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MathGroup Archive 1997

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Re: Plotting with a simplex

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5842] Re: [mg5518] Plotting with a simplex
  • From: Sherman Reed <Sherman.Reed at worldnet.att.net>
  • Date: Sun, 2 Feb 1997 01:30:06 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

At 12:26 AM 12/15/96 +0000, you wrote:
>Is there a way I can do plots for variables that are confined to a 
>simplex? 

The material I sent to you in December is probably the
end of the line as far as simple plots are concerned.
I will be glad to modify or whatever to suit your needs.

I could not think of something that had a simple 
presentation to extend beyond 3 dimensions.  I have 
done nothing on a two dimensional presentation.

For dimensions greater than 3, I offer the following:

Assume that a sample set is composed of set of frequencies
say {a,b,c,d,e} and that we have ten sample sets and that
we want to compare them.  I suggest that you compare the
first element of each sample set, then the second, etc.

Graphically, Graphics`Graphics` has an option that will do
exactly that without any horsing around.

One could also find means, medians, etc for each frequency
set. One could also apply some simple hypothesis testing to 
each frequency set.

The code below works on 2.2.3, if you want it on 3.0, I will
have to do a little work, but not much.  You will have to paste
this into Mma, and then convert it to input.Select all the 
material, then use Style, then CellStyle, then Input.  The code
should execute just fine.  I have tried it and it works.

Sherman C. Reed

data=Table[{.2+.1*(Random[]-.5),
			.3+.1*(Random[]-.5),
			.25+.1*(Random[]-.5),
			.1+.1*(Random[]-.5),
			0},{x,1,10,1}];
For[i=1,i<1+Length[data],i++,
	data[[i,5]]=1-Apply[Plus,data[[i]]]
	]
<<Graphics`Graphics`
BarChart[data[[1]],data[[2]],data[[3]],
	data[[4]],data[[5]],data[[6]],data[[7]],data[[8]],
	data[[9]],data[[10]],Frame->True,
	GridLines->{None,Automatic},
	PlotLabel->FontForm[PlotLabel,{"TimesBold",12}]
	]



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