4[gؗddlZddlZddlmZddlmZmZddlm Z m Z ddl m Z m Z mZmZmZddlmZddlmZej*ej.Zej*ej2ZGd d Zy) N) lsq_linear)Models Quadratic)Options Constants)cauchy_geometryspider_geometrynormal_byrd_omojokuntangential_byrd_omojokun$constrained_tangential_byrd_omojokun)qr_tangential_byrd_omojokun)get_arrays_tolceZdZdZdZedZedZedZedZ edZ edZ e jd Z ed Z e jd Z ed Zed ZedZedZedZedZedZdZdZdZdZdZdZdZdZd+dZdZdZdZ d Z!d!Z"d"Z#d#Z$d$Z%d,d%Z&d&Z'd'Z(d(Z)d)Z*d*Z+y)- TrustRegionz! Trust-region framework. c:||_t|j||_||_d|_d|_|j tj|j|_ tj|j|_ tj|j|_tj|j|_|j#|j$|t&j(|_|j,|_y)a  Initialize the trust-region framework. Parameters ---------- pb : `cobyqa.problem.Problem` Problem to solve. options : dict Options of the solver. constants : dict Constants of the solver. Raises ------ `cobyqa.utils.MaxEvalError` If the maximum number of evaluations is reached. `cobyqa.utils.TargetSuccess` If a nearly feasible point has been found with an objective function value below the target. `cobyqa.utils.FeasibleSuccess` If a feasible point has been found for a feasibility problem. `numpy.linalg.LinAlgError` If the initial interpolation system is ill-defined. rN)_pbr_models _constants_penalty _best_indexset_best_indexnpzeros m_linear_ub _lm_linear_ub m_linear_eq _lm_linear_eqm_nonlinear_ub_lm_nonlinear_ubm_nonlinear_eq_lm_nonlinear_eqset_multipliersx_bestrRHOBEG _resolution resolution_radius)selfpboptions constantss V/var/www/html/bid-api/venv/lib/python3.12/site-packages/scipy/_lib/cobyqa/framework.py__init__zTrustRegion.__init__s4dhh0 #   XXd&6&67XXd&6&67 ")<)< = ")<)< = T[[)#7>>2 c.|jjS)zt Number of variables. Returns ------- int Number of variables. )rnr*s r.r2z TrustRegion.nLsxxzzr0c.|jjS)z Number of linear inequality constraints. Returns ------- int Number of linear inequality constraints. )rrr3s r.rzTrustRegion.m_linear_ubXxx###r0c.|jjS)z Number of linear equality constraints. Returns ------- int Number of linear equality constraints. )rrr3s r.rzTrustRegion.m_linear_eqdr5r0c.|jjS)z Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. )rr r3s r.r zTrustRegion.m_nonlinear_ubpxx&&&r0c.|jjS)z Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. )rr"r3s r.r"zTrustRegion.m_nonlinear_eq|r8r0c|jS)zv Trust-region radius. Returns ------- float Trust-region radius. )r)r3s r.radiuszTrustRegion.radius||r0c||_|j|jtj|j zkr|j |_yy)z Set the trust-region radius. Parameters ---------- radius : float New trust-region radius. N)r)r;rrDECREASE_RADIUS_THRESHOLDr()r*r;s r.r;zTrustRegion.radiussG KKyBBCoo  ??DL  r0c|jS)z Resolution of the trust-region framework. The resolution is a lower bound on the trust-region radius. Returns ------- float Resolution of the trust-region framework. r'r3s r.r(zTrustRegion.resolutionsr0c||_y)z Set the resolution of the trust-region framework. Parameters ---------- resolution : float New resolution of the trust-region framework. Nr@)r*r(s r.r(zTrustRegion.resolutions &r0c|jS)zr Penalty parameter. Returns ------- float Penalty parameter. )rr3s r.penaltyzTrustRegion.penaltys}}r0c|jS)z Models of the objective function and constraints. Returns ------- `cobyqa.models.Models` Models of the objective function and constraints. )rr3s r.modelszTrustRegion.modelsr<r0c|jS)z Index of the best interpolation point. Returns ------- int Index of the best interpolation point. )rr3s r. best_indexzTrustRegion.best_indexsr0c`|jjj|jS)z Best interpolation point. Its value is interpreted as relative to the origin, not the base point. Returns ------- `numpy.ndarray` Best interpolation point. )rE interpolationpointrGr3s r.r%zTrustRegion.x_bests#{{((..t??r0cH|jj|jS)z Value of the objective function at `x_best`. Returns ------- float Value of the objective function at `x_best`. )rEfun_valrGr3s r.fun_bestzTrustRegion.fun_bests{{""4??33r0cP|jj|jddfS)z Values of the nonlinear inequality constraints at `x_best`. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Values of the nonlinear inequality constraints at `x_best`. N)rEcub_valrGr3s r.cub_bestzTrustRegion.cub_best"{{""4??A#566r0cP|jj|jddfS)z Values of the nonlinear equality constraints at `x_best`. Returns ------- `numpy.ndarray`, shape (m_nonlinear_eq,) Values of the nonlinear equality constraints at `x_best`. N)rEceq_valrGr3s r.ceq_bestzTrustRegion.ceq_best rQr0c$|jj||j|jjj |z|jjj z zz|j|jjj|z|jjjz zz|j|jj|zz|j|jj|zzS)a/ Evaluate the Lagrangian model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the Lagrangian model is evaluated. Returns ------- float Value of the Lagrangian model at `x`. )rEfunrrlineara_ubb_ubra_eqb_eqr!cubr#ceqr*xs r. lag_modelzTrustRegion.lag_models KKOOA   xx##a'$((//*>*>>@ @  xx##a'$((//*>*>>@ @ ##dkkooa&88  9 ##dkkooa&88  9 r0c|jj||j|jjj zz|j |jjjzz|j|jj|zz|j|jj|zzS)ah Evaluate the gradient of the Lagrangian model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the gradient of the Lagrangian model is evaluated. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the Lagrangian model at `x`. ) rEfun_gradrrrWrXrrZr!cub_gradr#ceq_gradr^s r.lag_model_gradzTrustRegion.lag_model_grad.s KK  #  488??#7#77 8  488??#7#77 8##dkk&:&:1&== >##dkk&:&:1&==  > r0c|jj}|jdkDr*||j|jj zz }|j dkDr*||j |jjzz }|S)z Evaluate the Hessian matrix of the Lagrangian model at a given point. Returns ------- `numpy.ndarray`, shape (n, n) Hessian matrix of the Lagrangian model at `x`. r)rEfun_hessr r!cub_hessr"r#ceq_hess)r*hesss r.lag_model_hesszTrustRegion.lag_model_hessDs{{{##%    " D))DKK,@,@,BB BD    " D))DKK,@,@,BB BD r0c|jj||j|jj|zz|j|jj |zzS)a Evaluate the right product of the Hessian matrix of the Lagrangian model with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the Lagrangian model is multiplied from the right. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the Lagrangian model with `v`. )rE fun_hess_prodr! cub_hess_prodr# ceq_hess_prodr*vs r.lag_model_hess_prodzTrustRegion.lag_model_hess_prodTsa$ KK % %a (##dkk&?&?&BB C##dkk&?&?&BB C r0c|jj||j|jj|zz|j|jj |zzS)ar Evaluate the curvature of the Lagrangian model along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the Lagrangian model is evaluated. Returns ------- float Curvature of the Lagrangian model along `v`. )rEfun_curvr!cub_curvr#ceq_curvrps r.lag_model_curvzTrustRegion.lag_model_curvks_ KK  ###dkk&:&:1&== >##dkk&:&:1&== > r0c|||jj|jd|j|zzzS)a} Evaluate the objective function of the SQP subproblem. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the objective function of the SQP subproblem is evaluated. Returns ------- float Value of the objective function of the SQP subproblem along `step`. g?)rErbr%rrr*steps r.sqp_funzTrustRegion.sqp_funs? KK  -D,,T22 3  r0c|jj|j|jj|j|zzS)a Evaluate the linearization of the nonlinear inequality constraints. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the linearization of the nonlinear inequality constraints is evaluated. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Value of the linearization of the nonlinear inequality constraints along `step`. )rEr\r%rcrys r.sqp_cubzTrustRegion.sqp_cub=" KKOODKK (kk""4;;/$6 7 r0c|jj|j|jj|j|zzS)a Evaluate the linearization of the nonlinear equality constraints. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the linearization of the nonlinear equality constraints is evaluated. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Value of the linearization of the nonlinear equality constraints along `step`. )rEr]r%rdrys r.sqp_ceqzTrustRegion.sqp_ceqr~r0Nc"||||j|\}}}|}|jdkDrb|jj|||}tj|r/||jtj j |zz }|S)av Evaluate the merit function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the merit function is evaluated. fun_val : float, optional Value of the objective function at `x`. If not provided, the objective function is evaluated at `x`. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Values of the nonlinear inequality constraints. If not provided, the nonlinear inequality constraints are evaluated at `x`. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Values of the nonlinear equality constraints. If not provided, the nonlinear equality constraints are evaluated at `x`. Returns ------- float Value of the merit function at `x`. r)rOrS)rr violationr count_nonzerolinalgnorm)r*r_rLrOrSm_valc_vals r.meritzTrustRegion.merits. ?go(, %GWg ==3 HH&&q'7&KE&)>>> r0ctj|jjjg|j j |gg}tj|jjj|jjj|zz |j j| g}tj|jjjg|j j|gg}tj|jjj|jjj|zz |j j| g}||||fS)a; Get the linearizations of the constraints at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the linearizations of the constraints are evaluated. Returns ------- `numpy.ndarray`, shape (m_linear_ub + m_nonlinear_ub, n) Left-hand side matrix of the linearized inequality constraints. `numpy.ndarray`, shape (m_linear_ub + m_nonlinear_ub,) Right-hand side vector of the linearized inequality constraints. `numpy.ndarray`, shape (m_linear_eq + m_nonlinear_eq, n) Left-hand side matrix of the linearized equality constraints. `numpy.ndarray`, shape (m_linear_eq + m_nonlinear_eq,) Right-hand side vector of the linearized equality constraints. ) rblockrrWrXrErcrYr\rZrdr[r])r*r_aubbubaeqbeqs r.get_constraint_linearizationsz)TrustRegion.get_constraint_linearizationss1(hh%%&%%a()   hh$$txx';';a'??##   hh%%&%%a()   hh$$txx';';a'??##   Cc!!r0c |j|j\}}}}|jjj|jz }|jjj |jz }|j tj|jz}t||||||||tjfi|j } |tjrt||} tj| | z|kstj|| | z krt!j"dt$dtj&j)| d|zkDrt!j"dt$dtj*|jdz| | zz }|| z}|| z}tj,||| zz d}|j.j1|j|j3| z} |jj4dvr7t7| |j2||||tjfi|j } n+t9| |j2|||||||df i|j } |tjrt||} tj| | z|kstj|| | z krt!j"d t$dtj&j)| | zdtj*dz|jzkDrt!j"d t$d| | fS) aK Get the trust-region step. The trust-region step is computed by solving the derivative-free trust-region SQP subproblem using a Byrd-Omojokun composite-step approach. For more details, see Section 5.2.3 of [1]_. Parameters ---------- options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Normal step. `numpy.ndarray`, shape (n,) Tangential step. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. z6the normal step does not respect the bound constraint.皙?z=the normal step does not respect the trust-region constraint.@r) unconstrainedzbound-constraineddebugz;The tangential step does not respect the bound constraints.zj"zkDrj"|z |z} jA| j jdkr| } tjB|| z | |z g}| | z| z }|| z|z }tEd ||tj,|fD}tjDtj,| |d }tjDtj,| || }tjDtj,| |ddf| z| }tGd |zd tj8j;| z}||krZj j%j| z|} t-| d t-|zk\rtjH| ||}|tjrt3||}tjJ||z|kstjJ|||z krtMjNdtPdtj8j;|dj"zkDrtMjNdtPd|S)a Get the geometry-improving step. Three different geometry-improving steps are computed and the best one is returned. For more details, see Section 5.2.7 of [1]_. Parameters ---------- k_new : int Index of the interpolation point to be modified. options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Geometry-improving step. Raises ------ `numpy.linalg.LinAlgError` If the computation of a determinant fails. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. z8The index `k_new` must be different from the best index.rrcPj|jjSNcurvrErIrqlagr*s r.z/TrustRegion.get_geometry_step..chhq$++";";.rr0)zlinearly constrainedznonlinearly constrainedc3JK|]}tj|dyw)rinitialN)rmax).0arrays r. z0TrustRegion.get_geometry_step..s& !8FF5#..!8s!#r$@g{Gz?g?z9The geometry step does not respect the bound constraints.rrz?The geometry step does not respect the trust-region constraint.))rrrGrsqueezeeyerEnptrrIgradr%rrrrr r; determinantsxptnewaxisr absrrrrTrrr2TINYrrrmincliprrrr)r*k_newr, coord_vecg_lagrrrzsigmarstep_alt sigma_altrrrrtol_bdtol_ubfree_xlfree_xufree_ubn_actq g_lag_projnorm_g_lag_projcbdr\r] maxcv_valrrs` @r.get_geometry_stepzTrustRegion.get_geometry_steps> 7== !( JI J(JJrvva%@A  KK % %  GMM "  dkk&?&?@XX__  $++ - XX__  $++ -   <   KK GMM "  ((t);UC KK % % ) )kk''++At ,JK L (+1t.B+B'CA4??# #$"   < 12J   KK GMM "  KK,,T[[8-CUK y>CJ &DE 88==  224;;? Cc3#B+F#C(FVGmGFlGVmG3 HE11ef91ef9%)?@J iinnZ8O5%488::%/D4;;Hns*Hns* "%sBFF3K!8  ffRVVHgX$67EffRVVHgX$67EffRVVC! $4x$?@#N$*dRYY^^H-E&EF# $ 8 8 h.!I9~s5z)99!wwxR8 7== ! R(CvvdSj2o&"&&dSj*A #"  yy~~d#cDKK&77 /"   r0c |j|j\}}}}|jjj|jz }|jjj |jz }t jj|} t||||||| |tjfi|j} |tjrt||} t j| | z|kst j|| | z krtj dt"dt jj| d| zkDrtj dt"d| S)aQ Get the second-order correction step. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Second-order correction step. zHThe second-order correction step does not respect the bound constraints.rrzNThe second-order correction step does not respect the trust-region constraint.)rr%rrrrrrrr rrrrrrrr) r*rzr,rrrrrrr;soc_steprs r. get_second_order_correction_stepz,TrustRegion.get_second_order_correction_steps7""?? LS#s XX__  $++ - XX__  $++ -%'        GMM "  oo   7== ! R(Cvvhnr)*bffR(S.5H.I 5"  yy~~h'#,6 ;"  r0c|j|j|j|j|j}|j|j|z|||}|j|jd|j j |j|j j|j}|j|j|z|j||j||j|}t||z tt||z zkDr||z t||z z Sy)a: Get the reduction ratio. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. fun_val : float Objective function value at the trial point. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,) Nonlinear inequality constraint values at the trial point. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,) Nonlinear equality constraint values at the trial point. Returns ------- float Reduction ratio. r) rr%rMrPrTrEr\r]r{r}rrr) r*rzrLrOrS merit_old merit_newmerit_model_oldmerit_model_news r.get_reduction_ratiozTrustRegion.get_reduction_ratioIs(JJ KK MM MM MM  JJt{{T17GWM ** KK  KKOODKK ( KKOODKK (   ** KK$  LL  LL  LL    0 1D3  !< 5   )S/1. r0c |j|j\}}}}ttjj tj tjd| |gtjj tj tjd||z|z ||z|z gz d}|j|}tjj tj |j|j|j|jg}t|tt|zkDrt|||z }|j} |j |j"t$j&|zkr?t|j"t$j(|zd|_|j+| |jk(S)z Increase the penalty parameter. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. r?)rr%rrrrrrr{rrr!r#rrrGrrrPENALTY_INCREASE_THRESHOLDPENALTY_INCREASE_FACTORr) r*rzrrrr viol_diffsqp_val thresholdbest_index_saves r.increase_penaltyzTrustRegion.increase_penaltyys"?? LS#s IINN 3- iinn 3d S(89d S(  # &,,t$IINN HH&&&&))))     y>D3w</ /Iw':;I// MMyCCD   A ABYNDM    !$//11r0cvt|j|j|_|jy)z1 Decrease the penalty parameter. N)rr_get_low_penaltyrr3s r.decrease_penaltyzTrustRegion.decrease_penaltys+DMM4+@+@+BC  r0c |j}|j|j|jj||jj |ddf|jj |ddf}|jj|j|jj |ddf|jj |ddf}dtzt|jj|jjztt|dz}t|jjD]}||jk7s|jjj!|}|j||jj||jj |ddf|jj |ddf}|jj||jj |ddf|jj |ddf}||ks|||zks||ks|}|}|} ||_y)z2 Set the index of the best point. Nrr)rGrr%rErLrOrSrmaxcvEPSrr2rrrangerIrJr) r*rGm_bestr_bestrkx_valrr_vals r.rzTrustRegion.set_best_indexs__  KK KK   + KK   A . KK   A .    KK KK   A . KK   A .   $++--1 2#f+s# $ t{{'ADOO# 1177: KK''*KK''1-KK''1-  KK''1-KK''1- 6>efsl&:uv~!"J"F"F#($&r0ctj|jjj|jjjdd|j tj fz dzd}|d}|}n|jj|}tjd|t|jtj|jz|jdzz dz}d||j <tj|tj |z}|tj"||fS)a Get the index of the interpolation point to remove. If `x_new` is not provided, the index returned should be used during the geometry-improvement phase. Otherwise, the index returned is the best index for included `x_new` in the interpolation set. Parameters ---------- x_new : `numpy.ndarray`, shape (n,), optional New point to be included in the interpolation set. Returns ------- int Index of the interpolation point to remove. float Distance between `x_best` and the removed point. Raises ------ `numpy.linalg.LinAlgError` If the computation of a determinant fails. Nrraxisrg@r)rsumrErIrrGrrrrrrLOW_RADIUS_FACTORr;r(argmaxrr)r*x_newdist_sqrweightsk_maxs r.get_index_to_removezTrustRegion.get_index_to_removes&2&& ))--++++//4??BJJ0NOP      =EGKK,,U3E  (C(CD++&     (,GDOO $ 'BFF5M12bgggen---r0ctjj|}||jtj kr1|xj |jtjzc_y||jtjkr:t|jtj|j z||_yt|jtj|j zt|jtj|j z|jtj|z|_y)z Update the trust-region radius. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. ratio : float Reduction ratio. N) rrrrr LOW_RATIOr;DECREASE_RADIUS_FACTOR HIGH_RATIOrrINCREASE_RADIUS_FACTORINCREASE_RADIUS_THRESHOLD)r*rzratios_norms r. update_radiuszTrustRegion.update_radiuss% DOOI$7$78 8 KK4??9+K+KL LK dooi&:&:; ; @ @A++DK  @ @A++OOI$D$DEkk"OOI$G$GH DKr0c|jtj|tjz|j kr1|xj |jtj zc_n|jtj|tjz|j kr9tj|j |tjz|_n|tj|_t|jtj|jz|j |_ y)z Enhance the resolution of the trust-region framework. Parameters ---------- options : dict Options of the solver. N) rrLARGE_RESOLUTION_THRESHOLDrRHOENDr(DECREASE_RESOLUTION_FACTORMODERATE_RESOLUTION_THRESHOLDrrrrr)r*r,s r.enhance_resolutionzTrustRegion.enhance_resolution9s OOI@@ Agnn% &oo  OOt44  O OOICC Dgnn% &oo !ggdoo(/(?'@ADO&gnn5DO OOI<< = L OO  r0cv|jjtj|j|y)z Shift the base point to `x_best`. Parameters ---------- options : dict Options of the solver. N)rE shift_x_basercopyr%rs r.rzTrustRegion.shift_x_baseZs%   !5w?r0c x|jjj|z|jjjk\}|jdk\}|jj j |k\}|jj j|k}tj|}tj|}tj|}tj|} ||z|jz|jzdkDr*tj|jj} tj| |ddf | |ddf|jjj|ddf|jj!|||jjj"|jj%|f} |jj'|} tj(| j*dtj, } d| d|| z|z|zt/| j0| | tj,fd}|j2|| z|| z|z|j4|<d|j4|<|j2|| z|z|| z|z|z|j6|<d|j6|<|j2|| z|z|z|| z|z|z|jz|j8dd|j2|| z|z|z|jzd|j:ddyy)aI Set the Lagrange multipliers. This method computes and set the Lagrange multipliers of the linear and nonlinear constraints to be the QP multipliers. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the Lagrange multipliers are computed. rrNbvls)rmethod)rrWrXrYrPrrrrrrr"rr2r_rErcrZrdrbfullshapeinfrrr_rr!rr#)r*r_incl_linear_ubincl_nonlinear_ubincl_xlincl_xurr m_xlm_xuidentityc_jacrxl_lmress r.r$zTrustRegion.set_multiplierses,--1TXX__5I5II MMS0((//$$)((//$$)&&~6 ))*;<(( . (4+;+; ;%% &() *vvdhhjj)HEE'1*%%!$$$^Q%67 $$Q(9:$$ $$Q' )E[[))!,FGGEKKNRVVG4EBEE>D4K+-> ?rvv C25t D4K+52D  ~ .36D   /7:uu"!!8D ! !"3 49tj|jjjtj ddf|jjj jz|jjjjz|jjjtj ddfz |jjf}|jjjtj ddf|jjj jz|jjjjz|jjjtj ddfz }tj|| |jj |jj g}tj||g}tj"|d}tj$|d}||j&t(j*|zk}tj,|rtj"|jj.}tj$|jj.}tj0d||} tj2||| z } | t4||z zkDr ||z | z } | Stj6} | Sd} | S)Nrrr)rc_rErIx_baserrrrrWrXrYrOrZr[rrSnanminnanmaxrrTHRESHOLD_RATIO_CONSTRAINTSrrLminimumrrr) r*r_val_ubr_val_eqrc_minc_maxindicesf_minf_max c_min_negc_diffrCs r.rzTrustRegion._get_low_penaltysi55 ))00Q?++++//112hhoo""$$  % hhoo""2::q=1  2 KK    !  KK % % , ,RZZ] ;kk''++-- . HHOO " "#&*XX__%9%9"**a-%HI88  ##$$$   (H-. %a( %a( ooiCCDuL M  66'?IIdkk112EIIdkk112E 3g7IVVE'NY67F .. 5=F2 &&Gr0)NNNr),__name__ __module__ __qualname____doc__r/propertyr2rrr r"r;setterr(rCrErGr%rMrPrTr`rerkrrrwr{r}rrrrrrrrrrrr rrr$rr0r.rrs.'`   $ $ $ $ ' ' ' '   ]]++"     & &         @ @ 4 4 7 7 7 7 0 ,  . * ( * *@,"\r,hUn0d.`62p(&T5.n@ B @IV(r0r)rnumpyrscipy.optimizerrErrsettingsrr subsolversr r r r r subsolvers.optimrutilsrfinfofloattinyrepsrrr;r0r.rFs^%%(:!rxxbhhuoAAr0