TinySparse.jl

TinySparse.jl is a Julia package for further compressing sparse matrices. Operations on TinySparseMat's are deferred until the matrix operates on a vector (see LinearMaps.jl).

Requirements

• Julia 0.5 and up
• GCC installed (Linux or macOS)
• Windows is unsupported at this time.

Instalation

julia> Pkg.add("TinySparse")
julia> Pkg.test("TinySparse")

What is TinySparse.jl?

TinySparse.jl compresses sparse matrices. Indexes are compressed using TinyInt.jl and only unique non-zero entries are stored.

Consider a gradient operator.

using TinySparse
nx, ny, nz = (100, 100, 100)
h = 0.5
G1 = spdiagm((fill(1.0, nx), fill(-1.0, nx)), (0, -1), nx+1, nx)
G2 = spdiagm((fill(1.0, ny), fill(-1.0, ny)), (0, -1), ny+1, ny)
G3 = spdiagm((fill(1.0, nz), fill(-1.0, nz)), (0, -1), nz+1, nz)
Gx = (1/h)*kron(speye(nz), kron(speye(ny), G1))
Gy = (1/h)*kron(speye(nz), kron(G2, speye(nx)))
Gz = (1/h)*kron(G3, kron(speye(ny), speye(nx)))
gradientOp = vcat(Gx, Gy, Gz)
tinyGradOp = pack(gradientOp)
Base.summarysize(gradientOp)
# 104000048
Base.summarysize(tinyGradOp)
# 22079893

Multiplication speed is sligthly slower than Julia's default method.

@time A_mul_B!(out, gradientOp, x)
# 0.014913 seconds (4 allocations: 160 bytes)
@time A_mul_B!(out, tinyGradOp, x)
# 0.018533 seconds (4 allocations: 160 bytes)

These times are from a quad-core Intel® Core™ i7-4790 CPU @ 3.60GHz

Functions

Function	Description
pack(x)	Compresses sparse matrix.
+, *, A_mul_B!...	All operations supported in LinearMaps.jl works here.

Notes

• The compressed sparse matrix is immutable. Once a compressed sparse matrix has been made, it's elements cannot be changed.
• Speed decreases as more unique values are present. Currently, only two or so unique values are competetive with Julia's ordinary sparse matrix vector multiplication. This is likely to change in the future (see next section).

To Do

• Implement CSC format. Currently COO sparse matrix format is implemented. If we change this to CSC, we can reduce the amount of memory calls to near the ordinary level of memory calls. This should speed up sparse matrix vector multiplication. It may even produce faster multiplication due to cache-locality of the unique non-zero elements.
• Implement SIMD operations. Through some testing, I've noticed gathering multiplication inputs into some linear buffer, performing SIMD operations on them, then scattering the results into the output vector offers some speed improvements over just serially accessesing the irregular memory pattern of the vectors. It would be nice to implement this.