How to get indexes of unique elements of a vector?
For instance if you have a vector v = [1,2,1,3,5,3], the unique elements are [1,2,3,5] (output of unique) and their indexes are ind = [1,2,4,5]. What function allows me to compute ind so that v[ind] = unique(v) ?
This is a solution for Julia 0.7:
findfirst.(isequal.(unique(x)), [x])
or similar working under Julia 0.6.3 and Julia 0.7:
findfirst.(map(a -> (y -> isequal(a, y)), unique(x)), [x])
and a shorter version (but it will not work under Julia 0.7):
findfirst.([x], unique(x))
It will probably not be the fastest.
If you need speed you can write something like (should work both under Julia 0.7 and 0.6.3):
function uniqueidx(x::AbstractArray{T}) where T
uniqueset = Set{T}()
ex = eachindex(x)
idxs = Vector{eltype(ex)}()
for i in ex
xi = x[i]
if !(xi in uniqueset)
push!(idxs, i)
push!(uniqueset, xi)
end
end
idxs
end
Another suggestion is
unique(i -> x[i], 1:length(x))
which is about as fast as the function in the accepted answer (in Julia 1.1), but a bit briefer.
If you don't care about finding the first index for each unique element, then you can use a combination of the unique and indexin functions:
julia> indexin(unique(v), v)
4-element Array{Int64,1}:
3
2
6
5
Which gets one index for each unique element of v in v. These are all in base and works in 0.6. This is about 2.5 times slower than #Bogumil's function, but it's a simple alternative.
A mix between mattswon and Bogumił Kamiński answers (thanks !):
uniqueidx(v) = unique(i -> v[i], eachindex(v))
eachindex allows to work with any kind of array, even views.
julia> v = [1,2,1,3,5,3];
julia> uniqueidx(v)
4-element Vector{Int64}:
1
2
4
5
julia> v2 = reshape(v, 2, 3)
2×3 Matrix{Int64}:
1 1 5
2 3 3
julia> subv2 = view(v2, 1:2, 1:2)
2×2 view(::Matrix{Int64}, 1:2, 1:2) with eltype Int64:
1 1
2 3
julia> uniqueidx(subv2)
3-element Vector{CartesianIndex{2}}:
CartesianIndex(1, 1)
CartesianIndex(2, 1)
CartesianIndex(2, 2)
Related
How can I convert a Set to an Array in Julia?
E.g. I want to transform the following Set to an Array.
x = Set([1,2,3])
x
Set{Int64} with 3 elements:
2
3
1
The collect() function can be used for this. E.g.
collect(x)
3-element Vector{Int64}:
2
3
1
Notice, however, that the order of the elements has changed. This is because sets are unordered.
You can also use the splat operator on sets:
julia> [x...]
3-element Vector{Int64}:
2
3
1
However, this is slower than collect.
You can use [ ] to create an array.
x = Set([1,2,3])
y = [a for a in x]
y
2
3
1
typeof(y)
Vector{Int64} (alias for Array{Int64, 1})
You can use a comprehension:
x = Set(1:5)
#time y = [i for i in x]
> 0.000006 seconds (2 allocations: 112 bytes)
typeof(y)
> Vector{Int64} (alias for Array{Int64, 1})
I am having trouble filtering a simple array-based on two conditions. For example, to filter out values between 3 and 5, I tried the following but I get an ERROR: TypeError: non-boolean (BitArray{1}) used in boolean context error.
arr = Array{Int64}([1,2,3,4,5,6])
arr[(arr .> 3) && (arr.< 5)]
Any idea how to solve it?
Also on a side note, I am wondering if there is a function opposite to isless. Something to find a value greater than a certain value.
Here are two ways to do it:
julia> arr = [1,2,3,4,5,6]
6-element Array{Int64,1}:
1
2
3
4
5
6
julia> arr[(arr .> 3) .& (arr.< 5)]
1-element Array{Int64,1}:
4
julia> filter(v -> 3 < v < 5, arr)
1-element Array{Int64,1}:
4
(I personally prefer filter).
To get the opposite of isless just reverse its arguments, or if needed define a new function:
isgreater(x, y) = isless(y, x)
I prefer a set comparison approach because it's quite intuitive:
julia> arr = Array{Int64}([1,2,3,4,5,6])
julia> intersect( arr[ arr .> 1 ], arr[ arr .< 4 ] )
2-element Array{Int64,1}:
2
3
Or list comprehension:
[ x for x in arr if 3 < x < 5]
# or
[ x for x in arr if 3 < x && x < 5]
Also to define an array literal with specific type Int64, there is a dedicated syntax to make it simpler:
arr = Int64[1,2,3,4,5,6]
I am trying to use a transpose operator over a vector in order to perform am element-wise addition.
For example, I want to add a column vector a = [a1;a2;a3] to a row vector b = [b1,b2] I should get matrix
M = a+b = [a1+b1, a1+b2; a2+b1, a2+b2; a3+b1, a3+b2].
In MATLAB it is equivalent (if both vectors are row vectors) M = a.'+b
I am trying to get the same in Julia but here is the problem, there is no .' operator in Julia starting from 1.0 version. There is the transpose operator which does not work in broadcasting mode. The adjoint operator is not Valid for me because I work with complex numbers.
a = Vector{ComplexF64}([1+3im,2])
b = Vector{ComplexF64}([0,0,0])
Z = zeros(ComplexF64,3,2)
G = zeros(ComplexF64,3,2)
#. Z = b + a' # Works but takes the complex conjugate
#. Z = b + transpose(a) # DOES NOT WORK!!!! The error is " DimensionMismatch("array could not be broadcast to match destination") "
Z = b .+ transpose(a) # Works but not efficient
#. Z = b + conj(a')
The third case Z = b .+ transpose(a) is not efficient because it makes 2 loops first one for addition b .+ transpose(a), than it runs the second loop one for the assignment of b .+ transpose(a) to Z. While the other 3 cases do it within one loop.
So which is the fastest way?
And why transpose doesn't within Broadcasting?
Thank you in advance
For Hermitian You can just type:
a' .+ b
Example
julia> a = ComplexF64.([1+3im,2])
2-element Array{Complex{Float64},1}:
1.0 + 3.0im
2.0 + 0.0im
julia> b = ComplexF64.([10,20,30])
3-element Array{Complex{Float64},1}:
10.0 + 0.0im
20.0 + 0.0im
30.0 + 0.0im
julia> a' .+ b
3×2 Array{Complex{Float64},2}:
11.0-3.0im 12.0+0.0im
21.0-3.0im 22.0+0.0im
31.0-3.0im 32.0+0.0im
If you want to have just transposition you could define your own unary operator (perhaps from the list of unused unary operators):
¬(a) = permutedims(a)
Now you could do
julia> ¬a
1×2 Matrix{ComplexF64}:
1.0+3.0im 2.0+0.0im
How do you do simply select a subset of an array based on a condition? I know Julia doesn't use vectorization, but there must be a simple way of doing the following without an ugly looking multi-line for loop
julia> map([1,2,3,4]) do x
return (x%2==0)?x:nothing
end
4-element Array{Any,1}:
nothing
2
nothing
4
Desired output:
[2, 4]
Observed output:
[nothing, 2, nothing, 4]
You are looking for filter
http://docs.julialang.org/en/release-0.4/stdlib/collections/#Base.filter
Here is example an
filter(x->x%2==0,[1,2,3,5]) #anwers with [2]
There are element-wise operators (beginning with a "."):
julia> [1,2,3,4] % 2 .== 0
4-element BitArray{1}:
false
true
false
true
julia> x = [1,2,3,4]
4-element Array{Int64,1}:
1
2
3
4
julia> x % 2 .== 0
4-element BitArray{1}:
false
true
false
true
julia> x[x % 2 .== 0]
2-element Array{Int64,1}:
2
4
julia> x .% 2
4-element Array{Int64,1}:
1
0
1
0
You can use the find() function (or the .== syntax) to accomplish this. E.g.:
julia> x = collect(1:4)
4-element Array{Int64,1}:
1
2
3
4
julia> y = x[find(x%2.==0)]
2-element Array{Int64,1}:
2
4
julia> y = x[x%2.==0] ## more concise and slightly quicker
2-element Array{Int64,1}:
2
4
Note the .== syntax for the element-wise operation. Also, note that find() returns the indices that match the criteria. In this case, the indices matching the criteria are the same as the array elements that match the criteria. For the more general case though, we want to put the find() function in brackets to denote that we are using it to select indices from the original array x.
Update: Good point #Lutfullah Tomak about the filter() function. I believe though that find() can be quicker and more memory efficient. (though I understand that anonymous functions are supposed to get better in version 0.5 so perhaps this might change?) At least in my trial, I got:
x = collect(1:100000000);
#time y1 = filter(x->x%2==0,x);
# 9.526485 seconds (100.00 M allocations: 1.554 GB, 2.76% gc time)
#time y2 = x[find(x%2.==0)];
# 3.187476 seconds (48.85 k allocations: 1.504 GB, 4.89% gc time)
#time y3 = x[x%2.==0];
# 2.570451 seconds (57.98 k allocations: 1.131 GB, 4.17% gc time)
Update2: Good points in comments to this post that x[x%2.==0] is faster than x[find(x%2.==0)].
Another updated version:
v[v .% 2 .== 0]
Probably, for the newer versions of Julia, one needs to add broadcasting dot before both % and ==
Does Julia have a build in command to find the index of the minimum of a vector? R, for example, has a which.min command (and a which.max, of course).
Obviously, I could write the following myself, but it would be nice not to have to.
function whichmin( x::Vector )
i = 1
min_x=minimum(x)
while( x[i] > min_x )
i+=1
end
return i
end
Apologies if this has been asked before, but I couldn't find it. Thanks!
Since 0.7-alpha, indmin and indmax are deprecated.
Use argmin and argmax instead.
For a vector it just returns the linear index
julia> x = rand(1:9, 4)
4-element Array{Int64,1}:
9
5
8
5
julia> argmin(x)
2
julia> argmax(x)
1
If looking for both the index and the value, use findmin and findmax.
For multidimensional array, all these functions return the CartesianIndex.
I believe indmax(itr) does what you want. From the julia documentation:
indmax(itr) → Integer
Returns the index of the maximum element in a collection.
And here's an example of it in use:
julia> x = [8, -4, 3.5]
julia> indmax(x)
1
There's also findmax, that returns both the maximum value and its position.
For multidim array, you'll have to switch between linear indexes et multidim indexes:
x = rand(1:9, 2,3)
# 2×3 Array{Int64,2}:
# 5 1 9
# 3 3 8
indmin(x)
# 3
# => third element in the column-major ordered array (value=1)
ind2sub(size(x),indmin(x))
# (1, 2)
# => (row,col) indexes: what you are looking for.
-- Maurice