Azure Workbook for R - Memoisation and Vectorization.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# R: Memoisation and Vectorization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Full of potential coding improvements, Efficient R Programming: A Practical Guide to Smarter Programming (https://www.goodreads.com/book/show/28646688-efficient-r-programming), the book makes two suggestions that are notable. Vectorization, explained here (http://www.noamross.net/blog/2014/4/16/vectorization-in-r--why.html) and here (http://alyssafrazee.com/2014/01/29/vectorization.html), and memoisation, caching prior results albeit with additional memory use, were relevant and significant. \n",
    "\n",
    "What follows is a demonstration of the speed improvements that might be achieved using these concepts."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set Up Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following code creates a slow function, memoises it, create a vectorized form of the slow function, and then memoises the vectorized form. In sections Pass 1 and Pass 2, you can see the result of the techniques against the original."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "SyntaxError",
     "evalue": "invalid syntax (<ipython-input-1-84e626264f6a>, line 3)",
     "traceback": [
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-1-84e626264f6a>\"\u001b[1;36m, line \u001b[1;32m3\u001b[0m\n\u001b[1;33m    monte_carlo = function(N) {\u001b[0m\n\u001b[1;37m                              ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "library(memoise)\n",
    "\n",
    "monte_carlo = function(N) {\n",
    "    hits = 0\n",
    "    for (i in seq_len(N)) {\n",
    "        u1 = runif(1)\n",
    "        u2 = runif(1)\n",
    "        if (u1 ^ 2 > u2)\n",
    "            hits = hits + 1\n",
    "        }\n",
    "    return(hits / N)\n",
    "}\n",
    "\n",
    "monte_carlo_memo <- memoise(monte_carlo)\n",
    "\n",
    "monte_carlo_vec <- function(N) mean(runif(N) ^ 2 > runif(N))\n",
    "\n",
    "monte_carlo_vec_memo <- memoise(monte_carlo_vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pass 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of the first pass shows that vectorization provides a vast improvement over a standard for loop, and that memoise provides little of an improvement over that. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'n' is not defined",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-2-11ebcd8f3a5b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mn\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[1;36m999999\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mplainFor\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmonte_carlo\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mmemoised\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmonte_carlo_memo\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mvectorised\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmonte_carlo_vec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mboth\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmonte_carlo_vec_memo\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'n' is not defined"
     ]
    }
   ],
   "source": [
    "n <- 999999\n",
    "plainFor <- system.time(monte_carlo(n))\n",
    "memoised <- system.time(monte_carlo_memo(n))\n",
    "vectorised <- system.time(monte_carlo_vec(n))\n",
    "both <- system.time(monte_carlo_vec_memo(n))\n",
    "\n",
    "result <- cbind(plainFor, memoised, vectorised, both)\n",
    "displayPass1 <- format(result, digits = 2, nsmall = 2)\n",
    "displayPass1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pass 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That said, on a a second pass over the same loops, memoisation is vastly faster, returning values in zero (0) seconds. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'plainFor' is not defined",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-3-a8ec04600910>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mplainFor\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmonte_carlo\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mmemoised\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmonte_carlo_memo\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mvectorised\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmonte_carlo_vec\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mboth\u001b[0m \u001b[1;33m<\u001b[0m\u001b[1;33m-\u001b[0m \u001b[0msystem\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmonte_carlo_vec_memo\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'plainFor' is not defined"
     ]
    }
   ],
   "source": [
    "plainFor <- system.time(monte_carlo(n))\n",
    "memoised <- system.time(monte_carlo_memo(n))\n",
    "vectorised <- system.time(monte_carlo_vec(n))\n",
    "both <- system.time(monte_carlo_vec_memo(n))\n",
    "\n",
    "result <- cbind(plainFor, memoised, vectorised, both)\n",
    "displayPass2 <- format(result, digits = 2, nsmall = 2)\n",
    "displayPass2"
   ]
  }
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