# Avoiding Plotting to dense plots, saveat not working

**URL:** <https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540>\
**Category:** Modelling & Simulations\
**Created:** [March 6, 2018, 4:11pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540 "2018-03-06T16:11:31Z")\
**Posts on this page:** 9\
**Page:** 1

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**Author:** ![Torkel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/torkel/32/5030_2.png) [@Torkel](https://discourse.julialang.org/u/Torkel)\
**Post date:** [March 6, 2018, 4:11pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/1 "2018-03-06T16:11:31Z")

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I am running simulations of SDEs and plotting the results. I keep having problem that Jupyter crashes, despite that the simulations shouldn’t be that intense. I think hat I have tracked the problems to the plots being to big. I have earlier had this issue and [got help with that](https://discourse.julialang.org/t/avoiding-high-plotting-densities-when-plotting-solutions-to-sde-with-small-time-steps/9168). However the use of `saveat` (as suggested there) only seems to get me that far.

I have been investigating and it seems like the plots still are much larger than `saveat` indicates. Here I have tried to make a minimal(ish) example:

```julia
using Plots
gr();
using DifferentialEquations

function positive_domain()
    condition(u,t,integrator) = (any(u .< 0))
    affect!(integrator) = integrator.u .= integrator.uprev
    return DiscreteCallback(condition,affect!) 
end;

rn = @reaction_network rnType begin
    0.01, (X) → ∅
end 
prob_sde = SDEProblem(rn,[1.],(0.,2000.))
sol = solve(prob_sde,ImplicitEM(),dt=0.001,callback=PositiveDomain(),saveat=1.);
length(sol)

```

using `saveat=1.` I would expect to get a solution about the size of `2000`, in fact its length is `2002002`, which is quite a lot. I can also change to `plotly()`, zoom in and confirm that a `plot(sol)` shows things at a very small scale. I have tried other `saveat` values, like `1` and `0.5`, but success.

Am I using `saveat` wrong somehow? I am having stochastic simulations over a time of about 2000, but not really interested in anything of a timescale less than 1, is there a good way to only plot about 2000 timepoints of my solution?

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [March 6, 2018, 4:15pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/2 "2018-03-06T16:15:18Z")

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You are using the default values for `save_positions` in the callback.

[http://docs.juliadiffeq.org/latest/features/callback\_functions.html#DiscreteCallback-1](http://docs.juliadiffeq.org/latest/features/callback_functions.html#DiscreteCallback-1)

Notice that it says that the defaults are `(true,true)`, so it’ll trigger a save just before and after each callback call. Of course, this is because if you want the full solution then this is required for proper discontinuity handling. But if you don’t want those saves, set `save_positions = (false,false)`.

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**Author:** ![Torkel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/torkel/32/5030_2.png) [@Torkel](https://discourse.julialang.org/u/Torkel)\
**Post date:** [March 6, 2018, 4:50pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/3 "2018-03-06T16:50:11Z")

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Thank you, that works.

Reading further, both you and the documents give warnings:

> required for proper discontinuity handling

> For discontinuous changes like a modification to `u` to be handled correctly (without error), one should set save\_positions=(true,true)

Does this mean that I might get faulty solutions? After all I do not actually want to do anything with the solver, only what it outputs. Intuitively what I want to do (receive/plot a solution taking up slightly less space) should not be a problem for accurately simulating the system?

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [March 6, 2018, 5:29pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/4 "2018-03-06T17:29:53Z")

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> [@Torkel](#):
>
> Does this mean that I might get faulty solutions? After all I do not actually want to do anything with the solver, only what it outputs. Intuitively what I want to do (receive/plot a solution taking up slightly less space) should not be a problem for accurately simulating the system?

It doesn’t matter for simulating the system. It matters for plotting though. If you don’t do this and you have an event that causes a discontinuity (say, adds 5 to every variable), then you might notice that the plot looks incorrect because instead of increasing vertically at that point it will do some weird connection between the previous time step and the value after the discontinuity. For SDEs it’s not bad because it just interpolates the line in there, but technically that line is incorrect because it should be linear to the point before the continuity, and then vertical at the continuity, then continue. So for plotting purposes, along with the post-solution interpolation, this needs discontinuity needs to be handled exactly. For intermediate interpolation (like `saveat` and event handling), the integrator handles this just fine. So you don’t need to worry about correctness, but you may want to be careful with the interpretation of results around “large enough” discontinuities.

Hope that helps.

P.S.

> [@Torkel](#):
>
> I keep having problem that Jupyter crashes, despite that the simulations shouldn’t be that intense. I think hat I have tracked the problems to the plots being to big.

If you use the GR backend, you can use `gr(fmt=:png)` to make the plots into PNGs, then they can have millions of points without a problem in Jupyter notebooks. Of course, that doesn’t fix your original problem so I didn’t mention it, but that’s something to keep in your back pocket if you really do need to plot a million points.

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<div class="post-metadata">

**Author:** ![Torkel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/torkel/32/5030_2.png) [@Torkel](https://discourse.julialang.org/u/Torkel)\
**Post date:** [March 6, 2018, 5:35pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/5 "2018-03-06T17:35:00Z")

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Thank, I see. So if I do not expect any large sudden event than I should not be worried about the plotting (although I maybe should be worried about my conviction that that is the case, but that is another issue).

Thanks for the `gr(fmt=:png)` tips, that might come in handy at some point.

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**Author:** ![swainarpit](https://avatars.discourse-cdn.com/v4/letter/s/7feea3/32.png) [@swainarpit](https://discourse.julialang.org/u/swainarpit)\
**Post date:** [May 23, 2018, 1:32pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/6 "2018-05-23T13:32:08Z")

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Hi Gaussia,

I am new to Julia and am struggling with the non-negative solution of a system of ODEs.

Could you tell me why you defined a function called positive\_domain() when you are using a pre-defined callback PositiveDomain()?  
And in your defined function, after you go back to the values of the previous step what would happen? I see you have fixed the step size.

Thanks

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<div class="post-metadata">

**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 23, 2018, 2:09pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/7 "2018-05-23T14:09:05Z")

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There are a few problems in the positivity enforcement done earlier in this thread. For one, it has the issues you discussed. But more importantly, it seems that the SDE itself is actually trying to go negative (in cases, of course it’s stochastic) which of course would mess with it. These issues were found later on and handled differently, so I wouldn’t use this as a guide for how to handle non-negativity handling. `PositiveDomain()` or setting `isoutofdomain` would be better.

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**Author:** ![swainarpit](https://avatars.discourse-cdn.com/v4/letter/s/7feea3/32.png) [@swainarpit](https://discourse.julialang.org/u/swainarpit)\
**Post date:** [May 23, 2018, 2:34pm UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/8 "2018-05-23T14:34:13Z")

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Hey, Chris.

Thank you for the reply.  
I have just posted a question that is troubling me with these implementations. I must be doing something very silly. Can you look over the post if you find time?

> [@PositiveDomain callback and isoutofdomain implementation](https://discourse.julialang.org/t/positivedomain-callback-and-isoutofdomain-implementation/11097):
>
> Hi, I have been trying to solve a system of differential equations in Julia. I have run into a few problems and am not clear on what I am doing wrong. Problem definition: The system I am working on is a model of the immune system. This is represented by 9 differential equations. One of the parameters is time-dependent and is a step function representing the lifetime of an infection in the immune system. This makes the system discontinuous at the time of entry and removal of the infection. To …

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<div class="post-metadata">

**Author:** ![Torkel](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/torkel/32/5030_2.png) [@Torkel](https://discourse.julialang.org/u/Torkel)\
**Post date:** [May 24, 2018, 9:18am UTC](https://discourse.julialang.org/t/avoiding-plotting-to-dense-plots-saveat-not-working/9540/9 "2018-05-24T09:18:17Z")

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Just re-iterating what Chris said that there are several irregularities with the above solution and you should not not spend to much time thinking on what is going on there.