Dj"xdZddlZddlmZdZefdZdZddZ dZ d Z d Z d Z d Zd ZdZddZdZdZy)zhelper functions conversion between moments contains: * conversion between central and non-central moments, skew, kurtosis and cummulants * cov2corr : convert covariance matrix to correlation matrix Author: Josef Perktold License: BSD-3 N)combctt|tt|tgrt j |St|tj r|S|S)N)any isinstancelisttuplenparrayndarray)xs dC:\Crop_Prediction\Backend\crop-ai-system\venv\Lib\site-packages\statsmodels\stats\moment_helpers.py_convert_to_multidimrsE Jq$ Au!5 67xx{ Arzz "cZt|jdkr||S|jS)N)lenshapeT)r totypes r _convert_from_multidimrs% 177|aay 33Jrcbt|}d}tj|d|}t|S)zvconvert central to non-central moments, uses recursive formula optionally adjusts first moment to return mean c |d}dgt|z}d|d<d|g}t|ddD]V\}}|dz}|jdt|dzD]*}||xxt ||d||z|||z zzz cc<,X|ddS)NrrTexactr enumerateappendranger)mcmeanmncnnmnks r _local_countszmc2mnc.._local_counts*s!uS48^1$ir!"v& KEBQA JJqM1q5\ KA$q!402a584AE?JJ K K 12wrrrr apply_along_axisr)r r r'ress r mc2mncr+$s4 R A   mQ 2C !# &&rcht|}fd}tj|d|}t|S)zvconvert non-central to central moments, uses recursive formula optionally adjusts first moment to return mean c |d}dgt|z}g}t|D]\\}}|jdt|dzD]5}d||z zt ||dz}||xx|||z|||z zzz cc<7^r||d<|ddS)NrrTrr)r"r!mur%r$r&sgn_combwmeans r r'zmnc2mc.._local_countsAs1vcDIo cN =DAq IIaL1q5\ =AE?T!Qd-CC1CF*Ta!e_<< = = BqE!"v rrr()r"r1Xr'r*s ` r mnc2mcr3;s5 S!A   mQ 2C !# &&rcbt|}d}tj|d|}t|S)zconvert non-central moments to cumulants recursive formula produces as many cumulants as moments References ---------- Kenneth Lange: Numerical Analysis for Statisticians, page 40 c ddg}|d}dgt|z}t|ddD]Y\}}|dz}|jdt|dz D]-}||xxt |dz |d|||z z||zz cc</[||d<|ddS)NrgrrTrr)kappar kappa0r#r$r%r&s r r'zcum2mc.._local_counts]sXqd5k!uQRy) KEBQA IIaL1q5\ K1a!eQd3eAElBRUJJ K K 1!"v rrr()r6r2r'r*s r cum2mcr8Ss4 U#A   mQ 2C !# &&rcbt|}d}tj|d|}t|S)zconvert non-central moments to cumulants recursive formula produces as many cumulants as moments https://en.wikipedia.org/wiki/Cumulant#Cumulants_and_moments c  dgt|z}dg}t|ddD]\\}}|dz}|j|td|D]2}t |dz |dz d}||xx|||z|||z zzcc<4^|ddS)NrTrr)r"r6r#r$r%r&num_wayss r r'zmnc2cum.._local_countsvscDIos12w' =EBQA LLO1a[ =Aq1uD9aHuQx/#a!e*<< = = QRyrrr()r"r2r'r*s r mnc2cumr<ns4 S!A   mQ 2C !# &&rczt|}t|tjr |j}t |S)z9 just chained because I have still the test case )r+rr r rr<)r first_steps r mc2cumr?s/J*bjj)\\ : rclt|}d}tj|d|}t|tS)z9convert mean, variance, skew, kurtosis to central momentscx|\}}}}dgdz}||d<||d<||dzz|d<|dz|dzz|d<t|S) Nrr?r@@)r)argsr/sig2skkurcnts r r'zmvsk2mc.._local_countss_ D"cfqjAAdck!A)ts{*ASzrrrr r)rrrGr2r'r*s r mvsk2mcrNs4T"A  mQ 2C !#u --rclt|}d}tj|d|}t|tS)z=convert mean, variance, skew, kurtosis to non-central momentsc|\}}}}|}|||zz}||dzz}|d|z|zz|dzz}|dz|dzz} | d|z|zzd|z|z|zz|dzz} |||| fS)NrCrFrDrErB) rGr mc2skewkurtr"mnc2mc3mnc3mc4mnc4s r r'zmvsk2mnc.._local_countss"CtR"W}cSj!QVc\!B!G+czcSj)QVc\!AFRK#$55a?T4&&rrrLrMs r mvsk2mncr[s4T"A'  mQ 2C !#u --rclt|}d}tj|d|}t|tS)z9convert central moments to mean, variance, skew, kurtosisc|\}}}}tj||dz}tj||dzdz }||||fS)NrCrErD)r divide)rGr rSrWrYrTrUs r r'zmc2mvsk.._local_countssL CcyycSj)yycSj)C/Ct$$rrrLrMs r mc2mvskr_s4T"A%  mQ 2C !#u --rclt|}d}tj|d|}t|tS)z>convert central moments to mean, variance, skew, kurtosis c|\}}}}|}|||zz }|d|z|z|dzzz }|d|z|zd|z|z|zz|dzzz }t||||fS)NrFrBrQ)r_) rGr"rVrXrZr rSrWrYs r r'zmnc2mvsk.._local_countss $T4 S3Ya"fslR1W,-a"fslQVb[3%66q@ACc*++rrrLrMs r mnc2mvskrbs6 T"A,  mQ 2C !#u --rctj|}tjtj|}|tj||z }|r||fS|S)a/ convert covariance matrix to correlation matrix Parameters ---------- cov : array_like, 2d covariance matrix, see Notes Returns ------- corr : ndarray (subclass) correlation matrix return_std : bool If this is true then the standard deviation is also returned. By default only the correlation matrix is returned. Notes ----- This function does not convert subclasses of ndarrays. This requires that division is defined elementwise. np.ma.array and np.matrix are allowed. )r asanyarraysqrtdiagouter)cov return_stdstd_corrs r cov2corrrlsO, -- C 772773< D $% %DTz rctj|}tj|}|tj||z}|S)a convert correlation matrix to covariance matrix given standard deviation Parameters ---------- corr : array_like, 2d correlation matrix, see Notes std : array_like, 1d standard deviation Returns ------- cov : ndarray (subclass) covariance matrix Notes ----- This function does not convert subclasses of ndarrays. This requires that multiplication is defined elementwise. np.ma.array are allowed, but not matrices. )r rdrg)rkstdrjrhs r corr2covros:, == D == D $% %C JrcRtjtj|S)a get standard deviation from covariance matrix just a shorthand function np.sqrt(np.diag(cov)) Parameters ---------- cov : array_like, square covariance matrix Returns ------- std : ndarray standard deviation from diagonal of cov )r rerf)rhs r se_covrqs 772773<  r)T)F)__doc__numpyr scipy.specialrrrrr+r3r8r<r?rNr[r_rbrlrorqrRrr rus] &* '.'0'6'0.$.& ..>>8!r