I've found that the discussions are interesting, generally speaking, peoples seem equally confident on R's optim/nlm and Excel's solver. The authors of the algorithm GRG2 (Generalized Reduced Gradient) are not cited in the documentation of optim(), so I'm wondering if the optimization algorithm implemented in Excel is "fondamentally" the same than that in R ? Thanks in advance -- Fan
Damon Wischik wrote:
Michael Rennie wrote:
Last, it's not even that I'm getting error messages anymore- I just can't get the solution that I get from Excel. If I try to let R find the solution, and give it starting values of c(1,2), it gives me an optimization solution, but an extremely poor one. However, if I give it the answer I got from excel, it comes right back with the same answer and solutions I get from excel. Using the 'trace' function, I can see that R gets stuck in a specific region of parameter space in looking for the optimization and just appears to give up. Even when it re-set itself, it keeps going back to this region, and thus doesn't even try a full range of the parameter space I've defined before it stops and gives me the wrong answer.
1. Either your function or the Excel solver is wrong. I executed your
source code (which defines f), then ran it over a grid of points, and
plotted the answer, using this code:
xvals <- seq(.2,2,by=.2)
yvals <- seq(1,3,by=.2)
z <- matrix(NA,nrow=length(xvals),ncol=length(yvals))
for (i in 1:length(xvals)) for (j in 1:length(yvals)) {
x <- xvals[i]
y <- yvals[j]
z[i,j] <- f(c(x,y))
}
filled.contour(x=xvals,y=yvals,z=log(z))
Your "solution" from Excel evaluates to
f(c(.558626306252032,1.66764519286918)) == 0.3866079
while I easily found a point which was much better,
f(c(.4,1)) = 7.83029e-05
You should have tried executing your function over a grid of points, and
plotting the results in a contour plot, to see if optim was working
sensibly. You could do the same grid in Excel and R to verify that the
function you've defined does the same thing in each.
Since your optimization is only over a 2D parameter space, it is easy for
you to plot the results, to see at a glance what the optimum is, and to
work out what is going wrong.
2. Your code executes very slowly because it is programmed inefficiently.
You need to iterate a function to get your final solution, but you don't
need to keep track of all the states you visit on the way. The way R
works, whenever you assign a value to a certain index in a vector, as in
A[i] <- 10,
the system actually copies the entire vector. So, in every iteration, you
are copying very many vectors, and this is needlessly slowing down the
program. Also, at the end of each iteration, you define
bio <- cbind(W, C, ASMR, SMR, A, F, U, SDA, Gr, Ed, GHg, EGK, Hg)
which creates a matrix. But you only ever use this matrix right at the
end, and so there is no need to create this 365*14 matrix at every single
iteration.
It looks to me as if you took some Excel code and translated it directly
into R. This will not produce efficient R code. Your iterative loop would
be more naturally expressed in R as
f <- function(q) {
p <- q[[1]]
ACT <- q[[2]]
# cat(paste("Trying p=",p," ACT=",ACT,"\n",sep=""))
state <- c(W=Wo,Hg=Hgo)
numdays <- length(temps)
for (i in 1:numdays)
state <- updateState(state,
jday=temps$jday[i],temp=temps$Temp[i],M=numdays,
p=p,ACT=ACT)
Wtmod <- state[["W"]]
Hgtmod <- state[["Hg"]]
(Wt-Wtmod)^2/Wt + (Hgt-Hgtmod)^2/Hgt
}
updateState <- function(state,jday,temp,M,p,ACT) {
# Given W[i-1] and Hg[i-1], want to compute W[i] and Hg[i]
W <- state[["W"]]
Hg <- state[["Hg"]]
# First compute certain parameters: Vc[i-1] ... Expegk[i-1]
Vc <- (CTM-temp)/(CTM-CTO)
Vr <- (RTM-temp)/(RTM-RTO)
C <- p * CA * W^CB * Vc^Xc * exp(Xc*(1-Vc)) * Pc
ASMR <- ACT * RA * W^RB * Vr^Xa * exp(Xa*(1-Vr))
...
# Now find W[i] and Hg[i]
Wnew <- if (!(jday==121 && Mat==1)) W+Gr/Ef
else W * (1-GSI*1.2)
Hgnew <- a*Hgp*C*(1-Expegk)/(Pc*W*EGK) + Hg*Expegk
c(W=Wnew,Hg=Hgnew)
}
In this code, I do not attempt to keep the entire array in memory. All I
need to know at each iteration is the value of state=(W,Hg) at time i-1,
and from this I compute the new value at time i.
3. You use some thoroughly weird code to read in a table. You should add a
row to the top of your table with variable names, then just use
temps <- read.table("TEMP.DAT", header=TRUE)
temps$Vc <- (CTM-temps$temp)/(CTM-CTO)
This would also avoid leaving global variables (like Day) hanging around
the place. Global variables cause confusion: see the next point.
4. Here are some lines taken from your code.
p <- NULL
ACT <- NULL
#starting values for p, ACT
p <- 1
ACT <- 2
f <- function (q)
{
F[i]<- (FA*((comp[i,3])^FB)*(exp(FG*p))*C[i])
# (and ACT is never referred to)
}
Why did you define p<-NULL and ACT<-NULL at the top? Those definitions are
irrelevant, because they are overridden by p<-1 and ACT<-2.
In the body of your function f, in defining F[i], you refer to the
variable p. The only assignment to p is in the line p<-1. I strongly
suspect this is an error. Probably you want to refer to q[1]. The best way
to do this (as you can see from my code above) is to define p and ACT at
the beginning of f.
5. Some minor comments on code. It's unwise to use T or F as variable
names in R, because of the potential for confusion with S-Plus, which uses
them for TRUE and False. Also, you don't need all those brackets: A*(B*C)
is the same as A*B*C, and ((A/B)/C) is more transparently written as
A/(B*C). Also, you should indent your code, since otherwise you'll just
confuse yourself and other people.
6. I've written a version of the code which takes all these comments into
account. It doesn't agree with your Excel solution. You haven't given us
enough real data for me to work out if there's a bug in my code or if the
Excel solution is wrong. Once you have worked out a function f which you
know to be correct (checked by drawing a contour plot), if you have any
more problems, share it with us and we may be able to help.
Damon Wischik.
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