I'm not quite sure what you mean. It looks like I could sort of replicate
my approach using @anon by just defining an @anon function right below my
initial function definition. Then I can use the @anon version elsewhere.
For example,
function FOC(x,w)
return x*w
end
p_FOC = @anon x -> FOC(x,w) # maybe I should say const p_FOC for
performance of global variables?
But this doesn't work because I haven't defined w anywhere. It would work
if I set a dummy value for w, like w = 5., but that looks sort of odd. It
would basically come down to what I'm doing above anyway.
Is that what you meant?
On Monday, July 20, 2015 at 10:01:12 PM UTC-4, Tim Holy wrote:
>
> @anon is supposed to work this way for you under the hood; it's a bit of a
> puzzle if it doesn't. Can you file an issue, with test case, with
> FastAnonymous?
>
> --Tim
>
> On Monday, July 20, 2015 06:14:24 PM Andrew wrote:
> > Update: I've found a significantly cleaner way to do this which avoids
> > FastAnonymous entirely and runs faster for me. Now in 0.4 arbitrary
> objects
> > can be overloaded to use the f() syntax using Base.call. I create an
> > accessory type for each function that I want to pass to a non-linear
> solver
> > or optimization routine. This accessory type encapsulates the parameters
> of
> > the function, Then I define a new method for Base.call which acts like a
> > single-variable function, and simply redirects the parameters stored in
> my
> > type into the function. It looks like this
> >
> > function
> > hoursFOC(UF::UtilityFunction,hours,state::State{IdioState1,AggState1},
> > aprime)
> > w = state.as.w
> > consump = budget_consump_givenhours(state, aprime, hours)
> > w*uc(UF,consump,hours) - ul(UF,consump,hours) # Is w*uc = ul
> > end
> >
> > immutable pars_hoursFOC{TUF <: UtilityFunction, TIS<:IdioState,
> > TAS<:AggState}
> > UF::TUF
> > state::State{TIS,TAS}
> > aprime::Float64
> > end
> > Base.call(f::pars_hoursFOC, h) = hoursFOC(f.UF, h, f.state, f.aprime)
> >
> > When I need the nonlinear equation solver, I do
> >
> > f = pars_hoursFOC(UF,state,aprime)
> > j = pars_JACOBhoursFOC(UF, state, aprime) # jacobian, same idea
> > hours = myNewton(f, j, hoursguess)
> >
> > f and j are treated like functions, so this works as expected.
> >
> > This is much cleaner than my previous method where I was using @anon to
> > store an anonymous function, then passing that function around
> everywhere.
> > Also it's faster for some reason. My new code runs in 14s, the version
> > using @anon was about 20s, and a version with nested functions(or
> regular
> > anonymous functions) would be >30s.
> >
> > I see mentioned in #8712 <https://github.com/JuliaLang/julia/pull/8712>
> that
> > there may be a Callable type. That would be useful, since currently
> these
> > callable types don't work with the Optim functions or anything else that
> > asks for a ::Function argument.
> >
> > On Thursday, July 16, 2015 at 9:20:51 PM UTC-4, Andrew wrote:
> > > fzero(f, j, guess) works for me when f and j are functions. f(Af,
> guess)
> > > works for me now when Af is an @anon function.
> > >
> > > On Tuesday, July 7, 2015 at 7:34:39 PM UTC-4, j verzani wrote:
> > >> Okay, this just got fixed as much as I could with v"0.1.15" (there is
> no
> > >> fzero(f,j,guess) signature).
> > >>
> > >> On Tuesday, July 7, 2015 at 4:38:41 PM UTC-4, Andrew wrote:
> > >>> 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.
>
>
