rned. 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) )