Nested derivate functions

[ovainola]

Hi, I got my code working with the help of last issue: #30. Though I found a another example how I would like to make my code to work

Like last example:

using ForwardDiff
f1(s) = (s/3)^2
f2(x) = x[1]^2 + exp(3*x[2]/sqrt(4))
function f(x)
    g = forwarddiff_gradient(f2, Float64, fadtype=:typed, n=2)
return f1(x[1]) + g(x)
end
g = forwarddiff_gradient(f, Float64, fadtype=:typed, n=2)
g([-1., 2.0])

ended up with error message:

LoadError: MethodError: `g` has no method matching g(::Array{ForwardDiff.GraDual{Float64,2},1})
while loading In[11], in expression starting on line 9

 in f at In[11]:6
 in g at C:\Users\ovax03\.julia\v0.4\ForwardDiff\src\typed_fad\GraDual.jl:188

I already found a workaround, but Im not sure should it work like this:

using ForwardDiff
f1(s) = (s/3)^2
f2(x) = x[1]^2 + exp(3*x[2]/sqrt(4))
function f(x)
    xd = map(t->t.v, x)
    g = forwarddiff_gradient(f2, Float64, fadtype=:typed, n=2)
    return f1(x[1]) + g(xd)
end
g = forwarddiff_gradient(f, Float64, fadtype=:typed, n=2)
g([-1., 2.0])

which gave me a hessia as expected:

2x2 Array{Float64,2}:
 -0.222222  0.0
 -0.222222  0.0

note: I'm working with finite element material models, which happen to have this kind of functions

[jrevels]

This is a really good use case, thanks for sharing. This is a problem with the new code in #27 as well - leaving a snippet here for later See comment below.

[jrevels]

Rereading your code, I realize that f is a vector-valued function (f: R^2 --> R^2), meaning we want to take the Jacobian, not the gradient. You might try, then:

using ForwardDiff
f1(s) = (s/3)^2
f2(x) = x[1]^2 + exp(3*x[2]/sqrt(4))
function f(x)
    g = forwarddiff_gradient(f2, Float64, fadtype=:typed, n=2)
return f1(x[1]) + g(x)
end
j = forwarddiff_jacobian(f, Float64, fadtype=:typed, n=2)
j([-1., 2.0])

I'm not sure whether that will actually work or not - it seems the old code uses the same implementation to take the gradient as it does the Jacobian. The #27 implementation, however, handles this fine:

julia> using ForwardDiff

julia> f1(s) = (s/3)^2;

julia> f2(x) = x[1]^2 + exp(3*x[2]/sqrt(4));

julia> f(x) = f1(x[1]) + gradient(f2, x, Partials{2});

julia> j = jacobian_func(f, Partials{2}, mutates=false);

julia> j([-1, 2.0])
2x2 Array{Float64,2}:
  1.77778    0.0
 -0.222222  45.1925

[ovainola]

Thanks for answering so soon! I couldn't the example code working but I'll get the idea you've implemented it in #27 and if it's coming within couple of weeks I can live with that. My model converges quite nicely with newton at least in 1D solution even if the jacobian might not be correctly evaluated.

[jrevels]

This now fixed on master as of the merging of #27.

[ovainola]

👍