a \:b!@sdZddlZddlmZddZefddZdd Zd"d d Z d dZ ddZ ddZ ddZ ddZddZddZd#ddZddZd d!ZdS)$zhelper functions conversion between moments contains: * conversion between central and non-central moments, skew, kurtosis and cummulants * cov2corr : convert covariance matrix to correlation matrix Author: Josef Perktold License: BSD-3 N)combcCs:tt|tt|tgr"t|St|tjr2|S|SdS)N)any isinstancelisttuplenpZarrayndarray)xr ?lib/python3.9/site-packages/statsmodels/stats/moment_helpers.py_convert_to_multidims   r cCst|jdkr||S|jS)N)lenshapeT)r Ztotyper r r _convert_from_multidimsrcCs&t|}dd}t|d|}t|S)zvconvert central to non-central moments, uses recursive formula optionally adjusts first moment to return mean c Ss|d}dgt|}d|d<d|g}t|ddD]Z\}}|d}|dt|dD]2}||t||dd|||||7<q\q6|ddS)Nrr Texactr enumerateappendranger)mcmeanmncnnmnkr r r _local_counts*s 2zmc2mnc.._local_countsrr rapply_along_axisr)rr r resr r r mc2mnc$s r$Tcs*t|}fdd}t|d|}t|S)zvconvert non-central to central moments, uses recursive formula optionally adjusts first moment to return mean c s|d}dgt|}g}t|D]b\}}|dt|dD]B}d||t||dd}||||||||7<q@q"r||d<|ddS)NrrTrr)rrmurrrZsgn_combwmeanr r r As (zmnc2mc.._local_countsrr!)rr(Xr r#r r'r mnc2mc;s r*cCs&t|}dd}t|d|}t|S)zconvert non-central moments to cumulants recursive formula produces as many cumulants as moments References ---------- Kenneth Lange: Numerical Analysis for Statisticians, page 40 c Ssddg}|d}dgt|}t|ddD]^\}}|d}|dt|dD]6}||t|d|dd|||||7<qTq.||d<|ddS)Nrgrr Trr)kapparZkappa0rrrrr r r r ]s 6zcum2mc.._local_countsrr!)r+r)r r#r r r cum2mcSs r,cCs&t|}dd}t|d|}t|S)zconvert non-central moments to cumulants recursive formula produces as many cumulants as moments https://en.wikipedia.org/wiki/Cumulant#Cumulants_and_moments c Ssdgt|}dg}t|ddD]d\}}|d}||td|D]>}t|d|ddd}||||||||8<qHq$|ddS)NrTrr)rr+rrrrZnum_waysr r r r vs (zmnc2cum.._local_countsrr!)rr)r r#r r r mnc2cumns r-cCs"t|}t|tjr|j}t|S)z9 just chained because I have still the test case )r$rrrrr-)rZ first_stepr r r mc2cums r.cCs(t|}dd}t|d|}t|tS)z9convert mean, variance, skew, kurtosis to central momentscSsR|\}}}}dgd}||d<||d<||d|d<|d|d|d<t|S) Nrr?r @@)r)argsr&Zsig2ZskZkurZcntr r r r s  zmvsk2mc.._local_countsrr rr"rrr4r)r r#r r r mvsk2mcs r7cCs(t|}dd}t|d|}t|tS)z=convert mean, variance, skew, kurtosis to non-central momentsc Ss|\}}}}|}|||}||d}|d|||d}|d|d} | d||d||||d} |||| fS)Nr0r3r1r2r/r ) r4rmc2skewkurtrmnc2mc3mnc3mc4mnc4r r r r s   (zmvsk2mnc.._local_countsrr5r6r r r mvsk2mncs rAcCs(t|}dd}t|d|}t|tS)z9convert central moments to mean, variance, skew, kurtosiscSs<|\}}}}t||d}t||dd}||||fS)Nr0r2r1)rZdivide)r4rr9r=r?r:r;r r r r s zmc2mvsk.._local_countsrr5r6r r r mc2mvsksrBcCs(t|}dd}t|d|}t|tS)z>convert central moments to mean, variance, skew, kurtosis c Ssl|\}}}}|}|||}|d|||d}|d||d||||d}t||||fS)Nr3r/r8)rB) r4rr<r>r@rr9r=r?r r r r s   (zmnc2mvsk.._local_countsrr5r6r r r mnc2mvsks rCFcCs>t|}tt|}|t||}|r6||fS|SdS)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. N)r asanyarraysqrtdiagouter)covZ return_stdstd_corrr r r cov2corrs  rKcCs(t|}t|}|t||}|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. )rrDrG)rJZstdrIrHr r r corr2covs  rLcCstt|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 )rrErF)rHr r r se_covsrM)T)F)__doc__ZnumpyrZ scipy.specialrr rrr$r*r,r-r.r7rArBrCrKrLrMr r r r s