fit

Vector

SYNTAX

error = data_vec.fit(fit_vec,"fcn",indep_vec,&p1,[&p2],...,[&pN])

DESCRIPTION

Use a simplex algorithm to find parameters p1 through pN such to minimize the mean squared error between the "data" contained in data_vec and the approximation generated by the user-supplied "fcn" applied to the elements of indep_vec.

fcn must take one argument which is the main independent variable followed by one or more arguments which are tunable parameters which will be optimized. Thus the arguments to .fit following "fcn" should be completely analogous to the arguments to fcn itself. The difference is that the args to fcn must all be scalars while the corresponding args to .fit will be a vector object (for the independent variable) and pointers to scalars (for the remaining parameters).

The results of a call to .fit are three-fold. First, the parameters of best fit are returned by setting the values of the variables p1 to pN (possible because they are passed as pointers). Second, the values of the vector fit_vec are set to the fitted function. If fit_vec is not passed with the same size as indep_vec and data_vec, it is resized accordingly. Third, the mean squared error between the fitted function and the data is returned by .fit. The .fit() call may be reiterated several times until the error has reached an acceptable level.

Care must be taken in selecting an initial set of parameter values. Although you need not be too close, wild discrepancies will cause the simplex algorithm to give up. Values of 0 are to be avoided. Trial and error is sometimes necessary.

Because calls to hoc have a high overhead, this procedure can be rather slow. Several commonly-used functions are provided directly in c code and will work much faster. In each case, if the name below is used, the builtin function will be used and the user is expected to provide the correct number of arguments (here denoted a,b,c...). 

"exp1": y = a * exp(-x/b)  
"exp2": y = a * exp(-x/b) + c * exp (-x/d)
"charging": y = a * (1-exp(-x/b)) + c * (1-exp(-x/d))
"line": y = a * x + b
"quad": y = a * x^2 + b*x + c

BUGS

This function is not very useful for fitting the results of simulation runs due to its argument organization. For that purpose the fit_praxis syntax is more suitable. This function should become a top-level function which merely takes a user error function name and a parameter list.

An alternative implementation of the simplex fitting algorithm is in the scopmath library.

SEE ALSO

fit_praxis

EXAMPLES

The nrnmainmenu.Miscellaneous.ParameterizedFunction widget uses this function and is implemented in nrn/lib/hoc/funfit.hoc

The following example demonstrates the strategy used by the simplex fitting algorithm to search for a minimum. The location of the parameter values is plotted on each call to the function. The sample function has a minimum at the point (1, .5)

execute following example 

objref g, dvec, fvec, ivec
g = new Graph()
g.size(0,3,0,3)

func fun() {local f
        if ($1 == 0) {
                g.line($2, $3)
                g.flush()
                print $1, $2, $3
        }
        return ($2 - 1)^2 +($3-.5)^2
}


dvec = new Vector(2)
fvec = new Vector(2)
fvec.fill(1)
ivec = new Vector(2)
ivec.indgen()

a = 2
b = 1
g.beginline()
error = dvec.fit(fvec, "fun", ivec, &a, &b)
print a, b, error

neuron/general/classes/vector/vfit.hel : May 13 2012