+ ,i^RIt^RIt^RIHt^RIHt^RIHtH t H t ]P!] 4Pt!RR4tRRRRR RR R/tR t!R R 4t!RR4tR#)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| R#)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) selfpboptions max_radiusvery_close_xl_idx close_xl_idxvery_close_xu_idx close_xu_idxkspreadk1k2s &&& :/usr/lib/python3/dist-packages/scipy/_lib/cobyqa/models.py__init__Interpolation.__init__s7gmm, 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%0c <VPP^,#zD Number of variables. Returns ------- int Number of variables. r"shaper#s&r/rInterpolation.n\xx~~a  r2c <VPP^,#zZ Number of interpolation points. Returns ------- int Number of interpolation points. r5r7s&r/nptInterpolation.npthr9r2c VP#)zb Interpolation points. Returns ------- `numpy.ndarray`, shape (n, npt) Interpolation points. )r r7s&r/r"Interpolation.xpttsyyr2c 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)rr6rr<r )r#r"s&&r/r"r?sG ;;;99! 22 2 r2c VP#)z Base point around which the models are expanded. Returns ------- `numpy.ndarray`, shape (n,) Base point around which the models are expanded. )rr7s&r/rInterpolation.x_bases||r2c |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)rr6rr)r#rs&&r/rrBs> ;;;<<$ 54 5 r2c 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&&r/pointInterpolation.pointsQ ;;;$DHH$ C&C C$ C&C C${{TXXad^++r2)rrr N)__name__ __module__ __qualname____firstlineno____doc__r0propertyrr<r"setterrrF__static_attributes____classdictcell__ __classdict__s@r/r r sD7L ! ! ! !   ZZ    ]]  ,,r2r r"a right_scalingrcf\R,eY\P!VP\R,4'd'\R,\R,\R,3#\P!\P P VP^R7\R7pVPV, pVPwr4\P!WC,^,WC,^,34pRVPV,R ,,VRV1RV13&R VRV1V3&VPVRV1V^,R13&R WTRV13&W%V^,R1RV13&\P!WC,^,4pR VR ,, VRV%VR ,Wd&WV^,R%\VR R 7wrx\P!VP4\R&\P!V4\R&\P!V4\R&Wx3\R&WVWx33#) 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. r"NrSrTr)axisinitialr r ?F) check_finite)_cacher array_equalr"maxlinalgnormEPSr6rTemptyrr) interpolationscale xpt_scalerr<rSrT eig_values eig_vectorss & r/ build_systemrhs"e} R^^6%=&&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) rr6r<r ValueError _get_model_const_grad_i_hessrr_e_hess)r#rcvaluesdebug_s&&&& r/r0Quadratic.__init__s$ ;;;<<!!$ 54 5   }2 2F ??Q&'q* 48??  4 0 TZqxx 01 r2c 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 ) rr6rrrprqrrr"rarsr#xrcx_diffs&&& r/__call__Quadratic.__call__(s ;;;77tvvi' I)I I'))) KKjj6! " 1 1 3 3f <DD<<'&01  r2c .VPP#r4)rqsizer7s&r/r Quadratic.nEszzr2c .VPP#)z Number of interpolation points used to define the quadratic model. Returns ------- int Number of interpolation points used to define the quadratic model. )rrrr7s&r/r< Quadratic.nptQs||   r2c 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`. ry)rr6rrrq hess_prodrzs&&& r/gradQuadratic.grad]sQ ;;;77tvvi' I)I I')))zzDNN6AAAr2c 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. rE)rsr"rrrnewaxisra)r#rcs&&r/hessQuadratic.hessrsG||m// LLBJJ '-*;*;*=*= =   r2c 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.)rr6rrsr"rrrar#vrcs&&&r/rQuadratic.hess_prodsk& ;;;77tvvi' I)I I'||a-"3"3 LLM--//!3 4#   r2c 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 )rr6rrsrrr"rars&&&r/curvQuadratic.curvsf" ;;;77tvvi' I)I I' q llm//11A5#== > r2c 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<r6rrsrrrouterrorprq) r#rck_newdir_old values_diffconstri_hessill_conditioneds &&&&& r/updateQuadratic.updates4 ;;;(( K*K K( K*K K(==% 65 6$$) :9 :  U+bhhw.HHH ! U04  0 ,V u  d   r2c VP'd$VPVP38XgQR4hV!W!4VnVP W!4VnW!P , p\P!VVPRVR\P3,,, VP,4pV;PWDP,, un R#)a Shift the point around which the quadratic model is defined. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Previous interpolation set. new_x_base : `numpy.ndarray`, shape (n,) Point that will replace ``interpolation.x_base``. 'The shape of `new_x_base` is not valid.r rEN)rr6rrprrqrrrr"rrrrsra)r#rc new_x_baseshiftrs&&& r/ shift_x_baseQuadratic.shift_x_bases ;;;##( 98 9:5 YYz9 111    uQ ]';!; ;t|| K  )) r2c \VPPwr#VP^8Xd&VP^,W2,^,8XgQR4h\V4wrEpWR\P 3,,p\P !\P!V44'd1\P !\P!V44'g \PPR4hVwr\P!V4\8p V RV 3,p RW,, p \P !V ^4(p V V PV,V R\P 3,,,p WR\P 3,,V 3#)a Solve the interpolation systems. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. rhs : `numpy.ndarray`, shape (npt + n + 1, m) Right-hand side vectors of the ``m`` interpolation systems. Returns ------- `numpy.ndarray`, shape (npt + n + 1, m) Solutions of the interpolation systems. `numpy.ndarray`, shape (m, ) Whether the interpolation systems are ill-conditioned. Raises ------ `numpy.linalg.LinAlgError` If the interpolation systems are ill-defined. z The shape of `rhs` is not valid.rEz(The interpolation system is ill-defined.rY) r"r6ndimrhrrallisfiniter^ LinAlgErrorabsr`ra)rcrhsrr<rSrTeig rhs_scaledrfrglarge_eig_valuesinv_eig_valuesrleft_scaled_solutionss&& r/ solve_systemsQuadratic.solve_systemssQ0""(( HHMciilcgk9 . - . 9!-] ;#BJJ77 r{{1~&&266"++j2I+J+J))'':  #& 66*-3!!%5"56 z;;66"2A66 + ]]Z '>!RZZ-+H H!  "!RZZ-$@ @   r2c  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. rlN) r6r<r"rjrrblockrra)rcrtrr<r{rs&& r/roQuadratic._get_modelBs4||      1 0 1 ""((&44  HHQ a  ay!!GHaK.!DSD!G*oEEr2)rprrsrqrrN)rHrIrJrKrLr0r}rMrr<rrrrrr staticmethodrrorOrPrQs@r/rjrjs  2D :   ! !B* $ 2 02h*0> > @(F(Fr2rjcha]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#)&Modelsinz. 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. rE)dtypeN)#rr rr _interpolationrcrFrfullrnan_fun_valr_cub_val_ceq_valr!MAX_EVALrfun_valcub_valceq_valis_feasibilitymaxcvFEASIBILITY_TOLrTARGETrrj_funrbm_nonlinear_ub_cubm_nonlinear_eq_ceq_check_interpolation_conditions) r#r$r%penaltyx_evalfun_initcub_initceq_initr+is &&&& r/r0Models.__init__ss`6gmm, +B8##))!,')&':$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 r2c .VPP#)zN Dimension of the problem. Returns ------- int Dimension of the problem. )rcrr7s&r/rModels.ns!!###r2c .VPP#r;)rcr<r7s&r/r< Models.npts!!%%%r2c <VPP^,#)zr Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. )rr6r7s&r/rModels.m_nonlinear_ub||!!!$$r2c <VPP^,#)zn Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. )rr6r7s&r/rModels.m_nonlinear_eqrr2c VP#)zZ Interpolation set. Returns ------- `cobyqa.models.Interpolation` Interpolation set. )rr7s&r/rcModels.interpolations"""r2c 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. )rr7s&r/rModels.fun_vals}}r2c 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. )rr7s&r/rModels.cub_val}}r2c 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. )rr7s&r/rModels.ceq_val,rr2c VP'd$VPVP38XgQR4hVPWP4#)a- Evaluate the quadratic model of the objective function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the quadratic model of the objective function. Returns ------- float Value of the quadratic model of the objective function at `x`. ry)rr6rrrcr#r{s&&r/fun Models.fun:s@ ;;;77tvvi' I)I I'yy..//r2c VP'd$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`. ry)rr6rrrrcrs&&r/fun_gradModels.fun_gradNsD ;;;77tvvi' I)I I'yy~~a!3!344r2c 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. )rrrcr7s&r/fun_hessModels.fun_hessbsyy~~d0011r2c VP'd$VPVP38XgQR4hVPP WP 4#)a Evaluate the right product of the Hessian matrix of the quadratic model of the objective function with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the quadratic model of the objective function is multiplied from the right. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the quadratic model of the objective function with `v`. r)rr6rrrrcr#rs&&r/ fun_hess_prodModels.fun_hess_prodnsF" ;;;77tvvi' I)I I'yy""1&8&899r2c VP'd$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)rr6rrrrcrs&&r/fun_curvModels.fun_curvsD" ;;;77tvvi' I)I I'yy~~a!3!344r2c VP'd$VPVP38XgQR4h\VPVP VP4pVP WP4#)a Evaluate the gradient of the alternative quadratic model of the objective function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradient of the alternative quadratic model of the objective function. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the alternative quadratic model of the objective function at `x`. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. ry)rr6rrjrcrr)r#r{models&& r/ fun_alt_gradModels.fun_alt_grads\, ;;;77tvvi' I)I I'$,,dllDKKHzz!//00r2Nc  LVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFq3!WP4NK up4#uupi)a Evaluate the quadratic models of the nonlinear inequality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the quadratic models of the nonlinear inequality functions. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Values of the quadratic model of the nonlinear inequality functions. ry!The shape of `mask` is not valid.)rr6rrrarray_get_cubrcr#r{maskrs&&& r/cub Models.cubs& ;;;77tvvi' I)I I'<4::##2$ 32 3xx7;}}T7J K7JeU1(( )7J K  KB!c  zVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK upRVP34#uupi)a Evaluate the gradients of the quadratic models of the nonlinear inequality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradients of the quadratic models of the nonlinear inequality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Gradients of the quadratic model of the nonlinear inequality functions. ryr) rr6rrrreshaperrrcrs&&& r/cub_gradModels.cub_grad& ;;;77tvvi' I)I I'<4::##2$ 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) rr6rrr rrrcrr#rrs&& r/cub_hessModels.cub_hess ;;;<4::##2$ 32 3zz9=t9L M9LZZ** +9L M    M#Bc  zVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK upRVP34#uupi)aJ Evaluate the right product of the Hessian matrices of the quadratic models of the nonlinear inequality functions with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrices of the quadratic models of the nonlinear inequality functions are multiplied from the right. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Right products of the Hessian matrices of the quadratic models of the nonlinear inequality functions with `v`. rrr) rr6rrrr rrrcr#rrrs&&& r/ cub_hess_prodModels.cub_hess_prod& ;;;77tvvi' I)I I'<4::##2$ 32 3zz"]]40 0E#5#560 L    r c  `VP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK up4#uupi)a Evaluate the curvature of the quadratic models of the nonlinear inequality functions along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the quadratic models of the nonlinear inequality functions is evaluated. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Curvature of the quadratic models of the nonlinear inequality functions along `v`. rr) rr6rrrrrrrcrs&&& r/cub_curvModels.cub_curv&& ;;;77tvvi' I)I I'<4::##2$ 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. ryr)rr6rrrr_get_ceqrcrs&&& r/ceq Models.ceqCs$ ;;;77tvvi' I)I I'<4::##2$ 32 3xx7;}}T7J K7JeU1(( )7J K  Krc  zVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK upRVP34#uupi)a Evaluate the gradients of the quadratic models of the nonlinear equality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradients of the quadratic models of the nonlinear equality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Gradients of the quadratic model of the nonlinear equality functions. ryrr) rr6rrrr rrrcrs&&& r/ceq_gradModels.ceq_grad^r r c HVP'd(Ve$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) rr6rrr rrrcrrs&& r/ceq_hessModels.ceq_hess|rrc  zVP'dKVPVP38XgQR4hVe$VPVP38XgQR4h\P !VP V4Uu.uFpVPWP4NK upRVP34#uupi)aD Evaluate the right product of the Hessian matrices of the quadratic models of the nonlinear equality functions with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrices of the quadratic models of the nonlinear equality functions are multiplied from the right. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Right products of the Hessian matrices of the quadratic models of the nonlinear equality functions with `v`. rrr) rr6rrrr rrrcrs&&& r/ ceq_hess_prodModels.ceq_hess_prodrr c  `VP'dKVPVP38XgQR4hVe$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) rr6rrrrrrrcrs&&& r/ceq_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. rEN) rjrcrrrr!rrrrrrr)r#rs& r/ reset_modelsModels.reset_modelssd00$,, L t**+A$"" QT" DIIaL, t**+A$"" QT" DIIaL, ;;;  0 0 2 r2c  DVP'd^Tu;8:dVP8gQR4hQR4hVPVP38XgQR4h\ V\ 4'gQR4hVPVP 38XgQR4hVPVP38XgQR4h\P!VP4p\P!VPP4p\P!VPP4pW0PV4, Wa&W@PV4, WqR3&WPPV4, WR3&W0PV&W@PVR3&WPPVR3&\P !VP"P$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$The shape of `ceq_val` is not valid.rE)rr<r6r isinstancefloatrrrrrrrrr rrrcr"rrrr!rrr) r#rx_newrrrfun_diffcub_diffceq_diffrrrs &&&&&& r/update_interpolationModels.update_interpolations8 ;;;(( K*K K( K*K K(;;466)+ 54 5+gu-- 32 3-==##% 65 6==##% 65 6 88DHH%88DLL../88DLL../!HHUO3$xx6$xx6& U!( UAX!( UAX''$,,00E:;+03E3E3L3L+Lq%x())**         t**+A-11D1D""A 2O,t**+A-11D1D""A 2O, ;;;  0 0 2r2c 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. r2Nrr r rY)rEr)rr6rr<rcrrrbr"rarjreyediag) r#r5rrnew_col inv_new_colbeta coord_vecalphataus &&& r/ determinantsModels.determinants@s7H ;;;;;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&&r2c VP'd$VPVP38XgQR4hVPP VP V4VP FpVP VP V4K! VPFpVP VP V4K! WP P, pVP ;PV, unVP ;PVR\P3,,un V\P,'dVP4R#R#)z Shift the base point without changing the interpolation set. Parameters ---------- new_x_base : `numpy.ndarray`, shape (n,) New base point. options : dict Options of the solver. rrEN)rr6rrrrcrrrr"rrrr r)r#rr%rrs&&& r/rModels.shift_x_bases ;;;##( 98 9 t11:>YYE   t11: >YYE   t11: >//666 !!U*! %2:: "66 7== ! !  0 0 2 "r2c HVf VP#VPV,#)a Get the quadratic models of the nonlinear inequality constraints. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to return. Returns ------- `numpy.ndarray` Quadratic models of the nonlinear inequality constraints. )rr#rs&&r/rModels._get_cub!Ltyy=diio=r2c HVf VP#VPV,#)a Get the quadratic models of the nonlinear equality constraints. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to return. Returns ------- `numpy.ndarray` Quadratic models of the nonlinear equality constraints. )rrIs&&r/rModels._get_ceqrKr2c  RpRpRp\VP4EFLp\P!V\P!VP VP PV44VPV,, 4.4p\P!\P!VPVP PV44VPVR3,, 4VR7p\P!\P!VPVP PV44VPVR3,, 4VR7pEKO R\P!\4,\VPVP4,pW\P!\P!VP4RR7,8d\ P"!R\$^4W%\P!\P!VP4RR7,8d\ P"!R\$^4W5\P!\P!VP4RR7,8d\ P"!R\$^4R #R #) z= Check the interpolation conditions of all quadratic models. rrErWg$@rYzJThe 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]rrrcrFrrrr rsqrtr`rwarningswarnRuntimeWarning)r# error_fun error_cub error_ceqr+tols& r/r&Models._check_interpolation_conditionss   txxAFF!3!3!9!9!!<= QOIHHT//55a89DLLA > 11r2r)rPnumpyr scipy.linalgrsettingsrutilsrrrfinfor4epsr`r r[rhrjrr2r/r_sr?? hhuor,r,j sD/4 F.7buFuFp KKr2