Visualization of complex functions

[najlkin]

This PR adds visualization of complex grid functions, which are represented different ways:

• magnitude
• phase
• real part
• imaginary part

To switch the representation, you may use Q key (like for quadratures) TODO: find a better one 😄
The functions can be loaded from files as normally (the file reader recognizes the format based on the header) or through a socket stream by the new command csolution (also automatically detected).

Magnitude and phase in example 22.

The complex solution can be also animated by varying the complex phase. To increase the phase rate, press Alt+Enter, and to decrease Alt+0. To stop/start Alt+. 🎞️ .

↪️dependency: #336

[najlkin]

@mlstowell , if you are testing it with example 22 in parallel, GLVis crashes quite often, but it is not fault of this PR. I realized the ordering is wrong there and should be fixed eventually. Check other examples, it should be:

• open socket
• send data
• MPI barrier
• ...

While you batch all operations which causes mismatches in received data as GLVis has no way to know what sockets should be grouped together 🤪 .

[mlstowell]

I'm just starting to look at this but I like it. I can visualize the four fields mentioned in the header but I haven't found the animation option. I can adjust the phase rate as you mention but I'm not seeing an animation so the phase rate doesn't seem to do anything.

Perhaps this feature is not available yet...

[najlkin]

It should be, it works for me 🤔 . Have you switched the representation? Magnitude does not show anything, because it is independent of the phase 😅 .

[mlstowell]

Okay, I see it now. The comment written to screen misled me. When I saw:
Representing complex function by: real part
I thought that was the only thing that would be available in that mode. Perhaps we can add to those comments. Something like:
Representing complex function by: real part (animate with ';')

Another thing I might change is the limits on the color bar. For the phase plot I would suggest a constant range from -pi to pi. For the real and imaginary parts I would suggest a constant range from -max(magnitude) to max(magnitude). I find these constant ranges are more illustrative during animations. What do you think?

[najlkin]

Ok, I generalized the detection of the value range to vector functions. These should be the combinations of complex value representations and vector representations:

cmplx\vec	magnitude	direction	component
magnitude	default	default	default
phase	[0, π √dim]	[-π,+π]	[-π,+π]
component	[|mag|min, |mag|max]	[-π,+π]	[-magmax, +magmax]

where mag_min/max is the minimal/maximal complex magnitude.

[najlkin]

After a discussion with @psocratis , I have changed the projection of magnitude and phase (which are nonlinear transformations in essence) from DOF projection to L2 space. This gives smoother visualizations for vector finite elements 😉

[najlkin]

🐛 A known bug, animations of solutions, which overload the internal buffer of socketstream (as GLVis lags behind) are broken due to the automatic detection of complex grid functions in the stream.
UPDATE: After multiple iterations, I have fallen back to just peeking the first character, because there seems to be no reliable way how to not extract/return characters to streams.

[najlkin]

I temporarily changed the base for easier reviewing 😉

[camierjs]

Being able to push directly the ComplexGridFunction is really neat! Works nicely!
Thank you @najlkin !

[najlkin]

❗ TODO: Before merging, the associated data pull request GLVis/data#8 should merged first and the submodule hash here should be updated to point to the merge commit on data/master .