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[MUG] How to plot with a constraint on the domain
| [MUG] How to plot with a constraint on the domain |
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Author: Anders Poulsen
Posted: Wed, 23 Oct 2002 08:34:12 +0200
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>> From: Anders Poulsen "Aup"
Dear MUG users,
I have a function, z=f(x1,x2,x3), with a contraint on the domain:
x1+x2+x3=1 and x1,x2,x3 all non-negative (the unit simplex). Thus z is only
a function of two variables, say x1 and x2:
z=g(x1,x2).
How can I instruct Maple to take this constraint into account, so I can
plot the curvature of the function z=g(x1,x2)? I'm only a Maple beginner,
but I haven't been able to find documentation about plotting with
constraints on the domain.
Thanks for your help,
Anders Poulsen
Assistant professor, Ph.D.
Department of Economics
The Aarhus School of Business
Silkeborgvej 2
DK-8000 Aarhus C
Denmark
E-mail: "aup"
----------------------------------------------
Anders Poulsen
Ph.D., Assistant Professor
Department of Economics, The Aarhus School of Business
Silkeborgvej 2, DK-8000 Aarhus C, Denmark
Phone: (0045) 89486400, Fax: (0045) 89486197,
E-mail: "aup"
Personal homepage: http://www.hha.dk/nat/anders/persoweb.htm
----------------------------------------------
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| [MUG] Re: How to plot with a constraint on the domain |
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Author: Carl Devore
Posted: Sun, 27 Oct 2002 11:31:10 -0500
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>> From: Carl Devore "devore"
On Wed, 23 Oct 2002, Anders Poulsen wrote:
> I have a function, z=f(x1,x2,x3), with a contraint on the domain:
> x1+x2+x3=1 and x1,x2,x3 all non-negative (the unit simplex). Thus z is only
> a function of two variables, say x1 and x2:
> z=g(x1,x2).
>
> How can I instruct Maple to take this constraint into account, so I can
> plot the curvature of the function z=g(x1,x2)?
I am not sure what you mean by "plot the curvature". But you can plot z=
g(x1,z2) like this:
plot3d(f(x1,x2,1-x1-x2), x1= 0..1-x2, x2= 0..1);
It might be useful to have the plotting domain be a perfect equilateral
triangle with vertices (1,0,0), (0,1,0), and (0,0,1). For ideas along
these lines, see my worksheet "Contour plots for three-ingredient mixing
problems" available at the Maple Applications Center
http://www.mapleapps.com in the Statistics category.
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