ó áp7]c @s5dZddlZddlmZddlmZddljj Z e d„Z e d„Z e d„Z edkr1ddljZd d gd Zd Zd ZejdejjeƒƒZejede ƒZed krded eejjeƒZned kr1deeejjeƒZndGHejeeƒd'GHdejeeƒfGHdejeeƒfGHdejeeƒfGHej eeddƒ\Z!Z"Z#ej$ede"ƒ\Z%Z&ej$ede#ƒ\Z'Z(de j)e%dee'dede!dedej*ƒfGHde eeƒfGHde eede+ƒfGHe eedde ƒ\Z,\Z-Z.Z/Z0Z1Z2de,fGHde2j3ƒfGHe eed de ƒ\Z,\Z-Z.Z/Z0Z1Z2d GHde,fGHde2j3ƒfGHejeƒZ4ejeƒZ5e4ed ej6dd!d"d#d$d gƒj7e8ƒZ9e5ed ej6dd!d"d#d$d gƒj7e8ƒZ:e eee9e:fde ƒ\Z,\Z-Z.Z/Z0Z1Z2d%GHde,fGHde2j3ƒfGHd Z;e;r1ddl<j=Z>e>j?eed&ƒej@eeƒjAƒZBe>j?eeBjCƒq1ndS((sæusing 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 iÿÿÿÿN(tstats(t gaussian_kdec Cst|ƒ}t|ƒ|ks-tdƒ‚ntj|tƒ}tj|tƒ}tj||fƒ}t|ƒ|ƒ}t|ƒ|ƒ}t|ƒ|ƒ}tj|ƒtj|ƒtj|ƒ}|jƒ|} |rÿtj dtj d| ƒƒ} | S| SdS(sCmutual information of two random variables estimated with kde s+both data arrays need to have the same sizegð?iþÿÿÿN( tlent ValueErrortnptasarraytfloattvstackRtlogtsumtsqrttexp( tytxtnormedtnobstyxtkde_xtkde_ytkde_yxtmi_obstmit mi_normed((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/mv_measures.pytmutualinfo_kdes ) c CsÛt|ƒ}tj|tƒ}tj|tƒ}t|jƒ|jƒ}t|jƒ|jƒ}tj|ƒtj|ƒ}t|ƒ|krtdƒ‚n|jƒ}|rÓtj dtj d|ƒƒ}|S|SdS(sCmutual information of two random variables estimated with kde sWrong number of observationsgð?iþÿÿÿN( RRRRRtTRRtmeanR R ( R R RRRRRRR((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/mv_measures.pytmutualinfo_kde_2sample4s   cCsft|ƒ}t|ƒ|ks-tdƒ‚ntj|tƒ}tj|tƒ}|dkrtj|ƒ}tj|ƒ}tjd|ƒ}tjddd|ƒ}|d|jt ƒ} dtj |j ƒ} | dcd 8<|| | } || | } nEtj |ƒdkr'|} |} n!t|ƒdkrH|\} } ntj |d | ƒ\} } tj |d | ƒ\}} tj||d | | fƒ\}} } |d|}| d|}|d|}|tj|d ƒtj|ƒd d …d ftj|ƒ}|jƒ}|r^tjdtjd |ƒƒ}||||| | f|fS|Sd S(s0mutual 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 s+both data arrays need to have the same sizetautog@iigð?gíµ ÷Æ°>itbinsg»½×Ùß|Û=Niþÿÿÿgíµ ÷ÆÀ>(RRRRRtsortR tlinspacetastypetinttonestshapetsizet histogramt histogram2dRtNoneR R (R R RRRtystxstqbin_sqrt quantilestquantile_indextshifttbinsytbinsxtfxtfytfyxtpyxtpxtpyRRR((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/mv_measures.pytmutualinfo_binnedJs@   'A  t__main__tlineart quadraticiiÈiitprependit correlationtpearsonrt spearmanrt kendalltauRit mutualinfogð?gV瞯ÒtetFalseRtpyx2tpy2tpx2tbinsy2tbinsx2RR R'R(tarrayRR tbytbxtdoplottmatplotlib.pyplottpyplottplttplottOLStfittolsrest fittedvalues(((sLlib/python2.7/site-packages/statsmodels/sandbox/distributions/mv_measures.pytsf    B  % !! 0 0 666