ftjddlZddlZddlmZddlmZddlmZm Z m Z ej e j ZGddZdZGd d ZGd d ZdS) N)eigh)Options) MaxEvalError TargetSuccessFeasibleSuccessceZdZdZdZedZedZedZej dZedZ e j dZ d Z d S) 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|tj|_dtj|jj|jjz z}|tj|krL||tjj <tj|tj |g|tj j <tj |j |_ |j|jjd|tjzzk}|jj||j|<|jjd|tjzz|jk|j|jj|tjzkz}tj|jj||tjz|jj||j|<|j|jjd|tjzz k}|jj||j|<|j|jjd|tjzz k|jj|tjz |jkz}tj|jj||tjz |jj||j|<tj|j|tjf|_t+d|tjD]{}||jkrL||dz r!|tj |j|dz |f<:|tj|j|dz |f<Z|d|jzkr|||jz dz r+d|tjz|j||jz dz |f<|||jz dz r+d|tjz|j||jz dz |f<|tj |j||jz dz |f<||jz dz |jz} |d| z|jzz dz } | | z|jz} |j| | dzf|j| |f<|j| | dzf|j| |f<}d|_dS)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 _lhs_cache) selfpboptions max_radiusvery_close_xl_idx close_xl_idxvery_close_xu_idx close_xu_idxkspreadk1k2s V/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/_lib/cobyqa/models.py__init__zInterpolation.__init__sgm, 26"),"=>>> 7> "Z / /,6GGN( ),.FGN+--GGN( )wru~~ K29<#0G*GG G *,6G)H %& IL3!88 84; F [BIL77>+BB BD %'J IL &)@ @ IL &% %  L! K29<#0G*GG G *,6G)H %& K"),ww~/F)FF F Y\GGN3 3t{ BD %'J IL &)@ @ IL &% %  L! HbdGGK$89:: q''+.// 7 7ABDyy$QU+A*1'.*A)ADHQUAX&&)0)@DHQUAX&&a"$h$QX\2I03ggn6M0MDHQX\1_--&q24x!|4I04ww~7N0NDHQX\1_--181H0HDHQX\1_--bd(Q,24/!f*,,q06kRT)"&(2rAv:"6Q"&(2rAv:"6Qc&|jjdS)t Number of variables. Returns ------- int Number of variables. rr$shaper&s r2r zInterpolation.n]x~a  r4c&|jjdS) Number of interpolation points. Returns ------- int Number of interpolation points. rr7r9s r2nptzInterpolation.nptir:r4c|jS)z Interpolation points. Returns ------- `numpy.ndarray`, shape (n, npt) Interpolation points. )r"r9s r2r$zInterpolation.xptus yr4cd|jr!|j|j|jfks Jd||_dS)z Set the interpolation points. Parameters ---------- xpt : `numpy.ndarray`, shape (n, npt) New interpolation points. z The shape of `xpt` is not valid.N)rr8r r=r")r&r$s r2r$zInterpolation.xptsR ; 29!2 r4c|jS)z Base point around which the models are expanded. Returns ------- `numpy.ndarray`, shape (n,) Base point around which the models are expanded. )rr9s r2rzInterpolation.x_bases |r4cX|jr|j|jfks Jd||_dS)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)rr8r r)r&rs r2rzInterpolation.x_basesK ; 5<$4 r4c~|jrd|cxkr |jks nJd|j|jdd|fzS)a< Get the `k`-th interpolation point. The return point is relative to the origin. Parameters ---------- k : int Index of the interpolation point. Returns ------- `numpy.ndarray`, shape (n,) `k`-th interpolation point. rzThe index `k` is not valid.N)rr=rr$)r&r.s r2pointzInterpolation.pointsZ ; D$$$$DH$$$$$&C$$${TXaaad^++r4N) __name__ __module__ __qualname____doc__r3propertyr r=r$setterrrCr4r2r r sEEEN ! !X ! ! !X !  X  ZZ   X  ]  ] ,,,,,r4r cB|j}|7tj|j|dr|d|d|dfStjtj|jdt}|j|z }|j\}}tj ||zd z||zd zf}d |j |zd zz|d|d|f<d |d||f<|j |d||d zdf<d ||d|f<|||d zdd|f<tj ||zd z}d |d zz |d|<|d z||<|||d zd<t|d \}} tj |jtj |tj ||| fd} | |_|||| ffS)a Build the left-hand side matrix of the interpolation system. The matrix below stores W * diag(right_scaling), where W is the theoretical matrix of the interpolation system. The right scaling matrices is chosen to keep the elements in the matrix well-balanced. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. Nr$a right_scalingrr)axisinitialrr r?F) check_finite)r$rLrMr)r%r array_equalr$maxlinalgnormEPSr8rTemptyrr) interpolation_cachescale xpt_scaler r=rLrM eig_values eig_vectors new_caches r2 build_systemras %Fbn6%=c{F?3VF^CC F29>>-"3!><`_. cR||_|jr|j|jfks Jd|j|jdzkrt d|jdzd|||\|_|_|_}tj |j|jf|_ dS)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) rr8r=r ValueError _get_model_const_grad_i_hessrr_e_hess)r&rZvaluesdebug_s r2r3zQuadratic.__init__s$ ; 5<!$4  }2 2 2* ?Q&*** 48??  4 4 0 TZqx 011 r4c|jr|j|jfks Jd||jz }|j|j|zzd|j|jj|zdzz||j z|zzzzS)a Evaluate the quadratic model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the quadratic model is evaluated. interpolation : `cobyqa.models.Interpolation` Interpolation set. Returns ------- float Value of the quadratic model at `x`. The shape of `x` is not valid.r r) rr8r rrirjrkr$rXrlr&xrZx_diffs r2__call__zQuadratic.__call__*s ; J7tvi''')I'''])) Kj6! " 1 3f <DD4<'&01  r4c|jjS)r6)rjsizer9s r2r z Quadratic.nGszr4c|jjS)z Number of interpolation points used to define the quadratic model. Returns ------- int Number of interpolation points used to define the quadratic model. )rkrwr9s r2r=z Quadratic.nptSs|  r4c|jr|j|jfks Jd||jz }|j|||zS)a 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`. rq)rr8r rrj hess_prodrrs r2gradzQuadratic.grad_sW ; J7tvi''')I''']))zDNN6=AAAAr4cr|j|j|jddtjf|jjzzzS)a; 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)rlr$rkrnewaxisrX)r&rZs r2hesszQuadratic.hessts<|m/ LBJ '-*;*= =   r4c|jr|j|jfks Jd|j|z|j|j|jj|zzzzS)a. Evaluate the right product of the Hessian matrix of the quadratic model with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the quadratic model is multiplied from the right. interpolation : `cobyqa.models.Interpolation` Interpolation set. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the quadratic model with `v`. The shape of `v` is not valid.)rr8r rlr$rkrXr&vrZs r2rzzQuadratic.hess_prodsb& ; J7tvi''')I'''|a-"3 LM-/!3 4#   r4c|jr|j|jfks Jd||jz|z|j|jj|zdzzzS)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)rr8r rlrkr$rXrs r2curvzQuadratic.curvsb" ; J7tvi''')I'''  q lm/1A5#== > r4c|jrTd|cxkr |jks nJd|j|jfks Jd|j|jfks Jd|xj|j|t j||zz c_d|j|<|||\}}}}|xj |z c_ |xj |z c_ |xj|z c_|S)a Update the quadratic model. This method applies the derivative-free symmetric Broyden update to the quadratic model. The `knew`-th interpolation point must be updated before calling this method. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Updated interpolation set. k_new : int Index of the updated interpolation point. dir_old : `numpy.ndarray`, shape (n,) Value of ``interpolation.xpt[:, k_new]`` before the update. values_diff : `numpy.ndarray`, shape (npt,) Differences between the values of the interpolated nonlinear function and the previous quadratic model at the updated interpolation points. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. rThe index `k_new` is not valid.z$The shape of `dir_old` is not valid.z(The shape of `values_diff` is not valid.) rr=r8r rlrkrouterrhrirj) r&rZk_newdir_old values_diffconstr{i_hessill_conditioneds r2updatezQuadratic.updates34 ; :(((((((((*K(((=%5$)9  U+bhw.H.HHH ! U04  0 0 ,tV_ u  d   r4c^|jr|j|jfks Jd||||_||||_||jz }tj||j d|ddtj fzz |j z}|xj ||j zz c_ dS)aB Shift the point around which the quadratic model is defined. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Previous interpolation set. new_x_base : `numpy.ndarray`, shape (n,) Point that will replace ``interpolation.x_base``. 'The shape of `new_x_base` is not valid.r N)rr8r rir{rjrrrr$r}rkrlrX)r&rZ new_x_baseshiftrs r2 shift_x_basezQuadratic.shift_x_bases ; 9#(8d:}55 YYz=99 ]11   uQQQ ]';!; ;t| K   )) r4c|jj\}}|jdkr|jd||zdzks Jdt|\}}}||ddtjfz}t jt j|r&t jt j|stj d|\}} t j |tk} | dd| f} d|| z } t j| d} | | j |z| ddtjfzz} | |ddtjfz| fS)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. r rrz The shape of `rhs` is not valid.Nz(The interpolation system is ill-defined.rQ) r$r8ndimrarr}allisfiniterU LinAlgErrorabsrWrX)rZrhsr r=rLrMeig rhs_scaledr^r_large_eig_valuesinv_eig_valuesrleft_scaled_solutionss r2 solve_systemszQuadratic.solve_systemsss0"(3 HMMcilcAgk999 -:9 9!-] ; ;=#=BJ77 r{1~~&& 26"+j2I2I+J+J )'':  #& K6*--3!!!!%5"56 z*:;;6"2A666 + ]Z '>!!!RZ-+H H!  "M!!!RZ-$@ @   r4c :|j|jfks Jd|jj\}}t|t j|t j|dzggj\}}||df||dzddf|d|df|fS)a 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. rerrN) r8r=r$rcrrblockrrX)rZrmr r=rsrs r2rhzQuadratic._get_modelDs4|      0   "(3&44  HQ     ?ay!C!GHHaK.!DSD!G*oEEr4N)rDrErFrGr3rurHr r=r{r~rzrrr staticmethodrrhrJr4r2rcrcs    2 2 2D   :  X  ! !X !BBB*   $   2   0222h***0> > \> @(F(F\(F(F(Fr4rccleZdZdZdZedZedZedZedZ edZ edZ ed Z ed Z d Zd Zd ZdZdZdZd#dZd#dZd#dZd#dZd#dZd#dZd#dZd#dZd#dZd#dZdZdZd#dZ dZ!d#d Z"d#d!Z#d"Z$dS)$Modelsz6 Models for a nonlinear optimization problem. c |tj|_t|||_|jd}|||\}}}tj|tj tj |_ tj|tj |j ftj |_ tj|tj |j ftj |_t|tj D]}||tjkrt"|dkr'||j|<||j|ddf<||j|ddf<nJ|j|}|||\|j|<|j|ddf<|j|ddf<|jrh||j||j|ddf|j|ddf|tjkrt0|j ||tjkrh||j||j|ddf|j|ddf|tjkrt4t7|j|j |tj|_tj|jt6|_tj|j t6|_!t|jD]?} t7|j|jdd| f|tj|j| <@t|j D]?} t7|j|jdd| f|tj|j!| <@|jr|"dSdS)aE 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 _interpolationrZrCrfullr!nan_fun_valrw_cub_val_ceq_valr#MAX_EVALrfun_valcub_valceq_valis_feasibilitymaxcvFEASIBILITY_TOLrTARGETrrc_funrYm_nonlinear_ub_cubm_nonlinear_eq_ceq_check_interpolation_conditions) r&r'r(penaltyx_evalfun_initcub_initceq_initr.is r2r3zModels.__init__us6gm, +B88#))!,,')r&'':':$(H 4bf== !5x} ErvNN !5x} ErvNN ww{+,,& $& $AGG,---""Avv"* Q%- QT"%- QT""+11!44JL"KKG Qad!3T\!QQQ$5G! &HH&,,Q//LAAA&LAAA& 723 44&%  a GGN$;;;HH&,,Q//LAAA&LAAA& 723 44$#   M GM "   HT0 BBB HT0 BBB t*++  A$" QQQT" &DIaLL t*++  A$" QQQT" &DIaLL ; 3  0 0 2 2 2 2 2 3 3r4c|jjS)z~ Dimension of the problem. Returns ------- int Dimension of the problem. )rZr r9s r2r zModels.ns!##r4c|jjS)r<)rZr=r9s r2r=z Models.npts!%%r4c&|jjdS)z Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. r)rr8r9s r2rzModels.m_nonlinear_ub|!!$$r4c&|jjdS)z Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. r)rr8r9s r2rzModels.m_nonlinear_eqrr4c|jS)z Interpolation set. Returns ------- `cobyqa.models.Interpolation` Interpolation set. )rr9s r2rZzModels.interpolations ""r4c|jS)z Values of the objective function at the interpolation points. Returns ------- `numpy.ndarray`, shape (npt,) Values of the objective function at the interpolation points. )rr9s r2rzModels.fun_vals }r4c|jS)a1 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. )rr9s r2rzModels.cub_val  }r4c|jS)a- 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. )rr9s r2rzModels.ceq_val.rr4c||jr|j|jfks Jd|||jS)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`. rq)rr8r rrZr&rss r2funz Models.fun<sF ; J7tvi''')I'''yyD.///r4c|jr|j|jfks Jd|j||jS)a 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`. rq)rr8r rr{rZrs r2fun_gradzModels.fun_gradPsH ; J7tvi''')I'''y~~a!3444r4c@|j|jS)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. )rr~rZr9s r2fun_hesszModels.fun_hessdsy~~d0111r4c|jr|j|jfks Jd|j||jS)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)rr8r rrzrZr&rs r2 fun_hess_prodzModels.fun_hess_prodpsJ" ; J7tvi''')I'''y""1d&8999r4c|jr|j|jfks Jd|j||jS)a 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)rr8r rrrZrs r2fun_curvzModels.fun_curvsH" ; J7tvi''')I'''y~~a!3444r4c|jr|j|jfks Jdt|j|j|j}|||jS)ap 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. rq)rr8r rcrZrr{)r&rsmodels r2 fun_alt_gradzModels.fun_alt_grads^, ; J7tvi''')I'''$,dlDKHHzz!T/000r4Ncjr8jjfks Jd||jjfks Jdt jfd|DS)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. rqN!The shape of `mask` is not valid.c2g|]}|jSrJrZ.0rr&rss r2 zModels.cub..( K K KeUU1d( ) ) K K Kr4rr8r rrarray_get_cubr&rsmasks`` r2cubz Models.cubs& ; 37tvi''')I'''<4:#2$$$2$$x K K K K Kt}}T7J7J K K K   r4cjr8jjfks Jd||jjfks Jdt jfd|DdjfS)a` Evaluate the gradients of the quadratic models of the nonlinear inequality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the gradients of the quadratic models of the nonlinear inequality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Gradients of the quadratic model of the nonlinear inequality functions. rqNrcFg|]}|jSrJr{rZrs r2rz#Models.cub_grad..: / / /ZZ4- . . / / /r4rr8r rrreshaperrs`` r2cub_gradzModels.cub_grad& ; 37tvi''')I'''<4:#2$$$2$$z / / / / /---- / / / L   r4cjr||jjfks Jdtjfd|DdjjfS)a Evaluate the Hessian matrices of the quadratic models of the nonlinear inequality functions. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Hessian matrices of the quadratic models of the nonlinear inequality functions. NrcDg|]}|jSrJr~rZrrr&s r2rz#Models.cub_hess..( M M MUZZ* + + M M Mr4r)rr8rrrrr r&rs` r2cub_hesszModels.cub_hess ; 3<4:#2$$$2$$z M M M Mt9L9L M M M     r4cjr8jjfks Jd||jjfks Jdt jfd|DdjfS)a Evaluate the right product of the Hessian matrices of the quadratic models of the nonlinear inequality functions with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrices of the quadratic models of the nonlinear inequality functions are multiplied from the right. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Right products of the Hessian matrices of the quadratic models of the nonlinear inequality functions with `v`. rNrcFg|]}|jSrJrzrZrrr&rs r2rz(Models.cub_hess_prod..!:   4#566   r4rrr&rrs`` r2 cub_hess_prodzModels.cub_hess_prod& ; 37tvi''')I'''<4:#2$$$2$$z     !]]400   L    r4cjr8jjfks Jd||jjfks Jdt jfd|DS)az Evaluate the curvature of the quadratic models of the nonlinear inequality functions along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the quadratic models of the nonlinear inequality functions is evaluated. mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Curvature of the quadratic models of the nonlinear inequality functions along `v`. rNrcFg|]}|jSrJrrZrs r2rz#Models.cub_curv..Arr4rrs`` r2cub_curvzModels.cub_curv(& ; 37tvi''')I'''<4:#2$$$2$$x / / / / /---- / / /   r4cjr8jjfks Jd||jjfks Jdt jfd|DS)a) Evaluate the quadratic models of the nonlinear equality functions at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which to evaluate the quadratic models of the nonlinear equality functions. mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to consider. Returns ------- `numpy.ndarray` Values of the quadratic model of the nonlinear equality functions. rqNrc2g|]}|jSrJrrs r2rzModels.ceq..]rr4rr8r rrr_get_ceqrs`` r2ceqz Models.ceqEs$ ; 37tvi''')I'''<4:#2$$$2$$x K K K K Kt}}T7J7J K K K   r4cjr8jjfks Jd||jjfks Jdt jfd|DdjfS)aZ 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. rqNrcFg|]}|jSrJrrs r2rz#Models.ceq_grad..yrr4rrr8r rrrr rs`` r2ceq_gradzModels.ceq_grad`rr4cjr||jjfks Jdtjfd|DdjjfS)a 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. NrcDg|]}|jSrJrrs r2rz#Models.ceq_hess..rr4r)rr8rrrr r rs` r2ceq_hesszModels.ceq_hess~rr4cjr8jjfks Jd||jjfks Jdt jfd|DdjfS)a 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`. rNrcFg|]}|jSrJrrs r2rz(Models.ceq_hess_prod..rr4rrrs`` r2 ceq_hess_prodzModels.ceq_hess_prodrr4cjr8jjfks Jd||jjfks Jdt jfd|DS)at 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`. rNrcFg|]}|jSrJrrs r2rz#Models.ceq_curv..rr4r rs`` r2ceq_curvzModels.ceq_curvrr4ct|j|j|j|_t |jD]4}t|j|jdd|f|j|j|<5t |j D]4}t|j|j dd|f|j|j |<5|jr| dSdS)a9 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) rcrZrrrr#rrrrrrr)r&rs r2 reset_modelszModels.reset_modelssd0$, LL t*++  A$" QQQT" DIaLL t*++  A$" QQQT" DIaLL ; 3  0 0 2 2 2 2 2 3 3r4c |jrd|cxkr |jks nJd|j|jfks Jdt |t s Jd|j|jfks Jd|j|jfks Jdtj |j}tj |j j}tj |j j}|| |z ||<|| |z ||ddf<|||z ||ddf<||j|<||j |ddf<||j |ddf<tj|jjdd|f} ||jjz |jjdd|f<|j|j|| |} t-|jD]6} | p1|j| |j|| |dd| f} 7t-|jD]6} | p1|j| |j|| |dd| f} 7|jr|| S)a Update the interpolation set. This method updates the interpolation set by replacing the `knew`-th interpolation point with `xnew`. It also updates the function values and the quadratic models. Parameters ---------- k_new : int Index of the updated interpolation point. x_new : `numpy.ndarray`, shape (n,) New interpolation point. Its value is interpreted as relative to the origin, not the base point. fun_val : float Value of the objective function at `x_new`. Objective function value at `x_new`. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,) Values of the nonlinear inequality constraints at `x_new`. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,) Values of the nonlinear equality constraints at `x_new`. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. rr"The shape of `x_new` is not valid.z The function value is not valid.z$The shape of `cub_val` is not valid.z$The shape of `ceq_val` is not valid.N)rr=r8r isinstancefloatrrrrrrrrr rrrZr$rrrr#rrr) r&rx_newrrrfun_diffcub_diffceq_diffrrrs r2update_interpolationzModels.update_interpolations8 ; 6(((((((((*K(((;46)+++4,++gu-- 3 32 3 3-=#%5=#%5 8DH%%8DL.//8DL.//!DHHUOO3$txx6$txx6& U!( UAAAX!( UAAAX'$,0E:;;+043E3L+Lqqq%x()**         t*++  A-11D1D"A 22OO t*++  A-11D1D"A 22OO ; 3  0 0 2 2 2r4c|jr;|j|jfks Jd|d|cxkr |jks nJd||jjz }t j|j|jzdzdf}d|jjj |zdzz|d|jdf<d||jdf<|||jdzddf<t |j|d}d||zdzz|dddf|dddfzz }|tt j |j|jzdz|j}t j t |j|d}|d|jdf} n_t j |j|jzdzd| }t |j|d|df}||df} ||z| dzzS) a Compute the normalized determinants of the new interpolation systems. Parameters ---------- x_new : `numpy.ndarray`, shape (n,) New interpolation point. Its value is interpreted as relative to the origin, not the base point. k_new : int, optional Index of the updated interpolation point. If `k_new` is not specified, all the possible determinants are computed. Returns ------- {float, `numpy.ndarray`, shape (npt,)} Determinant(s) of the new interpolation system. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. Notes ----- The determinants are normalized by the determinant of the current interpolation system. For stability reasons, the calculations are done using the formula (2.12) in [1]_. References ---------- .. [1] M. J. D. Powell. On updating the inverse of a KKT matrix. Technical Report DAMTP 2004/NA01, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK, 2004. rNrrrr rrQ)rr8r r=rZrrrYr$rXrcreyediag) r&r rrnew_col inv_new_colbeta coord_vecalphataus r2 determinantszModels.determinantsBs;H ; 1;46)+++4,++ e!6!6!6!6dh!6!6!6!6!60"7!66*11(DHtv-11566t)-/%7C??  $( A "! $)1 q !--d.@'JJ1M eem++gaaadmk!!!Q$>O.OO =tx$&014dh??IG''&E jj!m,CCtx$&014a%@@I++"  Qh E eQh'Ct|c3h&&r4c|jr|j|jfks Jd|j|j||jD]}||j||jD]}||j|||jjz }|jxj|z c_|jxj |ddtj fzc_ |tj r|dSdS)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)rr8r rrrZrrrr$rr}rrr)r&rr(rrs r2rzModels.shift_x_bases6 ; 9#(8 t1:>>>Y ? ?E   t1: > > > >Y ? ?E   t1: > > > >T/66 !!U*!! %2: "66 7= ! 3  0 0 2 2 2 2 2 3 3r4c.||jn |j|S)ao Get the quadratic models of the nonlinear inequality constraints. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to return. Returns ------- `numpy.ndarray` Quadratic models of the nonlinear inequality constraints. )rrs r2rzModels._get_cub!Ltyydio=r4c.||jn |j|S)ak Get the quadratic models of the nonlinear equality constraints. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to return. Returns ------- `numpy.ndarray` Quadratic models of the nonlinear equality constraints. )rrs r2r zModels._get_ceqr1r4c d}d}d}t|jD].}tj|tj||j||j|z g}tjtj| |j||j |ddfz |}tjtj| |j||j |ddfz |}0dtj tzt|j|jz}||tjtj|jdzkrt!jdt$d||tjtj|j dzkrt!jdt$d||tjtj|j dzkrt!jd t$ddSdS) zM Check the interpolation conditions of all quadratic models. rNrOg$@rQzJThe interpolation conditions for the objective function are not satisfied.r zVThe interpolation conditions for the inequality constraint function are not satisfied.zTThe interpolation conditions for the equality constraint function are not satisfied.)r#r=rrTrrrZrCrrrr rsqrtrWr warningswarnRuntimeWarning)r& error_fun error_cub error_ceqr.tols r2rz&Models._check_interpolation_conditionss[   tx  AF!3!9!9!!>>> >>>> 11111r4r)r5numpyr scipy.linalgrsettingsrutilsrrrfinforepsrWr rarcrrJr4r2rBs&??????????bhuoos,s,s,s,s,s,s,s,l272727juFuFuFuFuFuFuFuFp KKKKKKKKKKr4