streamline plots

[jasongrout]

Recently there was a thread on the matplotlib list where someone posted matplotlib code for a streamline plot. It looks very nice. If the code doesn't get included in matplotlib, we could still ask about including it in Sage to do streamline plots.

Mailing list message: http://permalink.gmane.org/gmane.comp.python.matplotlib.general/26362

Mailing list thread: http://comments.gmane.org/gmane.comp.python.matplotlib.general/26354

Example code: http://web.mit.edu/speth/Public/streamlines.py

Example plot: http://web.mit.edu/speth/Public/streamlines.png

Upstream: Completely fixed; Fix reported upstream

CC: @kcrisman @alauve @sagetrac-jakobkroeker @paulmasson @sagetrac-jhonrubia6

Component: graphics

Author: Paul Masson

Branch/Commit: 640cb6a

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/10775

[jasongrout]

comment:1

And here is another file from the same message with some fantastically nice plots:

Code: http://www.atm.damtp.cam.ac.uk/people/tjf37/streamplot.py

Result: http://www.atm.damtp.cam.ac.uk/people/tjf37/streamlines1.png

Result 2: http://www.atm.damtp.cam.ac.uk/people/tjf37/streamlines2.png

[jasongrout]

Attachment: streamlines.py.gz

Attachment: streamplot.py.gz

[jasongrout]

comment:2

I've attached both code files so that we have them even if the above links go down for whatever reason.

[jasongrout]

comment:3

See http://sagenb.org/home/pub/3237/ for a short example and rough Sage code (posted at http://sage.math.washington.edu/home/jason/sage-field-plots/)

[kcrisman]

comment:4

Yo, this is now in mpl!

• the file
• the commit
  I'm not sure how to figure out which release it's in, if it's in a release yet. It looks like it will probably be in 1.1.1, as 1.1.0 has been out for longer than this was in.

[kcrisman]

Upstream: Fixed upstream, but not in a stable release.

[jasongrout]

comment:5

See also http://sage.cs.drake.edu/home/pub/60/ for another example.

[jasongrout]

comment:6

Attachment: DE Solutions (1).sws.gz

I attached the example I pointed out in the sage.cs.drake.edu server.

[kcrisman]

comment:7

#13693 is for the appropriate mpl upgrade for this.

[kcrisman]

comment:12

Here are some upstream examples.

---

Here is another example from somewhere in this discussion, allowing phase plots. Not directly related but looks nice with such things.

# based on code from oddrobot, http://sagenb.org/home/pub/1532/
from sage.calculus.desolvers import desolve_system_rk4
x,y,t=var('x y t')
class DESolution:
    def __init__(self,system,time_range,initial,stepsize=0.05):
        
        self.tvar=time_range[0]
        self._times=srange(time_range[1],time_range[2],stepsize)
        self.vars=[v for v,_ in initial]
        self.dim=len(self.vars)
        self._soln=desolve_odeint(system, ics=[v for _,v in initial], times=self._times, dvars=self.vars, ivar=self.tvar)
        
    def phase_plot(self,vars=None,color='blue',**kwargs):
        # find which indices the specified variables are
        if vars is not None:
            vars_index=[self.vars.index(v) for v in vars]
        elif self.dim<=3:
            vars_index=range(self.dim)
        else:
            vars_index=range(2)
            
        p=line(self._soln[:,vars_index],color=color,**kwargs)
        # add an arrow head showing which way we are going around the phase line
        half=int(self._soln.shape[0]/2)
        p+=arrow(self._soln[half,vars_index], self._soln[half+1,vars_index],color=color)
        if len(vars_index)==2:
            p.axes_labels([str(self.vars[v]) for v in vars_index])
        return p
        
    def coordinates(self,colors=None,**kwargs):
        if colors is None:
            colors=rainbow(len(self.vars))
        p=Graphics()
        p+=sum(line(zip(self._times,self._soln[:,i]), color=colors[i], legend_label=str(self.vars[i]),**kwargs) for i in range(self.dim))
        return p

[tscrim]

comment:13

I was hoping we could resurrect this ticket as I am teaching a class on ODE's this semester and would like to plot streamlines on top of the slope fields. Does someone have some time to work on this? Alas, I don't know how much time I might have to do so.

So streamlines are included in matplotlib: http://matplotlib.org/examples/images_contours_and_fields/streamplot_demo_features.html

There is also another plot package I came across that is open-source python that does streamlines: https://plot.ly/python/streamline-plots/

[tscrim]

Changed upstream from Fixed upstream, but not in a stable release. to Completely fixed; Fix reported upstream

[paulmasson]

comment:14

Since I spent too much time today reading graphics code, I can take a crack at this. It looks like a new class is needed, modeled on PlotField but calling the pyplot method streamplot instead of quiver. It shouldn't be too difficult but won't happen overnight.

Travis, if you see a way to avoid a new class, then let me know before I dive in tomorrow.

[paulmasson]

comment:15

To clarify: by new class I mean an individual file like scatter_plot.py, which calls the pyplot method scatter.

[tscrim]

Changed commit from 9201066 to 584486b

[paulmasson]

Changed branch from u/tscrim/streamline_plot-10775 to u/paulmasson/streamline_plot-10775

[paulmasson]

comment:27

Ah, so that's what you had in mind for the additions.

The documentation would not build without some fixes. Sphinx plots do not allow ^ for exponentiation, needs to be **, and variable declarations do not carry over between them. Documentation now builds.

---

New commits:

9f3a5c2

Fix Sphinx plots

[paulmasson]

Changed commit from 584486b to 9f3a5c2

[paulmasson]

comment:28

Don't know if you noticed, Travis, but in the example with start_points the streamlines come close to the start points but do not pass through them. I thought it might be because you didn't process the start points as in this example

http://matplotlib.org/examples/images_contours_and_fields/streamplot_demo_start_points.html

but even with setting up a numpy array as indicated and transposing it, the streamlines still do not pass through the start points. In fact the resulting graph is exactly the same as not bothering to process the points, so apparently that isn't necessary.

Problem with streamplot? Thought you should know before any students ask what's going on.

[tscrim]

comment:29

Thanks for fixing that Paul. I guess we should add a note and example about the behavior of start_points. Also, do you want me to document the density option?

Actually, I think I should not be normalizing the input when we want to consider it as a slope field, which makes sense when considering plotting the tangent lines. I believe it just adds a unnecessary computation that cancels when considering splitting dy / dx to (dx, dy).

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

78c53a0	Improve documentation and example
478b1e1	Code block for start_points

[sagetrac-git]

Changed commit from 9f3a5c2 to 478b1e1

[paulmasson]

comment:31

Documentation for implemented plot options now included. I also updated your language for start_points using that from the matplotlib website and added the note.

I'm including a commented code block for the official way to handle start_points in the event it is useful later.

[tscrim]

comment:32

I disagree with adding start_points to the @options, where if that is changed, it is perpetuated in all future plots, which is not what we want. I will revert this back when I make my next round of changes.

Does the "official way" for start_points make any difference?

[paulmasson]

comment:33

Replying to @tscrim:

Does the "official way" for start_points make any difference?

Not that I can tell. xpos_array and ypos_array need to be explicit numpy arrays to avoid errors. The documentation says that start_points is also supposed to be a numpy array, so I added this block of commented code in case that is ever enforced, but you can remove it if you feel that is more appropriate.

[tscrim]

comment:34

Let's use the official way. Also (not that it makes any real difference), you don't need to pop off the option:

    if 'start_points' in options:
        xstart_array, ystart_array = [], []
        for point in options['start_points']:
            xstart_array.append(point[0])
            ystart_array.append(point[1])
        options['start_points'] = numpy.array([xstart_array, ystart_array]).T

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

79e8795

Update start_points handling

[sagetrac-git]

Changed commit from 478b1e1 to 79e8795

[tscrim]

comment:36

Thank you for all your work on this.

[kiwifb]

comment:37

Not sure what Volker will find in his current run but I am failing to build the documentation in sage-on-gentoo

[plotting ] /scratch2/portage/sci-mathematics/sage-9999/work/sage-9999/src-python2_7/build/lib/sage/plot/streamline_plot.py:docstring of sage.plot.streamline_plot.streamline_plot:35: WARNING: Exception occurred in plotting streamline_plot-1
[plotting ] from /scratch2/portage/sci-mathematics/sage-9999/work/sage-9999/src-python2_7/doc/en/reference/plotting/sage/plot/streamline_plot.rst:
[plotting ] Traceback (most recent call last):
[plotting ] File "/usr/lib64/python2.7/site-packages/matplotlib/sphinxext/plot_directive.py", line 517, in run_code
[plotting ] six.exec_(code, ns)
[plotting ] File "/usr/lib64/python2.7/site-packages/matplotlib/externals/six.py", line 672, in exec_
[plotting ] exec("""exec _code_ in _globs_, _locs_""")
[plotting ] File "<string>", line 1, in <module>
[plotting ] File "<string>", line 2, in <module>
[plotting ] File "/scratch2/portage/sci-mathematics/sage-9999/work/sage-9999/src-python2_7/build/lib/sage/misc/decorators.py", line 554, in wrapper
[plotting ] return func(*args, **options)
[plotting ] File "/scratch2/portage/sci-mathematics/sage-9999/work/sage-9999/src-python2_7/build/lib/sage/plot/streamline_plot.py", line 316, in streamline_plot
[plotting ] for point in options['start_points']:
[plotting ] TypeError: 'NoneType' object is not iterable

I have this several times. I note that the bots have a similar problem in their logs.

[tscrim]

comment:38

I had thought the first part of comment:32 was done by Paul. I removed start_points from the @options and did some little doc tweaking. Paul, can you make a quick check of my changes?

---

New commits:

1e2b2d0	Merge branch 'u/paulmasson/10775' of git://trac.sagemath.org/sage into u/tscrim/streamline_plot-10775
fa8cda9	Merge branch 'u/paulmasson/streamline_plot-10775' of git://trac.sagemath.org/sage into u/tscrim/streamline_plot-10775
640cb6a	Some last little touchups.

[tscrim]

Changed branch from u/paulmasson/streamline_plot-10775 to u/tscrim/streamline_plot-10775

[tscrim]

Changed commit from 79e8795 to 640cb6a

[paulmasson]

comment:39

Documentation now builds. Setting back to positive review.

[vbraun]

Changed branch from u/tscrim/streamline_plot-10775 to 640cb6a