Create a sparse symmetric random matrix in Julia - julia

Question

is there an easy way to create a sparse symmetric random matrix in Julia?
Julia has the command
sprand(m,n,d)
which "Creates a [sparse] m-by-n random matrix (of density d) with iid non-zero elements distributed uniformly on the half-open interval [0,1)[0,1)." But as far as I can tell this doesn't necessarily return a symmetric matrix.
I am looking for an equivalent command to MATLAB's
R = sprandsym(n,density)
which automatically creates a sparse symmetric random matrix. If such a command isn't implemented yet, what would be a workaround to transform the matrix returned by sprand(m,n,d) into a symmetric one?
Thank you!

Answer 1

You could Symmetric(sprand(10,10,0.4))

Answer 2

To avoid extra memory caveat mentioned in the comment to Michael Borregaard's answer, the following function takes a sparse matrix and drops the entries in the lower triangular part. If the SparseMatrixCSC format is unfamiliar, it also serves as a good presentation of how the format is manipulated:
function droplower(A::SparseMatrixCSC)
m,n = size(A)
rows = rowvals(A)
vals = nonzeros(A)
V = Vector{eltype(A)}()
I = Vector{Int}()
J = Vector{Int}()
for i=1:n
for j in nzrange(A,i)
rows[j]>i && break
push!(I,rows[j])
push!(J,i)
push!(V,vals[j])
end
end
return sparse(I,J,V,m,n)
end
Example usage:
julia> a = [0.5 1.0 0.0 ; 2.0 0.0 0.0 ; 0.0 0.0 0.0]
3×3 Array{Float64,2}:
0.5 1.0 0.0
2.0 0.0 0.0
0.0 0.0 0.0
julia> b = sparse(a)
3×3 SparseMatrixCSC{Float64,Int64} with 3 stored entries:
[1, 1] = 0.5
[2, 1] = 2.0
[1, 2] = 1.0
julia> c = droplower(b)
3×3 SparseMatrixCSC{Float64,Int64} with 2 stored entries:
[1, 1] = 0.5
[1, 2] = 1.0
julia> full(Symmetric(c)) # note this is symmetric although c isn't
3×3 Array{Float64,2}:
0.5 1.0 0.0
1.0 0.0 0.0
0.0 0.0 0.0

Answer 3

Operations on the SparseMatrixCSC often need to be customized for maximum efficiency. So, to get from a sparse matrix A to a symmetric sparse matrix with the same upper part, here is a custom version (it is a bit cryptic, but working):
function symmetrize(A::SparseMatrixCSC)
m,n = size(A)
m == n || error("argument expected to be square matrix")
rows = rowvals(A) ; vals = nonzeros(A)
a = zeros(Int,n) ; b = zeros(Int,n) ; c = 0
for i=1:n
for j in nzrange(A, i)
if rows[j]>=i
if rows[j]==i a[i] += 1 ; c += 1 ; end
break
end
a[i] += 1 ; b[rows[j]] += 1 ; c += 2
end
end
c == 0 && return SparseMatrixCSC(n, n, ones(n+1), nrows, nvals)
ncolptr = Vector{Int}(n+1)
nrows = Vector{Int}(c) ; nvals = Vector{eltype(A)}(c)
idx = 1
for i=1:n
ncolptr[i] = idx
if a[i]==0 a[i] = idx ; idx += b[i] ; continue ; end
for j in (0:a[i]-1)+first(nzrange(A, i))
nvals[idx] = vals[j] ; nrows[idx] = rows[j] ; idx += 1
rows[j] >= i && break
nvals[a[rows[j]]] = vals[j] ; nrows[a[rows[j]]] = i
a[rows[j]] += 1
end
a[i] = idx ; idx += b[i]
end
ncolptr[n+1] = idx
return SparseMatrixCSC(n, n, ncolptr, nrows, nvals)
end
And a sample run:
julia> f = sprand(5,5,0.2)
5×5 SparseMatrixCSC{Float64,Int64} with 5 stored entries:
[1, 1] = 0.981579
[3, 1] = 0.330961
[5, 1] = 0.527683
[4, 5] = 0.196898
[5, 5] = 0.579006
julia> full(f)
5×5 Array{Float64,2}:
0.981579 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
0.330961 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.196898
0.527683 0.0 0.0 0.0 0.579006
julia> full(symmetrize(f))
5×5 Array{Float64,2}:
0.981579 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.0
0.0 0.0 0.0 0.0 0.196898
0.0 0.0 0.0 0.196898 0.579006
This version should be faster than others, but this still needs to be benchmarked (and some #inbounds added in the for loops).