notes/execution-time.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Timing Python code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(n):\n",
    "    a = 0\n",
    "    for i in range(100_000 * n):\n",
    "        a += i\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 175 ms, sys: 4.38 ms, total: 180 ms\n",
      "Wall time: 181 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4499998500000"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time f(30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# also demos use of varargs!\n",
    "import time\n",
    "def gettime(f, *args):\n",
    "    \"Return time in seconds; %time, %timeit don't work in functions so we write our own\"\n",
    "    t0 = time.time()\n",
    "    f(*args)\n",
    "    t1 = time.time()\n",
    "    return t1 - t0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.182s\n"
     ]
    }
   ],
   "source": [
    "t = gettime(f, 30) # call f(30)\n",
    "print(f\"{t:.3f}s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Profiling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " "
     ]
    },
    {
     "data": {
      "text/plain": [
       "         24 function calls in 3.057 seconds\n",
       "\n",
       "   Ordered by: internal time\n",
       "\n",
       "   ncalls  tottime  percall  cumtime  percall filename:lineno(function)\n",
       "       20    3.057    0.153    3.057    0.153 <ipython-input-17-4989738166fa>:6(f)\n",
       "        1    0.000    0.000    3.057    3.057 <ipython-input-17-4989738166fa>:1(g)\n",
       "        1    0.000    0.000    3.057    3.057 {built-in method builtins.exec}\n",
       "        1    0.000    0.000    3.057    3.057 <string>:1(<module>)\n",
       "        1    0.000    0.000    0.000    0.000 {method 'disable' of '_lsprof.Profiler' objects}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def g(n):\n",
    "    for i in range(20):\n",
    "        f(n)\n",
    "    return None\n",
    "    \n",
    "def f(n):\n",
    "    a = 0\n",
    "    for i in range(100_000 * n):\n",
    "        a += i\n",
    "    return a\n",
    "\n",
    "# in the output look for calls to f and g:\n",
    "# <ipython-input-10-f95a342f71e7>:4(f)\n",
    "# and\n",
    "# <ipython-input-10-f95a342f71e7>:1(g)\n",
    "%prun g(30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting time vs work\n",
    "\n",
    "Let's compute and plot how long something takes for a variety of input sizes with:\n",
    "\n",
    "```python\n",
    "times = [gettime(f, i) for i in range(1,n,step)]\n",
    "```\n",
    "\n",
    "The visualization will give us an idea of whether it's linear or quadratic etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "def showtime(f, n, step=1):\n",
    "    times = [gettime(f, i) for i in range(1,n,step)]\n",
    "    plt.figure(figsize=(4,3))\n",
    "    plt.plot(range(1,n,step), times, '.', color='#fdae61', alpha=.9, markersize=15, markeredgewidth=.5, markeredgecolor='black')\n",
    "    plt.xlabel(\"Problem size\")\n",
    "    plt.ylabel(\"Time in seconds\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
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       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 288x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def g(n):\n",
    "    a = 0\n",
    "    for i in range(10*n):\n",
    "        zeroes = [0 for j in range(i)]\n",
    "        a += len(zeroes)\n",
    "    return a\n",
    "\n",
    "showtime(g,400,step=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Misc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 5\n"
     ]
    }
   ],
   "source": [
    "def log2(n):\n",
    "    if n <= 1:\n",
    "        return 0\n",
    "    count = 0\n",
    "    while n > 0:\n",
    "        n = n//2\n",
    "        count += 1\n",
    "    return count-1\n",
    "print( log2(2), log2(32) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Created `%mytime` as an alias for `%timeit -n 1 -r 5`.\n"
     ]
    }
   ],
   "source": [
    "# Define macro %mytime to run something once and return a TimeitResult object\n",
    "%alias_magic mytime --line timeit -p \"-n 1 -r 5\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "847 ns ± 463 ns per loop (mean ± std. dev. of 5 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%mytime log2(32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.05 µs ± 444 ns per loop (mean ± std. dev. of 5 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%mytime log2(1000)"
   ]
  }
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