I am trying to understand the new type system in Julia v0.6, based on reading the release notes.
Can anyone tell me what
inv(M::Matrix{T}) where T <: AbstractFloat
gives me which is different from using the classic
inv{T<:AbstractFloat}(M::Matrix{T})
?
The new syntax means the same thing but can be used in more circumstances and can express more constructs and eliminates a number of conceptual ambiguities, especially surrounding parametric constructors. The old syntax will be deprecated in 0.6 and some of the old syntax will be reclaimed with different meaning in 1.0. Fundamentally, the problem with F{T}(args...) is that the F{T} part is conceptually ambiguous – the parser knows what it means, but it's often confusing to humans:
In isolation F{T} means the parametric type F with type parameter T.
Followed by parens, not as part of a method definition, F{T}(args...) means to apply the type F{T} to the arguments args... as a function, typically constructing an instance of the type F{T}.
Followed by parens and equals, i.e. as part of a method definition as in F{T}(args...) = expr, it means to define a method for F as a function, with type parameters T formal arguments args... and definition expr.
In particular, there is no syntax for either of these:
Adding a method to F{T} for the concrete value of T in the current scope.
Adding a method to F{T} for each parametric value T.
This situation causes constructor syntax in Julia 0.5 and prior to be more confusing and unintuitive than necessary. In Julia 1.0 type parameters and constructors will be both more intuitive and consistent, following these principles:
The syntax used to define a method always matches the syntax used to call it.
The F{T} syntax always refers to the type F with parameter T.
Type parameters are always introduced by where clauses.
There will be a more detailed explanation of the changes when 0.6 comes out, probably in a blog post on highlights of the 0.6 release.
Related
I am new to Julia. Have a quick question.
In Fortran, we can do
implicit none
Therefore whenever we use a variable, we need to define it first. Otherwise it will give error.
In Julia, I want to do the same time thing. I want to define the type of each variable first, like Float64, Int64, etc. So that I wish that Julia no longer need to automatically do type conversion, which may slow down the code.
Because I know if Julia code looks like Fortran it usually runs fast.
So, in short, is there a way in Julia such that, I can force it to only use variables whose types has been defined, and otherwise give me an error message? I just want to be strict.
I just wanted to define all the variables first, then use them. Just like Fortran does.
Thanks!
[Edit]
As suggested by the experts who answers the questions, thank you very much! I know that perhaps in Julia there is no need to manually define each variables one by one. Because for one thing, if I do that, the code will become just like Fortran, and it can be very very long especially if I have many variables.
But if I do not define the type of the each variables, is Julia smart enough to know the type? Will it do some conversions which may slow down the code?
Also, even if there is no need to define variables one by one, is there in some situations we may have to manually define the type manually?
No, this is not possible* as such. You can, however, add type annotations at any point in your code, which will raise an error if the variable is not of the expected type:
julia> i = 1
1
julia> i::Int64
1
julia> i = 1.0
1.0
julia> i::Int64
ERROR: TypeError: in typeassert, expected Int64, got a value of type Float64
Stacktrace:
[1] top-level scope
# REPL[4]:1
julia> i=0x01::UInt8
0x01
*Julia is a dynamically-typed language, though there are packages such as https://github.com/aviatesk/JET.jl for static type-checking (i.e., no type annotations required) and https://github.com/JuliaDebug/Cthulhu.jl for exploring Julia's type inference system.
Strict type declaration is not how you achieve performance in Julia.
You achieve the performance by type stability.
Moreover declaring the types is usually not recommended because it decreases interoperability.
Consider the following function:
f(x::Int) = rand() < 4+x ? 1 : "0"
The types of everything seem to be known. However, this is a terrible (from performance point of view) function because the type of output can not be calcuated by looking types of input. And this is exactly how you write the performant code with regard to types.
So how to check your code? There is a special macro #code_warntype to detect such cases so you can correct your code:
Another type related issue are the containers that should not be specified by abstract elements. So you never want to have neither Vector{Any} nor Vector{Real} - rather than that you want Vector{Int} or Vector{Float64}.
See also https://docs.julialang.org/en/v1/manual/performance-tips/ for further discussion.
As I'm learning Julia, I am wondering how to properly do things I might have done in Python, Java or C++ before. For example, previously I might have used an abstract base class (or interface) to define a family of models through classes. Each class might then have a method like calculate. So to call it I might have model.calculate(), where the model is an object from one of the inheriting classes.
I get that Julia uses multiple dispatch to overload functions with different signatures such as calculate(model). The question I have is how to create different models. Do I use the type system for that and create different types like:
abstract type Model end
type BlackScholes <: Model end
type Heston <: Model end
where BlackScholes and Heston are different types of model? If so, then I can overload different calculate methods:
function calculate(model::BlackScholes)
# code
end
function calculate(model::Heston)
# code
end
But I'm not sure if this is a proper and idiomatic use of types in Julia. I will greatly appreciate your guidance!
This is a hard question to answer. Julia offers a wide range of tools to solve any given problem, and it would be hard for even a core developer of the language to assert that one particular approach is "right" or even "idiomatic".
For example, in the realm of simulating and solving stochastic differential equations, you could look at the approach taken by Chris Rackauckas (and many others) in the suite of packages under the JuliaDiffEq umbrella. However, many of these people are extremely experienced Julia coders, and what they do may be somewhat out of reach for less experienced Julia coders who just want to model something in a manner that is reasonably sensible and attainable for a mere mortal.
It is is possible that the only "right" answer to this question is to direct users to the Performance Tips section of the docs, and then assert that as long as you aren't violating any of the recommendations there, then what you are doing is probably okay.
I think the best way I can answer this question from my own personal experience is to provide an example of how I (a mere mortal) would approach the problem of simulating different Ito processes. It is actually not too far off what you have put in the question, although with one additional layer. To be clear, I make no claim that this is the "right" way to do things, merely that it is one approach that utilizes multiple dispatch and Julia's type system in a reasonably sensible fashion.
I start off with an abstract type, for nesting specific subtypes that represent specific models.
abstract type ItoProcess ; end
Now I define some specific model subtypes, e.g.
struct GeometricBrownianMotion <: ItoProcess
mu::Float64
sigma::Float64
end
struct Heston <: ItoProcess
mu::Float64
kappa::Float64
theta::Float64
xi::Float64
end
Note, in this case I don't need to add constructors that convert arguments to Float64, since Julia does this automatically, e.g. GeometricBrownianMotion(1, 2.0) will work out-of-the-box, as Julia will automatically convert 1 to 1.0 when constructing the type.
However, I might want to add some constructors for common parameterizations, e.g.
GeometricBrownianMotion() = GeometricBrownianMotion(0.0, 1.0)
I might also want some functions that return useful information about my models, e.g.
number_parameter(model::GeometricBrownianMotion) = 2
number_parameter(model::Heston) = 4
In fact, given how I've defined the models above, I could actually be a bit sneaky and define a method that works for all subtypes:
number_parameter(model::T) where {T<:ItoProcess} = length(fieldnames(typeof(model)))
Now I want to add some code that allows me to simulate my models:
function simulate(model::T, numobs::Int, stval) where {T<:ItoProcess}
# code here that is common to all subtypes of ItoProcess
simulate_inner(model, somethingelse)
# maybe more code that is common to all subtypes of ItoProcess
end
function simulate_inner(model::GeometricBrownianMotion, somethingelse)
# code here that is specific to GeometricBrownianMotion
end
function simulate_inner(model::Heston, somethingelse)
# code here that is specific to Heston
end
Note that I have used the abstract type to allow me to group all code that is common to all subtypes of ItoProcess in the simulate function. I then use multiple dispatch and simulate_inner to run any code that needs to be specific to a particular subtype of ItoProcess. For the aforementioned reasons, I hesitate to use the phrase "idiomatic", but let me instead say that the above is quite a common pattern in typical Julia code.
The one thing to be careful of in the above code is to ensure that the output type of the simulate function is type-stable, that is, the output type can be uniquely determined by the input types. Type stability is usually an important factor in ensuring performant Julia code. An easy way in this case to ensure type-stability is to always return Matrix{Float64} (if the output type is fixed for all subtypes of ItoProcess then obviously it is uniquely determined). I examine a case where the output type depends on input types below for my estimate example. Anyway, for simulate I might always return Matrix{Float64} since for GeometricBrownianMotion I only need one column, but for Heston I will need two (the first for price of the asset, the second for the volatility process).
In fact, depending on how the code is used, type-stability is not always necessary for performant code (see eg using function barriers to prevent type-instability from flowing through to other parts of your program), but it is a good habit to be in (for Julia code).
I might also want routines to estimate these models. Again, I can follow the same approach (but with a small twist):
function estimate(modeltype::Type{T}, data)::T where {T<:ItoProcess}
# again, code common to all subtypes of ItoProcess
estimate_inner(modeltype, data)
# more common code
return T(some stuff generated from function that can be used to construct T)
end
function estimate_inner(modeltype::Type{GeometricBrownianMotion}, data)
# code specific to GeometricBrownianMotion
end
function estimate_inner(modeltype::Type{Heston}, data)
# code specific to Heston
end
There are a few differences from the simulate case. Instead of inputting an instance of GeometricBrownianMotion or Heston, I instead input the type itself. This is because I don't actually need an instance of the type with defined values for the fields. In fact, the values of those fields is the very thing I am attempting to estimate! But I still want to use multiple dispatch, hence the ::Type{T} construct. Note also I have specified an output type for estimate. This output type is dependent on the ::Type{T} input, and so the function is type-stable (output type can be uniquely determined by input types). But common with the simulate case, I have structured the code so that code that is common to all subtypes of ItoProcess only needs to be written once, and code that is specific to the subtypes is separted out.
This answer is turning into an essay, so I should tie it off here. Hopefully this is useful to the OP, as well as anyone else getting into Julia. I just want to finish by emphasizing that what I have done above is only one approach, there are others that will be just as performant, but I have personally found the above to be useful from a structural perspective, as well as reasonably common across the Julia ecosystem.
I've got a symbol that represents the name of a function to be called:
julia> func_sym = :tanh
I can use that symbol to get the tanh function and call it using:
julia> eval(func_sym)(2)
0.9640275800758169
But I'd rather avoid the 'eval' there as it will be called many times and it's expensive (and func_sym can have several different values depending on context).
IIRC in Ruby you can say something like:
obj.send(func_sym, args)
Is there something similar in Julia?
EDIT: some more details on why I have functions represented by symbols:
I have a type (from a neural network) that includes the activation function, originally I included it as a funcion:
type NeuralLayer
weights::Matrix{Float32}
biases::Vector{Float32}
a_func::Function
end
However, I needed to serialize these things to files using JLD, but it's not possible to serialize a Function, so I went with a symbol:
type NeuralLayer
weights::Matrix{Float32}
biases::Vector{Float32}
a_func::Symbol
end
And currently I use the eval approach above to call the activation function. There are collections of NeuralLayers and each can have it's own activation function.
#Isaiah's answer is spot-on; perhaps even more-so after the edit to the original question. To elaborate and make this more specific to your case: I'd change your NeuralLayer type to be parametric:
type NeuralLayer{func_type}
weights::Matrix{Float32}
biases::Vector{Float32}
end
Since func_type doesn't appear in the types of the fields, the constructor will require you to explicitly specify it: layer = NeuralLayer{:excitatory}(w, b). One restriction here is that you cannot modify a type parameter.
Now, func_type could be a symbol (like you're doing now) or it could be a more functionally relevant parameter (or parameters) that tunes your activation function. Then you define your activation functions like this:
# If you define your NeuralLayer with just one parameter:
activation(layer::NeuralLayer{:inhibitory}) = …
activation(layer::NeuralLayer{:excitatory}) = …
# Or if you want to use several physiological parameters instead:
activation{g_K,g_Na,g_l}(layer::NeuralLayer{g_K,g_Na,g_l} = f(g_K, g_Na, g_l)
The key point is that functions and behavior are external to the data. Use type definitions and abstract type hierarchies to define behavior, as is coded in the external functions… but only store data itself in the types. This is dramatically different from Python or other strongly object-oriented paradigms, and it takes some getting used to.
But I'd rather avoid the 'eval' there as it will be called many times and it's expensive (and func_sym can have several different values depending on context).
This sort of dynamic dispatch is possible in Julia, but not recommended. Changing the value of 'func_sym' based on context defeats type inference as well as method specialization and inlining. Instead, the recommended approach is to use multiple dispatch, as detailed in the Methods section of the manual.
I am trying to create a function
import Language.Reflection
foo : Type -> TT
I tried it by using the reflect tactic:
foo = proof
{
intro t
reflect t
}
but this reflects on the variable t itself:
*SOQuestion> foo
\t => P Bound (UN "t") (TType (UVar 41)) : Type -> TT
Reflection in Idris is a purely syntactic, compile-time only feature. To predict how it will work, you need to know about how Idris converts your program to its core language. Importantly, you won't be able to get ahold of reflected terms at runtime and reconstruct them like you would with Lisp. Here's how your program is compiled:
Internally, Idris creates a hole that will expect something of type Type -> TT.
It runs the proof script for foo in this state. We start with no assumptions and a goal of type Type -> TT. That is, there's a term being constructed which looks like ?rhs : Type => TT . rhs. The ?foo : ty => body syntax shows that there's a hole called foo whose eventual value will be available inside of body.
The step intro t creates a function whose argument is t : Type - this means that we now have a term like ?foo_body : TT . \t : Type => foo_body.
The reflect t step then fills the current hole by taking the term on its right-hand side and converting it to a TT. That term is in fact just a reference to the argument of the function, so you get the variable t. reflect, like all other proof script steps, only has access to the information that is available directly at compile time. Thus, the result of filling in foo_body with the reflection of the term t is P Bound (UN "t") (TType (UVar (-1))).
If you could do what you are wanting here, it would have major consequences both for understanding Idris code and for running it efficiently.
The loss in understanding would come from the inability to use parametricity to reason about the behavior of functions based on their types. All functions would effectively become potentially ad-hoc polymorphic, because they could (say) run differently on lists of strings than on lists of ints.
The loss in performance would come from representing enough type information to do the reflection. After Idris code is compiled, there is no type information left in it (unlike in a system such as the JVM or .NET or a dynamically typed system such as Python, where types have a runtime representation that code can access). In Idris, types can be very large, because they can contain arbitrary programs - this means that far more information would have to be maintained, and computation occurring at the type level would also have to be preserved and repeated at runtime.
If you're wanting to reflect on the structure of a type for further proof automation at compile time, take a look at the applyTactic tactic. Its argument should be a function that takes a reflected context and goal and gives back a new reflected tactic script. An example can be seen in the Data.Vect source.
So I suppose the summary is that Idris can't do what you want, and it probably never will be able to, but you might be able to make progress another way.
This is similar to my previous question, but a bit more complicated.
Before I was defining a type with an associated integer as a parameter, Intp{p}. Now I would like to define a type using a vector as a parameter.
The following is the closest I can write to what I want:
type Extp{g::Vector{T}}
c::Vector{T}
end
In other words, Extp should be defined with respect to a Vector, g, and I want the contents, c, to be another Vector, whose entries should be the of the same type as the entries of g.
Well, this does not work.
Problem 1: I don't think I can use :: in the type parameter.
Problem 2: I could work around that by making the types of g and c arbitary and just making sure the types in the vectors match up in the constructor. But, even if I completely take everything out and use
type Extp{g}
c
end
it still doesn't seem to like this. When I try to use it the way I want to,
julia> Extp{[1,1,1]}([0,0,1])
ERROR: type: apply_type: in Extp, expected Type{T<:Top}, got Array{Int64,1}
So, does Julia just not like particular Vectors being associated with types? Does what I'm trying to do only work with integers, like in my Intp question?
EDIT: In the documentation I see that type parameters "can be any type at all (or an integer, actually, although here it’s clearly used as a type)." Does that mean that what I'm asking is impossible, and that that only types and integers work for Type parameters? If so, why? (what makes integers special over other types in Julia in this way?)
In Julia 0.4, you can use any "bitstype" as a parameter of a type. However, a vector is not a bitstype, so this is not going to work. The closest analog is to use a tuple: for example, (3.2, 1.5) is a perfectly valid type parameter.
In a sense vectors (or any mutable object) are antithetical to types, which cannot change at runtime.
Here is the relevant quote:
Both abstract and concrete types can be parameterized by other types
and by certain other values (currently integers, symbols, bools, and
tuples thereof).
So, your EDIT is correct. Widening this has come up on the Julia issues page (e.g., #5102 and #6081 were two related issues I found with some discussion), so this may change in the future - I'm guessing not in v0.4 though. It'd have to be an immutable type really to make any sense, so not Vector. I'm not sure I understand your application, but would a Tuple work?