (optional) The size of the window to use. (default: 50) :param fast: (optional) If ``True``, only use the largest ``2^n`` entries for efficiency. (default: False) )rrérN)r)rrrr Úsumrr)rrZwindowrr rÚtaurrrr;scCst|ƒt|ƒkrtdƒ‚t |¡ddd…}||}||}t |¡}|ddkr°t |dgf¡}t |ddd…dgf¡}t |ddd…|dgf¡}t ||dgf¡}n8t |ddd…dgf¡}t |ddd…|dgf¡}t ||¡ }t ||¡ }|t ||¡fS)a  Thermodynamic integration estimate of the evidence. :param betas: The inverse temperatures to use for the quadrature. :param logls: The mean log-likelihoods corresponding to ``betas`` to use for computing the thermodynamic evidence. :return ``(logZ, dlogZ)``: Returns an estimate of the log-evidence and the error associated with the finite number of temperatures at which the posterior has been sampled. The evidence is the integral of the un-normalized posterior over all of parameter space: .. math:: Z \equiv \int d\theta \, l(\theta) p(\theta) Thermodymanic integration is a technique for estimating the evidence integral using information from the chains at various temperatures. Let .. math:: Z(\beta) = \int d\theta \, l^\beta(\theta) p(\theta) Then .. math:: \frac{d \log Z}{d \beta} = \frac{1}{Z(\beta)} \int d\theta l^\beta p \log l = \left \langle \log l \right \rangle_\beta so .. math:: \log Z(1) - \log Z(0) = \int_0^1 d\beta \left \langle \log l \right\rangle_\beta By computing the average of the log-likelihood at the difference temperatures, the sampler can approximate the above integral. z6Need the same number of log(L) values as temperatures.Nr rr)rÚ ValueErrorr ZargsortÚcopyZ concatenateZtrapzÚabs)rZloglsÚorderZbetas0Zbetas2Zlogls2ZlogZZlogZ2rrrr as 0  )rF)rr!F) Ú __future__rrrrÚ__all__Únumpyr rrrr rrrrÚs   % &