M/Phn3^dZddlZGddZGddZdZ d dZd d ZdS) zM Created on Thu May 15 16:36:05 2014 Author: Josef Perktold License: BSD-3 Nc@eZdZdZdZdZdZdZedZ dS)LinearConstraintsaClass to hold linear constraints information Affine constraints are defined as ``R b = q` where `R` is the constraints matrix and `q` are the constraints values and `b` are the parameters. This is in analogy to patsy's LinearConstraints class but can be pickled. Parameters ---------- constraint_matrix : ndarray R matrix, 2-dim with number of columns equal to the number of parameters. Each row defines one constraint. constraint_values : ndarray 1-dim array of constant values variable_names : list of strings parameter names, used only for display kwds : keyword arguments keywords are attached to the instance. c ||_||_||_||_||_|j||j|jf|_dSN)constraint_matrixconstraint_valuesvariable_namescoefs constants__dict__updatetuple)selfrrr kwdss ]/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/base/_constraints.py__init__zLinearConstraints.__init__"sX"3!2,' * T""",d.DE c#$K|jEd{VdSrr)rs r__iter__zLinearConstraints.__iter__0s&:rc|j|Srr)ridxs r __getitem__zLinearConstraints.__getitem__3sz#rc d}g}t|D]\}}g}t||jD]d\}}|dkr|gkr||||z }!|dkr|d|||zz }:|dkr$|d|tj||zz }e|dt |zz }|d|d|S)Ncjtj|}|dkrt|dz|z}n|}|S)Nz * )npabsstr)vnamesss r prod_stringz.LinearConstraints.__str__..prod_string7s8q AAvvVVe^d*Irrz + z - z =  )zipr rrritemappendjoin)rr#constraints_stringsrqr"r r!s r__str__zLinearConstraints.__str__6s"   !J 4 4DAqBq$"566 ? ?466bBhh++a...BBUU%++a"6"666BBUU%++bfQii">">>>B %#affhh--' 'B  & &rwwr{{ 3 3 3 3yy,---rc:||j|j|jS)aLclass method to create instance from patsy instance Parameters ---------- lc : instance instance of patsy LinearConstraint, or other instances that have attributes ``lc.coefs, lc.constants, lc.variable_names`` Returns ------- instance of this class )r r r )clslcs r from_patsyzLinearConstraints.from_patsyNss28R\2+<===rN) __name__ __module__ __qualname____doc__rrrr- classmethodr1rrrr sx* F F F...0>>[>>>rrc&eZdZdZddZdZdZdS)TransformRestrictionaTransformation for linear constraints `R params = q` Note, the transformation from the reduced to the full parameters is an affine and not a linear transformation if q is not zero. Parameters ---------- R : array_like Linear restriction matrix q : arraylike or None values of the linear restrictions Notes ----- The reduced parameters are not sorted with respect to constraints. TODO: error checking, eg. inconsistent constraints, how? Inconsistent constraints will raise an exception in the calculation of the constant or offset. However, homogeneous constraints, where q=0, will can have a solution where the relevant parameters are constraint to be zero, as in the following example:: b1 + b2 = 0 and b1 + 2*b2 = 0, implies that b2 = 0. The transformation applied from full to reduced parameter space does not raise and exception if the constraint does not hold. TODO: maybe change this, what's the behavior in this case? The `reduce` transform is applied to the array of explanatory variables, `exog`, when transforming a linear model to impose the constraints. Nc@tj|x}|_|tj|x}|_|j\}}||c|_|_||z |_tj ||j tj |j z }tj |\}}||_||_|ddd|fx}|_|dd|df|_| |j tj |j |j |j |_dS#tj j$r} t-d| d} ~ wwxYwd|_dS)Nz6possibly inconsistent constraints. error generated by r)r atleast_2dRasarrayr,shapek_constrk_vars k_unconstreyeTdotlinalgpinveighevalsevecsL transf_matsolveconstant LinAlgError ValueError) rr<r,r?r@mrHrIrJes rrzTransformRestriction.__init__sz]1%%%DF =A &A7&%-v" t{ 8+ F6NNQSWWRY^^A%6%6%899 9y~~a(( u  111ixi<((DF899 - = = !  ac(J(J K K 9( = = = j78q"<=== =DMMMsAE))F=FFctj|}|j|jj|jzS)atransform from the reduced to the full parameter space Parameters ---------- params_reduced : array_like parameters in the transformed space Returns ------- params : array_like parameters in the original space Notes ----- If the restriction is not homogeneous, i.e. q is not equal to zero, then this is an affine transform. )rr=rKrDrCrM)rparams_reduceds rexpandzTransformRestriction.expands6$N33"">#3446FFrc^tj|}||jS)atransform from the full to the reduced parameter space Parameters ---------- params : array_like parameters or data in the original space Returns ------- params_reduced : array_like parameters in the transformed space This transform can be applied to the original parameters as well as to the data. If params is 2-d, then each row is transformed. )rr=rDrK)rparamss rreducezTransformRestriction.reduces' F##zz$/***rr)r2r3r4r5rrTrWr7rrr9r9`sU""H####JGGG*+++++rr9c(|||j}||jtj||||z }||z S)afind the parameters that statisfy linear constraint from unconstrained The linear constraint R params = q is imposed. Parameters ---------- params : array_like unconstrained parameters Sinv : ndarray, 2d, symmetric covariance matrix of the parameter estimate R : ndarray, 2d constraint matrix q : ndarray, 1d values of the constraint Returns ------- params_constraint : ndarray parameters of the same length as params satisfying the constraint Notes ----- This is the exact formula for OLS and other linear models. It will be a local approximation for nonlinear models. TODO: Is Sinv always the covariance matrix? In the linear case it can be (X'X)^{-1} or sigmahat^2 (X'X)^{-1}. My guess is that this is the point in the subspace that satisfies the constraint that has minimum Mahalanobis distance. Proof ? )rDrCrrErL)rVSinvr<r,rsr reductions rtransform_params_constraintr\skB %%++//!#  C !!")//#quuV}}q7H"I"IJJI I rc|}|i}||}}|j|j} }t||} | | } | | j} t|dr | |jz } || |}ddl } | | }d|vr|d=|j || fd| i|}|j dd|i|}| |j}| j|| jj}|||fS)a4fit model subject to linear equality constraints The constraints are of the form `R params = q` where R is the constraint_matrix and q is the vector of constraint_values. The estimation creates a new model with transformed design matrix, exog, and converts the results back to the original parameterization. Parameters ---------- model: model instance An instance of a model, see limitations in Notes section constraint_matrix : array_like, 2D This is R in the linear equality constraint `R params = q`. The number of columns needs to be the same as the number of columns in exog. constraint_values : This is `q` in the linear equality constraint `R params = q` If it is a tuple, then the constraint needs to be given by two arrays (constraint_matrix, constraint_value), i.e. (R, q). Otherwise, the constraints can be given as strings or list of strings. see t_test for details start_params : None or array_like starting values for the optimization. `start_params` needs to be given in the original parameter space and are internally transformed. **fit_kwds : keyword arguments fit_kwds are used in the optimization of the transformed model. Returns ------- params : ndarray ? estimated parameters (in the original parameterization cov_params : ndarray covariance matrix of the parameter estimates. This is a reverse transformation of the covariance matrix of the transformed model given by `cov_params()` Note: `fit_kwds` can affect the choice of covariance, e.g. by specifying `cov_type`, which will be reflected in the returned covariance. res_constr : results instance This is the results instance for the created transformed model. Notes ----- Limitations: Models where the number of parameters is different from the number of columns of exog are not yet supported. Requires a model that implement an offset option. Noffsetr start_paramsr7)endogexogr9rWrDrMsqueezehasattrr^copy_get_init_kwds __class__fitrTrVrK cov_paramsrC)modelrrr_fit_kwdsrr<r,r`ratransfexogp_str^rd init_kwds mod_constr res_constr params_origrhs rfit_constrainedrqs~t D /qA*di4E !!Q ' 'F}}T""H XXfo--// 0 0FtX$+ l33 KKK $--//00I9 h  xLLL)LLJFF\FXFFJ-- 122::<'>??CCFDUDWXXJ  J ..rc l|}ddlm}||j|}|j|j}}t |||||\} } } || dd} | | j_ | | j_ | dd} | dkr| | j z | j_ n d| j_ t|}| jxj|z c_| jxj|zc_t"|| j_|| j_| | j_| S) afit_constraint that returns a results instance This is a development version for fit_constrained methods or fit_constrained as standalone function. It will not work correctly for all models because creating a new results instance is not standardized for use outside the `fit` methods, and might need adjustements for this. This is the prototype for the fit_constrained method that has been added to Poisson and GLM. r) DesignInfo)r_rjF)r_maxiterwarn_convergencecov_type nonrobustN)patsyrs exog_nameslinear_constraintr r rqrg_resultsrVcov_params_defaultgetscalenormalized_cov_paramslendf_residdf_modelrr1 constraintsr?results_constrained)rirr_rjrrsr0r<r,rVcovroresrvr?s rfit_constrained_wraprWsQ D !     DO $ $ 6 6{ C CB 8R\qA.dAq;G7?AAAFC (($)  + +C CL&)CL#||J 44H;-0:3C-C **-1 *1vvHLX%LX%0;;B??CL$CL'1CL$ Jr)NNr)r5numpyrrr9r\rqrr7rrrsQ>Q>Q>Q>Q>Q>Q>Q>hp+p+p+p+p+p+p+p+f$$$P15Z/Z/Z/Z/z222222r