=h<SrSSKJr SSKJrJrJr SSKJr SSK J r SSK r SSK Jr SSjrS r"S S 5rSS jrSS jrSSjrSSjrSSjrSSjrSSjrSSjrSSjrg)z Functions that are general enough to use for any model fitting. The idea is to untie these from LikelihoodModel so that they may be re-used generally. ) annotations)SP_LT_15SP_LT_17 SP_LT_116)Sequence)AnyN)optimizec  [[UR555R[U55nU(aCSSKnUR SUSSR U5SSR U5S3[5 gg)NrzzKeyword arguments have been passed to the optimizer that have no effect. The list of allowed keyword arguments for method z is: z, z<. The list of unsupported keyword arguments passed include: z&. After release 0.14, this will raise.)setlistkeys differencewarningswarnjoin FutureWarning)kwargsallowedmethodextrars mC:\Users\julio\OneDrive\Documentos\Trabajo\Ideas Frescas\venv\Lib\site-packages\statsmodels/base/optimizer.py check_kwargsrs| V[[]# $ / /W >E   KheDIIg./011551A0BC- -    c.X;aSU-n[U5eg)NzUnknown fit method %s) ValueError)rmethodsmessages r _check_methodrs" )F2!!rc.\rSrSrSSjrSrSrSrg) Optimizer%Nc URS[55n /SQnXR5- nUR5n[ X~5 [ [ [[[[[[[S. nU (aURU 5 XnU"XX4UXU XUS9 unnXsXXU XS. nURU5 UUU4$)a Fit function for any model with an objective function. Parameters ---------- objective : function Objective function to be minimized. gradient : function The gradient of the objective function. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : dict[str, Any] Extra keyword arguments passed to the objective function, i.e. objective(x,**kwargs) hessian : str, optional Method for computing the Hessian matrix, if applicable. method : str {'newton','nm','bfgs','powell','cg','ncg','basinhopping', 'minimize'} Method can be 'newton' for Newton-Raphson, 'nm' for Nelder-Mead, 'bfgs' for Broyden-Fletcher-Goldfarb-Shanno, 'powell' for modified Powell's method, 'cg' for conjugate gradient, 'ncg' for Newton- conjugate gradient, 'basinhopping' for global basin-hopping solver, if available or a generic 'minimize' which is a wrapper for scipy.optimize.minimize. `method` determines which solver from scipy.optimize is used. The explicit arguments in `fit` are passed to the solver, with the exception of the basin-hopping solver. Each solver has several optional arguments that are not the same across solvers. See the notes section below (or scipy.optimize) for the available arguments and for the list of explicit arguments that the basin-hopping solver supports.. maxiter : int The maximum number of iterations to perform. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. disp : bool Set to True to print convergence messages. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. optim_settings : dict A dictionary that contains the parameters passed to the solver. Notes ----- The 'basinhopping' solver ignores `maxiter`, `retall`, `full_output` explicit arguments. Optional arguments for the solvers (available in Results.mle_settings):: 'newton' tol : float Relative error in params acceptable for convergence. 'nm' -- Nelder Mead xtol : float Relative error in params acceptable for convergence ftol : float Relative error in loglike(params) acceptable for convergence maxfun : int Maximum number of function evaluations to make. 'bfgs' gtol : float Stop when norm of gradient is less than gtol. norm : float Order of norm (np.inf is max, -np.inf is min) epsilon If fprime is approximated, use this value for the step size. Only relevant if LikelihoodModel.score is None. 'lbfgs' m : int The maximum number of variable metric corrections used to define the limited memory matrix. (The limited memory BFGS method does not store the full hessian but uses this many terms in an approximation to it.) pgtol : float The iteration will stop when ``max{|proj g_i | i = 1, ..., n} <= pgtol`` where pg_i is the i-th component of the projected gradient. factr : float The iteration stops when ``(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr * eps``, where eps is the machine precision, which is automatically generated by the code. Typical values for factr are: 1e12 for low accuracy; 1e7 for moderate accuracy; 10.0 for extremely high accuracy. See Notes for relationship to ftol, which is exposed (instead of factr) by the scipy.optimize.minimize interface to L-BFGS-B. maxfun : int Maximum number of iterations. epsilon : float Step size used when approx_grad is True, for numerically calculating the gradient approx_grad : bool Whether to approximate the gradient numerically (in which case func returns only the function value). 'cg' gtol : float Stop when norm of gradient is less than gtol. norm : float Order of norm (np.inf is max, -np.inf is min) epsilon : float If fprime is approximated, use this value for the step size. Can be scalar or vector. Only relevant if Likelihoodmodel.score is None. 'ncg' fhess_p : callable f'(x,*args) Function which computes the Hessian of f times an arbitrary vector, p. Should only be supplied if LikelihoodModel.hessian is None. avextol : float Stop when the average relative error in the minimizer falls below this amount. epsilon : float or ndarray If fhess is approximated, use this value for the step size. Only relevant if Likelihoodmodel.hessian is None. 'powell' xtol : float Line-search error tolerance ftol : float Relative error in loglike(params) for acceptable for convergence. maxfun : int Maximum number of function evaluations to make. start_direc : ndarray Initial direction set. 'basinhopping' niter : int The number of basin hopping iterations. niter_success : int Stop the run if the global minimum candidate remains the same for this number of iterations. T : float The "temperature" parameter for the accept or reject criterion. Higher "temperatures" mean that larger jumps in function value will be accepted. For best results `T` should be comparable to the separation (in function value) between local minima. stepsize : float Initial step size for use in the random displacement. interval : int The interval for how often to update the `stepsize`. minimizer : dict Extra keyword arguments to be passed to the minimizer `scipy.optimize.minimize()`, for example 'method' - the minimization method (e.g. 'L-BFGS-B'), or 'tol' - the tolerance for termination. Other arguments are mapped from explicit argument of `fit`: - `args` <- `fargs` - `jac` <- `score` - `hess` <- `hess` 'minimize' min_method : str, optional Name of minimization method to use. Any method specific arguments can be passed directly. For a list of methods and their arguments, see documentation of `scipy.optimize.minimize`. If no method is specified, then BFGS is used. extra_fit_funcs) newtonnmbfgslbfgspowellcgncg basinhoppingminimize) r$r%r&r'r)r*r(r+r,)dispmaxitercallbackretall full_outputhess) optimizer start_paramsr.r1r-fargsr/r0r#)getdictr lowerr _fit_newton_fit_nm _fit_bfgs _fit_lbfgs_fit_cg_fit_ncg _fit_powell_fit_basinhopping _fit_minimizeupdate)self objectivegradientr4r5rhessianrr.r1r-r/r0r#r fit_funcsfuncxoptretvalsoptim_settingss r_fitOptimizer._fit&sj!**%6?/''))f&"!-%      _ - Y,v"&($*")+ g (.%,"&H$*P f%Wn,,rc[e)z TODO: how to add constraints? Something like sm.add_constraint(Model, func) or model_instance.add_constraint(func) model_instance.add_constraint("x1 + x2 = 2") result = model_instance.fit() NotImplementedErrorrCparamss r_fit_constrainedOptimizer._fit_constraineds "!rc[eNrOrQs r_fit_regularizedOptimizer._fit_regularizeds "!r)Nr$dTTNF)__name__ __module__ __qualname____firstlineno__rLrSrW__static_attributes__rYrrr r %sEI.3Z-x ""rr c URSS5 /SQn UR5V V s0sHupX;dM X_M nn n X^S'XnS'/SQn/SQnUSU;aSn USU;aSn/S Qn[(dUS /- n[(dUS /- n/S QnS UR 5;aUSU;aUS nOSnSUR 5;aUSU;aUSnOSn[ R "XX4SXUUX~S9 nURnSnU (as[US[R5nURUURURURS.nU(a!URSUR!505 UU4$s sn n f)a Fit using scipy minimize, where kwarg `min_method` defines the algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : dict[str, Any] Extra keyword arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. min_methodBFGS)r#niterratolbounds constraintsr-r.) Nelder-MeadPowellCGrbCOBYLASLSQP)rgrhrjN)L-BFGS-BTNCrk trust-constrrhrg)rjrkrnrerfrY)argsrjacr2rerfr/optionsnitfopt iterationsfcallswarnflag convergedallvecs) setdefaultitemsrrr r r,xgetattrnpnanfunnfevstatussuccessrBvalues)fscorer4r5rr-r.r/r0r1r2 filter_optskvrqno_hessno_jac has_boundshas_constraintsrerfresrIrJrrs rrArAs^ lF+]K & G!2FtqtGGFO IIG 0F lw& lv%>J 8xj 8}o% 9O6;;= VL%9Z%G! %&*>/*Q]+    A%|@T %[%- @C 55DGc5"&&)77# XX3:: # -  NNIszz|4 5 =]Hs FFc [USS5 URSS5n URSS5n Sn [Rn[R"U5nU(aX/nX:Ga,[R "[R "UU- 5U :5(a[R"U "U55n[R"U S:H5(d.U[R"URS5==U - ss'UnU[RRUU"U55- nU(aWRU5 UbU"U5 U S - n X:a7[R "[R "UU- 5U :5(aMU"U/UQ76nX:Xa1S nU(a'[S 5 [S U-5 [S U -5 O0SnU(a'[S 5 [S U-5 [SU -5 U (aLX"U/UQ76X"U5U "U54unnnnnU(+nUUUUUUS.nU(aURSW05 UU4$UnSnUU4$)a# Fit using Newton-Raphson algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : dict[str, Any] Extra keyword arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. ridge_factor : float Regularization factor for Hessian matrix. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. )rd ridge_factorr$rdg:0yE>r绽|=rNz8Warning: Maximum number of iterations has been exceeded.z# Current function value: %fz Iterations: %dz%Optimization terminated successfully.z Iterations %d)rtrurHessianrwrxry)rrzr~infasarrayanyabsall diag_indicesshapelinalgsolveappendprintrB)rrr4r5rr-r.r/r0r1r2rrdru oldparams newparamshistoryHfvalrwrIrtrcgopthoptrxrJs rr9r9sbb0(;   E4 (C$$^U;LJI <(I (  BFF266)2;3<,=?B,C%D%D JJtI 'vvla'(( booaggaj) *l : *  53C DD  NN9 %   Y a   BFF266)2;3<,=?B,C%D%D Y  D    7$> ? +j8 9  9 : 7$> ? *Z7 8!1Y#7#7"E)$4Y) tU t!L ut" )+  NNIw/ 0 = =rc [USS5 URSS5n URS[R5n URSS5n [R "XXXU XiXXUS9 nU (aKU(d UunnnnnnnO UunnnnnnnnU(+nUUUUUUUS .nU(aUR S W05 X4$UnS nX4$) a Fit using Broyden-Fletcher-Goldfarb-Shannon algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : dict[str, Any] Extra keyword arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. gtolnormepsilonr&rh㈵>rrP>) rorrrr.r1r-r0r/)rtrHinvrvgcallsrwrxryN)rrzr~rr fmin_bfgsrB)rrr4r5rr-r.r/r0r1r2rrrrJrIrtrrrvrrwryrxs rr;r;s^4f=   V%; [ST"U/UQ7655$)Nc3&# UHo*v M g7frVrY).0r|s r /_fit_lbfgs....s"H/G!2/Gs)tuple)pars r_fit_lbfgs..sU"H/@/GQ/G"HHrfprimer-)r.r/rorerwgradfuncallsrr)rtrrvrwrxru) rrzlenr6rcopyrr fmin_l_bfgs_b)rrr4r5rr-r.r/r0r1r2renamesr| extra_kwargsrrrHextended_kwargsrJrIrtdrwrxrrvrurs @rr<r<3shl   x,#l:K)K LF h" HE*/?%Q;LAayL%L?**]E2K #6=jjD)G{DE E(%& &H !&X "'')Oy $$$    G dA Z=] y:uX 'i!+- =qz =E@s  E/ E/c b[USS5 URSS5n URSS5n URSS5n [R"XX;XU XUUS9 nU (aEU(d UunnnnnO UunnnnnnU(+nUUUUUS .nU(aUR S W05 X4$UnSnX4$) a Fit using Nelder-Mead algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : dict[str, Any] Extra keyword arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. )xtolftolrr%r-C6?rrN) rorrr.rr1r-r0r/rsry)rrzr fminrB)rrr4r5rr-r.r/r0r1r2rrrrJrIrtrcrvrwryrxs rr:r:s^3T:   VV ,D   VV ,D   x .FmmA%!%v(3v%-/G29 /D$vx;B 8D$vx L u# )+  NNIw/ 0 = =rc |[USS5 URSS5n URS[R5n URSS5n [R "XXU XXXS9 nU (aEU(d UunnnnnO UunnnnnnU(+nUUUUUS .nU(aUR S W05 X4$UnS nX4$) a Fit using Conjugate Gradient algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : dict[str, Any] Extra keyword arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. rr)rrrrr)rrrr.r1r-r0r/)rtrvrrwrxryN)rrzr~rr fmin_cgrB)rrr4r5rr-r.r/r0r1r2rrrrJrIrtrvrrwryrxs rr=r=s^4d;   V%; r>Ks^:EB 40G +ABG +ABG&*(/,7'- BG ;B 8D$ BD$' L 6V# )+  NNIw/ 0 = =rc [USS5 URSS5n URSS5n URSS5n URSS5n[R"XX;XU XXUS 9 nU (aIU(d UunnnnnnO UunnnnnnnU(+nUUUUUUS .nU(aUR S W05 UU4$UnSnUU4$) a Fit using Powell's conjugate direction algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : dict[str, Any] Extra keyword arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. )rrr start_direcr(rrrrNr) rorrr.rr1r-r0r/direc)rtrrurvrwrxry)rrzr fmin_powellrB)rrr4r5rr-r.r/r0r1r2rrrrrJrIrtrrcrvrwryrxs rr?r?s^BHM   VV ,D   VV ,D   x .F##M48K""1(,f/:*0)4 6G 9@ 6D$ufh @D$ufh L %u# )+  NNIw/ 0 = =rc [USS5 UR5V V s0sHupX_M nn n URSS5n URSS5nURSS5nURS S 5nURS S 5nURS 5nURS05nUUS'UUS'URSS5nU(a US:waU US'[R "XUXUUUUUUS9 nUR nU (a9URURURSURS;S.nUU4$SnUU4$s sn n f)a Fit using Basin-hopping algorithm. Parameters ---------- f : function Returns negative log likelihood given parameters. score : function Returns gradient of negative log likelihood with respect to params. start_params : array_like, optional Initial guess of the solution for the loglikelihood maximization. The default is an array of zeros. fargs : tuple Extra arguments passed to the objective function, i.e. objective(x,*args) kwargs : dict[str, Any] Extra keyword arguments passed to the objective function, i.e. objective(x,**kwargs) disp : bool Set to True to print convergence messages. maxiter : int The maximum number of iterations to perform. callback : callable callback(xk) Called after each iteration, as callback(xk), where xk is the current parameter vector. retall : bool Set to True to return list of solutions at each iteration. Available in Results object's mle_retvals attribute. full_output : bool Set to True to have all available output in the Results object's mle_retvals attribute. The output is dependent on the solver. See LikelihoodModelResults notes section for more information. hess : str, optional Method for computing the Hessian matrix, if applicable. Returns ------- xopt : ndarray The solution to the objective function retvals : dict, None If `full_output` is True then this is a dictionary which holds information returned from the solver used. If it is False, this is None. )rc niter_successTstepsizeinterval minimizerseedr+rcrZrNrg?rg?r2rrrorprrlr2) minimizer_kwargsrcrrrr-r/rrzcompleted successfullyr)rtrurvrx) rr{rzr6r r+r|rrrrr)rrr4r5rr-r.r/r0r1r2rrrcrrrrrrrrJrIs rr@r@sp^T &||~ .~tqad~F .   gs +E%%otr?r@rYrrrs#BB$  " q"q"p?C5:)-aH=A38:?eP;?16%)GTJMCGCL9=/4#'FR9=/4#'FR:>05$(HV=A38'+IXCG9>-1Sr