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probability of existsgap in circle dist.ipynb
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{
"cells": [
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "using Random\n\nfunction randsimplex!(x)\n x[end] = 1\n rand!(@view(x[1:end-1]))\n sort!(@view(x[1:end-1]))\n @view(x[2:end]) .= @view(x[2:end]) .- @view(x[1:end-1])\n x\nend\n\nfunction existsgap(x, p)\n for i in 2:lastindex(x)-1\n x[i] ≥ p && return true\n end\n x[1] + x[end] ≥ p && return true\n false\nend\n\nfunction calcprob(n, p; N=10^6)\n x = Array{Float64,1}(undef, n+1)\n c = 0 \n for i in 1:N\n randsimplex!(x)\n c += ifelse(existsgap(x, p), 1, 0)\n end\n c/N\nend\n\nexactprob(n, p) = n*(1-p)^(n-1)",
"execution_count": 1,
"outputs": [
{
"output_type": "execute_result",
"execution_count": 1,
"data": {
"text/plain": "exactprob (generic function with 1 method)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p = 0.75\nn = 2\n@time calcprob(n, p), exactprob(n, p)",
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"text": " 0.818145 seconds (7.99 M allocations: 411.982 MiB, 15.03% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 2,
"data": {
"text/plain": "(0.499822, 0.5)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p = 0.75\nn = 3\n@time calcprob(n, p), exactprob(n, p)",
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": " 0.277388 seconds (7.00 M allocations: 381.470 MiB, 11.41% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 3,
"data": {
"text/plain": "(0.187812, 0.1875)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p = 0.75\nn = 4\n@time calcprob(n, p), exactprob(n, p)",
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"text": " 0.298302 seconds (7.00 M allocations: 381.470 MiB, 9.83% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 4,
"data": {
"text/plain": "(0.062335, 0.0625)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "p = 0.75\nn = 5\n@time calcprob(n, p), exactprob(n, p)",
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"text": " 0.306866 seconds (7.00 M allocations: 396.729 MiB, 7.98% gc time)\n",
"name": "stdout"
},
{
"output_type": "execute_result",
"execution_count": 5,
"data": {
"text/plain": "(0.019682, 0.01953125)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "using PyPlot\np = 0.75\nnmax = 10\nns = 1:nmax\nsol_exact = exactprob.(ns, p)\n@time sol_approx = calcprob.(ns, p)\n@show sol_exact\n@show sol_approx;",
"execution_count": 6,
"outputs": [
{
"output_type": "stream",
"text": " 3.648384 seconds (68.43 M allocations: 3.760 GiB, 11.67% gc time)\nsol_exact = [1.0, 0.5, 0.1875, 0.0625, 0.0195313, 0.00585938, 0.00170898, 0.000488281, 0.000137329, 3.8147e-5]\nsol_approx = [1.0, 0.500896, 0.18729, 0.062311, 0.019535, 0.00588, 0.0017, 0.000498, 0.000177, 5.0e-5]\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "figure(figsize=(6,3))\nplot(ns, log.(sol_exact), label=\"\\$n(1-p)^{n-1}\\$\")\nplot(ns, log.(sol_approx), label=\"simulation\", ls=\"dashed\")\nlegend()\ngrid(ls=\":\")\nxlabel(\"n\")\nylabel(\"log(probability)\")\ntitle(\"log of probabilities, \\$p = $p\\$\");",
"execution_count": 7,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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",
"text/plain": "Figure(PyObject <Figure size 600x300 with 1 Axes>)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "using PyPlot\np = 0.6\nnmax = 10\nns = 1:nmax\nsol_exact = exactprob.(ns, p)\n@time sol_approx = calcprob.(ns, p)\n@show sol_exact\n@show sol_approx;",
"execution_count": 8,
"outputs": [
{
"output_type": "stream",
"text": " 3.462290 seconds (68.00 M allocations: 3.740 GiB, 13.33% gc time)\nsol_exact = [1.0, 0.8, 0.48, 0.256, 0.128, 0.06144, 0.028672, 0.0131072, 0.00589824, 0.00262144]\nsol_approx = [1.0, 0.799721, 0.479937, 0.256679, 0.12777, 0.061124, 0.028463, 0.013003, 0.005813, 0.002615]\n",
"name": "stdout"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "figure(figsize=(6,3))\nplot(ns, log.(sol_exact), label=\"\\$n(1-p)^{n-1}\\$\")\nplot(ns, log.(sol_approx), label=\"simulation\", ls=\"dashed\")\nlegend()\ngrid(ls=\":\")\nxlabel(\"n\")\nylabel(\"log(probability)\")\ntitle(\"log of probabilities, \\$p = $p\\$\");",
"execution_count": 9,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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",
"text/plain": "Figure(PyObject <Figure size 600x300 with 1 Axes>)"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "",
"execution_count": null,
"outputs": []
}
],
"metadata": {
"kernelspec": {
"name": "julia-1.0",
"display_name": "Julia 1.0.3",
"language": "julia"
},
"_draft": {
"nbviewer_url": "https://gist.github.com/20f00518c2759ea4fa459623ff06dd4e"
},
"language_info": {
"mimetype": "application/julia",
"file_extension": ".jl",
"version": "1.0.3",
"name": "julia"
},
"gist": {
"id": "20f00518c2759ea4fa459623ff06dd4e",
"data": {
"description": "probability of existsgap in circle dist.ipynb",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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