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MathGroup Archive 1998

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Plotting vector-valued functions



    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.  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.
    It seems that unless the head of the first argument to Plot is List,
Plot assumes that it will evaluate to a real number and returns with an
error if it later finds that it doesn't.  Why can't Plot trust the user
long enough to discover that the function will evaluate to a list?
Thanks for any solutions or explanations, Malcolm





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