# Finding Derivative of 2 arrays of numbers Using Zygote
**URL:** https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822
**Category:** General Usage
**Tags:** question, diffeq
**Created:** [July 6, 2022, 7:18am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822 "2022-07-06T07:18:42Z")
**Posts on this page:** 16
**Page:** 1
### Author:  [@alegeaa](https://discourse.julialang.org/u/alegeaa)
#### Post date: [July 6, 2022, 7:18am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/1 "2022-07-06T07:18:42Z")
Hello,
Please I am working on a physical system, and after running simulations I have 2 arrays of variables like this:
D = [0.01, 0.02, …, 0.05]
m = [1, 2, …, 5]
Please how do I find the derivative (∂D/∂m) using Zygote, given only the above 2 arrays of values. I have checked the docs and I do not understand it. I do not have a function, so I am thinking Zygote could compute the derivative directly.
Thank you in anticipation of your help.
Best,
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [July 6, 2022, 7:56am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/2 "2022-07-06T07:56:39Z")
Hello @alegeaa and welcome!
If you don’t have a function, you cannot compute a derivative. Indeed, the arrays `D` and `m` might have been generated by an arbitrary process we know nothing about.
However, what I mean by “function” is quite fuzzy, and it could encompass physical simulators. Do you have access to one or not at all?
---
### Author:  [@alegeaa](https://discourse.julialang.org/u/alegeaa)
#### Post date: [July 9, 2022, 12:25am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/3 "2022-07-09T00:25:07Z")
Hello @gdalle thank YOU FOR YOUR REPLY. I have access to all, i.e. both D and m arrays. I wrote a function to compute the derivative numerically by this formula, ∂D/∂m = [D(m1+delta/2) - D(m1-delta/2)]/ delta. However, I would like to use Zygote for this. Any directions please?
PS: sorry for the late reply.
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [July 9, 2022, 4:24am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/4 "2022-07-09T04:24:05Z")
You can create a function which takes in 2 values and “completes” D and m from that, and then calls your inner function.
---
### Author:  [@alegeaa](https://discourse.julialang.org/u/alegeaa)
#### Post date: [July 10, 2022, 9:39am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/5 "2022-07-10T09:39:41Z")
Thank you Chris, sadly I don’t understand what you mean by “completes”. Could you elaborate please?
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [July 10, 2022, 2:03pm UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/6 "2022-07-10T14:03:35Z")
Ok, so for instance if you have a function `compute_D` available, then you can use Zygote as follows:
```julia
using Zygote
D = compute_D(m)
JacD = Zygote.jacobian(compute_D, m)[1]
```
---
### Author:  [@alegeaa](https://discourse.julialang.org/u/alegeaa)
#### Post date: [July 11, 2022, 12:15am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/7 "2022-07-11T00:15:56Z")
I have a function that uses the D and m arrays to compute the differentials for corresponding D and m pairs in the arrays. The function looks like this:
```julia
function calc_differentials(delta, diameters, masses)
diffs = []
for i in range(1, length(diameters))
diff = ((diameters[i] * (masses[i] + delta / 2)) - (diameters[i] * (masses[i] - delta / 2))) / delta
append!(diffs, diff)
end;
return diffs
end;
```
So I understand, you are implying that I do sth like:
```julia
for i in range(1, length(diameters))
JacD = Zygote.jacobian(D[i], m[I])[1]
end
```
Is this correct?
Thanks
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [July 11, 2022, 5:19am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/8 "2022-07-11T05:19:23Z")
OK, so I think I’m starting to understand your problem. The formula you’re using only makes sense when D is a _function_ that you apply to m and not just a _value_.
To clarify, let me change notations, and suppose you want to compute the derivative of f: x \longmapsto y. The method of [finite differences](https://en.wikipedia.org/wiki/Finite_difference#Relation_with_derivatives) tells you
f'(x) = \frac{f(x + \delta / 2) - f(x - \delta / 2)}{\delta}
Instead, what you have been computing is the following quantity, which does not tell you anything useful:
\frac{y \times (x + \delta / 2) - y \times (x - \delta / 2)}{\delta}
One reason is that without the function f, you really cannot say anything about the relation between x and y. For instance, consider x = 0 and y = 0:
- This could be the result of f\_1(x) = x, in which case f\_1'(x) = 1
- This could be the result of f\_2(x) = -x, in which case f\_2'(x) = -1
The same goes if you have several input-ouput pairs (x\_i, y\_i). You need to have access to the function to differentiate it, whether you use finite differences, symbolic differentiation or automatic differentiation (with Zygote or ForwardDiff)
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [July 11, 2022, 5:23am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/9 "2022-07-11T05:23:47Z")
So my message above tells you why your function `calc_differentials` is not correct. You need access to the function `compute_D` if you want to retrieve any useful derivative information.
Supposing you do, then you would compute the derivative at a point `m` using the following syntax:
```julia
i = 3
Zygote.gradient(compute_D, m[i])[1]
```
I suggested `jacobian` because I thought `compute_D` took a vector as input and returned another vector. If the output is a real number, `gradient` is the way to go.
---
### Author:  [@alegeaa](https://discourse.julialang.org/u/alegeaa)
#### Post date: [July 11, 2022, 5:54am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/10 "2022-07-11T05:54:17Z")
Thank you so much. I understand the solution now. However, my `compute_D` function returns an array of all the D’s in the simulation. Also, the function has 4 arguments, can I do sth like this:
```julia
i = 3
Zygote.gradient(compute_D(arg1, arg2, arg3, arg4), m[i])[1]
```
or it doesn’t change, i.e,
```julia
i = 3
Zygote.gradient(compute_D, m[i])[1]
```
Thank you, and sorry for my endless questions.
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [July 11, 2022, 6:36am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/11 "2022-07-11T06:36:33Z")
It’s always a good idea to refer to the [package documentation](https://fluxml.ai/Zygote.jl/latest/) for questions about syntax. In this case, if you have a function f(x, y, z), the call
```julia
gs = Zygote.gradient(f, x, y, z)
```
returns a tuple whose first element is the gradient wrt x, second element wrt y, etc.
---
### Author:  [@alegeaa](https://discourse.julialang.org/u/alegeaa)
#### Post date: [July 11, 2022, 6:56am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/12 "2022-07-11T06:56:49Z")
thanks
---
### Author:  [@alegeaa](https://discourse.julialang.org/u/alegeaa)
#### Post date: [July 11, 2022, 7:34am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/13 "2022-07-11T07:34:43Z")
> [@gdalle](#):
>
> ```julia
> gs = Zygote.gradient(f, x, y, z)
>
> ```
It returns this error:
MethodError: no method matching zero(::Type{Any})
Closest candidates are:…
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [July 11, 2022, 10:35am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/14 "2022-07-11T10:35:18Z")
That is really hard to debug without a MWE
---
### Author:  [@gdalle](https://discourse.julialang.org/u/gdalle)
#### Post date: [July 11, 2022, 1:21pm UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/15 "2022-07-11T13:21:48Z")
@alegeaa reading this guide is probably a good idea if you want further help 🙃
> [@Please read: make it easier to help you](https://discourse.julialang.org/t/please-read-make-it-easier-to-help-you/14757):
>
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### Author:  [@alegeaa](https://discourse.julialang.org/u/alegeaa)
#### Post date: [July 12, 2022, 4:36am UTC](https://discourse.julialang.org/t/finding-derivative-of-2-arrays-of-numbers-using-zygote/83822/16 "2022-07-12T04:36:49Z")
> [@gdalle](#):
>
> `Zygote.jacobian(compute_D, m)[1]`
Thank you. I will.