# DiffEqCallbacks problem with DDE

**URL:** <https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921>\
**Category:** Modelling & Simulations\
**Tags:** diffeq\
**Created:** [February 9, 2021, 12:08pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921 "2021-02-09T12:08:00Z")\
**Posts on this page:** 11\
**Page:** 1

<div class="post-metadata">

**Author:** ![zamk](https://avatars.discourse-cdn.com/v4/letter/z/ecd19e/32.png) [@zamk](https://discourse.julialang.org/u/zamk)\
**Post date:** [February 9, 2021, 12:08pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/1 "2021-02-09T12:08:00Z")

</div>

I have created a `SavingCallback` which prints out and saves the `du`, here is my code:

```julia
prob = DDEProblem(model,u0,h,(0.0,120.0),p)
alg = MethodOfSteps(Tsit5())
saved_values = SavedValues(Float64,Array{Float64})
saving = SavingCallback((u,t,integrator)->begin
                            du = get_du(integrator)
                            println(du)
                            du
                         end,saved_values,saveat=0.0:1.0:120.0)
positive_domain = PositiveDomain(zeros(6))
sol = solve(prob,alg,reltol=1e-5,abstol=1e-5,verbose=false,
            callback=CallbackSet(positive_domain,saving))
saved_values.saveval

```

However, I get only copies of the same array in `saved_values.saveval`:

```julia
121-element Array{Array{Float64,N} where N,1}:
 [-0.10130122735023514, -0.12747378214637814, -0.9356362119311361, -0.14477642620179343, -3.214542262837749e-9, 0.0]
 [-0.10130122735023514, -0.12747378214637814, -0.9356362119311361, -0.14477642620179343, -3.214542262837749e-9, 0.0]
 [-0.10130122735023514, -0.12747378214637814, -0.9356362119311361, -0.14477642620179343, -3.214542262837749e-9, 0.0]
 [-0.10130122735023514, -0.12747378214637814, -0.9356362119311361, -0.14477642620179343, -3.214542262837749e-9, 0.0]
 ⋮

```

whereas the values that are printed out are:

```julia
[-9.758880078641988, 9.73926587110036, 0.0, 0.0010190401331306772, 1.731440765537098e-11, 0.0]
[-9.2710620972309, 8.437221518401948, 0.0, 0.02908298475881324, 7.167640978098638e-10, 0.0]
[-9.001511975595097, 7.750094269936375, 0.0, 0.03564680683011713, 1.0608697222391056e-9, 0.0]
[-8.68452543732975, 6.971780891579974, 0.0, 0.03913534215472937, 1.4286156914998178e-9, 0.0]
[-8.313055858601432, 6.100969249011655, 0.0, 0.039895854945804096, 1.8100876888516305e-9, 0.0]
[-7.890979385401242, 5.166178043953941, 0.0, 0.038391043227802596, 2.180181419839846e-9, 0.0]
[-7.419848644971299, 4.192318009030844, 0.0, 0.03509693089910976, 2.5152511392120506e-9, 0.0] 

```

Many thanks in advance for any input!

---

<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:** [February 9, 2021, 12:21pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/2 "2021-02-09T12:21:53Z")

</div>

can you open an issue in the DelayDiffEq repo? Seems like a bug but I don’t know what it would be off the top of my head.

---

<div class="post-metadata">

**Author:** ![zamk](https://avatars.discourse-cdn.com/v4/letter/z/ecd19e/32.png) [@zamk](https://discourse.julialang.org/u/zamk)\
**Post date:** [February 9, 2021, 12:34pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/3 "2021-02-09T12:34:56Z")

</div>

I opened the issue, thanks @ChrisRackauckas!

---

<div class="post-metadata">

**Author:** ![david-pl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/david-pl/32/6224_2.png) [@david-pl](https://discourse.julialang.org/u/david-pl)\
**Post date:** [February 9, 2021, 1:32pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/4 "2021-02-09T13:32:11Z")

</div>

@zamk You’re not copying the `du`, so it is still in use by the solver. So effectively you end up with the derivative of the final step stored in your `saved_values`. Try doing

```julia
saving = SavingCallback((u,t,integrator)->begin
                            du = get_du(integrator)
                            copy(du)
                         end,saved_values,saveat=0.0:1.0:120.0)

```

---

<div class="post-metadata">

**Author:** ![zamk](https://avatars.discourse-cdn.com/v4/letter/z/ecd19e/32.png) [@zamk](https://discourse.julialang.org/u/zamk)\
**Post date:** [February 9, 2021, 2:14pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/5 "2021-02-09T14:14:04Z")

</div>

Thanks a lot @david-pl! Since the saving is supposed to be done during solving, I find it strange that it only saves the last step. I was trying to find a workaround by writing `du` into `IOBuffer` and collecting the array from there instead of printing it out.

Is there a particular reason why it works like this, is it specific to delay differential equations? Because the following example (for ODE) seems to be working:

```julia
saved_values = SavedValues(Float64, Float64)
cb = SavingCallback((u,t,integrator)->get_du(integrator), saved_values,saveat=0.0:0.1:1.0)
f(u,p,t) = 1.01*u
u0 = 1/2
tspan = (0.0,1.0)
prob = ODEProblem(f,u0,tspan)
sol = solve(prob, Tsit5(), reltol=1e-8, abstol=1e-8,callback=cb)

```

---

<div class="post-metadata">

**Author:** ![david-pl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/david-pl/32/6224_2.png) [@david-pl](https://discourse.julialang.org/u/david-pl)\
**Post date:** [February 9, 2021, 2:37pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/6 "2021-02-09T14:37:51Z")

</div>

You’re welcome!

> Since the saving is supposed to be done during solving, I find it strange that it only saves the last step.

To be clear: saving is done at _every_ step, however the object that you save is then modified by the solver. To avoid allocations, `get_du` does not create a new copy, but simply points directly to the `du` in use by the solver. This is then overwritten at each step so finally you end up with only the derivative of the final step.  
Essentially what happens is this:

```julia
du = [1.0]
saved = Vector{Float64}[]
for i=1:10
    du[1] = i
    push!(saved, du)
end

```

i.e. at each iteration `du` is pushed into the array `saved`, but since `du` is modified until the iteration is complete, you end up with a list containing the final `du` 10 times.

> Is there a particular reason why it works like this, is it specific to delay differential equations?

I don’t think so. I think the difference in your examples isn’t ODE vs DDE but rather in-place vs out-of-place. Your OP is in-place, whereas the example you showed in your last post is out-of-place, which does create a copy for `du` (I think). If you make it in-place, you should see the same behavior.

---

<div class="post-metadata">

**Author:** ![zamk](https://avatars.discourse-cdn.com/v4/letter/z/ecd19e/32.png) [@zamk](https://discourse.julialang.org/u/zamk)\
**Post date:** [February 9, 2021, 2:56pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/7 "2021-02-09T14:56:11Z")

</div>

Thank you again for the detailed explanation! However, It seems like it saves the last step only if I change the code as follows:

```julia
prob = DDEProblem(model,u0,h,(0.0,120.0),p)
alg = MethodOfSteps(Tsit5())
saved_values = SavedValues(Float64,Array{Float64})
saving = SavingCallback((u,t,integrator)->get_du(integrator),
                        saved_values,saveat=0.0:1.0:120.0)
positive_domain = PositiveDomain(zeros(6),save=false)
sol = solve(prob,alg,reltol=1e-5,abstol=1e-5,verbose=false,
            callback=CallbackSet(positive_domain,saving));

```

I still see this output:

```julia
121-element Array{Array{Float64,N} where N,1}:
 [-0.10130122735023514, -0.12747378214637814, -0.9356362119311361, -0.14477642620179343, -3.214542262837749e-9, 0.0]
 [-0.10130122735023514, -0.12747378214637814, -0.9356362119311361, -0.14477642620179343, -3.214542262837749e-9, 0.0]
 [-0.10130122735023514, -0.12747378214637814, -0.9356362119311361, -0.14477642620179343, -3.214542262837749e-9, 0.0]
 [-0.10130122735023514, -0.12747378214637814, -0.9356362119311361, -0.14477642620179343, -3.214542262837749e-9, 0.0]
 ⋮

```

In addition, I have another problem if I use the `copy(du)`, it seems like solution has the copy of `u` for each step:

```julia
julia> diff(Array(sol),dims=2)
6×80 Array{Float64,2}:
 -0.294771 0.0 -2.48102 0.0 -4.65944 0.0 -5.67162 0.0 -7.07948 0.0 -8.32535 … -3.15653 0.0 -2.4754 0.0 -1.85137 0.0 -1.39768 0.0 -1.04499 0.0 -0.207552 0.0
  0.294474 0.0 2.45502 0.0 4.49682 0.0 5.2724 0.0 6.26922 0.0 6.92605 -3.50686 0.0 -2.8579 0.0 -2.20407 0.0 -1.70467 0.0 -1.29922 0.0 -0.260717 0.0
  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -5.41925 0.0 -7.03821 0.0 -7.76922 0.0 -8.08079 0.0 -7.97808 0.0 -1.86149 0.0
  1.54385e-5 0.0 0.00128393 0.0 0.00717181 0.0 0.015062 0.0 0.0253684 0.0 0.0354892 -0.476882 0.0 -0.852066 0.0 -1.08137 0.0 -1.20812 0.0 -1.23096 0.0 -0.288312 0.0
  2.61539e-13 0.0 2.28651e-11 0.0 1.41968e-10 0.0 3.4494e-10 0.0 6.91318e-10 0.0 1.17613e-9 5.13234e-8 0.0 3.39101e-8 0.0 1.51379e-8 0.0 -1.84307e-9 0.0 -1.68774e-8 0.0 -6.00476e-9 0.0
  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 … 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

```

---

<div class="post-metadata">

**Author:** ![david-pl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/david-pl/32/6224_2.png) [@david-pl](https://discourse.julialang.org/u/david-pl)\
**Post date:** [February 9, 2021, 3:04pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/8 "2021-02-09T15:04:27Z")

</div>

> [@zamk](#):
>
> I still see this output:

Yes, that is expected because you’re not copying.

> [@zamk](#):
>
> In addition, I have another problem if I use the `copy(du)` , it seems like solution has the copy of `u` for each step:

I’m not sure what you mean here. Why look at `sol`? That will always store `u`. The `du` is saved to `saved_values.saveval`.

---

<div class="post-metadata">

**Author:** ![zamk](https://avatars.discourse-cdn.com/v4/letter/z/ecd19e/32.png) [@zamk](https://discourse.julialang.org/u/zamk)\
**Post date:** [February 9, 2021, 3:12pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/9 "2021-02-09T15:12:56Z")

</div>

I would like to have both `u` and `du` in this case I need to save both of the values by using the `SavingCallback` I suppose. Still is it not a problem that duplicates of `u` are saved in `sol`? Does not it mean that I replaced the `du` value and interfered with the integration?

---

<div class="post-metadata">

**Author:** ![david-pl](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/david-pl/32/6224_2.png) [@david-pl](https://discourse.julialang.org/u/david-pl)\
**Post date:** [February 9, 2021, 3:46pm UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/10 "2021-02-09T15:46:36Z")

</div>

Either way should work, I think. Either return both a copy of `u` and `du` in the callback or use the callback for `du` only and get `u` from the `sol` (in that case you might want to set the same `saveat` in `solve` as you’re using in the callback).

As long as you don’t actually modify anything in the callback you shouldn’t be able to interfere with the integration. Returning a copy should be fine. Are you saying your integration changes depending on whether you use `copy` or not? That really shouldn’t happen.

---

<div class="post-metadata">

**Author:** ![zamk](https://avatars.discourse-cdn.com/v4/letter/z/ecd19e/32.png) [@zamk](https://discourse.julialang.org/u/zamk)\
**Post date:** [February 16, 2021, 10:50am UTC](https://discourse.julialang.org/t/diffeqcallbacks-problem-with-dde/54921/11 "2021-02-16T10:50:48Z")

</div>

Here’s how I solved the problem:

```julia
saving = SavingCallback((u,t,integrator)->integrator(t,Val{1}),
                        saved_values,saveat=0.0:1.0:120.0)

```

Instead of using `get_du` I used `integrator(t,Val{1})`. I do not have the problems that I mentioned above when I save the `du` like this.