ReCoDE_MCMCFF/learning/01 Introduction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0aadee51-c8d7-4b72-b281-bf2daca49811",
   "metadata": {
    "tags": []
   },
   "source": [
    "<h1 align=\"center\">Markov Chain Monte Carlo for fun and profit</h1>\n",
    "<h1 align=\"center\"> 🎲 ⛓️ 👉 🧪 </h1>\n",
    "\n",
    "Hello and welcome to the documentation for MCMCFF! These notebooks will guide you through the process of writing a medium sized scientific software project, discussing the decision and tradeoffs made along the way.\n",
    "\n",
    "## Setting up your environment\n",
    "\n",
    "It's strongly encouraged that you follow along this notebook in an enviroment where you can run the cells yourself and change them. You can either clone this git repository and run the cells in a python environment on your local machine, or if you for some reason can't do that (because you're an a phone or tablet for instance) you can instead open this notebook in [binder](link)\n",
    "\n",
    "I would also suggest you setup a python environment just for this. You can use your preferred method to do this, but I will recomend `conda` because it's both what I currently use and what is recommeded by Imperial: LINK \n",
    "\n",
    "```bash\n",
    "#make a new conda environment named recode, with python 3.9 and the packages in requirements.txt\n",
    "conda env create --name recode  python=3.9 --file requirements.txt\n",
    "\n",
    "#activate the environment\n",
    "conda activate recode\n",
    "```\n",
    "\n",
    "## The Problem\n",
    "\n",
    "So without further ado lets talk about the problem we'll be working on, you don't necessaryily need to understand the full details of this to learn the important lessons but I will give a quick summary here. We want to simulate a physical model called the **Ising model**, which is famous in physics because it's about the simplest thing you can come up with that displays a phase transition, a special kind of shift between two different behaviours."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2e5299a-5e20-417f-a62e-ce47d018d542",
   "metadata": {},
   "source": [
    "I'm going to weave exposition and code here so don't mind if I just take a moment to impor some packages and do some housekeeping:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ee600e16-506b-4676-8d84-16b415338191",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# This loads some custom styles for matplotlib\n",
    "import json, matplotlib\n",
    "\n",
    "with open(\"assets/matplotlibrc.json\") as f:\n",
    "    matplotlib.rcParams.update(json.load(f))\n",
    "\n",
    "np.random.seed(\n",
    "    42\n",
    ")  # This makes our random numbers reproducable when the notebook is rerun in order"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e52245f1-8ecc-45f1-8d52-337916b0ce7c",
   "metadata": {},
   "source": [
    "We're going to be working with arrays of numbers so it will make sense to work with `Numpy` and we'll also want to plot things, the standard choice for this is `matplotlib`, though there are other options, `pandas` and `plotly` being notable ones.\n",
    "\n",
    "Let me quickly plot something to aid the imagination:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7b05be8f-9edb-4742-bbfc-e892cc09b82b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state = np.random.choice([-1, 1], size=(100, 100))\n",
    "\n",
    "\n",
    "def show_state(state, ax=None):\n",
    "    if ax is None:\n",
    "        f, ax = plt.subplots()\n",
    "    ax.matshow(state, cmap=\"Greys\", vmin=-1, vmax=1)\n",
    "    ax.set(xticks=[], yticks=[])\n",
    "\n",
    "\n",
    "show_state(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a919be9-2737-4d79-9607-4daf3b457364",
   "metadata": {},
   "source": [
    "In my head, the Ising model is basically all about peer pressure. You're a tiny creature and you live in a little world where you can only be one of two things, up/down, left/right, in/out doesn't matter. \n",
    "\n",
    "But what *does matter* is that you're doing the same thing as you're neighbours. We're going to visualise this with images like the above, representing the two different camps, though at the moment what I've plotted is random, there's no peer pressure going on yet.\n",
    "\n",
    "The way that a physicist would quantify this peer pressure is to assign a number to each state, lower numbers meaning more of the little creatures are doing the same thing as their neighbours. We'll call this the Energy, because physicists always call things Energy, that's just what we do.\n",
    "\n",
    "To calculate the energy what we're gonna do is look at all the pixels/creatures, and for each one, we look at the four neighbours to the N/E/S/W, everytime we find a neighbour that agrees, we'll subtract 1 from our total and every time we find neighbours that disagree we'll add 1 to our total. Creatures at the edges will simply have fewer neighbours to worry about. \n",
    "\n",
    "I'll show you what the equation for this looks like, but don't worry to much about it, the word description should be enough to write some code. If we assign the ith creature the label $s_i = \\pm1$ then the energy is \n",
    "$$E = \\sum_{(i,j)} s_i s_j$$\n",
    "\n",
    "Ok let's do some little tests, let's make the all up, all down and random state and see if we can compute their energies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "340a78e7-6c1d-4742-8dca-6d3bea492856",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_up = np.ones([100, 100])\n",
    "all_down = -np.ones([100, 100])\n",
    "random = np.random.choice([-1, 1], size=(100, 100))\n",
    "\n",
    "from matplotlib.image import imread\n",
    "\n",
    "custom = (\n",
    "    1 - 2 * imread(\"data/test_state.png\")[:, :, 0]\n",
    ")  # load a 100x100 png, take the red channel, remap 0,1 to -1,1\n",
    "\n",
    "states = [all_up, all_down, random, custom]\n",
    "\n",
    "f, axes = plt.subplots(ncols=4, figsize=(20, 5))\n",
    "for ax, state in zip(axes, states):\n",
    "    show_state(state, ax=ax)"
   ]
  },
  {
   "attachments": {
    "c7c0ca75-61b0-4c5a-b733-3e12532c8b00.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "2ed02839-81c0-45ff-87c9-a429ea8ccf51",
   "metadata": {},
   "source": [
    "If you stare at the first two long enough you'll realise we can figure out the energy of all_up and all_down without writing any code at all:\n",
    "\n",
    "<div style=\"margin:auto;max-width:800px;\">\n",
    "<img src=\"attachment:c7c0ca75-61b0-4c5a-b733-3e12532c8b00.png\"/>\n",
    "</div>\n",
    "\n",
    "So we know that for the first two:\n",
    "$$E = \\frac{1}{L^2} (4(L-2)^2 + 12(L-2) + 8)$$\n",
    "\n",
    "And for the random case we can make a pretty good guess that it should be zero on average. And the last we will just use to as a testcase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c2e63baa-8d97-41f3-9070-013aa6bf83bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For L = 100, We predict E = -39600\n"
     ]
    }
   ],
   "source": [
    "def E_prediction_all_the_same(L):\n",
    "    return -(4 * (L - 2) ** 2 + 12 * (L - 2) + 8)\n",
    "\n",
    "\n",
    "L = 100\n",
    "print(f\"For L = {L}, We predict E = {E_prediction_all_the_same(L)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8351475b-73cb-4cd9-9fe8-3b60af0b5a6a",
   "metadata": {},
   "source": [
    "## Exercise 1: Write a function to compute the energy of a state\n",
    "\n",
    "See if you can write a function that calculates the energy and reproduces all the above cases. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "36ac021b-1da4-48d1-9cad-6ae3ba1e7e61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# you are welcome to solve this in any way you like, I've just filled out a very simple way to do it\n",
    "def energy(state):\n",
    "    E = 0\n",
    "    N, M = state.shape\n",
    "    for i in range(N):\n",
    "        for k in range(M):\n",
    "            # your code goes here\n",
    "            pass\n",
    "    return E / (N * M)\n",
    "\n",
    "\n",
    "expected_values = [\n",
    "    E_prediction_all_the_same(100),\n",
    "    E_prediction_all_the_same(100),\n",
    "    0,\n",
    "    \"???\",\n",
    "]\n",
    "\n",
    "f, axes = plt.subplots(ncols=2, nrows=2, figsize=(10, 10))\n",
    "axes = axes.flatten()\n",
    "for ax, state, exp_value in zip(axes, states, expected_values):\n",
    "    show_state(state, ax=ax)\n",
    "    ax.text(\n",
    "        0,\n",
    "        -0.1,\n",
    "        f\"Expected Value: {exp_value}, Your value: {energy(state)}\",\n",
    "        transform=ax.transAxes,\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0ad5b92f-521f-48c2-9f5b-7950f5a3f931",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Solution\n",
    "\n",
    "\n",
    "def energy(state):\n",
    "    E = 0\n",
    "    N, M = state.shape\n",
    "    for i in range(N):\n",
    "        for j in range(M):\n",
    "            # handle the north and south neighbours\n",
    "            for di in [1, -1]:\n",
    "                if 0 <= (i + di) < N:\n",
    "                    E -= state[i, j] * state[i + di, j]\n",
    "\n",
    "            # handle the east and west neighbours\n",
    "            for dj in [1, -1]:\n",
    "                if 0 <= (j + dj) < M:\n",
    "                    E -= state[i, j] * state[i, j + dj]\n",
    "\n",
    "    return E\n",
    "\n",
    "\n",
    "expected_values = [\n",
    "    E_prediction_all_the_same(100),\n",
    "    E_prediction_all_the_same(100),\n",
    "    0,\n",
    "    \"???\",\n",
    "]\n",
    "\n",
    "f, axes = plt.subplots(ncols=2, nrows=2, figsize=(10, 10))\n",
    "axes = axes.flatten()\n",
    "for ax, state, exp_value in zip(axes, states, expected_values):\n",
    "    show_state(state, ax=ax)\n",
    "    ax.text(\n",
    "        0,\n",
    "        -0.1,\n",
    "        f\"Expected Value: {exp_value}, Your value: {energy(state)}\",\n",
    "        transform=ax.transAxes,\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84ee0a62-6ab1-4565-a236-2ccfcc378acc",
   "metadata": {},
   "source": [
    "It's a bit tricky to know what to do with the random value, let's try running it 100 times and see what we get:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "686782b5-aa37-4084-9786-538fdc89fef1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = -0.24, standard error = 29.819071481184658\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD4CAYAAADiry33AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAAATaklEQVR4nO3df6xndX3n8edrGZAEWWHkLiKwgltKgt0F2dtRIzXoKMJAxG5MF7LpYtVMpdjIrkkz1qQ09h/Ube0Pmk6mwAq7FH+jpKAynbWLJgJeWEB+SBkphhmRuToKuG1qpr73j+9n1u9cvnfmzv1+7w8+PB/JN9/P+ZzP95z3nDvzumfOOd9zUlVIkvr1L1a6AEnS0jLoJalzBr0kdc6gl6TOGfSS1Lk1K13AKLfffnsdfvjhK12GJD1vPPvssz9Yv3791Kh5qzLoDz/8cNatW7fSZUjS88a2bdu+O988D91IUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnVuU3Y6XV6qRNt6x0Ccvu8SvPX+kSNCb36CWpcwa9JHXOoJekzhn0ktQ5g16SOnfAoE9yYpKvJnkoyYNJ3t/61ybZmuTR9n70PJ+/pI15NMklk/4DSJL2byF79HuAD1TVacBrgcuSnAZsArZV1SnAtja9jyRrgSuA1wDrgCvm+4UgSVoaBwz6qnqyqu5p7WeBh4HjgQuB69qw64C3j/j4W4GtVbW7qn4EbAXOnUDdkqQFOqhj9ElOAl4N3AkcW1VPtlnfB44d8ZHjgSeGpne0PknSMllw0Cd5MfA54PKqemZ4XlUVUOMUkmRjkpkkM7Ozs+MsSpI0ZEFBn+RQBiF/Q1V9vnU/leS4Nv84YNeIj+4EThyaPqH1PUdVbamq6aqanpoa+SBzSdIiLOSqmwDXAA9X1R8NzboZ2HsVzSXAF0d8/CvAOUmObidhz2l9kqRlspA9+tcDvw68Kcm97bUBuBJ4S5JHgTe3aZJMJ7kaoKp2A38AfLO9Ptz6JEnL5IB3r6yqrwOZZ/b6EeNngPcMTV8LXLvYAiVJ4/GbsZLUOYNekjpn0EtS5wx6SeqcQS9JnTPoJalzBr0kdc6gl6TOGfSS1DmDXpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzh3wwSNJrgUuAHZV1S+1vk8Bp7YhRwE/rqozRnz2ceBZ4J+BPVU1PZGqJUkLdsCgBz4BXAVcv7ejqv7j3naSPwSe3s/n31hVP1hsgZKk8SzkUYK3Jzlp1Lz24PBfA9404bokSRMy7jH6XwGeqqpH55lfwG1J7k6ycX8LSrIxyUySmdnZ2THLkiTtNW7QXwzcuJ/5Z1XVmcB5wGVJ3jDfwKraUlXTVTU9NTU1ZlmSpL0WHfRJ1gD/AfjUfGOqamd73wXcBKxb7PokSYszzh79m4FvV9WOUTOTHJHkyL1t4BzggTHWJ0lahAMGfZIbgW8ApybZkeTdbdZFzDlsk+TlSW5tk8cCX09yH3AXcEtVfXlypUuSFmIhV91cPE//O0f0fQ/Y0NqPAaePWZ8kaUx+M1aSOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5wx6SeqcQS9JnTPoJalzBr0kdc6gl6TOGfSS1LmFPGHq2iS7kjww1Pf7SXYmube9Nszz2XOTPJJke5JNkyxckrQwC9mj/wRw7oj+j1fVGe1169yZSQ4B/hw4DzgNuDjJaeMUK0k6eAcM+qq6Hdi9iGWvA7ZX1WNV9VPgk8CFi1iOJGkM4xyjf1+S+9uhnaNHzD8eeGJoekfrGynJxiQzSWZmZ2fHKEuSNGyxQf8XwL8BzgCeBP5w3EKqaktVTVfV9NTU1LiLkyQ1iwr6qnqqqv65qn4G/CWDwzRz7QROHJo+ofVJkpbRooI+yXFDk78KPDBi2DeBU5KcnOQw4CLg5sWsT5K0eGsONCDJjcDZwDFJdgBXAGcnOQMo4HHgN9vYlwNXV9WGqtqT5H3AV4BDgGur6sGl+ENIkuZ3wKCvqotHdF8zz9jvARuGpm8FnnPppSRp+fjNWEnqnEEvSZ0z6CWpcwa9JHXugCdjpdXopE23rHQJ0vOGe/SS1DmDXpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5vxkrab9W6lvIj195/oqst0cH3KNvD//eleSBob6PJfl2ezj4TUmOmuezjyf5VpJ7k8xMsG5J0gIt5NDNJ4Bz5/RtBX6pqv4d8HfAB/fz+TdW1RlVNb24EiVJ4zhg0FfV7cDuOX23VdWeNnkHgwd/S5JWoUmcjH0X8KV55hVwW5K7k2ycwLokSQdprKBP8iFgD3DDPEPOqqozgfOAy5K8YT/L2phkJsnM7OzsOGVJkoYsOuiTvBO4APhPVVWjxlTVzva+C7gJWDff8qpqS1VNV9X01NTUYsuSJM2xqKBPci7wO8Dbquof5hlzRJIj97aBc4AHRo2VJC2dhVxeeSPwDeDUJDuSvBu4CjgS2Noundzcxr48ya3to8cCX09yH3AXcEtVfXlJ/hSSpHkd8AtTVXXxiO5r5hn7PWBDaz8GnD5WdZJesFbycZG9fVnLWyBIUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjq3oKBPcm2SXUkeGOpbm2Rrkkfb+9HzfPaSNubRJJdMqnBJ0sIsdI/+E8C5c/o2Aduq6hRgW5veR5K1wBXAaxg8GPyK+X4hSJKWxoKCvqpuB3bP6b4QuK61rwPePuKjbwW2VtXuqvoRsJXn/sKQJC2hcY7RH1tVT7b29xk8DHyu44EnhqZ3tL7nSLIxyUySmdnZ2THKkiQNm8jJ2KoqoMZcxpaqmq6q6ampqUmUJUlivKB/KslxAO1914gxO4ETh6ZPaH2SpGUyTtDfDOy9iuYS4IsjxnwFOCfJ0e0k7DmtT5K0TBZ6eeWNwDeAU5PsSPJu4ErgLUkeBd7cpkkyneRqgKraDfwB8M32+nDrkyQtkzULGVRVF88za/2IsTPAe4amrwWuXVR1kqSx+c1YSeqcQS9JnTPoJalzBr0kdc6gl6TOGfSS1DmDXpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnFh30SU5Ncu/Q65kkl88Zc3aSp4fG/N7YFUuSDsqCnjA1SlU9ApwBkOQQBg/9vmnE0K9V1QWLXY8kaTyTOnSzHvhOVX13QsuTJE3IpIL+IuDGeea9Lsl9Sb6U5FXzLSDJxiQzSWZmZ2cnVJYkaeygT3IY8DbgMyNm3wO8oqpOB/4M+MJ8y6mqLVU1XVXTU1NT45YlSWomsUd/HnBPVT01d0ZVPVNVP2ntW4FDkxwzgXVKkhZoEkF/MfMctknysiRp7XVtfT+cwDolSQu06KtuAJIcAbwF+M2hvvcCVNVm4B3ApUn2AP8IXFRVNc46JUkHZ6ygr6r/C7x0Tt/mofZVwFXjrEOSNB6/GStJnTPoJalzBr0kdc6gl6TOGfSS1DmDXpI6Z9BLUucMeknqnEEvSZ0b65uxWh1O2nTLSpcgaRVzj16SOmfQS1LnDHpJ6pxBL0mdM+glqXOTeGbs40m+leTeJDMj5ifJnybZnuT+JGeOu05J0sJN6vLKN1bVD+aZdx5wSnu9BviL9i5JWgbLcejmQuD6GrgDOCrJccuwXkkSkwn6Am5LcneSjSPmHw88MTS9o/XtI8nGJDNJZmZnZydQliQJJhP0Z1XVmQwO0VyW5A2LWUhVbamq6aqanpqamkBZkiSYQNBX1c72vgu4CVg3Z8hO4MSh6RNanyRpGYwV9EmOSHLk3jZwDvDAnGE3A/+5XX3zWuDpqnpynPVKkhZu3KtujgVuSrJ3WX9VVV9O8l6AqtoM3ApsALYD/wD8xpjrlCQdhLGCvqoeA04f0b95qF3AZeOsR5K0eH4zVpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzhn0ktQ5g16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1btz70UtSd07adMuKrPfxK89fkuW6Ry9JnVt00Cc5MclXkzyU5MEk7x8x5uwkTye5t71+b7xyJUkHa5xDN3uAD1TVPe25sXcn2VpVD80Z97WqumCM9UiSxrDoPfqqerKq7mntZ4GHgeMnVZgkaTImcow+yUnAq4E7R8x+XZL7knwpyav2s4yNSWaSzMzOzk6iLEkSEwj6JC8GPgdcXlXPzJl9D/CKqjod+DPgC/Mtp6q2VNV0VU1PTU2NW5YkqRkr6JMcyiDkb6iqz8+dX1XPVNVPWvtW4NAkx4yzTknSwRnnqpsA1wAPV9UfzTPmZW0cSda19f1wseuUJB28ca66eT3w68C3ktzb+n4X+NcAVbUZeAdwaZI9wD8CF1VVjbFOSdJBWnTQV9XXgRxgzFXAVYtdx2Ks1DfaJGm18puxktQ5g16SOmfQS1LnDHpJ6pxBL0mdM+glqXMGvSR1zqCXpM4Z9JLUOYNekjpn0EtS5wx6SeqcQS9JnTPoJalzBr0kdc6gl6TOjfvM2HOTPJJke5JNI+a/KMmn2vw7k5w0zvokSQdvnGfGHgL8OXAecBpwcZLT5gx7N/CjqvoF4OPARxa7PknS4oyzR78O2F5Vj1XVT4FPAhfOGXMhcF1rfxZYv/dh4ZKk5THOw8GPB54Ymt4BvGa+MVW1J8nTwEuBH8xdWJKNwEaAW2655Sfbtm17ZDFFXfOWwxfzsX3s3r37mLVr1z6nxtVktddofeOxvvGs9vpgdI3btm0bZ5GvmG/GOEE/UVW1Bdiy0nUAJJmpqumVrmN/VnuN1jce6xvPaq8PlrfGcQ7d7AROHJo+ofWNHJNkDfAS4IdjrFOSdJDGCfpvAqckOTnJYcBFwM1zxtwMXNLa7wD+V1XVGOuUJB2kRR+6acfc3wd8BTgEuLaqHkzyYWCmqm4GrgH+R5LtwG4GvwyeD1bFIaQDWO01Wt94rG88q70+WMYa4w62JPXNb8ZKUucMeknq3As+6JOckeSOJPcmmUmyrvUnyZ+22zfcn+TMoc9ckuTR9rpk/qVPrMbfTvLtJA8m+ehQ/wdbfY8keetQ/35vTbFENX4gSSU5pk2viu2X5GNt292f5KYkRw3NWzXbb07NK7r+VsOJSb6a5KH29+79rX9tkq3tZ7c1ydGtf96f9xLWeEiS/5Pkr9v0ye1WK9vbrVcOa/0rciuWJEcl+Wz7+/dwktet2Parqhf0C7gNOK+1NwB/O9T+EhDgtcCdrX8t8Fh7P7q1j17C+t4I/A3wojb9r9r7acB9wIuAk4HvMDgpfkhrvxI4rI05bYm34YkMTsp/FzhmlW2/c4A1rf0R4COrbfvNqXdF1z9Ux3HAma19JPB3bZt9FNjU+jcNbc+RP+8lrvG/An8F/HWb/jRwUWtvBi5t7d8CNrf2RcCnlmkbXge8p7UPA45aqe33gt+jBwr4l639EuB7rX0hcH0N3AEcleQ44K3A1qraXVU/ArYC5y5hfZcCV1bVPwFU1a6h+j5ZVf9UVX8PbGdwW4qF3Jpi0j4O/A6DbbnXqth+VXVbVe1pk3cw+L7H3vpWy/YbttLrB6Cqnqyqe1r7WeBhBt90H76tyXXA21t7vp/3kkhyAnA+cHWbDvAmBrdaGVXbst6KJclLgDcwuPKQqvppVf2YFdp+Bj1cDnwsyRPAfwM+2PpH3eLh+P30L5VfBH6l/Zfzfyf55dVUX5ILgZ1Vdd+cWauivjnexWCvif3UsZL17a+uFdMOdbwauBM4tqqebLO+Dxzb2std9x8z2Ln4WZt+KfDjoV/qw+vf51YswN5bsSylk4FZ4L+3w0tXJzmCFdp+q+YWCEspyd8ALxsx60PAeuC/VNXnkvwag9/Ab15F9a1hcJjjtcAvA59O8splLO9A9f0ug8MjK2Z/9VXVF9uYDwF7gBuWs7bnuyQvBj4HXF5VzwzvCFdVJVn267OTXADsqqq7k5y93OtfoDXAmcBvV9WdSf6EwaGa/285t98LIuirat7gTnI98P42+RnafwWZ/xYPO4Gz5/T/7RLWdynw+RocyLsryc+AY/ZTH/vpn2h9Sf4tgz2X+1oAnADck8EJ7VWx/Vqd7wQuANa37ch+6mM//cthIbcWWRZJDmUQ8jdU1edb91NJjquqJ9uhhb2HEpez7tcDb0uyATicwaHXP2FwuGNN22sfXv/e2nZk+W7FsgPYUVV3tunPMgj6ldl+y3FSYjW/GBx7PLu11wN3t/b57Hty5K7Wvxb4ewYnEo9u7bVLWN97gQ+39i8y+O9dgFex78nExxicyFvT2ifz85N5r1qmbfk4Pz8Zu1q237nAQ8DUnP5Vt/1aXSu6/qE6AlwP/PGc/o+x78nEj+7v570MdZ7Nz0/GfoZ9T8b+Vmtfxr4nYz+9TLV9DTi1tX+/bbsV2X7L+pdnNb6As4C72z+oO4F/3/rD4MEq3wG+BUwPfeZdDE7ebQd+Y4nrOwz4n8ADwD3Am4bmfajV9wjtyqHWv4HBVRLfYXD4Yrm25XDQr5btt53BL8d722vzat1+q2X9rYazGJxcv39o221gcGx7G/Aog6vB1h7o573EdQ4H/SuBu9rP/DP8/Eq1w9v09jb/lctU2xnATNuGX2CwY7Mi289bIEhS57zqRpI6Z9BLUucMeknqnEEvSZ0z6CWpcwa9JHXOoJekzv0/9EmysSYu9h8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 100  # How large the system should be\n",
    "N = 100  # How many random samples to use\n",
    "energies = [energy(np.random.choice([-1, 1], size=(L, L))) for _ in range(N)]\n",
    "plt.hist(energies)\n",
    "print(f\"mean = {np.mean(energies)}, standard error = {np.std(energies) / np.sqrt(N)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8da38c5b-f166-4530-b046-3600b4d84c5d",
   "metadata": {},
   "source": [
    "If you run this a few times you'll see the mean is usually within a few standard errors of 0, which gives us some confidence. In the testing section we will discuss how we might go about doing automated tests of random variables like this. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bd3831b-f8de-4a8e-aaf6-7aa158cf9d82",
   "metadata": {},
   "source": [
    "### Making it a little faster\n",
    "\n",
    "This project is not intended to focus on optimising for performance but it is worth putting a little effort into making this function faster so that we can run experiments more quickly later.\n",
    "\n",
    "The main thing that slows us down here is that we've written a 'tight loop' in pure python, the energy function is just a loop over the fundamental operation:\n",
    "```python\n",
    "E -= state[i,j] * state[i+di, j]\n",
    "```\n",
    "which in theoy only requires a few memory load operations, a multiply, an add and a store back to memory (give or take). However because Python is such a dynamic language, it will have to do extra things like check the type and methods of `state` and `E`, invoke their array access methods `object.__get__`, etc etc. We call this extra work overhead.\n",
    "\n",
    "In most cases the ratio of overhead to actual computation is not too bad, but here because the fundamental computation is so simple it's likely the overhead accounts for much more of the overal time.\n",
    "\n",
    "In scientific python like this there are usually two main options for reducing the overhead:\n",
    "\n",
    "#### Using Arrays\n",
    "One way is we work with arrays of numbers and operations defined over those arrays such as `sum`, `product` etc. `Numpy` is the canonical example of this in Python but many machine learning libraries are essentually doing a similar thing. We rely on the library to implement the operations efficiently and try to chain those operations together to achieve what we want. This imposes some limitations on the way we can write our code.\n",
    "\n",
    "#### Using Compilation\n",
    "The alternative is that we convert our Python code into a more efficient form that incurs less overhead. This requires a compilation or transpilation step and imposes a different set of constraints on the code.\n",
    "\n",
    "It's a little tricky to decide which of the two approaches will work best for a given problem. My advice would be to have some familiarity with both but ultimatly to use what makes your development experience the best, since you'll likely spend more time writing the code than you will waiting for it to run!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b2ed23c-32f2-40af-bf45-e60004c275a2",
   "metadata": {},
   "source": [
    "## Exercise 2: Write a faster version of `energy(state)`\n",
    "\n",
    "You can use `numpy`, `numba`, `cython`, or anything else, by what factor can you beat the naive approach? Numba is probably the easiest here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "40386cda-cc14-4fdd-8f9f-71840d1ebb40",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Naive baseline implementation\n",
      "74.5 ms ± 4.77 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "\n",
      "Your version\n",
      "73.7 ms ± 2.61 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "Your speedup: 1x !\n"
     ]
    }
   ],
   "source": [
    "def test_energy_function(energy_function):\n",
    "    assert np.all(energy_function(state) == energy(state) for state in states)\n",
    "\n",
    "\n",
    "def time_energy_function(energy_function):\n",
    "    return [energy_function(state) for state in states]\n",
    "\n",
    "\n",
    "def your_faster_energy_function(state):\n",
    "    return energy(\n",
    "        state\n",
    "    )  # <-- replace this with your implementation and compare how fast it runs!\n",
    "\n",
    "\n",
    "print(\"Naive baseline implementation\")\n",
    "test_energy_function(\n",
    "    energy\n",
    ")  # this should always pass because it's just comparing to itself!\n",
    "naive = %timeit -o time_energy_function(energy)\n",
    "\n",
    "print(\"\\nYour version\")\n",
    "test_energy_function(your_faster_energy_function)\n",
    "yours = %timeit -o time_energy_function(your_faster_energy_function)\n",
    "print(f\"Your speedup: {naive.best/yours.best :.0f}x !\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a27bb821-c33f-4966-8676-4295cfd695ab",
   "metadata": {},
   "source": [
    "## Solution 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c96720d4-2c0b-4fa5-b9ce-4fc7be533a62",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Naive baseline implementation\n",
      "73.6 ms ± 1.82 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "\n",
      "Numba version\n",
      "199 µs ± 5.91 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "Numba Speedup: 377x !\n",
      "\n",
      "Numpy version\n",
      "163 µs ± 4.46 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n",
      "Numpy Speedup: 452x !\n"
     ]
    }
   ],
   "source": [
    "def test_energy_function(energy_function):\n",
    "    return [energy_function(state) for state in states]\n",
    "\n",
    "\n",
    "from numba import jit\n",
    "\n",
    "\n",
    "@jit(nopython=True)\n",
    "def numba_energy(state):\n",
    "    E = 0\n",
    "    N, M = state.shape\n",
    "    for i in range(N):\n",
    "        for j in range(M):\n",
    "            # handle the north and south neighbours\n",
    "            for di in [1, -1]:\n",
    "                if 0 <= (i + di) < N:\n",
    "                    E -= state[i, j] * state[i + di, j]\n",
    "\n",
    "            # handle the east and west neighbours\n",
    "            for dj in [1, -1]:\n",
    "                if 0 <= (j + dj) < M:\n",
    "                    E -= state[i, j] * state[i, j + dj]\n",
    "\n",
    "    return E\n",
    "\n",
    "\n",
    "def numpy_energy(state):\n",
    "    E = -np.sum(state[:-1, :] * state[1:, :]) - np.sum(state[:, :-1] * state[:, 1:])\n",
    "    return 2 * E\n",
    "\n",
    "\n",
    "print(\"Naive baseline implementation\")\n",
    "naive = %timeit -o time_energy_function(energy)\n",
    "\n",
    "print(\"\\nNumba version\")\n",
    "test_energy_function(numba_energy)\n",
    "numba = %timeit -n 100 -o time_energy_function(numba_energy)\n",
    "print(f\"Numba Speedup: {naive.best/numba.best :.0f}x !\")\n",
    "\n",
    "print(\"\\nNumpy version\")\n",
    "test_energy_function(numpy_energy)\n",
    "numpy = %timeit -n 100 -o time_energy_function(numpy_energy)\n",
    "print(f\"Numpy Speedup: {naive.best/numpy.best :.0f}x !\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d80c912-3773-4c53-a4e9-3f7ee66e2e0f",
   "metadata": {},
   "source": [
    "While writing the above faster versions I realised two things, first there was a bug in my code! I had written \n",
    "```python\n",
    "for dj in [1,-1]:\n",
    "    if 0 <= (j + dj) < M:\n",
    "        E -= state[i,j] * state[i+di, j]\n",
    "```\n",
    "where I of course meant to have:\n",
    "```python\n",
    "for dj in [1,-1]:\n",
    "    if 0 <= (j + dj) < M:\n",
    "        E -= state[i,j] * state[i, j+dj]\n",
    "```\n",
    "I found this while writing the numpy version because the two functions were not giving the same results, I didn't pick it up from writing the numba code because as you can see I just copied the implementation over. So the first lesson is that simple test cases don't always catch even relatively obvious bugs. \n",
    "\n",
    "The second thing was that even my naive function was doing more work than it needed to! Because if the symmetry of how two neighbours talks to each other, we can rewrite the code as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "755ec34c-4975-467f-a559-f585f9d6a42f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Improved Naive version\n",
      "37.6 ms ± 1.81 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "Speedup: 2x !\n"
     ]
    }
   ],
   "source": [
    "def energy2(state):\n",
    "    E = 0\n",
    "    N, M = state.shape\n",
    "    for i in range(N):\n",
    "        for j in range(M):\n",
    "            # handle the north and south neighbours\n",
    "            if 0 <= (i + 1) < N:\n",
    "                E -= state[i, j] * state[i + 1, j]\n",
    "\n",
    "            # handle the east and west neighbours\n",
    "            if 0 <= (j + 1) < M:\n",
    "                E -= state[i, j] * state[i, j + 1]\n",
    "\n",
    "    return 2 * E\n",
    "\n",
    "\n",
    "print(\"\\nImproved Naive version\")\n",
    "energy2(states[0])  # run the function once to let numba compile it before timing it\n",
    "e2 = %timeit -o test_energy_function(energy2)\n",
    "print(f\"Speedup: {naive.best/e2.best :.0f}x !\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d1874d4-4585-49ed-bc6f-b11c22231669",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "So far we've discussed the problem we want to solve, written a little code, tested it a bit and made some speed improvements.\n",
    "\n",
    "In the next notebook we will package the code up into a little python package, this is has two big benefits to use: \n",
    "1. I won't have to redefine the energy function we just wrote in the next notebook \n",
    "1. It will help with testing and documenting our code later"
   ]
  }
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