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Re: Plotting vector-valued functions

• To: mathgroup@smc.vnet.net
• Subject: [mg10525] Re: [mg10456] Plotting vector-valued functions
• From: Lou Talman <me@talmanl.mscd.edu>
• Date: Tue, 20 Jan 1998 02:23:12 -0500

Malcolm Boshier wrote:

> suppose that f[z] returns the eigenvalues of a 5 x 5
> matrix which is a function of z.  In general this function cannot be
> evaluated without a value for z, so
> Plot[ Evaluate[f[z]], {z, zmin, zmax}] doesn't work.
>     The only way around this that I have found is something like:
> 

> Plot[{f[z][[1]],  f[z][[2]], f[z][[3]], f[z][[4]], f[z][[5]]}, 

>     {z, zmin, zmax}]
> 

> which of course requires 5 evaluations of f[z] for each value of z.

This is inevitable if you simply use Set or SetDelayed in your
definition   of the function f:

     f[z_] = <stuff>

or

     f[z_] := <stuff>

Try instead

     f[z_] := f[z] = <stuff>

This syntax causes Mathematica to remember each value it computes for f.
See Section 2.4.9 or The Book.

--Lou Talman