@anon builds a type for you, creates a field called w, and defines call() for
that type. IF you're running julia 0.4, that is.
My point was simply, as a busy person I haven't read this long email chain
through and might forget about it. If there's something you want fixed, best to
file an issue with the appropriate package, with a test case that illustrates
the problem you're having.
Best,
--Tim
On Monday, July 20, 2015 09:57:24 PM Andrew wrote:
> 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.
