[Rd] Seeking opinions on possible change to nls() code

[J C Nash]

In our work on a Google Summer of Code project "Improvements to nls()",
the code has proved sufficiently entangled that we have found (so far!)
few straightforward changes that would not break legacy behaviour. One
issue that might be fixable is that nls() returns no result if it
encounters some computational blockage AFTER it has already found a
much better "fit" i.e. set of parameters with smaller sum of squares.
Here is a version of the Tetra example:

time=c( 1,  2,  3,  4,  6 , 8, 10, 12, 16)
conc = c( 0.7, 1.2, 1.4, 1.4, 1.1, 0.8, 0.6, 0.5, 0.3)
NLSdata <- data.frame(time,conc)
NLSstart <-c(lrc1=-2,lrc2=0.25,A1=150,A2=50) # a starting vector (named!)
NLSformula <-conc ~ A1*exp(-exp(lrc1)*time)+A2*exp(-exp(lrc2)*time)
tryit <- try(nls(NLSformula, data=NLSdata, start=NLSstart, trace=TRUE))
print(tryit)

If you run this, tryit does not give information that the sum of squares
has been reduced from > 60000 to < 2, as the trace shows.

Should we propose that this be changed so the returned object gives the
best fit so far, albeit with some form of message or return code to indicate
that this is not necessarily a conventional solution? Our concern is that
some examples might need to be adjusted slightly, or we might simply add
the "try-error" class to the output information in such cases.

Comments are welcome, as this is as much an infrastructure matter as a
computational one.

Best,

John Nash