[R] Creating 3 vectors that sum to 1

[Greg Snow]

Or we could expand a bit more:

require(TeachingDemos)
require(gtools)

n <- 1000
rtrg <- matrix(NA, n, 3)
for (i in 1:n) rtrg[i,] <- diff(c(0, sort(runif(2)), 1))

rtrg2 <- matrix(NA, n, 3)
for (i in 1:n) {
tmp <- runif(3)
rtrg2[i, ] <- tmp/sum(tmp)
}

rtrg3 <- matrix( rexp(n*3), ncol=3 )
rtrg3 <- rtrg3/rowSums(rtrg3)

rtrg4 <- rdirichlet(n, rep(1,3))

par(mfrow=c(2,2))
triplot(rtrg, pch='.')  # Looks more uniformly distributed
triplot(rtrg2, col=2, pch='.')  # Corners are sparsely populated
triplot(rtrg3, col=3, pch='.')
triplot(rtrg4, col=4, pch='.')




What could also be interesting in using vis.test (also TeachingDemos) to see which can be told apart from each other.  My guess is that rtrg2 method will be visible different from the other 3, but the other 3 will be indistinguishable from each other.

The last 2 have the advantage (the 2nd could be rewritten to have the same advantage) of being much quicker, not sure how to speed up the 1st noticibly.



-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111


> -----Original Message-----
> From: Ravi Varadhan [mailto:rvaradhan at jhmi.edu]
> Sent: Tuesday, March 29, 2011 12:59 PM
> To: Ravi Varadhan
> Cc: Greg Snow; r-help at r-project.org
> Subject: Re: [R] Creating 3 vectors that sum to 1
> 
> 
> Here is an exploration of two different 3-tuple generators (that sum to
> 1) based on Greg's triplot function:
> 
> require(TeachingDemos)
> 
> n <- 1000
> rtrg <- matrix(NA, n, 3)
> for (i in 1:n) rtrg[i,] <- diff(c(0, sort(runif(2)), 1))
> 
> rtrg2 <- matrix(NA, n, 3)
> for (i in 1:n) {
> tmp <- runif(3)
> rtrg2[i, ] <- tmp/sum(tmp)
> }
> 
> par(mfrow=c(2,1))
> triplot(rtrg)  # Looks more uniformly distributed
> triplot(rtrg2, col=2)  # Corners are sparsely populated
> 
> 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: Ravi Varadhan <rvaradhan at jhmi.edu>
> Date: Tuesday, March 29, 2011 2:33 pm
> Subject: Re: [R] Creating 3 vectors that sum to 1
> To: Greg Snow <Greg.Snow at imail.org>
> Cc: "r-help at r-project.org" <r-help at r-project.org>
> 
> 
> > The following one-liner generates uniformly distributed 3-tuples that
> > sum to 1:
> >
> > diff(c(0, sort(runif(2)), 1))
> >
> > More, generally you can generate n-tuples that sum to unity as:
> >
> > diff(c(0, sort(runif(n-1)), 1))
> >
> >
> > 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: Greg Snow <Greg.Snow at imail.org>
> > Date: Tuesday, March 29, 2011 1:02 pm
> > Subject: Re: [R] Creating 3 vectors that sum to 1
> > To: Christopher Desjardins <cddesjardins at gmail.com>,
> > "r-help at r-project.org" <r-help at r-project.org>
> >
> >
> > > Do a search for Dirichlet, that may give you the tools you need.
> > Also
> > > for plotting 3 vectors that sum to 1, instead of a 3d scatter plot
> > you
> > > should look into a triangle or trilinear plot, see ?triplot in the
> > > TeachingDemos package (the see also for that help page lists
> several
> >
> > > other implementations in other packages as well).
> > >
> > > --
> > > Gregory (Greg) L. Snow Ph.D.
> > > Statistical Data Center
> > > Intermountain Healthcare
> > > greg.snow at imail.org
> > > 801.408.8111
> > >
> > >
> > > > -----Original Message-----
> > > > From: r-help-bounces at r-project.org [
> > > > project.org] On Behalf Of Christopher Desjardins
> > > > Sent: Tuesday, March 29, 2011 10:20 AM
> > > > To: r-help at r-project.org
> > > > Subject: [R] Creating 3 vectors that sum to 1
> > > >
> > > > I have 3 vectors: p1, p2, and p3. I would like each vector to be
> any
> > > > possible value between 0 and 1 and p1 + p2 + p3 = 1. I want to
> graph
> > > > these
> > > > and I've thought about using scatterplot3d(). Here's what I have
> so
> > > > far.
> > > >
> > > > library(scatterplot3d)
> > > > p1 <- c(1,0,0,.5,.5,0,.5,.25,.25,.34,.33,.33,.8,.1,.1,.9,.05,.05)
> > > > p2 <- c(0,1,0,.5,0,.5,.25,.5,.25,.33,.34,.33,.1,.8,.1,.05,.9,.05)
> > > > p3 <- c(0,0,1,0,.5,.5,.25,.25,.5,.33,.33,.34,.1,.1,.8,.05,.05,.9)
> > > > scatterplot3d(p1,p2,p3)
> > > >
> > > >
> > > > However, I wonder if there is an easy way to create vectors p1,
> > p2,
> > > and
> > > > p3.
> > > >
> > > > 	[[alternative HTML version deleted]]
> > > >
> > > > ______________________________________________
> > > > R-help at r-project.org mailing list
> > > >
> > > > PLEASE do read the posting guide
> > > > guide.html
> > > > and provide commented, minimal, self-contained, reproducible
> code.
> > >
> > > ______________________________________________
> > > R-help at r-project.org mailing list
> > >
> > > PLEASE do read the posting guide
> > > and provide commented, minimal, self-contained, reproducible code.
> >
> > ______________________________________________
> > R-help at r-project.org mailing list
> >
> > PLEASE do read the posting guide
> > and provide commented, minimal, self-contained, reproducible code.