295 lines
7.8 KiB
Python
295 lines
7.8 KiB
Python
"""
|
|
=====================================================
|
|
Optimization and root finding (:mod:`scipy.optimize`)
|
|
=====================================================
|
|
|
|
.. currentmodule:: scipy.optimize
|
|
|
|
Optimization
|
|
============
|
|
|
|
Local Optimization
|
|
------------------
|
|
|
|
.. autosummary::
|
|
:toctree: generated/
|
|
|
|
minimize - Interface for minimizers of multivariate functions
|
|
minimize_scalar - 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-trustconstr
|
|
optimize.minimize-dogleg
|
|
optimize.minimize-trustncg
|
|
optimize.minimize-trustkrylov
|
|
optimize.minimize-trustexact
|
|
|
|
Constraints are passed to `minimize` function as a single object or
|
|
as a list of objects from the following classes:
|
|
|
|
.. autosummary::
|
|
:toctree: generated/
|
|
|
|
NonlinearConstraint - Class defining general nonlinear constraints.
|
|
LinearConstraint - Class defining general linear constraints.
|
|
|
|
Simple bound constraints are handled separately and there is a special class
|
|
for them:
|
|
|
|
.. autosummary::
|
|
:toctree: generated/
|
|
|
|
Bounds - Bound constraints.
|
|
|
|
Quasi-Newton strategies implementing `HessianUpdateStrategy`
|
|
interface can be used to approximate the Hessian in `minimize`
|
|
function (available only for the 'trust-constr' method). Available
|
|
quasi-Newton methods implementing this interface are:
|
|
|
|
.. autosummary::
|
|
:toctree: generated/
|
|
|
|
BFGS - Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy.
|
|
SR1 - Symmetric-rank-1 Hessian update strategy.
|
|
|
|
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
|
|
==================
|
|
|
|
General linear programming solver:
|
|
|
|
.. autosummary::
|
|
:toctree: generated/
|
|
|
|
linprog -- Unified interface for minimizers of linear programming problems
|
|
|
|
The `linprog` function supports the following methods:
|
|
|
|
.. toctree::
|
|
|
|
optimize.linprog-simplex
|
|
optimize.linprog-interior-point
|
|
|
|
The simplex method supports callback functions, such as:
|
|
|
|
.. autosummary::
|
|
:toctree: generated/
|
|
|
|
linprog_verbose_callback -- Sample callback function for 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
|
|
HessianUpdateStrategy - Interface for implementing Hessian update strategies
|
|
|
|
"""
|
|
|
|
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
|
|
from ._constraints import (NonlinearConstraint,
|
|
LinearConstraint,
|
|
Bounds)
|
|
from ._hessian_update_strategy import HessianUpdateStrategy, BFGS, SR1
|
|
|
|
__all__ = [s for s in dir() if not s.startswith('_')]
|
|
|
|
from scipy._lib._testutils import PytestTester
|
|
test = PytestTester(__name__)
|
|
del PytestTester
|