Just checked. So, Roots.fzero(f, guess) does work. However, Roots.fzero(f,
j, guess) doesn't work, and neither does Roots.newton(f, j, guess).
I looked at the Roots.jl source and I see ::Function annotations on the
methods with the jacobian, but not the regular one.
On Tuesday, July 7, 2015 at 4:22:17 PM UTC-4, j verzani wrote:
>
> It isn't your first choice, but `Roots.fzero` can have `@anon` functions
> passed to it, unless I forgot to tag a new version after making that change
> on master not so long ago.
>
> On Tuesday, July 7, 2015 at 2:29:51 PM UTC-4, Andrew wrote:
>>
>> I'm writing this in case other people are trying to do the same thing
>> I've done, and also to see if anyone has any suggestions.
>>
>> Recently I have been writing some code that requires solving lots(tens of
>> thousands) of simple non-linear equations. The application is economics, I
>> am solving an intratemporal first order condition for optimal labor supply
>> given the state and a savings decision. This requires solving the same
>> equation many times, but with different parameters.
>>
>> As far as I know, the standard ways to do this are to either define a
>> nested function which by the lexical scoping rules inherits the parameters
>> of the outer function, or use an anonymous function. Both these methods are
>> slow right now because Julia can't inline those functions. However, the
>> FastAnonymous package lets you define an anonymous "function", which
>> behaves exactly like a function but isn't type ::Function, which is fast.
>> Crucially for me, in Julia 0.4 you can modify the parameters of the
>> function you get out of FastAnonymous. I rewrote some code I had which
>> depended on solving a lot of non-linear equations, and it's now 3 times as
>> fast, running in 2s instead of 6s.
>>
>> Here I'll describe a simplified version of my setup and point out a few
>> issues.
>>
>> 1. I store the anonymous function in a type that I will pass along to the
>> function which needs to solve the nonlinear equation. I use a parametric
>> type here since the type of an anonymous function seems to vary with every
>> instance. For example,
>>
>> typeof(UF.fhoursFOC)
>> FastAnonymous.##Closure#11431{Ptr{Void}
>> @0x00007f2c2eb26e30,0x10e636ff02d85766,(:h,)}
>>
>>
>> To construct the type,
>>
>> immutable CRRA_labor{T1, T2} <: LaborChoice # <: means "subtype of"
>> sigmac::Float64
>> sigmal::Float64
>> psi::Float64
>> hoursmax::Float64
>> state::State # Encodes info on how to solve itself
>> fhoursFOC::T1
>> fJACOBhoursFOC::T2
>> end
>>
>> To set up the anonymous functions fhoursFOC and fJACOBhoursFOC (the
>> jacobian), I define a constructor
>>
>> function CRRA_labor(sigmac,sigmal,psi,hoursmax,state)
>> fhoursFOC = @anon h -> hoursFOC(CRRA_labor(sigmac,sigmal,psi,hoursmax
>> ,state,0., 0.) , h, state)
>> fJACOBhoursFOC = @anon jh -> JACOBhoursFOC(CRRA_labor(sigmac,sigmal,
>> psi,hoursmax,state,0., 0.) , jh, state)
>> CRRA_labor(sigmac,sigmal,psi,hoursmax,state,fhoursFOC, fJACOBhoursFOC
>> )
>> end
>>
>> This looks a bit complicated because the nonlinear equation I need to
>> solve, hoursFOC, relies on the type CRRA_labor, as well as some aggregate
>> and idiosyncratic state info, to set up the problem. To encode this
>> information, I define a dummy instance of CRRA_labor, where I supply 0's in
>> place of the anonymous functions. I tried to make a self-referential type
>> here as described in the documentation, but I couldn't get it to work, so I
>> went with the dummy instance instead.
>>
>> @anon sets up the anonymous function. This means that code like
>> fhoursFOC(0.5) will return a value.
>>
>> 2. Now that I have my anonymous function taking only 1 variable, I can
>> use the nonlinear equation solver. Unfortunately, the existing nonlinear
>> equation solvers like Roots.fzero and NLsolve ask the argument to be of
>> type ::Function. Since anonymous functions work like functions but are
>> actually some different type, they wouldn't accept my argument. Instead, I
>> wrote my own Newton method, which is like 5 lines of code, where I don't
>> restrict the argument type.
>>
>> I think it would be very straightforward to make this a multivariate
>> Newton method.
>>
>> function myNewton(f, j, x)
>> for n = 1:100
>> fx , jx = f(x), j(x)
>> abs(fx) < 1e-6 && return x
>> d = fx/jx
>> x = x - d
>> end
>> println("Too many iterations")
>> return NaN
>> end
>>
>> 3. The useful thing here in 0.4 is that you can edit the parameters of
>> the anonymous function. The parameters are encoded in a custom type
>> state::State, and I update the state. Then I call my nonlinear equation
>> solver
>>
>> UF.fhoursFOC.state, UF.fJACOBhoursFOC.state = state, state
>> f = UF.fhoursFOC
>> j = UF.fJACOBhoursFOC
>> hours = myNewton(f, j, hoursguess)
>>
>> This runs much faster than my old version which used NLsolve, which
>> itself ran faster than a version using Roots.fzero.
>>
>> Issues:
>>
>> 1. Since the type of the anonymous function isn't ::Function, I had to
>> write my own solver. I'm pretty sure a 1-line edit to Roots.fzero where I
>> just remove the ::Function type annotation would let it work there, but I'm
>> not aware of another workaround.
>>
>> 2. I would rather use NLsolve, which uses in-place updating of its
>> arguments ( f!(input::Array, output::Array) ), but I've tried constructing
>> an anonymous function that does that, and @anon didn't work. Perhaps there
>> is a workaround.
>>
>> 3. Since I'm using an anonymous function, I have to explicitly pass it
>> around. Encoding it into the type CRRA_labor wasn't really hard though.
>>
>>
>>
>>
>>
>>
>>
