4[g]7jddlZddlZddlmZej ejZdZ dZ dZ y)N)get_arrays_tolc L|rNt|tsJt|tjr|jdk(sJt j j|sJt|tjr|j|jk(sJt|tjr|j|jk(sJt|tsJt|tsJt||}tj||ksJtj|| k\sJtj|r|dkDsJtj|d}tj|d}t||||||\}} t| | fd||||\} } t!| t!| k\r|n| } |r[tj|| ksJtj| |ksJtj"j%| d|zksJ| S)a' 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 the constrained Cauchy direction. 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`. 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. c| S)N)xcurvs `/var/www/html/bid-api/venv/lib/python3.12/site-packages/scipy/_lib/cobyqa/subsolvers/geometry.pyz!cauchy_geometry..[s 47(皙?) isinstancefloatnpndarrayndiminspect signaturebindshapeboolrallisfiniteminimummaximum _cauchy_geomabslinalgnorm) constgradr xlxudeltadebugtolstep1q_val1step2q_val2steps ` r cauchy_geometryr. st %'''$ + Q>>  &++D111"bjj)bhh$**.DDD"bjj)bhh$**.DDD%'''%&&&R$vvbCi   vvbSDj!!!{{5!eck11 B B B B !dBE5IME6      ME6K3v;.5ED vvbDj!!!vvdbj!!!yy~~d#cEk111 Krc|rt|tsJt|tjr|jdk(sJt j |j|sJt|tjr+|jdk(r|jd|jk(sJt|tjr|j|jk(sJt|tjr|j|jk(sJt|tsJt|tsJt||}tj||ksJtj|| k\sJtj|r|dkDsJtj|d}tj|d}tj |} |} tj"j%|d} |tj& kD|j(t* |zkDz} |tj& kD|j(t*|zkz} |tj&k|j(t*|zkDz}|tj&k|j(t* |zkz}tj,tj.|| j| |j(| z }tj0|dtj& }tj.tj2||jd}tj,tj.|| j| |j(| z }tj0|dtj&}tj.tj2||jd}tj,tj.||j||j(|z }tj0|dtj& }tj.tj2||jd}tj,tj.||j||j(|z }tj0|dtj&}tj.tj2||jd}t5|jdD]S}| |t*|zkDrt1|| |z d}n't1t7||||d}t7t1||||d}||dd|fz}||dd|f}|dk\r |t* |zks|dkr|t* |zkDrt1| |z d}ntj&}|dk\r |t*|zkDs|dkr|t*|zkrt7| |z d}ntj& }t7||}t1| |}|||zzd|d zz|zz}|||zzd|d zz|zz}||kr/|||zzd|d zz|zz} t9| t9|kDr|}| }||kDr/|||zzd|d zz|zz}!t9|!t9|kDr|}|!}t9|t9|k\r 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. 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