o ñ h]7ã@sDddlZddlZddlmZe e¡jZdd„Z dd„Z dd „Z dS) éNé)Úget_arrays_tolc sŠ|rmt|tƒs J‚t|tjƒr|jdksJ‚t ˆ¡ |¡s J‚t|tjƒr,|j|jks.J‚t|tjƒr:|j|jks float`` returns :math:`s^{\mathsf{T}} H s`. xl : `numpy.ndarray`, shape (n,) Lower bounds :math:`l` as shown above. xu : `numpy.ndarray`, shape (n,) Upper bounds :math:`u` as shown above. delta : float Trust-region radius :math:`\Delta` as shown above. debug : bool Whether to make debugging tests during the execution. Returns ------- `numpy.ndarray`, shape (n,) Approximate solution :math:`s`. Notes ----- This function is described as the first alternative in Section 6.5 of [1]_. It is assumed that the origin is feasible with respect to the bound constraints and that `delta` is finite and positive. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. éçcs ˆ|ƒ S)N©)Úx©ÚcurvrúY/var/www/vscode/kcb/lib/python3.10/site-packages/scipy/_lib/cobyqa/subsolvers/geometry.pyÚ[s z!cauchy_geometry..çš™™™™™ñ?)Ú isinstanceÚfloatÚnpÚndarrayÚndimÚinspectÚ signatureÚbindÚshapeÚboolrÚallÚisfiniteÚminimumÚmaximumÚ _cauchy_geomÚabsÚlinalgÚnorm) ÚconstÚgradr ÚxlÚxuÚdeltaÚdebugÚtolÚstep1Úq_val1Ústep2Úq_val2Ústeprrr Úcauchy_geometry s<:    ù r+c"Cs°|r‚t|tƒs J‚t|tjƒr|jdksJ‚t |¡ |¡s J‚t|tjƒr3|jdkr3|jd|j ks5J‚t|tjƒrA|j|jksCJ‚t|tjƒrO|j|jksQJ‚t|tƒsXJ‚t|t ƒs_J‚t ||ƒ}t  ||k¡smJ‚t  || k¡swJ‚t  |¡r€|dks‚J‚t |d¡}t |d¡}t |¡} |} tjj|dd} |tj k|jt |k@} |tj k|jt|k@} |tjk|jt|k@}|tjk|jt |k@}t t || j¡| |j| ¡}tj|dtj d}t t |¡|jd¡}t t || j¡| |j| ¡}tj|dtjd}t t |¡|jd¡}t t ||j¡||j|¡}tj|dtj d}t t |¡|jd¡}t t ||j¡||j|¡}tj|dtjd}t t |¡|jd¡}t|jdƒD]>}| |t|krˆt|| |dƒ}nqrtt||||ƒdƒ}tt||||ƒdƒ}||dd…|f}||dd…|fƒ}|dkrÃ|t |ksÐ|dkrÙ|t |krÙt| |dƒ}ntj}|dkrè|t|ksô|dkrý|t|krýt| |dƒ}ntj }t||ƒ}t| |ƒ}|||d|d |}|||d|d |}||krH|||d|d |} t| ƒt|ƒkrH|}| }||krh|||d|d |}!t|!ƒt|ƒkrh|}|!}t|ƒt|ƒkrt|ƒt| ƒkrt ||dd…|f||¡} |} qrt|ƒt|ƒkr°t|ƒt| ƒkr°t ||dd…|f||¡} |} qr|rÖt  || k¡s¿J‚t  | |k¡sÉJ‚tj | ¡d |ksÖJ‚| S) aÕ Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region. This function solves approximately .. math:: \max_{s \in \mathbb{R}^n} \quad \bigg\lvert c + g^{\mathsf{T}} s + \frac{1}{2} s^{\mathsf{T}} H s \bigg\rvert \quad \text{s.t.} \quad \left\{ \begin{array}{l} l \le s \le u,\\ \lVert s \rVert \le \Delta, \end{array} \right. by maximizing the objective function along given straight lines. Parameters ---------- const : float Constant :math:`c` as shown above. grad : `numpy.ndarray`, shape (n,) Gradient :math:`g` as shown above. curv : callable Curvature of :math:`H` along any vector. ``curv(s) -> float`` returns :math:`s^{\mathsf{T}} H s`. xpt : `numpy.ndarray`, shape (n, npt) Points defining the straight lines. The straight lines considered are the ones passing through the origin and the points in `xpt`. xl : `numpy.ndarray`, shape (n,) Lower bounds :math:`l` as shown above. xu : `numpy.ndarray`, shape (n,) Upper bounds :math:`u` as shown above. delta : float Trust-region radius :math:`\Delta` as shown above. debug : bool Whether to make debugging tests during the execution. Returns ------- `numpy.ndarray`, shape (n,) Approximate solution :math:`s`. Notes ----- This function is described as the second alternative in Section 6.5 of [1]_. It is assumed that the origin is feasible with respect to the bound constraints and that `delta` is finite and positive. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. rrrr)Úaxis)r,ÚinitialNçà?ç@r )r rrrrrrrrÚsizerrrrrrÚ zeros_likerrÚinfÚTÚTINYÚ atleast_2dÚ broadcast_toÚmaxÚ atleast_1dÚrangeÚminrÚclip)"rr r Úxptr!r"r#r$r%r*Úq_valÚs_normÚi_xl_posÚi_xl_negÚi_xu_posÚi_xu_negÚ alpha_xl_posÚ alpha_xl_negÚ alpha_xu_negÚ alpha_xu_posÚkÚalpha_trÚ alpha_bd_posÚ alpha_bd_negÚ grad_stepÚ curv_stepÚalpha_quad_posÚalpha_quad_negÚ alpha_posÚ alpha_negÚ q_val_posÚ q_val_negÚq_val_quad_posÚq_val_quad_negrrr Úspider_geometryjsÎ< ÿ     ÿÿÿÿ     ÿÿ ÿþÿ ÿþÿ$$€rUcCsŒ|dk|dk@}|dk|dk@}t |¡} ||| |<||| |<tj | ¡|kr‹||B} tj || ¡} t |d| | | | ¡} | tt| ƒkrWt| | dƒ} nn3| || | | <| | |k@}| | |k@}t |¡swt |¡swn||| |<||| |<| ||B@} q.|| }|dkrtj | ¡}|t|kr¨t||dƒ}nd}|| ƒ}|t |kr¾t| |dƒ}ntj }|tj k| t|k@}|tj k| t|k@}tj ||| |tj d}tj ||| |tj d}t ||ƒ}t |||ƒ}t  || ||¡}|||d|d|}nt |¡}|}|rBt  ||k¡s+J‚t  ||k¡s5J‚tj |¡d|ksBJ‚||fS)zM Same as `bound_constrained_cauchy_step` without the absolute value. rTr/)r-r.r ) rr1rrÚsqrtr4rr7Úanyr2r:r;r)rr r r!r"r#r$Úfixed_xlÚfixed_xuÚ cauchy_stepÚworkingÚg_normÚ delta_reducedÚmurKr>rHrLÚ alpha_quadÚi_xlÚi_xuÚalpha_xlÚalpha_xuÚalpha_bdÚalphar*r=rrr r8sb   ÿ    ì      r) rÚnumpyrÚutilsrÚfinforÚtinyr4r+rUrrrrr Ús  _ O