Basic vectorization and distributed computation (Numpy and Dask and Numba).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: basic vectorization and distributed computation\n",
    "\n",
    "Loops are fast, as fast as your CPU, but they often only use a little part of the available bandwith/flow rate so to speak. \n",
    "\n",
    "Vectorized approaches try to frame problems so the number of calculations which can be done in one iteration aim to be as large, or larger than the capacity of the CPU.\n",
    "\n",
    "Distributed computing (clusters) allows you to use multiple cores, possibly other machines and CGUs.\n",
    "\n",
    "Here is the difference in performance for a popular question: how to calculate pi using a monte carlo simulation. \n",
    "\n",
    "The algorithm is easy to understand, and inefficient: a perfect example to demonstrate the difference in computing power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from dask import delayed\n",
    "from dask.distributed import Client, LocalCluster\n",
    "from time import sleep\n",
    "\n",
    "# graphviz for visuals \n",
    "import os\n",
    "os.environ[\"PATH\"] += os.pathsep + 'C:/Program Files (x86)/Graphviz2.38/bin/'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Non vectorized approach\n",
    "\n",
    "The default python sum uses iteration = a loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def pi_1(accuracy):\n",
    "    v = np.random.rand(accuracy)**2 + np.random.rand(accuracy)**2 < 1\n",
    "    return 4*sum(v) / accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.11 s per loop\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.14956"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%timeit -n1 pi_1(10**5)\n",
    "pi_1(10**5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Okak, it gets an answer.\n",
    "\n",
    "### Numpy vectorized\n",
    "\n",
    "- Try to avoid any loop where possible. \n",
    "- Rephrase command and control statements (if else) as matrix dot multiplications, additions, ...\n",
    "\n",
    "In this case replacing the sum by np.sum suffices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 8.7 ms per loop\n",
      "1 loop, best of 3: 937 ms per loop\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3.1424264"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def pi_2(accuracy):\n",
    "    c = np.sum(np.random.rand(accuracy)**2 +\n",
    "               np.random.rand(accuracy)**2\n",
    "               < 1)\n",
    "    return 4*c / accuracy\n",
    "\n",
    "%timeit -n1 pi_2(10**5)\n",
    "%timeit -n1 pi_2(10**7)\n",
    "pi_2(10**7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thats about a **100x** as fast. At this point the generation of the random arrays has become the most costly part of the calculation.\n",
    "\n",
    "### Using Dask with a scheduler, no clients.\n",
    "\n",
    "After vectorization, you're all set and ready to go to use more cores, GPUs, [machines](https://www.raspberrypi.org/products/), ... or some cloud. These gains are smaller, and more costly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Same as before\n",
      "1 loop, best of 3: 937 ms per loop\n",
      "\n",
      "Same as before, with overhead\n",
      "1 loop, best of 3: 970 ms per loop\n",
      "\n",
      "Same as before, using the default scheduler\n",
      "1 loop, best of 3: 660 ms per loop\n"
     ]
    }
   ],
   "source": [
    "def pi_3(accuracy,n):\n",
    "    q = accuracy//n\n",
    "    graph = average([step(accuracy//n) for _ in range(n)],n)\n",
    "    return graph.compute()\n",
    "\n",
    "@delayed\n",
    "def step(accuracy):\n",
    "    c = np.sum(np.random.rand(accuracy)**2+\n",
    "               np.random.rand(accuracy)**2\n",
    "               < 1.0)\n",
    "    return 4*c / accuracy\n",
    "\n",
    "@delayed\n",
    "def average(args,n):\n",
    "    return sum(args)/n\n",
    "\n",
    "problem_size = 10**7\n",
    "cores = 4\n",
    "\n",
    "print('Same as before')\n",
    "%timeit -n1 pi_2(problem_size)\n",
    "print('\\nSame as before, with overhead')\n",
    "%timeit -n1 pi_3(problem_size,1)\n",
    "print('\\nSame as before, using the default scheduler')\n",
    "%timeit -n1 pi_3(problem_size,cores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still no C, but getting more decent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using a scheduler and dedicated workers\n",
    "\n",
    "- Using a cluster scheduler incurs some cost, try to use tasks > 100ms.\n",
    "- Launching clients takes some time. \n",
    " There is some overhead, but in many cases it's easier to just leave them running.\n",
    "- Many tasks can be linked to a cluster.\n",
    "- Should be faster using unix forks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 21.4 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "cluster = LocalCluster(n_workers=4,threads_per_worker=4)\n",
    "client = Client(cluster)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Client: scheduler='tcp://127.0.0.1:57446' processes=4 cores=16>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "client"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 554 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit -n10 pi_3(problem_size-1,cores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note there is only a limited gain compared to the vectorized approach.\n",
    "\n",
    "### Just a bit larger"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 1: 59.3 s per loop\n",
      "1 loop, best of 1: 23.4 s per loop\n",
      "1 loop, best of 1: 14.9 s per loop\n",
      "1 loop, best of 1: 9.85 s per loop\n"
     ]
    }
   ],
   "source": [
    "problem_size = 2*10**8\n",
    "cores = 4\n",
    "\n",
    "%timeit -n1 -r1 pi_2(problem_size)\n",
    "%timeit -n1 -r1 pi_3(problem_size,1)\n",
    "%timeit -n1 -r1 pi_3(problem_size,cores)\n",
    "%timeit -n1 -r1 pi_3(problem_size,cores**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, my CPU should have been wide awake at this point. Still a **3x** increase compared to vanilla numpy on my humble machine.\n",
    "\n",
    "### Visualize\n",
    "\n",
    "You can see what is happeing: using the delayed doesn't compute, but creates a task plan. The compute() call gives this structure to the scheduler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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7tXv3bq1evfqCn1dPT4+8vMbXVOqSkhL5+/v3C4BKSkqUnp7er3PpUunp6ZGP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\nDS4uLiTglkM3btxAamrqoE3VA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ebNm6W+vt7M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\nVaoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def pi_3(accuracy,n):\n",
    "    q = accuracy//n\n",
    "    graph = average([step(accuracy//n) for _ in range(n)],n)\n",
    "    return graph\n",
    "\n",
    "graph = pi_3(problem_size,cores**2)\n",
    "graph.visualize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1415714799999996"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph.compute()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, i hope you've learned some things today, i did. \n",
    "\n",
    "- no GIL helps, but it's a poot substiture for [a better algorithm](https://stackoverflow.com/questions/19/what-is-the-fastest-way-to-get-the-value-of-%CF%80).\n",
    "- Vectorization is genuinely \"awesome\", and a good first step toward distributed computations.\n",
    "- Distributed computations can only yield a few power of 2.\n",
    "\n",
    "Inspired by [this reddit post](https://old.reddit.com/r/learnpython/comments/ahy84c/can_i_make_estimating_pi_with_the_monte_carlo/): Thanks u\\ikar1234.\n",
    "\n",
    "### Bonus unsing Numba\n",
    "\n",
    "Thanks u\\DiogenicOrder\n",
    "\n",
    "Boilerplate demo from site"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import jit\n",
    "import random\n",
    "\n",
    "@jit(nopython=True)\n",
    "def monte_carlo_pi(nsamples):\n",
    "    acc = 0\n",
    "    for i in range(nsamples):\n",
    "        x = random.random()\n",
    "        y = random.random()\n",
    "        if (x**2 + y**2) < 1.0:\n",
    "            acc += 1\n",
    "    return 4.0 * acc / nsamples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.1417957"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monte_carlo_pi(2*10**8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 1: 8.13 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1 monte_carlo_pi(problem_size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I notice only one core is used, meaning some dask could be used?"
   ]
  }
 ],
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