[Rd] Using the nls package

[Telford Tendys]

I'm a bit confused about the nls package, I'm trying to use it for curve fitting.

First off, the documentation for nls says ``see `nlsControl' for the
names of the settable control values'' -- this is wrong, it should be
nls.control (minor point but had me confused for a moment).

Now I'll try something very simple (maybe too simple):
----------------------------------------------------------------------
> q <- data.frame( x=1:10 )
> q$y <- eval( expression( 4 + 5 * x ), q )
> library( nls )
> w <- nls( y ~ P1 + P2 * x, q, start=list( P1=1, P2=1 )) 
Error in nls(y ~ P1 + P2 * x, q, start = list(P1 = 1, P2 = 1)) : 
        maximum number of iterations exceeded
> w <- nls( y ~ P1 + P2 * x, q, start=list( P1=1, P2=1 ), trace=T, control=nls.control( maxiter=10 ))
7570 :  1 1 
7.888609e-29 :  4 5 
0 :  4 5 
0 :  4 5 
0 :  4 5 
0 :  4 5 
0 :  4 5 
0 :  4 5 
0 :  4 5 
0 :  4 5 
0 :  4 5 
----------------------------------------------------------------------

There is something I really don't understand here -- it seems to
go right to the answer but then cannot detect that it should
terminate the search. The default tolerance of 1e-5 seems reasonable.
Same happens with a slightly harder problem:

----------------------------------------------------------------------
> q$y <- eval( expression( 4 + 5 / x + 7 * x ), q )> w <- nls( y ~ P1 + P2 / x + P3 * x, q, start=list( P1=1, P2=1, P3=1 ), trace=T, control=nls.control( maxiter=10 ))
16505.09 :  1 1 1 
3.578718e-14 :  4 5 7 
2.650573e-28 :  4 5 7 
1.262177e-29 :  4 5 7 
0 :  4 5 7 
0 :  4 5 7 
0 :  4 5 7 
0 :  4 5 7 
0 :  4 5 7 
0 :  4 5 7 
0 :  4 5 7 
----------------------------------------------------------------------

It knows what the answer should be but does not know that it has the
answer, try injecting some noise in the sample points:

----------------------------------------------------------------------
> q$y <- eval( expression( 4 + 5 / x + 7 * x + runif( 10 )), q )
> w <- nls( y ~ P1 + P2 / x + P3 * x, q, start=list( P1=1, P2=1, P3=1 ), trace=T, control=nls.control( maxiter=10 ))
16882.09 :  1 1 1 
0.4923209 :  4.796474 5.290280 6.947685 
----------------------------------------------------------------------

OK, now it stops right away with an approximate solution...
must be alergic to getting the right answer!
I guess with all that noise, this answer is probably the best possible.

Well, I'm sure that isn't such a big bug to fix, probably
a test for >0 when it should be >=0 or something. Maybe just
detect exceptionally small sum of squares (i.e. zero) and bail
out right there. Do statisticians have an instinct to disbelieve that
their sample data could ever fit the model?

Now a bigger problem (for me), I want to be able to use complex
numbers in the calculation:

----------------------------------------------------------------------
> q$y <- eval( expression( 4 + x*(0+1i)), q )
> w <- nls( y ~ P1 + P2 * x, q, start=list( P1=1, P2=1 ), trace=T, control=nls.control( maxiter=10 ))
Error in model.frame(formula, rownames, variables, varnames, extras, extranames,  : 
        invalid variable type
> traceback()
[1] "model.frame.default(formula = ~y + x, data = q)"                  
[2] "model.frame(formula = ~y + x, data = q)"                          
[3] "eval(expr, envir, enclos)"                                        
[4] "eval(mf, sys.frame(sys.parent()))"                                
[5] "as.list(eval(mf, sys.frame(sys.parent())))"                       
[6] "nls(y ~ P1 + P2 * x, q, start = list(P1 = 1, P2 = 1), trace = T, "
[7] "    control = nls.control(maxiter = 10))"                         
> model.frame.default( y ~ x, q )
Error in model.frame(formula, rownames, variables, varnames, extras, extranames,  : 
        invalid variable type
----------------------------------------------------------------------

Is there any chance of getting this to work? Should I split up the
complex numbers into components and write my equations are equivalent
expressions in reals (ugly but I could do it if I have to)?

Seems like something in the .Internal(model.frame(...)) is barfing
at a complex number. Is that necessary or just an accident? Surely
R has enough complex number capabilities to handle them here too...

Sorry about whinging all the time :-)

	- Tel
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