[R] fit to spike with exponential decay : optim() question

[Robert D. Merithew]

I finally got (mostly) what I wanted.  In an attempt to figure out how to
get nls to deal with a non-differentiable function, I had (stupidly)
'simplified' the problem until it became singular.

Can I do something to make optim() less sensitive to my initial guess? For
this example, I get a lousy solution if I make the initial guess for t0 =
min(t) = 0.05.

Thanks again,
--
Robert Merithew
LASSP, Clark Hall
Cornell University, Ithaca NY


-----------

t <- c(0.05,0.9,1.4,2.38,3.42,5.4,8.31,12.4)
amp <- c(1.0,0.85,7.4, 6.1, 4.95, 3.5, 2.3, 1.5)

spike <- function (x, t) {
  b0 <- x[1]
  b1 <- x[2]
  tau <- x[3]
  t0 <- x[4]
  
  temp <- exp((-t+t0)/tau)
  (b0 + (b1 * temp)  * (t > t0))
}

spike.sos <- function (x) {
  sum((amp - spike(x, t))^2)
}

guess <- c(min(amp), max(amp)-min(amp), (max(t)-min(t))/3, 0)

decay.opt <- optim(guess, spike.sos, control=list(trace=T))

xr <- (0:140)/10
plot (xr, spike(decay.opt$par, xr), type="l", col="blue")
points (t, amp)

--------


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