Hi Shenghui

I have been playing around and it looks very promising. The only drawback I have found is that the curves are different from the slow ones I got. It's probably a precision problem and/or the Chop function. I will continue researching on the item to see if I can improve the curves.

I will try also to force ListPlot to first substitute the f value and then compute the Inverse matrix. This could be faster, I hope.

Stefan

Dear Shenghui

I see that the code can be improved, but how?

Could you please explain how to do it? What should I take care off?

Thank you very much.

Stefan

A count of the number of constants, operators and variables in just one of the items you want to plot

In[40]:= LeafCount[20 Log10[Abs[ Yiideal[2. Pi I f]]]]

Out[40]= 547063

I tried an assortment of simple things, like replacing 0.+0.I by 0, etc. and, while that removed a few tens of thousands of redundant terms, nothing made a significant dent in the half million items needed to be evaluated hundreds or likely thousands of times to make each plot.

When the function to plot is expensive I have sometimes been able to significantly speed things up by constructing a Table of equally spaced evaluations (Log spaced in this case) and then do a ListPlot with Joined->True to reduce the number of evaluations by sometimes an order of magnitude with modest reduction in the publication quality of the graph. Unfortunately with the appearance of your plots I don't think this will likely be acceptable.