I'm trying to make a function f such that
f(1) == ((1,),)
f(2) == ((1,), (2,), (1,2))
f(3) == ((1,), (2,), (3,), (1,2), (1,3), (2,3), (1,2,3))
f(4) == ((1,), (2,), (3,), (4,), (1,2), (1,3), (1,4), (2,3), (2,4), (3,4), (1,2,3), (1,2,4), (1,3,4), (2,3,4), (1,2,3,4))
and so on. Anyone have any clever ideas on how to generate this programmatically? I'm sure there's some fancy name for this operation but I'm not sure what it is.
The combinatorics package has this:
using Combinatorics
combinations(1:n) # iterator of all combinations
For example
julia> collect(combinations(1:3))
7-element Array{Array{Int64,1},1}:
[1]
[2]
[3]
[1, 2]
[1, 3]
[2, 3]
[1, 2, 3]
Note that combinations is an iterator, you can use it in a for loop
for c in combinations(1:n)
...
end
without creating all combinations in memory at once (you only create them if you collect the iterator). combinations returns a Vector instead of a tuple so that the type of c does not change from iteration to iteration.
There is some additional information at https://discourse.julialang.org/t/generate-all-subsets-of-a-set/12810/10.
Two answers which were suggested to me on the julialang slack:
using Combinatorics
f(n) = unique(sort.(vcat([collect(permutations(1:n, i)) for i in 1:n]...)))
jointuple(x,y) = (x...,y...)
function f(x)
if x == 0
[]
elseif x == 1
[(1,);]
else
a = f(x-1)
vcat(a,(x,),map(z->jointuple(z,x),a))
end
end
Related
I want to loop over a list of variables nad output the variable name and value. E.g., say I have x=1 and y=2, then I want an output
x is 1
y is 2
I suspect I need to use Symbols for this. Here is my approach, but it isn't working:
function t(x,y)
for i in [x,y]
println("$(Symbol(i)) is $(eval(i))") # outputs "1 is 1" and "2 is 2"
end
end
t(1, 2)
Is there a way to achieve this? I guess a Dictionary would work, but would be interested to see if Symbols can also be used here.
One option is to use a NamedTuple:
julia> x = 1; y = 2
2
julia> vals = (; x, y)
(x = 1, y = 2)
julia> for (n, v) ∈ pairs(vals)
println("$n is $v")
end
x is 1
y is 2
Note the semicolon in (; x, y), which turns the x and y into kwargs so that the whole expression becomes shorthand for (x = x, y = y).
I will also add that your question looks like like you are trying to dynamically work with variable names in global scope, which is generally discouraged and an indication that you probably should be considering a datastructure that holds values alongside labels, such as the dictionary proposed in the other answer or a NamedTuple. You can google around if you want to read more on this, here's a related SO question:
Is it a good idea to dynamically create variables?
You can do this by passing the variable names:
x = 1
y = 2
function t(a, b)
for i in [a, b]
println("$(i) is $(eval(i))")
end
end
t(:x, :y)
x is 1
y is 2
At the start of the function, there's no record of the "x"-ness of x, or the "y"-ness of y. The function only sees 1 and 2. It's a bit confusing that you also called your two local variables x and y, I renamed them to show what's happening more clearly.
A solution with dictionaries would be nicer:
dict = Dict()
dict[:x] = 1
dict[:y] = 2
function t(d)
for k in keys(d)
println("$(k) is $(d[k])")
end
end
t(dict)
y is 2
x is 1
If you rather want to see programmatically what variables are present you could use varinfo or names:
julia> x=5; y=7;
julia> varinfo()
name size summary
–––––––––––––––– ––––––––––– –––––––
Base Module
Core Module
InteractiveUtils 316.128 KiB Module
Main Module
ans 8 bytes Int64
x 8 bytes Int64
y 8 bytes Int64
julia> names(Main)
7-element Vector{Symbol}:
:Base
:Core
:InteractiveUtils
:Main
:ans
:x
With any given name it's value can be obtained via getfield:
julia> getfield(Main, :x)
5
If you are rather inside a function than use #locals macro:
julia> function f(a)
b=5
c=8
#show Base.#locals
end;
julia> f(1)
#= REPL[13]:4 =# Base.#locals() = Dict{Symbol, Any}(:a => 1, :b => 5, :c => 8)
Dict{Symbol, Any} with 3 entries:
:a => 1
:b => 5
:c => 8
Suppose we have
A = [1 2; 3 4]
In numpy, the following syntax will produce
A[[1,2],[1,2]] = [1,4]
But, in julia, the following produce a permutation which output
A[[1,2],[1,2]] = [1 2; 3 4]
Is there a concise way to achieve the same thing as numpy without using for loops?
To get what you want I would use CartesianIndex like this:
julia> A[CartesianIndex.([(1,1), (2,2)])]
2-element Vector{Int64}:
1
4
or
julia> A[[CartesianIndex(1,1), CartesianIndex(2,2)]]
2-element Vector{Int64}:
1
4
Like Bogumil said, you probably want to use CartesianIndex. But if you want to get your result from supplying the vectors of indices for each dimensions, as in your Python [1,2],[1,2] example, you need to zip these indices first:
julia> A[CartesianIndex.(zip([1,2], [1,2]))]
2-element Vector{Int64}:
1
4
How does this work? zip traverses both vectors of indices at the same time (like a zipper) and returns an iterator over the tuples of indices:
julia> zip([1,2],[1,2]) # is a lazy iterator
zip([1, 2], [1, 2])
julia> collect(zip([1,2],[1,2])) # collect to show all the tuples
2-element Vector{Tuple{Int64, Int64}}:
(1, 1)
(2, 2)
and then CartesianIndex turns them into cartesian indices, which can then be used to get the corresponding values in A:
julia> CartesianIndex.(zip([1,2],[1,2]))
2-element Vector{CartesianIndex{2}}:
CartesianIndex(1, 1)
CartesianIndex(2, 2)
I'm trying to perform set operations between a given set y and all items in some array of sets X as follows:
X=Array{Set}([Set([1,2,1]), Set([4,6,8 ]), Set([4,5])])
y=Set{Int16}([2,8,4])
z=broadcast(intersect, y, X)
println(z)
Which gives me empty sets, instead of sets with the singletons in y, for my example.
You have to protect y from being iterated over. Normally you would get an error but unfortunately y has three elements as well as vector X. Let us create a bigger vector then so see the problem:
julia> X=Array{Set}([Set([1,2,1]), Set([4,6,8 ]), Set([4,5]), Set([7])])
4-element Array{Set,1}:
Set([2, 1])
Set([4, 8, 6])
Set([4, 5])
Set([7])
julia> y=Set{Int16}([2,8,4])
Set{Int16} with 3 elements:
4
2
8
julia> z=broadcast(intersect, y, X)
ERROR: DimensionMismatch("arrays could not be broadcast to a common size; got a dimension with lengths 3 and 4")
How to solve it - wrap y in a 0-dimensional container with Ref(y) like this:
julia> z=broadcast(intersect, Ref(y), X)
4-element Array{Set{Int16},1}:
Set([2])
Set([4, 8])
Set([4])
Set()
or equivalently just write:
julia> z=intersect.(Ref(y), X)
4-element Array{Set{Int16},1}:
Set([2])
Set([4, 8])
Set([4])
Set()
I have a two-element vector whose elements can only be 0 or 1. For the sake of this example, suppose x = [0, 1]. Suppose also there are four objects y00, y01, y10, y11. My goal is to update the corresponding y (y01 in this example) according to the current value of x.
I am aware I can do this using a series of if statements:
if x == [0, 0]
y00 += 1
elseif x == [0, 1]
y01 += 1
elseif x == [1, 0]
y10 += 1
elseif x == [1, 1]
y11 += 1
end
However, I understand this can be done more succinctly using Julia's metaprogramming, although I'm unfamiliar with its usage and can't figure out how.
I want to be able to express something like y{x[1]}{x[2]} += 1 (which is obviously wrong); basically, be able to refer and modify the correct y according to the current value of x.
So far, I've been able to call the actual value of the correct y (but I can't summon the y object itself) with something like
eval(Symbol(string("y", x[1], x[2])))
I'm sorry if I did not use the appropriate lingo, but I hope I made myself clear.
There's a much more elegant way using StaticArrays. You can define a common type for your y values, which will behave like a matrix (which I assume the ys represent?), and defines a lot of things for you:
julia> mutable struct Thing2 <: FieldMatrix{2, 2, Float64}
y00::Float64
y01::Float64
y10::Float64
y11::Float64
end
julia> M = rand(Thing2)
2×2 Thing2 with indices SOneTo(2)×SOneTo(2):
0.695919 0.624941
0.404213 0.0317816
julia> M.y00 += 1
1.6959194941562996
julia> M[1, 2] += 1
1.6249412302897646
julia> M * [2, 3]
2-element SArray{Tuple{2},Float64,1,2} with indices SOneTo(2):
10.266662679181893
0.9037708026795666
(Side note: Julia indices begin at 1, so it might be more idiomatic to use one-based indices for y as well. Alternatively, can create array types with custom indexing, but that's more work, again.)
How about using x as linear indices into an array Y?
x = reshape(1:4, 2, 2)
Y = zeros(4);
Y[ x[1,2] ] += 1
Any time you find yourself naming variables with sequential numbers it's a HUGE RED FLAG that you should just use an array instead. No need to make it so complicated with a custom static array or linear indexing — you can just make y a plain old 2x2 array. The straight-forward transformation is:
y = zeros(2,2)
if x == [0, 0]
y[1,1] += 1
elseif x == [0, 1]
y[1,2] += 1
elseif x == [1, 0]
y[2,1] += 1
elseif x == [1, 1]
y[2,2] += 1
end
Now you can start seeing a pattern here and simplify this by using x as an index directly into y:
y[(x .+ 1)...] += 1
I'm doing two things there: I'm adding one to all the elements of x and then I'm splatting those elements into the indexing expression so they're treated as a two-dimensional lookup. From here, you could make this more Julian by just using one-based indices from the get-go and potentially making x a Tuple or CartesianIndex for improved performance.
I am trying to construct all possible combinations of four vectors (parameters in a model) that would give me a big nx4 matrix and I could then run simulation on each set (row) of parameters. In R I would achieve this by using expand.grid in Mathematica style, I could use something like outer product with vcat and reduce the output using hcat.
Is there some function analog of expand.grid from R or outer map function?
Toy example:
A = [1 2]
B = [3 4]
some magic
output = [1 3, 1 4, 2 3, 2 4]
Using the Iterators package, it might look like this:
using Iterators
for p in product([1,2], [3,4])
println(p)
end
where you would replace println with your algorithm. You can also use collect if it's important to get the set of all combinations.
Not the exact notation you show, but a comprehension might be useful.
julia> a=[1, 2];
julia> b=[3, 4];
julia> [[i, j] for j in b, i in a]
2x2 Array{Any,2}:
[1,3] [2,3]
[1,4] [2,4]
julia> [[i, j] for j in b, i in a][:]
4-element Array{Any,1}:
[1,3]
[1,4]
[2,3]
[2,4]