U mdp @s2dZddlZddlmZddlmZddlmm Z d,ddZ d-dd Z d.d d Z e d kr.ddlmZd dgdZdZdZedejeZejeddZedkrdedeejeZed krdeeejeZedeeeededeeeedeeeedeeeej eedd\Z!Z"Z#ej$ee"d\Z%Z&ej$ee#d\Z'Z(ede j)e%dee'dede!deej*dede eeed e eed!d"e eeddd"\Z+\Z,Z-Z.Z/Z0Z1ed#e+ed$e12e eed%dd"\Z+\Z,Z-Z.Z/Z0Z1ed%ed#e+ed$e12eeZ3eeZ4e3ede5dd&d'd(d)dg6e7Z8e4ede5dd&d'd(d)dg6e7Z9e eee8e9fdd"\Z+\Z,Z-Z.Z/Z0Z1ed*ed#e+ed$e12dZ:e:r.ddl;meed+e?ee@ZAe=>eeAjBdS)/ausing multivariate dependence and divergence measures The standard correlation coefficient measures only linear dependence between random variables. kendall's tau measures any monotonic relationship also non-linear. mutual information measures any kind of dependence, but does not distinguish between positive and negative relationship mutualinfo_kde and mutualinfo_binning follow Khan et al. 2007 Shiraj Khan, Sharba Bandyopadhyay, Auroop R. Ganguly, Sunil Saigal, David J. Erickson, III, Vladimir Protopopescu, and George Ostrouchov, Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data, Phys. Rev. E 76, 026209 (2007) http://pre.aps.org/abstract/PRE/v76/i2/e026209 N)stats) gaussian_kdeTc Cst|}t||kstdt|t}t|t}t||f}t||}t||}t||}t|t|t|}||} |rt dt d| } | S| SdS)Cmutual information of two random variables estimated with kde +both data arrays need to have the same size?N) len ValueErrornpasarrayfloatZvstackrlogsumsqrtexp) yxnormednobsZyxkde_xkde_yZkde_yxmi_obsmi mi_normedrf/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/sandbox/distributions/mv_measures.pymutualinfo_kdes       rc Cst|}t|t}t|t}t|j|j}t|j|j}t|t|}t||krhtd|}|rt dt d|}|S|SdS)rzWrong number of observationsrrN) rr r r rTr r Zmeanrr) rrrrrrrrrrrrmutualinfo_kde_2sample4s   rcCst|}t||kstdt|t}t|t}|dkrt|}t|}td|}tddd|}|d|t } dt |j } | dd8<|| | } || | } n,t |dkr|} |} nt|d kr|\} } tj || d \} } tj || d \}} tj||| | fd \}} } |d|}| d|}|d|}|t|d t|d d d ft|}|}|rtdtd |}||||| | f|fS|Sd S)a0mutual information of two random variables estimated with kde Notes ----- bins='auto' selects the number of bins so that approximately 5 observations are expected to be in each bin under the assumption of independence. This follows roughly the description in Kahn et al. 2007 rautog@rrgư>g>binsg|=Nr)rr r r r sortrZlinspaceastypeintZonesshapesize histogram histogram2dr rr)rrr#rrysxsZqbin_sqr quantilesZquantile_indexshiftbinsybinsxZfxfyZfyxpyxpxpyrrrrrrmutualinfo_binnedJs@           2r5__main__ZlinearZ quadraticr r!)prependZ correlation)rr pearsonr spearmanr kendalltaur" mutualinforgV瞯<)Zlogbasezmutualinfo_kde normedzmutualinfo_kde F)rzmutualinfo_binned normedzmutualinfo_binned rg?g?g333333?g?r-o)T)T)T)C__doc__numpyr ZscipyrZ scipy.statsrZstatsmodels.sandbox.infotheoZsandboxZinfotheorrr5__name__Zstatsmodels.apiapismZfuntypersigr$randomZrandnrZ add_constantZexogrprintZcorrcoefr:r;r<r*Zpxyr0r/r)r3Zbinsx_r4Zbinsy_r>erZpyx2py2Zpx2Zbinsy2Zbinsx2rrr+r,arrayr%r&ZbyZbxZdoplotZmatplotlib.pyplotZpyplotZpltZplotZOLSfitZolsresZ fittedvaluesrrrrsp     B       ((