From: Uwe Ligges <ligges_at_statistik.uni-dortmund.de>

Date: Sun 26 Jun 2005 - 19:59:18 EST

*> 0.0011715433 5835 20.55812 -0.0021601140 0.0021601140
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*>
*

*> My question is how to improve the precision of b (which is x) here.
*

*> It seems that seq(20.55806,20.55816,length=10000 ) is only precise to
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*> 5 or so digits, and thus, is equivalent for numerous succesive
*

*>
*

>

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sun Jun 26 20:01:13 2005

Date: Sun 26 Jun 2005 - 19:59:18 EST

Gregory Gentlemen wrote:

> Spencer: Thank you for the helpful suggestions. I have another

*> question following some code I wrote. The function below gives a
**> crude approximation for the x of interest (that value of x such that
**> g(x,n) is less than 0 for all n).
**>
**> # // btilda optimize g(n,x) for some fixed x, and then approximately
**> finds that g(n,x) # such that abs(g(n*,x)=0 // btilda <-
**> function(range,len) { # range: over which to look for x bb <-
**> seq(range[1],range[2],length=len) OBJ <- sapply(bb,function(x) {fixed
**> <- c(x,1000000,692,500000,1600,v1,217227);
**> return(optimize(g,c(1,1000),maximum=TRUE,tol=0.0000001,x=fixed)$objective)})
**> tt <- data.frame(b=bb,obj=OBJ) tt$absobj <- abs(tt$obj) d <-
**> tt[order(tt$absobj),][1:3,] return(as.vector(d)) }
**>
**> For instance a run of
**>
*

>> btilda(c(20.55806,20.55816),10000) .... returns:

>

> b obj absobj 5834 20.55812

> -0.0004942848 0.0004942848 5833 20.55812 0.0011715433

Why do you think so? It is much more accurate! See ?.Machine

Uwe Ligges

> values. How can I get around this?

*>
**>
**> Spencer Graves <spencer.graves@pdf.com> wrote: Part of the R culture
**> is a statement by Simon Blomberg immortalized in library(fortunes)
**> as, "This is R. There is no if. Only how."
**>
**> I can't see now how I would automate a complete solution to your
**> problem in general. However, given a specific g(x, n), I would start
**> by writing a function to use "expand.grid" and "contour" to make a
**> contour plot of g(x, n) over specified ranges for x = seq(0, x.max,
**> length=npts) and n = seq(0, n.max, npts) for a specified number of
**> points npts. Then I'd play with x.max, n.max, and npts until I got
**> what I wanted. With the right choices for x.max, n.max, and npts, the
**> solution will be obvious from the plot. In some cases, nothing more
**> will be required.
**>
**> If I wanted more than that, I would need to exploit further some
**> specifics of the problem. For that, permit me to restate some of what
**> I think I understood of your specific problem:
**>
**> (1) For fixed n, g(x, n) is monotonically decreasing in x>0.
**>
**> (2) For fixed x, g(x, n) has only two local maxima, one at n=0 (or
**> n=eps>0, esp arbitrarily small) and the other at n2(x), say, with a
**> local minimum in between at n1(x), say.
**>
**> With this, I would write functions to find n1(x) and n2(x) given x. I
**> might not even need n1(x) if I could figure out how to obtain n2(x)
**> without it. Then I'd make a plot with two lines (using "plot" and
**> "lines") of g(x, 0) and g(x, n2(x)) vs. x.
**>
**> By the time I'd done all that, if I still needed more, I'd probably
**> have ideas about what else to do.
**>
**> hope this helps. spencer graves
**>
**>
**> Gregory Gentlemen wrote:
**>
**>
*

>> Im trying to ascertain whether or not the facilities of R are >> sufficient for solving an optimization problem I've come accross. >> Because of my limited experience with R, I would greatly appreciate >> some feedback from more frequent users. The problem can be >> delineated as such: >> >> A utility function, we shall call g is a function of x, n ... >> g(x,n). g has the properties: n > 0, x lies on the real line. g may >> take values along the real line. g is such that g(x,n)=g(-x,n). g >> is a decreasing function of x for any n; for fixed x, g(x,n) is >> smooth and intially decreases upon reaching an inflection point, >> thereafter increasing until it reaches a maxima and then declinces >> (neither concave nor convex). >> >> My optimization problem is to find the largest positive x such that >> g(x,n) is less than zero for all n. In fact, because of the >> symmetry of g around x, we need only consider x > 0. Such an x does >> exists in this problem, and of course g obtains a maximum value of >> 0 at some n for this value of x. my issue is writing some code to >> systematically obtain this value. >> >> Is R capable of handling such a problem? (i.e. through some sort of >> optimization fucntion, or some sort of grid search with the >> relevant constraints) >> >> Any suggestions would be appreciated. >> >> Gregory Gentlemen gregory_gentlemen@yahoo.ca >> >> >> >> The following is a sketch of an optimization problem I need to >> solve. >> >> __________________________________________________ >> >> >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help@stat.math.ethz.ch mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the >> posting guide! http://www.R-project.org/posting-guide.html

>

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Sun Jun 26 20:01:13 2005

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