ó ʽ÷Xc@`s‚dZddlmZmZmZddlZddlZddl m Z m Z gZ d ddd„Zde fd„ƒYZdS( s"Dog-leg trust-region optimization.i(tdivisiontprint_functiontabsolute_importNi(t_minimize_trust_regiontBaseQuadraticSubproblemc K`s^|dkrtdƒ‚n|dkr6tdƒ‚nt||d|d|d|dt|S(s  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. s,Jacobian is required for dogleg minimizations+Hessian is required for dogleg minimizationtargstjacthesst subproblemN(tNonet ValueErrorRtDoglegSubproblem(tfuntx0RRRttrust_region_options((sA/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_trustregion_dogleg.pyt_minimize_dogleg s  R cB`s)eZdZd„Zd„Zd„ZRS(s0Quadratic subproblem solved by the dogleg methodcC`s[|jdkrT|j}|j|ƒ}tj||ƒtj||ƒ ||_n|jS(sV The Cauchy point is minimal along the direction of steepest descent. N(t _cauchy_pointR Rthessptnptdot(tselftgtBg((sA/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_trustregion_dogleg.pyt cauchy_point+s  -cC`sV|jdkrO|j}|j}tjj|ƒ}tjj||ƒ |_n|jS(sS The Newton point is a global minimum of the approximate function. N(t _newton_pointR RRtscipytlinalgt cho_factort cho_solve(RRtBtcho_info((sA/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_trustregion_dogleg.pyt newton_point5s   c C`s½|jƒ}tjj|ƒ|kr4t}||fS|jƒ}tjj|ƒ}||kr||||}t}||fS|j||||ƒ\}}||||}t}||fS(sŒ 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. (RRRtnormtFalseRtTruetget_boundaries_intersections( Rt trust_radiustp_bestt hits_boundarytp_utp_u_normt p_boundaryt_ttb((sA/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_trustregion_dogleg.pytsolve@s"     (t__name__t __module__t__doc__RRR,(((sA/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_trustregion_dogleg.pyR (s ((R/t __future__RRRtnumpyRt scipy.linalgRt _trustregionRRt__all__R RR (((sA/tmp/pip-build-7oUkmx/scipy/scipy/optimize/_trustregion_dogleg.pyts