diff --git a/benchmarks/LinearSolve/MatrixDepot.jmd b/benchmarks/LinearSolve/MatrixDepot.jmd index f979359cc..9f8de473f 100644 --- a/benchmarks/LinearSolve/MatrixDepot.jmd +++ b/benchmarks/LinearSolve/MatrixDepot.jmd @@ -30,9 +30,35 @@ cols = [:red, :blue, :green, :magenta, :turqoise] # one color per alg allmatrices_md = listnames("*/*") @info "Total number of matrices: $(allmatrices_md.content[1].rows)" + times = fill(NaN, length(allmatrices_md.content[1].rows), length(algs)) percentage_sparsity = fill(NaN, length(allmatrices_md.content[1].rows)) +spaced_out_sparsity = fill(NaN, length(allmatrices_md.content[1].rows)) matrix_size = fill(NaN, length(allmatrices_md.content[1].rows)) +bandedness_five = fill(NaN, length(allmatrices_md.content[1].rows)) +bandedness_ten = fill(NaN, length(allmatrices_md.content[1].rows)) +bandedness_twenty = fill(NaN, length(allmatrices_md.content[1].rows)) + +function compute_bandedness(A, bandwidth) + n = size(A, 1) + total_band_positions = 0 + non_zero_in_band = 0 + bandwidth = bandwidth + for r in 1:n + for c in 1:n + if abs(r - c) <= bandwidth + total_band_positions += 1 # This position belongs to the band + if A[r, c] != 0 + non_zero_in_band += 1 # This element is non-zero in the band + end + end + end + end + + percentage_filled = non_zero_in_band / total_band_positions * 100 + return percentage_filled +end + ``` ```julia @@ -47,12 +73,34 @@ for z in 1:length(allmatrices_md.content[1].rows) A = mdopen(currMTX).A A = convert(SparseMatrixCSC, A) n = size(A, 1) - matrix_size[z] = n - percentage_sparsity[z] = length(nonzeros(A)) / n^2 - @info "$n × $n" - - n > 500 && error("Skipping too large matrices") + + mtx_copy = copy(A) + @info "$n × $n" + n > 100 && error("Skipping too large matrices") + + ## COMPUTING SPACED OUT SPARSITY + rows, cols = size(mtx_copy) + new_rows = div(rows, 2) + new_cols = div(cols, 2) + condensed = zeros(Int, new_rows, new_cols) + while size(mtx_copy, 1) > 32 || size(mtx_copy, 2) > 32 + + rows, cols = size(mtx_copy) + new_rows = div(rows, 2) + new_cols = div(cols, 2) + condensed = sparse(zeros(Int, new_rows, new_cols)) + + for r in 1:2:rows-1 + for c in 1:2:cols-1 + block = mtx_copy[r:min(r+1, rows), c:min(c+1, cols)] + condensed[div(r-1, 2) + 1, div(c-1, 2) + 1] = (length(nonzeros(block)) >= 2) ? 1 : 0 + end + end + mtx_copy = condensed + end + + ## COMPUTING FACTORIZATION TIME b = rand(rng, n) u0 = rand(rng, n) @@ -65,6 +113,13 @@ for z in 1:length(allmatrices_md.content[1].rows) times[z,j] = bt end + bandedness_five[z] = compute_bandedness(A, 5) + bandedness_ten[z] = compute_bandedness(A, 10) + bandedness_twenty[z] = compute_bandedness(A, 20) + percentage_sparsity[z] = length(nonzeros(A)) / n^2 + spaced_out_sparsity[z] = length(nonzeros(mtx_copy)) * percentage_sparsity[z] + matrix_size[z] = n + #= p = bar(algnames, times[z, :]; ylabel = "Time/s", @@ -86,6 +141,19 @@ for z in 1:length(allmatrices_md.content[1].rows) println(e) end end + +percentage_sparsity = percentage_sparsity[.!isnan.(percentage_sparsity)] +spaced_out_sparsity = spaced_out_sparsity[.!isnan.(spaced_out_sparsity)] +spaced_out_sparsity = replace(spaced_out_sparsity, 0 => 1e-10) +bandedness_five = bandedness_five[.!isnan.(bandedness_five)] +bandedness_five = replace(bandedness_five, 0 => 1e-10) +bandedness_ten = bandedness_ten[.!isnan.(bandedness_ten)] +bandedness_ten = replace(bandedness_ten, 0 => 1e-10) +bandedness_twenty = bandedness_twenty[.!isnan.(bandedness_twenty)] +bandedness_twenty = replace(bandedness_twenty, 0 => 1e-10) +matrix_size = matrix_size[.!isnan.(matrix_size)] +nanrows = any(isnan, times; dims=2) +times = times[.!vec(nanrows), :] ``` ```julia @@ -122,6 +190,51 @@ p = scatter(matrix_size, times; legend = :outertopright) ``` +```julia +p = scatter(spaced_out_sparsity, times; + ylabel = "Time/s", + yscale = :log10, + xlabel = "Spaced Out Sparsity", + xscale = :log10, + label = algnames_transpose, + title = "Factorization Time vs Spaced Out Sparsity", + fmt = :png, + legend = :outertopright) +``` + +```julia +p = scatter(bandedness_five, times; + ylabel = "Time/s", + yscale = :log10, + xlabel = "Bandedness", + xscale = :log10, + label = algnames_transpose, + title = "Factorization Time vs Bandedness, Bandwidth=5", + fmt = :png, + legend = :outertopright) +``` +```julia +p = scatter(bandedness_ten, times; + ylabel = "Time/s", + yscale = :log10, + xlabel = "Bandedness", + xscale = :log10, + label = algnames_transpose, + title = "Factorization Time vs Bandedness, Bandwidth=10", + fmt = :png, + legend = :outertopright) +``` +```julia +p = scatter(bandedness_twenty, times; + ylabel = "Time/s", + yscale = :log10, + xlabel = "Bandedness", + xscale = :log10, + label = algnames_transpose, + title = "Factorization Time vs Bandedness, Bandwidth=20", + fmt = :png, + legend = :outertopright) +``` ## Appendix