Classe « BroydenFirst »

Informations générales

Héritage

builtins.object
    Jacobian
        GenericBroyden
            BroydenFirst

Définition

class BroydenFirst(GenericBroyden):

help(BroydenFirst)

Find a root of a function, using Broyden's first Jacobian approximation.

This method is also known as "Broyden's good method".

Parameters
----------
%(params_basic)s
%(broyden_params)s
%(params_extra)s

See Also
--------
root : Interface to root finding algorithms for multivariate
       functions. See ``method='broyden1'`` in particular.

Notes
-----
This algorithm implements the inverse Jacobian Quasi-Newton update

.. math:: H_+ = H + (dx - H df) dx^\dagger H / ( dx^\dagger H df)

which corresponds to Broyden's first Jacobian update

.. math:: J_+ = J + (df - J dx) dx^\dagger / dx^\dagger dx


References
----------
.. [1] B.A. van der Rotten, PhD thesis,
   "A limited memory Broyden method to solve high-dimensional
   systems of nonlinear equations". Mathematisch Instituut,
   Universiteit Leiden, The Netherlands (2003).
   https://math.leidenuniv.nl/scripties/Rotten.pdf

Examples
--------
The following functions define a system of nonlinear equations

>>> def fun(x):
...     return [x[0]  + 0.5 * (x[0] - x[1])**3 - 1.0,
...             0.5 * (x[1] - x[0])**3 + x[1]]

A solution can be obtained as follows.

>>> from scipy import optimize
>>> sol = optimize.broyden1(fun, [0, 0])
>>> sol
array([0.84116396, 0.15883641])