# Plotting functions given by huge summations

I have to plot some functions of one variable. The problem is that these functions are given by very huge summations of some sine and cosine functions and, as a result, I easily exceed the memory. I was wondering if you have some suggestions in order to reduce the memory used by this kind of plotting.

Here is an example of code

m = RandomVariate[GaussianOrthogonalMatrixDistribution[1/60, 65000]];
dataRMT = Eigenvalues[m // N];

SFFRMT[t_] = Total[Exp[-(I t) dataRMT]] Total[Exp[(I t) dataRMT]];

M = 300;
Table[(m =
RandomVariate[GaussianOrthogonalMatrixDistribution[1/60, 65000]];
dataRMT = Eigenvalues[m // N];
SFFRMT[t_] =
SFFRMT[t] +
Total[Exp[-(I t) dataRMT]] Total[Exp[(I t) dataRMT]];), {i, 1,
M}];

LogLogPlot[Evaluate[SFFRMT[T]], {T, 0.1, 10^8}]


Thank you.

Cheers

• Can you give us an example of such a function? Without it it's hard to know what specifically will help your case. – b3m2a1 Mar 11 '18 at 10:08
• yes. A typical example takes a form like Sum[Sum[Exp[I * Subscript[a, ij]*t], {i, 1, 65000}], {j, 1, 200}] – Dario Rosa Mar 11 '18 at 10:19
• That's not a function other people can plot. If you don't give an example of something other people can easily feed into Plot[], then you won't be able to get much help. – J. M. is away Mar 11 '18 at 10:31
• You are right. Let me simplify the thing: I can create a small piece of code that realizes an example and post it – Dario Rosa Mar 11 '18 at 10:35
• Note that you perform also quite a lot symbolic computations by adding more and more symbolic expressions to SFFRMT[t]. That's also not very efficient. Sorry, apart from that, I have no helpful comments. I use to ask people if they really need all the eigenvalues when I see them having performance problems... – Henrik Schumacher Mar 11 '18 at 12:37