Rare event sampling - Functions and Plots.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.special as sc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10000.     0.     0.     0.     0.     0.     0.     0.     0.]\n",
      " [ 4930.  5070.     0.     0.     0.     0.     0.     0.     0.]\n",
      " [ 2433.  5026.  2541.     0.     0.     0.     0.     0.     0.]\n",
      " [ 1209.  3725.  3782.  1284.     0.     0.     0.     0.     0.]\n",
      " [  605.  2429.  3843.  2486.   637.     0.     0.     0.     0.]\n",
      " [  309.  1526.  3109.  3200.  1517.   339.     0.     0.     0.]\n",
      " [  154.   929.  2346.  3184.  2312.   907.   168.     0.     0.]\n",
      " [   84.   520.  1639.  2768.  2752.  1634.   516.    87.     0.]\n",
      " [   48.   282.  1095.  2163.  2769.  2203.  1091.   307.    42.]]\n"
     ]
    }
   ],
   "source": [
    "def simple_sampling_rw(max_samples,max_length):\n",
    "    \n",
    "    \"\"\"Produce multiple, max_length + 1, distributions of one-dimensional unbiased random walks \n",
    "   based on the total number of steps to the right.\n",
    "   \n",
    "   Parameters\n",
    "   ----------\n",
    "   max_length: maximum length of the walk\n",
    "   max_samples: total number of samples\n",
    "   \n",
    "   Returns\n",
    "   -------\n",
    "   A square matrix s, where the k-th column is the number of steps to the right and the n-th row is \n",
    "   the total length of the random walk, both from 0 to max_length + 1. Each entry s[n,k] is the number of samples\n",
    "   that took k steps to the right in a random walk of n steps.\n",
    "    \"\"\"\n",
    "    \n",
    "    # Initialise a zero matrix where each entry represents the number of samples with k steps to the right.\n",
    "    s = np.zeros((max_length+1,max_length+1))\n",
    "    # Iterate over the number of stationary (n = 0) random walk samples with zero steps to the right (k = 0)\n",
    "    # until in reaches the maximum number of samples.\n",
    "    while s[0,0] < max_samples:\n",
    "        s[0,0] += 1\n",
    "        # Intialise n and k to represent the total length and total number of steps to the right respectively.\n",
    "        n = k = 0 \n",
    "        while n < max_length:\n",
    "            n += 1\n",
    "           # Generate a random number between 0 and 1.\n",
    "            r = random.random()\n",
    "            if r < 1/2:\n",
    "                k += 1\n",
    "                # Add 1 to represent moving the right with a chance of 1/2.\n",
    "            else:\n",
    "                # Not adding 1 represents moving to the left.\n",
    "                pass\n",
    "            # Fill the corresponding sample entry.\n",
    "            s[n,k] += 1\n",
    "            \n",
    "    return s\n",
    "\n",
    "# example\n",
    "max_samples,max_length = 10 ** 4,8\n",
    "s = simple_sampling_rw(max_samples,max_length)\n",
    "print(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def biased_sampling_rw(p,max_samples,max_length):\n",
    "    \n",
    "    \"\"\"Produce multiple, max_length + 1, distributions of biased one-dimensional random walks \n",
    "    based on the total number of steps to the right.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    p: the probability moving to the right \n",
    "    max_length: total length of the walk\n",
    "    max_samples: total number of samples\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    Two matrices:\n",
    "    \n",
    "    The square matrix s, where the k-th column is the number of steps to the right and the n-th row is \n",
    "    the total length of the random walk, both from 0 to max_length + 1. Each entry s[n,k] is the number of samples\n",
    "    that took k steps to the right in a random walk of n steps.\n",
    "    \n",
    "    The w matrix, containing the corresponding weights for the sample entry s[n,k].\n",
    "    \"\"\"\n",
    "\n",
    "    # Initialise two zero matrices, s and w\n",
    "    # where each entry represents the number of samples with k step to the right\n",
    "    # and w contains the corresponding weights.\n",
    "    s = np.zeros((max_length+1,max_length+1))\n",
    "    w = np.zeros((max_length+1,max_length+1))\n",
    "    # Iterate over the number of stationary (n = 0) random walk samples with zero steps to the right (k = 0)\n",
    "    # until in reaches the maximum number of samples.\n",
    "    while s[0,0] < max_samples:\n",
    "        s[0,0] += 1\n",
    "        # Intialise n and k to represent the total length and total number of steps to the right respectively.\n",
    "        n = k = 0\n",
    "        # Iterate over the corresponding weight of s[0,0] until the maximum number of samples is reached.\n",
    "        weight = 1\n",
    "        w[0,0] += weight\n",
    "        while n < max_length:\n",
    "            n += 1\n",
    "            # Generate a random number between 0 and 1.\n",
    "            r = random.random()\n",
    "            if r < p:\n",
    "                k += 1\n",
    "                # Correct the weights to counteract the bias p by a multiplicative factor of 0.5/p and move right.\n",
    "                weight *= 0.5/p\n",
    "            else:\n",
    "                # If the condition doesn't hold, we multiply the weight by 0.5/(1-p) and don't move to the right. \n",
    "                weight *= 0.5/(1-p)\n",
    "            # Fill the corresponding sample entry.\n",
    "            # Add the calculated weight to the corresponding entry s[n,k].\n",
    "            s[n,k] += 1; w[n,k] += weight         \n",
    "            \n",
    "    return s,w\n",
    "\n",
    "# example\n",
    "max_samples,max_length = 10 ** 5,50\n",
    "fig,(ax1,ax2) = plt.subplots(1,2,figsize=(16,5))\n",
    "for p in [0.15,0.5,0.85]:\n",
    "    s,w=biased_sampling_rw(p,max_samples,max_length)\n",
    "    ax1.plot(s[-1,:],label=str(p))\n",
    "    ax1.set_ylabel('s', rotation = 0)\n",
    "    ax1.set_xlabel('k')\n",
    "    ax2.plot(w[-1,:],'x',label=str(p))\n",
    "    ax2.set_yscale(\"log\")\n",
    "    ax2.set_xlabel('k')\n",
    "    ax1.legend()\n",
    "    ax2.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def uniform_sampling_rw(max_samples, max_length):\n",
    "    \n",
    "    \"\"\"Produce multiple, max_length + 1 uniform distributions of an unbaised one-dimensional random walks \n",
    "    based on the total number of steps to the right.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    max_length: maximum length of the walk\n",
    "    max_samples: total number of samples\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    Two matrices:\n",
    "    \n",
    "    The square matrix s, where the k-th column is the number of steps to the right and the n-th row is \n",
    "    the total length of the random walk, both from 0 to max_length + 1. Each entry s[n,k] is the number of samples\n",
    "    that took k steps to the right in a random walk of n steps.\n",
    "    \n",
    "    The w matrix, containing the corresponding weights for the sample entry s[n,k].\n",
    "    \"\"\"\n",
    "    \n",
    "    # Define the local biases for each s[n,k] samples of the random walk.\n",
    "    p = lambda n,k:(k+1)/(n+2)\n",
    "    # Store all of the local biases in a matrix.\n",
    "    bias = np.fromfunction(p,(max_length+1,max_length+1))\n",
    "    # Initialise two zero matrices, s and w\n",
    "    # where each entry represents the number of samples with k step to the right\n",
    "    # and w contains the corresponding weights.\n",
    "    s = np.zeros((max_length+1,max_length+1))\n",
    "    w = np.zeros((max_length+1,max_length+1))\n",
    "    # Iterate over the number of stationary (n = 0) random walk samples with zero steps to the right (k = 0)\n",
    "    # until in reaches the maximum number of samples.\n",
    "    while s[0,0]<max_samples:\n",
    "        s[0,0] += 1\n",
    "        # Initialise n and k to represent the total length and total number of steps to the right, respectively.\n",
    "        n = k = 0\n",
    "        # Iterate over the corresponding weight of s[0,0] until the maximum number of samples is reached.\n",
    "        weight = 1 \n",
    "        w[0,0] += weight\n",
    "        while n < max_length:\n",
    "            # Generate a random number between 0 and 1.\n",
    "            r = random.random()\n",
    "            if r < bias[n,k]:\n",
    "                # Correct the weights to counteract the bias p \n",
    "                # by a multiplicative factor of 0.5/bias[n,k] and move right.\n",
    "                weight *= 0.5/bias[n,k]\n",
    "                k += 1\n",
    "            else:\n",
    "                # If the condition doesn't hold, we multiply the weight\n",
    "                # by 0.5/(1-bias[n,k]) and don't move to the right. \n",
    "                weight *= 0.5/(1-bias[n,k])\n",
    "            n += 1\n",
    "            # Fill the corresponding sample entry.\n",
    "            # Add the calculated weight to the corresponding entry s[n,k].\n",
    "            s[n,k] += 1; w[n,k] += weight\n",
    "            \n",
    "    return s,w\n",
    "\n",
    "# example\n",
    "max_samples,max_length = 10 ** 5,50\n",
    "fig,(ax1,ax2) = plt.subplots(1,2,figsize=(16,5))\n",
    "s,w = uniform_sampling_rw(max_samples, max_length)\n",
    "ax1.plot(s[-1,:])\n",
    "ax1.set_ylim([0,2500])\n",
    "ax1.set_ylabel('s', rotation = 0)\n",
    "ax1.set_xlabel('k')\n",
    "ax2.plot(w[-1,:])\n",
    "ax2.set_yscale(\"log\")\n",
    "ax2.set_xlabel('k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def perm_sampling_rw(max_samples, max_length, max_tours):\n",
    "    \n",
    "    \"\"\"Produce multiple,max_length + 1, roughly uniform distributions of an unbaised one-dimensional random walks \n",
    "    based on the total number of steps to the right using the prune and enrichment method.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    max_length: maximum length of the walk\n",
    "    max_samples: total number of samples\n",
    "    max_tours: maximum number of tours\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    Two matrices:\n",
    "    \n",
    "    The square matrix s, where the k-th column is the number of steps to the right and the n-th row is \n",
    "    the total length of the random walk, both from 0 to max_length + 1. Each entry s[n,k] is the number of samples\n",
    "    that took k steps to the right in a random walk of n steps.\n",
    "    \n",
    "    The w matrix, containing the corresponding weights for the sample entry s[n,k].\n",
    "    \"\"\"\n",
    "       \n",
    "    # Assign target weights.\n",
    "    target_weight = lambda n,k: (n+1)*sc.comb(n,k)/2**n\n",
    "    W = np.fromfunction(target_weight,(max_length+1,max_length+1))\n",
    "    # Initialise two zero matrices, s and w\n",
    "    # where each entry represents the number of samples with k step to the right\n",
    "    # and w contains the corresponding weights.\n",
    "    s = np.zeros((max_length+1,max_length+1))\n",
    "    w = np.zeros((max_length+1,max_length+1))\n",
    "    # Initialise an empty list to represent the number of steps to the right.\n",
    "    k = np.zeros(max_length+1,dtype=int)\n",
    "    # Initialise a zero matrix whose entries represent the estimated weights\n",
    "    # of each step of the walk with length n.\n",
    "    weight = np.zeros(max_length+1)\n",
    "    # Initialise a zero matrix whose entries represent the number of enrichment copies\n",
    "    # of each step of the walk with length n.\n",
    "    copy = np.zeros(max_length+1)\n",
    "    tours = n = 0\n",
    "    weight[0] = 1\n",
    "    s[0,k[0]] += 1\n",
    "    w[0,k[0]] += weight[0]\n",
    "    # Iterate over the number of tours.\n",
    "    while tours < max_tours:\n",
    "        # If the maximal length has been reached, don't grow.\n",
    "        if n == max_length:\n",
    "            # Set the number of enrichment copies to zero.\n",
    "            copy[n] = 0\n",
    "        else:\n",
    "            # Prune/enrich step by comparing with target weight.\n",
    "            ratio = weight[n]/W[n,k[n]]\n",
    "            p, r1 = ratio % 1, random.random()\n",
    "            if r1 < p:\n",
    "                copy[n] = np.floor(ratio) + 1\n",
    "            else:\n",
    "                copy[n] = np.floor(ratio)\n",
    "            weight[n] = W[n,k[n]]    \n",
    "        if copy[n] == 0: \n",
    "            # Shrink to last enrichment point or size to zero.\n",
    "            while n > 0 and copy[n] == 0:\n",
    "                n -= 1\n",
    "        if n == 0 and copy[0] == 0:\n",
    "            # If configuration shrunk to zero, start a new tour.\n",
    "            tours += 1\n",
    "            n = k[0] = 0\n",
    "            weight[0] = 1\n",
    "            s[n,k[n]] += 1\n",
    "            w[n,k[n]] += weight[n]\n",
    "        else:\n",
    "            # Decrease the number of enrichment copies.\n",
    "            copy[n] -= 1\n",
    "            # Draw another random number between 0 and 1.\n",
    "            r2 = random.random()\n",
    "            if r2 < 1/2:\n",
    "                # Grow by one step.\n",
    "                k[n+1] = k[n] + 1\n",
    "            else:\n",
    "                k[n+1] = k[n]\n",
    "            weight[n+1] = weight[n]\n",
    "            n += 1\n",
    "            # Fill the corresponding sample entry.\n",
    "            # Add the calculated weight to the corresponding entry s[n,k].\n",
    "            s[n,k[n]] += 1; w[n,k[n]] += weight[n]          \n",
    "            \n",
    "    return s,w\n",
    "\n",
    "# example\n",
    "fig,(ax1,ax2) = plt.subplots(1,2,figsize=(16,5))\n",
    "max_samples,max_length,max_tours = 10 ** 5,50,70000\n",
    "s,w = perm_sampling_rw(max_samples, max_length, max_tours)\n",
    "ax1.plot(s[-1,:])\n",
    "ax1.set_ylim([0,2500])\n",
    "ax1.set_ylabel('s', rotation = 0)\n",
    "ax1.set_xlabel('k')\n",
    "ax2.plot(w[-1,:])\n",
    "ax2.set_yscale(\"log\")\n",
    "ax2.set_xlabel('k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def blind_perm_sampling_rw(max_samples, max_length, max_tours):\n",
    "    \n",
    "    \"\"\"Produce multiple, max_length + 1, roughly uniform distributions of unbaised one-dimensional random walks \n",
    "    based on the total number of steps to the right using the blind pruned and enrichment method.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    max_length: maximum length of the walk\n",
    "    max_samples: total number of samples\n",
    "    max_tours: maximum number of tours\n",
    "    \n",
    "    Returns\n",
    "    -------\n",
    "    Two matrices:\n",
    "    \n",
    "    The square matrix s, where the k-th column is the number of steps to the right and the n-th row is \n",
    "    the total length of the random walk, both from 0 to max_length + 1. Each entry s[n,k] is the number of samples\n",
    "    that took k steps to the right in a random walk of n steps.\n",
    "    \n",
    "    The w matrix, containing the corresponding weights for the sample entry s[n,k].\n",
    "    \"\"\"\n",
    "      \n",
    "    # Initialise an empty matrix whose entries represent estimated target weights.  \n",
    "    W = np.zeros((max_length+1,max_length+1))\n",
    "    # Initialise two zero matrices, s and w\n",
    "    # where each entry represents the number of samples with k step to the right\n",
    "    # and w contains the corresponding weights.\n",
    "    s = np.zeros((max_length+1,max_length+1))\n",
    "    w = np.zeros((max_length+1,max_length+1))\n",
    "    # Initialise an empty list to represent the number of steps to the right.\n",
    "    k = np.zeros(max_length+1,dtype=int)\n",
    "    # Initialise a zero matrix whose entries represent the estimated weights\n",
    "    # of each step of the walk with length n.\n",
    "    weight = np.zeros(max_length+1)\n",
    "    # Initialise a zero matrix whose entries represent the number of enrichment copies\n",
    "    # of each step of the walk with length n.\n",
    "    copy = np.zeros(max_length+1)\n",
    "    tours = n = 0\n",
    "    weight[0] = 1\n",
    "    s[0,k[0]] += 1; w[0,k[0]] += weight[0]\n",
    "    # Iterate over the number of tours.\n",
    "    while tours < max_tours:\n",
    "        # If the maximal length has been reached, don't grow.\n",
    "        if n == max_length:\n",
    "            # Set the number of enrichment copys to zero.\n",
    "            copy[n] = 0\n",
    "        else:\n",
    "            # Prune/enrich step by comparing with the estimated target weight.\n",
    "            W[n,k[n]] = (n+1)*w[n,k[n]]/np.sum(w[n,:])\n",
    "            ratio = weight[n]/W[n,k[n]]\n",
    "            p, r1 = ratio % 1, random.random()\n",
    "            if r1 < p:\n",
    "                copy[n] = np.floor(ratio) + 1\n",
    "            else:\n",
    "                copy[n] = np.floor(ratio)\n",
    "            weight[n] = W[n,k[n]]    \n",
    "        if copy[n] == 0: \n",
    "            # Shrink to last enrichment point or size to zero.\n",
    "            while n > 0 and copy[n] == 0:\n",
    "                n -= 1\n",
    "        if n == 0 and copy[0] == 0:\n",
    "            # If configuration shrunk to zero, start a new tour.\n",
    "            tours += 1\n",
    "            n = k[0] = 0\n",
    "            weight[0] = 1\n",
    "            s[n,k[n]] += 1; w[n,k[n]] += weight[n]\n",
    "        else:\n",
    "            # Decrease the number of enrichment copies.\n",
    "            copy[n] -= 1\n",
    "            # Draw another random number between 0 and 1.\n",
    "            r2 = random.random()\n",
    "            if r2 < 1/2:\n",
    "                # Grow by one step.\n",
    "                k[n+1] = k[n] + 1\n",
    "            else:\n",
    "                k[n+1] = k[n]\n",
    "            weight[n+1] = weight[n]\n",
    "            n += 1\n",
    "            # Fill the corresponding sample entry.\n",
    "            # Add the calculated weight to the corresponding entry s[n,k].\n",
    "            s[n,k[n]] += 1; w[n,k[n]] += weight[n]\n",
    "            \n",
    "    return s,w\n",
    "\n",
    "# example\n",
    "fig,(ax1,ax2) = plt.subplots(1,2,figsize=(16,5))\n",
    "max_samples,max_length,max_tours = 10 ** 5,50,70000\n",
    "s,w = blind_perm_sampling_rw(max_samples, max_length, max_tours)\n",
    "ax1.plot(s[-1,:])\n",
    "ax1.set_ylim([0,2500])\n",
    "ax1.set_ylabel('s', rotation = 0)\n",
    "ax1.set_xlabel('k')\n",
    "ax2.plot(w[-1,:])\n",
    "ax2.set_yscale(\"log\")\n",
    "ax2.set_xlabel('k')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def simple_sampling_saw(max_samples,max_length):\n",
    "\n",
    "    \"\"\"Produce an exponential distribution of a two-dimensional self-avoiding walk based on\n",
    "    the total length of the walk.\n",
    "   \n",
    "   Parameters\n",
    "   ----------\n",
    "   max_length: maximum length of the walk\n",
    "   max_samples: total number of samples\n",
    "   \n",
    "   Returns\n",
    "   -------\n",
    "   \n",
    "   A list where each entry s[n] represents how many samples are of length n, \n",
    "   from n = 0 to n = max_length + 1.  \n",
    "    \"\"\"\n",
    "    \n",
    "    # Initialise a zero list to represent the number of samples.\n",
    "    s, *steps = np.zeros(max_length+1), [1,0],[-1,0],[0,1],[0,-1]\n",
    "    # Iterate over the total number of samples of length zero.\n",
    "    while s[0] < max_samples:\n",
    "        n, site = 0, (0,0)\n",
    "        s[0] += 1\n",
    "        occupied_sites = [site]\n",
    "        while n < max_length:\n",
    "            # Draw one of the neighbouring sites uniformly at random.\n",
    "            step = random.choice(steps)\n",
    "            site = tuple(i+j for i,j in zip(site,step))\n",
    "            # If occupied, reject walk and exit loop.\n",
    "            if site in occupied_sites:\n",
    "                break\n",
    "            else:\n",
    "                # Step to new site.\n",
    "                occupied_sites.append(site)\n",
    "                n += 1\n",
    "                s[n] += 1\n",
    "    \n",
    "    return s\n",
    "\n",
    "# example\n",
    "max_samples, max_length = 10 ** 6, 50\n",
    "s = simple_sampling_saw(max_samples,max_length)\n",
    "plt.figure(figsize=(9, 5))\n",
    "plt.xlabel('Size')\n",
    "plt.ylabel('Samples')\n",
    "plt.plot(s,'-+r')\n",
    "plt.xlim([0, max_length+1])\n",
    "plt.ylim([0, max(s)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rosenbluth_sampling_saw(max_samples,max_size):\n",
    "    \n",
    "    \"\"\"Produce an exponential distribution of a two-dimensional self-avoiding walk based on\n",
    "    the total size of the walk using the Rosenbluth sampling method.\n",
    "   \n",
    "   Parameters\n",
    "   ----------\n",
    "   max_size: maximum size of the walk\n",
    "   max_samples: total number of samples\n",
    "   \n",
    "   Returns\n",
    "   -------\n",
    "   \n",
    "   Two lists s and w where each entry of s, s[n], represents how many samples are of at least size n, \n",
    "   from n = 0 to n = max_size + 1 and the entries of w, w[n], the corresponding weights.\n",
    "    \"\"\"\n",
    "\n",
    "    # Initialise a zero list to represent the number of samples.\n",
    "    s,w = np.zeros(max_size+1),np.zeros(max_size+1)\n",
    "    # Iterate over the total number of samples of at least size zero.\n",
    "    while s[0] < max_samples:\n",
    "        n, weight = 0, 1\n",
    "        s[0] += 1; w[0] += weight\n",
    "        # Start at origin.\n",
    "        site = (0,0)\n",
    "        occupied_sites, *steps = [site], [1,0],[-1,0],[0,1],[0,-1]\n",
    "        # Create list of neighbouring unoccupied sites, determine the atmosphere a.\n",
    "        while n < max_size:\n",
    "            unoccupied_sites = []\n",
    "            for step in steps:\n",
    "                new_step = tuple(i+j for i,j in zip(site,step))\n",
    "                if new_step not in occupied_sites:\n",
    "                    unoccupied_sites.append(new_step)\n",
    "            a = len(unoccupied_sites)\n",
    "            # If walk cannot continue, reject entire walk and exit loop.\n",
    "            if a == 0:\n",
    "                break\n",
    "            else:\n",
    "                # Draw one of the neighbouring unoccupied sites uniformly at random.\n",
    "                # Step to new site.\n",
    "                site = random.choice(unoccupied_sites)\n",
    "                occupied_sites.append(site)\n",
    "                n += 1\n",
    "                weight *= a\n",
    "                s[n] += 1; w[n] += weight\n",
    "\n",
    "    return s,w\n",
    "\n",
    "# example (comparing rosenbluth sampling to simple sampling.)\n",
    "max_samples, max_size = 10 ** 4, 250\n",
    "s,w = rosenbluth_sampling_saw(max_samples,max_size)\n",
    "s_simple = simple_sampling_saw(max_samples,max_size)\n",
    "plt.figure(figsize=(9, 6))\n",
    "plt.xlabel('Size')\n",
    "plt.ylabel('Samples')\n",
    "plt.plot(s,'--g')\n",
    "plt.plot(s_simple, 'r')\n",
    "plt.xlim([0, max_size+1])\n",
    "plt.ylim([0, max(s)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def perm_sampling_saw(max_size,max_tours):\n",
    "    \n",
    "    \"\"\"Produce a roughly uniform distribution of a two-dimensional self-avoiding walk based on\n",
    "    the total size and number of tours of the walk using the Pruned and enrichment sampling method.\n",
    "   \n",
    "   Parameters\n",
    "   ----------\n",
    "   max_size: maximum size of the walk\n",
    "   max_samples: total number of samples\n",
    "   \n",
    "   Returns\n",
    "   -------\n",
    "   \n",
    "   Two lists s,w where each entry of s, s[n], represents how many samples are of at least size n, \n",
    "   from n = 0 to n = max_size + 1 and the entries of w, the corresponding weights.\n",
    "    \"\"\"\n",
    "    \n",
    "    s = np.zeros(max_size+1)\n",
    "    w = np.zeros(max_size+1)\n",
    "    copy = np.zeros(max_size+1)\n",
    "    weight = np.zeros(max_size+1)\n",
    "    tours = n = 0\n",
    "    # Start new walk at origin and step size zero.\n",
    "    a = copy[0] = weight[0] = 1\n",
    "    s[0] += 1; w[0] += weight[0]\n",
    "    site = (0,0)\n",
    "    occupied_sites,*steps = [site], [1,0],[-1,0],[0,1],[0,-1]\n",
    "    while tours < max_tours:\n",
    "        unoccupied_sites = []\n",
    "        # If maximal length has been reached or the atmosphere is zero: Don't grow.\n",
    "        if n == max_size or a == 0:\n",
    "            copy[n] = 0\n",
    "        else:\n",
    "            # Pruning/enrichment by comparing with target weight with the normalised weight estimate.\n",
    "            ratio = weight[n]/(w[n]/s[0])\n",
    "            p, r = ratio % 1, random.random()\n",
    "            # Generate a random number between 0 and 1\n",
    "            if r < p:\n",
    "                copy[n] = np.floor(ratio) + 1\n",
    "            else:\n",
    "                copy[n] = np.floor(ratio)\n",
    "            weight[n] = w[n]/s[0]\n",
    "        if copy[n] == 0:\n",
    "            while n > 0 and copy[n] == 0:\n",
    "                # Delete last site of walk.\n",
    "                occupied_sites = occupied_sites[:-1] \n",
    "                site = occupied_sites[-1]\n",
    "                n -= 1\n",
    "        if n == 0 and copy[0] == 0:\n",
    "            # Start new tour.\n",
    "            tours += 1\n",
    "            # Start new walk with step size zero.\n",
    "            a, copy[0] = 1, 1\n",
    "            s[0] += 1; w[0] += weight[0]\n",
    "            site = (0,0)\n",
    "            occupied_sites, unoccupied_sites, *steps = [site], [], [1,0],[-1,0],[0,1],[0,-1]\n",
    "        else:\n",
    "            # Create list of neighboring unoccupied sites, determine the atmosphere a.\n",
    "            for step in steps:\n",
    "                new_step = tuple(i+j for i,j in zip(site,step))\n",
    "                if new_step not in occupied_sites:\n",
    "                    unoccupied_sites.append(new_step)\n",
    "            a = len(unoccupied_sites)\n",
    "            # If the walk cannot continue, reject entire walk and exit loop.\n",
    "            if a > 0:\n",
    "                copy[n] -= 1\n",
    "                # Draw one of the neighbouring unoccupied sites uniformly at random.\n",
    "                # Step to new site.\n",
    "                site = random.choice(unoccupied_sites)\n",
    "                occupied_sites.append(site)\n",
    "                n += 1\n",
    "                weight[n] = weight[n-1]*a\n",
    "                s[n] += 1; w[n] += weight[n]\n",
    "    s[0] -= 1; w[0] -= 1\n",
    "    \n",
    "    return s,w/s[0]\n",
    "\n",
    "# examlpe (comparing PERM to rosenbluth sampling)\n",
    "max_samples, max_size, max_tours = 10 ** 4 ,250, 10 ** 4\n",
    "s,w = perm_sampling_saw(max_size,max_tours)\n",
    "s_rosenbluth, w = rosenbluth_sampling_saw(max_samples,max_size)\n",
    "plt.figure(figsize=(9, 5))\n",
    "plt.plot(s)\n",
    "plt.plot(s_rosenbluth, 'r')\n",
    "plt.xlabel('Size')\n",
    "plt.ylabel('Samples')\n",
    "plt.xlim([0, max_size+1])\n",
    "plt.ylim([0, max_tours*1.5])\n",
    "plt.show()"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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 },
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}