296 lines
7.8 KiB
Python
296 lines
7.8 KiB
Python
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"""
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=====================================================
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Optimization and root finding (:mod:`scipy.optimize`)
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=====================================================
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.. currentmodule:: scipy.optimize
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Optimization
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============
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Local Optimization
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------------------
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.. autosummary::
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:toctree: generated/
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minimize - Interface for minimizers of multivariate functions
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minimize_scalar - Interface for minimizers of univariate functions
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OptimizeResult - The optimization result returned by some optimizers
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OptimizeWarning - The optimization encountered problems
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The `minimize` function supports the following methods:
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.. toctree::
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optimize.minimize-neldermead
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optimize.minimize-powell
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optimize.minimize-cg
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optimize.minimize-bfgs
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optimize.minimize-newtoncg
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optimize.minimize-lbfgsb
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optimize.minimize-tnc
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optimize.minimize-cobyla
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optimize.minimize-slsqp
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optimize.minimize-trustconstr
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optimize.minimize-dogleg
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optimize.minimize-trustncg
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optimize.minimize-trustkrylov
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optimize.minimize-trustexact
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Constraints are passed to `minimize` function as a single object or
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as a list of objects from the following classes:
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.. autosummary::
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:toctree: generated/
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NonlinearConstraint - Class defining general nonlinear constraints.
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LinearConstraint - Class defining general linear constraints.
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Simple bound constraints are handled separately and there is a special class
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for them:
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.. autosummary::
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:toctree: generated/
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Bounds - Bound constraints.
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Quasi-Newton strategies implementing `HessianUpdateStrategy`
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interface can be used to approximate the Hessian in `minimize`
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function (available only for the 'trust-constr' method). Available
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quasi-Newton methods implementing this interface are:
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.. autosummary::
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:toctree: generated/
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BFGS - Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy.
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SR1 - Symmetric-rank-1 Hessian update strategy.
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The `minimize_scalar` function supports the following methods:
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.. toctree::
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optimize.minimize_scalar-brent
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optimize.minimize_scalar-bounded
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optimize.minimize_scalar-golden
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The specific optimization method interfaces below in this subsection are
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not recommended for use in new scripts; all of these methods are accessible
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via a newer, more consistent interface provided by the functions above.
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General-purpose multivariate methods:
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.. autosummary::
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:toctree: generated/
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fmin - Nelder-Mead Simplex algorithm
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fmin_powell - Powell's (modified) level set method
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fmin_cg - Non-linear (Polak-Ribiere) conjugate gradient algorithm
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fmin_bfgs - Quasi-Newton method (Broydon-Fletcher-Goldfarb-Shanno)
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fmin_ncg - Line-search Newton Conjugate Gradient
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Constrained multivariate methods:
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.. autosummary::
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:toctree: generated/
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fmin_l_bfgs_b - Zhu, Byrd, and Nocedal's constrained optimizer
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fmin_tnc - Truncated Newton code
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fmin_cobyla - Constrained optimization by linear approximation
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fmin_slsqp - Minimization using sequential least-squares programming
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differential_evolution - stochastic minimization using differential evolution
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Univariate (scalar) minimization methods:
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.. autosummary::
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:toctree: generated/
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fminbound - Bounded minimization of a scalar function
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brent - 1-D function minimization using Brent method
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golden - 1-D function minimization using Golden Section method
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Equation (Local) Minimizers
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---------------------------
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.. autosummary::
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:toctree: generated/
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leastsq - Minimize the sum of squares of M equations in N unknowns
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least_squares - Feature-rich least-squares minimization.
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nnls - Linear least-squares problem with non-negativity constraint
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lsq_linear - Linear least-squares problem with bound constraints
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Global Optimization
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-------------------
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.. autosummary::
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:toctree: generated/
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basinhopping - Basinhopping stochastic optimizer
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brute - Brute force searching optimizer
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differential_evolution - stochastic minimization using differential evolution
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Rosenbrock function
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-------------------
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.. autosummary::
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:toctree: generated/
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rosen - The Rosenbrock function.
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rosen_der - The derivative of the Rosenbrock function.
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rosen_hess - The Hessian matrix of the Rosenbrock function.
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rosen_hess_prod - Product of the Rosenbrock Hessian with a vector.
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Fitting
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=======
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.. autosummary::
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:toctree: generated/
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curve_fit -- Fit curve to a set of points
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Root finding
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============
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Scalar functions
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----------------
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.. autosummary::
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:toctree: generated/
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brentq - quadratic interpolation Brent method
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brenth - Brent method, modified by Harris with hyperbolic extrapolation
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ridder - Ridder's method
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bisect - Bisection method
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newton - Secant method or Newton's method
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Fixed point finding:
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.. autosummary::
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:toctree: generated/
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fixed_point - Single-variable fixed-point solver
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Multidimensional
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----------------
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General nonlinear solvers:
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.. autosummary::
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:toctree: generated/
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root - Unified interface for nonlinear solvers of multivariate functions
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fsolve - Non-linear multi-variable equation solver
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broyden1 - Broyden's first method
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broyden2 - Broyden's second method
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The `root` function supports the following methods:
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.. toctree::
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optimize.root-hybr
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optimize.root-lm
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optimize.root-broyden1
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optimize.root-broyden2
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optimize.root-anderson
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optimize.root-linearmixing
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optimize.root-diagbroyden
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optimize.root-excitingmixing
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optimize.root-krylov
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optimize.root-dfsane
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Large-scale nonlinear solvers:
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.. autosummary::
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:toctree: generated/
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newton_krylov
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anderson
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Simple iterations:
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.. autosummary::
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:toctree: generated/
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excitingmixing
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linearmixing
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diagbroyden
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:mod:`Additional information on the nonlinear solvers <scipy.optimize.nonlin>`
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Linear Programming
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==================
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General linear programming solver:
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.. autosummary::
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:toctree: generated/
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linprog -- Unified interface for minimizers of linear programming problems
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The `linprog` function supports the following methods:
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.. toctree::
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optimize.linprog-simplex
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optimize.linprog-interior-point
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The simplex method supports callback functions, such as:
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.. autosummary::
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:toctree: generated/
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linprog_verbose_callback -- Sample callback function for linprog (simplex)
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Assignment problems:
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.. autosummary::
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:toctree: generated/
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linear_sum_assignment -- Solves the linear-sum assignment problem
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Utilities
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=========
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.. autosummary::
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:toctree: generated/
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approx_fprime - Approximate the gradient of a scalar function
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bracket - Bracket a minimum, given two starting points
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check_grad - Check the supplied derivative using finite differences
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line_search - Return a step that satisfies the strong Wolfe conditions
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show_options - Show specific options optimization solvers
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LbfgsInvHessProduct - Linear operator for L-BFGS approximate inverse Hessian
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HessianUpdateStrategy - Interface for implementing Hessian update strategies
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"""
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from __future__ import division, print_function, absolute_import
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from .optimize import *
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from ._minimize import *
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from ._root import *
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from .minpack import *
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from .zeros import *
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from .lbfgsb import fmin_l_bfgs_b, LbfgsInvHessProduct
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from .tnc import fmin_tnc
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from .cobyla import fmin_cobyla
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from .nonlin import *
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from .slsqp import fmin_slsqp
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from .nnls import nnls
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from ._basinhopping import basinhopping
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from ._linprog import linprog, linprog_verbose_callback
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from ._hungarian import linear_sum_assignment
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from ._differentialevolution import differential_evolution
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from ._lsq import least_squares, lsq_linear
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from ._constraints import (NonlinearConstraint,
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LinearConstraint,
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Bounds)
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from ._hessian_update_strategy import HessianUpdateStrategy, BFGS, SR1
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__all__ = [s for s in dir() if not s.startswith('_')]
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from scipy._lib._testutils import PytestTester
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test = PytestTester(__name__)
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del PytestTester
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