{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Random Sampling in Julia - speed check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Written in Julia 1.7.0\n",
    "\n",
    "using Random, Distributions, BenchmarkTools\n",
    "# See docs: http://juliastats.org/Distributions.jl/stable/starting/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set seed\n",
    "Random.seed!(123);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.4632513788889214"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# base Julia has rand() and randn()\n",
    "rand() # random [0, 1]\n",
    "randn() # random Normal(μ=0, σ=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "how long does it take to sample 1M from a normal distribution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 946 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m4.317 ms\u001b[22m\u001b[39m … \u001b[35m 10.960 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 25.03%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m4.923 ms               \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m5.282 ms\u001b[22m\u001b[39m ± \u001b[32m803.382 μs\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m5.40% ±  9.83%\n",
       "\n",
       "  \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▃\u001b[39m█\u001b[39m▂\u001b[39m█\u001b[34m▁\u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m▂\u001b[39m▃\u001b[39m▄\u001b[39m▅\u001b[39m▅\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m▆\u001b[39m▅\u001b[39m▇\u001b[39m▄\u001b[39m▃\u001b[32m▄\u001b[39m\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▃\u001b[39m▂\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▂\u001b[39m \u001b[39m▃\n",
       "  4.32 ms\u001b[90m         Histogram: frequency by time\u001b[39m        7.78 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m7.63 MiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m2\u001b[39m."
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sample from normal distribution\n",
    "@benchmark s = rand(Normal(5, 2), 10^6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is....really fast."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "how long does it take to sample 1M from a triangular distribution?\n",
    "\n",
    "*note: Triangular takes arguments (min, max, mode) whereas numpy took (min, mode, max)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 517 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m8.436 ms\u001b[22m\u001b[39m … \u001b[35m17.522 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 20.14%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m9.096 ms              \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m9.669 ms\u001b[22m\u001b[39m ± \u001b[32m 1.212 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m3.82% ±  7.18%\n",
       "\n",
       "  \u001b[39m \u001b[39m \u001b[39m \u001b[39m▃\u001b[39m▆\u001b[39m█\u001b[39m▂\u001b[34m▁\u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m▃\u001b[39m▄\u001b[39m▇\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m█\u001b[39m\u001b[39m▇\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[32m▃\u001b[39m\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▃\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▃\u001b[39m▂\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▁\u001b[39m▂\u001b[39m \u001b[39m▃\n",
       "  8.44 ms\u001b[90m        Histogram: frequency by time\u001b[39m        14.1 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m7.63 MiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m2\u001b[39m."
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark rand(TriangularDist(0, 5, 3), 10^6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So ~10ms vs python's 435 ms. Wow!\n",
    "\n",
    "Let's try 1M samples from a discrete distribution with 3 potential values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DiscreteNonParametric{Int64, Float64, Vector{Int64}, Vector{Float64}}(support=[0, 1, 2], p=[0.2, 0.7, 0.1])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = Distributions.DiscreteNonParametric([0, 1, 2], [0.2, 0.7, 0.1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: 397 samples with 1 evaluation.\n",
       " Range \u001b[90m(\u001b[39m\u001b[36m\u001b[1mmin\u001b[22m\u001b[39m … \u001b[35mmax\u001b[39m\u001b[90m):  \u001b[39m\u001b[36m\u001b[1m10.955 ms\u001b[22m\u001b[39m … \u001b[35m18.581 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmin … max\u001b[90m): \u001b[39m0.00% … 0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[34m\u001b[1mmedian\u001b[22m\u001b[39m\u001b[90m):     \u001b[39m\u001b[34m\u001b[1m12.150 ms              \u001b[22m\u001b[39m\u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmedian\u001b[90m):    \u001b[39m0.00%\n",
       " Time  \u001b[90m(\u001b[39m\u001b[32m\u001b[1mmean\u001b[22m\u001b[39m ± \u001b[32mσ\u001b[39m\u001b[90m):   \u001b[39m\u001b[32m\u001b[1m12.602 ms\u001b[22m\u001b[39m ± \u001b[32m 1.195 ms\u001b[39m  \u001b[90m┊\u001b[39m GC \u001b[90m(\u001b[39mmean ± σ\u001b[90m):  \u001b[39m2.94% ± 5.79%\n",
       "\n",
       "  \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m▁\u001b[39m \u001b[39m▄\u001b[39m█\u001b[39m▆\u001b[39m▄\u001b[39m \u001b[39m▂\u001b[34m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[32m \u001b[39m\u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \u001b[39m \n",
       "  \u001b[39m▂\u001b[39m▂\u001b[39m▁\u001b[39m▄\u001b[39m▅\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[39m█\u001b[34m▇\u001b[39m\u001b[39m▆\u001b[39m█\u001b[39m▅\u001b[39m▅\u001b[32m▆\u001b[39m\u001b[39m▅\u001b[39m▇\u001b[39m▅\u001b[39m▅\u001b[39m▄\u001b[39m▄\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▄\u001b[39m▅\u001b[39m▆\u001b[39m▄\u001b[39m▅\u001b[39m▂\u001b[39m▃\u001b[39m▄\u001b[39m▃\u001b[39m▄\u001b[39m▂\u001b[39m▂\u001b[39m▃\u001b[39m▂\u001b[39m▂\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▃\u001b[39m▂\u001b[39m▁\u001b[39m▂\u001b[39m▁\u001b[39m▂\u001b[39m▁\u001b[39m▃\u001b[39m▂\u001b[39m \u001b[39m▃\n",
       "  11 ms\u001b[90m           Histogram: frequency by time\u001b[39m        16.2 ms \u001b[0m\u001b[1m<\u001b[22m\n",
       "\n",
       " Memory estimate\u001b[90m: \u001b[39m\u001b[33m7.63 MiB\u001b[39m, allocs estimate\u001b[90m: \u001b[39m\u001b[33m7\u001b[39m."
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark rand(d, 10^6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Discrete distribution takes about 13 ms vs the 43 ms it took Python, still very impressive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bottom Line: Use Julia!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "file_extension": ".jl",
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