U Kv f3ã@sHdZddlZGdd„dƒZGdd„dƒZdd„Zd d d „Zddd„ZdS)zM Created on Thu May 15 16:36:05 2014 Author: Josef Perktold License: BSD-3 éNc@s<eZdZdZdd„Zdd„Zdd„Zdd „Zed d„ƒZ dS) ÚLinearConstraintsa»Class 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. cKs<||_||_||_||_||_|j |¡|j|jf|_dS©N)Úconstraint_matrixÚconstraint_valuesÚvariable_namesÚcoefsÚ constantsÚ__dict__ÚupdateÚtuple)ÚselfrrrÚkwds©rúA/tmp/pip-unpacked-wheel-2v6byqio/statsmodels/base/_constraints.pyÚ__init__#szLinearConstraints.__init__ccs|jEdHdSr©r)rrrrÚ__iter__1szLinearConstraints.__iter__cCs |j|Srr)rÚidxrrrÚ__getitem__4szLinearConstraints.__getitem__cCsÂdd„}g}t|ŽD]¢\}}g}t||jƒD]d\}}|dkrT|gkrT||||ƒ7}q,|dkrp|d|||ƒ7}q,|dkr,|d|t |¡|ƒ7}q,|dt| ¡ƒ7}| d |¡¡qd |¡S) NcSs,t |¡}|dkr$t|ƒd|}n|}|S)Néz * )ÚnpÚabsÚstr)ÚvÚnameÚssrrrÚprod_string8s z.LinearConstraints.__str__..prod_stringrz + z - z = ÚÚ )ÚziprrrrÚitemÚappendÚjoin)rrZconstraints_stringsÚrÚqrrrrrrÚ__str__7szLinearConstraints.__str__cCs||j|j|jƒS)aLclass method to create instance from patsy instance Parameters ---------- lc : instance instance of patsy LinearConstraint, or other instances that have attributes ``lc.coefs, lc.constants, lc.variable_names`` Returns ------- instance of this class )rrr)ÚclsÚlcrrrÚ from_patsyOszLinearConstraints.from_patsyN) Ú__name__Ú __module__Ú__qualname__Ú__doc__rrrr%Úclassmethodr(rrrrr src@s*eZdZdZd dd„Zdd„Zdd„ZdS) ÚTransformRestrictionaTransformation for linear constraints `R params = q` Note, the transformation from the reduced to the full parameters is an affine and not a linear transformation if q is not zero. Parameters ---------- R : array_like Linear restriction matrix q : arraylike or None values of the linear restrictions Notes ----- The reduced parameters are not sorted with respect to constraints. TODO: error checking, eg. inconsistent constraints, how? Inconsistent constraints will raise an exception in the calculation of the constant or offset. However, homogeneous constraints, where q=0, will can have a solution where the relevant parameters are constraint to be zero, as in the following example:: b1 + b2 = 0 and b1 + 2*b2 = 0, implies that b2 = 0. The transformation applied from full to reduced parameter space does not raise and exception if the constraint does not hold. TODO: maybe change this, what's the behavior in this case? The `reduce` transform is applied to the array of explanatory variables, `exog`, when transforming a linear model to impose the constraints. Nc Cs.t |¡}|_|dk r(t |¡}|_|j\}}|||_|_|||_t |¡|j tj |¡j ¡}tj |¡\}}||_||_|dd…d|…f}|_|dd…|d…f|_|dk r$z(|j tj |j |j ¡|j ¡¡|_Wn8tjjjk r } ztd| fƒ‚W5d} ~ XYnXnd|_dS)Nz8possibly inconsistent constraints. error generated by %rr)rZ atleast_2dÚRÚasarrayr$ÚshapeÚk_constrÚk_varsZ k_unconstrZeyeÚTÚdotÚlinalgZpinvZeighÚevalsÚevecsÚLÚ transf_matÚsolveÚconstantZLinAlgErrorÚ ValueError) rr/r$r2r3Úmr7r8r9Úerrrr†s( (ÿzTransformRestriction.__init__cCs t |¡}|j |j¡j|jS)a·transform 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. )rr0r:r5r4r<)rZparams_reducedrrrÚexpand«s zTransformRestriction.expandcCst |¡}| |j¡S)a¾transform 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. )rr0r5r:)rÚparamsrrrÚreduceÀs zTransformRestriction.reduce)N)r)r*r+r,rr@rBrrrrr.as$ %r.cCs@| |¡ |j¡}| |j¡ tj || |¡|¡¡}||S)a¢find 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 ? )r5r4rr6r;)rAZSinvr/r$ZrsrZ reductionrrrÚtransform_params_constraintÔs!&rCcCsö|}|dkri}||}}|j|j}} t||ƒ} | | ¡}| | j ¡¡}t|dƒr`||j7}|dk rr| |¡}ddl } | | ¡¡}d|kr–|d=|j||fd|i|—Ž}|jfd|i|—Ž}| |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. NÚoffsetrÚstart_params)ÚendogÚexogr.rBr5r<ZsqueezeÚhasattrrDÚcopyZ_get_init_kwdsÚ __class__Úfitr@rAr:Ú cov_paramsr4)ÚmodelrrrEÚfit_kwdsrr/r$rFrGZtransfZexogp_strDrIZ init_kwdsZ mod_constrÚ res_constrZparams_origrLrrrÚfit_constrainedûs*: rPcKsÜ|}ddlm}||jƒ |¡}|j|j}}t|||||d\} } }|j| ddd}| |j_ | |j_ | dd¡} | dkrŠ| |j|j_ nd|j_ t|ƒ}|jj|7_|jj|8_t |¡|j_||j_||j_|S) aÃfit_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)Ú DesignInfo)rErNF)rEÚmaxiterZwarn_convergenceÚcov_typeZ nonrobustN)ZpatsyrQZ exog_namesZlinear_constraintrrrPrKZ_resultsrAZcov_params_defaultÚgetZscaleZnormalized_cov_paramsÚlenZdf_residZdf_modelrr(Úconstraintsr2Zresults_constrained)rMrVrErNrrQr'r/r$rAZcovrOÚresrSr2rrrÚfit_constrained_wrapXs0þÿrX)NN)N)r,Znumpyrrr.rCrPrXrrrrÚsTs(ÿ ]