`scipy.optimize._optimize:fmin_ncg`

source: /scipy/optimize/_optimize.py :1881

Signature

   def     fmin_ncg (    f    ,    x0    ,    fprime    ,    fhess_p    =  None   ,    fhess    =  None   ,    args    =  ()   ,    avextol    =  1e-05   ,    epsilon    =  1.4901161193847656e-08   ,    maxiter    =  None   ,    full_output    =  0   ,    disp    =  1   ,    retall    =  0   ,    callback    =  None   ,    c1    =  0.0001   ,    c2    =  0.9     )

Summary

Unconstrained minimization of a function using the Newton-CG method.

Parameters

f : callable ``f(x, *args)``: Objective function to be minimized.
x0 : ndarray: Initial guess.
fprime : callable ``f'(x, *args)``: Gradient of f.
fhess_p : callable ``fhess_p(x, p, *args)``, optional: Function which computes the Hessian of f times an arbitrary vector, p.
fhess : callable ``fhess(x, *args)``, optional: Function to compute the Hessian matrix of f.
args : tuple, optional: Extra arguments passed to f, fprime, fhess_p, and fhess (the same set of extra arguments is supplied to all of these functions).
epsilon : float or ndarray, optional: If fhess is approximated, use this value for the step size.
callback : callable, optional: An optional user-supplied function which is called after each iteration. Called as callback(xk), where xk is the current parameter vector.
avextol : float, optional: Convergence is assumed when the average relative error in the minimizer falls below this amount.
maxiter : int, optional: Maximum number of iterations to perform.
full_output : bool, optional: If True, return the optional outputs.
disp : bool, optional: If True, print convergence message.
retall : bool, optional: If True, return a list of results at each iteration.
c1 : float, default: 1e-4: Parameter for Armijo condition rule.
c2 : float, default: 0.9: Parameter for curvature condition rule

Returns

xopt : ndarray: Parameters which minimize f, i.e., f(xopt) == fopt.
fopt : float: Value of the function at xopt, i.e., fopt = f(xopt).
fcalls : int: Number of function calls made.
gcalls : int: Number of gradient calls made.
hcalls : int: Number of Hessian calls made.
warnflag : int: Warnings generated by the algorithm. 1 : Maximum number of iterations exceeded. 2 : Line search failure (precision loss). 3 : NaN result encountered.
allvecs : list: The result at each iteration, if retall is True (see below).

Notes

Only one of fhess_p or fhess need to be given. If fhess is provided, then fhess_p will be ignored. If neither fhess nor fhess_p is provided, then the hessian product will be approximated using finite differences on fprime. fhess_p must compute the hessian times an arbitrary vector. If it is not given, finite-differences on fprime are used to compute it.

Newton-CG methods are also called truncated Newton methods. This function differs from scipy.optimize.fmin_tnc because

scipy.optimize.fmin_ncg is written purely in Python using NumPy
and scipy while scipy.optimize.fmin_tnc calls a C function.
scipy.optimize.fmin_ncg is only for unconstrained minimization
while scipy.optimize.fmin_tnc is for unconstrained minimization or box constrained minimization. (Box constraints give lower and upper bounds for each variable separately.)

Parameters c1 and c2 must satisfy 0 < c1 < c2 < 1.

Aliases