[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'
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.
Syntax:
fmax(model)
maximise the model, using current model or guessed parameters. Return best parameters
fmax(model, pars)
maximise the model, starting with given parameters and return best parameter set
when pars is given as [], current/guessed parameters are used
fmax(model, pars, 'optimizer')
maximise the model, as above, using given optimizer with its default configuration
for instance: fmax(model, [], 'fminpso')
fmax(model, pars, options)
maximise the model, as above, using given optimizer configuration
for instance: fmax(model, [], 'optimizer=fminpso; OutputFcn=fminplot; 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:
fminpso: Particle Swarm Optimization
fminpowell: Powell with Coggins line search
fminhooke: Hooke-Jeeves direct search
fminralg: Shor R-algorithm
fminsimpsa: Simplex/simulated annealing
fminimfil: 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 'fminplot', which is provided in Optimizers.
Refer to the Fit page for more information about fminplot. A simpler/faster
alternative is the 'fminstop' 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: Nov. 26, 2018
See also: fminsearch, optimset, iFunc/fmin
(c) E.Farhi, ILL. License: EUPL.