# Incorrect jacobian using ForwardDiff and sparse functions

Hi all,

Does anybody know why the following code produces different (incorrect) jacobians using ForwardDiff? The function being differentiated contains sparse matrices, but if I don’t expand them to dense matrices the jacobian from the sparse function is incorrect…

``````using SparseArrays, ForwardDiff, LinearAlgebra

# setup data
θ = [30.0, 70.0, 90.0]
x = [1.9873817034700316, 3.9747634069400632, 1.9873817034700316, 1.9873817034700316, 1.9873817034700316, 3.9747634069400632, 1.9873817034700316, 0.028391167192429023, 0.022082018927444796, 0.13249211356466878, 0.13249211356466878]
ν = [ 0.0, 0.0, 0.028391167192429023, 0.24290220820189273,0.7287066246056783, 0.0, 1.9873817034700316, 3.9747634069400632, 5.962145110410095, 7.9495268138801265,]
λ = zeros(24)
λ[end] = -1.9873817034700316

S = [
1.0  0.0  0.0  0.0  0.0  0.0  -1.0
0.0  1.0  0.0  0.0  0.0  0.0  -2.0
0.0  0.0  1.0  0.0  0.0  0.0  -1.0
0.0  0.0  0.0  1.0  0.0  0.0  -1.0
0.0  0.0  0.0  0.0  1.0  0.0  -1.0
0.0  0.0  0.0  0.0  0.0  1.0  -2.0
]

se_vars = ((2, -1.0), (3, -1.0),(3, -3.0), (1, -2.0), (1, -1.0),)

Cp = spzeros(11)
Cp[8] = 1; Cp[9] = 2; Cp[10] = 3; Cp[11] = 4
clb, cub = ([0.0], [1.0])
xlb = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
xub = [100.0, 100.0, 100.0, 100.0, 100.0, 100.0, 100.0, 10.0, 10.0, 10.0, 10.0]

# create functions
Se(θ) = sparse(
[1, 2, 3, 4, 3],
[3, 4, 4, 5, 5],
[k / θ[idx] for (idx, k) in se_vars],
4,
7,
)

E(θ) = [
S spzeros(6, 4)
Se(θ) I(4)
]

d = _ -> spzeros(10)

_c = spzeros(11)
_c[7] = -1.0
c = _ -> _c

M = _ -> [
-I(11)
I(11)
-Cp'
Cp'
]

h = _ -> [-xlb; xub; -clb; cub]

Q = _ -> spzeros(11, 11)

xidxs = 1:length(x)
νidxs = last(xidxs) .+ (1:length(ν))
λidxs = last(νidxs) .+ (1:length(λ))
θidxs = last(λidxs) .+ (1:length(θ))

sparse_F(z) = [
Q(z[θidxs]) * z[xidxs] + c(z[θidxs]) -
E(z[θidxs])' * z[νidxs] - M(z[θidxs])' * z[λidxs]
E(z[θidxs]) * z[xidxs] - d(z[θidxs])
spdiagm(z[λidxs]) * (M(z[θidxs]) * z[xidxs] - h(z[θidxs]))
]

dense_F(z) = [
Array(Q(z[θidxs])) * z[xidxs] + Array(c(z[θidxs])) -
Array(E(z[θidxs]))' * z[νidxs] - Array(M(z[θidxs]))' * z[λidxs]
Array(E(z[θidxs])) * z[xidxs] - Array(d(z[θidxs]))
diagm(z[λidxs]) * (Array(M(z[θidxs])) * z[xidxs] - Array(h(z[θidxs])))
]

z = [x; ν; λ; θ]

dense_jac = ForwardDiff.jacobian(dense_F, z)
sparse_jac = ForwardDiff.jacobian(sparse_F, z)

# large differences
maximum(dense_jac - sparse_jac)
unique(dense_jac)
unique(sparse_jac)
``````

Casting everything to dense arrays works fine, but it is quite slow, since the dimensions of my problem are large. The way I am constructing these sparse functions may seem contrived, but it is part of a package I am working on

Does anybody have any ideas?

Okay, the problem has been updated, the error persists!

This seems to be another example of the problem fixed by #481, like this post.

Interesting, how do I check out that branch? I tried

``````(DifferentiableMetabolism) pkg> add ForwardDiff#mcabbott:measurezero