+ /i^RIt^RIt^RIHt^RIHt^RIHtH t H t ]P!] 4Pt!RR4tRt!RR 4t!R R 4tR#) N)eigh)Options) MaxEvalError TargetSuccessFeasibleSuccessca]tRt^ toRtRt]R4t]R4t]R4t ] PR4t ]R4t ] PR4t R t R t VtR #) Interpolationz Interpolation set. This class stores a base point around which the models are expanded and the interpolation points. The coordinates of the interpolation points are relative to the base point. c V\P,VnR\P!VP P VP P, 4,pV\P,V8deW2\PP&\P!V\P,V.4V\PP&\P!VP4Vn VPVP PRV\P,,,8*pVP PV,VPV&VP PRV\P,,,VP8VPVP PV\P,,8*,p\P!VP PV,V\P,,VP P V,4VPV&VPVP P RV\P,,, 8pVP P V,VPV&VPVP P RV\P,,, 8VP P V\P,, VP8*,p\P !VP P V,V\P,, VP PV,4VPV&\P"!VP$V\P&,34Vn\+^V\P&,4EFypWP$8:duWh^, ,'d1V\P,)VP,V^, V3&KYV\P,VP,V^, V3&KV^VP$,8:EdWHVP$, ^, ,'dHRV\P,,VP,WP$, ^, V3&EKWhVP$, ^, ,'dHRV\P,,VP,WP$, ^, V3&EK{V\P,)VP,WP$, ^, V3&EKWP$, ^, VP$,p V^V ,VP$,, ^, p W,VP$,p VP,W^,3,VP,W3&VP,W^,3,VP,W3&EK| RVnR#)z Initialize the interpolation set. Parameters ---------- pb : `cobyqa.problem.Problem` Problem to be solved. options : dict Options of the solver. ?@Ng)rDEBUG_debugnpminboundsxuxlRHOBEGvalueRHOENDcopyx0_x_basex_baseminimummaximumzerosnNPT_xptrangexpt _lhs_cache) selfpboptions max_radiusvery_close_xl_idx close_xl_idxvery_close_xu_idx close_xu_idxkspreadk1k2s &&& V/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/_lib/cobyqa/models.py__init__Interpolation.__init__s@gmm, 266")),,"=>> 7>> "Z /,6GNN(( ),.FFGNN+-GGNN(( )wwruu~ KK299<<#0G*GG G *,6G)H %& IILL3!88 84;; F [[BIILL77>>+BB BD %'JJ IILL &)@ @ IILL &%  L! KK299<<#0G*GG G *,6G)H %& KK")),,ww~~/F)FF F YY\\GGNN3 3t{{ BD %'JJ IILL &)@ @ IILL &%  L! HHbddGGKK$89: q''++./ADDy$U++*1'..*A)ADHHQUAX&)0)@DHHQUAX&a"$$h$X\2203ggnn6M0MDHHQX\1_-&244x!|4404ww~~7N0NDHHQX\1_-181H0HDHHQX\1_-dd(Q,244/!f*,,q0kRTT)"&((2Av:"6"&((2Av:"6%0&c <VPP^,#zD Number of variables. Returns ------- int Number of variables. r"shaper$s&r0rInterpolation.n]xx~~a  r3c <VPP^,#zZ Number of interpolation points. Returns ------- int Number of interpolation points. r6r8s&r0nptInterpolation.nptir:r3c VP#)zb Interpolation points. Returns ------- `numpy.ndarray`, shape (n, npt) Interpolation points. )r r8s&r0r"Interpolation.xptusyyr3c VP'd/VPVPVP38XgQR4hWnR#)zz Set the interpolation points. Parameters ---------- xpt : `numpy.ndarray`, shape (n, npt) New interpolation points. z The shape of `xpt` is not valid.N)rr7rr=r )r$r"s&&r0r"r@sG ;;;99! 22 2 r3c VP#)z Base point around which the models are expanded. Returns ------- `numpy.ndarray`, shape (n,) Base point around which the models are expanded. )rr8s&r0rInterpolation.x_bases||r3c |VP'd$VPVP38XgQR4hWnR#)z Set the base point around which the models are expanded. Parameters ---------- x_base : `numpy.ndarray`, shape (n,) New base point around which the models are expanded. z#The shape of `x_base` is not valid.N)rr7rr)r$rs&&r0rrCs> ;;;<<$ 54 5 r3c VP'd)^Tu;8:dVP8gQR4hQR4hVPVPRV3,,#)z Get the `k`-th interpolation point. The return point is relative to the origin. Parameters ---------- k : int Index of the interpolation point. Returns ------- `numpy.ndarray`, shape (n,) `k`-th interpolation point. zThe index `k` is not valid.NNN)rr=rr")r$r,s&&r0pointInterpolation.pointsQ ;;;$DHH$ C&C C$ C&C C${{TXXad^++r3)rr#rr N)__name__ __module__ __qualname____firstlineno____doc__r1propertyrr=r"setterrrG__static_attributes____classdictcell__ __classdict__s@r0r r sEN ! ! ! !   ZZ    ]]  ,,r3r c  VPpVeI\P!VPVR,4'dVR,VR,VR,3#\P!\P P VP^R7\R7pVPV, pVPwrE\P!WT,^,WT,^,34pRVPV,R ,,VRV1RV13&R VRV1V3&VPVRV1V^,R13&R WeRV13&W6V^,R1RV13&\P!WT,^,4pR VR ,, VRV%VR ,Wu&W'V^,R%\VR R 7wrR\P!VP4R\P!V4R\P!V4RW3/p WnWgW33#) aa Build the left-hand side matrix of the interpolation system. The matrix below stores W * diag(right_scaling), where W is the theoretical matrix of the interpolation system. The right scaling matrices is chosen to keep the elements in the matrix well-balanced. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. Nr"a right_scalingr)axisinitialr r ?F) check_finite)r#r array_equalr"maxlinalgnormEPSr7rTemptyrr) interpolation_cachescale xpt_scalerr=rUrV eig_values eig_vectors new_caches & r0 build_systemrjs % %Fbnn6%=c{F?3VF^CC FF299>>-"3"3!>`_. c W0nVP'd$VPVP38XgQR4hVPVP^,8d!\ RVP^, R24hVP VV4wVnVnVnp\P!VPVP34Vn R#)a Initialize the quadratic model. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. values : `numpy.ndarray`, shape (npt,) Values of the interpolated function at the interpolation points. debug : bool Whether to make debugging tests during the execution. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. #The shape of `values` is not valid.z4The number of interpolation points must be at least .N) rr7r=r ValueError _get_model_const_grad_i_hessrr_e_hess)r$rcvaluesdebug_s&&&& r0r1Quadratic.__init__s$ ;;;<<!!$ 54 5   }2 2F ??Q&'q* 48??  4 0 TZqxx 01 r3c VP'd$VPVP38XgQR4hWP, pVPVP V,,RVP VPPV,R,,W0P,V,,,,#)a! Evaluate the quadratic model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the quadratic model is evaluated. interpolation : `cobyqa.models.Interpolation` Interpolation set. Returns ------- float Value of the quadratic model at `x`. The shape of `x` is not valid.r r ) rr7rrrrrsrtr"rarur$xrcx_diffs&&& r0__call__Quadratic.__call__*s ;;;77tvvi' I)I I'))) KKjj6! " 1 1 3 3f <DD<<'&01  r3c .VPP#r5)rssizer8s&r0r Quadratic.nGszzr3c .VPP#)z Number of interpolation points used to define the quadratic model. Returns ------- int Number of interpolation points used to define the quadratic model. )rtrr8s&r0r= Quadratic.nptSs||   r3c VP'd$VPVP38XgQR4hWP, pVPVP W24,#)aZ Evaluate the gradient of the quadratic model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the gradient of the quadratic model is evaluated. interpolation : `cobyqa.models.Interpolation` Interpolation set. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the quadratic model at `x`. r{)rr7rrrs hess_prodr|s&&& r0gradQuadratic.grad_sQ ;;;77tvvi' I)I I')))zzDNN6AAAr3c VPVPVPR\P3,VPP ,,,#)z Evaluate the Hessian matrix of the quadratic model. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. Returns ------- `numpy.ndarray`, shape (n, n) Hessian matrix of the quadratic model. rF)rur"rtrnewaxisra)r$rcs&&r0hessQuadratic.hesstsG||m// LLBJJ '-*;*;*=*= =   r3c VP'd$VPVP38XgQR4hVPV,VPVP VPP V,,,,#)a Evaluate the right product of the Hessian matrix of the quadratic model with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the quadratic model is multiplied from the right. interpolation : `cobyqa.models.Interpolation` Interpolation set. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the quadratic model with `v`. The shape of `v` is not valid.)rr7rrur"rtrar$vrcs&&&r0rQuadratic.hess_prodsk& ;;;77tvvi' I)I I'||a-"3"3 LLM--//!3 4#   r3c VP'd$VPVP38XgQR4hWP,V,VPVP P V,R,,,#)a\ Evaluate the curvature of the quadratic model along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the quadratic model is evaluated. interpolation : `cobyqa.models.Interpolation` Interpolation set. Returns ------- float Curvature of the quadratic model along `v`. rr )rr7rrurtr"rars&&&r0curvQuadratic.curvsf" ;;;77tvvi' I)I I' q llm//11A5#== > r3c nVP'do^Tu;8:dVP8gQR4hQR4hVPVP38XgQR4hVPVP38XgQR4hV;PVP V,\ P!W34,, unRVP V&VPVV4wrVrxV;PV, un V;PV, un V;P V, unV#)a Update the quadratic model. This method applies the derivative-free symmetric Broyden update to the quadratic model. The `knew`-th interpolation point must be updated before calling this method. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Updated interpolation set. k_new : int Index of the updated interpolation point. dir_old : `numpy.ndarray`, shape (n,) Value of ``interpolation.xpt[:, k_new]`` before the update. values_diff : `numpy.ndarray`, shape (npt,) Differences between the values of the interpolated nonlinear function and the previous quadratic model at the updated interpolation points. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. The index `k_new` is not valid.z$The shape of `dir_old` is not valid.z(The shape of `values_diff` is not valid.) rr=r7rrurtrouterrqrrrs) r$rck_newdir_old values_diffconstri_hessill_conditioneds &&&&& r0updateQuadratic.updates4 ;;;(( K*K K( K*K K(==% 65 6$$) :9 :  U+bhhw.HHH ! U04  0 ,V u  d   r3c VP'd$VPVP38XgQR4hV!W!4VnVP W!4VnW!P , p\P!VVPRVR\P3,,, VP,4pV;PWDP,, un R#)a Shift the point around which the quadratic model is defined. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Previous interpolation set. new_x_base : `numpy.ndarray`, shape (n,) Point that will replace ``interpolation.x_base``. 'The shape of `new_x_base` is not valid.r rFN)rr7rrrrrsrrrr"rrtrura)r$rc new_x_baseshiftrs&&& r0 shift_x_baseQuadratic.shift_x_bases ;;;##( 98 9:5 YYz9 111    uQ ]';!; ;t|| K  )) r3c \VPPwr#VP^8Xd&VP^,W2,^,8XgQR4h\V4wrEpWR\P 3,,p\P !\P!V44'd1\P !\P!V44'g \PPR4hVwr\P!V4\8p V RV 3,p RW,, p \P !V ^4(p V V PV,V R\P 3,,,p WR\P 3,,V 3#)a Solve the interpolation systems. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. rhs : `numpy.ndarray`, shape (npt + n + 1, m) Right-hand side vectors of the ``m`` interpolation systems. Returns ------- `numpy.ndarray`, shape (npt + n + 1, m) Solutions of the interpolation systems. `numpy.ndarray`, shape (m, ) Whether the interpolation systems are ill-conditioned. Raises ------ `numpy.linalg.LinAlgError` If the interpolation systems are ill-defined. z The shape of `rhs` is not valid.rFz(The interpolation system is ill-defined.rZ) r"r7ndimrjrrallisfiniter^ LinAlgErrorabsr`ra)rcrhsrr=rUrVeig rhs_scaledrgrhlarge_eig_valuesinv_eig_valuesrleft_scaled_solutionss&& r0 solve_systemsQuadratic.solve_systemssQ0""(( HHMciilcgk9 . - . 9!-] ;#BJJ77 r{{1~&&266"++j2I+J+J))'':  #& 66*-3!!%5"56 z;;66"2A66 + ]]Z '>!RZZ-+H H!  "!RZZ-$@ @   r3c  tVPVP38XgQR4hVPPwr#\P V\ P !V\ P!V^,4..4P4wrEWC^3,WC^,R1^3,VRV1^3,V3#)a3 Solve the interpolation system. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. values : `numpy.ndarray`, shape (npt,) Values of the interpolated function at the interpolation points. Returns ------- float Constant term of the quadratic model. `numpy.ndarray`, shape (n,) Gradient of the quadratic model at ``interpolation.x_base``. `numpy.ndarray`, shape (npt,) Implicit Hessian matrix of the quadratic model. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. rnN) r7r=r"rlrrblockrra)rcrvrr=r}rs&& r0rqQuadratic._get_modelDs4||      1 0 1 ""((&44  HHQ a  ay!!GHaK.!DSD!G*oEEr3)rrrrursrtN)rIrJrKrLrMr1rrNrr=rrrrrr staticmethodrrqrPrQrRs@r0rlrls  2D :   ! !B* $ 2 02h*0> > @(F(Fr3rlcha]tRtRtoRtRt]R4t]R4t]R4t ]R4t ]R4t ]R 4t ]R 4t ]R 4tR tR tRtRtRtRtR%RltR%RltR%RltR%RltR%RltR%RltR%RltR%RltR%RltR%RltRtRt R%Rlt!R t"R%R!lt#R%R"lt$R#t%R$t&Vt'R#)&Modelsipz. Models for a nonlinear optimization problem. c P V\P,Vn\W4VnVP P ^4pV!WC4wrVp\P!V\P,\P4Vn \P!V\P,VP3\P4Vn \P!V\P,VP3\P4Vn\V\P,4EFpW\P ,8d\"hV^8Xd0WPP$V&W`P&VR3&WpP(VR3&MSVP P V4pV!VV4wVP$V&VP&VR3&VP(VR3&VP*'dsVP-VP P V4VP&VR3,VP(VR3,4V\P.,8:d\0hVPV,V\P2,8:gEKbVP-VP P V4VP&VR3,VP(VR3,4V\P.,8:gEK\4h \7VP VPV\P,4Vn\P:!VP<\6R7Vn\P:!VP@\6R7Vn!\VP<4FOp \7VP VP&RV 3,V\P,4VP>V &KQ \VP@4FOp \7VP VP(RV 3,V\P,4VPBV &KQ VP'dVPE4R#R#)a Initialize the models. Parameters ---------- pb : `cobyqa.problem.Problem` Problem to be solved. options : dict Options of the solver. penalty : float Penalty parameter used to select the point in the filter to forward to the callback function. 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 interpolation system is ill-defined. rF)dtypeN)#rr rr _interpolationrcrGrfullrnan_fun_valr_cub_val_ceq_valr!MAX_EVALrfun_valcub_valceq_valis_feasibilitymaxcvFEASIBILITY_TOLrTARGETrrl_funrbm_nonlinear_ub_cubm_nonlinear_eq_ceq_check_interpolation_conditions) r$r%r&penaltyx_evalfun_initcub_initceq_initr,is &&&& r0r1Models.__init__us`6gmm, +B8##))!,')&':$H 4bff= !5x}} ErvvN !5x}} ErvvN ww{{+,AG,,--""Av"* Q%- QT"%- QT"++11!4JLKG Qad!3T\\!Q$5G!!!HH&&,,Q/LLA&LLA& 7223 4&%  a GGNN$;;HH&&,,Q/LLA&LLA& 7223 4$#M-R    MM GMM "  HHT00 B HHT00 B t**+A$"" QT" &DIIaL, t**+A$"" QT" &DIIaL, ;;;  0 0 2 r3c .VPP#)zN Dimension of the problem. Returns ------- int Dimension of the problem. )rcrr8s&r0rModels.ns!!###r3c .VPP#r<)rcr=r8s&r0r= Models.npts!!%%%r3c <VPP^,#)zr Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. )rr7r8s&r0rModels.m_nonlinear_ub||!!!$$r3c <VPP^,#)zn Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. )rr7r8s&r0rModels.m_nonlinear_eqrr3c VP#)zZ Interpolation set. Returns ------- `cobyqa.models.Interpolation` Interpolation set. )rr8s&r0rcModels.interpolations"""r3c VP#)z Values of the objective function at the interpolation points. Returns ------- `numpy.ndarray`, shape (npt,) Values of the objective function at the interpolation points. )rr8s&r0rModels.fun_vals}}r3c VP#)z Values of the nonlinear inequality constraint functions at the interpolation points. Returns ------- `numpy.ndarray`, shape (npt, m_nonlinear_ub) Values of the nonlinear inequality constraint functions at the interpolation points. )rr8s&r0rModels.cub_val }}r3c VP#)z Values of the nonlinear equality constraint functions at the interpolation points. Returns ------- `numpy.ndarray`, shape (npt, m_nonlinear_eq) Values of the nonlinear equality constraint functions at the interpolation points. )rr8s&r0rModels.ceq_val.rr3c VP'd$VPVP38XgQR4hVPWP4#)a- Evaluate the quadratic model of the objective function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the quadratic model of the objective function. Returns ------- float Value of the quadratic model of the objective function at `x`. r{)rr7rrrcr$r}s&&r0fun Models.fun<s@ ;;;77tvvi' I)I I'yy..//r3c VP'd$VPVP38XgQR4hVPP WP 4#)af Evaluate the gradient of the quadratic model of the objective function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradient of the quadratic model of the objective function. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the quadratic model of the objective function at `x`. r{)rr7rrrrcrs&&r0fun_gradModels.fun_gradPsD ;;;77tvvi' I)I I'yy~~a!3!344r3c LVPPVP4#)z Evaluate the Hessian matrix of the quadratic model of the objective function. Returns ------- `numpy.ndarray`, shape (n, n) Hessian matrix of the quadratic model of the objective function. )rrrcr8s&r0fun_hessModels.fun_hessdsyy~~d0011r3c VP'd$VPVP38XgQR4hVPP WP 4#)a Evaluate the right product of the Hessian matrix of the quadratic model of the objective function with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the quadratic model of the objective function is multiplied from the right. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the quadratic model of the objective function with `v`. r)rr7rrrrcr$rs&&r0 fun_hess_prodModels.fun_hess_prodpsF" ;;;77tvvi' I)I I'yy""1&8&899r3c VP'd$VPVP38XgQR4hVPP WP 4#)ai Evaluate the curvature of the quadratic model of the objective function along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the quadratic model of the objective function is evaluated. Returns ------- float Curvature of the quadratic model of the objective function along `v`. r)rr7rrrrcrs&&r0fun_curvModels.fun_curvsD" ;;;77tvvi' I)I I'yy~~a!3!344r3c VP'd$VPVP38XgQR4h\VPVP VP4pVP WP4#)a Evaluate the gradient of the alternative quadratic model of the objective function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradient of the alternative quadratic model of the objective function. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the alternative quadratic model of the objective function at `x`. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. r{)rr7rrlrcrr)r$r}models&& r0 fun_alt_gradModels.fun_alt_grads\, ;;;77tvvi' I)I I'$,,dllDKKHzz!//00r3Nc  LVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFq3!WP4NK up4#uupi)a Evaluate the quadratic models of the nonlinear inequality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the quadratic models of the nonlinear inequality functions. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Values of the quadratic model of the nonlinear inequality functions. r{!The shape of `mask` is not valid.)rr7rrrarray_get_cubrcr$r}maskrs&&& r0cub Models.cubs& ;;;77tvvi' I)I I'<4::##2$ 32 3xx7;}}T7J K7JeU1(( )7J K  KB!c  zVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK upRVP34#uupi)a Evaluate the gradients of the quadratic models of the nonlinear inequality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradients of the quadratic models of the nonlinear inequality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Gradients of the quadratic model of the nonlinear inequality functions. r{r) rr7rrrreshaperrrcrs&&& r0cub_gradModels.cub_grad& ;;;77tvvi' I)I I'<4::##2$ 32 3zz--- /-ZZ-- .- / L   /$B8c HVP'd(Ve$VPVP38XgQR4h\P!VP V4Uu.uFq"P VP4NK upRVPVP34#uupi)aV Evaluate the Hessian matrices of the quadratic models of the nonlinear inequality functions. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Hessian matrices of the quadratic models of the nonlinear inequality functions. rr ) rr7rrr rrrcrr$rrs&& r0cub_hessModels.cub_hess ;;;<4::##2$ 32 3zz9=t9L M9LZZ** +9L M    M#Bc  zVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK upRVP34#uupi)aJ Evaluate the right product of the Hessian matrices of the quadratic models of the nonlinear inequality functions with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrices of the quadratic models of the nonlinear inequality functions are multiplied from the right. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Right products of the Hessian matrices of the quadratic models of the nonlinear inequality functions with `v`. rrr ) rr7rrrr rrrcr$rrrs&&& r0 cub_hess_prodModels.cub_hess_prod& ;;;77tvvi' I)I I'<4::##2$ 32 3zz"]]40 0E#5#560 L    rc  `VP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK up4#uupi)a Evaluate the curvature of the quadratic models of the nonlinear inequality functions along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the quadratic models of the nonlinear inequality functions is evaluated. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Curvature of the quadratic models of the nonlinear inequality functions along `v`. rr) rr7rrrrrrrcrs&&& r0cub_curvModels.cub_curv(& ;;;77tvvi' I)I I'<4::##2$ 32 3xx--- /-ZZ-- .- /   /$B+c  LVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFq3!WP4NK up4#uupi)a Evaluate the quadratic models of the nonlinear equality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the quadratic models of the nonlinear equality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Values of the quadratic model of the nonlinear equality functions. r{r)rr7rrrr_get_ceqrcrs&&& r0ceq Models.ceqEs$ ;;;77tvvi' I)I I'<4::##2$ 32 3xx7;}}T7J K7JeU1(( )7J K  Krc  zVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK upRVP34#uupi)a Evaluate the gradients of the quadratic models of the nonlinear equality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradients of the quadratic models of the nonlinear equality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Gradients of the quadratic model of the nonlinear equality functions. r{rr ) rr7rrrr r!rrcrs&&& r0ceq_gradModels.ceq_grad`rrc HVP'd(Ve$VPVP38XgQR4h\P!VP V4Uu.uFq"P VP4NK upRVPVP34#uupi)aR Evaluate the Hessian matrices of the quadratic models of the nonlinear equality functions. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Hessian matrices of the quadratic models of the nonlinear equality functions. rr ) rr7rrr r!rrcrrs&& r0ceq_hessModels.ceq_hess~rrc  zVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK upRVP34#uupi)aD Evaluate the right product of the Hessian matrices of the quadratic models of the nonlinear equality functions with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrices of the quadratic models of the nonlinear equality functions are multiplied from the right. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Right products of the Hessian matrices of the quadratic models of the nonlinear equality functions with `v`. rrr ) rr7rrrr r!rrcrs&&& r0 ceq_hess_prodModels.ceq_hess_prodrrc  `VP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK up4#uupi)a Evaluate the curvature of the quadratic models of the nonlinear equality functions along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the quadratic models of the nonlinear equality functions is evaluated. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Curvature of the quadratic models of the nonlinear equality functions along `v`. rr) rr7rrrrr!rrcrs&&& r0ceq_curvModels.ceq_curvrrc "\VPVPVP4Vn\ VP 4FDp\VPVPRV3,VP4VPV&KF \ VP4FDp\VPVPRV3,VP4VPV&KF VP'dVP4R#R#)z Set the quadratic models of the objective function, nonlinear inequality constraints, and nonlinear equality constraints to the alternative quadratic models. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. rFN) rlrcrrrr!rrrrrrr)r$rs& r0 reset_modelsModels.reset_modelssd00$,, L t**+A$"" QT" DIIaL, t**+A$"" QT" DIIaL, ;;;  0 0 2 r3c  DVP'd^Tu;8:dVP8gQR4hQR4hVPVP38XgQR4h\ V\ 4'gQR4hVPVP 38XgQR4hVPVP38XgQR4h\P!VP4p\P!VPP4p\P!VPP4pW0PV4, Wa&W@PV4, WqR3&WPPV4, WR3&W0PV&W@PVR3&WPPVR3&\P !VP"P$RV3,4p W P"P&, VP"P$RV3&VP(P+VP"VV V4p \-VP 4FEp T ;'g9VP.V ,P+VP"VV VRV 3,4p KG \-VP4FEp T ;'g9VP0V ,P+VP"VV VRV 3,4p KG VP'dVP34V #)aG Update the interpolation set. This method updates the interpolation set by replacing the `knew`-th interpolation point with `xnew`. It also updates the function values and the quadratic models. Parameters ---------- k_new : int Index of the updated interpolation point. x_new : `numpy.ndarray`, shape (n,) New interpolation point. Its value is interpreted as relative to the origin, not the base point. fun_val : float Value of the objective function at `x_new`. Objective function value at `x_new`. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,) Values of the nonlinear inequality constraints at `x_new`. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,) Values of the nonlinear equality constraints at `x_new`. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. r"The shape of `x_new` is not valid.z The function value is not valid.z$The shape of `cub_val` is not valid.z$The shape of `ceq_val` is not valid.rF)rr=r7r isinstancefloatrrrrrrrrr"rrrcr"rrrr!rrr) r$rx_newrrrfun_diffcub_diffceq_diffrrrs &&&&&& r0update_interpolationModels.update_interpolations8 ;;;(( K*K K( K*K K(;;466)+ 54 5+gu-- 32 3-==##% 65 6==##% 65 6 88DHH%88DLL../88DLL../!HHUO3$xx6$xx6& U!( UAX!( UAX''$,,00E:;+03E3E3L3L+Lq%x())**         t**+A-11D1D""A 2O,t**+A-11D1D""A 2O, ;;;  0 0 2r3c LVP'dQVPVP38XgQR4hVe*^Tu;8:dVP8gQR4hQR4hWPP , p\ P!VPVP,^,^34pRVPPPV,R,,VRVP1^3&RW@P^3&W4VP^,R1^3&\PVPV4^,pRW3,R,,VR,VR,,, pVf\ P!VPVP,^,VP4p\ P!\PVPV4^,4pVRVP1^3,p Mu\ P!VPVP,^,^V)4p\PVPV4^,V^3,pWR^3,p W,V R,,#)a Compute the normalized determinants of the new interpolation systems. Parameters ---------- x_new : `numpy.ndarray`, shape (n,) New interpolation point. Its value is interpreted as relative to the origin, not the base point. k_new : int, optional Index of the updated interpolation point. If `k_new` is not specified, all the possible determinants are computed. Returns ------- {float, `numpy.ndarray`, shape (npt,)} Determinant(s) of the new interpolation system. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. Notes ----- The determinants are normalized by the determinant of the current interpolation system. For stability reasons, the calculations are done using the formula (2.12) in [1]_. References ---------- .. [1] M. J. D. Powell. On updating the inverse of a KKT matrix. Technical Report DAMTP 2004/NA01, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK, 2004. r4Nrr r rZ)rFr)rr7rr=rcrrrbr"rarlreyediag) r$r7rrnew_col inv_new_colbeta coord_vecalphataus &&& r0 determinantsModels.determinantsBs7H ;;;;;466)+ 54 5+ e!6dhh!6 10 16!6 10 16**111((DHHtvv-1156t))--//%7C??  $(( A "! $)1 q !--d.@.@'J1M em++gdmk$>O.OO =txx$&&014dhh?IGG''&&E jj!m,Ctxx$&&014a%@I++""  Qh E Qh'C|c3h&&r3c VP'd$VPVP38XgQR4hVPP VP V4VP FpVP VP V4K! VPFpVP VP V4K! WP P, pVP ;PV, unVP ;PVR\P3,,un V\P,'dVP4R#R#)z Shift the base point without changing the interpolation set. Parameters ---------- new_x_base : `numpy.ndarray`, shape (n,) New base point. options : dict Options of the solver. rrFN)rr7rrrrcrrrr"rrrr r)r$rr&rrs&&& r0rModels.shift_x_bases ;;;##( 98 9 t11:>YYE   t11: >YYE   t11: >//666 !!U*! %2:: "66 7== ! !  0 0 2 "r3c HVf VP#VPV,#)a Get the quadratic models of the nonlinear inequality constraints. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to return. Returns ------- `numpy.ndarray` Quadratic models of the nonlinear inequality constraints. )rr$rs&&r0rModels._get_cub!Ltyy=diio=r3c HVf VP#VPV,#)a Get the quadratic models of the nonlinear equality constraints. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to return. Returns ------- `numpy.ndarray` Quadratic models of the nonlinear equality constraints. )rrKs&&r0r!Models._get_ceqrMr3c  RpRpRp\VP4EFLp\P!V\P!VP VP PV44VPV,, 4.4p\P!\P!VPVP PV44VPVR3,, 4VR7p\P!\P!VPVP PV44VPVR3,, 4VR7pEKO R\P!\4,\VPVP4,pW\P!\P!VP4RR7,8d\ P"!R\$^4W%\P!\P!VP4RR7,8d\ P"!R\$^4W5\P!\P!VP4RR7,8d\ P"!R\$^4R #R #) z= Check the interpolation conditions of all quadratic models. rrFrXg$@rZzJThe interpolation conditions for the objective function are not satisfied.zVThe interpolation conditions for the inequality constraint function are not satisfied.zTThe interpolation conditions for the equality constraint function are not satisfied.N)r!r=rr]rrrcrGrrrr"rsqrtr`rwarningswarnRuntimeWarning)r$ error_fun error_cub error_ceqr,tols& r0r&Models._check_interpolation_conditionss   txxAFF!3!3!9!9!!<= QOIHHT//55a89DLLA > 11r3r)rRnumpyr scipy.linalgrsettingsrutilsrrrfinfor6epsr`r rjrlrr3r0rasZ?? hhuos,s,l27juFuFp KKr3