DjeddlZdZGddZGddeZGddeZGd d eZGd d eZGd deZGddeZ GddeZ GddeZ ddZ y)Nc6|jdk\dzdz }||zS)zabsolute value function that changes complex sign based on real sign This could be useful for complex step derivatives of functions that need abs. Not yet used. r)real)xsigns \C:\Crop_Prediction\Backend\crop-ai-system\venv\Lib\site-packages\statsmodels/robust/norms.py_cabsr s$ FFaK1 q D !8Oc.eZdZdZdZdZdZdZdZy) RobustNormaZ The parent class for the norms used for robust regression. Lays out the methods expected of the robust norms to be used by statsmodels.RLM. See Also -------- statsmodels.rlm Notes ----- Currently only M-estimators are available. References ---------- PJ Huber. 'Robust Statistics' John Wiley and Sons, Inc., New York, 1981. DC Montgomery, EA Peck. 'Introduction to Linear Regression Analysis', John Wiley and Sons, Inc., New York, 2001. R Venables, B Ripley. 'Modern Applied Statistics in S' Springer, New York, 2002. ct)z| The robust criterion estimator function. Abstract method: -2 loglike used in M-estimator NotImplementedErrorselfzs r rhozRobustNorm.rho* "!r ct)z Derivative of rho. Sometimes referred to as the influence function. Abstract method: psi = rho' rrs r psizRobustNorm.psi4rr ct)z_ Returns the value of psi(z) / z Abstract method: psi(z) / z rrs r weightszRobustNorm.weights>rr ct)z Derivative of psi. Used to obtain robust covariance matrix. See statsmodels.rlm for more information. Abstract method: psi_derive = psi' rrs r psi_derivzRobustNorm.psi_derivHs "!r c$|j|SzH Returns the value of estimator rho applied to an input rrs r __call__zRobustNorm.__call__Txx{r N) __name__ __module__ __qualname____doc__rrrrrr r r r s 2""" "r r c(eZdZdZdZdZdZdZy) LeastSquaresz Least squares rho for M-estimation and its derived functions. See Also -------- statsmodels.robust.norms.RobustNorm c|dzdzS)z The least squares estimator rho function Parameters ---------- z : ndarray 1d array Returns ------- rho : ndarray rho(z) = (1/2.)*z**2 r?r%rs r rzLeastSquares.rhods!tczr c,tj|S)a  The psi function for the least squares estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z )npasarrayrs r rzLeastSquares.psius"zz!}r ctj|}tj|jtjS)a@ The least squares estimator weighting function for the IRLS algorithm. The psi function scaled by the input z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = np.ones(z.shape) )r+r,onesshapefloat64rs r rzLeastSquares.weightss*" JJqMwwqww ++r c^tj|jtjS)z The derivative of the least squares psi function. Returns ------- psi_deriv : ndarray ones(z.shape) Notes ----- Used to estimate the robust covariance matrix. )r+r.r/r0rs r rzLeastSquares.psi_derivswwqww ++r N)r!r"r#r$rrrrr%r r r'r'[s"&,( ,r r'c6eZdZdZd dZdZdZdZdZdZ y) HuberTz Huber's T for M estimation. Parameters ---------- t : float, optional The tuning constant for Huber's t function. The default value is 1.345. See Also -------- statsmodels.robust.norms.RobustNorm c||_yN)t)rr6s r __init__zHuberT.__init__ r ctj|}tjtj||jS)zE Huber's T is defined piecewise over the range for z )r+r, less_equalabsr6rs r _subsetzHuberT._subsets. JJqM}}RVVAY//r ctj|}|j|}|dz|dzzd|z tj||jzd|jdzzz zzS)a8 The robust criterion function for Huber's t. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = .5*z**2 for \|z\| <= t rho(z) = \|z\|*t - .5*t**2 for \|z\| > t r)rr)r+r,r<r;r6rrtests r rz HuberT.rhosh JJqM||As QT!TbffQi$&&03?BCD Er ctj|}|j|}||zd|z |jztj|zzS)aE The psi function for Huber's t estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= t psi(z) = sign(z)*t for \|z\| > t r)r+r,r<r6rr>s r rz HuberT.psisG$ JJqM||Aax1t8tvv- :::r ctj|}tj|}|j|}tj|}d||<|d|z |j z|z z}|r|d}|S)aa Huber's t weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= t weights(z) = t/\|z\| for \|z\| > t ?rr)r+isscalar atleast_1dr<r;r6)rr z_isscalarr?abszvs r rzHuberT.weightsso$[[^ MM! ||AvvayT AH&- - !Ar ctjtj||jj t S)z The derivative of Huber's t psi function Notes ----- Used to estimate the robust covariance matrix. )r+r:r;r6astypefloatrs r rzHuberT.psi_derivs,}}RVVAY/66u==r N)gQ? r!r"r#r$r7r<rrrrr%r r r3r3s& 0E*;,<>r r3c0eZdZdZddZdZdZdZdZy) RamsayEz Ramsay's Ea for M estimation. Parameters ---------- a : float, optional The tuning constant for Ramsay's Ea function. The default value is 0.3. See Also -------- statsmodels.robust.norms.RobustNorm c||_yr5arrPs r r7zRamsayE.__init__)r8r c tj|}dtj|j tj|zd|jtj|zzzz |jdzz S)a  The robust criterion function for Ramsay's Ea. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = a**-2 * (1 - exp(-a*\|z\|)*(1 + a*\|z\|)) rrr+r,exprPr;rs r rz RamsayE.rho,sj JJqMBFFDFF7RVVAY./TVVbffQi'')),0FFAI6 6r ctj|}|tj|j tj|zzS)a The psi function for Ramsay's Ea estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z*exp(-a*\|z\|) rSrs r rz RamsayE.psi>s8 JJqM266466'BFF1I-...r ctj|}tj|j tj|zS)a" Ramsay's Ea weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = exp(-a*\|z\|) rSrs r rzRamsayE.weightsQs3" JJqMvvtvvgq )**r c|j}tj| tj|z}| |ztj|z}|}d}||z||zzS)z The derivative of Ramsay's Ea psi function. Notes ----- Used to estimate the robust covariance matrix. r)rPr+rTr;r)rrrPrdxydys r rzRamsayE.psi_derives] FF FFA2q > "R!Vbggaj   2vBr N)g333333?) r!r"r#r$r7rrrrr%r r rMrMs  6$/&+( r rMc6eZdZdZd dZdZdZdZdZdZ y) AndrewWavea Andrew's wave for M estimation. Parameters ---------- a : float, optional The tuning constant for Andrew's Wave function. The default value is 1.339. See Also -------- statsmodels.robust.norms.RobustNorm c||_yr5rOrQs r r7zAndrewWave.__init__r8r ctj|}tjtj||jtj zS)zI Andrew's wave is defined piecewise over the range of z. )r+r,r:r;rPpirs r r<zAndrewWave._subsets6 JJqM}}RVVAY77r c|j}tj|}|j|}||dzzdtj||z z zd|z |dzzdzzS)a{ The robust criterion function for Andrew's wave. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray The elements of rho are defined as: .. math:: rho(z) & = a^2 *(1-cos(z/a)), |z| \leq a\pi \\ rho(z) & = 2a, |z|>q\pi rr)rPr+r,r<cosrrrPr?s r rzAndrewWave.rhosg( FF JJqM||Aq!t q266!a%=01TQT!A%& 'r c|j}tj|}|j|}||ztj||z zS)aR The psi function for Andrew's wave The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = a * sin(z/a) for \|z\| <= a*pi psi(z) = 0 for \|z\| > a*pi )rPr+r,r<sinrbs r rzAndrewWave.psisB& FF JJqM||Aax"&&Q-''r c|j}tj|}|j|}||z }tj|tj tj jk}tj|r@tj|}|}||}||tj|z|z ||<|S|tj|z|z }|S)a} Andrew's wave weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = sin(z/a) / (z/a) for \|z\| <= a*pi weights(z) = 0 for \|z\| > a*pi ) rPr+r,r<r;finfodoubleepsany ones_likerd)rrrPr?ratiosmallrlarges r rzAndrewWave.weightss$ FF JJqM||AAu  3 7 77 66%=ll5)GFE%LE!%[266%=85@GENRVVE]*U2Gr cn|j|}|tj||jz zS)z The derivative of Andrew's wave psi function Notes ----- Used to estimate the robust covariance matrix. )r<r+rarPr>s r rzAndrewWave.psi_derivs-||AbffQZ(((r N)gCl?rKr%r r r\r\us& 8'4(0@ )r r\c6eZdZdZd dZdZdZdZdZdZ y) TrimmedMeana Trimmed mean function for M-estimation. Parameters ---------- c : float, optional The tuning constant for Ramsay's Ea function. The default value is 2.0. See Also -------- statsmodels.robust.norms.RobustNorm c||_yr5crrss r r7zTrimmedMean.__init__r8r ctj|}tjtj||jS)zN Least trimmed mean is defined piecewise over the range of z. )r+r,r:r;rsrs r r<zTrimmedMean._subsets. JJqM}}RVVAY//r ctj|}|j|}||dzzdzd|z |jdzzdzzS)aA The robust criterion function for least trimmed mean. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = (1/2.)*z**2 for \|z\| <= c rho(z) = (1/2.)*c**2 for \|z\| > c rr)rr+r,r<rsr>s r rzTrimmedMean.rhosL" JJqM||Aad{S AH #9C#???r cXtj|}|j|}||zS)aQ The psi function for least trimmed mean The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= c psi(z) = 0 for \|z\| > c r+r,r<r>s r rzTrimmedMean.psis'$ JJqM||Aaxr cRtj|}|j|}|S)an Least trimmed mean weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= c weights(z) = 0 for \|z\| > c ryr>s r rzTrimmedMean.weights2s#$ JJqM||A r c(|j|}|S)z The derivative of least trimmed mean psi function Notes ----- Used to estimate the robust covariance matrix. )r<r>s r rzTrimmedMean.psi_derivHs||A r N)@rKr%r r rprps& 0@*,, r rpc6eZdZdZd dZdZdZdZdZdZ y) Hampela; Hampel function for M-estimation. Parameters ---------- a : float, optional b : float, optional c : float, optional The tuning constants for Hampel's function. The default values are a,b,c = 2, 4, 8. See Also -------- statsmodels.robust.norms.RobustNorm c.||_||_||_yr5)rPbrs)rrPrrss r r7zHampel.__init__fsr ctjtj|}tj||j}tj||j tj ||jz}tj||jtj ||j z}|||fS)zL Hampel's function is defined piecewise over the range of z )r+r;r,r:rPrgreaterrs)rrt1t2t3s r r<zHampel._subsetks FF2::a= ! ]]1dff % ]]1dff % 1dff(= = ]]1dff % 1dff(= =2rzr c<|j|j|j}}}tj|}tj |}|j |\}}}||z} tj|jd} tj|j| } tj|}||dzdz| |<|||z|dzdzz | |<||||z dzz||z z dz| |<| | xx|||z|z zdzz cc<|r| d} | S)a The robust criterion function for Hampel's estimator Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = z**2 / 2 for \|z\| <= a rho(z) = a*\|z\| - 1/2.*a**2 for a < \|z\| <= b rho(z) = a*(c - \|z\|)**2 / (c - b) / 2 for b < \|z\| <= c rho(z) = a*(b + c - a) / 2 for \|z\| > c rJdtyperr)gr rPrrsr+rCrDr< promote_typesrzerosr/r;) rrrPrrsrErrrt34dtrGs r rz Hampel.rhous(&&$&&$&&a1[[^ MM! \\!_ BRj   aggw / HHQWWB ' FF1I"q3"QrUQTCZ'"Q2YN"a!e,5" #!q1uqy/C'' !Ar c |j|j|j}}}tj|}tj |}|j |\}}}tj|jd} tj|j| } tj|} tj|} ||| |<|| |z| |<|| |z|| |z z||z z | |<|r| d} | S)a The psi function for Hampel's estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z for \|z\| <= a psi(z) = a*sign(z) for a < \|z\| <= b psi(z) = a*sign(z)*(c - \|z\|)/(c-b) for b < \|z\| <= c psi(z) = 0 for \|z\| > c rJrr rPrrsr+rCrDr<rrrr/rr;) rrrPrrsrErrrrrGszas r rz Hampel.psis,&&$&&$&&a1[[^ MM! \\!_ B   aggw / HHQWWB ' GGAJ VVAY""AbE "AbE QBZ(AE2" !Ar c|j|j|j}}}tj|}tj |}|j |\}}}tj|jd} tj|j| } d| |<tj|} || |z | |<| |} ||| z z| ||z zz | |<|r| d} | S)a$ Hampel weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray weights(z) = 1 for \|z\| <= a weights(z) = a/\|z\| for a < \|z\| <= b weights(z) = a*(c - \|z\|)/(\|z\|*(c-b)) for b < \|z\| <= c weights(z) = 0 for \|z\| > c rJrrBrr) rrrPrrsrErrrrrGabs_zabs_zt3s r rzHampel.weightss,&&$&&$&&a1[[^ MM! \\!_ B   aggw / HHQWWB '"q E"I ")Q[!WA%67" !Ar c|j|j|j}}}tj|}tj |}|j |\}}}tj|jd} tj|j| } d| |<||} |tj| z| z tj| ||z zz | |<|r| d} | S)zGDerivative of psi function, second derivative of rho function. rJrrBrr) rrrPrrsrEr_rrdzt3s r rzHampel.psi_derivs&&$&&$&&a1[[^ MM! LLO Ar   aggw / HHQWWB '"ebggcl"S()RVVC[AE-BC" !Ar N)r|g@g @rKr%r r r~r~Ts(" 'R'R'Rr r~c6eZdZdZd dZdZdZdZdZdZ y) TukeyBiweighta Tukey's biweight function for M-estimation. Parameters ---------- c : float, optional The tuning constant for Tukey's Biweight. The default value is c = 4.685. Notes ----- Tukey's biweight is sometime's called bisquare. c||_yr5rrrts r r7zTukeyBiweight.__init__r8r ctjtj|}tj||jS)zK Tukey's biweight is defined piecewise over the range of z )r+r;r,r:rsrs r r<zTukeyBiweight._subsets/ FF2::a= !}}Q''r c|j|}|jdzdz }d||jz dzz dz |z|z|zS)a^ The robust criterion function for Tukey's biweight estimator Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray rho(z) = -(1 - (z/c)**2)**3 * c**2/6. for \|z\| <= R rho(z) = 0 for \|z\| > R rg@rr<rs)rrsubsetfactors r rzTukeyBiweight.rhosP aRa$&&j1_$q((61F:VCCr ctj|}|j|}|d||jz dzz dzz|zS)ar The psi function for Tukey's biweight estimator The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray psi(z) = z*(1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R rrrwrrrs r rzTukeyBiweight.psi3sD& JJqMaATVVa'!++f44r cZ|j|}d||jz dzz dz|zS)a~ Tukey's biweight weighting function for the IRLS algorithm The psi function scaled by z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray psi(z) = (1 - (z/c)**2)**2 for \|z\| <= R psi(z) = 0 for \|z\| > R rrrrs r rzTukeyBiweight.weightsJs2&aQZ!O#a'&00r c|j|}|d||jz dzz dzd|dzz|jdzz d||jz dzz zz zS)z The derivative of Tukey's biweight psi function Notes ----- Used to estimate the robust covariance matrix. rrrrs r rzTukeyBiweight.psi_deriv`ska!qx!m+a/adF46619,AdffHq=ABC Cr N)g= ףp@rKr%r r rrs' (D(5.1, Cr rc:eZdZdZdZdZdZdZdZdZ dZ y ) MQuantileNormuM-quantiles objective function based on a base norm This norm has the same asymmetric structure as the objective function in QuantileRegression but replaces the L1 absolute value by a chosen base norm. rho_q(u) = abs(q - I(q < 0)) * rho_base(u) or, equivalently, rho_q(u) = q * rho_base(u) if u >= 0 rho_q(u) = (1 - q) * rho_base(u) if u < 0 Parameters ---------- q : float M-quantile, must be between 0 and 1 base_norm : RobustNorm instance basic norm that is transformed into an asymmetric M-quantile norm Notes ----- This is mainly for base norms that are not redescending, like HuberT or LeastSquares. (See Jones for the relationship of M-quantiles to quantiles in the case of non-redescending Norms.) Expectiles are M-quantiles with the LeastSquares as base norm. References ---------- .. [*] Bianchi, Annamaria, and Nicola Salvati. 2015. “Asymptotic Properties and Variance Estimators of the M-Quantile Regression Coefficients Estimators.” Communications in Statistics - Theory and Methods 44 (11): 2416–29. doi:10.1080/03610926.2013.791375. .. [*] Breckling, Jens, and Ray Chambers. 1988. “M-Quantiles.” Biometrika 75 (4): 761–71. doi:10.2307/2336317. .. [*] Jones, M. C. 1994. “Expectiles and M-Quantiles Are Quantiles.” Statistics & Probability Letters 20 (2): 149–53. doi:10.1016/0167-7152(94)90031-0. .. [*] Newey, Whitney K., and James L. Powell. 1987. “Asymmetric Least Squares Estimation and Testing.” Econometrica 55 (4): 819–47. doi:10.2307/1911031. c ||_||_yr5)q base_norm)rrrs r r7zMQuantileNorm.__init__s"r ct|}|dk}tj|}d|jz ||<|j||<|S)Nrr)lenr+emptyr)rrnobsmask_negqqs r _get_qzMQuantileNorm._get_qsF1vE XXd^466z8 H9  r c`|j|}||jj|zS)z The robust criterion function for MQuantileNorm. Parameters ---------- z : array_like 1d array Returns ------- rho : ndarray )rrrrrrs r rzMQuantileNorm.rhos+[[^DNN&&q)))r c`|j|}||jj|zS)z The psi function for MQuantileNorm estimator. The analytic derivative of rho Parameters ---------- z : array_like 1d array Returns ------- psi : ndarray )rrrrs r rzMQuantileNorm.psis+[[^DNN&&q)))r c`|j|}||jj|zS)a  MQuantileNorm weighting function for the IRLS algorithm The psi function scaled by z, psi(z) / z Parameters ---------- z : array_like 1d array Returns ------- weights : ndarray )rrrrs r rzMQuantileNorm.weightss+[[^DNN**1---r c`|j|}||jj|zS)a The derivative of MQuantileNorm function Parameters ---------- z : array_like 1d array Returns ------- psi_deriv : ndarray Notes ----- Used to estimate the robust covariance matrix. )rrrrs r rzMQuantileNorm.psi_derivs+"[[^DNN,,Q///r c$|j|Srrrs r rzMQuantileNorm.__call__r r N) r!r"r#r$r7rrrrrrr%r r rrms+/b#* *$.$0(r rc | t}|tj||}n|}t|D]}|j ||z |z } tj | |z|tj | |z } tj tjtj|| z ||zr| cS| }td|z)a M-estimator of location using self.norm and a current estimator of scale. This iteratively finds a solution to norm.psi((a-mu)/scale).sum() == 0 Parameters ---------- a : ndarray Array over which the location parameter is to be estimated scale : ndarray Scale parameter to be used in M-estimator norm : RobustNorm, optional Robust norm used in the M-estimator. The default is HuberT(). axis : int, optional Axis along which to estimate the location parameter. The default is 0. initial : ndarray, optional Initial condition for the location parameter. Default is None, which uses the median of a. niter : int, optional Maximum number of iterations. The default is 30. tol : float, optional Toleration for convergence. The default is 1e-06. Returns ------- mu : ndarray Estimate of location z6location estimator failed to converge in %d iterations) r3r+medianrangersumalllessr; ValueError) rPscalenormaxisinitialmaxitertolmurWnmus r estimate_locationrsB |x YYq$   7^ LL!B$ &ffQqS$"&&D/1 66"''"&&c*ECK8 9JB  M  r )NrNgư>) numpyr+r r r'r3rMr\rpr~rrrr%r r rs HHVN,:N,bj>Zj>\XjXvt)t)pd*dNnZnbeCJeCPKJK\<@&-1 r