+ /i%NRt^RIt^RIt^RIHtHt.tRRlt !RR]4t R#)z"Dog-leg trust-region optimization.N)_minimize_trust_regionBaseQuadraticSubproblemc Vf \R4h\V4'g \R4h\W3RVRVRVR\/VB#)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 minimizationargsjachess subproblem) ValueErrorcallablerDoglegSubproblem)funx0rrrtrust_region_optionss&&&&&,`/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/optimize/_trustregion_dogleg.py_minimize_doglegr s^( {GHH D>>FGG !# : :# :D :-= :$8 ::c6a]tRt^&toRtRtRtRtRtVt R#)r z0Quadratic subproblem solved by the dogleg methodc VPf\VPpVPV4p\P!W4\P!W4, )V,VnVP#)zF The Cauchy point is minimal along the direction of steepest descent. ) _cauchy_pointrhesspnpdot)selfgBgs& r cauchy_pointDoglegSubproblem.cauchy_point)sW    %AAB#%66!<"&&-#?!@1!DD !!!rc VPf]VPpVPp\PP V4p\PP W14)VnVP#)zC The Newton point is a global minimum of the approximate function. ) _newton_pointrrscipylinalg cho_factor cho_solve)rrBcho_infos& r newton_pointDoglegSubproblem.newton_point3s\    %A A||..q1H"',,"8"8"E!ED !!!rc pVP4p\PPV4V8dRpW#3#VP 4p\PPV4pWQ8dWAV, ,pRpWc3#VP WBV, V4wrxWHW$, ,,pRpWc3#)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%rr 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)rrN) __name__ __module__ __qualname____firstlineno____doc__rr%r2__static_attributes____classdictcell__) __classdict__s@rr r &s:" "<)<)rr )NN) r8numpyr scipy.linalgr _trustregionrr__all__rr r<rrrAs*(K ::T).T)r