!gn3PdZddlZGddZGddZdZ d dZd d Zy) zM Created on Thu May 15 16:36:05 2014 Author: Josef Perktold License: BSD-3 Nc8eZdZdZdZdZdZdZedZ y)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 ||j|jf|_yN)constraint_matrixconstraint_valuesvariable_namescoefs constants__dict__updatetuple)selfrrr kwdss Z/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/base/_constraints.py__init__zLinearConstraints.__init__"sV"3!2,' * T",,d.D.DE c#8K|jEd{y7wrr)rs r__iter__zLinearConstraints.__iter__0s::s c |j|Srr)ridxs r __getitem__zLinearConstraints.__getitem__3szz#rc d}g}t|D]\}}g}t||jD]Y\}}|dk7r|gk(r ||||z }|dkDr|d|||zz }2|dks8|d|tj||zz }[|dt |j zz }|j dj|dj|S)Ncdtj|}|dk7rt|dz|z}|S|}|S)Nz * )npabsstr)vnamesss r prod_stringz.LinearConstraints.__str__..prod_string7s;q AAvVe^d*IIrrz + z - z =  )zipr rrritemappendjoin)rr#constraints_stringsrqr"r r!s r__str__zLinearConstraints.__str__6s !J 4DAqBq$"5"56 ?46bBh+a..BU%+a"666BU%+bffQi">>>B  ? %#affh-' 'B  & &rwwr{ 3 4yy,--rcR||j|j|jS)aLclass method to create instance from patsy instance Parameters ---------- lc : instance instance of patsy LinearConstraint, or other instances that have attributes ``lc.coefs, lc.constants, lc.variable_names`` Returns ------- instance of this class )r r r )clslcs r from_patsyzLinearConstraints.from_patsyNs!288R\\2+<+<==rN) __name__ __module__ __qualname____doc__rrrr- classmethodr1rrrr s0* F.0>>rrc$eZdZdZddZdZdZy)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. Ncntj|x}|_|tj|x}|_|j \}}||c|_|_||z |_tj||jjtjj|jz }tjj|\}}||_||_|ddd|fx}|_|dd|df|_|m |jjtjj'|jj|j|j|_yd|_y#tjj*$r} t-d| d} ~ wwxYw)Nz6possibly inconsistent constraints. error generated by r)r atleast_2dRasarrayr,shapek_constrk_vars k_unconstreyeTdotlinalgpinveighevalsevecsL transf_matsolveconstant LinAlgError ValueError) rr<r,r?r@mrHrIrJes rrzTransformRestriction.__init__sZ]]1%%DF =A &A77&%-v" t{ 8+ FF6NQSSWWRYY^^A%6%8%89 9yy~~a( u  1ixi<((DF89 - = = !  acc(J K DM 99(( = 78"<== =sA+FF4!F//F4ctj|}|jj|jj|j zS)atransform from the reduced to the full parameter space Parameters ---------- params_reduced : array_like parameters in the transformed space Returns ------- params : array_like parameters in the original space Notes ----- If the restriction is not homogeneous, i.e. q is not equal to zero, then this is an affine transform. )rr=rKrDrCrM)rparams_reduceds rexpandzTransformRestriction.expands<$N3"">#3#3466FFrcbtj|}|j|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`s"H#JG*+rr9c|j|j|j}|j|jjtjj ||j||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\sbB %%+//!## C !!"))//#quuV}q7H"IJI I rc|}|i}||}}|j|j} }t||} | j| } | j | j j } t|dr| |jz } || j|}ddl } | j|j}d|vr|d=|j|| fd| i|}|jdd|i|}| j|jj }| jj |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_constrainedrqsUt D /qA**dii4E !!Q 'F}}T"H XXfoo--/ 0FtX$++ l3  $--/0I9 h  xLL)LJF\FXFJ-- 1 12::?CCFDUDUDWDWXJ  J ..rc |}ddlm}||jj|}|j|j }}t |||||\} } } |j| dd} | | j_ | | j_ |jdd} | dk(r| | jz | j_ nd| j_ t|}| jxj|z c_| jxj |zc_t"j%|| 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_wraprWs0 D ! DOO $ 6 6{ CB 88R\\qA.dAq;G7?AFC (($)  +C CLL&)CLL#||J 4H;-0:3C3C-C *-1 *1vHLLX%LLX%0;;B?CLL$CLL'1CLL$ Jr)NNr)r5numpyrrr9r\rqrr7rrrs@Q>Q>hp+p+f$P15Z/z2r