Cleanup differential equations examples. #22043

anntzer · 2021-12-23T12:53:53Z

PR Summary

Slightly cleanup the lorenz_attractor example; also use Euler's method
for the double pendulum. It is less accurate, but sufficient for
illustrative purposes (also, 1. the double pendulum is chaotic anyways
so even RK4 will end up quite far from the actual behavior, if one waits
for long enough, as can be checked by trying various integrators in
solve_ivp; 2. we're fine with using Euler's method for the also chaotic
lorenz_attractor).

The point is also to make fewer examples dependent on scipy.

PR Checklist

Tests and Styling

Has pytest style unit tests (and pytest passes).
Is Flake 8 compliant (install flake8-docstrings and run flake8 --docstring-convention=all).

Documentation

New features are documented, with examples if plot related.
New features have an entry in doc/users/next_whats_new/ (follow instructions in README.rst there).
API changes documented in doc/api/next_api_changes/ (follow instructions in README.rst there).
Documentation is sphinx and numpydoc compliant (the docs should build without error).

jklymak · 2021-12-23T13:10:55Z

examples/mplot3d/lorenz_attractor.py

-    ys[i + 1] = ys[i] + (y_dot * dt)
-    zs[i + 1] = zs[i] + (z_dot * dt)
-
+    xyzs[i + 1] = xyzs[i] + lorenz(*xyzs[i]) * dt


I'm not sure how idiomatic we want to be in python - many scientific programmers, moving between languages, are not going to understand what you are doing here with the *xyzs. Even if it is more typing and even a bit more error prone, I think writing the code out is easier to parse than nice encapsulations like this.

Fair point. Would you think it would be better if lorenz() took a single xyz as sole arg, and did x, y, z = xyz?

+1 for array in, array out

The * is still here?

oops, fixed.

timhoffm · 2021-12-23T16:15:20Z

examples/animation/double_pendulum.py

@@ -51,7 +50,7 @@ def derivs(state, t):
    return dydx

 # create a time array from 0..t_stop sampled at 0.02 second steps
-dt = 0.02
+dt = 0.01


Please check if this is really necessary. This doubles the number of frames and thus likely the size of the generated file.

I decreased the end time by a factor of two as well; the shorter time step does appear to improve the accuracy.

But that means that you're only going half the path from before. Please check if that's still a reasonable path length. I'm afraid that might be a bit short.

I can imagine that the shorter time step improves accuracy. But does that matter here? Alternatively, one could also render only every second step, but that adds additional compelity to the code and I'm not sure that's worth it.

Of course, one could also change to another example like a regular single pendulum. That's simpler to calculate and one could have a continuous cyclic animation with, a period of e.g. 2s.

I did check, the path length is fine.

timhoffm · 2021-12-23T16:18:43Z

examples/animation/double_pendulum.py

@@ -64,8 +63,13 @@ def derivs(state, t):
 # initial state
 state = np.radians([th1, w1, th2, w2])

-# integrate your ODE using scipy.integrate.
-y = integrate.odeint(derivs, state, t)
+# integrate the ODE using Euler's method


This makes the example longer and IMHO a little harder to understand. Does this outweigh the benefit of not depending on scipy in this example?

The only other use of scipy in the docs can also easily be removed (I have another patch ready for that) so we could entirely drop the dependency on scipy for building the docs, which may or may not be a useful thing (e.g., with the yearly release cycle of cpython, I fear that we're always going to have a small period between having scipy wheels available after the new cpython release, and scipy is significantly harder to build from source (e.g., due to fortran sources) than other dependencies, even numpy).

I think dropping SciPy would be pretty helpful if we don't need it. I think its a pretty heavy dependency to carry around for a couple of examples.

We have oscillated back and forth on having a scipy documentation dependencies a couple of times. I do not have a strong preference either way.

timhoffm · 2021-12-23T16:22:02Z

examples/mplot3d/lorenz_attractor.py

-    ys[i + 1] = ys[i] + (y_dot * dt)
-    zs[i + 1] = zs[i] + (z_dot * dt)
-
+    xyzs[i + 1] = xyzs[i] + lorenz(*xyzs[i]) * dt


+1 for array in, array out

examples/mplot3d/lorenz_attractor.py

examples/animation/double_pendulum.py

Slightly cleanup the lorenz_attractor example; also use Euler's method for the double pendulum. It is less accurate, but sufficient for illustrative purposes (also, 1. the double pendulum is chaotic anyways so even RK4 will end up quite far from the actual behavior, if one waits for long enough, as can be checked by trying various integrators in solve_ivp; 2. we're fine with using Euler's method for the also chaotic lorenz_attractor). The point is also to make fewer examples dependent on scipy.

jklymak

When doc CI finishes, I think this can be merged...

anntzer added the Documentation label Dec 23, 2021

anntzer changed the title ~~Dps~~ Cleanup differential equations examples. Dec 23, 2021

jklymak reviewed Dec 23, 2021

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timhoffm reviewed Dec 23, 2021

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anntzer force-pushed the dps branch from 237a228 to 22f9b01 Compare December 23, 2021 16:26

QuLogic reviewed Dec 23, 2021

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anntzer force-pushed the dps branch from 22f9b01 to d85d4eb Compare December 23, 2021 21:59

timhoffm reviewed Dec 24, 2021

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anntzer force-pushed the dps branch from d85d4eb to d72ac3c Compare December 24, 2021 09:24

anntzer force-pushed the dps branch from d72ac3c to e67514f Compare January 5, 2022 09:00

jklymak approved these changes Jan 5, 2022

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QuLogic merged commit 14a94c3 into matplotlib:main Jan 5, 2022

QuLogic added this to the v3.6.0 milestone Jan 5, 2022

anntzer deleted the dps branch January 5, 2022 22:44

anntzer mentioned this pull request Jan 5, 2022

Drop dependency on scipy in the docs. #22120

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Cleanup differential equations examples. #22043

Cleanup differential equations examples. #22043

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anntzer commented Dec 23, 2021 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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timhoffm Dec 23, 2021 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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anntzer commented Dec 23, 2021 •

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timhoffm Dec 23, 2021 •

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