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Module « scipy.optimize »

Fonction fmin_powell - module scipy.optimize

Signature de la fonction fmin_powell

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

Description

help(scipy.optimize.fmin_powell)

Minimize a function using modified Powell's method.

This method only uses function values, not derivatives.

Parameters
----------
func : callable f(x,*args)
    Objective function to be minimized.
x0 : ndarray
    Initial guess.
args : tuple, optional
    Extra arguments passed to func.
xtol : float, optional
    Line-search error tolerance.
ftol : float, optional
    Relative error in ``func(xopt)`` acceptable for convergence.
maxiter : int, optional
    Maximum number of iterations to perform.
maxfun : int, optional
    Maximum number of function evaluations to make.
full_output : bool, optional
    If True, ``fopt``, ``xi``, ``direc``, ``iter``, ``funcalls``, and
    ``warnflag`` are returned.
disp : bool, optional
    If True, print convergence messages.
retall : bool, optional
    If True, return a list of the solution at each iteration.
callback : callable, optional
    An optional user-supplied function, called after each
    iteration.  Called as ``callback(xk)``, where ``xk`` is the
    current parameter vector.
direc : ndarray, optional
    Initial fitting step and parameter order set as an (N, N) array, where N
    is the number of fitting parameters in `x0`. Defaults to step size 1.0
    fitting all parameters simultaneously (``np.eye((N, N))``). To
    prevent initial consideration of values in a step or to change initial
    step size, set to 0 or desired step size in the Jth position in the Mth
    block, where J is the position in `x0` and M is the desired evaluation
    step, with steps being evaluated in index order. Step size and ordering
    will change freely as minimization proceeds.

Returns
-------
xopt : ndarray
    Parameter which minimizes `func`.
fopt : number
    Value of function at minimum: ``fopt = func(xopt)``.
direc : ndarray
    Current direction set.
iter : int
    Number of iterations.
funcalls : int
    Number of function calls made.
warnflag : int
    Integer warning flag:
        1 : Maximum number of function evaluations.
        2 : Maximum number of iterations.
        3 : NaN result encountered.
        4 : The result is out of the provided bounds.
allvecs : list
    List of solutions at each iteration.

See also
--------
minimize: Interface to unconstrained minimization algorithms for
    multivariate functions. See the 'Powell' method in particular.

Notes
-----
Uses a modification of Powell's method to find the minimum of
a function of N variables. Powell's method is a conjugate
direction method.

The algorithm has two loops. The outer loop merely iterates over the inner
loop. The inner loop minimizes over each current direction in the direction
set. At the end of the inner loop, if certain conditions are met, the
direction that gave the largest decrease is dropped and replaced with the
difference between the current estimated x and the estimated x from the
beginning of the inner-loop.

The technical conditions for replacing the direction of greatest
increase amount to checking that

1. No further gain can be made along the direction of greatest increase
   from that iteration.
2. The direction of greatest increase accounted for a large sufficient
   fraction of the decrease in the function value from that iteration of
   the inner loop.

References
----------
Powell M.J.D. (1964) An efficient method for finding the minimum of a
function of several variables without calculating derivatives,
Computer Journal, 7 (2):155-162.

Press W., Teukolsky S.A., Vetterling W.T., and Flannery B.P.:
Numerical Recipes (any edition), Cambridge University Press

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

>>> from scipy import optimize

>>> minimum = optimize.fmin_powell(f, -1)
Optimization terminated successfully.
         Current function value: 0.000000
         Iterations: 2
         Function evaluations: 16
>>> minimum
array(0.0)

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