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fitter.functional - Function

	Package	utility
	Module	fitting
	Tool	fitter

Solve a general fitting problem

Synopsis
functional(fnct, x, y, sd, wt, mxiter, id)

Arguments

fnct	in	functional to be fitted
		Allowed:	a functional
		Default:	unset
x	in	the x coordinate values
		Allowed:	vector
y	in	the ordinate values
		Allowed:	vector
sd	in	standard deviation of equations
		Allowed:	one or more values used cyclically
		Default:	unset
wt	in	an optional alternate for sd
		Allowed:	one or more values used cyclically
		Default:	1
mxiter	in	the maximum number of iterations
		Allowed:	integer
		Default:	50
id	in	the id of a sub-tool
		Allowed:	fitter id
		Default:	0

Returns
bool or fail

Description
functional will make a non-linear least squares solution for the points through the ordinates at the x values, using the specified fnct. Details can be found in the linear description.

Example

- include 'fitting.g'                   # create default fitter
- x := [1:10];                          # some x values
- y := 3*x*x;                           # some y values
- dfit.functional(dfs.poly(2), x, y);   # solve 2nd order polynomial
T
- dfit.solution();
[-1.10049e-15 7.44482e-16 3]  
- include 'functionals.g'               # allow functionals
- anonlin := function() {			# encapsulate some code
z:=dfs.compiled('p0+p1*x0+p2*x1')       # a 2-d functional
x:=[1,2,3,4,5,6]                        # 3 observations
z.setparameters([1,2,3])		# set parameters to get ys
print 'y=', y:=z.f(x)			
dfit.functional(z,x,y)			# fit
print 'non-linear:', dfit.solution()
z:=dfs.compiled('p0+p1*x0')             # try a 1-d funtional	
x:=[1,3,5]
z.setparameters([1,2])
print 'y=', y:=z.f(x)
dfit.functional(z,x,y)
print 'non-linear:', dfit.solution()
z:=dfs.compiled('6+p0')			# try a 0-d functional
x:=[]
print 'y=', y:=z.f([1:3])-2
dfit.functional(z,x,y)
print 'non-linear:', dfit.solution()
return T
}
- anonlin()
y= [9 19 29] 
non-linear [1 2 3] 
y= [3 7 11] 
non-linear [1 2] 
y= [4 4 4] 
non-linear -2
T