# Defining a function using the output of another function

**URL:** <https://discourse.julialang.org/t/defining-a-function-using-the-output-of-another-function/39589>\
**Category:** General Usage\
**Tags:** question, diffeq, metaprogramming\
**Created:** [May 16, 2020, 3:35pm UTC](https://discourse.julialang.org/t/defining-a-function-using-the-output-of-another-function/39589 "2020-05-16T15:35:30Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Himanshu\_Chaudhary](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/himanshu_chaudhary/32/14903_2.png) [@Himanshu\_Chaudhary](https://discourse.julialang.org/u/Himanshu_Chaudhary)\
**Post date:** [May 16, 2020, 3:35pm UTC](https://discourse.julialang.org/t/defining-a-function-using-the-output-of-another-function/39589/1 "2020-05-16T15:35:31Z")

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I have a function that takes an array and returns its derivative.

```julia
function dy(y, δx)

    N = length(y)
    dy = zeros(N)
    for j = 4:N-3
        dy[j]=( 5*(y[j+1] - y[j-1])
            + 4*(y[j+2] - y[j-2])
            + 1*(y[j+3] - y[j-3]))/(32*δx)
    end

    j=3
    dy[j]=( 2*(y[j+1] - y[j-1])
        + 1*(y[j+2] - y[j-2]))/(8*δx)

    j=N-2
    dy[j]=( 2*(y[j+1] - y[j-1])
        + 1*(y[j+2] - y[j-2]))/(8*δx)

    j=2
    dy[j]=(y[j+1] - y[j-1])/(2*δx)

    j=N-1
    dy[j]=(y[j+1] - y[j-1])/(2*δx)

    dy[1]=2*dy[2]-dy[3]
    dy[N]=(y[N-2]-4*y[N-1]+3*y[N])/(2*δx)

    return dy

end

```

There are basically two things required to define such a function:

1. The coefficients multiplying the values [-1,-4,-5,5,4,1]./12
2. The corresponding array positions wrt to the current element [-3,-2,-1,1,2,3]

I have written a different function which gives me these two things for a given order of derivative and stencil size. For example, it will return the following arrays for second-order derivate using five stencil points

### Coefficients

| | | | | |
| --- | --- | --- | --- | --- |
| 2.91667 | -8.66667 | 9.5 | -4.66667 | 0.916667 |
| 0.916667 | -1.66667 | 0.5 | 0.333333 | -0.0833333 |
| -0.0833333 | 1.33333 | -2.5 | 1.33333 | -0.0833333 |
| -0.0833333 | 1.33333 | -2.5 | 1.33333 | -0.0833333 |
| -0.0833333 | 1.33333 | -2.5 | 1.33333 | -0.0833333 |
| -0.0833333 | 1.33333 | -2.5 | 1.33333 | -0.0833333 |
| -0.0833333 | 1.33333 | -2.5 | 1.33333 | -0.0833333 |
| -0.0833333 | 1.33333 | -2.5 | 1.33333 | -0.0833333 |
| -0.0833333 | 1.33333 | -2.5 | 1.33333 | -0.0833333 |
| -0.0833333 | 0.333333 | 0.5 | -1.66667 | 0.916667 |
| 0.916667 | -4.66667 | 9.5 | -8.66667 | 2.91667 |

### Relative positions

| | | | | |
| --- | --- | --- | --- | --- |
| 0 | 1 | 2 | 3 | 4 |
| -1 | 0 | 1 | 2 | 3 |
| -2 | -1 | 0 | 1 | 2 |
| -2 | -1 | 0 | 1 | 2 |
| -2 | -1 | 0 | 1 | 2 |
| -2 | -1 | 0 | 1 | 2 |
| -2 | -1 | 0 | 1 | 2 |
| -2 | -1 | 0 | 1 | 2 |
| -2 | -1 | 0 | 1 | 2 |
| -3 | -2 | -1 | 0 | 1 |
| -4 | -3 | -2 | -1 | 0 |

Is there a way to use this information to write the function dy ?

One dirty way is to simply use the above arrays and string manipulation to write a file with the new version of dy during execution and then include it.  
But, I think there should be a better way to do this.

---

<div class="post-metadata">

**Author:** ![yha](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/yha/32/3502_2.png) [@yha](https://discourse.julialang.org/u/yha)\
**Post date:** [May 16, 2020, 4:00pm UTC](https://discourse.julialang.org/t/defining-a-function-using-the-output-of-another-function/39589/2 "2020-05-16T16:00:24Z")

</div>

I’m not sure if I understood the problem correctly, but perhaps just pass the coefficients and offsets as parameters? Something like

```julia
function dy(y, δx, coeffs, offsets)
    N = length(y)
    dy = zeros(N)
    for j in eachindex(y)
        denom = 32*δx # and something else near the edges?
        dy[j] = sum(y[j+i]*c for (i,c) in zip(offsets,coeffs) if j+i in eachindex(y)) / denom
    end
    dy
end

```

(I’m not sure what that denominator is for and where the numbers 32,8,2 come from).  
You might want to take a look at `ImageFiltering.jl`, and specifically `ImageFiltering.imfilter`. It does exactly what it seems you are trying to do, except maybe near the edges (since I’m not sure what is going on near the edges in your code).