(phSSKrSSKrSSKJr SSKJrJr SSKJ r J r SSK J r J r JrJrJr SSKJr SSKJr \R*"\5R.r\R*"\5R2r"S S 5rg) N) lsq_linear)Models Quadratic)Options Constants)cauchy_geometryspider_geometrynormal_byrd_omojokuntangential_byrd_omojokun$constrained_tangential_byrd_omojokun)qr_tangential_byrd_omojokun)get_arrays_tolc\rSrSrSrSr\S5r\S5r\S5r \S5r \S5r \S 5r \ RS 5r \S 5r\RS 5r\S 5r\S5r\S5r\S5r\S5r\S5r\S5rSrSrSrSrSrSrSrSrS-SjrSrSr S r!S!r"S"r#S#r$S$r%S%r&S.S&jr'S'r(S(r)S)r*S*r+S+r,S,r-g)/ TrustRegionz Trust-region framework. cRSUlXl[URX R5UlX0lSUlUR5 [R"UR5Ul [R"UR5Ul [R"UR5Ul[R"UR 5UlUR%UR&5 U[(R*UlUR.Ulg)aa Initialize the trust-region framework. Parameters ---------- pb : `cobyqa.problem.Problem` Problem to solve. options : dict Options of the solver. constants : dict Constants of the solver. Raises ------ `cobyqa.utils.MaxEvalError` If the maximum number of evaluations is reached. `cobyqa.utils.TargetSuccess` If a nearly feasible point has been found with an objective function value below the target. `cobyqa.utils.FeasibleSuccess` If a feasible point has been found for a feasibility problem. `numpy.linalg.LinAlgError` If the initial interpolation system is ill-defined. rN)_penalty_pbrpenalty_models _constants _best_indexset_best_indexnpzeros m_linear_ub _lm_linear_ub m_linear_eq _lm_linear_eqm_nonlinear_ub_lm_nonlinear_ubm_nonlinear_eq_lm_nonlinear_eqset_multipliersx_bestrRHOBEG _resolution resolution_radius)selfpboptions constantss N/var/www/html/venv/lib/python3.13/site-packages/scipy/_lib/cobyqa/framework.py__init__TrustRegion.__init__s4 dhh> #  XXd&6&67XXd&6&67 ")<)< = ")<)< = T[[)#7>>2 c.URR$)zD Number of variables. Returns ------- int Number of variables. )rnr,s r0r5 TrustRegion.nLsxxzzr3c.URR$)zl Number of linear inequality constraints. Returns ------- int Number of linear inequality constraints. )rrr6s r0rTrustRegion.m_linear_ubXxx###r3c.URR$)zh Number of linear equality constraints. Returns ------- int Number of linear equality constraints. )rr r6s r0r TrustRegion.m_linear_eqdr:r3c.URR$)zr Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. )rr"r6s r0r"TrustRegion.m_nonlinear_ubpxx&&&r3c.URR$)zn Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. )rr$r6s r0r$TrustRegion.m_nonlinear_eq|r?r3cUR$)zF Trust-region radius. Returns ------- float Trust-region radius. )r+r6s r0radiusTrustRegion.radius||r3cXlURUR[RUR -::aUR Ulgg)za Set the trust-region radius. Parameters ---------- radius : float New trust-region radius. N)r+rCrrDECREASE_RADIUS_THRESHOLDr*)r,rCs r0rCrDsE KKyBBCoo  ??DL  r3cUR$)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)r6s r0r*TrustRegion.resolutionsr3cXlg)z Set the resolution of the trust-region framework. Parameters ---------- resolution : float New resolution of the trust-region framework. NrI)r,r*s r0r*rJs &r3cUR$)zB Penalty parameter. Returns ------- float Penalty parameter. )rr6s r0rTrustRegion.penaltys}}r3cUR$)z Models of the objective function and constraints. Returns ------- `cobyqa.models.Models` Models of the objective function and constraints. )rr6s r0modelsTrustRegion.modelsrEr3cUR$)zh Index of the best interpolation point. Returns ------- int Index of the best interpolation point. )rr6s r0 best_indexTrustRegion.best_indexsr3c`URRRUR5$)z Best interpolation point. Its value is interpreted as relative to the origin, not the base point. Returns ------- `numpy.ndarray` Best interpolation point. )rO interpolationpointrRr6s r0r'TrustRegion.x_bests#{{((..t??r3cHURRUR$)zv Value of the objective function at `x_best`. Returns ------- float Value of the objective function at `x_best`. )rOfun_valrRr6s r0fun_bestTrustRegion.fun_bests{{""4??33r3cPURRURSS24$)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)rOcub_valrRr6s r0cub_bestTrustRegion.cub_best"{{""4??A#566r3cPURRURSS24$)z Values of the nonlinear equality constraints at `x_best`. Returns ------- `numpy.ndarray`, shape (m_nonlinear_eq,) Values of the nonlinear equality constraints at `x_best`. N)rOceq_valrRr6s r0ceq_bestTrustRegion.ceq_best r`r3c$URRU5URURRR U-URRR - --URURRRU-URRR- --URURRU5--URURRU5--$)z Evaluate the Lagrangian model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the Lagrangian model is evaluated. Returns ------- float Value of the Lagrangian model at `x`. )rOfunrrlineara_ubb_ubr!a_eqb_eqr#cubr%ceqr,xs r0 lag_modelTrustRegion.lag_models KKOOA   xx##a'$((//*>*>>@ @  xx##a'$((//*>*>>@ @ ##dkkooa&88  9 ##dkkooa&88  9 r3cURRU5URURRR --UR URRR--URURRU5--URURRU5--$)a 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`. ) rOfun_gradrrrgrhr!rjr#cub_gradr%ceq_gradrns r0lag_model_gradTrustRegion.lag_model_grad.s KK  #  488??#7#77 8  488??#7#77 8##dkk&:&:1&== >##dkk&:&:1&==  > r3cURR5nURS:a)XRURR 5-- nUR S:a)XR URR5-- nU$)z Evaluate the Hessian matrix of the Lagrangian model at a given point. Returns ------- `numpy.ndarray`, shape (n, n) Hessian matrix of the Lagrangian model at `x`. r)rOfun_hessr"r#cub_hessr$r%ceq_hess)r,hesss r0lag_model_hessTrustRegion.lag_model_hessDsw{{##%    " ))DKK,@,@,BB BD    " ))DKK,@,@,BB BD r3cURRU5URURRU5--URURR U5--$)at Evaluate the right product of the Hessian matrix of the Lagrangian model with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the Lagrangian model is multiplied from the right. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the Lagrangian model with `v`. )rO fun_hess_prodr# cub_hess_prodr% ceq_hess_prodr,vs r0lag_model_hess_prodTrustRegion.lag_model_hess_prodTsa$ KK % %a (##dkk&?&?&BB C##dkk&?&?&BB C r3cURRU5URURRU5--URURR U5--$)a Evaluate the curvature of the Lagrangian model along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the Lagrangian model is evaluated. Returns ------- float Curvature of the Lagrangian model along `v`. )rOfun_curvr#cub_curvr%ceq_curvrs r0lag_model_curvTrustRegion.lag_model_curvks_ KK  ###dkk&:&:1&== >##dkk&:&:1&== > r3c|UURRUR5SURU5---$)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?)rOrsr'rr,steps r0sqp_funTrustRegion.sqp_funs? KK  -D,,T22 3  r3cURRUR5URRUR5U--$)as 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`. )rOrlr'rtrs r0sqp_cubTrustRegion.sqp_cub=" KKOODKK (kk""4;;/$6 7 r3cURRUR5URRUR5U--$)am 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`. )rOrmr'rurs r0sqp_ceqTrustRegion.sqp_ceqrr3Nc>UbUbUcURXR5up#nUnURS:acURRXUS9n[R "U5(a.XPR[R RU5-- nU$)a Evaluate the merit function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the merit function is evaluated. fun_val : float, optional Value of the objective function at `x`. If not provided, the objective function is evaluated at `x`. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Values of the nonlinear inequality constraints. If not provided, the nonlinear inequality constraints are evaluated at `x`. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Values of the nonlinear equality constraints. If not provided, the nonlinear equality constraints are evaluated at `x`. Returns ------- float Value of the merit function at `x`. r)r]rb)rrr violationr count_nonzerolinalgnorm)r,rorYr]rbm_valc_vals r0meritTrustRegion.merits. ?go(,LL(A %Gg ==3 HH&&q7&KE&&)>>> r3c[R"URRR/UR R U5//5n[R"URRRURRRU-- UR RU5*/5n[R"URRR/UR RU5//5n[R"URRRURRRU-- UR RU5*/5nX#XE4$)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. ) rblockrrgrhrOrtrirlrjrurkrm)r,roaubbubaeqbeqs r0get_constraint_linearizations)TrustRegion.get_constraint_linearizationss-(hh%%&%%a()   hh$$txx';';a'??##   hh%%&%%a()   hh$$txx';';a'??##   !!r3c URUR5up#pEURRRUR- nURRR UR- nUR [RUR-n[UUUUUUUU[R40UR D6n U[R(a[Xg5n [R"X-U:5(d [R"XyU - :5(a[ R""S[$S5 [R&R)U 5SU-:a[ R""S[$S5 [R*"URS-X-- 5nXi-nXy-n[R,"X2U -- S5nUR.R1UR5UR3U 5-n URR4S;a7[7U UR2UUUU[R40UR D6n O+[9U UR2UUUUUUUS4 0UR D6n U[R(a[Xg5n [R"X-U:5(d [R"X|U - :5(a[ R""S [$S5 [R&R)X-5S[R*"S5-UR-:a[ R""S [$S5 X4$) a Get the trust-region step. The trust-region step is computed by solving the derivative-free trust-region SQP subproblem using a Byrd-Omojokun composite-step approach. For more details, see Section 5.2.3 of [1]_. Parameters ---------- options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Normal step. `numpy.ndarray`, shape (n,) Tangential step. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. z6the normal step does not respect the bound constraint.皙?z=the normal step does not respect the trust-region constraint.@r) unconstrainedzbound-constraineddebugz;The tangential step does not respect the bound constraints.zTR"-:GaTR"U- U-n TRAU TR R5S:aU *n [RB"XZ- X- /5nX-U - nX-U- nS UU[R,"U5455n[RD"[R,"U U)5SS 9n[RD"[R,"U U)5US 9n[RD"[R,"U U)SS24U -5US 9n[GS U-S [R8R;U 5-5nUU::a[TR R%TRU -U5n [-U 5S [-U5-:a[RH"XU5nU[R(a[3XV5n[RJ"UU-U:5(d [RJ"XgU- :5(a[LRN"S[PS5 [R8R;U5STR"-:a[LRN"S[PS5 U$)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.rrcP>TRUTRR5$NcurvrOrUrlagr,s r0/TrustRegion.get_geometry_step..chhq$++";";TRUTRR5$rrrs r0rrrr3)zlinearly constrainedznonlinearly constrainedc3L# UHn[R"USS9v M g7f)rinitialN)rmax).0arrays r0 0TrustRegion.get_geometry_step..s" !8FF5#.!8s"$r$@g{Gz?g?z9The geometry step does not respect the bound constraints.rrz?The geometry step does not respect the trust-region constraint.))rrrRrsqueezeeyerOnptrrUgradr'rrrrr rC determinantsxptnewaxisr absrrrrTrrr5TINYrrrmincliprrrr)r,k_newr. coord_vecg_lagrrrsigmarstep_alt sigma_altrrrrtol_bdtol_ubfree_xlfree_xufree_ubn_actq g_lag_projnorm_g_lag_projcbdrlrm maxcv_valrrs` @r0get_geometry_stepTrustRegion.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;;? Cc#B+F#C(FVGmGFlGVmG3 HE11ef91ef9%)?@J iinnZ8O5%488::%%/D4;;ns*ns* "%sBFF3K!8  ffRVVHgX$67EffRVVHgX$67EffRVVC! $4x$?@#N$*dRYY^^H-E&EF# $ 8 8 h.!I9~s5z)99!wwxR8 7== ! (CvvdSj2o&&"&&Sj*A*A #"  yy~~d#cDKK&77 /"   r3c URUR5up4pVURRRUR- nURRR UR- n[ RRU5n [UUUUUUU U[R40URD6n U[R(a[Xx5n [ R"X-U:5(d [ R"XU - :5(a[R "S["S5 [ RRU 5SU -:a[R "S["S5 U $)z 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,rr.rrrrrrrCsoc_steprs r0 get_second_order_correction_step,TrustRegion.get_second_order_correction_steps3""?? L# XX__  $++ - XX__  $++ -%'        GMM "  oo   7== ! (Cvvhnr)**bffRS.5H.I.I 5"  yy~~h'#,6 ;"  r3cURURURURUR5nURURU-X#U5nURURSUR R UR5UR RUR55nURURU-URU5URU5URU55n[Xx- 5[[XV- 5-:aXV- [Xx- 5- $g)a Get the reduction ratio. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. fun_val : float Objective function value at the trial point. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,) Nonlinear inequality constraint values at the trial point. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,) Nonlinear equality constraint values at the trial point. Returns ------- float Reduction ratio. r) rr'rZr^rcrOrlrmrrrrr) r,rrYr]rb merit_old merit_newmerit_model_oldmerit_model_news r0get_reduction_ratioTrustRegion.get_reduction_ratioIs(JJ KK MM MM MM  JJt{{T17WM ** KK  KKOODKK ( KKOODKK (   ** KK$  LL  LL  LL    0 1D3  !< 5  )S1. r3c URUR5up#pE[[RR [R "[R"SU*5U/55[RR [R "[R"SX!-U- 5XA-U- /55- S5nURU5n[RR [R "URURURUR/55n[U5[[U5-:a[XU- 5nURn UR UR"[$R&U-::a?[UR"[$R(U-S5UlUR+5 XR:H$)zr Increase the penalty parameter. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. r?)rr'rrrrrrrrr!r#r%rrrRrrrPENALTY_INCREASE_THRESHOLDPENALTY_INCREASE_FACTORr) r,rrrrr viol_diffsqp_val thresholdbest_index_saves r0increase_penaltyTrustRegion.increase_penaltyys"?? L# IINN 3- iinn 3 S(89 S(  # &,,t$IINN HH&&&&))))     y>D3w</ /I':;I// MMyCCD   A ABYNDM    !//11r3cv[URUR55UlUR5 g)z! Decrease the penalty parameter. N)rr_get_low_penaltyrr6s r0decrease_penaltyTrustRegion.decrease_penaltys+DMM4+@+@+BC  r3c URnURURURRUURR USS24URR USS245nURRURURR USS24URR USS245nS[-[URRURR5-[[U5S5-n[URR5GH nXPR:wdMURRR!U5nURUURRUURR USS24URR USS245nURRUURR USS24URR USS245nXr:dXrU-:dMX:dGMUnUnUnGM Xlg)z" Set the index of the best point. Nrr)rRrr'rOrYr]rbrmaxcvEPSrr5rrrangerUrVr) r,rRm_bestr_bestrkx_valrr_vals r0rTrustRegion.set_best_indexs__  KK KK   + KK   A . KK   A .    KK KK   A . KK   A .   $++--1 2#f+s# $ t{{'AOO# 1177: KK''*KK''1-KK''1-  KK''1-KK''1- >esl&:u~!"J"F"F#($&r3c[R"URRRURRRSS2UR [R 4- S-SS9nUcSnUnOURRU5n[R"SU[UR[RUR-UR5S-- 5S-nSX@R '[R"U[R "U5-5nU[R""X%54$)aO 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)rsumrOrUrrRrrrrrrLOW_RADIUS_FACTORrCr*argmaxrr)r,x_newdist_sqrweightsk_maxs r0get_index_to_removeTrustRegion.get_index_to_removes"2&& ))--++++//4??BJJ0NOP      =EGKK,,U3E  (C(CD++&     (,GOO $ 'BFF5M12bgggn---r3c[RRU5nX R[R ::a1U=R UR[R-slgX R[R::a:[UR[RUR -U5Ulg[UR[RUR -[UR[RUR -UR[RU-55Ulg)z Update the trust-region radius. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. ratio : float Reduction ratio. N) rrrrr LOW_RATIOrCDECREASE_RADIUS_FACTOR HIGH_RATIOrrINCREASE_RADIUS_FACTORINCREASE_RADIUS_THRESHOLD)r,rratios_norms r0 update_radiusTrustRegion.update_radiuss% OOI$7$78 8 KK4??9+K+KL LK ooi&:&:; ; @ @A++DK  @ @A++OOI$D$DEkk"OOI$G$GH DKr3cUR[RU[R-UR :a1U=R UR[R -slOUR[RU[R-UR :a:[R"UR U[R-5UlOU[RUl[UR[RUR-UR 5Ul g)zx Enhance the resolution of the trust-region framework. Parameters ---------- options : dict Options of the solver. N) rrLARGE_RESOLUTION_THRESHOLDrRHOENDr*DECREASE_RESOLUTION_FACTORMODERATE_RESOLUTION_THRESHOLDrrrr'r+r,r.s r0enhance_resolutionTrustRegion.enhance_resolution9s OOI@@ Agnn% &oo  OOt44  O OOICC Dgnn% &oo !ggdoo(/(?'@ADO&gnn5DO OOI<< = L OO  r3cxURR[R"UR5U5 g)zd Shift the base point to `x_best`. Parameters ---------- options : dict Options of the solver. N)rO shift_x_basercopyr'r4s r0r8TrustRegion.shift_x_baseZs%   !5w?r3c pURRRU-URRR:nURS:nURR R U:nURR RU:*n[R"U5n[R"U5n[R"U5n[R"U5n Xg-UR-UR-S:Ga"[R"URR5n [RXSS24*XSS24URRRUSS24URR!X5URRR"URR%U54n URR'U5n [R("U R*S[R,*5n SU SX-U-U-&[/U R0U *U [R,4SS9nUR2X-X-U-UR4U'SUR4U)'UR2UU -U-UU -U-U-UR6U'SUR6U)'UR2UU -U-U-UU -U-U-UR-UR8SS&UR2X-U-U-UR-SUR:SS&gg)a  Set the Lagrange multipliers. This method computes and set the Lagrange multipliers of the linear and nonlinear constraints to be the QP multipliers. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the Lagrange multipliers are computed. rrNbvls)rmethod)rrgrhrir^rrrrrr r$rr5r_rOrtrjrursfullshapeinfrrrorr#r!r%)r,roincl_linear_ubincl_nonlinear_ubincl_xlincl_xurr"m_xlm_xuidentityc_jacrxl_lmress r0r&TrustRegion.set_multiplierses--1TXX__5I5II MMS0((//$$)((//$$)&&~6 ))*;<((  (4+;+; ;%% &() *vvdhhjj)HEE1*%%!$$$^Q%67 $$Q:$$ $$Q' )E[[))!,FGGEKKNRVVG4EBEE>DK+-> ?rvv C25 DK+52D  ~ .36D   /7:uu"!!8D ! !"3 49rqsZ%%(:! xxhhuoAAr3