Specializing method calls in order in meta-programming - julia

I have issue after calling my macro:
#introspectable square(x) = x * x
Then when calling
square(3)
i should be able to get 9, cause the function call has been specialized to execute an attribute of the structure which is Julia code, however when I enter the macro, the code seems to be directly evaluated.
What i have tried:
struct IntrospectableFunction
name
parameters
native_function
end
(f::IntrospectableFunction)(x) = f.native_function(x)
macro introspectable(expr)
name = expr.args[1].args[1]
parameters = tuple(expr.args[1].args[2:end]...)
body = expr.args[2].args[2]
:( global $name = IntrospectableFunction( :( name ), $parameters, :( body ) ))
end
#introspectable square(x) = x * x
square(3)
The answer should be 9 , however i get "Object of type symbol are not callable ". However if i replace :( body ) with x -> x * x i get the desired result, my objective is generalizing the macro-call.

I usually find it easier to work with expressions in macros (it is not the shortest way to write things, but, from my experience, it is much easier to control what gets generated).
Therefore I would rewrite your code as:
macro introspectable(expr)
name = expr.args[1].args[1]
parameters = expr.args[1].args[2:end]
anon = Expr(Symbol("->"), Expr(:tuple, parameters...), expr.args[2].args[2])
constr = Expr(:call, :IntrospectableFunction, QuoteNode(name), Tuple(parameters), anon)
esc(Expr(:global, Expr(Symbol("="), name, constr)))
end
Now, as you said you wanted generality I would define your functor like this:
(f::IntrospectableFunction)(x...) = f.native_function(x...)
(in this way you allow multiple positional arguments to be passed).
Now let us test our definitions:
julia> #introspectable square(x) = x * x
IntrospectableFunction(:square, (:x,), getfield(Main, Symbol("##3#4"))())
julia> square(3)
9
julia> #macroexpand #introspectable square(x) = x * x
:(global square = IntrospectableFunction(:square, (:x,), ((x,)->x * x)))
julia> #introspectable toarray(x,y) = [x,y]
IntrospectableFunction(:toarray, (:x, :y), getfield(Main, Symbol("##5#6"))())
julia> toarray("a", 10)
2-element Array{Any,1}:
"a"
10
julia> #macroexpand #introspectable toarray(x,y) = [x,y]
:(global toarray = IntrospectableFunction(:toarray, (:x, :y), ((x, y)->[x, y])))
julia> function localscopetest()
#introspectable globalfun(x...) = x
end
localscopetest (generic function with 1 method)
julia> localscopetest()
IntrospectableFunction(:globalfun, (:(x...),), getfield(Main, Symbol("##9#10"))())
julia> globalfun(1,2,3,4,5)
(1, 2, 3, 4, 5)
julia> function f()
v = 100
#introspectable localbinding(x) = (v, x)
end
f (generic function with 1 method)
julia> f()
IntrospectableFunction(:localbinding, (:x,), getfield(Main, Symbol("##11#12")){Int64}(100))
julia> localbinding("x")
(100, "x")
(note that it is useful to use #macroexpand to make sure our macro works as expected)
EDIT - how to handle a minimal multiple dispatch
I am writing a non-macro example because it is related to the data structure:
Use e.g. such a definition:
struct IntrospectableFunction
name::Symbol
method_array::Vector{Pair{Type{<:Tuple}, Function}}
end
function (f::IntrospectableFunction)(x...)
for m in f.method_array
if typeof(x) <: first(m)
return last(m)(x...)
end
end
error("signature not found")
end
and now you can write:
julia> square = IntrospectableFunction(:square, [Tuple{Any}=>x->x*x,Tuple{Any,Any}=>(x,y)->x*y])
IntrospectableFunction(:square, Pair{DataType,Function}[Tuple{Any}=>##9#11(), Tuple{Any,Any}=>##10#12()])
julia> square(3)
9
julia> square(2,3)
6
Keep in mind that the approach I present is not perfect and universal - it just serves to give a very simple example how you could do it.

Related

Using ForwardDiff.jl for a function of many variables and parameters Julia

The github repo for ForwardDiff.jl has some examples. I am trying to extend the example to take in addition to a vector of variables, a parameter. I cannot get it to work.
This is the example (it is short so I will show it rather than linking)
using ForwardDiff
x = rand(5)
f(x::Vector) = sum(sin, x) .+ prod(tan, x) * sum(sqrt, x);
g = x -> ForwardDiff.gradient(f, x);
g(x) # this outputs the gradient.
I want to modify this since I use functions with multiple parameters as well as variables. As a simple modification I have tried adding a single parameter.
f(x::Vector, y) = (sum(sin, x) .+ prod(tan, x) * sum(sqrt, x)) * y;
I have tried the following to no avail:
fp = x -> ForwardDiff.gradient(f, x);
fp = x -> ForwardDiff.gradient(f, x, y);
y = 1
println("test grad: ", fp(x, y))
I get the following error message:
ERROR: LoadError: MethodError: no method matching (::var"#73#74")(::Array{Float64,1}, ::Int64)
A similar question was not answered in 2017. A comment led me to here and it seems the function can only accept one input?
The target function must be unary (i.e., only accept a single argument). ForwardDiff.jacobian is an exception to this rule.
Has this changed? It seems very limited to only be able to differentiate unary functions.
A possible workaround would be to concatenate the list of variables and parameters and then just slice the returned gradient to not include the gradients with respect to the parameters, but this seems silly.
I personally think it makes sense to have this unary-only syntax for ForwardDiff. In your case, you could just pack/unpack x and y into a single vector (nominally x2 below):
julia> using ForwardDiff
julia> x = rand(5)
5-element Array{Float64,1}:
0.4304735670747184
0.3939269364431113
0.7912705403776603
0.8942024934250143
0.5724373306715196
julia> f(x::Vector, y) = (sum(sin, x) .+ prod(tan, x) * sum(sqrt, x)) * y;
julia> y = 1
1
julia> f(x2::Vector) = f(x2[1:end-1], x2[end]) % unpacking in f call
f (generic function with 2 methods)
julia> fp = x -> ForwardDiff.gradient(f, x);
julia> println("test grad: ", fp([x; y])) % packing in fp call
test grad: [2.6105844240785796, 2.741442601659502, 1.9913192377198885, 1.9382805843854594, 2.26202717745402, 3.434350946190029]
But my preference would be to explicitly name the partial derivatives differently:
julia> ∂f∂x(x,y) = ForwardDiff.gradient(x -> f(x,y), x)
∂f∂x (generic function with 1 method)
julia> ∂f∂y(x,y) = ForwardDiff.derivative(y -> f(x,y), y)
∂f∂y (generic function with 1 method)
julia> ∂f∂x(x, y)
5-element Array{Float64,1}:
2.6105844240785796
2.741442601659502
1.9913192377198885
1.9382805843854594
2.26202717745402
julia> ∂f∂y(x, y)
3.434350946190029
Here's a quick attempt at a function which takes multiple arguments, the same signature as Zygote.gradient:
julia> using ForwardDiff, Zygote
julia> multigrad(f, xs...) = ntuple(length(xs)) do i
g(y) = f(ntuple(j -> j==i ? y : xs[j], length(xs))...)
xs[i] isa AbstractArray ? ForwardDiff.gradient(g, xs[i]) :
xs[i] isa Number ? ForwardDiff.derivative(g, xs[i]) : nothing
end;
julia> f1(x,y,z) = sum(x.^2)/y;
julia> multigrad(f1, [1,2,3], 4)
([0.5, 1.0, 1.5], -0.875)
julia> Zygote.gradient(f1, [1,2,3], 4)
([0.5, 1.0, 1.5], -0.875)
For a function with several scalar arguments, this evaluates each derivative separately, and perhaps it would be more efficient to use one evaluation with some Dual(x, (dx, dy, dz)). With large-enough array arguments, ForwardDiff.gradient will already perform multiple evaluations, each with some number of perturbations (the chunk size, which you can control).

Julia Metaprogramming: Function for Mathematical Series

I'm trying to build a function that will output an expression to be assigned to a new in-memory function. I might be misinterpreting the capability of metaprogramming but, I'm trying to build a function that generates a math series and assigns it to a function such as:
main.jl
function series(iter)
S = ""
for i in 1:iter
a = "x^$i + "
S = S*a
end
return chop(S, tail=3)
end
So, this will build the pattern and I'm temporarily working with it in the repl:
julia> a = Meta.parse(series(4))
:(x ^ 1 + x ^ 2 + x ^ 3 + x ^ 4)
julia> f =eval(Meta.parse(series(4)))
120
julia> f(x) =eval(Meta.parse(series(4)))
ERROR: cannot define function f; it already has a value
Obviously eval isn't what I'm looking for in this case but, is there another function I can use? Or, is this just not a viable way to accomplish the task in Julia?
The actual error you get has to do nothing with metaprogramming, but with the fact that you are reassigning f, which was assigned a value before:
julia> f = 10
10
julia> f(x) = x + 1
ERROR: cannot define function f; it already has a value
Stacktrace:
[1] top-level scope at none:0
[2] top-level scope at REPL[2]:1
It just doesn't like that. Call either of those variables differently.
Now to the conceptual problem. First, what you do here is not "proper" metaprogramming in Julia: why deal with strings and parsing at all? You can work directly on expressions:
julia> function series(N)
S = Expr(:call, :+)
for i in 1:N
push!(S.args, :(x ^ $i))
end
return S
end
series (generic function with 1 method)
julia> series(3)
:(x ^ 1 + x ^ 2 + x ^ 3)
This makes use of the fact that + belongs to the class of expressions that are automatically collected in repeated applications.
Second, you don't call eval at the appropriate place. I assume you meant to say "give me the function of x, with the body being what series(4) returns". Now, while the following works:
julia> f3(x) = eval(series(4))
f3 (generic function with 1 method)
julia> f3(2)
30
it is not ideal, as you newly compile the body every time the function is called. If you do something like that, it is preferred to expand the code once into the body at function definition:
julia> #eval f2(x) = $(series(4))
f2 (generic function with 1 method)
julia> f2(2)
30
You just need to be careful with hygiene here. All depends on the fact that you know that the generated body is formulated in terms of x, and the function argument matches that. In my opinion, the most Julian way of implementing your idea is through a macro:
julia> macro series(N::Int, x)
S = Expr(:call, :+)
for i in 1:N
push!(S.args, :($x ^ $i))
end
return S
end
#series (macro with 1 method)
julia> #macroexpand #series(4, 2)
:(2 ^ 1 + 2 ^ 2 + 2 ^ 3 + 2 ^ 4)
julia> #series(4, 2)
30
No free variables remaining in the output.
Finally, as has been noted in the comments, there's a function (and corresponding macro) evalpoly in Base which generalizes your use case. Note that this function does not use code generation -- it uses a well-designed generated function, which in combination with the optimizations results in code that is usually equal to the macro-generated code.
Another elegant option would be to use the multiple-dispatch mechanism of Julia and dispatch the generated code on type rather than value.
#generated function series2(p::Val{N}, x) where N
S = Expr(:call, :+)
for i in 1:N
push!(S.args, :(x ^ $i))
end
return S
end
Usage
julia> series2(Val(20), 150.5)
3.5778761722367333e43
julia> series2(Val{20}(), 150.5)
3.5778761722367333e43
This task can be accomplished with comprehensions. I need to RTFM...
https://docs.julialang.org/en/v1/manual/arrays/#Generator-Expressions

Changing the input (i.e. x+2y) of a macro to an expression ( :(x+2y)), How to produce the same output?

The code at the end of this post constructs a function which is bound to the variables of a given dictionary. Furthermore, the function is not bound to the actual name of the dictionary (as I use the Ref() statement).
An example:
julia> D = Dict(:x => 4, :y => 5)
julia> f= #mymacro4(x+2y, D)
julia> f()
14
julia> DD = D
julia> D = nothing
julia> f()
14
julia> DD[:x] = 12
julia> f()
22
Now I want to be able to construct exactly the same function when I only have access to the expression expr = :(x+2y).
How do I do this? I tried several things, but was not able to find a solution.
julia> f = #mymacro4(:(x+2y), D)
julia> f() ### the function evaluation should also yield 14. But it yields:
:(DR.x[:x] + 2 * DR.x[:y])
(I actually want to use it within another macro in which the dictionary is automatically created. I want to store this dictionary and the function within a struct, such that I'm able to call this function at a later point in time and manipulate the objects in the dictionary. If necessary, I may post the complete example and explain the complete problem.)
_freevars2(literal) = literal
function _freevars2(s::Symbol)
try
if typeof(eval(s)) <: Function
return s
else
return Meta.parse("DR.x[:$s]")
end
catch
return Meta.parse("DR.x[:$s]")
end
end
function _freevars2(expr::Expr)
for (it, s) in enumerate(expr.args)
expr.args[it] = _freevars2(s)
end
return expr
end
macro mymacro4(expr, D)
expr2 = _freevars2(expr)
quote
let DR = Ref($(esc(D)))
function mysym()
$expr2
end
end
end
end

Restricting function signatures while using ForwardDiff in Julia

I am trying to use ForwardDiff in a library where almost all functions are restricted to only take in Floats. I want to generalise these function signatures so that ForwardDiff can be used while still being restrictive enough so functions only take numeric values and not things like Dates. I have alot of functions with the same name but different types (ie functions that take in "time" as either a float or a Date with the same function name) and do not want to remove the type qualifiers throughout.
Minimal Working Example
using ForwardDiff
x = [1.0, 2.0, 3.0, 4.0 ,5.0]
typeof(x) # Array{Float64,1}
function G(x::Array{Real,1})
return sum(exp.(x))
end
function grad_F(x::Array)
return ForwardDiff.gradient(G, x)
end
G(x) # Method Error
grad_F(x) # Method error
function G(x::Array{Float64,1})
return sum(exp.(x))
end
G(x) # This works
grad_F(x) # This has a method error
function G(x)
return sum(exp.(x))
end
G(x) # This works
grad_F(x) # This works
# But now I cannot restrict the function G to only take numeric arrays and not for instance arrays of Dates.
Is there are a way to restict functions to only take numeric values (Ints and Floats) and whatever dual number structs that ForwardDiff uses but not allow Symbols, Dates, etc.
ForwardDiff.Dual is a subtype of the abstract type Real. The issue you have, however, is that Julia's type parameters are invariant, not covariant. The following, then, returns false.
# check if `Array{Float64, 1}` is a subtype of `Array{Real, 1}`
julia> Array{Float64, 1} <: Array{Real, 1}
false
That makes your function definition
function G(x::Array{Real,1})
return sum(exp.(x))
end
incorrect (not suitable for your use). That's why you get the following error.
julia> G(x)
ERROR: MethodError: no method matching G(::Array{Float64,1})
The correct definition should rather be
function G(x::Array{<:Real,1})
return sum(exp.(x))
end
or if you somehow need an easy access to the concrete element type of the array
function G(x::Array{T,1}) where {T<:Real}
return sum(exp.(x))
end
The same goes for your grad_F function.
You might find it useful to read the relevant section of the Julia documentation for types.
You might also want to type annotate your functions for AbstractArray{<:Real,1} type rather than Array{<:Real, 1} so that your functions can work other types of arrays, like StaticArrays, OffsetArrays etc., without a need for redefinitions.
This would accept any kind of array parameterized by any kind of number:
function foo(xs::AbstractArray{<:Number})
#show typeof(xs)
end
or:
function foo(xs::AbstractArray{T}) where T<:Number
#show typeof(xs)
end
In case you need to refer to the type parameter T inside the body function.
x1 = [1.0, 2.0, 3.0, 4.0 ,5.0]
x2 = [1, 2, 3,4, 5]
x3 = 1:5
x4 = 1.0:5.0
x5 = [1//2, 1//4, 1//8]
xss = [x1, x2, x3, x4, x5]
function foo(xs::AbstractArray{T}) where T<:Number
#show xs typeof(xs) T
println()
end
for xs in xss
foo(xs)
end
Outputs:
xs = [1.0, 2.0, 3.0, 4.0, 5.0]
typeof(xs) = Array{Float64,1}
T = Float64
xs = [1, 2, 3, 4, 5]
typeof(xs) = Array{Int64,1}
T = Int64
xs = 1:5
typeof(xs) = UnitRange{Int64}
T = Int64
xs = 1.0:1.0:5.0
typeof(xs) = StepRangeLen{Float64,Base.TwicePrecision{Float64},Base.TwicePrecision{Float64}}
T = Float64
xs = Rational{Int64}[1//2, 1//4, 1//8]
typeof(xs) = Array{Rational{Int64},1}
T = Rational{Int64}
You can run the example code here: https://repl.it/#SalchiPapa/Restricting-function-signatures-in-Julia

Julia-Lang Metaprogramming: turn expression into function with expression-dependent arguments

Given a dictionary of values,
values = {:A => 3, :B => 1}
turn an (arbitrary) expression like
expr = :(2*A)
into a function foo(values) that evaluates the expression, so in this case foo(values) = 6. The resulting function will be called millions of times, so speed is an important consideration. I am happy to adopt a slightly different approach if necessary, as long as it can be automatised.
Things I tried:
The conversion using convert(Function, expr), as suggested here. Fails for me (Julia 0.3.8-pre):
convert has no method matching convert(::Type{Function}, ::Expr)
Using #eval one can do
#eval foo(A) = $(expr)
and then call foo(values[:A]), but that would require knowing that expr depends on A (and only on A).
I wrote a function find_vars(exp) to return the symbols in expr (in this case [:A]), but couldn't find how to use them in the #eval approach.
Base.Cartesian has an unexported function lreplace which may be what you're after. Then you can do something like:
julia> values = Dict(:A=>3, :B=>1)
Dict{Symbol,Int64} with 2 entries:
:B => 1
:A => 3
julia> import Base.Cartesian.lreplace
julia> expr = :(2*A)
:(2A)
julia> function lreplace_all(expr, d)
for (k, v) in d
expr = lreplace(expr, k, v)
end
expr
end
lreplace_all (generic function with 1 method)
julia> lreplace_all(expr, values)
:(2 * 3)
julia> #eval foo(A) = $(lreplace_all(:(2A), values))
foo (generic function with 1 method)
julia> foo(1)
6
Although, since A is defined by the values dict, it makes more sense to define foo as a zero-argument function (unless I've missed something).
EDIT:
After rereading your question it seems like you want to pass in the actual dictionary to the function rather than have the values available at compile time as I've done above. In that case, we have get a little creative:
First we need an lreplace like function that will work with expressions which is easy enough
julia> dictreplace!(ex, s, v) = ex
dictreplace! (generic function with 1 method)
julia> dictreplace!(ex::Symbol, s, v) = s == ex ? v : ex
dictreplace! (generic function with 2 methods)
julia> function dictreplace!(ex::Expr, s, v)
for i=1:length(ex.args)
ex.args[i] = dictreplace!(ex.args[i], s, v)
end
ex
end
dictreplace! (generic function with 3 methods)
julia> dictreplace(ex, s, v) = dictreplace!(copy(ex), s, v)
dictreplace (generic function with 1 method)
Now we want to replace every occurence of a symbol in our dict keys with a dictionary lookup
julia> function dictreplace_all(expr, kys, dsym)
for k in kys
expr = dictreplace(expr, k, :($(dsym)[$(QuoteNode(k))]))
end
expr
end
dictreplace_all (generic function with 1 method)
julia> dictreplace_all(:(2A), keys(values), :d)
:(2 * d[:A])
julia> #eval foo(args) = $(dictreplace_all(:(2A), keys(values), :args))
foo (generic function with 1 method)
julia> values[:A] = -99
-99
julia> foo(values)
-198
Thanks to the solution by #ptb and another metaprogramming question I found a simpler yet slower solution:
function foo(values, expr)
expr = quote
A = values[:A]
B = values[:B]
return $(expr)
end
eval(expr)
end
Reading in the values from the dictionary can also be done programmatically by replacing the inner evaluation by
$([:($k = $v) for (k, v) in values]...)
return $(expr)

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