*To*: mathgroup@smc.vnet.net*Subject*: [mg10456] Plotting vector-valued functions*From*: Malcolm Boshier <m.g.boshier@sussex.ac.uk>*Date*: Fri, 16 Jan 1998 04:34:42 -0500*Organization*: Physics Department, University of Sussex

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

**Follow-Ups**:**Re: Plotting vector-valued functions***From:*seanross@worldnet.att.net