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genkuroki/MFmean by Julia.ipynb

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MFmean by Julia.ipynb
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MFmean by Julia.ipynb
{
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{
"metadata": {
"trusted": true
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"cell_type": "code",
"source": "versioninfo()",
"execution_count": 1,
"outputs": [
{
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"text": "Julia Version 1.1.0\nCommit 80516ca202 (2019-01-21 21:24 UTC)\nPlatform Info:\n OS: Windows (x86_64-w64-mingw32)\n CPU: Intel(R) Core(TM) i7-4770HQ CPU @ 2.20GHz\n WORD_SIZE: 64\n LIBM: libopenlibm\n LLVM: libLLVM-6.0.1 (ORCJIT, haswell)\nEnvironment:\n JULIA_CMDSTAN_HOME = C:\\CmdStan\n JULIA_NUM_THREADS = 4\n JULIA_PKGDIR = C:\\JuliaPkg\n",
"name": "stdout"
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{
"metadata": {
"trusted": true
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"cell_type": "code",
"source": "using Distributions\nusing Random: randn!\nusing RandomNumbers.Xorshifts\nconst XOROSHIRO128PLUS = Xoroshiro128Plus()\n\nusing Plots\nENV[\"PLOTS_TEST\"] = \"true\"\ngr()",
"execution_count": 2,
"outputs": [
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"data": {
"text/plain": "Plots.GRBackend()"
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"metadata": {
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"cell_type": "code",
"source": "function summary_MF(M, F)\n MM = M[.!(isnan.(M))]\n FF = F[.!(isnan.(F))]\n @show median(MM), median(FF)\n @show mean(MM), mean(FF)\n @show std(MM), std(FF)\n @show count(isnan.(M)), count(isnan.(F))\n @show count(M .> F)\n @show count(M .< F)\nend\n\nfunction plot_MF(M, F;\n bins=range(max(2.0, mean(dist)-4std(FF)), mean(dist)+4std(FF), length=50),\n figsize=(500, 300),\n kwargs...)\n MM = M[.!(isnan.(M))]\n FF = F[.!(isnan.(F))]\n histogram([MM, FF], label=[\"M\", \"F\"], alpha=0.7; bins=bins, size=figsize, kwargs...)\nend",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": "plot_MF (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
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"cell_type": "code",
"source": "function mfmean(; n=10^6, N=1000, p=0.3, t=2.0)\n Mmean = zeros(n)\n Fmean = zeros(n)\n M = zeros(N)\n F = zeros(N)\n for i in 1:n\n randn!(M)\n randn!(F)\n f = F[F .> t]\n Mmean[i] = mean(M[M .> t])\n Fmean[i] = mean(@view f[1:round(Int, length(f)*p)])\n end\n Mmean, Fmean\nend\n\n@time M, F = mfmean(; n=10^6, N=1000, p=0.3, t=2.0)\nsummary_MF(M, F)\nplot_MF(M, F, bins=range(2.0, 3.0, length=50))",
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"outputs": [
{
"output_type": "stream",
"text": " 29.046963 seconds (13.98 M allocations: 9.127 GiB, 4.87% gc time)\n(median(MM), median(FF)) = (2.3692721938100814, 2.3600456745956366)\n(mean(MM), mean(FF)) = (2.3731864361142145, 2.3732336567502634)\n(std(MM), std(FF)) = (0.07253761787211951, 0.13238713490179752)\n(count(isnan.(M)), count(isnan.(F))) = (0, 0)\ncount(M .> F) = 524741\ncount(M .< F) = 475259\n",
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"source": "function mfmean_Xoroshiro128Plus(; n=10^6, N=1000, p=0.3, t=2.0)\n Mmean = zeros(n)\n Fmean = zeros(n)\n M = zeros(N)\n F = zeros(N)\n for i in 1:n\n randn!(XOROSHIRO128PLUS, M)\n randn!(XOROSHIRO128PLUS, F)\n f = F[F .> t]\n Mmean[i] = mean(M[M .> t])\n Fmean[i] = mean(@view f[1:round(Int, length(f)*p)])\n end\n Mmean, Fmean\nend\n\n@time M, F = mfmean_Xoroshiro128Plus(; n=10^6, N=1000, p=0.3, t=2.0)\nsummary_MF(M, F)\nplot_MF(M, F, bins=range(2.0, 3.0, length=50))",
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"text": " 15.061378 seconds (13.26 M allocations: 9.092 GiB, 7.26% gc time)\n(median(MM), median(FF)) = (2.369391029041538, 2.3600583244468893)\n(mean(MM), mean(FF)) = (2.3732821067912475, 2.3732173869949995)\n(std(MM), std(FF)) = (0.07254981589802849, 0.13262921798920727)\n(count(isnan.(M)), count(isnan.(F))) = (0, 0)\ncount(M .> F) = 524674\ncount(M .< F) = 475326\n",
"name": "stdout"
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"source": "function mfmean_Xoroshiro128Plus_Ver2(; n=10^6, N=1000, p=0.3, t=2.0)\n Mmean = zeros(n)\n Fmean = zeros(n)\n M = zeros(N)\n F = zeros(N)\n for i in 1:n\n randn!(XOROSHIRO128PLUS, M)\n randn!(XOROSHIRO128PLUS, F)\n Mmean[i] = mean(M[k] for k in 1:N if M[k] ≥ t)\n m = 0\n for k in 1:N\n if F[k] ≥ t\n m += 1\n F[m] = F[k]\n end\n end\n Fmean[i] = mean(F[k] for k in 1:round(Int, p*m))\n end\n Mmean, Fmean\nend\n\n@time M, F = mfmean_Xoroshiro128Plus_Ver2(; n=10^6, N=1000, p=0.3, t=2.0)\nsummary_MF(M, F)\nplot_MF(M, F, bins=range(2.0, 3.0, length=50))",
"execution_count": 6,
"outputs": [
{
"output_type": "stream",
"text": " 10.144046 seconds (6.18 M allocations: 176.866 MiB, 0.26% gc time)\n(median(MM), median(FF)) = (2.369333090186332, 2.3598376135652868)\n(mean(MM), mean(FF)) = (2.373258705036385, 2.3731435435046486)\n(std(MM), std(FF)) = (0.07251480489113193, 0.13242613895355249)\n(count(isnan.(M)), count(isnan.(F))) = (0, 0)\ncount(M .> F) = 525047\ncount(M .< F) = 474953\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 6,
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"source": "function sim_tnd_MF(; t=2.0, N=1000, p=0.3, n=10^4)\n M = zeros(n)\n F = zeros(n)\n tnd = TruncatedNormal(0.0, 1.0, t, Inf)\n p_bin = ccdf(Normal(0.0, 1.0), t)\n bin = Binomial(N, p_bin)\n for i in 1:n\n M[i] = mean(rand(tnd, rand(bin)))\n F[i] = mean(rand(tnd, round(Int, p*rand(bin))))\n end\n tnd, M, F\nend\nsim_tnd_MF(n=10^3) # compile\nGC.gc()\n\n@time tnd, M, F = sim_tnd_MF(t=2.0, N=1000, p=0.3, n=10^6)\nsummary_MF(M, F)\nplot_MF(M, F, bins=range(2.0, 3.0, length=50))",
"execution_count": 7,
"outputs": [
{
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"text": " 2.736865 seconds (2.02 M allocations: 403.416 MiB, 1.34% gc time)\n(median(MM), median(FF)) = (2.3693389346883755, 2.360191465060133)\n(mean(MM), mean(FF)) = (2.373175129868477, 2.373357467179366)\n(std(MM), std(FF)) = (0.07249434710518572, 0.13247871435315237)\n(count(isnan.(M)), count(isnan.(F))) = (0, 0)\ncount(M .> F) = 524058\ncount(M .< F) = 475942\n",
"name": "stdout"
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{
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"source": "function sim_tnd_MF_Ver2(; t=2.0, N=1000, p=0.3, n=10^4)\n M = zeros(n)\n F = zeros(n)\n tnd = TruncatedNormal(0.0, 1.0, t, Inf)\n p_bin = ccdf(Normal(0.0, 1.0), t)\n bin = Binomial(N, p_bin)\n for i in 1:n\n M[i] = mean(k->rand(tnd), 1:rand(bin))\n F[i] = mean(k->rand(tnd), 1:round(Int, p*rand(bin)))\n end\n tnd, M, F\nend\nsim_tnd_MF_Ver2(n=10^3) # compile\nGC.gc()\n\n@time tnd, M, F = sim_tnd_MF_Ver2(t=2.0, N=1000, p=0.3, n=10^6)\nsummary_MF(M, F)\nplot_MF(M, F, bins=range(2.0, 3.0, length=50))",
"execution_count": 8,
"outputs": [
{
"output_type": "stream",
"text": " 2.045361 seconds (9.46 k allocations: 15.780 MiB)\n(median(MM), median(FF)) = (2.369385472835822, 2.3600769716008676)\n(mean(MM), mean(FF)) = (2.3732029684624014, 2.373334869690733)\n(std(MM), std(FF)) = (0.07249116004204485, 0.13263651358155584)\n(count(isnan.(M)), count(isnan.(F))) = (0, 0)\ncount(M .> F) = 524815\ncount(M .< F) = 475185\n",
"name": "stdout"
},
{
"output_type": "execute_result",
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"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "function simpi(n)\n s = 0\n for i in 1:n\n s += ifelse(rand()^2 + rand()^2 < 1.0, 1, 0)\n end\n 4s/n\nend\nsimpi(10^5) # compile\n\n@time simpi(10^7)",
"execution_count": 9,
"outputs": [
{
"output_type": "stream",
"text": " 0.038209 seconds (1.93 k allocations: 115.887 KiB)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 9,
"data": {
"text/plain": "3.1421304"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@time simpi(10^8)",
"execution_count": 10,
"outputs": [
{
"output_type": "stream",
"text": " 0.356153 seconds (1.93 k allocations: 115.887 KiB)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 10,
"data": {
"text/plain": "3.14132636"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@time simpi(10^9)",
"execution_count": 11,
"outputs": [
{
"output_type": "stream",
"text": " 3.792615 seconds (6 allocations: 192 bytes)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 11,
"data": {
"text/plain": "3.141545184"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "function simpi_Xoroshiro128Plus(n)\n s = 0\n for i in 1:n\n s += ifelse(rand(XOROSHIRO128PLUS)^2 + rand(XOROSHIRO128PLUS)^2 < 1.0, 1, 0)\n end\n 4s/n\nend\nsimpi_Xoroshiro128Plus(10^5) # compile\n\n@time simpi_Xoroshiro128Plus(10^7)",
"execution_count": 12,
"outputs": [
{
"output_type": "stream",
"text": " 0.061850 seconds (6 allocations: 192 bytes)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 12,
"data": {
"text/plain": "3.140606"
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"metadata": {}
}
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},
{
"metadata": {
"trusted": true
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"cell_type": "code",
"source": "@time simpi_Xoroshiro128Plus(10^8)",
"execution_count": 13,
"outputs": [
{
"output_type": "stream",
"text": " 0.622216 seconds (6 allocations: 192 bytes)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 13,
"data": {
"text/plain": "3.14168644"
},
"metadata": {}
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]
},
{
"metadata": {
"trusted": true
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"cell_type": "code",
"source": "@time simpi_Xoroshiro128Plus(10^9)",
"execution_count": 14,
"outputs": [
{
"output_type": "stream",
"text": " 6.105230 seconds (6 allocations: 192 bytes)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 14,
"data": {
"text/plain": "3.141479288"
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"cell_type": "code",
"source": "simpi_count(n) = 4count(rand(n).^2 .+ rand(n).^2 .< 1.0)/n\nsimpi_count(10^5) # compile\n\n@time simpi_count(10^7)",
"execution_count": 15,
"outputs": [
{
"output_type": "stream",
"text": " 0.191046 seconds (16 allocations: 153.785 MiB, 55.34% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 15,
"data": {
"text/plain": "3.1410048"
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"metadata": {}
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]
},
{
"metadata": {
"trusted": true
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"cell_type": "code",
"source": "@time simpi_count(10^8)",
"execution_count": 16,
"outputs": [
{
"output_type": "stream",
"text": " 1.045771 seconds (16 allocations: 1.502 GiB, 18.86% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 16,
"data": {
"text/plain": "3.14158204"
},
"metadata": {}
}
]
},
{
"metadata": {
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"source": "simpi_Xoroshiro128Plus_count(n) = 4count(rand(XOROSHIRO128PLUS,n).^2 .+ rand(XOROSHIRO128PLUS,n).^2 .< 1.0)/n\nsimpi_Xoroshiro128Plus_count(10^5) # compile\n\n@time simpi_Xoroshiro128Plus_count(10^7)",
"execution_count": 17,
"outputs": [
{
"output_type": "stream",
"text": " 0.327133 seconds (16 allocations: 153.785 MiB, 70.27% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 17,
"data": {
"text/plain": "3.1412792"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "@time simpi_Xoroshiro128Plus_count(10^8)",
"execution_count": 18,
"outputs": [
{
"output_type": "stream",
"text": " 1.168187 seconds (16 allocations: 1.502 GiB, 19.40% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 18,
"data": {
"text/plain": "3.141661"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "",
"execution_count": null,
"outputs": []
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