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Julia DiffResults examples?

Julia's ForwardDiff documentation suggests that computing the function value, gradient and Hessian can be computed in one fell swoop using the DiffResults API, but there are NO examples. The DiffResults package itself has no examples either, and no documentation to speak of. The use case for this is self-evident: suppose I have a function f of a vector argument x, and I want to minimize it using Newton's method. Below is the blunt approach, where things get recomputed three times - how would I write it with DiffResults?

ForwardDiff

DiffResults

DiffResults

f

x

DiffResults

function NewtMin(f, x0, eps)
fgrad = x-> ForwardDiff.gradient(f, x)
fhess = x-> ForwardDiff.hessian(f, x)
oldval = f(x0)
newx = x0 - fhess(x0)fgrad(x0)
newval = f(newx)
while abs(newval - oldval) > eps
oldval = newval
newx = newx - fhess(newx)fgrad(newx)
newval = f(newx)
end
return newx
end


1 Answer
1

There are examples in the DiffResults.jl documentation from http://www.juliadiff.org/DiffResults.jl/stable/.

DiffResults.jl

And this is a simple rewriting of Newtmin using DiffResults, it works in julia v0.6.4. But I guess it can be refactored and optimized to be more elegant and performant.

Newtmin

DiffResults

using ForwardDiff
using DiffResults

function NewtMin(f, x0, eps)
result = DiffResults.HessianResult(x0)
ForwardDiff.hessian!(result, f, x0)
fhess_x0 = DiffResults.hessian(result)
fgrad_x0 = DiffResults.gradient(result)
oldval = DiffResults.value(result)
newx = x0 - fhess_x0fgrad_x0
newval = f(newx)
while abs(newval - oldval) > eps
oldval = newval
ForwardDiff.hessian!(result, f, newx)
fhess_newx = DiffResults.hessian(result)
fgrad_newx = DiffResults.gradient(result)
newx = newx - fhess_newxfgrad_newx
newval = f(newx)
end
return newx
end

foo(x) = sum(x.^2)

NewtMin(foo, [1.,1.,1.], 0.01)
## which should give a correct result at [0., 0., 0.]


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