[R] Creating 3 vectors that sum to 1

[Ravi Varadhan]

Hi Greg,

Thanks. 

Here is one approach to speeding up the 1st method that I had suggested:

n <- 10000
set.seed(123)
rtrg <- matrix(NA, n, 3)
system.time(for (i in 1:n) rtrg[i,] <- diff(c(0, sort(runif(2)), 1)))

set.seed(123)
system.time({
tmp <- matrix(runif(n*2), n, 2, byrow=TRUE)
rtrg.1 <- cbind(pmin(tmp[,1], tmp[,2]), abs(tmp[,1] - tmp[,2]),1 - pmax(tmp[,1], tmp[,2]))
})

all.equal(rtrg, rtrg.1)

Now, how can we use vis.test to test differences between these?  

Best,
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 3:42 pm
Subject: RE: [R] Creating 3 vectors that sum to 1
To: Ravi Varadhan <rvaradhan at jhmi.edu>
Cc: "r-help at r-project.org" <r-help at r-project.org>


> 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 [
> > 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.