My functions (array of functions) are defined like:
and what I am trying to evaluate is:
evalf(add(add(f[i, j](i, j, x, y), i = 1 .. 50), j = 1 .. 100))
And I am plotting the summation by plot3d and takes about 5 hours; But, when I decrease intervals and evaluate this summation, e.g.:
evalf(add(add(f[i, j](i, j, x, y), i = 1 .. 50), j = 1 .. 5))
plot3d plots it in 2':30''. But the time increases exponentially as the interval of i and j increases, and for 100 intervals, it takes more than 5 hours. So I think it makes sense if I calculate each function values numerically, and add them up. the number of subfuncs are 50*100=5000 against 5*50=250. meaning by summing them up numerically, it should take 5000/250*(2':30'') = 50', not 5 hours!
If there is no alternative, then SurfacePlot seems to be the best way. But still I don't have any idea about why it is taking much longer time strangely. Am I mistaken somewhere?