I’m trying to compute all third partial derivatives of a function using ForwardDiff, but cannot get it to be type stable and I don’t understand why. Here is a minimal example:
using ForwardDiff
using StaticArrays
function tf( x )
return ( exp( 0.1*x[1] + 0.2*x[2] ) )
end
function get_derivatives( f )
∇f(x) = ForwardDiff.gradient( f , x )
∇²f(x) = ForwardDiff.hessian( f , x )
∇³f(x) = ForwardDiff.jacobian( ∇²f , x )
return ∇f, ∇²f, ∇³f
end
∇tf, ∇²tf, ∇³tf = get_derivatives( tf )
@code_warntype ∇³tf( @SVector [1.0,1.0] )
The output of @code_warntype is:
Variables
#self#::Core.Const(var"#∇³f#329"{var"#∇²f#328"{typeof(tf)}}(var"#∇²f#328"{typeof(tf)}(tf)))
x::SVector{2, Float64}
Body::Any
1 ─ %1 = ForwardDiff.jacobian::Core.Const(ForwardDiff.jacobian)
│ %2 = Core.getfield(#self#, :∇²f)::Core.Const(var"#∇²f#328"{typeof(tf)}(tf))
│ %3 = (%1)(%2, x)::Any
└── return %3
The gradient and hessian are both type stable. Searching around for related topics I read about the ForwardDiff chunk size, so I also tried implementing the following:
function get_derivatives_2( f )
cfg_grad = ForwardDiff.GradientConfig( f , SVector{2}( [1.0,1.0] ) , ForwardDiff.Chunk{1}() )
∇f(x) = ForwardDiff.gradient( f , x , cfg_grad )
cfg_jac_1 = ForwardDiff.JacobianConfig( ∇f , SVector{2}( [1.0,1.0] ) , ForwardDiff.Chunk{1}() )
∇²f(x) = ForwardDiff.jacobian( ∇f , x , cfg_jac_1 )
cfg_jac_2 = ForwardDiff.JacobianConfig( ∇²f , SVector{2}( [1.0,1.0] ) , ForwardDiff.Chunk{1}() )
∇³f(x) = ForwardDiff.jacobian( ∇²f , x , cfg_jac_2 )
return ∇f, ∇²f, ∇³f
end
However, this yielded the same result with the gradient and hessian being type stable, but the third derivative failing to be so.
Julia version: 1.6.2
ForwardDiff version: v0.10.19
Any help with this would be much appreciated.