example.jl

using Metis
using JLD
using UnicodePlots
using SparseArrays

function compute_flops2(A)
  v = Metis.separator(A)
  lf = findall(v .== 1)
  rt = findall(v .== 2)
  sep = findall(v .== 3)
  # println((length(v), length(rt), length(lf), length(sep)))
  if length(sep) > 0
    flops = length(sep)^3
    flops += length(rt) >= 1 ? compute_flops2(A[rt, rt]) : length(rt)^3
    flops += length(lf) >= 1 ? compute_flops2(A[lf, lf]) : length(lf)^3
  else
    flops = length(v)^3
  end
  return flops
end

function comp_perm(A)
  v = Metis.separator(A)
  lf = findall(v .== 1)
  rt = findall(v .== 2)
  sep = findall(v .== 3)
  if length(lf) > 0 && length(rt) > 0
    lf = lf[comp_perm(A[lf, lf])]
    rt = rt[comp_perm(A[rt, rt])]
  end
  ind = [lf; rt; sep]
  return ind
end

M = try
  load("matrices_1_17.jld")
catch
  download("https://nps.box.com/shared/static/lokpepb39l3ysq2woj4q9neh97leyf9q.jld", "matrices_1_17.jld")
  load("matrices_1_17.jld")
end

A2 = M["A2"]; A2 = A2 + A2'
B2 = M["B2"]; B2 = B2 + B2'
C2 = M["C2"]; C2 = C2 + C2'
G2 = M["G2"]; G2 = G2 + G2'

println("monolithic")
A_my_ind = comp_perm(A2)
A_ind, _ = Metis.permutation(A2)
println("original")
display(spy(A2))
println("my permuted")
display(spy(A2[A_my_ind, A_my_ind]))
println("metris permutation")
display(spy(A2[A_ind, A_ind]))
println("")
println("---------------------------------------------")
println("")
println("displacement")
C_my_ind = comp_perm(C2)
C_ind, _ = Metis.permutation(C2)
println("original")
display(spy(C2))
println("my permuted")
display(spy(C2[C_my_ind, C_my_ind]))
println("metris permutation")
display(spy(C2[C_ind, C_ind]))
println("")
println("---------------------------------------------")
println("")
println("trace")
B_my_ind = comp_perm(B2)
B_ind, _ = Metis.permutation(B2)
println("original")
display(spy(B2))
println("my permuted")
display(spy(B2[B_my_ind, B_my_ind]))
println("metris permutation")
display(spy(B2[B_ind, B_ind]))
println("")
println("---------------------------------------------")
println("")
println("single block")
G_my_ind = comp_perm(G2)
G_ind, _ = Metis.permutation(G2)
println("original")
display(spy(G2))
println("my permuted")
display(spy(G2[G_my_ind, G_my_ind]))
println("metris permutation")
display(spy(G2[G_ind, G_ind]))

Manifest.toml

# This file is machine-generated - editing it directly is not advised

[[ArnoldiMethod]]
deps = ["LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "f87e559f87a45bece9c9ed97458d3afe98b1ebb9"
uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
version = "0.1.0"

[[Artifacts]]
deps = ["Pkg"]
git-tree-sha1 = "c30985d8821e0cd73870b17b0ed0ce6dc44cb744"
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
version = "1.3.0"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[Blosc]]
deps = ["Blosc_jll"]
git-tree-sha1 = "84cf7d0f8fd46ca6f1b3e0305b4b4a37afe50fd6"
uuid = "a74b3585-a348-5f62-a45c-50e91977d574"
version = "0.7.0"

[[Blosc_jll]]
deps = ["Libdl", "Lz4_jll", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "aa9ef39b54a168c3df1b2911e7797e4feee50fbe"
uuid = "0b7ba130-8d10-5ba8-a3d6-c5182647fed9"
version = "1.14.3+1"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "919c7f3151e79ff196add81d7f4e45d91bbf420b"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.25.0"

[[Crayons]]
git-tree-sha1 = "3f71217b538d7aaee0b69ab47d9b7724ca8afa0d"
uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
version = "4.0.4"

[[DataAPI]]
git-tree-sha1 = "ad84f52c0b8f05aa20839484dbaf01690b41ff84"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.4.0"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "4437b64df1e0adccc3e5d1adbc3ac741095e4677"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.9"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[FileIO]]
deps = ["Pkg"]
git-tree-sha1 = "fee8955b9dfa7bec67117ef48085fb2b559b9c22"
uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
version = "1.4.5"

[[HDF5]]
deps = ["Blosc", "Compat", "HDF5_jll", "Libdl", "Mmap", "Random", "Requires"]
git-tree-sha1 = "947d696a6b6dbc14018a1668c4724fdc6236a3d3"
uuid = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
version = "0.15.2"

[[HDF5_jll]]
deps = ["Artifacts", "JLLWrappers", "LibCURL_jll", "Libdl", "OpenSSL_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "fd83fa0bde42e01952757f01149dd968c06c4dba"
uuid = "0234f1f7-429e-5d53-9886-15a909be8d59"
version = "1.12.0+1"

[[Inflate]]
git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
version = "0.1.2"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[JLD]]
deps = ["FileIO", "HDF5", "Printf"]
git-tree-sha1 = "bb5606484571a52df34077bccc271e17a06ac2a9"
uuid = "4138dd39-2aa7-5051-a626-17a0bb65d9c8"
version = "0.12.1"

[[JLLWrappers]]
git-tree-sha1 = "a431f5f2ca3f4feef3bd7a5e94b8b8d4f2f647a0"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.2.0"

[[LibCURL_jll]]
deps = ["LibSSH2_jll", "Libdl", "MbedTLS_jll", "Pkg", "Zlib_jll", "nghttp2_jll"]
git-tree-sha1 = "897d962c20031e6012bba7b3dcb7a667170dad17"
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "7.70.0+2"

[[LibGit2]]
deps = ["Printf"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibSSH2_jll]]
deps = ["Libdl", "MbedTLS_jll", "Pkg"]
git-tree-sha1 = "717705533148132e5466f2924b9a3657b16158e8"
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.9.0+3"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[LightGraphs]]
deps = ["ArnoldiMethod", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
git-tree-sha1 = "432428df5f360964040ed60418dd5601ecd240b6"
uuid = "093fc24a-ae57-5d10-9952-331d41423f4d"
version = "1.3.5"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[Lz4_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "51b1db0732bbdcfabb60e36095cc3ed9c0016932"
uuid = "5ced341a-0733-55b8-9ab6-a4889d929147"
version = "1.9.2+2"

[[METIS_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "2dc1a9fc87e57e32b1fc186db78811157b30c118"
uuid = "d00139f3-1899-568f-a2f0-47f597d42d70"
version = "5.1.0+5"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "6a8a2a625ab0dea913aba95c11370589e0239ff0"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.6"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[MbedTLS_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0eef589dd1c26a3ac9d753fe1a8bcad63f956fa6"
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.16.8+1"

[[Metis]]
deps = ["LightGraphs", "LinearAlgebra", "METIS_jll", "SparseArrays"]
git-tree-sha1 = "c2fbb518580d5e9efd0c2601fc8116b2c76d945e"
uuid = "2679e427-3c69-5b7f-982b-ece356f1e94b"
version = "1.0.0"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "ed61674a0864832495ffe0a7e889c0da76b0f4c8"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "0.4.4"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "71bbbc616a1d710879f5a1021bcba65ffba6ce58"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.1+6"

[[OrderedCollections]]
git-tree-sha1 = "cf59cfed2e2c12e8a2ff0a4f1e9b2cd8650da6db"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.3.2"

[[Pkg]]
deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "cfbac6c1ed70c002ec6361e7fd334f02820d6419"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.2"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "daf7aec3fe3acb2131388f93a4c409b8c7f62226"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.3"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures", "Random", "Test"]
git-tree-sha1 = "03f5898c9959f8115e30bc7226ada7d0df554ddd"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "0.3.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "9da72ed50e94dbff92036da395275ed114e04d49"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.0.1"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics"]
git-tree-sha1 = "7bab7d4eb46b225b35179632852b595a3162cb61"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.2"

[[Test]]
deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[UnicodePlots]]
deps = ["Crayons", "Dates", "SparseArrays", "StatsBase"]
git-tree-sha1 = "1a63e6eea76b291378ff9f95801f8b6d96213208"
uuid = "b8865327-cd53-5732-bb35-84acbb429228"
version = "1.3.0"

[[Zlib_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "320228915c8debb12cb434c59057290f0834dbf6"
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.11+18"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6f1abcb0c44f184690912aa4b0ba861dd64f11b9"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.4.5+2"

[[nghttp2_jll]]
deps = ["Libdl", "Pkg"]
git-tree-sha1 = "8e2c44ab4d49ad9518f359ed8b62f83ba8beede4"
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.40.0+2"

Project.toml

[deps]
JLD = "4138dd39-2aa7-5051-a626-17a0bb65d9c8"
Metis = "2679e427-3c69-5b7f-982b-ece356f1e94b"
SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
UnicodePlots = "b8865327-cd53-5732-bb35-84acbb429228"

julia> include("example.jl")
monolithic
original
                Sparsity Pattern
         ┌──────────────────────────────┐
       1 │⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀│ > 0
         │⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀│ < 0
         │⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀│
         │⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣄⢷│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢐⠘⣿│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⡀⠀⠀⢰⡎⢹│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢣⡅⣾│
         │⣤⣀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⣀⠤⣈⢻⢖⠸⠹│
   19872 │⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠒⠶⠤⠶⠦⢤⣝⣶⣤⣎⣉⣡⣭⣖⡂⠑⢄│
         └──────────────────────────────┘
         1                          19872
                  nz = 1064064
my permuted
                Sparsity Pattern
         ┌──────────────────────────────┐
       1 │⣿⣿⣀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈│ > 0
         │⠤⠼⠿⣧⡄⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ < 0
         │⠀⠀⠀⠭⠿⣧⡄⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠│
         │⠤⠄⠀⠤⠤⠭⠿⣧⡀⡀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠨⠿⣧⡄⣬⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠│
         │⠀⠀⠀⠀⠀⠀⠀⢀⡀⣭⣿⢟⡀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
         │⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠐⠒⠒⠚⢻⣶⡰⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠻⣦⣰⠆⠀⠀⡅⠀⠀⠀⠀⠀⠀⠘│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠞⠿⣧⡠⠀⡄⠀⠀⠀⠀⠀⠀⢨│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⣦⡇⠀⠀⠀⠀⠀⠀⠰│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠉⠉⠉⣻⣾⡀⡇⠀⠀⠀⢠│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠬⠿⣧⡀⡀⠀⢸│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⣧⡀⣨│
   19872 │⡀⢀⠀⠀⠀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⡀⣀⢀⡀⠀⣀⣀⣀⡀⣨⣿⣿│
         └──────────────────────────────┘
         1                          19872
                  nz = 1064064
metris permutation
                Sparsity Pattern
         ┌──────────────────────────────┐
       1 │⣿⣿⣀⡅⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ > 0
         │⠄⠼⠿⣧⡄⡀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠│ < 0
         │⠀⠀⠀⠩⠿⣧⡄⡆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘│
         │⠤⠀⠀⠤⠠⠭⠿⣧⣄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈│
         │⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢻⣶⣰⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢻⣶⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨│
         │⠀⠐⠒⠂⠒⠂⠀⠀⠒⠒⠒⠂⠐⠚⢻⣶⣠⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣶⣠⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠾⠿⣧⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡇⠀⠀⠀⠀⠀⠀⢠│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠻⣦⡇⢠⠀⠀⠀⠘│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣿⣿⡀⡀⠀⢰│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⢇⣀⢸│
   19872 │⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⡀⡀⡀⣀⣀⣀⣀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣘⣻⣾│
         └──────────────────────────────┘
         1                          19872
                  nz = 1064064

---------------------------------------------

displacement
original
                Sparsity Pattern
         ┌──────────────────────────────┐
       1 │⢿⣷⣄⠈⠛⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀│ > 0
         │⡀⠙⢿⣷⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⢀⡀⠄│ < 0
         │⢿⣀⣠⠋⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
         │⠈⠉⠀⠀⠀⠉⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡤⠀⠀⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⣄⠀⠀⠒⠀⠠⠄⠀⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡲│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⠛⣤⣄⠀⠒⠀⠀⠀⠀⢀⣤⠀⠀⠀⠈⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠉⢿⣷⣄⠀⠁⠀⠀⠀⠀⢀⠖⠀│
         │⠀⠀⢠⠀⠀⠀⠰⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣧⣄⠀⠀⠀⠠⠋⠀⣤│
         │⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣤⡴⠁⠀⠀⠙⠿⣧⡄⠀⠀⠀⠀⠀│
         │⢀⠂⠀⠀⠀⠀⠀⠀⣠⡤⠃⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠉⠿⣧⡄⠀⠀⠀│
         │⠂⠀⠀⢀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠉⠿⣧⣄⠀│
   18144 │⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢠⡰⠂⠀⠀⠀⠘⠁⠀⣤⠀⠀⠀⠀⠀⠙⢿⣷│
         └──────────────────────────────┘
         1                          18144
                  nz = 1280064
my permuted
                Sparsity Pattern
         ┌──────────────────────────────┐
       1 │⠿⣧⣼⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤│ > 0
         │⠒⠛⠻⣦⡀⢰⡆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟│ < 0
         │⢀⣀⢀⣈⣿⣿⡃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀│
         │⠈⠈⠈⠉⠉⠈⠿⣧⣸⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄│
         │⠀⠀⠀⠀⠀⠀⠒⠚⢻⣶⣀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀│
         │⠀⠀⠀⠀⠀⠀⢀⣀⠀⣘⣻⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚│
         │⠀⠀⠈⠉⠀⠈⠈⠉⠉⠀⠈⠉⣻⣾⣘⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠼⠿⣧⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⢻⣶⣀⡆⠀⠀⡄⠀⠀⠀⠈⡁│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⣧⣠⠀⡆⠀⠀⠀⠛⠇│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣦⡇⠀⠀⠀⠰⢤│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠿⣧⣼⠀⣟⣎│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠻⣦⣿⠋│
   18144 │⠀⣤⣤⠄⠀⠠⠀⠤⠀⢀⣠⢠⢄⣀⢲⡶⠴⠆⠆⠠⠿⠄⠐⣆⡻⢽⡿⠛⢻⣶│
         └──────────────────────────────┘
         1                          18144
                  nz = 1280064
metris permutation
                Sparsity Pattern
         ┌──────────────────────────────┐
       1 │⠿⣧⣸⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤│ > 0
         │⠒⠚⢻⣶⡀⣸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤│ < 0
         │⠀⢀⣀⣨⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉│
         │⠀⠀⠀⠀⠀⠘⠿⣧⣸⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤│
         │⠀⠀⠀⠀⠀⠀⠒⠚⠻⣦⡆⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛│
         │⠀⠀⠀⠀⠀⠀⣀⢀⢈⣉⣻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛│
         │⠉⠉⠈⠀⠀⠀⠉⠈⠈⠁⠉⠉⢿⣷⡆⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣿│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣻⣾⡇⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢸⣏│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⣿⣸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠘⠋│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠿⣧⡄⢠⠄⠀⠀⠀⠀⠀⠸⣧│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣉⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠉⠉⠀⠁⠀⠉⣻⣾⡇⣿⠀⠀⠛⠉│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣿⣿⣀⠀⡿⠇│
         │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡿⣦│
   18144 │⠀⣤⠀⣤⡄⢠⠀⣤⣤⠀⣤⢀⣤⣶⡶⢶⡶⠀⠶⣦⡄⠀⡟⠀⠿⠏⠻⣯⣿⣿│
         └──────────────────────────────┘
         1                          18144
                  nz = 1280064

---------------------------------------------

trace
original
               Sparsity Pattern
        ┌──────────────────────────────┐
      1 │⣿⣿⣧⡄⠀⠈⠉⠷⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⡒⠀│ > 0
        │⠉⠿⡿⣯⣥⠀⠀⢀⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀│ < 0
        │⡀⠀⠁⠛⡟⣭⣤⣘⡛⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠃⠀⠀⠀⣼⠃⠀⠀⠀│
        │⢧⡄⠀⢀⣀⢻⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠰⠟│
        │⠈⠙⠛⠛⠛⠈⠈⠙⢻⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⡀⠀│
        │⠀⠘⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀│
        │⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣧⣤⠀⠀⠀⠶⠀⢀⣀⠀⠀⠀⠀⠸⠇⠀⠀│
        │⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣤⡀⠀⠀⠈⠛⠀⠀⠀⡿⠀⠀⠀⢀│
        │⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⡄⠀⠀⢀⡀⠀⠀⠃⠀⠀⠀⣾│
        │⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠉⢿⣷⣤⠈⠁⠀⠀⢀⣼⠃⠀⠀│
        │⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⢀⡀⠛⢿⣷⣀⠀⠀⣼⠟⠀⠀⣀│
        │⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢿⣷⣦⠀⠀⠀⣴⡏│
        │⠘⠀⠀⠀⣀⣤⠀⠀⠀⠓⠀⠀⠀⠀⣤⡤⠤⠀⠀⢀⣀⣤⠈⠛⠛⣤⣀⠐⠛⠡│
        │⠀⢀⠰⠛⠉⠀⠀⠀⠀⢀⣠⣤⠶⠆⠀⠀⠀⠀⠶⠛⠛⠁⠀⠀⢀⠘⠻⣦⡀⠀│
   1728 │⠘⠈⠀⠀⠀⠀⣴⠆⠀⠈⠉⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⢠⡴⠿⠟⡀⠀⠈⠿⣧│
        └──────────────────────────────┘
        1                           1728
                  nz = 189216
my permuted
               Sparsity Pattern
        ┌──────────────────────────────┐
      1 │⣿⣿⣀⣀⣛⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀│ > 0
        │⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿│ < 0
        │⠛⠘⠉⠛⢻⣶⣶⢀⡀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈│
        │⠀⠀⠀⠀⠘⢛⣻⣾⡇⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀│
        │⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷│
        │⢠⣤⠀⠀⠰⠶⢶⣤⡘⠻⠿⣧⣀⢀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣾⡇⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⡆⣛⠀│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣬⡼⠏⠀│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣿⣿⣿⢟⡂⠀⠀⠀⠀⠀⠀⠀⠻⠽⠆⠀│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠈⠈⣿⣿⠀⠀⢿⠀⠀⠀⣤⠀⠀⣤│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⢸⡇⠇⠀⠀│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠛⠋⢱⣶⣶⣤⢠⠂⠰⣦│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⣿⣿⣿⣿⡇⠀⠉│
        │⢀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠰⠶⣂⡿⣟⡆⠀⠛⠭⠍⠠⠒⠿⠿⠿⢇⡀⠚│
   1728 │⠈⠉⣤⣄⡀⠈⠉⠀⢷⣾⣿⠛⠛⠘⠋⠁⠈⠁⠀⣤⠀⠀⠰⣦⡄⠀⣠⠈⠻⣦│
        └──────────────────────────────┘
        1                           1728
                  nz = 189216
metris permutation
               Sparsity Pattern
        ┌──────────────────────────────┐
      1 │⡿⣯⡐⢢⣟⡆⣠⠀⠂⡛⣀⡶⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠛│ > 0
        │⠰⣈⠱⣦⣾⠀⣭⠑⢷⡗⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢤⡖│ < 0
        │⠻⠽⠚⠛⠛⣤⣚⣀⣻⣄⣤⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛│
        │⠀⠚⢇⠛⠚⢸⡻⢎⡿⣋⡇⢬⡡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣀│
        │⣬⠠⢽⠷⠛⢾⡿⢫⠻⣦⡳⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣤│
        │⢠⡼⣆⣀⠀⢿⡉⣍⡹⠎⠻⣦⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀│
        │⠐⠂⠈⠉⠀⠿⠁⠎⠁⠀⠿⠈⠿⣧⡤⠀⣤⣄⠀⢠⡄⠀⠀⠀⠀⠀⠀⢡⡌⠅│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⣤⡘⠻⣧⢠⢼⣄⢄⡲⠆⣈⣉⡀⠀⣘│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡈⠻⣦⡀⠀⣳⠙⠂⣀⠘⠓⢛⠙⠚⠫│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⣛⠀⠈⣻⣾⠋⣵⠦⠿⣦⣶⠸⢆⡀⠀│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢷⣝⠚⢏⣤⣻⣾⡳⠁⣤⣄⣀⡌⠀⣐│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡱⠈⢠⣬⡇⠝⠊⡱⣮⡷⣴⢶⡆⠀⠀│
        │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢡⢶⠀⢨⣿⠀⢿⢙⣯⠻⣦⣠⡄⣰⠆│
        │⡀⣀⠠⢀⡀⠀⢀⠠⠄⠀⠀⠠⠄⣀⠃⠸⣟⠐⠲⢆⡀⠼⠸⠷⠀⠾⠻⢆⡛⠛│
   1728 │⣿⠉⢠⠷⣤⠀⠀⢠⠀⣿⠀⠰⠆⠍⣀⢠⡾⡀⠀⠈⢀⢠⠀⠀⠰⠞⣿⠈⠿⣧│
        └──────────────────────────────┘
        1                           1728
                  nz = 189216

---------------------------------------------

single block
original
              Sparsity Pattern
       ┌──────────────────────────────┐
     1 │⣻⣾⣷⣟⢷⣻⣾⣷⣟⢷⡱⢌⠳⣝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ > 0
       │⣽⢿⣿⣿⡷⣽⢿⣿⣿⡷⣝⢦⡑⣌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│ < 0
       │⣽⣳⣝⣯⣟⣽⣳⣝⣯⣟⣬⡳⣝⢦⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
       │⢾⣿⣿⣷⣝⢾⣿⣿⣷⣝⢾⣿⣮⡳⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
       │⢿⣝⢿⡿⣯⢿⣝⢿⡿⣯⢿⣝⢿⡿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
       │⡑⢎⠳⣝⢦⡻⣾⣷⣟⢷⣻⣾⣷⣟⣷⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
       │⣝⢦⡑⢬⠳⣝⢮⡻⣿⡷⣽⢿⣿⣿⡷⣽⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
       │⠈⠓⠙⠂⠙⠈⠓⠙⠊⠛⣽⣻⣝⣯⣟⣽⣻⣝⣯⣟⣤⡠⣄⢤⡀⣄⠠⣄⢤⡀│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣟⢾⣿⣿⣷⣟⢾⣿⣮⡳⣝⢦⡓⢌⠳⣝│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⢿⣽⢿⡿⣯⢷⣽⢿⡿⣮⠳⣝⢮⡱⢌│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣾⣷⣝⣷⣻⣾⣷⣝⣷⣻⣾⣷⣝⣷│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢮⡻⣿⡷⣝⢿⣿⣿⡷⣝⢿⣿⣿⡷│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠳⣝⢮⡛⣽⣻⣝⢯⣟⣽⣻⣝⢯⣟│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡙⢌⡳⣝⢾⣿⣿⣷⣟⢾⣿⣿⣷⣟│
   324 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢦⡑⢎⢷⣽⢿⡿⣯⢷⣽⢿⡿⣯│
       └──────────────────────────────┘
       1                            324
                 nz = 17604
my permuted
              Sparsity Pattern
       ┌──────────────────────────────┐
     1 │⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠀⠀│ > 0
       │⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⡄⠀⠀│ < 0
       │⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣷⠀⠀│
       │⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡅│
       │⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿│
       │⣤⣤⣤⣤⢤⣤⣿⠿⡿⣿⡿⣯⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣟⠻│
       │⠇⠀⠀⠿⠈⠻⠿⠿⠿⠿⠻⠿⠿⣧⣤⣤⣤⣤⡄⠀⠀⠀⠀⡤⠀⣤⠼⠻⠛⠀│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣄⢿⣷⣄⠀⠀│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠉⣷⣯⠉⠀⠀│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢱⣶⣶⣶⣶⢿⣿⠉⠉⠿⢶⠄│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠸⣿⠀⠀⢠⣿⣿│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⣤⣤⣼⣟⣛⡛⢛⣴⣿⠀⣤⣤⡟⠛│
       │⣤⣤⡄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣝⢧⣤⡟⠛⠛⠛⠛⠛⠛⣤⣼⡟⠛⠀│
       │⡟⠛⠛⠾⢿⣿⡄⠀⠀⣀⠀⣷⣶⡃⠙⢿⡏⠛⣧⡄⠀⣀⠀⣿⣶⠿⢿⣷⣄⣀│
   324 │⠀⠀⠀⠀⠀⠀⠟⠦⣷⣿⣿⡙⠛⠀⠀⠀⠀⠀⠘⠗⣿⣿⣿⠉⠛⠀⠀⢹⣿⣿│
       └──────────────────────────────┘
       1                            324
                 nz = 17604
metris permutation
              Sparsity Pattern
       ┌──────────────────────────────┐
     1 │⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⢿⣿⣾│ > 0
       │⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⢰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢘⣛⣻⣛│ < 0
       │⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣛⢙⢹⠉│
       │⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣽⣉⣹│
       │⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⣿⣭⣽│
       │⣤⣤⣤⣤⣤⣤⣿⣿⣿⢿⡿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣧⣿⢲⢺│
       │⠿⠶⠔⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⣧⣄⣤⣤⣤⡄⠀⠀⠀⠀⣤⣤⠿⢿⣿⡼⠸│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡆⡅⢸⣿⣯⣿│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣅⡃⣼⣿⣛⣿│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢱⣶⣶⣶⣶⣿⣿⢿⠏⢵⢵⡾│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⡇⣿⣿⣿│
       │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣼⣿⣿⣿⣻⣾⣿⣦⣦⣾⢺⢳│
       │⡤⠤⠤⠠⠤⢠⣤⣤⡤⠤⠤⣤⣤⡟⠌⠭⠥⠹⣿⣟⣿⡿⠻⣿⣿⣿⣷⣶⣴⣴│
       │⣷⣖⣶⢰⣟⢘⣍⣭⣭⣭⣭⣿⣿⣷⣶⣶⣶⣿⢏⣅⣭⣭⣨⣿⢹⣿⣿⣿⣿⣿│
   324 │⣻⣿⣿⢺⡗⠒⣇⣸⣇⣿⣸⣒⣒⡋⣯⣿⣿⣼⣱⡷⣿⣿⢾⣒⢐⣿⣿⣿⣿⣿│
       └──────────────────────────────┘
       1                            324
                 nz = 17604