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Module « scipy.optimize »

Fonction fmin - module scipy.optimize

Signature de la fonction fmin

def fmin(func, x0, args=(), xtol=0.0001, ftol=0.0001, maxiter=None, maxfun=None, full_output=0, disp=1, retall=0, callback=None, initial_simplex=None) 

Description

help(scipy.optimize.fmin)

Minimize a function using the downhill simplex algorithm.

This algorithm only uses function values, not derivatives or second
derivatives.

Parameters
----------
func : callable func(x,*args)
    The objective function to be minimized.
x0 : ndarray
    Initial guess.
args : tuple, optional
    Extra arguments passed to func, i.e., ``f(x,*args)``.
xtol : float, optional
    Absolute error in xopt between iterations that is acceptable for
    convergence.
ftol : number, optional
    Absolute error in func(xopt) between iterations that is acceptable for
    convergence.
maxiter : int, optional
    Maximum number of iterations to perform.
maxfun : number, optional
    Maximum number of function evaluations to make.
full_output : bool, optional
    Set to True if fopt and warnflag outputs are desired.
disp : bool, optional
    Set to True to print convergence messages.
retall : bool, optional
    Set to True to return list of solutions at each iteration.
callback : callable, optional
    Called after each iteration, as callback(xk), where xk is the
    current parameter vector.
initial_simplex : array_like of shape (N + 1, N), optional
    Initial simplex. If given, overrides `x0`.
    ``initial_simplex[j,:]`` should contain the coordinates of
    the jth vertex of the ``N+1`` vertices in the simplex, where
    ``N`` is the dimension.

Returns
-------
xopt : ndarray
    Parameter that minimizes function.
fopt : float
    Value of function at minimum: ``fopt = func(xopt)``.
iter : int
    Number of iterations performed.
funcalls : int
    Number of function calls made.
warnflag : int
    1 : Maximum number of function evaluations made.
    2 : Maximum number of iterations reached.
allvecs : list
    Solution at each iteration.

See also
--------
minimize: Interface to minimization algorithms for multivariate
    functions. See the 'Nelder-Mead' `method` in particular.

Notes
-----
Uses a Nelder-Mead simplex algorithm to find the minimum of function of
one or more variables.

This algorithm has a long history of successful use in applications.
But it will usually be slower than an algorithm that uses first or
second derivative information. In practice, it can have poor
performance in high-dimensional problems and is not robust to
minimizing complicated functions. Additionally, there currently is no
complete theory describing when the algorithm will successfully
converge to the minimum, or how fast it will if it does. Both the ftol and
xtol criteria must be met for convergence.

Examples
--------
>>> def f(x):
...     return x**2

>>> from scipy import optimize

>>> minimum = optimize.fmin(f, 1)
Optimization terminated successfully.
         Current function value: 0.000000
         Iterations: 17
         Function evaluations: 34
>>> minimum[0]
-8.8817841970012523e-16

References
----------
.. [1] Nelder, J.A. and Mead, R. (1965), "A simplex method for function
       minimization", The Computer Journal, 7, pp. 308-313

.. [2] Wright, M.H. (1996), "Direct Search Methods: Once Scorned, Now
       Respectable", in Numerical Analysis 1995, Proceedings of the
       1995 Dundee Biennial Conference in Numerical Analysis, D.F.
       Griffiths and G.A. Watson (Eds.), Addison Wesley Longman,
       Harlow, UK, pp. 191-208.

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