gao_implementation_scaling_comparison.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Internal performance comparison of GAlibrate's core genetic algorithm implementations\n",
    "\n",
    "In this notebook we will do some performance analysis and comparisons of the core genetic algorithms implemented in [GAlibrate](https://github.com/blakeaw/GAlibrate). GAlibrate has three implementations of the core genetic algorithm: Python-only, Numba-accelerated, and Cython-accelerated. We'll compare how each implementation compares when scaling the number of parameters (or dimensionality), population size, and the number of generations. We'll look at each in turn.\n",
    "\n",
    "To run this notebook we need to have galibrate installed along with both Numba and Cython, as well as pandas, matplotlib. The Python version used for this analysis was 3.7.4.\n",
    "\n",
    "First we'll do all our imports:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Non-galibrate imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "# Notebook magic to inline plots\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/blake/src/python/GAlibrate/galibrate/gao.py:10: RuntimeWarning: ------Running GAO with numba optimization.------\n",
      "  warnings.warn(\"------Running GAO with numba optimization.------\", RuntimeWarning)\n"
     ]
    }
   ],
   "source": [
    "# galibrate imports\n",
    "import galibrate\n",
    "from galibrate import gao\n",
    "from galibrate.sampled_parameter import SampledParameter\n",
    "# Manually import each of the run_gao modules -- normally galibrate does this internally\n",
    "# and automatically assigns the version based whether Numba and/or Cython are installed.\n",
    "# Python-only\n",
    "from galibrate import run_gao_py\n",
    "# Numba accelerated\n",
    "from galibrate import run_gao_numba\n",
    "# Cython accelerated -- uses pyximport\n",
    "import pyximport; pyximport.install(language_level=3)\n",
    "from galibrate import run_gao_cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model problem and fitness function\n",
    "\n",
    "For the purposes of this testing we'll use the Egg carton landscape from the [GAlibrate examples](https://github.com/blakeaw/GAlibrate/blob/master/examples/eggcarton/GAO_eggcarton.py). Parmeters will be defined on \\[0:10pi\\].\n",
    "\n",
    "Here is the fitness function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the fitness function (-loglikelihood of eggcarton)\n",
    "def fitness(theta):\n",
    "    chi = (np.cos(theta)).prod()\n",
    "    return (2. + chi)**5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling with the number of parameters (dimensionality)\n",
    "\n",
    "We'll start by examining the scaling with the number of parameters while holding the population size and number of generations fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the number of parameters (ndims), population size (popsize), and \n",
    "# number of generations (ngenerations)\n",
    "ndims = list([10, 50, 100, 500, 1000, 5000])\n",
    "popsize = 100\n",
    "ngenerations = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   n_dim  avg_time\n",
      "0     10  0.046661\n",
      "1     50  0.094814\n",
      "2    100  0.162354\n",
      "3    500  0.668255\n",
      "4   1000  1.389021\n",
      "5   5000  7.600903\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Python-only version \n",
    "gao.run_gao = run_gao_py\n",
    "timings = dict()\n",
    "timings['n_dim'] = list()\n",
    "timings['avg_time'] = list()\n",
    "# Loop over the dimensionality (number of parameters)\n",
    "for ndim in ndims:\n",
    "    timings['n_dim'].append(ndim)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, popsize, generations=ngenerations)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings['avg_time'].append(ti.average)\n",
    "timings = pd.DataFrame(timings)\n",
    "print(timings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   n_dim  avg_time\n",
      "0     10  0.033811\n",
      "1     50  0.023361\n",
      "2    100  0.028075\n",
      "3    500  0.093578\n",
      "4   1000  0.156955\n",
      "5   5000  0.805910\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Numba version \n",
    "gao.run_gao = run_gao_numba\n",
    "timings_n = dict()\n",
    "timings_n['n_dim'] = list()\n",
    "timings_n['avg_time'] = list()\n",
    "# Loop over the dimensionality (number of parameters)\n",
    "for ndim in ndims:\n",
    "    timings_n['n_dim'].append(ndim)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, popsize, generations=ngenerations)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings_n['avg_time'].append(ti.average)\n",
    "timings_n = pd.DataFrame(timings_n)\n",
    "print(timings_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   n_dim  avg_time\n",
      "0     10  0.029318\n",
      "1     50  0.028422\n",
      "2    100  0.035196\n",
      "3    500  0.102143\n",
      "4   1000  0.185692\n",
      "5   5000  0.901800\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Cython version \n",
    "gao.run_gao = run_gao_cython\n",
    "timings_c = dict()\n",
    "timings_c['n_dim'] = list()\n",
    "timings_c['avg_time'] = list()\n",
    "# Loop over the dimensionality (number of parameters)\n",
    "for ndim in ndims:\n",
    "    timings_c['n_dim'].append(ndim)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, popsize, generations=ngenerations)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings_c['avg_time'].append(ti.average)\n",
    "timings_c = pd.DataFrame(timings_c)\n",
    "print(timings_c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(timings['n_dim'].values, timings['avg_time'].values, label='Python')\n",
    "plt.plot(timings_n['n_dim'].values, timings_n['avg_time'].values, label='Numba')\n",
    "plt.plot(timings_c['n_dim'].values, timings_c['avg_time'].values, label='Cython')\n",
    "plt.xlabel(\"Number of parameters\")\n",
    "plt.ylabel(\"Average time (seconds)\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The run times appear to roughly scale linearily with number of parameters. It's clear that the Numba and Cython implementations have pretty similar performance, both outperforming the Python-only version. \n",
    "\n",
    "Now let's look at the relative performance (speedup factors) of the implementations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "py_o_n = timings['avg_time'].values/timings_n['avg_time'].values\n",
    "plt.plot(timings['n_dim'].values, py_o_n, label='Numba/Python')\n",
    "py_o_c = timings['avg_time'].values/timings_c['avg_time'].values\n",
    "plt.plot(timings_n['n_dim'].values, py_o_c, label='Cython/Python')\n",
    "c_o_n = timings_c['avg_time'].values/timings_n['avg_time'].values\n",
    "plt.plot(timings_c['n_dim'].values, c_o_n, label='Numba/Cython')\n",
    "plt.xlabel(\"Number of parameters\")\n",
    "plt.ylabel(\"Speedup Factor\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The speedup factors appear to roughly scale exponentially with the number of parameters. We can see that the Numba version has a little bit of performance advantage over the Cython implementation, but both approach an order of magnitude speedup over the Python-only implementation at the largest number of parameters tested here. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling with population size\n",
    "\n",
    "Now let's examine the scaling with the population size while holding the number of parameters and number of generations fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the number of parameters (ndim), population sizes (popsizes), and \n",
    "# number of generations (ngenerations)\n",
    "ndim = 100\n",
    "popsizes = list([10, 50, 100, 500, 1000, 5000, 10000, 20000])\n",
    "ngenerations = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   pop_size   avg_time\n",
      "0        10   0.022110\n",
      "1        50   0.096393\n",
      "2       100   0.184697\n",
      "3       500   0.885211\n",
      "4      1000   1.732032\n",
      "5      5000   9.317504\n",
      "6     10000  17.987358\n",
      "7     20000  35.292584\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Python-only version \n",
    "gao.run_gao = run_gao_py\n",
    "timings = dict()\n",
    "timings['pop_size'] = list()\n",
    "timings['avg_time'] = list()\n",
    "# Loop over the population sizes\n",
    "for ps in popsizes:\n",
    "    timings['pop_size'].append(ps)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, ps, generations=ngenerations)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings['avg_time'].append(ti.average)\n",
    "timings = pd.DataFrame(timings)\n",
    "print(timings)\n",
    "#gao.run_gao"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   pop_size  avg_time\n",
      "0        10  0.006087\n",
      "1        50  0.017009\n",
      "2       100  0.030592\n",
      "3       500  0.129576\n",
      "4      1000  0.257825\n",
      "5      5000  1.366818\n",
      "6     10000  2.653046\n",
      "7     20000  5.507251\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Numba version \n",
    "gao.run_gao = run_gao_numba\n",
    "timings_n = dict()\n",
    "timings_n['pop_size'] = list()\n",
    "timings_n['avg_time'] = list()\n",
    "# Loop over the population sizes\n",
    "for ps in popsizes:\n",
    "    timings_n['pop_size'].append(ps)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, ps, generations=ngenerations)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings_n['avg_time'].append(ti.average)\n",
    "timings_n = pd.DataFrame(timings_n)\n",
    "print(timings_n)\n",
    "#gao.run_gao"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   pop_size  avg_time\n",
      "0        10  0.007568\n",
      "1        50  0.022084\n",
      "2       100  0.037462\n",
      "3       500  0.162417\n",
      "4      1000  0.316073\n",
      "5      5000  1.624344\n",
      "6     10000  3.156744\n",
      "7     20000  6.309421\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Cython version \n",
    "gao.run_gao = run_gao_cython\n",
    "timings_c = dict()\n",
    "timings_c['pop_size'] = list()\n",
    "timings_c['avg_time'] = list()\n",
    "# Loop over the population sizes\n",
    "for ps in popsizes:\n",
    "    timings_c['pop_size'].append(ps)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, ps, generations=ngenerations)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings_c['avg_time'].append(ti.average)\n",
    "timings_c = pd.DataFrame(timings_c)\n",
    "print(timings_c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(timings['pop_size'].values, timings['avg_time'].values, label='Python')\n",
    "plt.plot(timings_n['pop_size'].values, timings_n['avg_time'].values, label='Numba')\n",
    "plt.plot(timings_c['pop_size'].values, timings_c['avg_time'].values, label='Cython')\n",
    "plt.xlabel(\"Population Size\")\n",
    "plt.ylabel(\"Average time (seconds)\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The run times appear to roughly scale linearily with number of parameters. The Numba and Cython implementations have pretty similar performance, both outperforming the Python-only version. \n",
    "\n",
    "Now let's look at the relative performance (speedup factors) of the implementations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "py_o_n = timings['avg_time'].values/timings_n['avg_time'].values\n",
    "plt.plot(timings['pop_size'].values, py_o_n, label='Numba/Python')\n",
    "py_o_c = timings['avg_time'].values/timings_c['avg_time'].values\n",
    "plt.plot(timings_n['pop_size'].values, py_o_c, label='Cython/Python')\n",
    "c_o_n = timings_c['avg_time'].values/timings_n['avg_time'].values\n",
    "plt.plot(timings_c['pop_size'].values, c_o_n, label='Numba/Cython')\n",
    "plt.xlabel(\"Population Size\")\n",
    "plt.ylabel(\"Speedup Factor\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The speedup factors appear to roughly scale exponentially with the population size, topping out around 6-7x and 5-6x for the Numba and Cython implementations, respectively. We can see that the Numba version has a little bit of performance advantage over the Cython implementation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling with the number of generations\n",
    "\n",
    "Finally, let's examine the scaling with the number of generations while holding the number of parameters and population size fixed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the number of parameters (ndim), population size (popsize), and \n",
    "# numbers of generations (ngenerations)\n",
    "ndim = 100\n",
    "popsize = 100\n",
    "ngenerations = list([10, 50, 100, 500])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   n_generations  avg_time\n",
      "0             10  0.040427\n",
      "1             50  0.171226\n",
      "2            100  0.328255\n",
      "3            500  1.695642\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Python-only version \n",
    "gao.run_gao = run_gao_py\n",
    "timings = dict()\n",
    "timings['n_generations'] = list()\n",
    "timings['avg_time'] = list()\n",
    "# Loop over the dimensionality (number of parameters)\n",
    "for ngen in ngenerations:\n",
    "    timings['n_generations'].append(ngen)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, popsize, generations=ngen)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings['avg_time'].append(ti.average)\n",
    "timings = pd.DataFrame(timings)\n",
    "print(timings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   n_generations  avg_time\n",
      "0             10  0.007827\n",
      "1             50  0.032107\n",
      "2            100  0.058829\n",
      "3            500  0.281847\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Numba version \n",
    "gao.run_gao = run_gao_numba\n",
    "timings_n = dict()\n",
    "timings_n['n_generations'] = list()\n",
    "timings_n['avg_time'] = list()\n",
    "# Loop over the dimensionality (number of parameters)\n",
    "for ngen in ngenerations:\n",
    "    timings_n['n_generations'].append(ngen)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, popsize, generations=ngen)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings_n['avg_time'].append(ti.average)\n",
    "timings_n = pd.DataFrame(timings_n)\n",
    "print(timings_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   n_generations  avg_time\n",
      "0             10  0.008799\n",
      "1             50  0.038928\n",
      "2            100  0.074576\n",
      "3            500  0.350769\n"
     ]
    }
   ],
   "source": [
    "# Manually set the run_gao version -- Cython version \n",
    "gao.run_gao = run_gao_cython\n",
    "timings_c = dict()\n",
    "timings_c['n_generations'] = list()\n",
    "timings_c['avg_time'] = list()\n",
    "# Loop over the dimensionality (number of parameters)\n",
    "for ngen in ngenerations:\n",
    "    timings_c['n_generations'].append(ngen)\n",
    "    sampled_parameters = [SampledParameter(name=i, loc=0.0, width=10.0*np.pi) for i in range(ndim)]\n",
    "    go = gao.GAO(sampled_parameters, fitness, popsize, generations=ngen)\n",
    "    #print(ndim, popsize, gen)\n",
    "    ti = %timeit -n 3 -r 2 -o -q go.run()\n",
    "    timings_c['avg_time'].append(ti.average)\n",
    "timings_c = pd.DataFrame(timings_c)\n",
    "print(timings_c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(timings['n_generations'].values, timings['avg_time'].values, label='Python')\n",
    "plt.plot(timings_n['n_generations'].values, timings_n['avg_time'].values, label='Numba')\n",
    "plt.plot(timings_c['n_generations'].values, timings_c['avg_time'].values, label='Cython')\n",
    "plt.xlabel(\"Number of Generations\")\n",
    "plt.ylabel(\"Average time (seconds)\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The run times appear to roughly scale linearily with number of generations. The Numba and Cython implementations have pretty similar performance, both outperforming the Python-only version. \n",
    "\n",
    "Now let's look at the relative performance (speedup factors) of the implementations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "py_o_n = timings['avg_time'].values/timings_n['avg_time'].values\n",
    "plt.plot(timings['n_generations'].values, py_o_n, label='Numba/Python')\n",
    "py_o_c = timings['avg_time'].values/timings_c['avg_time'].values\n",
    "plt.plot(timings_n['n_generations'].values, py_o_c, label='Cython/Python')\n",
    "c_o_n = timings_c['avg_time'].values/timings_n['avg_time'].values\n",
    "plt.plot(timings_c['n_generations'].values, c_o_n, label='Numba/Cython')\n",
    "plt.xlabel(\"Number of Generations\")\n",
    "plt.ylabel(\"Speedup Factor\")\n",
    "plt.legend(loc=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The speedup factors don't have as strong of dependence on the number of generations, staying around 5-6x and 4-5x for the Numba and Cython implementations, respectively. As in the other cases, we can see that the Numba version has a little bit of a performance advantage over the Cython implementation. And based on the other scaling results, the Numba and Cython implementations would likely offer a larger perfarmace advantage over the Python-only one if the number of parameters or population size were increased."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "The analysis here shows that the Numba and Cython versions can offer anywhere from about a 2-10 fold speed increase over the Python-only version dependent on the dimensionality of the problem (i.e., the number of parameters) and the choice of GA population size and number of generations (i.e., number of iterations); the benefit tends to increase as the aforementioned quantities increase. the  Additionally, this analysis shows that the Numba implementation offers slightly better performace than the Cython one.\n",
    "\n",
    "It is worth noting that here we only tested a single model system and fitness function. It would be interesting to test other models and fitness functions as well."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}