max(1,min(50,n/2)). Defaults to -1. maxfun : int, optional Maximum number of function evaluation. If None, maxfun is set to max(100, 10*len(x0)). Defaults to None. Note that this function may violate the limit because of evaluating gradients by numerical differentiation. eta : float, optional Severity of the line search. If < 0 or > 1, set to 0.25. Defaults to -1. stepmx : float, optional Maximum step for the line search. May be increased during call. If too small, it will be set to 10.0. Defaults to 0. accuracy : float, optional Relative precision for finite difference calculations. If <= machine_precision, set to sqrt(machine_precision). Defaults to 0. fmin : float, optional Minimum function value estimate. Defaults to 0. ftol : float, optional Precision goal for the value of f in the stopping criterion. If ftol < 0.0, ftol is set to 0.0 defaults to -1. xtol : float, optional Precision goal for the value of x in the stopping criterion (after applying x scaling factors). If xtol < 0.0, xtol is set to sqrt(machine_precision). Defaults to -1. pgtol : float, optional Precision goal for the value of the projected gradient in the stopping criterion (after applying x scaling factors). If pgtol < 0.0, pgtol is set to 1e-2 * sqrt(accuracy). Setting it to 0.0 is not recommended. Defaults to -1. rescale : float, optional Scaling factor (in log10) used to trigger f value rescaling. If 0, rescale at each iteration. If a large value, never rescale. If < 0, rescale is set to 1.3. callback : callable, optional Called after each iteration, as callback(xk), where xk is the current parameter vector. Returns ------- x : ndarray The solution. nfeval : int The number of function evaluations. rc : int Return code, see below See also -------- minimize: Interface to minimization algorithms for multivariate functions. See the 'TNC' `method` in particular. Notes ----- The underlying algorithm is truncated Newton, also called Newton Conjugate-Gradient. This method differs from scipy.optimize.fmin_ncg in that 1. it wraps a C implementation of the algorithm 2. it allows each variable to be given an upper and lower bound. The algorithm incorporates the bound constraints by determining the descent direction as in an unconstrained truncated Newton, but never taking a step-size large enough to leave the space of feasible x's. The algorithm keeps track of a set of currently active constraints, and ignores them when computing the minimum allowable step size. (The x's associated with the active constraint are kept fixed.) If the maximum allowable step size is zero then a new constraint is added. At the end of each iteration one of the constraints may be deemed no longer active and removed. A constraint is considered no longer active is if it is currently active but the gradient for that variable points inward from the constraint. The specific constraint removed is the one associated with the variable of largest index whose constraint is no longer active. Return codes are defined as follows:: -1 : Infeasible (lower bound > upper bound) 0 : Local minimum reached (|pg| ~= 0) 1 : Converged (|f_n-f_(n-1)| ~= 0) 2 : Converged (|x_n-x_(n-1)| ~= 0) 3 : Max. number of function evaluations reached 4 : Linear search failed 5 : All lower bounds are equal to the upper bounds 6 : Unable to progress 7 : User requested end of minimization References ---------- Wright S., Nocedal J. (2006), 'Numerical Optimization' Nash S.G. (1984), "Newton-Type Minimization Via the Lanczos Method", SIAM Journal of Numerical Analysis 21, pp. 770-778 NŠ