# Gradients of a simple function using ForwardDiff yields errorenous results? - Or am I doing something wrong?

**URL:** <https://discourse.julialang.org/t/gradients-of-a-simple-function-using-forwarddiff-yields-errorenous-results-or-am-i-doing-something-wrong/50035>\
**Category:** New to Julia\
**Tags:** package\
**Created:** [November 12, 2020, 8:51am UTC](https://discourse.julialang.org/t/gradients-of-a-simple-function-using-forwarddiff-yields-errorenous-results-or-am-i-doing-something-wrong/50035 "2020-11-12T08:51:33Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![vettert](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/vettert/32/30599_2.png) [@vettert](https://discourse.julialang.org/u/vettert)\
**Post date:** [November 12, 2020, 8:51am UTC](https://discourse.julialang.org/t/gradients-of-a-simple-function-using-forwarddiff-yields-errorenous-results-or-am-i-doing-something-wrong/50035/1 "2020-11-12T08:51:33Z")

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I would like to calculate the gradient of a simple function using FowardDiff.gradient, but I have been encountering problems, where I have gotten different answers from code that should seemingly be doing the same thing.

Since what I am trying to do is rather basic (calculating a gradient of a function) and I wouldn’t expect the ForwardDiff package to mess up with this, I am expecting the problem to be on my end 🙂

I have reduced my code to a MWE in the following way. I realize what the code does now doesn’t make much sense, but it illustrates the problem that I am having:

**Start minimum working example:**

```julia
using ForwardDiff

function f1(x)
    z = x
    gammax = x
    gammaz = z
    return sum(x.*(log.(x) .+ log.(gammax) .- log.(z) .- log.(gammaz)))
end

function f2(x)
    z = [0.1 0.9]
    gammax = x
    gammaz = z
    return sum(x.*(log.(x) .+ log.(gammax) .- log.(z) .- log.(gammaz)))
end

g1 = x -> ForwardDiff.gradient(f1,x)
g2 = x -> ForwardDiff.gradient(f2,x)
fval1 = f1([0.1 0.9])
fval2 = f2([0.1 0.9])
gval1 = g1([0.1 0.9])
gval2 = g2([0.1 0.9])

```

**Expected answers:**  
In function f1 the terms in the brackets involving logarithms are expected to be zero, regardless of what x is. The same is true if I am giving [0.1 0.9] as input argument to f2. Therefore, the function values fval1 and fval2 are expected to be zero and so are the gradients.

**Outputs:**

```julia
fval1
0.0
fval2
0.0
gval1
1×2 Array{Float64,2}:
 0.0 0.0
gval2
1×2 Array{Float64,2}:
 2.0 2.0

```

→ fval1, fval2, gval1 are all as expected. gval2 seems wrong?

Can anyone help me in understanding this? It’s completely puzzling to me 🙂

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**Author:** ![tomaklutfu](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomaklutfu/32/2411_2.png) [@tomaklutfu](https://discourse.julialang.org/u/tomaklutfu)\
**Post date:** [November 12, 2020, 9:13am UTC](https://discourse.julialang.org/t/gradients-of-a-simple-function-using-forwarddiff-yields-errorenous-results-or-am-i-doing-something-wrong/50035/2 "2020-11-12T09:13:03Z")

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`(log.(x) .+ log.(gammax) .- log.(z) .- log.(gammaz))' = (1 ./ x .+ (gammax')./gammax .- (z')./x .- (gammaz')./gammaz)`. When `z`, and `gammaz` are independent on `x`(they are constants in `f2`), then, their partial derivatives are 0s (`z' = gammaz' = some zeros`) so the derivatives are different.

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**Author:** ![vettert](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/vettert/32/30599_2.png) [@vettert](https://discourse.julialang.org/u/vettert)\
**Post date:** [November 12, 2020, 9:21am UTC](https://discourse.julialang.org/t/gradients-of-a-simple-function-using-forwarddiff-yields-errorenous-results-or-am-i-doing-something-wrong/50035/3 "2020-11-12T09:21:07Z")

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Thanks! Sorry, should have thought about this better before posting; classic math fail! 🙂