
plotting a realvalued function but with imaginary errors
Posted:
Aug 6, 2011 11:56 AM


If you are interested in seeing a display of y=f(x), over a real interval 0<=x<=10, say, and where f is realvalued, finite, continuous, etc. on that interval, there are many programs that are available to help.
What if f is realvalued (etc.) but the program that you use to compute f has some roundoff error that results in small imaginary parts? How might you deal with this as a policy in a plotting program?
Some possibilities that come to (my) mind:
1. Instead of plotting f(x), plot realpart(f(x)), perhaps making some kind of warning noise. This assumes imagpart(f(x)) is smaller than some ignorable relative quantity compared to realpart. (difficulty: what if realpart is small too???). 1b. (Same as 1 except no warning)
2. Leave blank spots on the display where the values of f(x) are not purely real. 2b. (Same as 2 except issue warnings)
Suggestions?
.......
This should only be an issue if f(x) is computed by some formula that you have concocted.
If f(x) is a good library function f:Real>Real, it should not product results with nonzero imaginary components.
This problem came up in plotting, in Mathematica 7, this function:
JacobiSN[x,3] which is real for 3<x<5, yet a plot of it shows a gap around 4.
If you have Mathematica available, you can see the result from executing this:
Plot[{Re[JacobiSN[u, 3]], JacobiSN[u, 3]}, {u, 3, 5}, PlotStyle > {Orange, Thick}]
In my view the program computing JacobiSN should not be returning complex values for real arguments, ever.

