(ph%LSrSSKrSSKrSSKJrJr /rSSjr "SS\5r g) z"Dog-leg trust-region optimization.N)_minimize_trust_regionBaseQuadraticSubproblemc |Uc [S5e[U5(d [S5e[X4X#U[S.UD6$)a Minimization of scalar function of one or more variables using the dog-leg trust-region algorithm. Options ------- initial_trust_radius : float Initial trust-region radius. max_trust_radius : float Maximum value of the trust-region radius. No steps that are longer than this value will be proposed. eta : float Trust region related acceptance stringency for proposed steps. gtol : float Gradient norm must be less than `gtol` before successful termination. z,Jacobian is required for dogleg minimizationz+Hessian is required for dogleg minimization)argsjachess subproblem) ValueErrorcallablerDoglegSubproblem)funx0rrr trust_region_optionss U/var/www/html/venv/lib/python3.13/site-packages/scipy/optimize/_trustregion_dogleg.py_minimize_doglegr sM( {GHH D>>FGG !# :D-= :$8 ::c*\rSrSrSrSrSrSrSrg)r &z0Quadratic subproblem solved by the dogleg methodcURcSURnURU5n[R"X5[R"X5- *U-UlUR$)zF The Cauchy point is minimal along the direction of steepest descent. ) _cauchy_pointrhesspnpdot)selfgBgs r cauchy_pointDoglegSubproblem.cauchy_point)sW    %AAB#%66!<"&&-#?!@1!DD !!!rcURc\URnURn[RR U5n[RR X15*UlUR$)zC The Newton point is a global minimum of the approximate function. ) _newton_pointrr scipylinalg cho_factor cho_solve)rrBcho_infos r newton_pointDoglegSubproblem.newton_point3s\    %A A||..q1H"',,"8"8"E!ED !!!rc<UR5n[RRU5U:aSnX#4$UR 5n[RRU5nXQ:a XAU- -nSnXc4$UR XBU- U5upxXHX$- --nSnXc4$)a Minimize a function using the dog-leg trust-region algorithm. This algorithm requires function values and first and second derivatives. It also performs a costly Hessian decomposition for most iterations, and the Hessian is required to be positive definite. Parameters ---------- trust_radius : float We are allowed to wander only this far away from the origin. Returns ------- p : ndarray The proposed step. hits_boundary : bool True if the proposed step is on the boundary of the trust region. Notes ----- The Hessian is required to be positive definite. References ---------- .. [1] Jorge Nocedal and Stephen Wright, Numerical Optimization, second edition, Springer-Verlag, 2006, page 73. FT)r(r"r#normrget_boundaries_intersections) r trust_radiusp_best hits_boundaryp_up_u_norm p_boundary_tbs rsolveDoglegSubproblem.solve>sD""$ <<  V $| 3!M( (!<<$$S)  #x 78J M, ,11#|2>@..  ((r)rr!N) __name__ __module__ __qualname____firstlineno____doc__rr(r5__static_attributes__rrr r &s:" "<)rr )r=NN) r;numpyr scipy.linalgr" _trustregionrr__all__rr r=rrrBs*(K ::T).T)r