ó áp7]c@sìdZddlmZddlZddlmZddlmZde fd„ƒYZ de fd „ƒYZ d e fd „ƒYZ d „Z d d„Zd„ZedkrèdZejeƒZejjdeƒZddejeƒdejjeƒZejeƒZe deƒZeeejƒƒejZeeeƒƒe deƒZeeej ej!ej"eƒƒej#ƒƒeeej$ej#ƒƒƒe deƒZ%ee%j&dƒeej&dƒe ee%ƒndS(s8Recipes for more efficient work with linalg using classes intended for use for multivariate normal and linear regression calculations x is the data (nobs, nvars) m is the moment matrix (x'x) or a covariance matrix Sigma examples: x'sigma^{-1}x z = Px where P=Sigma^{-1/2} or P=Sigma^{1/2} Initially assume positive definite, then add spectral cutoff and regularization of moment matrix, and extend to PCA maybe extend to sparse if some examples work out (transformation matrix P for random effect and for toeplitz) Author: josef-pktd Created on 2010-10-20 iÿÿÿÿ(tprint_functionN(tlinalg(tcache_readonlytPlainMatrixArraycBsËeZdZddd„Zed„ƒZd„Zd„Zed„ƒZ ed„ƒZ d„Z d„Z d „Z d „Zed „ƒZed „ƒZed „ƒZed„ƒZed„ƒZRS(s³Class that defines linalg operation on an array simplest version as benchmark linear algebra recipes for multivariate normal and linear regression calculations cCs£|dk rZ|dkrKtj|ƒ|_tj|jj|jƒ|_qŸtdƒ‚nE|dk r“tj|ƒ|_tj|jj Œ|_n tdƒ‚dS(Ns!data and sym cannot be both givens#either data or sym need to be given( tNonetnptasarraytxtdottTtmt ValueErrorteyetshape(tselftdatatsym((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyt__init__)s  ! cCstjj|jƒS(N(RRtinvR (R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytminv7scCstj|j|ƒS(N(RRR (Rty((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytm_y;scCstj|j|ƒS(N(RRR(RR((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytminv_y>scCstj|jƒS(N(RtpinvR (R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytmpinvAscCstj|jƒS(N(RRR(R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytxpinvEscCs"tj|jtj|j|ƒƒS(N(RRR R (RR((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytyt_m_yIscCs"tj|jtj|j|ƒƒS(N(RRR R(RR((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyt yt_minv_yLscCs"tj|tj|j|jƒƒS(N(RRR R (RR((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyty_m_ytPscCs"tj|tj|j|jƒƒS(N(RRRR (RR((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyt y_minv_ytSscCstj|jƒS(N(RtdetR (R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytmdetVscCstjtj|jƒƒS(N(RtlogRRR (R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytmlogdetZscCsRtj|jƒ\}}tj|ƒddd…}|||dd…|ffS(Niÿÿÿÿ(RteighR Rtargsort(Rtevalstevecstsortind((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytmeigh^scCs/|j\}}tjtj|dƒ|jƒS(Ngà?(R'RRtdiagR (RR$R%((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytmhalfdscCs3|j\}}tj|dtj|ƒ|jƒS(Ngð?(R'RRtsqrtR (RR$R%((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytminvhalfksN(t__name__t __module__t__doc__RRRRRRRRRRRRRR!R'R)R+(((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR s       tSvdArraycBseZdZd d d„Zd„Zed„ƒZed„ƒZed„ƒZ ed„ƒZ ed„ƒZ ed„ƒZ ed „ƒZ RS( s´Class that defines linalg operation on an array svd version, where svd is taken on original data array, if or when it matters no spectral cutoff in first version cCs˜tt|ƒjd|d|ƒtjj|jddƒ\}}}||||_|_|_ tj |tj Œ|_ tj d|tj Œ|_ dS(NRRt full_matricesigð?(tsuperR/RRRtsvdRtutstvtdiagsvdR tsdiagtsinvdiag(RRRR3R4R5((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR{s $cCs"tjtj|j|ƒtjŒS(N(RR6RtpowerR4RR (Rtp((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyt _sdiagpowƒscCs+tj|j|jƒ}tj|j|ƒS(N(RRR8R5R (Rtsinvv((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR†scCs#|jj}|jd}||fS(Ni(R5R R4(RR%R$((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR'‹s  cCs|jdjƒS(Ni(R'tprod(R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR‘scCstj|jdƒjƒS(Ni(RR R'tsum(R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR!•scCstjtj|jƒ|jƒS(N(RRR(R4R5(R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR)™scCstj|j|jƒS(N(RRR3R7(R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pytxxthalfscCstj|j|jƒS(N(RRR3R8(R((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyt xxtinvhalf¡sN(R,R-R.RRR;RRR'RR!R)R?R@(((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR/rs t CholArraycBs&eZdZddd„Zd„ZRS(sÞClass that defines linalg operation on an array cholesky version, where svd is taken on original data array, if or when it matters plan: use cholesky factor and cholesky solve nothing implemented yet cCs#tt|ƒjd|d|ƒdS(NRR(R1R/R(RRR((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR°scCs(tjttjtj|jƒtƒƒS(s;xSigmainvx doesn't use stored cholesky yet (RRRRt cho_solvet cho_factorR (RR((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyR´sN(R,R-R.RRR(((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyRA¦sc Csƒddlm}m}d}||j|jd|ƒtj|jjdƒƒdd…df}tj|jjdƒƒdd…df}||}||j|j|d|ƒ||j |j d|ƒ|j \}} |j \} } ||| d|ƒtj| jdƒƒ}tj| jdƒƒ}||}|| | |d|ƒ||j |j ddƒ||j |j ddƒdS( Niÿÿÿÿ(tassert_almost_equaltassert_approx_equali tdecimaliit significanti ( t numpy.testingRDRERRtsignR)R>RR+R'RR!( tm1tm2RDRERFts1ts2tscorrtevals1tevecs1tevals2tevecs2((sJlib/python2.7/site-packages/statsmodels/sandbox/archive/linalg_decomp_1.pyt testcompare¿s"++  gV瞯Òs8 R4    + / &