scipy.optimize.fmin_powell¶

scipy.optimize.
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)[source]¶ Minimize a function using modified Powell’s method.
This method only uses function values, not derivatives.
 Parameters
 funccallable f(x,*args)
Objective function to be minimized.
 x0ndarray
Initial guess.
 argstuple, optional
Extra arguments passed to func.
 xtolfloat, optional
Linesearch error tolerance.
 ftolfloat, optional
Relative error in
func(xopt)
acceptable for convergence. maxiterint, optional
Maximum number of iterations to perform.
 maxfunint, optional
Maximum number of function evaluations to make.
 full_outputbool, optional
If True,
fopt
,xi
,direc
,iter
,funcalls
, andwarnflag
are returned. dispbool, optional
If True, print convergence messages.
 retallbool, optional
If True, return a list of the solution at each iteration.
 callbackcallable, optional
An optional usersupplied function, called after each iteration. Called as
callback(xk)
, wherexk
is the current parameter vector. direcndarray, 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.ones((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
 xoptndarray
Parameter which minimizes func.
 foptnumber
Value of function at minimum:
fopt = func(xopt)
. direcndarray
Current direction set.
 iterint
Number of iterations.
 funcallsint
Number of function calls made.
 warnflagint
 Integer warning flag:
1 : Maximum number of function evaluations. 2 : Maximum number of iterations. 3 : NaN result encountered.
 allvecslist
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 innerloop.
The technical conditions for replacing the direction of greatest increase amount to checking that
No further gain can be made along the direction of greatest increase from that iteration.
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):155162.
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: 18 >>> minimum array(0.0)