U Kv f!@sdZddlZddlmZddZefddZdd Zd"d d Z d dZ ddZ ddZ ddZ ddZddZddZd#ddZddZd d!ZdS)$zhelper functions conversion between moments contains: * conversion between central and non-central moments, skew, kurtosis and cummulants * cov2corr : convert covariance matrix to correlation matrix Author: Josef Perktold License: BSD-3 N)combcCs:tt|tt|tgr"t|St|tjr2|S|SdS)N)any isinstancelisttuplenparrayndarray)xr D/tmp/pip-unpacked-wheel-2v6byqio/statsmodels/stats/moment_helpers.py_convert_to_multidims   r cCst|jdkr||S|jS)N)lenshapeT)r Ztotyper r r _convert_from_multidimsrcCs&t|}dd}t|d|}t|S)zvconvert central to non-central moments, uses recursive formula optionally adjusts first moment to return mean c Ss|d}dgt|}d|d<d|g}t|ddD]Z\}}|d}|dt|dD]2}||t||dd|||||7<q\q6|ddS)NrrTexactr enumerateappendranger)mcmeanmncnnmnkr r r _local_counts*s 2zmc2mnc.._local_countsrr rapply_along_axisr)rr r!resr r r mc2mnc$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)rrmurrr Zsgn_combwmeanr r r!As (zmnc2mc.._local_countsrr")rr)Xr!r$r r(r mnc2mc;s r+cCs&t|}dd}t|d|}t|S)zconvert non-central moments to cumulants recursive formula produces as many cumulants as moments References ---------- Kenneth Lange: Numerical Analysis for Statisticians, page 40 c Ssddg}|d}dgt|}t|ddD]^\}}|d}|dt|dD]6}||t|d|dd|||||7<qTq.||d<|ddS)NrgrrTrr)kapparZkappa0rrrr r r r r!]s 6zcum2mc.._local_countsrr")r,r*r!r$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$|ddS)NrTrr)rr,rrrr Znum_waysr r r r!vs (zmnc2cum.._local_countsrr")rr*r!r$r r r mnc2cumns r.cCs"t|}t|tjr|j}t|S)z9 just chained because I have still the test case )r%rrr rr.)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'Zsig2skZkurZcntr r r r!s  zmvsk2mc.._local_countsrr rr#rrr5r*r!r$r r r mvsk2mcs r9cCs(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)Nr1r4r2r3r0r ) r5rmc2skewkurtrmnc2mc3mnc3mc4mnc4r r r r!s   (zmvsk2mnc.._local_countsrr7r8r r r mvsk2mncs rCcCs(t|}dd}t|d|}t|tS)z9convert central moments to mean, variance, skew, kurtosiscSs<|\}}}}t||d}t||dd}||||fS)Nr1r3r2)rdivide)r5rr;r?rAr<r=r r r r!s zmc2mvsk.._local_countsrr7r8r r r mc2mvsksrEcCs(t|}dd}t|d|}t|tS)z>convert central moments to mean, variance, skew, kurtosis c Ssl|\}}}}|}|||}|d|||d}|d||d||||d}t||||fS)Nr4r0r:)rE) r5rr>r@rBrr;r?rAr r r r!s   (zmnc2mvsk.._local_countsrr7r8r r r mnc2mvsks rFFcCs>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  rNcCs(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. )rrGrJ)rMZstdrLrKr r r corr2covs  rOcCstt|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 )rrHrI)rKr r r se_covsrP)T)F)__doc__ZnumpyrZ scipy.specialrr rrr%r+r-r.r/r9rCrErFrNrOrPr r r r s