ó áp7]c@sPdZddlZdefd„ƒYZd„Zddd„Zdd„ZdS(sM Created on Thu May 15 16:36:05 2014 Author: Josef Perktold License: BSD-3 i˙˙˙˙NtTransformRestrictioncBs,eZdZdd„Zd„Zd„ZRS(sTransformation 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 doesn't 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. c CsŒtj|ƒ}|_|dk r;tj|ƒ}|_n|j\}}|||_|_|||_ tj |ƒ|j j tj j|ƒj ƒ}tj j|ƒ\}}||_||_|dd…d|…f}|_|dd…|d…f|_|dk ry:|j j tj j|j j |j ƒ|j ƒƒ|_Wqˆtj j jk r{} td| fƒ‚qˆXn d|_dS(Ns8possibly inconsistent constraints. error generated by %ri(tnpt atleast_2dtRtNonetasarraytqtshapetk_constrtk_varst k_unconstrteyetTtdottlinalgtpinvteightevalstevecstLt transf_mattsolvetconstantt LinAlgErrort ValueError( tselfRRRR tmRRRte((s<lib/python2.7/site-packages/statsmodels/base/_constraints.pyt__init__3s&  .  # :cCs,tj|ƒ}|jj|jƒj|jS(s¸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. (RRRR R R(Rtparams_reduced((s<lib/python2.7/site-packages/statsmodels/base/_constraints.pytexpandXscCstj|ƒ}|j|jƒS(sżtransform 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. (RRR R(Rtparams((s<lib/python2.7/site-packages/statsmodels/base/_constraints.pytreducensN(t__name__t __module__t__doc__RRRR (((s<lib/python2.7/site-packages/statsmodels/base/_constraints.pyR s$ % cCsZ|j|ƒj|jƒ}|j|jƒjtjj||j|ƒ|ƒƒ}||S(sĄfind the parameters that statisfy linear constraint from unconstraint The linear constraint R params = q is imposed. Parameters ---------- params : array_like unconstraint 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 ? (R R RRR(RtSinvRRtrsrt reduction((s<lib/python2.7/site-packages/statsmodels/base/_constraints.pyttransform_params_constraintƒs"7cCsa|}|dkri}n||}}|j|j}} t||ƒ} | j| ƒ} | j| jjƒƒ} t|dƒr| |j 7} n|dk rŽ| j|ƒ}nddl } | j |j ƒƒ}d|krĺ|d=n|j || d| |}|j d||}| j|jƒjƒ}| jj|jƒƒj| jjƒ}|||fS(s6fit 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. toffseti˙˙˙˙Nt start_params(RtendogtexogRR R RtsqueezethasattrR(tcopyt_get_init_kwdst __class__tfitRRRt cov_paramsR (tmodeltconstraint_matrixtconstraint_valuesR)tfit_kwdsRRRR*R+ttransftexogp_stR(R.t init_kwdst mod_constrt res_constrt params_origR2((s<lib/python2.7/site-packages/statsmodels/base/_constraints.pytfit_constrainedŤs*<       'cKs6|}ddlm}||jƒj|ƒ}|j|j}}t|||d|d|ƒ\} } } |jd| dddtƒ} | | j _ | | j _ |j dd ƒ} | d krŇ| | j | j _n d | j _t|ƒ}| j j|7_| j j|8_|| j _|| j _| | j _| S( sÄfit_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. i˙˙˙˙(t DesignInfoR)R6tmaxiteritwarn_convergencetcov_typet nonrobustN(tpatsyR>t exog_namestlinear_constrainttcoefst constantsR=R1tFalset_resultsRtcov_params_defaulttgettscaletnormalized_cov_paramsRtlentdf_residtdf_modelt constraintsRtresults_constrained(R3RQR)R6RR>tlcRRRtcovR;tresRAR((s<lib/python2.7/site-packages/statsmodels/base/_constraints.pytfit_constrained_wrap s,         ( R#tnumpyRtobjectRR'RR=RV(((s<lib/python2.7/site-packages/statsmodels/base/_constraints.pyts  v )^