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"""
=====================================================
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 <scipy.optimize.nonlin>`
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
"""
from __future__ import division, print_function, absolute_import
from .optimize import *
from ._minimize import *
from ._root import *
from .minpack import *
from .zeros import *
from .lbfgsb import fmin_l_bfgs_b, LbfgsInvHessProduct
from .tnc import fmin_tnc
from .cobyla import fmin_cobyla
from .nonlin import *
from .slsqp import fmin_slsqp
from .nnls import nnls
from ._basinhopping import basinhopping
from ._linprog import linprog, linprog_verbose_callback
from ._hungarian import linear_sum_assignment
from ._differentialevolution import differential_evolution
from ._lsq import least_squares, lsq_linear
__all__ = [s for s in dir() if not s.startswith('_')]
from numpy.testing import Tester
test = Tester().test
bench = Tester().bench
|
