Example for adaptive step size choice #372
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| @@ -179,6 +179,52 @@ class PIDController( | |||
| common to refer to solving an equation to specific tolerances, without | |||
| necessarily stating which solver was used.) | |||
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| !!! Example | |||
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This is quite a long example, so let's maybe make it expandable with ???
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That sounds great!
| ``` | ||
| We can integrate this using: | ||
| ```python | ||
| def integrator(dynamics, state0, stepsize_controller): |
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I think it'd be good to make this example a little more concise. Perhaps something like this:
import diffrax as dfx
def dynamics(t, y, args):
dtheta = y["omega"]
domega = - jnp.sin(y["theta"])
return dict(theta=dtheta, omega=domega)
y0 = dict(theta=0.1, omega=0)
term = dfx.ODETerm(dynamics)
sol = dfx.diffeqsolve(
term, solver, t0=0, t1=1000, dt0=0.1, y0,
saveat=dfx.SaveAts(ts=jnp.linspace(0, 1000, 10000),
max_steps=2**20,
stepsize_controller=...
)WDYT?
(WIth a little ..., as we discuss different choices of that below.)
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That works well,
yeah the class was a vestige of the much larger system I simplified for this, but this is much better as an example
| The phase portraits of the pendulum from the different tolerances clearly | ||
| illustrate the impact of the choice of `rtol` and `atol` on the accuracy of | ||
| the solution. | ||
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I probably wouldn't use "incorrect" in the title here, as it's suggestive of a bug. This is the numerical method doing exactly what's expected, namely a cheap low-accuracy solution!
Maybe something like "less accurate" and "more accurate" instead?
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Sounds good, here is the corrected plot.
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Just following up to see if anything else is needed |
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Can you push your changes from the last round of comments? |
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Alright, merged -- thank you for the contribution! |
PR to complete #371
Added example to PIDController with a simple pendulum example illustrating the effect of tolerance of adaptive step choice controller.