# Autodiff using custom Structs

**URL:** <https://discourse.julialang.org/t/autodiff-using-custom-structs/121143>\
**Category:** General Usage\
**Tags:** autodiff, enzyme\
**Created:** [October 10, 2024, 1:13pm UTC](https://discourse.julialang.org/t/autodiff-using-custom-structs/121143 "2024-10-10T13:13:24Z")\
**Posts on this page:** 2\
**Page:** 1

<div class="post-metadata">

**Author:** ![thealanjason](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/thealanjason/32/213969_2.png) [@thealanjason](https://discourse.julialang.org/u/thealanjason)\
**Post date:** [October 10, 2024, 1:13pm UTC](https://discourse.julialang.org/t/autodiff-using-custom-structs/121143/1 "2024-10-10T13:13:24Z")

</div>

Hello everyone,

I want to be able to use Enzyme to differentiate a scalar-valued function with respect to only part of the fields of an arbitrary `struct`.

As an example, in my MWE below, I would like to differentiate the `calculate_area` function with respect to the z-positions of all the `points` in my surface `s`. For starters, I try to differentiate w.r.t. `s` completely. However, I get the following error:

```julia
ERROR: Enzyme Mutability Error: Cannot add one in place to immutable value 1.0 tup[i]=0.0 i=1 w=1 tup=(0.0, -0.0)
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] runtime_generic_rev(activity::Type{…}, runtimeActivity::Val{…}, width::Val{…}, ModifiedBetween::Val{…}, tape::Enzyme.Compiler.Tape{…}, f::typeof(-), df::Nothing, primal_1::Float64, shadow_1_1::Float64, primal_2::Float64, shadow_2_1::Float64)
    @ Enzyme.Compiler ~/.julia/packages/Enzyme/Vjlrr/src/rules/jitrules.jl:584
  [3] calculate_area
    @ ~/Work/Projects/geom-sensitivity/enzyme_mwe.jl:249 [inlined]
  [4] calculate_area
    @ ~/Work/Projects/geom-sensitivity/enzyme_mwe.jl:0 [inlined]
  [5] diffejulia_calculate_area_2754_inner_1wrap
    @ ~/Work/Projects/geom-sensitivity/enzyme_mwe.jl:0
  [6] macro expansion
    @ ~/.julia/packages/Enzyme/Vjlrr/src/compiler.jl:8839 [inlined]
  [7] enzyme_call
    @ ~/.julia/packages/Enzyme/Vjlrr/src/compiler.jl:8405 [inlined]
  [8] CombinedAdjointThunk
    @ ~/.julia/packages/Enzyme/Vjlrr/src/compiler.jl:8178 [inlined]
  [9] autodiff
    @ ~/.julia/packages/Enzyme/Vjlrr/src/Enzyme.jl:491 [inlined]
 [10] autodiff(mode::ReverseMode{…}, f::typeof(calculate_area), ::Type{…}, args::Duplicated{…})
    @ Enzyme ~/.julia/packages/Enzyme/Vjlrr/src/Enzyme.jl:512
 [11] top-level scope
    @ ~/Work/Projects/geom-sensitivity/enzyme_mwe.jl:263
Some type information was truncated. Use `show(err)` to see complete types.

```

Following is the MWE:

```julia
using Enzyme

mutable struct Point
    x::Real
    y::Real
    z::Real
end

function Point(x, y, z_func::Function)
    z = z_func(x, y)
    Point(x, y, z)
end

struct Edge
    from::Integer
    to::Integer
end

struct Triangle
    p1::Integer
    p2::Integer
    p3::Integer
end

struct Surface
    points::Vector{Point}
    edges::Vector{Edge}
    triangles::Vector{Triangle}
end

# X, Y grid positions for points
positions = Dict{Integer, Vector{Real}}(
    1=>[-0.5, -0.5],
    2=>[0.5, -0.5],
    3=>[0.5, 0.5],
    4=>[-0.5, 0.5],
    5=>[-0.3, -0.5],
    6=>[-0.1, -0.5],
    7=>[0.1, -0.5],
    8=>[0.3, -0.5],
    9=>[0.5, -0.3],
    10=>[0.5, -0.1],
    11=>[0.5, 0.1],
    12=>[0.5, 0.3],
    13=>[0.3, 0.5],
    14=>[0.1, 0.5],
    15=>[-0.1, 0.5],
    16=>[-0.3, 0.5],
    17=>[-0.5, 0.3],
    18=>[-0.5, 0.1],
    19=>[-0.5, -0.1],
    20=>[-0.5, -0.3],
    21=>[-0.3, -0.3],
    22=>[-0.1, -0.3],
    23=>[0.1, -0.3],
    24=>[0.3, -0.3],
    25=>[0.3, -0.1],
    26=>[0.3, 0.1],
    27=>[0.3, 0.3],
    28=>[0.1, 0.3],
    29=>[-0.1, 0.3],
    30=>[-0.3, 0.3],
    31=>[-0.3, 0.1],
    32=>[-0.3, -0.1],
    33=>[-0.1, -0.1],
    34=>[0.1, -0.1],
    35=>[0.1, 0.1],
    36=>[-0.1, 0.1],
)

# Height Function
height(x, y) = 500 - (x^2 + y^2) * 10

# Creating points on the surface
points = Point[]
for i in eachindex(1:length(positions))
    push!(points, Point(positions[i][1], positions[i][2], height))
end

# Setup Edge connectivity
edges = Edge[
    Edge(1, 5), #1
    Edge(5, 6), #2
    Edge(6, 7), #3
    Edge(7, 8), #4
    Edge(8, 2), #5
    Edge(2, 9), #6
    Edge(9, 10), #7
    Edge(10, 11), #8
    Edge(11, 12), #9
    Edge(12, 3), #10
    Edge(3, 13), #11
    Edge(13, 14), #12
    Edge(14, 15), #13
    Edge(15, 16), #14
    Edge(16, 4), #15
    Edge(4, 17), #16
    Edge(17, 18), #17
    Edge(18, 19), #18
    Edge(19, 20), #19
    Edge(20, 1), #20
    Edge(20, 21), #21
    Edge(21, 22), #22
    Edge(22, 23), #23
    Edge(23, 24), #24
    Edge(24, 9), #25
    Edge(19, 32), #26
    Edge(32, 33), #27
    Edge(33, 34), #28
    Edge(34, 25), #29
    Edge(25, 10), #30
    Edge(18, 31), #31
    Edge(31, 36), #32
    Edge(36, 35), #33
    Edge(35, 26), #34
    Edge(26, 11), #35
    Edge(17, 30), #36
    Edge(30, 29), #37
    Edge(29, 28), #38
    Edge(28, 27), #39
    Edge(27, 12), #40
    Edge(5, 21), #41
    Edge(21, 32), #42
    Edge(32, 31), #43
    Edge(31, 30), #44
    Edge(30, 16), #45
    Edge(6, 22), #46
    Edge(22, 33), #47
    Edge(33, 36), #48
    Edge(36, 29), #49
    Edge(29, 15), #50
    Edge(7, 23), #51
    Edge(23, 34), #52
    Edge(34, 35), #53
    Edge(35, 28), #54
    Edge(28, 14), #55
    Edge(8, 24), #56
    Edge(24, 25), #57
    Edge(25, 26), #58
    Edge(26, 27), #59
    Edge(27, 13), #60
    Edge(1, 21), #61
    Edge(5, 22), #62
    Edge(6, 23), #63
    Edge(7, 24), #64
    Edge(8, 9), #65
    Edge(20, 32), #66
    Edge(21, 33), #67
    Edge(22, 34), #68
    Edge(23, 25), #69
    Edge(24, 10), #70
    Edge(19, 31), #71
    Edge(32, 36), #72
    Edge(33, 35), #73
    Edge(34, 26), #74
    Edge(25, 11), #75
    Edge(18, 30), #76
    Edge(31, 29), #77
    Edge(36, 28), #78
    Edge(35, 27), #79
    Edge(26, 12), #80
    Edge(17, 16), #81
    Edge(30, 15), #82
    Edge(29, 14), #83
    Edge(28, 13), #84
    Edge(27, 3), #85
]

# Setup Face connectivity
triangles = Triangle[
    Triangle(1,5,21),
    Triangle(5,6,22),
    Triangle(6,7,23),
    Triangle(7,8,24),
    Triangle(8,2,9),
    Triangle(1,21,20),
    Triangle(5,22,21),
    Triangle(6,23,22),
    Triangle(7,24,23),
    Triangle(8,9,24),
    Triangle(20,21,32),
    Triangle(21,22,33),
    Triangle(22,23,34),
    Triangle(23,24,25),
    Triangle(24,9,10),
    Triangle(20,32,19),
    Triangle(21,33,32),
    Triangle(22,34,33),
    Triangle(23,25,34),
    Triangle(24,10,9),
    Triangle(19,32,31),
    Triangle(32,33,36),
    Triangle(33,34,35),
    Triangle(35,25,26),
    Triangle(25,10,11),
    Triangle(19,31,18),
    Triangle(32,36,31),
    Triangle(33,35,36),
    Triangle(34,26,35),
    Triangle(25,11,26),
    Triangle(18,31,30),
    Triangle(31,36,29),
    Triangle(36,35,28),
    Triangle(35,26,27),
    Triangle(26,11,12),
    Triangle(18,30,17),
    Triangle(31,29,30),
    Triangle(36,28,29),
    Triangle(35,27,28),
    Triangle(26,12,27),
    Triangle(17,30,16),
    Triangle(30,29,15),
    Triangle(29,28,14),
    Triangle(28,27,13),
    Triangle(27,12,3),
    Triangle(17,16,4),
    Triangle(30,15,16),
    Triangle(29,14,15),
    Triangle(28,13,14),
    Triangle(27,3,13),
]

# Create surface
s = Surface(points, edges, triangles)

function calculate_area(s::Surface)
    area = 0.0
    for triangle in s.triangles
        x1 = s.points[triangle.p1].x
        y1 = s.points[triangle.p1].y
        z1 = s.points[triangle.p1].z
        x2 = s.points[triangle.p2].x
        y2 = s.points[triangle.p2].y
        z2 = s.points[triangle.p2].z
        x3 = s.points[triangle.p3].x
        y3 = s.points[triangle.p3].y
        z3 = s.points[triangle.p3].z
        u1 = x2 - x1
        u2 = y2 - y1
        u3 = z2 - z1
        v1 = x3 - x1
        v2 = y3 - y1
        v3 = z3 - z1
        area += 0.5 * sqrt((u2*v3 - u3*v2)^2 + (u3*v1-u1*v3)^2 + (u1*v2-u2*v1)^2)
    end
    return area
end

calculate_area(s)

ds = deepcopy(s)
for i in eachindex(ds.points)
    ds.points[i].x = 0.0
    ds.points[i].y = 0.0
    ds.points[i].z = 1.0
end
Enzyme.autodiff(Reverse, calculate_area, Const, Duplicated(s, ds))

```

On the other hand, using `Zygote` I am able to get the gradient without any issue, and it also ignores the fields having structs involving only integers.  
All I need to do is:

```julia
using Zygote

ds = gradient(calculate_area, s)
# ((points = @NamedTuple{x::Float64, y::Float64, z::Float64}[(x = 1.6816612310819545, y = -1.7344882854613735, z = -0.6339246525544604), (x = 0.008804509063256116, y = -0.017609018126512232, z = -0.42261643503629953), (x = 1.725683776398136, y = -1.6728567220187194, z = -0.6339246525544604), (x = -0.008804509063256116, y = 0.017609018126512232, z = -0.42261643503629953), (x = 0.7357816691599668, y = -2.004896671653612, z = -1.066666666666638), (x = -2.147125321541682, y = -1.1881166765601836, z = -1.0263834223756458), (x = -4.571552002947907, y = -3.313695835806661, z = -0.8310166963474414), (x = -5.86692575011869, y = -7.062454279801859, z = -0.6113082175181475), (x = 0.019327603161698126, y = -3.004637588201552, z = -3.0113082175181356), (x = 1.8646020919901334, y = -1.3942506430834438, z = -0.4930500890423126) … (x = 9.447877599958657, y = -0.007566278284033556, z = 2.6310441645923865), (x = 1.9903061459690947, y = 6.274385700856671, z = 3.1663573686795106), (x = -8.238190034026063, y = 3.80098806245576, z = 2.72186511510064), (x = -14.000475935202989, y = -4.92425414159782, z = 1.7704399505975197), (x = -10.090331899443346, y = -8.052581033706907, z = 1.5311316630442386), (x = -3.812455430534781, y = -11.615446302781455, z = 0.40218636850508027), (x = -3.0384345019264316, y = -6.842144905546649, z = 2.6639788117457117), (x = 2.5273878910781, y = -6.684578626092981, z = 1.544401872924625), (x = 6.27753593731042, y = 3.2121382526298734, z = 5.917081683388485), (x = -5.788945407332804, y = 1.0208251410105178, z = 3.999487497523498)], edges = nothing, triangles = nothing),)

```

However, it is not possible in `Zygote` to make only the Z-values of each point active, while keeping the X and Y values as constant. So I was trying out `Enzyme`

I tried reading the documentation, and going through other issues here on discord, but was not able to fix the issue.  
Could anyone explain what I’m doing wrong?

@wsmoses Any help is appreciated 🙂

Thanks  
Alan

---

<div class="post-metadata">

**Author:** ![wsmoses](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/wsmoses/32/26497_2.png) [@wsmoses](https://discourse.julialang.org/u/wsmoses)\
**Post date:** [October 20, 2024, 11:30pm UTC](https://discourse.julialang.org/t/autodiff-using-custom-structs/121143/2 "2024-10-20T23:30:10Z")

</div>

Sorry just noticed this. So the mutability issue you hit seems to come from some type instability. Making your point struct type stable, resolve it like below:

```julia
using Enzyme

mutable struct Point
    x::Float64
    y::Float64
    z::Float64
end

function Point(x, y, z_func::Function)
    z = z_func(x, y)
    Point(x, y, z)
end

struct Edge
    from::Integer
    to::Integer
end

struct Triangle
    p1::Integer
    p2::Integer
    p3::Integer
end

struct Surface
    points::Vector{Point}
    edges::Vector{Edge}
    triangles::Vector{Triangle}
end

# X, Y grid positions for points
positions = Dict{Integer, Vector{Real}}(
    1=>[-0.5, -0.5],
    2=>[0.5, -0.5],
    3=>[0.5, 0.5],
    4=>[-0.5, 0.5],
    5=>[-0.3, -0.5],
    6=>[-0.1, -0.5],
    7=>[0.1, -0.5],
    8=>[0.3, -0.5],
    9=>[0.5, -0.3],
    10=>[0.5, -0.1],
    11=>[0.5, 0.1],
    12=>[0.5, 0.3],
    13=>[0.3, 0.5],
    14=>[0.1, 0.5],
    15=>[-0.1, 0.5],
    16=>[-0.3, 0.5],
    17=>[-0.5, 0.3],
    18=>[-0.5, 0.1],
    19=>[-0.5, -0.1],
    20=>[-0.5, -0.3],
    21=>[-0.3, -0.3],
    22=>[-0.1, -0.3],
    23=>[0.1, -0.3],
    24=>[0.3, -0.3],
    25=>[0.3, -0.1],
    26=>[0.3, 0.1],
    27=>[0.3, 0.3],
    28=>[0.1, 0.3],
    29=>[-0.1, 0.3],
    30=>[-0.3, 0.3],
    31=>[-0.3, 0.1],
    32=>[-0.3, -0.1],
    33=>[-0.1, -0.1],
    34=>[0.1, -0.1],
    35=>[0.1, 0.1],
    36=>[-0.1, 0.1],
)

# Height Function
height(x, y) = 500 - (x^2 + y^2) * 10

# Creating points on the surface
points = Point[]
for i in eachindex(1:length(positions))
    push!(points, Point(positions[i][1], positions[i][2], height))
end

# Setup Edge connectivity
edges = Edge[
    Edge(1, 5), #1
    Edge(5, 6), #2
    Edge(6, 7), #3
    Edge(7, 8), #4
    Edge(8, 2), #5
    Edge(2, 9), #6
    Edge(9, 10), #7
    Edge(10, 11), #8
    Edge(11, 12), #9
    Edge(12, 3), #10
    Edge(3, 13), #11
    Edge(13, 14), #12
    Edge(14, 15), #13
    Edge(15, 16), #14
    Edge(16, 4), #15
    Edge(4, 17), #16
    Edge(17, 18), #17
    Edge(18, 19), #18
    Edge(19, 20), #19
    Edge(20, 1), #20
    Edge(20, 21), #21
    Edge(21, 22), #22
    Edge(22, 23), #23
    Edge(23, 24), #24
    Edge(24, 9), #25
    Edge(19, 32), #26
    Edge(32, 33), #27
    Edge(33, 34), #28
    Edge(34, 25), #29
    Edge(25, 10), #30
    Edge(18, 31), #31
    Edge(31, 36), #32
    Edge(36, 35), #33
    Edge(35, 26), #34
    Edge(26, 11), #35
    Edge(17, 30), #36
    Edge(30, 29), #37
    Edge(29, 28), #38
    Edge(28, 27), #39
    Edge(27, 12), #40
    Edge(5, 21), #41
    Edge(21, 32), #42
    Edge(32, 31), #43
    Edge(31, 30), #44
    Edge(30, 16), #45
    Edge(6, 22), #46
    Edge(22, 33), #47
    Edge(33, 36), #48
    Edge(36, 29), #49
    Edge(29, 15), #50
    Edge(7, 23), #51
    Edge(23, 34), #52
    Edge(34, 35), #53
    Edge(35, 28), #54
    Edge(28, 14), #55
    Edge(8, 24), #56
    Edge(24, 25), #57
    Edge(25, 26), #58
    Edge(26, 27), #59
    Edge(27, 13), #60
    Edge(1, 21), #61
    Edge(5, 22), #62
    Edge(6, 23), #63
    Edge(7, 24), #64
    Edge(8, 9), #65
    Edge(20, 32), #66
    Edge(21, 33), #67
    Edge(22, 34), #68
    Edge(23, 25), #69
    Edge(24, 10), #70
    Edge(19, 31), #71
    Edge(32, 36), #72
    Edge(33, 35), #73
    Edge(34, 26), #74
    Edge(25, 11), #75
    Edge(18, 30), #76
    Edge(31, 29), #77
    Edge(36, 28), #78
    Edge(35, 27), #79
    Edge(26, 12), #80
    Edge(17, 16), #81
    Edge(30, 15), #82
    Edge(29, 14), #83
    Edge(28, 13), #84
    Edge(27, 3), #85
]

# Setup Face connectivity
triangles = Triangle[
    Triangle(1,5,21),
    Triangle(5,6,22),
    Triangle(6,7,23),
    Triangle(7,8,24),
    Triangle(8,2,9),
    Triangle(1,21,20),
    Triangle(5,22,21),
    Triangle(6,23,22),
    Triangle(7,24,23),
    Triangle(8,9,24),
    Triangle(20,21,32),
    Triangle(21,22,33),
    Triangle(22,23,34),
    Triangle(23,24,25),
    Triangle(24,9,10),
    Triangle(20,32,19),
    Triangle(21,33,32),
    Triangle(22,34,33),
    Triangle(23,25,34),
    Triangle(24,10,9),
    Triangle(19,32,31),
    Triangle(32,33,36),
    Triangle(33,34,35),
    Triangle(35,25,26),
    Triangle(25,10,11),
    Triangle(19,31,18),
    Triangle(32,36,31),
    Triangle(33,35,36),
    Triangle(34,26,35),
    Triangle(25,11,26),
    Triangle(18,31,30),
    Triangle(31,36,29),
    Triangle(36,35,28),
    Triangle(35,26,27),
    Triangle(26,11,12),
    Triangle(18,30,17),
    Triangle(31,29,30),
    Triangle(36,28,29),
    Triangle(35,27,28),
    Triangle(26,12,27),
    Triangle(17,30,16),
    Triangle(30,29,15),
    Triangle(29,28,14),
    Triangle(28,27,13),
    Triangle(27,12,3),
    Triangle(17,16,4),
    Triangle(30,15,16),
    Triangle(29,14,15),
    Triangle(28,13,14),
    Triangle(27,3,13),
]

# Create surface
s = Surface(points, edges, triangles)

function calculate_area(s::Surface)
    area = 0.0
    for triangle in s.triangles
        x1 = s.points[triangle.p1].x
        y1 = s.points[triangle.p1].y
        z1 = s.points[triangle.p1].z
        x2 = s.points[triangle.p2].x
        y2 = s.points[triangle.p2].y
        z2 = s.points[triangle.p2].z
        x3 = s.points[triangle.p3].x
        y3 = s.points[triangle.p3].y
        z3 = s.points[triangle.p3].z
        u1 = x2 - x1
        u2 = y2 - y1
        u3 = z2 - z1
        v1 = x3 - x1
        v2 = y3 - y1
        v3 = z3 - z1
        area += 0.5 * sqrt((u2*v3 - u3*v2)^2 + (u3*v1-u1*v3)^2 + (u1*v2-u2*v1)^2)
    end
    return area
end

calculate_area(s)

ds = deepcopy(s)
for i in eachindex(ds.points)
    ds.points[i].x = 0.0
    ds.points[i].y = 0.0
    ds.points[i].z = 1.0
end
Enzyme.autodiff(Reverse, calculate_area, Const, Duplicated(s, ds))

@show Enzyme.gradient(Reverse, calculate_area, s)

```

Note that your initialization of ds as above is incorrect. Reverse mode will += the derivative of the result wrt all differentiable inputs. So here you’d just compute ds.points[:].x = dresult/dx, ds.points[:].y = dresult/dy, ds.points[:].z = 1 + dresult/dz, not your intended only derivative wrt z.

Enzyme currently supports marking entire variables as differentiable or not (though it has been discussed adding support for marking some struct elements as non differentiable). In that regard, if you want to not differentiate wrt x and y, you should pass in three arguments, x, y, and z, and only ask for the z derivative. For example, like the following.

```julia
using Enzyme

struct Edge
    from::Integer
    to::Integer
end

struct Triangle
    p1::Integer
    p2::Integer
    p3::Integer
end

struct Surface
    edges::Vector{Edge}
    triangles::Vector{Triangle}
end

# X, Y grid positions for points
positions = Dict{Integer, Vector{Real}}(
    1=>[-0.5, -0.5],
    2=>[0.5, -0.5],
    3=>[0.5, 0.5],
    4=>[-0.5, 0.5],
    5=>[-0.3, -0.5],
    6=>[-0.1, -0.5],
    7=>[0.1, -0.5],
    8=>[0.3, -0.5],
    9=>[0.5, -0.3],
    10=>[0.5, -0.1],
    11=>[0.5, 0.1],
    12=>[0.5, 0.3],
    13=>[0.3, 0.5],
    14=>[0.1, 0.5],
    15=>[-0.1, 0.5],
    16=>[-0.3, 0.5],
    17=>[-0.5, 0.3],
    18=>[-0.5, 0.1],
    19=>[-0.5, -0.1],
    20=>[-0.5, -0.3],
    21=>[-0.3, -0.3],
    22=>[-0.1, -0.3],
    23=>[0.1, -0.3],
    24=>[0.3, -0.3],
    25=>[0.3, -0.1],
    26=>[0.3, 0.1],
    27=>[0.3, 0.3],
    28=>[0.1, 0.3],
    29=>[-0.1, 0.3],
    30=>[-0.3, 0.3],
    31=>[-0.3, 0.1],
    32=>[-0.3, -0.1],
    33=>[-0.1, -0.1],
    34=>[0.1, -0.1],
    35=>[0.1, 0.1],
    36=>[-0.1, 0.1],
)

# Height Function
height(x, y) = 500 - (x^2 + y^2) * 10

# Creating points on the surface
xpoints = Float64[]
ypoints = Float64[]

zpoints = Float64[]
for i in eachindex(1:length(positions))
    push!(xpoints, positions[i][1])
    push!(ypoints, positions[i][2])
    push!(zpoints, height(positions[i][1], positions[i][2]))
end

# Setup Edge connectivity
edges = Edge[
    Edge(1, 5), #1
    Edge(5, 6), #2
    Edge(6, 7), #3
    Edge(7, 8), #4
    Edge(8, 2), #5
    Edge(2, 9), #6
    Edge(9, 10), #7
    Edge(10, 11), #8
    Edge(11, 12), #9
    Edge(12, 3), #10
    Edge(3, 13), #11
    Edge(13, 14), #12
    Edge(14, 15), #13
    Edge(15, 16), #14
    Edge(16, 4), #15
    Edge(4, 17), #16
    Edge(17, 18), #17
    Edge(18, 19), #18
    Edge(19, 20), #19
    Edge(20, 1), #20
    Edge(20, 21), #21
    Edge(21, 22), #22
    Edge(22, 23), #23
    Edge(23, 24), #24
    Edge(24, 9), #25
    Edge(19, 32), #26
    Edge(32, 33), #27
    Edge(33, 34), #28
    Edge(34, 25), #29
    Edge(25, 10), #30
    Edge(18, 31), #31
    Edge(31, 36), #32
    Edge(36, 35), #33
    Edge(35, 26), #34
    Edge(26, 11), #35
    Edge(17, 30), #36
    Edge(30, 29), #37
    Edge(29, 28), #38
    Edge(28, 27), #39
    Edge(27, 12), #40
    Edge(5, 21), #41
    Edge(21, 32), #42
    Edge(32, 31), #43
    Edge(31, 30), #44
    Edge(30, 16), #45
    Edge(6, 22), #46
    Edge(22, 33), #47
    Edge(33, 36), #48
    Edge(36, 29), #49
    Edge(29, 15), #50
    Edge(7, 23), #51
    Edge(23, 34), #52
    Edge(34, 35), #53
    Edge(35, 28), #54
    Edge(28, 14), #55
    Edge(8, 24), #56
    Edge(24, 25), #57
    Edge(25, 26), #58
    Edge(26, 27), #59
    Edge(27, 13), #60
    Edge(1, 21), #61
    Edge(5, 22), #62
    Edge(6, 23), #63
    Edge(7, 24), #64
    Edge(8, 9), #65
    Edge(20, 32), #66
    Edge(21, 33), #67
    Edge(22, 34), #68
    Edge(23, 25), #69
    Edge(24, 10), #70
    Edge(19, 31), #71
    Edge(32, 36), #72
    Edge(33, 35), #73
    Edge(34, 26), #74
    Edge(25, 11), #75
    Edge(18, 30), #76
    Edge(31, 29), #77
    Edge(36, 28), #78
    Edge(35, 27), #79
    Edge(26, 12), #80
    Edge(17, 16), #81
    Edge(30, 15), #82
    Edge(29, 14), #83
    Edge(28, 13), #84
    Edge(27, 3), #85
]

# Setup Face connectivity
triangles = Triangle[
    Triangle(1,5,21),
    Triangle(5,6,22),
    Triangle(6,7,23),
    Triangle(7,8,24),
    Triangle(8,2,9),
    Triangle(1,21,20),
    Triangle(5,22,21),
    Triangle(6,23,22),
    Triangle(7,24,23),
    Triangle(8,9,24),
    Triangle(20,21,32),
    Triangle(21,22,33),
    Triangle(22,23,34),
    Triangle(23,24,25),
    Triangle(24,9,10),
    Triangle(20,32,19),
    Triangle(21,33,32),
    Triangle(22,34,33),
    Triangle(23,25,34),
    Triangle(24,10,9),
    Triangle(19,32,31),
    Triangle(32,33,36),
    Triangle(33,34,35),
    Triangle(35,25,26),
    Triangle(25,10,11),
    Triangle(19,31,18),
    Triangle(32,36,31),
    Triangle(33,35,36),
    Triangle(34,26,35),
    Triangle(25,11,26),
    Triangle(18,31,30),
    Triangle(31,36,29),
    Triangle(36,35,28),
    Triangle(35,26,27),
    Triangle(26,11,12),
    Triangle(18,30,17),
    Triangle(31,29,30),
    Triangle(36,28,29),
    Triangle(35,27,28),
    Triangle(26,12,27),
    Triangle(17,30,16),
    Triangle(30,29,15),
    Triangle(29,28,14),
    Triangle(28,27,13),
    Triangle(27,12,3),
    Triangle(17,16,4),
    Triangle(30,15,16),
    Triangle(29,14,15),
    Triangle(28,13,14),
    Triangle(27,3,13),
]

# Create surface
s = Surface(edges, triangles)

function calculate_area(s::Surface, xpoints, ypoints, zpoints)
    area = 0.0
    for triangle in s.triangles
        x1 = xpoints[triangle.p1]
        y1 = ypoints[triangle.p1]
        z1 = zpoints[triangle.p1]
        x2 = xpoints[triangle.p2]
        y2 = ypoints[triangle.p2]
        z2 = zpoints[triangle.p2]
        x3 = xpoints[triangle.p3]
        y3 = ypoints[triangle.p3]
        z3 = zpoints[triangle.p3]
        u1 = x2 - x1
        u2 = y2 - y1
        u3 = z2 - z1
        v1 = x3 - x1
        v2 = y3 - y1
        v3 = z3 - z1
        area += 0.5 * sqrt((u2*v3 - u3*v2)^2 + (u3*v1-u1*v3)^2 + (u1*v2-u2*v1)^2)
    end
    return area
end

calculate_area(s, xpoints, ypoints, zpoints)

@show Enzyme.gradient(Reverse, calculate_area, Const(s), Const(xpoints), Const(ypoints), zpoints)

using Zygote, BenchmarkTools

@show Zygote.gradient(calculate_area, s, xpoints, ypoints, zpoints)

@btime Enzyme.gradient(Reverse, $calculate_area, $(Const(s)), $(Const(xpoints)), $(Const(ypoints)), $(zpoints))
# 62.000 μs (361 allocations: 41.61 KiB)
# (nothing, nothing, nothing, [-0.1408721450121023, -0.14087214501209985, -0.1408721450121023, -0.14087214501209985, -0.13333333333332764, -0.143672232115815, -0.1436722321158125, -0.13333333333333264, -0.2666666666666653, -0.010338898782480455 … 0.09049890913642407, 0.13554687099016932, 0.13554687099016688, 0.09049890913643148, 0.13554687099016688, 0.13554687099016935, 0.3332906247936249, 0.2362763747790916, 0.4303048748081582, 0.3332906247936249])

@btime Zygote.gradient($calculate_area, $s, $xpoints, $ypoints, $zpoints)
# 1.043 ms (17118 allocations: 635.86 KiB)
# (nothing, [-0.008804509063236488, 0.008804509063256116, 0.008804509063236154, -0.008804509063256116, 0.7691150024933462, 0.2715520029479166, -0.2715520029479066, -0.7691150024933762, 0.8024483358267235, 0.7235145845699962 … 0.5419365898655986, 0.27741340607116555, -0.27741340607115533, -0.5419365898656485, -0.7529730203651925, -0.7529730203652125, -0.4706492344625691, 0.4949027969662021, 0.44639567195893615, -0.4706492344625691], [-0.008804509063236488, -0.008804509063256116, 0.008804509063236154, 0.008804509063256116, -0.9691150024934266, -0.5568479179033298, -0.5568479179033498, -0.9691150024933873, 0.4024483358267018, 0.6382186696145582 … 0.5419365898655986, 0.7529730203652125, 0.7529730203651925, 0.5419365898656485, 0.2774134060711553, -0.2774134060711654, -0.47064923446256907, -0.4706492344625691, 0.4706492344625691, 0.4706492344625691], [-0.1408721450121023, -0.14087214501209985, -0.1408721450121023, -0.14087214501209985, -0.13333333333332764, -0.143672232115815, -0.1436722321158125, -0.13333333333333264, -0.2666666666666653, -0.010338898782480455 … 0.09049890913642401, 0.13554687099016938, 0.13554687099016688, 0.09049890913643151, 0.13554687099016688, 0.13554687099016935, 0.3332906247936249, 0.2362763747790916, 0.4303048748081582, 0.3332906247936249])

@btime Enzyme.gradient(Reverse, $calculate_area, $s, $xpoints, $ypoints, $zpoints)
# 88.625 μs (510 allocations: 59.20 KiB)
# (Surface(Edge[Edge(1, 5), Edge(5, 6), Edge(6, 7), Edge(7, 8), Edge(8, 2), Edge(2, 9), Edge(9, 10), Edge(10, 11), Edge(11, 12), Edge(12, 3) … Edge(18, 30), Edge(31, 29), Edge(36, 28), Edge(35, 27), Edge(26, 12), Edge(17, 16), Edge(30, 15), Edge(29, 14), Edge(28, 13), Edge(27, 3)], Triangle[Triangle(1, 5, 21), Triangle(5, 6, 22), Triangle(6, 7, 23), Triangle(7, 8, 24), Triangle(8, 2, 9), Triangle(1, 21, 20), Triangle(5, 22, 21), Triangle(6, 23, 22), Triangle(7, 24, 23), Triangle(8, 9, 24) … Triangle(17, 30, 16), Triangle(30, 29, 15), Triangle(29, 28, 14), Triangle(28, 27, 13), Triangle(27, 12, 3), Triangle(17, 16, 4), Triangle(30, 15, 16), Triangle(29, 14, 15), Triangle(28, 13, 14), Triangle(27, 3, 13)]), [-0.008804509063236488, 0.008804509063256116, 0.008804509063236154, -0.008804509063256116, 0.7691150024933462, 0.2715520029479166, -0.2715520029479066, -0.7691150024933762, 0.8024483358267235, 0.7235145845699962 … 0.5419365898655986, 0.27741340607116566, -0.27741340607115533, -0.5419365898656485, -0.7529730203651925, -0.7529730203652124, -0.470649234462569, 0.4949027969662021, 0.44639567195893604, -0.4706492344625691], [-0.008804509063236488, -0.008804509063256116, 0.008804509063236154, 0.008804509063256116, -0.9691150024934265, -0.5568479179033299, -0.5568479179033499, -0.9691150024933872, 0.4024483358267017, 0.6382186696145582 … 0.5419365898655986, 0.7529730203652125, 0.7529730203651925, 0.5419365898656485, 0.2774134060711553, -0.2774134060711656, -0.47064923446256907, -0.4706492344625691, 0.4706492344625689, 0.4706492344625691], [-0.1408721450121023, -0.14087214501209985, -0.1408721450121023, -0.14087214501209985, -0.13333333333332764, -0.143672232115815, -0.1436722321158125, -0.13333333333333264, -0.2666666666666653, -0.010338898782480455 … 0.09049890913642407, 0.13554687099016932, 0.13554687099016688, 0.09049890913643148, 0.13554687099016688, 0.13554687099016935, 0.3332906247936249, 0.2362763747790916, 0.4303048748081582, 0.3332906247936249])

```

In this case we see that not differentiating gives us a small speedup over Enzyme differentiating x y and z, and a substantial speedup over using Zygote.