ó ʽ÷Xc@`s[dZddlmZmZmZddlTddlTddlTddlTddl Tddl m Z m Z ddl mZddlmZddlTddlmZdd lmZdd lmZdd lmZmZdd lmZdd lmZddlmZm Z ge!ƒD]Z"e"j#dƒse"^qZ$ddl%m&Z&e&ƒj'Z'dS(s‰ ===================================================== Optimization and root finding (:mod:`scipy.optimize`) ===================================================== .. currentmodule:: scipy.optimize Optimization ============ Local Optimization ------------------ .. autosummary:: :toctree: generated/ minimize - Unified interface for minimizers of multivariate functions minimize_scalar - Unified interface for minimizers of univariate functions OptimizeResult - The optimization result returned by some optimizers OptimizeWarning - The optimization encountered problems The `minimize` function supports the following methods: .. toctree:: optimize.minimize-neldermead optimize.minimize-powell optimize.minimize-cg optimize.minimize-bfgs optimize.minimize-newtoncg optimize.minimize-lbfgsb optimize.minimize-tnc optimize.minimize-cobyla optimize.minimize-slsqp optimize.minimize-dogleg optimize.minimize-trustncg The `minimize_scalar` function supports the following methods: .. toctree:: optimize.minimize_scalar-brent optimize.minimize_scalar-bounded optimize.minimize_scalar-golden The specific optimization method interfaces below in this subsection are not recommended for use in new scripts; all of these methods are accessible via a newer, more consistent interface provided by the functions above. General-purpose multivariate methods: .. autosummary:: :toctree: generated/ fmin - Nelder-Mead Simplex algorithm fmin_powell - Powell's (modified) level set method fmin_cg - Non-linear (Polak-Ribiere) conjugate gradient algorithm fmin_bfgs - Quasi-Newton method (Broydon-Fletcher-Goldfarb-Shanno) fmin_ncg - Line-search Newton Conjugate Gradient Constrained multivariate methods: .. autosummary:: :toctree: generated/ fmin_l_bfgs_b - Zhu, Byrd, and Nocedal's constrained optimizer fmin_tnc - Truncated Newton code fmin_cobyla - Constrained optimization by linear approximation fmin_slsqp - Minimization using sequential least-squares programming differential_evolution - stochastic minimization using differential evolution Univariate (scalar) minimization methods: .. autosummary:: :toctree: generated/ fminbound - Bounded minimization of a scalar function brent - 1-D function minimization using Brent method golden - 1-D function minimization using Golden Section method Equation (Local) Minimizers --------------------------- .. autosummary:: :toctree: generated/ leastsq - Minimize the sum of squares of M equations in N unknowns least_squares - Feature-rich least-squares minimization. nnls - Linear least-squares problem with non-negativity constraint lsq_linear - Linear least-squares problem with bound constraints Global Optimization ------------------- .. autosummary:: :toctree: generated/ basinhopping - Basinhopping stochastic optimizer brute - Brute force searching optimizer differential_evolution - stochastic minimization using differential evolution Rosenbrock function ------------------- .. autosummary:: :toctree: generated/ rosen - The Rosenbrock function. rosen_der - The derivative of the Rosenbrock function. rosen_hess - The Hessian matrix of the Rosenbrock function. rosen_hess_prod - Product of the Rosenbrock Hessian with a vector. Fitting ======= .. autosummary:: :toctree: generated/ curve_fit -- Fit curve to a set of points Root finding ============ Scalar functions ---------------- .. autosummary:: :toctree: generated/ brentq - quadratic interpolation Brent method brenth - Brent method, modified by Harris with hyperbolic extrapolation ridder - Ridder's method bisect - Bisection method newton - Secant method or Newton's method Fixed point finding: .. autosummary:: :toctree: generated/ fixed_point - Single-variable fixed-point solver Multidimensional ---------------- General nonlinear solvers: .. autosummary:: :toctree: generated/ root - Unified interface for nonlinear solvers of multivariate functions fsolve - Non-linear multi-variable equation solver broyden1 - Broyden's first method broyden2 - Broyden's second method The `root` function supports the following methods: .. toctree:: optimize.root-hybr optimize.root-lm optimize.root-broyden1 optimize.root-broyden2 optimize.root-anderson optimize.root-linearmixing optimize.root-diagbroyden optimize.root-excitingmixing optimize.root-krylov optimize.root-dfsane Large-scale nonlinear solvers: .. autosummary:: :toctree: generated/ newton_krylov anderson Simple iterations: .. autosummary:: :toctree: generated/ excitingmixing linearmixing diagbroyden :mod:`Additional information on the nonlinear solvers ` Linear Programming ================== Simplex Algorithm: .. autosummary:: :toctree: generated/ linprog -- Linear programming using the simplex algorithm linprog_verbose_callback -- Sample callback function for linprog The `linprog` function supports the following methods: .. toctree:: optimize.linprog-simplex Assignment problems: .. autosummary:: :toctree: generated/ linear_sum_assignment -- Solves the linear-sum assignment problem Utilities ========= .. autosummary:: :toctree: generated/ approx_fprime - Approximate the gradient of a scalar function bracket - Bracket a minimum, given two starting points check_grad - Check the supplied derivative using finite differences line_search - Return a step that satisfies the strong Wolfe conditions show_options - Show specific options optimization solvers LbfgsInvHessProduct - Linear operator for L-BFGS approximate inverse Hessian i(tdivisiontprint_functiontabsolute_importi(t*(t fmin_l_bfgs_btLbfgsInvHessProduct(tfmin_tnc(t fmin_cobyla(t fmin_slsqp(tnnls(t basinhopping(tlinprogtlinprog_verbose_callback(tlinear_sum_assignment(tdifferential_evolution(t least_squarest lsq_lineart_(tTesterN((t__doc__t __future__RRRtoptimizet _minimizet_roottminpacktzerostlbfgsbRRttncRtcobylaRtnonlintslsqpRR t _basinhoppingR t_linprogR R t _hungarianR t_differentialevolutionRt_lsqRRtdirtst startswitht__all__t numpy.testingRttest(((s6/tmp/pip-build-7oUkmx/scipy/scipy/optimize/__init__.pytäs(      +