Bad results in sparse matrix assignment with logical indexing - julia

Question

In Matlab/Octave, I can use logical indexing to assign a value to matrix B in every location that meets a certain requirement in matrix A.
octave:1> A = [.1;.2;.3;.4;.11;.13;.14;.01;.04;.09];
octave:2> C = A < .12
C =
1
0
0
0
1
0
0
1
1
1
octave:3> B = spalloc(10,1);
octave:4> B(C) = 1
B =
Compressed Column Sparse (rows = 10, cols = 1, nnz = 5 [50%])
(1, 1) -> 1
(5, 1) -> 1
(8, 1) -> 1
(9, 1) -> 1
(10, 1) -> 1
However, if I attempt essentially the same code in Julia, the results are incorrect:
julia> A = [.1;.2;.3;.4;.11;.13;.14;.01;.04;.09];
julia> B = spzeros(10,1)
10x1 sparse matrix with 0 Float64 entries:
julia> C = A .< .12
10-element BitArray{1}:
true
false
false
false
true
false
false
true
true
true
julia> B[C] = 1
1
julia> B
10x1 sparse matrix with 5 Float64 entries:
[0 , 1] = 1.0
[0 , 1] = 1.0
[1 , 1] = 1.0
[1 , 1] = 1.0
[1 , 1] = 1.0
Have I made a mistake in the syntax somewhere, am I misunderstanding something, or is this a bug? Note, I get the correct results if I use full matrices in Julia, but since the matrix in my application is really sparse (essential boundary conditions in a finite element simulation), I would much prefer to use the sparse matrices

Answer 1

It looks as if sparse has some problems with BitArray's.
julia> VERSION
v"0.3.5"
julia> A = [.1;.2;.3;.4;.11;.13;.14;.01;.04;.09]
julia> B = spzeros(10,1)
julia> C = A .< .12
julia> B[C] = 1
julia> B
10x1 sparse matrix with 5 Float64 entries:
[0 , 1] = 1.0
[0 , 1] = 1.0
[1 , 1] = 1.0
[1 , 1] = 1.0
[1 , 1] = 1.0
So I get the same thing as the questioner. However when I do things "my way"
julia> B = sparse(C)
ERROR: `sparse` has no method matching sparse(::BitArray{1})
julia> B = sparse(float(C))
10x1 sparse matrix with 5 Float64 entries:
[1 , 1] = 1.0
[5 , 1] = 1.0
[8 , 1] = 1.0
[9 , 1] = 1.0
[10, 1] = 1.0
So this works if you convert the BitArray to Float. I imagine that this workaround will get you going, but it does seem that sparse should work with BitArray.
Some Additional Thoughts (Edit)
As I thought further about this, it occurs to me that one reason why there is no BitArray method for sparse() is that it is not terribly useful to implement sparse storage for an already highly compact type. Considering B and C from above:
julia> sizeof(C)
8
julia> sizeof(B)
40
So for these data, the sparse version is much larger than the original. It's actually worse than this simple (perhaps simplistic) check shows at first glance. sizeof(::BitArray{1}) appears to be the size of the entire array, but sizeof(::SparseMatrixCSC{}) shows the size of each element stored. So the real size disparity is something like 8 versus 200 bytes.
Of course if the data is sparse enough (somewhat less than 1% true), sparse storage begins to win out, despite it's high overhead.
julia> C = rand(10^6) .< 0.01
julia> B = sparse(float(C))
julia> sizeof(C)
125000
julia> sum(C)*sizeof(B)
394520
julia> C = rand(10^6) .< 0.001
julia> B = sparse(float(C))
julia> sizeof(C)
125000
julia> sum(C)*sizeof(B)
40280
So perhaps it is not an oversight that sparse() has no BitArray method. Cases where it would represent a significant space saving may be less common than one might think at first glance.