# Creating a sparse matrix from find operation on dense matrix

I have a large matrix `x`. I’d like to create a sparse representation of the values that meet a certain criteria, e.g. `xi < 1`.

I’d like to do something like the following:

``````x = rand(1000, 1000)
i = findall(xi -> xi < 0.01, x)
xs = sparse(x, i)
``````

I wasn’t able to find a sparse constructor that used `CartesianIndices`. What is the recommended way to do this? Ideally without copying values from x (though I’m not sure this would be faster).

This should work:

``````sparse(x .* (x .< 0.01))
``````

Otherwise, if you want to go through the indices, then you could so something like

``````CI = findall(<(0.01), x)
using Unzip # not sure it's needed but I find it convenient
i, j = unzip(Tuple.(CI))
xs = sparse(i, j, x[CI], size(x)...)
``````

Thanks for the lightning response and the slick one-liner!

Here’s a quick comparison of the hack I have been working with, your two approaches, and one i found here.

``````using BenchmarkTools, SparseArrays, Unzip
x = rand(1000,1000)
d = 0.01

@btime begin
m = x .< d
i,j, = findnz(m)
xs = sparse(i ,j, view(x, m), size(x)...)
end
# 1.489 ms (38 allocations: 851.00 KiB)

@btime xs = sparse(x .* (x .< d))
# 2.482 ms (12 allocations: 7.79 MiB)

@btime begin
CI = findall(x .< d)
i, j = unzip(Tuple.(CI))
xs = sparse(i, j, view(x, CI), size(x)...)
end
# 1.190 ms (45 allocations: 927.47 KiB)

@btime begin
CI = findall(x .< d)
CI′ = reinterpret(Int, reshape(CI, 1, :))
xs = sparse(view(CI′, 1, :), view(CI′, 2, :), view(x, CI), size(x)...)
end
#  1.044 ms (40 allocations: 617.20 KiB)
``````

I did not make any promises on performance! FWIW, I reckon doing `findall(x .< d)` is actually better than `findall(<(d), x)`. Maybe try to compare with this?

``````CI = findall(x .< d)
i, j = unzip(Tuple.(CI))
sparse(i, j, view(x,CI), size(x)...)
``````

But I should let the performance pros chime in!

You’re right. Updated the above per your suggestions