Re: Plotting vector-valued functions
- To: mathgroup@smc.vnet.net
- Subject: [mg10571] Re: Plotting vector-valued functions
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Date: Tue, 20 Jan 1998 16:54:13 -0500
- Organization: University of Western Australia
- References: <69na52$860@smc.vnet.net>
Malcolm Boshier wrote:
> I have a problem which is related to the recent thread about
> plotting lists of functions. In the case when a vector-valued function
> is expensive or impossible to Evaluate before plotting, Plot apparently
> forces you to evaluate the function repeatedly at each value of the
> independent parameter. This can be very inefficient.
> As an example, suppose that f[z] returns the eigenvalues of a 5 x 5
> matrix which is a function of z.
Ok, say,
In[1]:= m[z_] = {{2, 1, 9, 5, 1}, {5, 5, 1, 3, 7}, {9, 4, 8, 7, 5},
{3, 8, 1 + z, 8, 7}, {7 - 2*z, 2, 3, 8, 8}};
In[2]:= f[z_] := Eigenvalues[m[z]]
> In general this function cannot be evaluated without a value for z,
Actually, it _can_ be evaluated as a function of z in terms of
(algebraic) Root objects. Try entering f[z].
> so Plot[ Evaluate[f[z]], {z, zmin, zmax}] doesn't work.
This does work for me:
In[3]:= Plot[Evaluate[Re[f[z]]], {z, -10, 10}];
> 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.
Dynamic programming can be used to avoid this. E.g., you could define
In[3]:= f[z_?NumericQ] := f[z] = Eigenvalues[m[z]]
Then, when f[z][[1]] is evaluated for a particular z, f[z] is recorded
and saved.
Cheers,
Paul
____________________________________________________________________
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul@physics.uwa.edu.au AUSTRALIA
http://www.pd.uwa.edu.au/~paul
God IS a weakly left-handed dice player
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