(ph]7jSSKrSSKrSSKJr \R "\5RrSr Sr Sr g)N)get_arrays_tolc ^U(Ga[U[5(de[U[R5(aURS:Xde[ R "T5RU5(de[U[R5(aURUR:Xde[U[R5(aURUR:Xde[U[5(de[U[5(de[X45n[R"X7:*5(de[R"XG*:5(de[R"U5(aUS:de[R"US5n[R"US5n[XTX4XV5up[U*U*U4SjUUUU5up[!U 5[!U 5:aUOU n U(af[R"X<:*5(de[R"X:*5(de[R"R%U 5SU-:deU $)ao Maximize approximately the absolute value of a quadratic function subject to bound constraints in a trust region. This function solves approximately .. math:: \max_{s \in \mathbb{R}^n} \quad \bigg\lvert c + g^{\mathsf{T}} s + \frac{1}{2} s^{\mathsf{T}} H s \bigg\rvert \quad \text{s.t.} \quad \left\{ \begin{array}{l} l \le s \le u,\\ \lVert s \rVert \le \Delta, \end{array} \right. by maximizing the objective function along the constrained Cauchy direction. Parameters ---------- const : float Constant :math:`c` as shown above. grad : `numpy.ndarray`, shape (n,) Gradient :math:`g` as shown above. curv : callable Curvature of :math:`H` along any vector. ``curv(s) -> float`` returns :math:`s^{\mathsf{T}} H s`. xl : `numpy.ndarray`, shape (n,) Lower bounds :math:`l` as shown above. xu : `numpy.ndarray`, shape (n,) Upper bounds :math:`u` as shown above. delta : float Trust-region radius :math:`\Delta` as shown above. debug : bool Whether to make debugging tests during the execution. Returns ------- `numpy.ndarray`, shape (n,) Approximate solution :math:`s`. Notes ----- This function is described as the first alternative in Section 6.5 of [1]_. It is assumed that the origin is feasible with respect to the bound constraints and that `delta` is finite and positive. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. c>T"U5*$)N)xcurvs X/var/www/html/venv/lib/python3.13/site-packages/scipy/_lib/cobyqa/subsolvers/geometry.py!cauchy_geometry..[s 47(皙?) isinstancefloatnpndarrayndiminspect signaturebindshapeboolrallisfiniteminimummaximum _cauchy_geomabslinalgnorm) constgradr xlxudeltadebugtolstep1q_val1step2q_val2steps ` r cauchy_geometryr/ st %''''$ ++ Q>>  &++D1111"bjj))bhh$**.DDD"bjj))bhh$**.DDD%''''%&&&&R$vvbi    vvbDj!!!!{{5!!eck11 B B B B !dBEIME      MEK3v;.5ED vvbj!!!!vvdj!!!!yy~~d#cEk111 KrcU(Ga[U[5(de[U[R5(aURS:Xde[ R "U5RU5(de[U[R5(a-URS:XaURSUR:Xde[U[R5(aURUR:Xde[U[R5(aURUR:Xde[U[5(de[U[5(de[XE5n[R"XH:*5(de[R"XX*:5(de[R"U5(aUS:de[R"US5n[R"US5n[R "U5n Un [R"R%USS9n U[R&*:UR([**U-:-n U[R&*:UR([*U-:-n U[R&:UR([*U-:-nU[R&:UR([**U-:-n[R,"[R."XLR5U UR(U - 5n[R0"US[R&*S9n[R."[R2"U5URS5n[R,"[R."XMR5U UR(U - 5n[R0"US[R&S9n[R."[R2"U5URS5n[R,"[R."X_R5UUR(U- 5n[R0"US[R&*S9n[R."[R2"U5URS5n[R,"[R."X^R5UUR(U- 5n[R0"US[R&S9n[R."[R2"U5URS5n[5URS5GHgnU U[*U-:a[1XkU- S5nOM([1[7UUUU5S5n[7[1UUUU5S5nXSS2U4-nU"USS2U45nUS:aU[**U-:dUS::aU[**U-:a[1U*U- S5nO[R&nUS:a U[*U-:dUS::aU[*U-:a[7U*U- S5nO[R&*nU5n[1U*U5nUUU--SUS --U--nUUU--SUS --U--nUU:a0UUU--SUS --U--n [9U 5[9U5:aUnU nUU:a0UUU--SUS --U--n![9U!5[9U5:aUnU!n[9U5[9U5:a>[9U5[9U 5:a&[R:"UUSS2U4-XE5n Un GM[9U5[9U5:dGM)[9U5[9U 5:dGMD[R:"UUSS2U4-XE5n Un GMj U(af[R"XI:*5(de[R"X:*5(de[R"R%U 5S U-:deU $) 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 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. 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