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plotting bandedness for 5, 10, 20
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@anastasia21112
anastasia21112 committed Nov 28, 2024
1 parent 655c211 commit 8eba943
Showing 1 changed file with 72 additions and 33 deletions.
105 changes: 72 additions & 33 deletions benchmarks/LinearSolve/MatrixDepot.jmd
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Original file line number Diff line number Diff line change
Expand Up @@ -30,11 +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 = 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
Expand All @@ -50,18 +74,16 @@ for z in 1:length(allmatrices_md.content[1].rows)
A = convert(SparseMatrixCSC, A)
n = size(A, 1)


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)
Expand All @@ -74,12 +96,11 @@ for z in 1:length(allmatrices_md.content[1].rows)
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
mtx_copy = condensed
end

## COMPUTING FACTORIZATION TIME
b = rand(rng, n)
u0 = rand(rng, n)

Expand All @@ -92,22 +113,13 @@ for z in 1:length(allmatrices_md.content[1].rows)
times[z,j] = bt
end

total_band_positions = 0
non_zero_in_band = 0
bandwidth = 5
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
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

percentage_filled = non_zero_in_band / total_band_positions * 100
bandedness[z] = percentage_filled
#=
p = bar(algnames, times[z, :];
ylabel = "Time/s",
Expand All @@ -133,6 +145,12 @@ 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), :]
Expand Down Expand Up @@ -161,41 +179,62 @@ p = scatter(percentage_sparsity, times;
```

```julia
p = scatter(bandedness, times;
p = scatter(matrix_size, times;
ylabel = "Time/s",
yscale = :log10,
xlabel = "Bandedness",
xlabel = "Matrix Size",
xscale = :log10,
label = algnames_transpose,
title = "Factorization Time vs Bandedness",
title = "Factorization Time vs Matrix Size",
fmt = :png,
legend = :outertopright)
```

```julia
p = scatter(matrix_size, times;
p = scatter(spaced_out_sparsity, times;
ylabel = "Time/s",
yscale = :log10,
xlabel = "Matrix Size",
xlabel = "Spaced Out Sparsity",
xscale = :log10,
label = algnames_transpose,
title = "Factorization Time vs Matrix Size",
title = "Factorization Time vs Spaced Out Sparsity",
fmt = :png,
legend = :outertopright)
```

```julia
p = scatter(spaced_out_sparsity, times;
p = scatter(bandedness_five, times;
ylabel = "Time/s",
yscale = :log10,
xlabel = "Spaced Out Sparsity",
xlabel = "Bandedness",
xscale = :log10,
label = algnames_transpose,
title = "Factorization Time vs Spaced Out Sparsity",
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

Expand Down

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