[Octave-patch-tracker] [patch #9859] missing functions: stream2, stream3, streamline

[Hg200]

Follow-up Comment #3, patch #9859 (project octave):

Hi,

#1
thank you for your response. I have moved the source file to dldfcns. My
question is what flags do i have to give in libinterp/dldfcn/module-files if i
don't use any extra libraries?

#2
As far as accuracy is concerned, I've done tests using three different methods
that are often used for streamline integration (for example see Paraview's
Stream Tracer). These were

- Single Step Euler (explicite)
- Heun's Scheme 
- Runge Kutta 4th-Order 

The attached PDF shows a benchmark 3D problem on a 6x6x11 grid, including the
analytic streamline solution. In order to penalize the different computational
effort, the step size of the Heun Scheme was set twice and the RK4 step size
four times as high as Euler's (20 steps/cell). Euler Single Step does not
converge very well, while Heun and RK4 are in good agreement with the analytic
solution.

In fact it is possible to implement all three methods into one patch. However,
then the function interface must be changed to provide a choice and it will
increase also code size. Therefore, in the attached patch the Euler- and RK4
integrators were removed and Heun's Scheme was kept. You can run 'demo
streamline' to see the benchmark between Heun's Scheme and the analytic
solution.

#3
To examine the impact of the integrator scheme on other functions, I also
implemented a streamtube function (missing as well) and added it to the patch.
You may run 'demo streamtube'.

#4
Finally one last question (see stream_euler.cc line 112): I was wondering if
there is an API solution to easily implement a matrix operation like
B=A(1:N,:) or A(N:end,:)=[] ?

best regards


(file #47924, file #47925)
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Additional Item Attachment:

File name: benchmark_20191123.pdf         Size:68 KB
    <https://savannah.gnu.org/file/benchmark_20191123.pdf?file_id=47924>

File name: patch_streamline-20191123.diff Size:45 KB
   
<https://savannah.gnu.org/file/patch_streamline-20191123.diff?file_id=47925>



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