iFit/fmax

 [Maxmimum,FVAL,EXITFLAG,OUTPUT] = fmax(FUN,PARS,[OPTIONS],[X,Y,...]) Best maximizer

 This maximization method is determined automatically from the objective function
 behaviour and number of free parameters. You can however force a specific 
 optimizer by setting e.g. options.optimizer='fminpso'

 fmin(model)
   minimize the model, using current model or guessed parameters. Return best parameters
 fmin(model, pars)
   minimize the model, starting with given parameters and return best parameter set 
   when pars is given as [], current/guessed parameters are used
 fmin(model, pars, 'optimizer')
   minimize the model, as above, using given optimizer with its default configuration
   for instance: fmin(model, [], 'fminpso')
 fmin(model, pars, options)
   minimize the model, as above, using given optimizer configuration
   for instance: fmin(model, [], 'optimizer=fminpso; OutputFcn=iter; Display=iter')

 WARNING: as the selected optimizer may change from one call to an other, the
 solution found may vary as well. To avoid that, rather use a specific optimizer.

 Best optimizers are:
   fmaxpso:    Particle Swarm Optimization
   fmaxpowell: Powell with Coggins line search
   fmaxhooke:  Hooke-Jeeves direct search
   fmaxralg:   Shor R-algorithm
   fmaxsimpsa: Simplex/simulated annealing
   fmaximfil:  Unconstrained Implicit filtering
 Type <a href="matlab:doc(iData,'Optimizers')">doc(iData,'Optimizers')</a> to access the Optimizers Documentation.

 Calling:
   fmax(fun, pars) asks to maximize the 'fun' iFunc model with starting
     parameters 'pars' (vector)
   fmax(fun, pars, 'optimizer') 
     use optimizer with its default options
   fmax(fun, pars, options) 
     same as above, with customized options (optimset)
   fmax(fun, pars, options, x,y,...) 
     same as above, with specific axes

 The options structure may contain the following members, in agreement with 'optimset':
    options.Display: Level of display [ off | iter | notify | final ]. Default is 'off'
    options.MaxFunEvals: Maximum number of function evaluations allowed, sometimes referred as the 'cost' or 'budget'.
    options.MaxIter: Maximum number of iterations allowed
    options.TolFun: Termination tolerance on the function value (absolute value or change). Use 'x%' to specify a relative function change.
    options.TolX: Termination tolerance on parameter change. Use 'x%' to specify a relative parameter change.
    options.OutputFcn: Name of an output function. When set, it is called at each iteration step. You may use 'fmaxplot', which is provided in Optimizers. Refer to the Fit page for more information about fmaxplot. A simpler/faster alternative is the 'fmaxstop' option.
    options.PlotFcns: same as OutputFcn, but can be a set of function in a cell array.
    options.FunValCheck: Check for invalid values, such as NaN or complex
    options.MinFunEvals: when set, waits for a given number of iterations before testing for convergence
    options.optimizer: the optimizer to use

 Input:
  FUN is the iFunc model to maximize (handle or string)

  PARS is a vector with initial guess parameters. You must input an
  initial guess. PARS can also be given as a single-level structure.

  OPTIONS is a structure with settings for the optimizer, 
  compliant with optimset. Default options may be obtained with
     o=fmax('defaults')
  options.MinFunEvals sets the minimum number of function evaluations to reach
  An empty OPTIONS sets the default configuration. 

  X,Y,...: additional axes to use.

 Output:
          MAXIMUM is the solution which generated the smallest encountered
            value when input into FUN.
          FVAL is the value of the FUN function evaluated at MAXIMUM.
          EXITFLAG return state of the optimizer
          OUTPUT additional information returned as a structure.

 Example:
  model= gauss1;
  fix(model, 'all'); model.Intensity='free';
  model.Intensity=1; model.HalfWidth=.5;
  xlim(model, 'Intensity',[-2 2])
  fmax(model)

 Version: Aug. 22, 2017
 See also: fmaxsearch, optimset, iFunc/fmin
 (c) E.Farhi, ILL. License: EUPL.