# Hessian of a buffer array in Zygote

**URL:** <https://discourse.julialang.org/t/hessian-of-a-buffer-array-in-zygote/100249>\
**Category:** General Usage\
**Tags:** zygote, ad\
**Created:** [June 12, 2023, 10:25pm UTC](https://discourse.julialang.org/t/hessian-of-a-buffer-array-in-zygote/100249 "2023-06-12T22:25:38Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![tomkimpson](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tomkimpson/32/39168_2.png) [@tomkimpson](https://discourse.julialang.org/u/tomkimpson)\
**Post date:** [June 12, 2023, 10:25pm UTC](https://discourse.julialang.org/t/hessian-of-a-buffer-array-in-zygote/100249/1 "2023-06-12T22:25:38Z")

</div>

I have a function which takes some coordinates, a parameter, and creates a 2D array.

I want to get the Jacobian and the Hessian of this array w.r.t the input coordinates using Zygote.

The Jacobian works fine, but the Hessian does not:

```julia

using Zygote

function some_array(coords,a) # `coords` is a vector length 4, `a` is a scalar 

    xs = zeros(typeof(a),4,4)
    g = Zygote.bufferfrom(xs) #a 4x4 buffered Zygote object

    t,r,θ,ϕ = coords[1],coords[2],coords[3],coords[4] #unpack the coordinates

    g[1,1] = 2*r #assign array element

    return copy(g)

end 

#Coordinates [t,r,θ,ϕ] and parameter `a` 
t = 0.0
r = 10.0
θ = π/2.0 
ϕ = 0.0 
a = 0.1
coords = [t,r,θ,ϕ]

#Create an array. Works ok.
some_array(coords,a)

#Get jacobian of array. Works ok.
array_jacobian = jacobian(x -> some_array(x,a), coords)[1]
array_jacobian = reshape(array_jacobian,(4,4,4)) #array_jacobian[:, :, i] is the derivative of some_array w.r.t. coords[i]

#Get hessian of array. Does not work?
array_hessian = hessian(x -> some_array(x,a), coords)[1]

```

Whilst `array_jacobian` returns what I expect, `array_hessian` throws an error:

`LoadError: MethodError: no method matching Float64(::ForwardDiff.Dual{Nothing, Float64, 4})`

Can someone guide me as to where I am going wrong?