modified laplacian_matrix to achieve speed-up

[dahtah]

For some reason sparse + Diagonal is very slow. Modified laplacian_matrix to use sparse + sparse instead. This achieves a 100x speed-up in some cases.

[dahtah]

Ref: #1168

[codecov]

Codecov Report

Merging #1191 into master will increase coverage by <.01%.
The diff coverage is 100%.

@@            Coverage Diff             @@
##           master    #1191      +/-   ##
==========================================
+ Coverage   99.62%   99.62%   +<.01%     
==========================================
  Files          93       93              
  Lines        4270     4271       +1     
==========================================
+ Hits         4254     4255       +1     
  Misses         16       16

[sbromberger]

Could you post some benchmarks?

[dahtah]

Here are some numbers (v1.0.3 on Linux). On some graphs the gain is massive. For

G = Grid([50,50])

The old version gives:

BenchmarkTools.Trial: 
  memory estimate:  1.07 MiB
  allocs estimate:  2571
  --------------
  minimum time:     16.163 ms (0.00% GC)
  median time:      16.205 ms (0.00% GC)
  mean time:        16.508 ms (1.55% GC)
  maximum time:     67.344 ms (75.87% GC)
  --------------
  samples:          303
  evals/sample:     1

and the new

BenchmarkTools.Trial: 
  memory estimate:  914.52 KiB
  allocs estimate:  2560
  --------------
  minimum time:     272.325 μs (0.00% GC)
  median time:      277.983 μs (0.00% GC)
  mean time:        338.724 μs (16.49% GC)
  maximum time:     50.634 ms (99.29% GC)
  --------------
  samples:          10000
  evals/sample:     1

On

G = Grid([30,30,30])

Old:

BenchmarkTools.Trial: 
  memory estimate:  11.96 MiB
  allocs estimate:  27074
  --------------
  minimum time:     1.845 s (0.00% GC)
  median time:      1.877 s (0.00% GC)
  mean time:        1.867 s (0.23% GC)
  maximum time:     1.879 s (0.00% GC)
  --------------
  samples:          3
  evals/sample:     1

New:

BenchmarkTools.Trial: 
  memory estimate:  11.57 MiB
  allocs estimate:  27060
  --------------
  minimum time:     5.150 ms (0.00% GC)
  median time:      5.881 ms (6.01% GC)
  mean time:        5.727 ms (7.57% GC)
  maximum time:     59.003 ms (89.62% GC)
  --------------
  samples:          872
  evals/sample:     1

On other graphs the difference is less spectacular but still significant:

G = SimpleDiGraph(1000,10000)

Old:

BenchmarkTools.Trial: 
  memory estimate:  2.89 MiB
  allocs estimate:  14782
  --------------
  minimum time:     4.098 ms (0.00% GC)
  median time:      4.164 ms (0.00% GC)
  mean time:        4.418 ms (5.01% GC)
  maximum time:     55.348 ms (92.26% GC)
  --------------
  samples:          1131
  evals/sample:     1

New:

BenchmarkTools.Trial: 
  memory estimate:  2.87 MiB
  allocs estimate:  14772
  --------------
  minimum time:     1.496 ms (0.00% GC)
  median time:      1.556 ms (0.00% GC)
  mean time:        1.758 ms (10.77% GC)
  maximum time:     52.933 ms (96.66% GC)
  --------------
  samples:          2838
  evals/sample:     1

[sbromberger]

These benchmarks are really compelling. Thanks.