Very nice, Hans! I didn't know of the existence of Lambert W function (a.k.a Omega function) before. I didn't know that it occurs in the solution of exponential decay with delay: dy/dy = a * y(t - 1). Apparently it is more than 250 years old!
Thanks, Ravi. -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Hans W Borchers Sent: Wednesday, July 28, 2010 11:11 AM To: r-h...@stat.math.ethz.ch Subject: Re: [R] Optimization problem with nonlinear constraint Uli Kleinwechter <u.kleinwechter <at> uni-hohenheim.de> writes: > > Dear Ravi, > > As I've already written to you, the problem indeed is to find a solution > to the transcendental equation y = x * T^(x-1), given y and T and the > optimization problem below only a workaround. I don't think optimization is the right approach for simply inverting a simple function. The inverse of the function x \to x * e^x is the Lambert W function. So the solution in your case is: W(log(T)*y*T) / log(T) # hope I transformed it correctly. Now, how to compute Lambert's W ? Well, look into the 'gsl' package and, alas, there is the function lambert_W0. Your example: ---- y <- 3 T <- 123 library(gsl) lambert_W0(log(T)*y*T)/log(T) # [1] 1.191830 ---- Regards, Hans Werner > > John C. Nash has been so kind to help me on here. In case anyone faces a > similar problem in the future, the solution looks as follows: > > ***** > > func1 <- function(y,x,T){ > out <- x*T^(x-1)-y > return(out) > } > > # Assign the known values to y and T: > y <- 3 > T <- 123 > > root <- uniroot(func1,c(-10,100),y=y,T=T) > print(root) > > ******** > > Somewhat simpler than I thought.... > > Thanks again! > > Uli > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
