o ?Hh@sddlZddlZddlmZddlmZddlmZm Z m Z e e j ZGdddZdddddZd d ZGd d d ZGd ddZdS)N)eigh)Options) MaxEvalError TargetSuccessFeasibleSuccessc@sleZdZdZddZeddZeddZedd Zej d d Zed d Z e j d d Z ddZ dS) 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 Cs|tj|_dt|jj|jj}|tj|kr.||tjj <t|tj |g|tj j <t |j |_ |j|jjd|tjk}|jj||j|<|jjd|tj|jk|j|jj|tjk@}t|jj||tj|jj||j|<|j|jjd|tjk}|jj||j|<|j|jjd|tjk|jj|tj|jk@}t|jj||tj|jj||j|<t|j|tjf|_td|tjD]}||jkr||dr|tj |j|d|f<q|tj|j|d|f<q|d|jkrP|||jdr#d|tj|j||jd|f<q|||jdr?d|tj|j||jd|f<q|tj |j||jd|f<q||jd|j} |d| |jd} | | |j} |j| | df|j| |f<|j| | df|j| |f<qdS)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_idxkspreadk1k2r.X/home/air/sanwanet/gpt-api/venv/lib/python3.10/site-packages/scipy/_lib/cobyqa/models.py__init__s`         $$"zInterpolation.__init__cC |jjdS)t Number of variables. Returns ------- int Number of variables. rr!shaper"r.r.r/r\ zInterpolation.ncCr1) Number of interpolation points. Returns ------- int Number of interpolation points. rr3r5r.r.r/npthr6zInterpolation.nptcC|jS)z Interpolation points. Returns ------- `numpy.ndarray`, shape (n, npt) Interpolation points. )rr5r.r.r/r!t zInterpolation.xptcCs*|jr|j|j|jfksJd||_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)r r4rr8r)r"r!r.r.r/r!s  cCr9)z Base point around which the models are expanded. Returns ------- `numpy.ndarray`, shape (n,) Base point around which the models are expanded. )rr5r.r.r/rr:zInterpolation.x_basecCs&|jr|j|jfksJd||_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)r r4rr)r"rr.r.r/rs  cCsD|jrd|kr|jksJdJd|j|jdd|fS)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)r r8rr!)r"r*r.r.r/points&zInterpolation.pointN) __name__ __module__ __qualname____doc__r0propertyrr8r!setterrr;r.r.r.r/r s F       r)r!a right_scalingrc Cstddurt|jtdrtdtdtdfStjtjj|jddtd}|j|}|j\}}t ||d ||d f}d |j |d |d|d|f<d |d||f<|j |d||d df<d ||d|f<|||d dd|f<t ||d }d |d |d|<|d ||<|||d d<t |d d\}}t |jtd<t |td<t |td<||ftd<||||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. r!NrBrCrr)axisinitialrr r ?F) check_finite)_cacher array_equalr!maxlinalgnormEPSr4rTemptyrr) interpolationscale xpt_scalerr8rBrC eig_values eig_vectorsr.r.r/ build_systems.   "  rVc@seZdZdZddZddZeddZedd Zd d Z d d Z ddZ ddZ ddZ ddZeddZeddZdS) Quadratica: Quadratic model. This class stores the Hessian matrix of the quadratic model using the implicit/explicit representation designed by Powell for NEWUOA [1]_. References ---------- .. [1] M. J. D. Powell. The NEWUOA software for unconstrained optimization without derivatives. In G. Di Pillo and M. Roma, editors, *Large-Scale Nonlinear Optimization*, volume 83 of Nonconvex Optim. Appl., pages 255--297. Springer, Boston, MA, USA, 2006. `doi:10.1007/0-387-30065-1_16 `_. cCsz||_|jr|j|jfksJd|j|jdkr$td|jdd|||\|_|_|_}t |j|jf|_ dS)a Initialize the quadratic model. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Interpolation set. values : `numpy.ndarray`, shape (npt,) Values of the interpolated function at the interpolation points. debug : bool Whether to make debugging tests during the execution. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. #The shape of `values` is not valid.rz4The number of interpolation points must be at least .N) r r4r8r ValueError _get_model_const_grad_i_hessrr_e_hess)r"rQvaluesdebug_r.r.r/r0s$zQuadratic.__init__cCs^|jr|j|jfksJd||j}|j|j|d|j|jj|d||j |S)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 ) r r4rrr\r]r^r!rOr_r"xrQx_diffr.r.r/__call__(s  zQuadratic.__call__cC|jjS)r2)r]sizer5r.r.r/rE z Quadratic.ncCrh)z Number of interpolation points used to define the quadratic model. Returns ------- int Number of interpolation points used to define the quadratic model. )r^rir5r.r.r/r8Qrjz Quadratic.nptcCs8|jr|j|jfksJd||j}|j|||S)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`. rc)r r4rrr] hess_prodrdr.r.r/grad]s zQuadratic.gradcCs(|j|j|jddtjf|jjS)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)r_r!r^rnewaxisrO)r"rQr.r.r/hessrszQuadratic.hesscCs>|jr|j|jfksJd|j||j|j|jj|S)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.)r r4rr_r!r^rOr"vrQr.r.r/rks  zQuadratic.hess_prodcCs@|jr|j|jfksJd||j||j|jj|dS)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`. ror )r r4rr_r^r!rOrpr.r.r/curvs  zQuadratic.curvc Cs|jr,d|kr|jksJdJd|j|jfks!Jd|j|jfks,Jd|j|j|t||7_d|j|<|||\}}}}|j |7_ |j |7_ |j|7_|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$The shape of `dir_old` is not valid.z(The shape of `values_diff` is not valid.) r r8r4rr_r^routerr[r\r]) r"rQk_newdir_old values_diffconstrli_hessill_conditionedr.r.r/updates,&   zQuadratic.updatecCs|jr|j|jfksJd||||_||||_||j}t||j d|ddtj f|j }|j ||j 7_ dS)aB Shift the point around which the quadratic model is defined. Parameters ---------- interpolation : `cobyqa.models.Interpolation` Previous interpolation set. new_x_base : `numpy.ndarray`, shape (n,) Point that will replace ``interpolation.x_base``. 'The shape of `new_x_base` is not valid.r N)r r4rr\rlr]rrrur!rmr^r_rO)r"rQ new_x_baseshiftr|r.r.r/ shift_x_bases    zQuadratic.shift_x_basecCs|jj\}}|jdkr|jd||dksJdt|\}}}||ddtjf}tt|rr?r0rgr@rr8rlrnrkrrr|r staticmethodrr[r.r.r.r/rWs$"   4 @rWc@sJeZdZdZddZeddZeddZedd Zed d Z ed d Z eddZ eddZ eddZ ddZddZddZddZddZddZdCd!d"ZdCd#d$ZdCd%d&ZdCd'd(ZdCd)d*ZdCd+d,ZdCd-d.ZdCd/d0ZdCd1d2ZdCd3d4Zd5d6Zd7d8ZdCd9d:Z d;d<Z!dCd=d>Z"dCd?d@Z#dAdBZ$d S)DModelsz6 Models for a nonlinear optimization problem. c Cs~|tj|_t|||_|jd}|||\}}}t|tj tj |_ t|tj |j ftj |_ t|tj |j ftj |_t|tj D]}||tjkrSt|dkro||j|<||j|ddf<||j|ddf<n|j|}|||\|j|<|j|ddf<|j|ddf<|jr||j||j|ddf|j|ddf|tjkrt|j ||tjkr||j||j|ddf|j|ddf|tjkrtqHt|j|j |tj|_tj|jtd|_tj|j td|_!t|jD]} t|j|jdd| f|tj|j| <qt|j D]} t|j|jdd| f|tj|j!| <q|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)#rr r r_interpolationrQr;rfullrnan_fun_valri_cub_val_ceq_valr MAX_EVALrfun_valcub_valceq_valis_feasibilitymaxcvFEASIBILITY_TOLrTARGETrrW_funrPm_nonlinear_ub_cubm_nonlinear_eq_ceq_check_interpolation_conditions) r"r#r$penaltyx_evalfun_initcub_initceq_initr*ir.r.r/r0ssz     ,    zModels.__init__cCrh)z~ Dimension of the problem. Returns ------- int Dimension of the problem. )rQrr5r.r.r/rrjzModels.ncCrh)r7)rQr8r5r.r.r/r8rjz Models.nptcCr1)z Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. r)rr4r5r.r.r/rr6zModels.m_nonlinear_ubcCr1)z Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. r)rr4r5r.r.r/rr6zModels.m_nonlinear_eqcCr9)z Interpolation set. Returns ------- `cobyqa.models.Interpolation` Interpolation set. )rr5r.r.r/rQr:zModels.interpolationcCr9)z Values of the objective function at the interpolation points. Returns ------- `numpy.ndarray`, shape (npt,) Values of the objective function at the interpolation points. )rr5r.r.r/rr:zModels.fun_valcCr9)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. )rr5r.r.r/r zModels.cub_valcCr9)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. )rr5r.r.r/r,rzModels.ceq_valcCs*|jr|j|jfksJd|||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`. rc)r r4rrrQr"rer.r.r/fun:sz Models.funcC,|jr|j|jfksJd|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`. rc)r r4rrrlrQrr.r.r/fun_gradNszModels.fun_gradcCs|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. )rrnrQr5r.r.r/fun_hessbs zModels.fun_hesscCr)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`. ro)r r4rrrkrQr"rqr.r.r/ fun_hess_prodnzModels.fun_hess_prodcCr)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`. ro)r r4rrrrrQrr.r.r/fun_curvrzModels.fun_curvcCs<|jr|j|jfksJdt|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. rc)r r4rrWrQrrl)r"remodelr.r.r/ fun_alt_gradszModels.fun_alt_gradNcZjrjjfksJd|dus|jjfksJdtfdd|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. rcN!The shape of `mask` is not valid.cg|]}|jqSr.rQ.0rrr.r/ zModels.cub..r r4rrrarray_get_cubr"remaskr.rr/cubs z Models.cubcbjrjjfksJd|dus|jjfksJdtfdd|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. rcNrcg|] }|jqSr.rlrQrrr.r/rz#Models.cub_grad..r r4rrrreshaperrr.rr/cub_grad  zModels.cub_gradcNjr|dus|jjfksJdtfdd|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. Nrcg|]}|jqSr.rnrQrr5r.r/rrz#Models.cub_hess..r)r r4rrrrrr"rr.r5r/cub_hess  zModels.cub_hesscr)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`. roNrcrr.rkrQrrr.r/r z(Models.cub_hess_prod..rrr"rqrr.rr/ cub_hess_prod  zModels.cub_hess_prodcr)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`. roNrcrr.rrrQrrr.r/r?rz#Models.cub_curv..rrr.rr/cub_curv&  zModels.cub_curvcr)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. rcNrcrr.rrrr.r/r[rzModels.ceq..r r4rrrr_get_ceqrr.rr/ceqCs z Models.ceqcr)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. rcNrcrr.rrrr.r/rwrz#Models.ceq_grad..rr r4rrrrrrr.rr/ceq_grad^rzModels.ceq_gradcr)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. Nrcrr.rrr5r.r/rrz#Models.ceq_hess..r)r r4rrrrrrr.r5r/ceq_hess|rzModels.ceq_hesscr)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`. roNrcrr.rrrr.r/rrz(Models.ceq_hess_prod..rrrr.rr/ ceq_hess_prodrzModels.ceq_hess_prodcr)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`. roNrcrr.rrrr.r/rrz#Models.ceq_curv..rrr.rr/ceq_curvrzModels.ceq_curvcCst|j|j|j|_t|jD]}t|j|jdd|f|j|j|<qt|j D]}t|j|j dd|f|j|j |<q)|jrG| 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) rWrQrr rr rrrrrrr)r"rr.r.r/ reset_modelss     zModels.reset_modelsc Cs|jr@d|kr|jksJdJd|j|jfks!Jdt|ts*Jd|j|jfks5Jd|j|jfks@Jdt |j}t |j j}t |j j}|| |||<|| |||ddf<|||||ddf<||j|<||j |ddf<||j |ddf<t|jjdd|f} ||jj|jjdd|f<|j|j|| |} t|jD]} | p|j| |j|| |dd| f} qt|jD]} | p|j| |j|| |dd| f} q|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. rrs"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$The shape of `ceq_val` is not valid.N)r r8r4r isinstancefloatrrrrrrrrrrrrQr!rrr|r rrr) r"rvx_newrrrfun_diffcub_diffceq_diffrwr{rr.r.r/update_interpolationsh&   zModels.update_interpolationc Cs|jr%|j|jfksJd|dus%d|kr |jks%JdJd||jj}t|j|jddf}d|jjj |d|d|jdf<d||jdf<|||jdddf<t |j|d}d||d|dddf|dddf}|durt |j|jd|j}t t |j|d}|d|jdf} n!t |j|jdd| }t |j|d|df}||df} ||| dS) a Compute the normalized determinants of the new interpolation systems. Parameters ---------- x_new : `numpy.ndarray`, shape (n,) New interpolation point. Its value is interpreted as relative to the origin, not the base point. k_new : int, optional Index of the updated interpolation point. If `k_new` is not specified, all the possible determinants are computed. Returns ------- {float, `numpy.ndarray`, shape (npt,)} Determinant(s) of the new interpolation system. Raises ------ `numpy.linalg.LinAlgError` If the interpolation system is ill-defined. Notes ----- The determinants are normalized by the determinant of the current interpolation system. For stability reasons, the calculations are done using the formula (2.12) in [1]_. References ---------- .. [1] M. J. D. Powell. On updating the inverse of a KKT matrix. Technical Report DAMTP 2004/NA01, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK, 2004. rNrrsrr r rG)r r4rr8rQrrrPr!rOrWreyediag) r"rrvrnew_col inv_new_colbeta coord_vecalphataur.r.r/ determinants@sN$ 0 zModels.determinantscCs|jr|j|jfksJd|j|j||jD] }||j|q|jD] }||j|q&||jj}|jj|7_|jj |ddt j f8_ |t j rX|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. r}N)r r4rrrrQrrrr!rrmrr r)r"r~r$rrr.r.r/rs"      zModels.shift_x_basecC|dur|jS|j|S)ao Get the quadratic models of the nonlinear inequality constraints. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Mask of the quadratic models to return. Returns ------- `numpy.ndarray` Quadratic models of the nonlinear inequality constraints. N)rrr.r.r/rzModels._get_cubcCr)ak Get the quadratic models of the nonlinear equality constraints. Parameters ---------- mask : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Mask of the quadratic models to return. Returns ------- `numpy.ndarray` Quadratic models of the nonlinear equality constraints. N)rrr.r.r/rrzModels._get_ceqc CsXd}d}d}t|jD]L}t|t||j||j|g}tjt| |j||j |ddf|d}tjt| |j||j |ddf|d}q dt tt|j|j}||tjt|jddkr|tdtd||tjt|j ddkrtdtd||tjt|j ddkrtd tddSdS) zM Check the interpolation conditions of all quadratic models. rtNrEg$@rGzJThe 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 r8rrKrrrQr;rrrrrsqrtrNrwarningswarnRuntimeWarning)r" error_fun error_cub error_ceqr*tolr.r.r/rsV""z&Models._check_interpolation_conditions)N)%r<r=r>r?r0r@rr8rrrQrrrrrrrrrrrrrrrrrrrrrrrrrrr.r.r.r/rnsTc                    SJ   r)rnumpyr scipy.linalgrsettingsrutilsrrrfinforepsrNrrIrVrWrr.r.r.r/s   61z