# How to test differentiability efficiently

Hello.

As the tile suggest I am interested in testing (using Test) the “AD” capabilities of functions I write. My idea is to simply compare if `Zygote.gradient()` and finite differences give the same answer.

Many times I have functions which have multiple inputs say `my_func(a,b,c,d,e)`. So far what I do is generate `f = x -> my_func(x, b, c, d, e)` and test and so on.

Is there a better way of doing this? By better I mean less verbose than generating 5 functions for each function I make and then testing each. Perhaps to do it in fewer lines and more automatically.

One concern I have is that I want to know which input the test fails. Which splitting it this way makes it easier.

Any suggestions.

Thank you!

1 Like

Change it to take a single vector argument (e.g. `x -> my_func(x...)`) and compute the Jacobian?

1 Like

woudn’t that make it hard to see which input is cousing troubles?

Depending on which components of the Jacobian are wrong, you will know immediately which input screwed up. It’s exactly the same information, just all at once

2 Likes

Maybe, but if you split it you can see when the test fails which part did. If you just see Jacobian[2, 12] was miscalculated that is hard? Or is there a way of making that meaningful in tests?

This makes the output a bit verbose, but you could wrap the tests in their own `@testset` with an appropriate name. Perhaps group the tests by the corresponding column of the jacobian and attach the name of the variable only to the corresponding `@testset`.

I had something like this in mind, but I’m not sure if it suits your needs

``````using Test

f(x) = x * x'

@testset "Differentiability" begin
variableNames = [:x, :y]

testInputs = [[1, 2], [3, 4]]

for xVal in testInputs
jac = f(xVal)
@testset "point = \$(xVal)" begin
for (i, (x, c)) in enumerate(zip(variableNames, eachcol(jac)))
@testset "\$x = \$(xVal[i])" begin @test c == [1, 2] end
end
end
end
end
``````

Using `NamedTuples` instead of putting the variables names in a separate vector might even be more convenient.

I think it is very cool. Thank you!

1 Like