add computations of PSL eigenvalues

Manifest.toml

@@ -6,6 +6,24 @@ git-tree-sha1 = "da0bf98d73f2f34c35d58981fcf139f16749a394"
 uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
 version = "0.7.1"
 
+[[ArnoldiMethod]]
+deps = ["DelimitedFiles", "LinearAlgebra", "Random", "SparseArrays", "StaticArrays", "Test"]
+git-tree-sha1 = "2b6845cea546604fb4dca4e31414a6a59d39ddcd"
+uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
+version = "0.0.4"
+
+[[Arpack]]
+deps = ["Arpack_jll", "Libdl", "LinearAlgebra"]
+git-tree-sha1 = "2ff92b71ba1747c5fdd541f8fc87736d82f40ec9"
+uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
+version = "0.4.0"
+
+[[Arpack_jll]]
+deps = ["Libdl", "OpenBLAS_jll", "Pkg"]
+git-tree-sha1 = "e214a9b9bd1b4e1b4f15b22c0994862b66af7ff7"
+uuid = "68821587-b530-5797-8361-c406ea357684"
+version = "3.5.0+3"
+
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
@@ -81,6 +99,12 @@ git-tree-sha1 = "ed2c4abadf84c53d9e58510b5fc48912c2336fbb"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
 version = "2.2.0"
 
+[[CompilerSupportLibraries_jll]]
+deps = ["Libdl", "Pkg"]
+git-tree-sha1 = "7c4f882c41faa72118841185afc58a2eb00ef612"
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
+version = "0.3.3+0"
+
 [[DataStructures]]
 deps = ["InteractiveUtils", "OrderedCollections"]
 git-tree-sha1 = "b7720de347734f4716d1815b00ce5664ed6bbfd4"
@@ -162,6 +186,11 @@ git-tree-sha1 = "5c49dab19938b119fe204fd7d7e8e174f4e9c68b"
 uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
 version = "0.8.8"
 
+[[Inflate]]
+git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
+uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
+version = "0.1.2"
+
 [[IniFile]]
 deps = ["Test"]
 git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
@@ -209,11 +238,18 @@ uuid = "1b4a561d-cfcb-5daf-8433-43fcf8b4bea3"
 version = "0.4.1"
 
 [[LibGit2]]
+deps = ["Printf"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
 
 [[Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
+[[LightGraphs]]
+deps = ["ArnoldiMethod", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
+git-tree-sha1 = "e85fa18ae33a3ef55243d2c2c9f6ccea6f541566"
+uuid = "093fc24a-ae57-5d10-9952-331d41423f4d"
+version = "1.3.2"
+
 [[LinearAlgebra]]
 deps = ["Libdl"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -221,6 +257,12 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 [[Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
+[[MacroTools]]
+deps = ["Markdown", "Random"]
+git-tree-sha1 = "f7d2e3f654af75f01ec49be82c231c382214223a"
+uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
+version = "0.5.5"
+
 [[Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
@@ -257,11 +299,17 @@ git-tree-sha1 = "928b8ca9b2791081dc71a51c55347c27c618760f"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 version = "0.3.3"
 
+[[OpenBLAS_jll]]
+deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
+git-tree-sha1 = "2ee3e636e94b9fd95fa8364d5cba2e20dae16609"
+uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
+version = "0.3.9+2"
+
 [[OpenSpecFun_jll]]
-deps = ["Libdl", "Pkg"]
-git-tree-sha1 = "65f672edebf3f4e613ddf37db9dcbd7a407e5e90"
+deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
+git-tree-sha1 = "d51c416559217d974a1113522d5919235ae67a87"
 uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
-version = "0.5.3+1"
+version = "0.5.3+3"
 
 [[OrderedCollections]]
 deps = ["Random", "Serialization", "Test"]
@@ -285,6 +333,12 @@ version = "0.3.10"
 deps = ["Dates", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "UUIDs"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
+[[Primes]]
+deps = ["Test"]
+git-tree-sha1 = "ff1a2323cb468ec5f201838fcbe3c232266b1f95"
+uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
+version = "0.4.0"
+
 [[Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
@@ -305,6 +359,14 @@ version = "0.3.1"
 deps = ["InteractiveUtils", "Markdown", "Sockets"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 
+[[RamanujanGraphs]]
+deps = ["LightGraphs", "LinearAlgebra", "Primes"]
+git-tree-sha1 = "8d9d25a274aeec5d5265829d05784276a4841f6d"
+repo-rev = "master"
+repo-url = "https://github.com/kalmarek/RamanujanGraphs.jl"
+uuid = "e7bd6bc6-b6b8-11e9-1ec2-2f89442c0d6c"
+version = "0.3.0"
+
 [[Random]]
 deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -336,6 +398,12 @@ version = "0.2.0"
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
+[[SimpleTraits]]
+deps = ["InteractiveUtils", "MacroTools"]
+git-tree-sha1 = "2ee666b24ab8be6a922f9d6c11a86e1a703a7dda"
+uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
+version = "0.9.2"
+
 [[Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 

Project.toml

@@ -1,8 +1,10 @@
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
+Arpack = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 GroupRings = "0befed6a-bd73-11e8-1e41-a1190947c2f5"
 Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
 PropertyT = "03b72c93-0167-51e2-8a1e-eb4ff1fb940d"
+RamanujanGraphs = "e7bd6bc6-b6b8-11e9-1ec2-2f89442c0d6c"
 SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"

src/PSL.jl

@@ -0,0 +1,19 @@
+using RamanujanGraphs
+using RamanujanGraphs.LightGraphs
+using Arpack
+
+Γ, eigenvalues = let q = 109
+      a = RamanujanGraphs.PSL₂{q}([  0  1
+                                   108 11])
+      b = RamanujanGraphs.PSL₂{q}([57  2
+                                   52 42])
+
+      S = unique([[a^i for i in 1:4]; [b^i for i in 1:4]])
+
+      @info "Generating set S of $(eltype(S))" S
+      @time Γ, verts, vlabels, elabels = RamanujanGraphs.cayley_graph((q^3 - q)÷2, S)
+      @assert all(degree(Γ,i) == length(S) for i in vertices(Γ))
+      A = adjacency_matrix(Γ)
+      @time eigenvalues, _ = eigs(A, nev=5)
+      @show Γ eigenvalues
+end