M/Ph!zdZddlZddlmZdZefdZdZddZ d Z d Z d Z d Z d ZdZdZddZdZdZdS)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|tjr|S|S)N)any isinstancelisttuplenparrayndarray)xs `/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/stats/moment_helpers.py_convert_to_multidimrsY Jq$  Au!5!5 677x{{ Arz " "cVt|jdkr ||S|jS)N)lenshapeT)r totypes r _convert_from_multidimrs* 17||avayy 3Jrcpt|}d}tj|d|}t|S)zvconvert central to non-central moments, uses recursive formula optionally adjusts first moment to return mean c Z|d}dgt|z}d|d<d|g}t|ddD]f\}}|dz}|dt|dzD]4}||xxt ||d||z|||z zzz cc<5g|ddS)NrrTexactr enumerateappendranger)mcmeanmncnnmnks r _local_countszmc2mnc.._local_counts*s!uS488^1$ir!""v&& K KEBQA JJqMMM1q5\\ K KA$q!40002a584AE?JJ K122wrrrr apply_along_axisr)r r r'ress r mc2mncr+$sD R  A    mQ 2 2C !# & &&rTcvt|}fd}tj|d|}t|S)zvconvert non-central to central moments, uses recursive formula optionally adjusts first moment to return mean c X|d}dgt|z}g}t|D]l\}}|dt|dzD]?}d||z zt ||dz}||xx|||z|||z zzz cc<@mr||d<|ddS)NrrTrr)r"r!mur%r$r&sgn_combwmeans r r'zmnc2mc.._local_countsAs1vcDIIo cNN = =DAq IIaLLL1q5\\ = =AE?T!Qd-C-C-CC1CF*Ta!e_<< =  BqE!""v rrr()r"r1Xr'r*s ` r mnc2mcr3;sO S!!A      mQ 2 2C !# & &&rcpt|}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 fddg}|d}dgt|z}t|ddD]l\}}|dz}|dt|dz D]:}||xxt |dz |d|||z z||zz cc<;m||d<|ddS)NrgrrTrr)kappar kappa0r#r$r%r&s r r'zcum2mc.._local_counts]sXqd5kk!uQRRy)) K KEBQA IIaLLL1q5\\ K K1a!eQd333eAElBRUJJ K1!""v rrr()r6r2r'r*s r cum2mcr8SsD U##A    mQ 2 2C !# & &&rcpt|}d}tj|d|}t|S)zconvert non-central moments to cumulants recursive formula produces as many cumulants as moments https://en.wikipedia.org/wiki/Cumulant#Cumulants_and_moments c Pdgt|z}dg}t|ddD]o\}}|dz}||td|D]?}t |dz |dz d}||xx|||z|||z zzcc<@p|ddS)NrTrr)r"r6r#r$r%r&num_wayss r r'zmnc2cum.._local_countsvscDIIos122w'' = =EBQA LLOOO1a[[ = =Aq1uD999aHuQx/#a!e*<< =QRRyrrr()r"r2r'r*s r mnc2cumr<nsD S!!A    mQ 2 2C !# & &&rct|}t|tjr|j}t |S)z9 just chained because I have still the test case )r+rr r rr<)r first_steps r mc2cumr?s8J*bj))"\ :  rc|t|}d}tj|d|}t|tS)z9convert mean, variance, skew, kurtosis to central momentsc|\}}}}dgdz}||d<||d<||dzz|d<|dz|dzz|d<t|S) Nrr?r@@)r)argsr/sig2skkurcnts r r'zmvsk2mc.._local_countssa D"cfqjAAdck!A)ts{*ASzzrrrr r)rrrGr2r'r*s r mvsk2mcrNsDT""A mQ 2 2C !#u - --rc|t|}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[sDT""A''' mQ 2 2C !#u - --rc|t|}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_countssN CcycSj))ycSj))C/Ct$$rrrLrMs r mc2mvskr_sDT""A%%% mQ 2 2C !#u - --rc|t|}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 mnc2mvskrbsF T""A,,, mQ 2 2C !#u - --rFctj|}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 cov2corrrlsW, -  C 7273<< 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 $%% %C JrcNtjtj|S)a get standard deviation from covariance matrix just a shorthand function np.sqrt(np.diag(cov)) Parameters ---------- cov : array_like, square covariance matrix Returns ------- std : ndarray standard deviation from diagonal of cov )r rerf)rhs r se_covrqs 7273<<  r)T)F)__doc__numpyr scipy.specialrrrrr+r3r8r<r?rNr[r_rbrlrorqrRrr rus  &* '''.''''0'''6'''0...$...& . . ....>>8!!!!!r