Category Archives: Julia

Constraint Solver Part 3: More Pruning & Benchmarking

Series: Constraint Solver in Julia

This is part 3 of the series about: How to build a Constraint Programming solver?

In this part we want to make a minor but important update to the old post as I missed something as well as doing some bechmarking with other constraint programming solvers or specialized sudoku solvers.

Let’s have a look at the video from the last post:

Explanation:

Last time we have set a value while backtracking and then removed values from the search space and maybe set new values due to fixing this single value.

  • black: Given values
  • blue:
    • beginning: pruned before backtracking
    • later: set or pruned during backtracking (might be wrong)
  • green cell: last set by backtracking
  • orange cell: pruned by green cell (or later other orange cells)

At that moment I didn’t completely think that through and only when I had a look at the visualization I made I realized that it’s a bit stupid not to further propagate the new changes as well.

That is the only change on the code basis for this post and after that I’ll show you some benchmarking results which will not be that awesome yet as it’s more like a spoiler and preparation for the next post which will be longer.

So after the first pruning in our backtrack function: GitHub Line

we add a part to prune further on the fixed values:

# prune on fixed vals
co_idx = 1
constraint_idxs_dict = Dict{Int, Bool}()
# get all constraints which need to be called (only once)
while co_idx < length(constraint_outputs)
    constraint_output = constraint_outputs[co_idx]
    for fixed_ind in keys(constraint_output.fixed)
        inner_constraints = com.constraints[com.subscription[fixed_ind]]
        for constraint in inner_constraints
            constraint_idxs_dict[constraint.idx] = true
        end
    end
    co_idx += 1
end
constraint_idxs = collect(keys(constraint_idxs_dict))

There we just check which constraints need to be called again and the in a while loop we call the constraints and add constraints to our list if some cell got fixed:

con_counter = 0
# while we haven't called every constraint
while length(constraint_idxs_dict) > 0
    con_counter += 1
    constraint = com.constraints[constraint_idxs[con_counter]]
    delete!(constraint_idxs_dict, constraint.idx)

    constraint_output = constraint.fct(com, constraint.indices; logs = false)
    push!(constraint_outputs, constraint_output)
    push!(constraints, constraint)
    if !constraint_output.feasible
        feasible = false
        break
    end

    # if we fixed another value => add the corresponding constraint to the list
    # iff the constraint will not be called anyway in the list 
    for ind in keys(constraint_output.idx_changed)
        for constraint in com.constraints[com.subscription[ind]]
            if !haskey(constraint_idxs_dict, constraint.idx)
                constraint_idxs_dict[constraint.idx] = true
                push!(constraint_idxs, constraint.idx)
            end
        end
    end
end

Now you might say that looks awful why is that so much code and it seems like we did that already. You know what, you’re damn right.
Therefore the code gets it’s own function prune!(com, constraints, constraint_outputs) and returns feasible, constraints, constraint_outputs and it will also be called in our main solve function directly after calling every constraint function ones.

Additionally I found that we always backtrack from left to right and then pruning isn’t working that well in Sudoku because all the surrounding cells are already fixed.

Therefore…

How my Julia coding style changed

By: Tamás K. Papp

Re-posted from: https://tamaspapp.eu/post/2019-09-07-coding_style_retrospective/

The recent redesign of DynamicHMC.jl provides an opportunity to reflect on how my Julia coding style changed. I started this package two years ago, and did not do any major refactoring after it became usable, mostly because I did not have a good comprehensive test suite or a solid conceptual understanding of all the ramifications of the algorithm, especially the adaptation, and I was afraid of breaking something that I just got working. Consequently, the code before the redesign largely reflected the coding style I developed for Julia 0.5 and then partly 0.6.

I am one of those people who recognize the benefits of reflecting on the past from time to time, but are too busy lazy to keep a diary. But code under version control is effectively a diary about the life of software, and I find it interesting to think about how my Julia coding style has changed in the past to years.

It is important to emphasize that this writeup reflects how I code at the moment. I recognize that other coding styles in Julia can be perfectly legitimate, and when I contribute to packages, I do my best to follow existing style. Also, it is very likely that my own coding style will change as the language evolves. In this blog post, I won’t address details of coding style about which there is a more or less general agreement — see the Style Guide in the manual and YASGuide for useful summaries. Finally, some examples are stylized adaptations of real code for simpler exposition.

Randomness

Random numbers are very important for scientific computing, but at the same time present an important challenge for writing bug-free parallel code and unit testing. A lot of code in Random and Base follows the interface conventions

rand([rng], ...)

making the random number generator an optional first argument, and defaulting to the global one.

While this can be convenient for user code, in packages I find that it is better to keep the random number generator as an explicit argument to almost all methods. This paves the way for making the code work nicely with composable multi-threading too.

If random and deterministic parts of the algorithm can be separated, it should be done, as it usually makes the code cleaner, and unit testing much easier. An example of this is factoring out the random directions for tree doubling in NUTS: drawing a single set of bit flags once and providing this to the tree building algorithm, the latter can treat the doubling directions as predetermined. This also made it much easier to verify detailed balance in the unit tests.

Named tuples

Named tuples are extremely useful for organizing multiple values as inputs and outputs when a composite type (struct) is not warranted or needed. If a function returns multiple values, especially more than two, I now always default to using named tuples, ie

function f(x, y)
    a = ...
    b = ...
    c = ...
    (a = a, b = b, c = c)
end

then use @unpack from Parameters.jl for destructuring:

@unpack a, b = f(x, y) # I don't need c here

This is costless and makes the interfaces more flexible: for example, I can add extra fields, or eventually make the returned value a composite type later, without changing anything in the callers.

Multi-liners as opposed to one-liners

Almost all the “clever” one liners are now expunged from the code. Compare

EBFMI(x) = (πs = map(x -> x.π, x); mean(abs2, diff(πs)) / var(πs))

with

function EBFMI(tree_statistics)
    πs = map(x -> x.π, tree_statistics)
    mean(abs2, diff(πs)) / var(πs)
end

The first one is kind of crammed, and difficult to read, while the second one makes it clear that an interim value is obtained for the calculation.

When a function returns multiple values, I find it nice to assign each to a variable first, ie

function f(x, y)
    a = g(x, y)
    b = h(x, y)
    a, b
end

as opposed to

f(x, y) = g(x, y), h(x, y)

This makes the returned structure much more readable when I need to look at some code later.

That said, I still have a strong preference for writing small functions that “do one thing”. This again is frequently an optimal strategy for Julia, as the compiler is very good about inlining decisions (and when not, can be nudged with @inline).

Abstract types can be an implementation detail

Abstract types can be very useful for organizing method dispatch: code like

abstract type SomeAbstractType end

f(x::SomeAbstractType) = do_something()

struct ThatSubType{T} <: SomeAbstractType
    y::T
end

g(x::ThatSubType) = do_something_else(x.y)

can help avoid repetition.

But abstract types are just one convenient tool for this, and building a type tree is a tool, not an end in itself. When they are no longer adequate, other solutions such as traits should be used instead.

Consequently, these days I mostly consider type hierarchies an implementation detail and I am wary of exposing them in the API of a package. This is especially important if some functionality requires that the user of a package implements their own custom types, e.g. for a model. Requiring that

UserDefinedModel <: SomePackage.ModelType

to work with some API is usually unnecessary, and can cause unnecessary complications when the user would want UserDefinedModel to implement some other API. Either duck typing, or an explicit interface check like

implements_model(::Any) = false
implements_model(::Type{<:UserDefinedModel}) = true

can work better (returning types when that is necessary, eg for further dispatch — see Base.IteratorSize for an example).

Small type unions

The ability of the compiler create efficient code for small type unions made code organization much easier for me. For example, DynamicHMC.adjacent_tree attempts to build a tree next to some position, but this can fail because of divergence or turning in the leapfrog integrator, in which case it is useful to bail out early and return information about the reason. Consequently, this function either returns a tree, or an InvalidTree, which is a container with the aforementioned diagnostic information. The compiler recognizes this and generates fast code.

Some attention should be paid to avoid combinatoric type explosions, but when used well, small type unions can make code much simpler at little or no extra cost.

Functional is often the best solution

Preallocating containers for outputs can make code faster, but at the cost of extra complexity, especially that of having to figure out type parameters for said containers.

My general strategy is to write code in a functional, side-effect-free style until I am really convinced that preallocation would help, and then confine it to carefully compartmentalized parts of the code. This is of course ideal only for some kinds of code — when allocations dominate, a functional style is not optimal.

That said, Julia’s compiler is getting more and more clever about optimizing allocations, so I frequently find that I never rewrite code with preallocated containers, and occasionally even revert from preallocated code to a functional style without a relevant performance cost.

When in doubt, document

Some readers of the code of DynamicHMC.jl will have the impression that it is overdocumented. Probably 20–25% of the lines in the source are docstrings, and most internal interfaces and convenience functions have one.

Primarily, this is driven by instances of the embarassing realization of having written some code two years ago which kind of works, but no longer being sure of all the details that would be nice to know before refactoring. But another consideration is encouraging contributions, or uses of the packages for research — besides being an implementation of the NUTS sampler, DynamicHMC.jl is also a platform for experimenting, which is easier to do when the internals are documented.

Julia’s documentation ecosystem is now very mature and robust. Besides the excellent Documenter.jl, I also find DocStringExtensions.jl very useful.

Internal interfaces have high return on investment

Many packages, especially those that are work in progress or experimental, do not document their user interfaces very carefully. This is of course understandable, but I have developed a preference for abstracting out and documenting interfaces in internally used code, too, as the package matures.

This makes refactoring and compartmentalization much easier, and makes sense even if a particular interface has only a single implementation in the package, because unit tests can just provide a “dummy” implementation and test related code that way. An example of this is the code for “trees” and the related tests: trees here are an abstraction for walking integer positions in two directions. This is key for the NUTS algorithm, but can be handled as an abstraction separate from the details of leapfrog integrators.

Julia夏季会议@Beijing – 本地化奖

By: JuliaLang - The Julia programming language

Re-posted from: https://julialang.org/blog/2019/09/julia-workshop-beijing-zh_cn/

JuliaCN在8月24日,中国北京举办了自2016以来第五次Julia会议。我们非常感谢Julia社区对本次活动的支持, 以及彩云科技, 微软中国, 集智俱乐部, 机器之心对本次活动的大力支持。本次活动有100余人注册,实到50余人。 线上直播在线人数达1600余人。

Read more