Homework 131 - Random Walks.ipynb

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    "colab": {
      "name": "CS166PW131.ipynb",
      "version": "0.3.2",
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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  "cells": [
    {
      "metadata": {
        "id": "k7CWWZYk_Oje",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### CS166 Pre-class Work for Session 13.1:\n",
        "\n",
        "### Random Walks\n",
        "\n",
        "_Yoav Rabinovich, April 2019_\n",
        "\n",
        "_________________"
      ]
    },
    {
      "metadata": {
        "id": "_312BjMc_Z2I",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### Exercise 2: Diffusion Through a Crack\n",
        "\n",
        "_Simulate an unbiased random walk (Pr(H) = Pr(T) = 0.5) with some obstacles._\n",
        "\n",
        "(a) *Put a reflection barrier at x = –4, i.e., the walk may land at –4 but may not stay there, and\n",
        "the next step must be to –3. Plot a sample path and a histogram.*\n",
        "\n",
        "(b) *Next, add a partial block at x = 6, i.e., at x = 6 there is only a 0.25 chance of going to 7\n",
        "and a 0.75 chance of going to 5 (same for 7 to 6 ). Plot a histogram.*"
      ]
    },
    {
      "metadata": {
        "id": "vx1JGWeoMBj7",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "I implemented a more general case, where one can list an arbitrary number of reflectors and filters by stating their positions, and where one can input any bias to the random walk:"
      ]
    },
    {
      "metadata": {
        "id": "zJqNrd6-_Me4",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "class Diffusion_1D():\n",
        "    \n",
        "    def __init__(self,bias=0.5,reflectors=[],filters=[]):\n",
        "        \n",
        "        self.state = 0\n",
        "        self.p = bias\n",
        "        self.reflectors=reflectors\n",
        "        self.filters=filters\n",
        "        \n",
        "    def step(self):\n",
        "        \n",
        "        if self.state in self.reflectors:\n",
        "            self.state -= 1*np.sign(self.state)\n",
        "            return\n",
        "        \n",
        "        if np.random.uniform(0,1)<self.p:\n",
        "            if self.state in self.filters:\n",
        "                if np.random.uniform(0,1)<0.5:\n",
        "                    self.state += 1\n",
        "                else:\n",
        "                    self.state -= 1\n",
        "            else:\n",
        "                self.state+=1\n",
        "        else:\n",
        "            if self.state-1 in self.filters:\n",
        "                if np.random.uniform(0,1)<0.5:\n",
        "                    self.state -= 1\n",
        "                else:\n",
        "                    self.state += 1\n",
        "            else:\n",
        "                self.state -= 1  \n",
        "    \n",
        "    def run(self,steps):\n",
        "        \n",
        "        for i in range(steps):\n",
        "            self.step()\n",
        "            \n",
        "        return(self.state)\n",
        "    \n",
        "    def analyze(self,runs,steps):\n",
        "        \n",
        "        endpoints=[]\n",
        "        for i in range(runs):\n",
        "            self.state=0\n",
        "            endpoints.append(self.run(steps))\n",
        "            \n",
        "        return(endpoints)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "XMR_0EuOOJvK",
        "colab_type": "code",
        "outputId": "a5d6b00c-0909-4000-b270-1adb006b2b30",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 606
        }
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      "cell_type": "code",
      "source": [
        "runs = 1000\n",
        "steps = 50\n",
        "\n",
        "sim_a = Diffusion_1D(0.5,[-4])\n",
        "endpoints_a = sim_a.analyze(runs,steps)\n",
        "sim_b = Diffusion_1D(0.5,filters=[6])\n",
        "endpoints_b = sim_b.analyze(runs,steps)\n",
        "sim_c = Diffusion_1D(0.5,[-4],[6])\n",
        "endpoints_c = sim_c.analyze(runs,steps)\n",
        "sim_d = Diffusion_1D(0.75,[-4],[6])\n",
        "endpoints_d = sim_d.analyze(runs,steps)\n",
        "sim_e = Diffusion_1D(0.5,np.random.randint(-steps,steps,10),np.random.randint(-steps,steps,10))\n",
        "endpoints_e = sim_e.analyze(runs,steps)\n",
        "sim_f = Diffusion_1D(0.75,np.random.randint(-steps,steps,10),np.random.randint(-steps,steps,10))\n",
        "endpoints_f = sim_f.analyze(runs,steps)\n",
        "\n",
        "\n",
        "plt.figure(figsize=(18,10))\n",
        "plt.subplot(2,3,1)\n",
        "plt.title(\"Unbiased Walk with a Reflector\")\n",
        "plt.xlim(-steps,steps)\n",
        "plt.hist(endpoints_a,density=True)\n",
        "plt.subplot(2,3,2)\n",
        "plt.title(\"Unbiased Walk with a Filter\")\n",
        "plt.xlim(-steps,steps)\n",
        "plt.hist(endpoints_b,density=True)\n",
        "plt.subplot(2,3,3)\n",
        "plt.title(\"Unbiased Walk with Both\")\n",
        "plt.xlim(-steps,steps)\n",
        "plt.hist(endpoints_c,density=True)\n",
        "plt.subplot(2,3,4)\n",
        "plt.title(\"Biased Walk (p=0.75) with Both\")\n",
        "plt.xlim(-steps,steps)\n",
        "plt.hist(endpoints_d,density=True)\n",
        "plt.subplot(2,3,5)\n",
        "plt.title(\"Unbiased Walk with Many Obstacles\")\n",
        "plt.xlim(-steps,steps)\n",
        "plt.hist(endpoints_e,density=True)\n",
        "plt.subplot(2,3,6)\n",
        "plt.title(\"Biased Walk (p=0.75) with Many Obstacles\")\n",
        "plt.xlim(-steps,steps)\n",
        "plt.hist(endpoints_f,density=True)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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            "text/plain": [
              "<Figure size 1296x720 with 6 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "1JorqoLFSESO",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### Exercise 4: Wiener Process / Brownian Motion\n",
        "\n",
        "*Plot the density of end positions for varying step count and step size variance for a Weiner Process walk.*"
      ]
    },
    {
      "metadata": {
        "id": "LVUQx2FnPFdz",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "class Weiner_2D():\n",
        "    \n",
        "    def __init__(self,variance):\n",
        "        \n",
        "        self.state = [0,0]\n",
        "        self.var = variance\n",
        "        \n",
        "    def step(self):\n",
        "        \n",
        "        degree = np.random.uniform(0,2*np.pi)\n",
        "        size = np.random.normal(0,self.var)\n",
        "        dx = size*np.cos(degree)\n",
        "        dy = size*np.sin(degree)\n",
        "        \n",
        "        self.state = [self.state[0]+dx,self.state[1]+dy]\n",
        "        \n",
        "    def run(self,steps):\n",
        "        \n",
        "        for i in range(steps):\n",
        "            self.step()\n",
        "            \n",
        "        return(self.state)\n",
        "    \n",
        "    def analyze(self,runs,steps):\n",
        "        \n",
        "        endpoints=[]\n",
        "        for i in range(runs):\n",
        "            self.state=[0,0]\n",
        "            endpoints.append(self.run(steps))\n",
        "            \n",
        "        return(endpoints)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "A_C3URP6TFec",
        "colab_type": "code",
        "outputId": "d2e8ae2c-2496-4270-d300-218df83627a0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 787
        }
      },
      "cell_type": "code",
      "source": [
        "counts = [20,400,1600]\n",
        "varss = [0.5,1,2]\n",
        "runs = 100\n",
        "\n",
        "plt.figure(figsize=(12,12))\n",
        "plt.suptitle(\"Final States, increasing step counts with rows and step size variance with columns\")\n",
        "for i in range(len(counts)):\n",
        "    for j in range(len(varss)):\n",
        "        sim = Weiner_2D(varss[j])\n",
        "        endpoints = sim.analyze(runs,counts[i])\n",
        "        ax = plt.subplot(3,3,1+3*i+j)\n",
        "        ax.set_xlim([-200,200])\n",
        "        ax.set_ylim([-200,200])\n",
        "        ax.scatter([x[0] for x in endpoints],[x[1] for x in endpoints])\n",
        "        \n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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phRdekLe3t959912lpKQoMjJSPXv21NmzZ/XOO+8Ues5hw4bpqaeeUufOnfXj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\niIiIVGAiTURERESkwv8HdqSpuFUD3AwAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x864 with 9 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "rvWQAa5baqkB",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "#### Exercise 9a: : Diffusion in the Plane\n",
        "\n",
        "_Starting at the origin in the plane, carry out a random walk on the lattice of integer coordinate\n",
        "points over the square [–20, 20] × [–20, 20]. Assume that there is a square hole whose boundary is\n",
        "(13, 7), (14, 7), (14, 8), and (13, 8). Walks that reach this hole are absorbed, along with any walk\n",
        "which reaches the boundary. Show the distribution of final positions for walks of various steps and\n",
        "especially the fraction that enters the hole._"
      ]
    },
    {
      "metadata": {
        "id": "yLNEAvCkb7E0",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "I implemented instead a class which accepts inputs for the size of the plane and the coordinates of the hole."
      ]
    },
    {
      "metadata": {
        "id": "oPhf6RUjTOaH",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "class Doughnut_2D():\n",
        "    \n",
        "    def __init__(self,size,hole):\n",
        "        \n",
        "        self.bounds = ((-np.int(size[0]/2),np.int(size[0]/2)), \\\n",
        "                      (-np.int(size[1]/2),np.int(size[1]/2)))\n",
        "        self.holex = range(hole[0][0],hole[1][0]+1)\n",
        "        self.holey = range(hole[0][1],hole[1][1]+1)\n",
        "        self.state = [0,0]\n",
        "        \n",
        "    def step(self):\n",
        "        \n",
        "        # Periodic boundaries\n",
        "        dimension = np.random.choice([0,1])\n",
        "        direction = np.random.choice([1,-1])\n",
        "       \n",
        "        self.state[dimension] = self.state[dimension]+direction\n",
        "        \n",
        "        if self.state[dimension] > self.bounds[dimension][1]:\n",
        "            self.state[dimension]=self.bounds[dimension][0]\n",
        "        elif self.state[dimension] < self.bounds[dimension][0]:\n",
        "            self.state[dimension]=self.bounds[dimension][1]\n",
        "        \n",
        "    def run(self,steps):\n",
        "        \n",
        "        for i in range(steps):\n",
        "            if (self.state[0] in self.holex) and (self.state[1] in self.holey):\n",
        "                break\n",
        "            self.step()\n",
        "            \n",
        "        return(self.state)\n",
        "    \n",
        "    def analyze(self,runs,steps):\n",
        "        \n",
        "        endpoints=[]\n",
        "        for i in range(runs):\n",
        "            self.state=[0,0]\n",
        "            endpoints.append(self.run(steps))\n",
        "            \n",
        "        return(endpoints)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "itJw04ZNgL2q",
        "colab_type": "code",
        "outputId": "d2962674-e59d-4d5e-901a-580df553fa9f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 770
        }
      },
      "cell_type": "code",
      "source": [
        "size=(40,40)\n",
        "holes=[((13,7),(14,8)),((2,7),(10,12))]\n",
        "counts=[10,100,1000,10000]\n",
        "runs = 100\n",
        "\n",
        "plt.figure(figsize=(24,12))\n",
        "plt.suptitle(\"Final States, with step count 10, 100, 1000 and 10000\")\n",
        "for h in range(2):\n",
        "    for i in range(len(counts)):\n",
        "        sim = Doughnut_2D(size,holes[h])\n",
        "        endpoints = sim.analyze(runs,counts[i])\n",
        "        xs = [x[0] for x in endpoints]\n",
        "        ys = [x[1] for x in endpoints]\n",
        "        absorbed = 0\n",
        "        for j in range(len(xs)):\n",
        "            if xs[j] in sim.holex and ys[j] in sim.holey:\n",
        "                absorbed += 1\n",
        "        ax = plt.subplot(2,4,1+4*h+i)\n",
        "        ax.set_title(\"Absorption Rate: \" +str(absorbed/runs))\n",
        "        ax.set_xlim(sim.bounds[0])\n",
        "        ax.set_ylim(sim.bounds[1])\n",
        "        ax.set_xticks(range(sim.bounds[0][0],sim.bounds[0][1]))\n",
        "        ax.set_yticks(range(sim.bounds[1][0],sim.bounds[1][1]))\n",
        "        ax.set_xticklabels([])\n",
        "        ax.set_yticklabels([])\n",
        "        ax.scatter(xs,ys)\n",
        "        ax.fill([sim.holex[0],sim.holex[0],sim.holex[-1],sim.holex[-1]] \\\n",
        "                ,[sim.holey[0],sim.holey[-1],sim.holey[-1],sim.holey[0]],\"black\",alpha=0.5)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LMY4BAACrirgmaUVFTcj3XS5ns2WRyttaFq24tCX+ckYrLm0xb04r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\nE9ZXXw4mYiVriTa6XSPbRjeGtTneY1m2Od7j+Jp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BNWZSCzp4ZExWeyoYkI4eGlZ/rNty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\nYvqJl/ZLOx1jboq5nm2NnKG+aESzc5mSz/VGu2Rkc8XPur0vlcrW008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Fx1350Duutgn7oTHXxfaACHiAAA0GK5gqmFxTWZBdPzf9ntisf0pd//uP5u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\ncFw72H5hAABgqaXXJO33x3Ofj6Lw3rZl7au22YpLX/zLaSsuf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            "text/plain": [
              "<Figure size 1728x864 with 8 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}