Merge pull request #1128 from anastasia21112/banded-mtx

Banded Matrix Metric

Author: ChrisRackauckas

benchmarks/LinearSolve/MatrixDepot.jmd

@@ -30,10 +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
@@ -49,18 +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)
@@ -73,12 +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)
 
@@ -90,9 +112,24 @@ for z in 1:length(allmatrices_md.content[1].rows)
                 alias_b = true))
             times[z,j] = bt
         end
-        matrix_size[z] = n
+
+        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",
+            yscale = :log10,
+            title = "Time on $(currMTX)",
+            fmt = :png,
+            legend = :outertopright)
+        display(p)
+        =#
+
         println("successfully factorized $(currMTX)")
     catch e
         matrix = allmatrices_md.content[1].rows[z]
@@ -108,6 +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), :]
@@ -159,6 +202,39 @@ p = scatter(spaced_out_sparsity, times;
     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