(phSSKrSSKrSSKJr SSKJr SSKJrJ r J r \R"\ 5Rr"SS5rSSSSS.rS r"S S 5r"S S 5rg)N)eigh)Options) MaxEvalError TargetSuccessFeasibleSuccessc\rSrSrSrSr\S5r\S5r\S5r \ RS5r \S5r \ RS 5r S r S r g ) Interpolation z 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. cD U[RUlS[R"UR R UR R- 5-nU[RU:a`X2[RR'[R"U[RU/5U[RR'[R"UR5Ul URUR RSU[R--:*nUR RUURU'UR RSU[R--UR:URUR RU[R-:*-n[R"UR RUU[R-UR R U5URU'URUR R SU[R-- :nUR R UURU'URUR R SU[R-- :UR R U[R- UR:*-n[R "UR R UU[R- UR RU5URU'[R""UR$U[R&45Ul[+SU[R&5GHnXR$::a[XhS- (a(U[R*UR,US- U4'MGU[RUR,US- U4'MnUSUR$-::aXHUR$- S- (a6SU[R-UR,XR$- S- U4'MXhUR$- S- (a7SU[R-UR,XR$- S- U4'GM U[R*UR,XR$- S- U4'GMUXR$- S- UR$-n USU -UR$-- S- n X-UR$-n UR,XS-4UR,X4'UR,XS-4UR,X4'GM g)z Initialize the interpolation set. Parameters ---------- pb : `cobyqa.problem.Problem` Problem to be solved. options : dict Options of the solver. ?r@gN)rDEBUG_debugnpminboundsxuxlRHOBEGvalueRHOENDcopyx0_x_basex_baseminimummaximumzerosnNPT_xptrangexpt) selfpboptions max_radiusvery_close_xl_idx close_xl_idxvery_close_xu_idx close_xu_idxkspreadk1k2s K/var/www/html/venv/lib/python3.13/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\203ggnn6M0MDHHQX\1_-&244x!|404ww~~7N0NDHHQX\1_-181H0HDHHQX\1_-dd(Q,244/!f*,,q0kRTT)"&((2Av:"6"&((2Av:"6%0c4URRS$)D Number of variables. Returns ------- int Number of variables. rr%shaper&s r2r!Interpolation.n\xx~~a  r5c4URRS$)Z Number of interpolation points. Returns ------- int Number of interpolation points. rr8r:s r2nptInterpolation.npthr<r5cUR$)zb Interpolation points. Returns ------- `numpy.ndarray`, shape (n, npt) Interpolation points. )r#r:s r2r%Interpolation.xpttsyyr5cUR(a-URURUR4:XdS5eXlg)zz Set the interpolation points. Parameters ---------- xpt : `numpy.ndarray`, shape (n, npt) New interpolation points. z The shape of `xpt` is not valid.N)rr9r!r?r#)r&r%s r2r%rBsE ;;99! 22 2 r5cUR$)z Base point around which the models are expanded. Returns ------- `numpy.ndarray`, shape (n,) Base point around which the models are expanded. )rr:s r2rInterpolation.x_bases||r5cvUR(a"URUR4:XdS5eXlg)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)rr9r!r)r&rs r2rrEs< ;;<<$ 54 5 r5cUR(a&SUs=::aUR:dS5e S5eURURSS2U4-$)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. rzThe index `k` is not valid.N)rr?rr%)r&r.s r2pointInterpolation.pointsO ;;$DHH$ C&C C$ C&C C${{TXXad^++r5)rrr#N)__name__ __module__ __qualname____firstlineno____doc__r3propertyr!r?r%setterrrH__static_attributes__r5r2r r sD7L ! ! ! !   ZZ    ]]  ,r5r )r%a right_scalingrc[SbG[R"UR[S5(a[S[S[S4$[R"[R R URSS9[S9nURU- nURup4[R"XC-S -XC-S -45nS URU-S --USU2SU24'S USU2U4'URUSU2US -S24'S XTSU24'X%US -S2SU24'[R"XC-S -5nS US -- USU&US -Xd'XUS -S&[US S9upx[R"UR5[S'[R"U5[S'[R"U5[S'Xx4[S'XVXx44$)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%NrSrTrr)axisinitialrr r?F) check_finite)_cacher array_equalr%maxlinalgnormEPSr9r Temptyrr) interpolationscale xpt_scaler!r?rSrT eig_values eig_vectorss r2 build_systemrhs"e} R^^6%=&&c{F?3VF^CC FF299>>-"3"3!>`_. cX0lUR(a"URUR4:XdS5eURURS-:a[ SURS-S35eUR UU5uUlUlUln[R"URUR45Ul g)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.rz4The number of interpolation points must be at least .N) rr9r?r! ValueError _get_model_const_grad_i_hessrr _e_hess)r&rcvaluesdebug_s r2r3Quadratic.__init__s$ ;;<<!!$ 54 5   }2 2F ??Q&'q* 48??  4 0 TZqxx 01 r5c:UR(a"URUR4:XdS5eXR- nURUR U--SUR URRU-S--X0R-U----$)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) rr9r!rrqrrrsr%rartr&xrcx_diffs r2__call__Quadratic.__call__(s ;;77tvvi' I)I I'))) KKjj6! " 1 1 3 3f <DD<<'&01  r5c.URR$)r7)rrsizer:s r2r! Quadratic.nEszzr5c.URR$)z Number of interpolation points used to define the quadratic model. Returns ------- int Number of interpolation points used to define the quadratic model. )rsrr:s r2r? Quadratic.nptQs||   r5cUR(a"URUR4:XdS5eXR- nURUR X25-$)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`. rz)rr9r!rrr hess_prodr{s r2gradQuadratic.grad]sO ;;77tvvi' I)I I')))zzDNN6AAAr5cURURURSS2[R4URR ---$)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. N)rtr%rsrnewaxisra)r&rcs r2hessQuadratic.hessrsG||m// LLBJJ '-*;*;*=*= =   r5cUR(a"URUR4:XdS5eURU-URUR URR U----$)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.)rr9r!rtr%rsrar&vrcs r2rQuadratic.hess_prodsi& ;;77tvvi' I)I I'||a-"3"3 LLM--//!3 4#   r5cUR(a"URUR4:XdS5eXR-U-URUR R U-S---$)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)rr9r!rtrsr%rars r2curvQuadratic.curvsd" ;;77tvvi' I)I I' q llm//11A5#== > r5c4UR(ajSUs=::aUR:dS5e S5eURUR4:XdS5eURUR4:XdS5eU=RUR U[ R"X35-- slSUR U'URUU5upVpxU=RU- sl U=RU- sl U=R U- slU$)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. rThe 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?r9r!rtrsrouterrprqrr) r&rck_newdir_old values_diffconstri_hessill_conditioneds r2updateQuadratic.updates4 ;;(( K*K K( K*K K(==% 65 6$$) :9 :  U+bhhw.HHH ! U04  0 ,V u  d   r5cUR(a"URUR4:XdS5eU"X!5UlUR X!5UlX!R - n[R"UURSUSS2[R4-- UR-5nU=RXDR-- sl g)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 N)rr9r!rqrrrrrrr%rrsrtra)r&rc new_x_baseshiftrs r2 shift_x_baseQuadratic.shift_x_bases ;;##( 98 9:5 YYz9 111    uQ ]';!; ;t|| K  )) r5cURRup#URS:XaURSX2-S-:XdS5e[U5upEnXSS2[R 4-n[R "[R"U55(a/[R "[R"U55(d[RRS5eUup[R"U5[:n U SS2U 4n SX- n [R "U S5)n U U RU-U SS2[R 4--n XSS2[R 4-U 4$)a Solve the interpolation systems. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. rhs : `numpy.ndarray`, shape (npt + n + 1, m) Right-hand side vectors of the ``m`` interpolation systems. Returns ------- `numpy.ndarray`, shape (npt + n + 1, m) Solutions of the interpolation systems. `numpy.ndarray`, shape (m, ) Whether the interpolation systems are ill-conditioned. Raises ------ `numpy.linalg.LinAlgError` If the interpolation systems are ill-defined. rrrz The shape of `rhs` is not valid.Nz(The interpolation system is ill-defined.rY) r%r9ndimrhrrallisfiniter^ LinAlgErrorabsr`ra)rcrhsr!r?rSrTeig rhs_scaledrfrglarge_eig_valuesinv_eig_valuesrleft_scaled_solutionss r2 solve_systemsQuadratic.solve_systemssQ0""(( HHMciilcgk9 . - . 9!-] ;#BJJ77 r{{1~&&266"++j2I+J+J))'':  #& 66*-3!!%5"56 z;;66"2A66 + ]]Z '>!RZZ-+H H!  "!RZZ-$@ @   r5c JURUR4:XdS5eURRup#[R U[ R "U[ R"US-5//5R5upEXCS4XCS-S2S4USU2S4U4$)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. rmrrN) r9r?r%rjrrblockr ra)rcrur!r?r|rs r2rpQuadratic._get_modelBs4||      1 0 1 ""((&44  HHQ a  ay!!GHaK.!DSD!G*oEEr5)rqrrtrrrsN)rJrKrLrMrNr3r~rOr!r?rrrrrr staticmethodrrprQrRr5r2rjrjs  2D :   ! !B* $ 2 02h*0> > @(F(Fr5rjc\\rSrSrSrSr\S5r\S5r\S5r \S5r \S5r \S 5r \S 5r \S 5rS rS rSrSrSrSrS%SjrS%SjrS%SjrS%SjrS%SjrS%SjrS%SjrS%SjrS%SjrS%SjrSrSr S%Sjr!S r"S%S!jr#S%S"jr$S#r%S$r&g)&Modelsinz. Models for a nonlinear optimization problem. c U[RUl[X5UlUR R S5nU"XC5upVn[R"U[R[R5Ul [R"U[RUR4[R5Ul [R"U[RUR4[R5Ul[U[R5GHnX[R :a["eUS:Xa3XPR$U'X`R&USS24'XpR(USS24'OWUR R U5nU"UU5uUR$U'UR&USS24'UR(USS24'UR*(aiUR-UR R U5UR&USS24UR(USS245U[R.::a[0eURUU[R2::dGMQUR-UR R U5UR&USS24UR(USS245U[R.::dGM[4e [7UR URU[R5Ul[R:"UR<[6S9Ul[R:"UR@[6S9Ul![UR<5HIn [7UR UR&SS2U 4U[R5UR>U 'MK [UR@5HIn [7UR UR(SS2U 4U[R5URBU 'MK UR(aURE5 gg)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. rN)dtype)#rrrr _interpolationrcrHrfullr"nan_fun_valr_cub_val_ceq_valr$MAX_EVALrfun_valcub_valceq_valis_feasibilitymaxcvFEASIBILITY_TOLrTARGETrrj_funrbm_nonlinear_ub_cubm_nonlinear_eq_ceq_check_interpolation_conditions) r&r'r(penaltyx_evalfun_initcub_initceq_initr.is r2r3Models.__init__ss[6gmm, +B8##))!,')&':$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$"" QT" &DIIaL, ;;  0 0 2 r5c.URR$)zN Dimension of the problem. Returns ------- int Dimension of the problem. )rcr!r:s r2r!Models.ns!!###r5c.URR$)r>)rcr?r:s r2r? Models.npts!!%%%r5c4URRS$)zr Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. r)rr9r:s r2rModels.m_nonlinear_ub||!!!$$r5c4URRS$)zn Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. r)rr9r:s r2rModels.m_nonlinear_eqrr5cUR$)zZ Interpolation set. Returns ------- `cobyqa.models.Interpolation` Interpolation set. )rr:s r2rcModels.interpolations"""r5cUR$)z Values of the objective function at the interpolation points. Returns ------- `numpy.ndarray`, shape (npt,) Values of the objective function at the interpolation points. )rr:s r2rModels.fun_vals}}r5cUR$)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. )rr:s r2rModels.cub_val}}r5cUR$)z Values of the nonlinear equality constraint functions at the interpolation points. Returns ------- `numpy.ndarray`, shape (npt, m_nonlinear_eq) Values of the nonlinear equality constraint functions at the interpolation points. )rr:s r2rModels.ceq_val,rr5cUR(a"URUR4:XdS5eURXR5$)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`. rz)rr9r!rrcr&r|s r2fun Models.fun:s> ;;77tvvi' I)I I'yy..//r5cUR(a"URUR4:XdS5eURR XR 5$)af Evaluate the gradient of the quadratic model of the objective function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradient of the quadratic model of the objective function. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the quadratic model of the objective function at `x`. rz)rr9r!rrrcrs r2fun_gradModels.fun_gradNsB ;;77tvvi' I)I I'yy~~a!3!344r5cLURRUR5$)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. )rrrcr:s r2fun_hessModels.fun_hessbsyy~~d0011r5cUR(a"URUR4:XdS5eURR XR 5$)a Evaluate the right product of the Hessian matrix of the quadratic model of the objective function with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the quadratic model of the objective function is multiplied from the right. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the quadratic model of the objective function with `v`. r)rr9r!rrrcr&rs r2 fun_hess_prodModels.fun_hess_prodnsD" ;;77tvvi' I)I I'yy""1&8&899r5cUR(a"URUR4:XdS5eURR XR 5$)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)rr9r!rrrcrs r2fun_curvModels.fun_curvsB" ;;77tvvi' I)I I'yy~~a!3!344r5cUR(a"URUR4:XdS5e[URUR UR5nUR XR5$)a Evaluate the gradient of the alternative quadratic model of the objective function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradient of the alternative quadratic model of the objective function. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the alternative quadratic model of the objective function at `x`. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. rz)rr9r!rjrcrr)r&r|models r2 fun_alt_gradModels.fun_alt_gradsZ, ;;77tvvi' I)I I'$,,dllDKKHzz!//00r5Nc FUR(aGURUR4:XdS5eUb"URUR4:XdS5e[R "UR U5Vs/sHo3"XR5PM sn5$s snf)a Evaluate the quadratic models of the nonlinear inequality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the quadratic models of the nonlinear inequality functions. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Values of the quadratic model of the nonlinear inequality functions. rz!The shape of `mask` is not valid.)rr9r!rrarray_get_cubrcr&r|maskrs r2cub Models.cubs& ;;77tvvi' I)I I'<4::##2$ 32 3xx7;}}T7J K7JeU1(( )7J K  K<Bc tUR(aGURUR4:XdS5eUb"URUR4:XdS5e[R "UR U5Vs/sHnURXR5PM snSUR45$s snf)a Evaluate the gradients of the quadratic models of the nonlinear inequality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradients of the quadratic models of the nonlinear inequality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Gradients of the quadratic model of the nonlinear inequality functions. rzr) rr9r!rrreshaperrrcrs r2cub_gradModels.cub_grad& ;;77tvvi' I)I I'<4::##2$ 32 3zz--- /-ZZ-- .- / L   /<%B5cDUR(a%Ub"URUR4:XdS5e[R"UR U5Vs/sHo"R UR5PM snSURUR45$s snf)aV Evaluate the Hessian matrices of the quadratic models of the nonlinear inequality functions. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Hessian matrices of the quadratic models of the nonlinear inequality functions. rr ) rr9rrr rrrcr!r&rrs r2cub_hessModels.cub_hess ;;<4::##2$ 32 3zz9=t9L M9LZZ** +9L M    M$Bc tUR(aGURUR4:XdS5eUb"URUR4:XdS5e[R "UR U5Vs/sHnURXR5PM snSUR45$s snf)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 ) rr9r!rrr rrrcr&rrrs r2 cub_hess_prodModels.cub_hess_prod& ;;77tvvi' I)I I'<4::##2$ 32 3zz"]]40 0E#5#560 L    rc ZUR(aGURUR4:XdS5eUb"URUR4:XdS5e[R "UR U5Vs/sHnURXR5PM sn5$s snf)a Evaluate the curvature of the quadratic models of the nonlinear inequality functions along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the quadratic models of the nonlinear inequality functions is evaluated. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Curvature of the quadratic models of the nonlinear inequality functions along `v`. rr) rr9r!rrrrrrcrs r2cub_curvModels.cub_curv&& ;;77tvvi' I)I I'<4::##2$ 32 3xx--- /-ZZ-- .- /   /<%B(c FUR(aGURUR4:XdS5eUb"URUR4:XdS5e[R "UR U5Vs/sHo3"XR5PM sn5$s snf)a Evaluate the quadratic models of the nonlinear equality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the quadratic models of the nonlinear equality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Values of the quadratic model of the nonlinear equality functions. rzr)rr9r!rrr_get_ceqrcrs r2ceq Models.ceqCs$ ;;77tvvi' I)I I'<4::##2$ 32 3xx7;}}T7J K7JeU1(( )7J K  Krc tUR(aGURUR4:XdS5eUb"URUR4:XdS5e[R "UR U5Vs/sHnURXR5PM snSUR45$s snf)a Evaluate the gradients of the quadratic models of the nonlinear equality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradients of the quadratic models of the nonlinear equality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Gradients of the quadratic model of the nonlinear equality functions. rzrr ) rr9r!rrr r rrcrs r2ceq_gradModels.ceq_grad^r rcDUR(a%Ub"URUR4:XdS5e[R"UR U5Vs/sHo"R UR5PM snSURUR45$s snf)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 ) rr9rrr r rrcr!rs r2ceq_hessModels.ceq_hess|rrc tUR(aGURUR4:XdS5eUb"URUR4:XdS5e[R "UR U5Vs/sHnURXR5PM snSUR45$s snf)aD Evaluate the right product of the Hessian matrices of the quadratic models of the nonlinear equality functions with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrices of the quadratic models of the nonlinear equality functions are multiplied from the right. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Right products of the Hessian matrices of the quadratic models of the nonlinear equality functions with `v`. rrr ) rr9r!rrr r rrcrs r2 ceq_hess_prodModels.ceq_hess_prodrrc ZUR(aGURUR4:XdS5eUb"URUR4:XdS5e[R "UR U5Vs/sHnURXR5PM sn5$s snf)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) rr9r!rrrr rrcrs r2ceq_curvModels.ceq_curvrrc[URURUR5Ul[ UR 5HBn[URURSS2U4UR5URU'MD [ UR5HBn[URURSS2U4UR5URU'MD UR(aUR5 gg)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. N) rjrcrrrr$rrrrrrr)r&rs r2 reset_modelsModels.reset_modelssd00$,, L t**+A$"" QT" DIIaL, t**+A$"" QT" DIIaL, ;;  0 0 2 r5c UR(aSUs=::aUR:dS5e S5eURUR4:XdS5e[ U[ 5(dS5eURUR 4:XdS5eURUR4:XdS5e[R"UR5n[R"URR5n[R"URR5nX0RU5- Xa'X@RU5- XqSS24'XPRU5- XSS24'X0RU'X@RUSS24'XPRUSS24'[R "UR"R$SS2U45n X R"R&- UR"R$SS2U4'UR(R+UR"UU U5n [-UR 5H>n U =(d2 UR.U R+UR"UU USS2U 45n M@ [-UR5H>n U =(d2 UR0U R+UR"UU USS2U 45n M@ UR(aUR35 U $)aG Update the interpolation set. This method updates the interpolation set by replacing the `knew`-th interpolation point with `xnew`. It also updates the function values and the quadratic models. Parameters ---------- k_new : int Index of the updated interpolation point. x_new : `numpy.ndarray`, shape (n,) New interpolation point. Its value is interpreted as relative to the origin, not the base point. fun_val : float Value of the objective function at `x_new`. Objective function value at `x_new`. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,) Values of the nonlinear inequality constraints at `x_new`. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,) Values of the nonlinear equality constraints at `x_new`. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. rr"The shape of `x_new` is not valid.z The function value is not valid.z$The shape of `cub_val` is not valid.z$The shape of `ceq_val` is not valid.N)rr?r9r! isinstancefloatrrrr rrrrr!rrrcr%rrrr$rrr) r&rx_newrrrfun_diffcub_diffceq_diffrrrs r2update_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''$,,00E:;+03E3E3L3L+Lq%x())**         t**+A-11D1D""A 2O,t**+A-11D1D""A 2O, ;;  0 0 2r5cxUR(aLURUR4:XdS5eUb'SUs=::aUR:dS5e S5eXRR - n[ R"URUR-S-S45nSURRRU-S--USUR2S4'SX@RS4'X4URS-S2S4'[RURU5SnSX3-S--USS2S4USS2S4-- nUc[ R"URUR-S-UR5n[ R"[RURU5S5nUSUR2S4n Oa[ R"URUR-S-SU*5n[RURU5SUS4nXRS4n X-U S--$) 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. r3Nrrrr rrY)rr9r!r?rcrrrbr%rarjreyediag) r&r6rrnew_col inv_new_colbeta coord_vecalphataus r2 determinantsModels.determinants@s=H ;;;;466)+ 54 5+ e!6dhh!6 10 16!6 10 16**111((DHHtvv-1156t))--//%7C??  $(( A "! $)1 q !--d.@.@'J1M em++gadmk!Q$>O.OO =txx$&&014dhh?IGG''&&E jj!m,Ctxx$&&014a%@I++""  Qh E Qh'C|c3h&&r5cUR(a"URUR4:XdS5eURR UR U5 UR HnUR UR U5 M! URHnUR UR U5 M! XR R- nUR =RU- slUR =RUSS2[R4-sl U[R(aUR5 gg)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. rN)rr9r!rrrcrrrr%rrrrr)r&rr(rrs r2rModels.shift_x_bases  ;;##( 98 9 t11:>YYE   t11: >YYE   t11: >//666 !!U*! %2:: "66 7== !  0 0 2 "r5c>Uc UR$URU$)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 r2rModels._get_cub!Ltyy=diio=r5c>Uc UR$URU$)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. )rrJs r2r Models._get_ceqrLr5c $SnSnSn[UR5GH2n[R"U[R"UR UR RU55URU- 5/5n[R"[R"URUR RU55URUSS24- 5US9n[R"[R"URUR RU55URUSS24- 5US9nGM5 S[R"[5-[URUR5-nX[R"[R"UR5SS9-:a[ R""S[$S5 X%[R"[R"UR5SS9-:a[ R""S[$S5 X5[R"[R"UR5SS9-:a[ R""S [$S5 gg) z= Check the interpolation conditions of all quadratic models. rNrWg$@rYzJThe interpolation conditions for the objective function are not satisfied.rzVThe interpolation conditions for the inequality constraint function are not satisfied.zTThe interpolation conditions for the equality constraint function are not satisfied.)r$r?rr]rrrcrHrrrr!rsqrtr`r!warningswarnRuntimeWarning)r& error_fun error_cub error_ceqr.tols r2r&Models._check_interpolation_conditionss   txxAFF!3!3!9!9!!<= QOIHHT//55a89DLLA > 1r5r)rQnumpyr scipy.linalgrsettingsrutilsrrrfinfor5epsr`r r[rhrjrrRr5r2r_sj?? hhuor,r,jD4 F.7buFuFp KKr5