From: Ravi Varadhan <rvaradhan_at_jhmi.edu>

Date: Wed, 17 Aug 2011 18:32:50 +0000

Ravi Varadhan, Ph.D.

Assistant Professor,

Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University

Date: Wed, 17 Aug 2011 18:32:50 +0000

Yes, the culprit is the evaluation of expm(A*t). This is a lazy way of solving the system of ODEs, where you save analytic effort, but you pay for it dearly in terms of computational effort!

Even in this lazy approach, I am sure there ought to be faster ways to evaluating exponent of a matrix than that in "Matrix" package.

Ravi.

Ravi Varadhan, Ph.D.

Assistant Professor,

Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University

Ph. (410) 502-2619

email: rvaradhan_at_jhmi.edu

-----Original Message-----

From: r-devel-bounces_at_r-project.org [mailto:r-devel-bounces_at_r-project.org] On Behalf Of cberry_at_tajo.ucsd.edu
Sent: Wednesday, August 17, 2011 1:08 PM
To: r-devel_at_stat.math.ethz.ch

Subject: Re: [Rd] An example of very slow computation

John C Nash <nashjc_at_uottawa.ca> writes:

> This message is about a curious difference in timing between two ways of computing the

*> same function. One uses expm, so is expected to be a bit slower, but "a bit" turned out to
**> be a factor of >1000. The code is below. We would be grateful if anyone can point out any
**> egregious bad practice in our code, or enlighten us on why one approach is so much slower
**> than the other.
*

Looks like A*t in expm(A*t) is a "matrix".

'getMethod("expm","matrix")' coerces it arg to a "Matrix", then calls expm(), whose method coerces its arg to a "dMatrix" and calls expm(), whose method coerces its arg to a 'dgeMatrix' and calls expm(), whose method finally calls '.Call(dgeMatrix_exp, x)'

Whew!

The time difference between 'expm( diag(10)+1 )' and 'expm( as( diag(10)+1, "dgeMatrix" ))' is a factor of 10 on my box.

Dunno 'bout the other factor of 100.

Chuck

> The problem arose in an activity to develop guidelines for nonlinear

*> modeling in ecology (at NCEAS, Santa Barbara, with worldwide participants), and we will be
**> trying to include suggestions of how to prepare problems like this for efficient and
**> effective solution. The code for nlogL was the "original" from the worker who supplied the
**> problem.
**>
**> Best,
**>
**> John Nash
**>
**> --------------------------------------------------------------------------------------
**>
**> cat("mineral-timing.R == benchmark MIN functions in R\n")
**> # J C Nash July 31, 2011
**>
**> require("microbenchmark")
**> require("numDeriv")
**> library(Matrix)
**> library(optimx)
**> # dat<-read.table('min.dat', skip=3, header=FALSE)
**> # t<-dat[,1]
**> t <- c(0.77, 1.69, 2.69, 3.67, 4.69, 5.71, 7.94, 9.67, 11.77, 17.77,
**> 23.77, 32.77, 40.73, 47.75, 54.90, 62.81, 72.88, 98.77, 125.92, 160.19,
**> 191.15, 223.78, 287.70, 340.01, 340.95, 342.01)
**>
**> # y<-dat[,2] # ?? tidy up
**> y<- c(1.396, 3.784, 5.948, 7.717, 9.077, 10.100, 11.263, 11.856, 12.251, 12.699,
**> 12.869, 13.048, 13.222, 13.347, 13.507, 13.628, 13.804, 14.087, 14.185, 14.351,
**> 14.458, 14.756, 15.262, 15.703, 15.703, 15.703)
**>
**>
**> ones<-rep(1,length(t))
**> theta<-c(-2,-2,-2,-2)
**>
**>
**> nlogL<-function(theta){
**> k<-exp(theta[1:3])
**> sigma<-exp(theta[4])
**> A<-rbind(
**> c(-k[1], k[2]),
**> c( k[1], -(k[2]+k[3]))
**> )
**> x0<-c(0,100)
**> sol<-function(t)100-sum(expm(A*t)%*%x0)
**> pred<-sapply(dat[,1],sol)
**> -sum(dnorm(dat[,2],mean=pred,sd=sigma, log=TRUE))
**> }
**>
**> getpred<-function(theta, t){
**> k<-exp(theta[1:3])
**> sigma<-exp(theta[4])
**> A<-rbind(
**> c(-k[1], k[2]),
**> c( k[1], -(k[2]+k[3]))
**> )
**> x0<-c(0,100)
**> sol<-function(tt)100-sum(expm(A*tt)%*%x0)
**> pred<-sapply(t,sol)
**> }
**>
**> Mpred <- function(theta) {
**> # WARNING: assumes t global
**> kvec<-exp(theta[1:3])
**> k1<-kvec[1]
**> k2<-kvec[2]
**> k3<-kvec[3]
**> # MIN problem terbuthylazene disappearance
**> z<-k1+k2+k3
**> y<-z*z-4*k1*k3
**> l1<-0.5*(-z+sqrt(y))
**> l2<-0.5*(-z-sqrt(y))
**> val<-100*(1-((k1+k2+l2)*exp(l2*t)-(k1+k2+l1)*exp(l1*t))/(l2-l1))
**> } # val should be a vector if t is a vector
**>
**> negll <- function(theta){
**> # non expm version JN 110731
**> pred<-Mpred(theta)
**> sigma<-exp(theta[4])
**> -sum(dnorm(dat[,2],mean=pred,sd=sigma, log=TRUE))
**> }
**>
**> theta<-rep(-2,4)
**> fand<-nlogL(theta)
**> fsim<-negll(theta)
**> cat("Check fn vals: expm =",fand," simple=",fsim," diff=",fand-fsim,"\n")
**>
**> cat("time the function in expm form\n")
**> tnlogL<-microbenchmark(nlogL(theta), times=100L)
**> tnlogL
**>
**> cat("time the function in simpler form\n")
**> tnegll<-microbenchmark(negll(theta), times=100L)
**> tnegll
**>
**> ftimes<-data.frame(texpm=tnlogL$time, tsimp=tnegll$time)
**> # ftimes
**>
**>
**> boxplot(log(ftimes))
**> title("Log times in nanoseconds for matrix exponential and simple MIN fn")
**>
*

-- Charles C. Berry cberry_at_tajo.ucsd.edu ______________________________________________ R-devel_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel ______________________________________________ R-devel_at_r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-develReceived on Wed 17 Aug 2011 - 18:34:57 GMT

This quarter's messages: by month, or sorted: [ by date ] [ by thread ] [ by subject ] [ by author ]

*
Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.
Archive generated by hypermail 2.2.0, at Wed 17 Aug 2011 - 21:30:19 GMT.
*

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-devel.
Please read the posting
guide before posting to the list.
*