Merge pull request #9 from fgasdia/triangledomain

Support multithreading option

Manifest.toml

@@ -5,24 +5,25 @@ uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
 [[ColorTypes]]
 deps = ["FixedPointNumbers", "Random"]
-git-tree-sha1 = "c73d9cfc2a9d8433dc77f5bff4bddf46b1d78c20"
+git-tree-sha1 = "607c0ea16cb32af49ea2976f90c0c5acbca37d21"
 uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
-version = "0.10.3"
+version = "0.10.8"
 
 [[Colors]]
 deps = ["ColorTypes", "FixedPointNumbers", "InteractiveUtils", "Reexport"]
-git-tree-sha1 = "db9c215e2d92379d341e40dd1d5be893af2bfeb2"
+git-tree-sha1 = "008d6bc68dea6beb6303fdc37188cb557391ebf2"
 uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
-version = "0.12.1"
+version = "0.12.4"
 
 [[Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
 [[FixedPointNumbers]]
-git-tree-sha1 = "3ba9ea634d4c8b289d590403b4a06f8e227a6238"
+deps = ["Statistics"]
+git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
 uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
-version = "0.8.0"
+version = "0.8.4"
 
 [[GeometricalPredicates]]
 git-tree-sha1 = "04776c0dc233eafa617b1a52ca58db2338b08836"
@@ -82,6 +83,14 @@ uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 [[Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
+[[SparseArrays]]
+deps = ["LinearAlgebra", "Random"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[Statistics]]
+deps = ["LinearAlgebra", "SparseArrays"]
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
 [[UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

Project.toml

@@ -1,19 +1,21 @@
 name = "RootsAndPoles"
 uuid = "a0859a10-ccb4-11e8-145d-674b3750773a"
 authors = ["Forrest Gasdia <[email protected]>"]
-version = "1.0.0"
+version = "1.1.0"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 VoronoiDelaunay = "72f80fcb-8c52-57d9-aff0-40c1a3526986"
 
 [compat]
-julia = "1.4"
 VoronoiDelaunay = "0.4.0"
+julia = "1.4"
 
 [extras]
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 
 [targets]
 test = ["SpecialFunctions", "Test"]
+benchmark = ["BenchmarkTools", "LinearAlgebra"]

README.md

@@ -63,15 +63,21 @@ By default, the value of `tess_sizehint` is 5000 and the `tolerance` is 1e-9, bu
 zroots, zpoles = grpf(simplefcn, origcoords, GRPFParams(5000, 1e-9))
 ```
 
+Beginning version 1.1.0, calls to the provided function, e.g. `simplefcn`, can be **multithreaded** using Julia's `@threads` capability. The function is called at every node of the triangulation and the results should be independent of one another. For fast-running functions like `simplefcn`, the overall runtime of `grpf` is dominated by the Delaunay Triangulation itself, but for more complicated functions, threading can provide a significant advantage. To enable multithreading of the function calls, specify so as a `GRPFParams` argument
+```julia
+zroots, zpoles = grpf(simplefcn, origcoords, GRPFParams(5000, 1e-9, true))
+```
+By default, `multithreading = false`.
+
 Additional parameters which can be controlled are `maxiterations`, `maxnodes`, and `skinnytriangle`. `maxiterations` sets the maximum number of mesh refinement iterations and `maxnodes` sets the maximum number of nodes allowed in the `DelaunayTessellation2D` before returning. `skinnytriangle` is the maximum allowed ratio of the longest to shortest side length in a tesselation triangle before the triangle is automatically subdivided in the mesh refinement step. Default values are
 
   - `maxiterations`: 100
   - `maxnodes`: 500000
   - `skinnytriangle`: 3
 
-These can be specified along with the `tess_sizehint` and `tolerance` as, e.g.
+These can be specified along with the `tess_sizehint`, `tolerance` and `multithreading` as, e.g.
 ```julia
-zroots, zpoles = grpf(simplefcn, origcoords, GRPFParams(100, 500000, 3, 5000, 1e-9))
+zroots, zpoles = grpf(simplefcn, origcoords, GRPFParams(100, 500000, 3, 5000, 1e-9, true))
 ```
 
 ### Plot data

benchmark/Manifest.toml

@@ -0,0 +1,87 @@
+# This file is machine-generated - editing it directly is not advised
+
+[[Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[BenchmarkTools]]
+deps = ["JSON", "Logging", "Printf", "Statistics", "UUIDs"]
+git-tree-sha1 = "9e62e66db34540a0c919d72172cc2f642ac71260"
+uuid = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+version = "0.5.0"
+
+[[Dates]]
+deps = ["Printf"]
+uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
+
+[[Distributed]]
+deps = ["Random", "Serialization", "Sockets"]
+uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+
+[[InteractiveUtils]]
+deps = ["Markdown"]
+uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+
+[[JSON]]
+deps = ["Dates", "Mmap", "Parsers", "Unicode"]
+git-tree-sha1 = "b34d7cef7b337321e97d22242c3c2b91f476748e"
+uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+version = "0.21.0"
+
+[[Libdl]]
+uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
+
+[[LinearAlgebra]]
+deps = ["Libdl"]
+uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+
+[[Logging]]
+uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
+
+[[Markdown]]
+deps = ["Base64"]
+uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
+
+[[Mmap]]
+uuid = "a63ad114-7e13-5084-954f-fe012c677804"
+
+[[Parsers]]
+deps = ["Dates", "Test"]
+git-tree-sha1 = "8077624b3c450b15c087944363606a6ba12f925e"
+uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
+version = "1.0.10"
+
+[[Printf]]
+deps = ["Unicode"]
+uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
+
+[[Random]]
+deps = ["Serialization"]
+uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+
+[[SHA]]
+uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
+
+[[Serialization]]
+uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+
+[[Sockets]]
+uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
+
+[[SparseArrays]]
+deps = ["LinearAlgebra", "Random"]
+uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
+[[Statistics]]
+deps = ["LinearAlgebra", "SparseArrays"]
+uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
+[[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"

benchmark/Project.toml

@@ -0,0 +1,3 @@
+[deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

benchmark/benchmarks.jl

@@ -0,0 +1,113 @@
+using BenchmarkTools
+using LinearAlgebra
+
+using RootsAndPoles
+
+# Define a parent BenchmarkGroup to contain our suite
+const suite = BenchmarkGroup()
+
+# Add some child groups to our benchmark suite.
+suite["grpf"] = BenchmarkGroup(["functions"])  # BenchmarkGroup "tags"
+
+simplefcn(z) = (z - 1)*(z - im)^2*(z + 1)^3/(z + im)
+
+function defaultfcn(z)
+    f = 1e9
+    ϵᵣ = 5 - 2im
+    μᵣ = 1 - 2im
+    d = 1e-2
+    c = 3e8
+    ω = 2π*f
+    k₀ = ω/c
+    cc = ϵᵣ^2*(k₀*d)^2*(ϵᵣ*μᵣ - 1)
+    w = ϵᵣ^2*z^2 + z^2*tan(z)^2 - cc
+end
+
+function wvgd(z)
+    ns = 0.065-4im
+    n1 = 1.5835
+    nc = 1.0
+    d1 = 1.81e-6
+    λ₀ = 0.6328e-6
+    k₀ = 2π/λ₀
+    k₀d1 = k₀*d1
+    κ1 = sqrt(n1^2 - z^2)
+    γs = sqrt(z^2 - ns^2)
+    γc = sqrt(z^2 - nc^2)
+    m11 = cos(κ1*k₀d1)
+    m12 = im/κ1*sin(κ1*k₀d1)
+    m21 = im*κ1*sin(κ1*k₀d1)
+    m22 = cos(κ1*k₀d1)
+    w = det([1.0    -m11+im*γc*m12
+           im*γs  -m21+im*γc*m22])
+end
+
+function graphenefunction(z)
+    f = 1e12
+    c = 299792458
+    μ₀ = 4π*1e-7
+    ϵ₀ = 1/(μ₀*c^2)
+
+    e = 1.602176565e-19
+    kB = 1.3806488e-23
+    hk = 1.05457168e-34
+    vFe = 1e6
+    muc = 0.05*e
+    t = 0.135e-12
+    T = 300
+    ϵᵣ₁ = 1.0
+    ϵᵣ₂ = 11.9
+
+    ω = 2π*f
+    k₀ = ω/c
+    kᵣ₀ = -im*z*k₀
+
+    Slo=-im*e^2*kB*T*log(2+2*cosh(muc/kB/T)) / (π*hk^2*(ω-im/t))
+
+    a = -3*vFe^2*Slo/(4*(ω-im/t)^2)
+    b = a/3
+
+    Y1TM = ω*ϵᵣ₁*ϵ₀/sqrt(ϵᵣ₁*k₀^2 - kᵣ₀^2);
+    Y2TM = ω*ϵᵣ₂*ϵ₀/sqrt(ϵᵣ₂*k₀^2 - kᵣ₀^2);
+    YSTM = Slo + 1*a*kᵣ₀^2 + 1*b*kᵣ₀^2;
+
+    w = (Y1TM + Y2TM + YSTM)*(-Y1TM + Y2TM + YSTM)*(Y1TM - Y2TM + YSTM)*(-Y1TM - Y2TM + YSTM) # four Riemann sheets
+end
+
+testfcns = (simplefcn, defaultfcn, wvgd, graphenefunction)
+
+# Add some benchmarks to the "grpf" group
+for f in testfcns
+    sf = string(f)
+    if sf == "simplefcn"
+        origcoords = rectangulardomain(complex(-2, -2), complex(2, 2), 0.1)
+        suite["grpf"][sf] = @benchmarkable grpf($f, $origcoords)
+    elseif sf == "defaultfcn"
+        origcoords = rectangulardomain(complex(-2, -2), complex(2, 2), 0.2)
+        suite["grpf"][sf] = @benchmarkable grpf($f, $origcoords)
+    elseif sf == "wvgd"
+        origcoords = rectangulardomain(complex(1.0, -1.0), complex(2.5, 2.5), 0.5)
+        suite["grpf"][sf] = @benchmarkable grpf($f, $origcoords)
+    elseif sf == "graphenefunction"
+        origcoords = rectangulardomain(complex(-100, -100), complex(400, 400), 18)
+        suite["grpf"][sf] = @benchmarkable grpf($f, $origcoords)
+    end
+end
+
+# If a cache of tuned parameters already exists, use it, otherwise, tune and cache
+# the benchmark parameters. Reusing cached parameters is faster and more reliable
+# than re-tuning `suite` every time the file is included.
+paramspath = joinpath(dirname(@__FILE__), "params.json")
+
+if isfile(paramspath)
+    loadparams!(suite, BenchmarkTools.load(paramspath)[1], :evals);
+else
+    tune!(suite)
+    BenchmarkTools.save(paramspath, params(suite));
+end
+
+# run with a time limit of ~5 second per benchmark
+results = run(suite, verbose = true, seconds = 5)
+
+# Appends results into `paramspath`
+BenchmarkTools.save(paramspath, results)

benchmark/params.json

@@ -0,0 +1 @@
+[{"Julia":"1.5.0","BenchmarkTools":"0.4.3"},[["BenchmarkGroup",{"data":{"grpf":["BenchmarkGroup",{"data":{"graphenefunction":["BenchmarkTools.Trial",{"allocs":1685594,"gctimes":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.8377349e7,3.7560222e7,4.2090254e7,4.3536983e7,4.5636256e7,4.3935513e7,4.2781782e7,4.0985667e7,4.5994165e7,4.3518752e7,5.1209756e7,4.4080055e7,5.0555615e7,4.4950588e7,4.538121e7,4.4690217e7,2.5815729e7],"memory":35615056,"params":["BenchmarkTools.Parameters",{"gctrial":true,"time_tolerance":0.05,"samples":10000,"evals":1,"gcsample":false,"seconds":5.0,"overhead":0.0,"memory_tolerance":0.01}],"times":[1.16774699e8,1.1790765e8,1.18843719e8,1.19018573e8,1.19889117e8,1.20459466e8,1.23482436e8,1.25326429e8,1.27215843e8,1.29410009e8,1.73388478e8,2.00133859e8,2.01600198e8,2.06497644e8,2.0766166e8,2.10527016e8,2.11002776e8,2.11576493e8,2.12367266e8,2.14024589e8,2.15949301e8,2.16793587e8,2.17620736e8,2.19141054e8,2.2049842e8,2.20871796e8,2.44331003e8,2.50976914e8]}],"defaultfcn":["BenchmarkTools.Trial",{"allocs":939326,"gctimes":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.023543e7,3.4456552e7,3.5728176e7,3.9456359e7,4.1571941e7,4.2933843e7,3.708878e7,3.9650727e7,4.2477862e7,4.2892042e7,4.1435797e7,4.1050154e7,4.1954723e7,3.9864644e7,4.3373541e7,4.1779057e7,4.2542738e7,4.1369169e7,4.2410585e7],"memory":20342672,"params":["BenchmarkTools.Parameters",{"gctrial":true,"time_tolerance":0.05,"samples":10000,"evals":1,"gcsample":false,"seconds":5.0,"overhead":0.0,"memory_tolerance":0.01}],"times":[5.7249571e7,5.7596017e7,5.7714169e7,5.7857532e7,5.796645e7,5.8094101e7,5.8152668e7,5.8300313e7,5.8317658e7,5.8406451e7,5.853215e7,5.8622883e7,5.863337e7,5.8784439e7,5.8845108e7,5.88956e7,5.91483e7,5.9226895e7,5.9320294e7,5.9456249e7,5.9563889e7,5.9851044e7,6.0792737e7,6.1099997e7,6.2641904e7,6.3884481e7,6.4152613e7,6.4615093e7,6.5109376e7,6.5257594e7,6.5302257e7,6.6485915e7,6.6906795e7,6.9495708e7,1.25186411e8,1.26972144e8,1.34478052e8,1.41755302e8,1.45367022e8,1.46446274e8,1.49216159e8,1.49304989e8,1.49516083e8,1.51494799e8,1.51542085e8,1.52635021e8,1.52915057e8,1.54242468e8,1.5494753e8,1.56112041e8,1.57093894e8,1.57201147e8,1.59255604e8,1.66389965e8]}],"wvgd":["BenchmarkTools.Trial",{"allocs":1019469,"gctimes":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,2.9386304e7,0.0,3.4905534e7,3.3759077e7,3.9559143e7,3.9468545e7,4.0005239e7,3.9517808e7,4.0555033e7,3.679492e7,4.0279999e7,4.2299871e7,4.0045418e7,3.5973045e7,3.8485127e7],"memory":24507872,"params":["BenchmarkTools.Parameters",{"gctrial":true,"time_tolerance":0.05,"samples":10000,"evals":1,"gcsample":false,"seconds":5.0,"overhead":0.0,"memory_tolerance":0.01}],"times":[1.05196049e8,1.05203842e8,1.0589738e8,1.06068718e8,1.06112954e8,1.06348562e8,1.06733635e8,1.07191338e8,1.08141607e8,1.09699448e8,1.09705338e8,1.10162601e8,1.1109799e8,1.12140929e8,1.12545276e8,1.12922188e8,1.13028329e8,1.13709811e8,1.17297188e8,1.28822539e8,1.73592435e8,1.74473972e8,1.83528033e8,1.84760643e8,1.87161363e8,1.90208378e8,1.91212638e8,1.94663849e8,1.95658729e8,1.9620709e8,1.97058605e8,1.98850271e8,1.98901154e8,2.00208212e8,2.02481013e8]}],"simplefcn":["BenchmarkTools.Trial",{"allocs":1210968,"gctimes":[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,3.2871564e7,3.5685863e7,4.1620177e7,3.8835973e7,4.374455e7,4.4678978e7,5.0154919e7,4.4663906e7,4.3873183e7,4.276452e7,4.422872e7,3.9704931e7,3.9711808e7,4.5161195e7,4.0825662e7,4.2414777e7,5.0587504e7],"memory":26013056,"params":["BenchmarkTools.Parameters",{"gctrial":true,"time_tolerance":0.05,"samples":10000,"evals":1,"gcsample":false,"seconds":5.0,"overhead":0.0,"memory_tolerance":0.01}],"times":[8.3892557e7,8.4098241e7,8.4223144e7,8.4912725e7,8.5119866e7,8.5244104e7,8.5776601e7,8.5930871e7,8.6172936e7,8.6265951e7,8.7520456e7,8.947034e7,9.0291317e7,9.0718493e7,9.1043918e7,9.1314387e7,9.4306066e7,9.664579e7,9.7600447e7,1.20678702e8,1.33173146e8,1.61808386e8,1.70276365e8,1.7342738e8,1.74677113e8,1.77253928e8,1.8121091e8,1.81243803e8,1.8192631e8,1.82996581e8,1.83033048e8,1.83934326e8,1.8411772e8,1.84894951e8,1.85613949e8,1.87803731e8,1.89296369e8,2.12534728e8]}]},"tags":["functions"]}]},"tags":[]}]]]