det not handled correctly?

[PetrKryslUCSD]

The following code gives different results for the LinearAlgebra det and a hand-written determinant function:
MWE

using LinearAlgebra
using ForwardDiff: derivative, gradient, jacobian, hessian

E, nu = (7.0e6, 0.3) 
lambda = E * nu / (1 + nu) / (1 - 2*(nu));
mu = E / 2. / (1+nu);

function strain6vto3x3t!(t::Array{T,2}, v::Array{T,1}) where {T}
    t[1,1] = v[1];
    t[2,2] = v[2];
    t[3,3] = v[3];
    t[1,2] = v[4]/2.;
    t[2,1] = v[4]/2.;
    t[1,3] = v[5]/2.;
    t[3,1] = v[5]/2.;
    t[3,2] = v[6]/2.;
    t[2,3] = v[6]/2.;
    return t
end

function strain3x3tto6v!(v::Array{T,1}, t::Array{T,2}) where {T}
    v[1] = t[1,1];
    v[2] = t[2,2];
    v[3] = t[3,3];
    v[4] = t[1,2] + t[2,1];
    v[5] = t[1,3] + t[3,1];
    v[6] = t[3,2] + t[2,3];
    return v
end

mydet(C) = begin
C[1,1] * C[2,2] * C[3,3] + 
C[1,2] * C[2,3] * C[3,1] + 
C[1,3] * C[2,1] * C[3,2] - 
C[1,3] * C[2,2] * C[3,1] - 
C[1,2] * C[2,1] * C[3,3] - 
C[1,1] * C[2,3] * C[3,2]
end

for i in 1:100
	a = rand(3, 3)
	@assert (det(a) - mydet(a)) / det(a) <= 1.0e-6
end

function strainenergy(Cv, lambda, mu)
	C = fill(zero(eltype(Cv)), 3, 3)
	strain6vto3x3t!(C, Cv)
	J = sqrt(mydet(C))
	lJ = log(J)
	return mu/2*(tr(C)-3) - mu*lJ + (lambda/2)*lJ^2;
end

function strainenergy1(Cv, lambda, mu)
	C = fill(zero(eltype(Cv)), 3, 3)
	strain6vto3x3t!(C, Cv)
	J = sqrt(det(C))
	lJ = log(J)
	return mu/2*(tr(C)-3) - mu*lJ + (lambda/2)*lJ^2;
end

Fn1 = [1.1 0 0; 0 1.0 0; 0 0 1.0]
Fn = [1.0 0 0; 0 1.0 0; 0 0 1.0]
C = Fn1'*Fn1;
Cv = fill(0.0, 6)
strain3x3tto6v!(Cv, C)
@show Da = hessian(Cv -> strainenergy(Cv, lambda, mu), Cv);
@show Da = hessian(Cv -> strainenergy1(Cv, lambda, mu), Cv);

Julia Version 1.3.0-alpha.0
Commit 6c11e7c2c4 (2019-07-23 01:46 UTC)
Platform Info:
OS: Windows (x86_64-w64-mingw32)
CPU: Intel(R) Core(TM) i7-8705G CPU @ 3.10GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-6.0.1 (ORCJIT, skylake)

Status `C:\Users\PetrKrysl\.julia\environments\v1.3\Project.toml`               

[f6369f11] ForwardDiff v0.10.3

[fredrikekre]

#197

[PetrKryslUCSD]

Sorry, I don't follow. How is #197 related?

[PetrKryslUCSD]

I think I got your point: When Cis diagonal, a special version of the function for the determinant is called which does not properly account for the derivatives of the quantity.

This issue is two years old at this point. Is there no solution?

[KristofferC]

Closing as dup