LFD Problem 3_3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 3.3 For the double semi circle task in Problem 3.1 , set sep = -5 and generate 2, 000 examples. (a) What will happen if you run PLA on those examples?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PLA took 3917 iterations to converge\n",
      "z = [-15.          -7.90420471  -4.58885576]\n",
      "slope = -1.7224783518568119\n",
      "intercept = -3.2687887316080677\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x648 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#parameters\n",
    "rad = 10\n",
    "thk = 5\n",
    "sep = -5\n",
    "\n",
    "plt.figure(figsize=(8,9))\n",
    "\n",
    "#n data points,(x1,y1) are the coordinates of the top semi-circle\n",
    "def generatedata(rad,thk,sep,n,x1=0,y1=0):\n",
    "    # center of the top semi-circle\n",
    "    X1 = x1\n",
    "    Y1 = y1\n",
    "\n",
    "    # center of the bottom semi-circle\n",
    "    X2 = X1 + rad + thk / 2\n",
    "    Y2 = Y1 - sep\n",
    "    \n",
    "    # data points in the top semi-circle\n",
    "    top = []\n",
    "    # data points in the bottom semi-circle\n",
    "    bottom = []\n",
    "    \n",
    "    # parameters\n",
    "    r1 = rad + thk\n",
    "    r2 = rad\n",
    "    \n",
    "    cnt = 1\n",
    "    while(cnt <= n):\n",
    "        #uniformed generated points\n",
    "        x = np.random.uniform(-r1,r1)\n",
    "        y = np.random.uniform(-r1,r1)\n",
    "        \n",
    "        d = x**2 + y**2\n",
    "        if(d >= r2**2 and d <= r1**2):\n",
    "            if (y > 0):\n",
    "                top.append([X1 + x,Y1 + y])\n",
    "                cnt += 1\n",
    "            else:\n",
    "                bottom.append([X2 + x,Y2 + y])\n",
    "                cnt += 1\n",
    "        else:\n",
    "            continue\n",
    "\n",
    "    return top,bottom\n",
    "\n",
    "\n",
    "top,bottom = generatedata(rad,thk,sep,1000)\n",
    "\n",
    "X1 = [i[0] for i in top]\n",
    "Y1 = [i[1] for i in top]\n",
    "\n",
    "X2 = [i[0] for i in bottom]\n",
    "Y2 = [i[1] for i in bottom]\n",
    "\n",
    "\n",
    "plt.scatter(X1,Y1,s = 1)\n",
    "plt.scatter(X2,Y2,s = 1)\n",
    "\n",
    "\n",
    "# pre-processing the data for (a)\n",
    "x1 = [[1] + i + [1] for i in top]\n",
    "x2 = [[1] + i + [-1] for i in bottom]\n",
    "data = x1 + x2\n",
    "\n",
    "X= [np.array(data[i][:3])for i in range(1000)]\n",
    "Y= [np.array(data[i][3])for i in range(1000)]\n",
    "    \n",
    "\n",
    "def Perceptron(X, Y):\n",
    "\n",
    "    weights = np.array([0,0,0])\n",
    "\n",
    "    epoch = 100\n",
    "    iteration = 0\n",
    "    \n",
    "    for k in range(epoch):\n",
    "        for i, n in enumerate(X):\n",
    "\n",
    "            predicted_y =  np.sign(np.dot(X[i] ,(np.transpose(weights))))\n",
    "\n",
    "            actual_y = Y[i]\n",
    "\n",
    "            if predicted_y == actual_y:\n",
    "                weights = weights\n",
    "            else:\n",
    "                iteration = iteration + 1\n",
    "                weights = weights + (X[i] * Y[i])\n",
    "                   \n",
    "    print(\"PLA took \" + str(iteration) + \" iterations to converge\")\n",
    "    return weights\n",
    " \n",
    "\n",
    "z = Perceptron(X,Y)\n",
    "\n",
    "w0 = z[0]\n",
    "w1 = z[1]\n",
    "w2 = z[2]\n",
    "\n",
    "slope = -w1/w2\n",
    "intercept = -w0/w2\n",
    "\n",
    "print(\"z =\", z)\n",
    "print(\"slope =\",slope)\n",
    "print(\"intercept =\",intercept)\n",
    "\n",
    "# Plot a line from slope and intercept\n",
    "def abline(slope, intercept):\n",
    "     \n",
    "     ax = plt.gca()\n",
    "     x_value = np.array(ax.get_xlim())\n",
    "     y_value = intercept + slope * x_value\n",
    "     plt.plot(x_value, y_value, '--')\n",
    "        \n",
    "abline(slope,intercept)         \n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PLA will  not  stop updating and converge in this case hence we are limiting the iterations and force stopping."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3(b) Run the pocket algorithm for 100, 000 iterations and plot Ein versus the iteration number t."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import *\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#parameters\n",
    "rad = 10\n",
    "thk = 5\n",
    "sep = -5\n",
    "\n",
    "#plt.figure(figsize=(8,9))\n",
    "\n",
    "#n data points,(x1,y1) are the coordinates of the top semi-circle\n",
    "def generatedata(rad,thk,sep,n,x1=0,y1=0):\n",
    "    # center of the top semi-circle\n",
    "    X1 = x1\n",
    "    Y1 = y1\n",
    "\n",
    "    # center of the bottom semi-circle\n",
    "    X2 = X1 + rad + thk / 2\n",
    "    Y2 = Y1 - sep\n",
    "    \n",
    "    # data points in the top semi-circle\n",
    "    top = []\n",
    "    # data points in the bottom semi-circle\n",
    "    bottom = []\n",
    "    \n",
    "    # parameters\n",
    "    r1 = rad + thk\n",
    "    r2 = rad\n",
    "    \n",
    "    cnt = 1\n",
    "    while(cnt <= n):\n",
    "        #uniformed generated points\n",
    "        x = np.random.uniform(-r1,r1)\n",
    "        y = np.random.uniform(-r1,r1)\n",
    "        \n",
    "        d = x**2 + y**2\n",
    "        if(d >= r2**2 and d <= r1**2):\n",
    "            if (y > 0):\n",
    "                top.append([X1 + x,Y1 + y])\n",
    "                cnt += 1\n",
    "            else:\n",
    "                bottom.append([X2 + x,Y2 + y])\n",
    "                cnt += 1\n",
    "        else:\n",
    "            continue\n",
    "\n",
    "    return top,bottom\n",
    "\n",
    "top,bottom = generatedata(rad,thk,sep,1000)\n",
    "\n",
    "X1 = [i[0] for i in top]\n",
    "Y1 = [i[1] for i in top]\n",
    "\n",
    "X2 = [i[0] for i in bottom]\n",
    "Y2 = [i[1] for i in bottom]\n",
    "\n",
    "\n",
    "#plt.scatter(X1,Y1,s = 1)\n",
    "#plt.scatter(X2,Y2,s = 1)\n",
    "\n",
    "# pre-processing the data for (a)\n",
    "x1 = [[1] + i + [1] for i in top]\n",
    "x2 = [[1] + i + [-1] for i in bottom]\n",
    "data = x1 + x2\n",
    "\n",
    "X= [np.array(data[i][:3])for i in range(1000)]\n",
    "Y= [np.array(data[i][3])for i in range(1000)]\n",
    "    \n",
    "    \n",
    "def Ein_calc(X,Y,weights):\n",
    "    \n",
    "    Ein = 0\n",
    "    for i, n in enumerate(X):\n",
    "\n",
    "        predicted_y =  np.sign(np.dot(X[i] ,(np.transpose(weights))))\n",
    "        actual_y = Y[i]\n",
    "        if predicted_y != actual_y:            \n",
    "            Ein = Ein + 1\n",
    "                        \n",
    "    return Ein\n",
    "    \n",
    "def Perceptron(X, Y):\n",
    "\n",
    "    weights = np.array([0,0,0])\n",
    "    pocket_weight = weights\n",
    "    epoch_weight = pocket_weight\n",
    "    Ein = []   \n",
    "    epoch = 100\n",
    "    iteration = []\n",
    "    pocket_error = 0                        # initializing the pocket error to be 0 at start for pocket_weight =0\n",
    "    updated_error = []                      # final error\n",
    "    \n",
    "    for k in range(epoch):\n",
    "        \n",
    "        pocket_Ein = Ein_calc(X,Y,pocket_weight)  # runs Ein_calc using pocket weight and gets the number of error points for X    \n",
    "        Ein.append(k)                   # appending epch value to Ein for reference\n",
    "        iteration.append(k)             # appending the epoch  \n",
    "        for i, n in enumerate(X):         \n",
    "            predicted_y =  np.sign(np.dot(X[i] ,(np.transpose(weights))))\n",
    "            actual_y = Y[i]\n",
    "            if predicted_y == actual_y:\n",
    "                weights = weights\n",
    "                pocket_weight=weights  \n",
    "            else:             \n",
    "                weights = weights + (X[i] * Y[i]) \n",
    "                pocket_weight = weights\n",
    "                misclass_Ein = Ein_calc(X,Y, weights) # Using the new weight, runs Ein_calc and find no.of errored points for X               \n",
    "                if misclass_Ein < pocket_Ein:        # Compares Ein for old weight and new weight\n",
    "                    pocket_weight = weights          # if new weight has less points than old, new weight is best\n",
    "                    Ein[k] = misclass_Ein            # Stores the error in a separate array\n",
    "        \n",
    "        if ((Ein[k] < pocket_error)):\n",
    "            pocket_error = Ein[k]                 # Assign Ein as pocket error and append it to updated error list\n",
    "            updated_error.append(Ein[k])                    \n",
    "        elif(k>=1):   \n",
    "            updated_error.append(pocket_error)    # if pocket error is less append it to updated error list\n",
    "        else:\n",
    "            pocket_error = Ein[k]\n",
    "            updated_error.append(pocket_error)   # if both Ein equal, retain pocket error\n",
    "        \n",
    "    #print(len(Ein),len(iterate))\n",
    "    plt.xlabel('Iterations')\n",
    "    plt.ylabel('Ein')\n",
    "    plt.plot(iteration,updated_error,color='blue')\n",
    "    plt.show()\n",
    "    \n",
    "    \n",
    "    return pocket_weight               \n",
    "                          \n",
    "            \n",
    "z = Perceptron(X,Y)\n",
    "\n",
    "\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3 (c) Plot the data and the final hypothesis in part (b ) ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time_elapsed 6.418875409508473e-05\n",
      "z = [-19.         -16.02805146  -5.0163038 ]\n",
      "slope = -3.195191539593822\n",
      "intercept = -3.7876493851148245\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import *\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "time_start = time.clock()\n",
    "#run your code\n",
    "time_elapsed = (time.clock() - time_start)\n",
    "print('time_elapsed', time_elapsed)\n",
    "\n",
    "plt.figure(figsize=(8,9))\n",
    "\n",
    "#parameters\n",
    "rad = 10\n",
    "thk = 5\n",
    "sep = -5\n",
    "\n",
    "#n data points,(x1,y1) are the coordinates of the top semi-circle\n",
    "def generatedata(rad,thk,sep,n,x1=0,y1=0):\n",
    "    # center of the top semi-circle\n",
    "    X1 = x1\n",
    "    Y1 = y1\n",
    "\n",
    "    # center of the bottom semi-circle\n",
    "    X2 = X1 + rad + thk / 2\n",
    "    Y2 = Y1 - sep\n",
    "    \n",
    "    # data points in the top semi-circle\n",
    "    top = []\n",
    "    # data points in the bottom semi-circle\n",
    "    bottom = []\n",
    "    \n",
    "    # parameters\n",
    "    r1 = rad + thk\n",
    "    r2 = rad\n",
    "    \n",
    "    cnt = 1\n",
    "    while(cnt <= n):\n",
    "        #uniformed generated points\n",
    "        x = np.random.uniform(-r1,r1)\n",
    "        y = np.random.uniform(-r1,r1)\n",
    "        \n",
    "        d = x**2 + y**2\n",
    "        if(d >= r2**2 and d <= r1**2):\n",
    "            if (y > 0):\n",
    "                top.append([X1 + x,Y1 + y])\n",
    "                cnt += 1\n",
    "            else:\n",
    "                bottom.append([X2 + x,Y2 + y])\n",
    "                cnt += 1\n",
    "        else:\n",
    "            continue\n",
    "\n",
    "    return top,bottom\n",
    "\n",
    "top,bottom = generatedata(rad,thk,sep,1000)\n",
    "\n",
    "X1 = [i[0] for i in top]\n",
    "Y1 = [i[1] for i in top]\n",
    "\n",
    "X2 = [i[0] for i in bottom]\n",
    "Y2 = [i[1] for i in bottom]\n",
    "\n",
    "\n",
    "plt.scatter(X1,Y1,s = 1)\n",
    "plt.scatter(X2,Y2,s = 1)\n",
    "\n",
    "# pre-processing the data for (a)\n",
    "x1 = [[1] + i + [1] for i in top]\n",
    "x2 = [[1] + i + [-1] for i in bottom]\n",
    "data = x1 + x2\n",
    "\n",
    "X= [np.array(data[i][:3])for i in range(1000)]\n",
    "Y= [np.array(data[i][3])for i in range(1000)]\n",
    "    \n",
    "    \n",
    "def Ein_calc(X,Y,weights):\n",
    "    \n",
    "    Ein = 0\n",
    "    for i, n in enumerate(X):\n",
    "\n",
    "        predicted_y =  np.sign(np.dot(X[i] ,(np.transpose(weights))))\n",
    "        actual_y = Y[i]\n",
    "        if predicted_y != actual_y:            \n",
    "            Ein = Ein + 1\n",
    "                        \n",
    "    return Ein\n",
    "    \n",
    "def Perceptron(X, Y):\n",
    "\n",
    "    weights = np.array([0,0,0])\n",
    "    pocket_weight = weights\n",
    "    epoch_weight = pocket_weight\n",
    "    Ein = []   \n",
    "    pocket_Ein = Ein_calc(X,Y,pocket_weight)  # runs Ein_calc using weights =0 and gets the number of error points for X\n",
    "    epoch = 100\n",
    "    iteration = []\n",
    "    pocket_error = 0\n",
    "    updated_error = []\n",
    "    \n",
    "    for k in range(epoch):\n",
    "            \n",
    "        Ein.append(k)\n",
    "        iteration.append(k)    \n",
    "        for i, n in enumerate(X):         \n",
    "            predicted_y =  np.sign(np.dot(X[i] ,(np.transpose(weights))))\n",
    "            actual_y = Y[i]\n",
    "            if predicted_y == actual_y:\n",
    "                weights = weights\n",
    "                pocket_weight=weights  \n",
    "            else:             \n",
    "                weights = weights + (X[i] * Y[i]) \n",
    "                pocket_weight = weights\n",
    "                misclass_Ein = Ein_calc(X,Y, weights) # Using the new weight, runs Ein_calc and find no.of errored points for X               \n",
    "                if misclass_Ein < pocket_Ein:         # Compares Ein for old weight and new weight\n",
    "                    pocket_weight = weights           # if new weight has less error points than old, new weight is best\n",
    "                    Ein[k] = misclass_Ein             # Storing the Errored points in a separate array \n",
    "        \n",
    "    if ((Ein[k] < pocket_error)):          \n",
    "        pocket_error = Ein[k]                # Assign Ein as pocket error and append it to updated error list\n",
    "        updated_error = Ein[k]            \n",
    "    elif(k>=1):   \n",
    "        updated_error.append(pocket_error)   # if pocket error is less append it to updated error list\n",
    "    else:\n",
    "        pocket_error = Ein[k]\n",
    "        updated_error.append(pocket_error)   # if both Ein equal, retain pocket error\n",
    "            \n",
    "    \n",
    "    return pocket_weight               \n",
    "                          \n",
    "            \n",
    "z = Perceptron(X,Y)\n",
    "\n",
    "w0 = z[0]\n",
    "w1 = z[1]\n",
    "w2 = z[2]\n",
    "\n",
    "slope = -w1/w2\n",
    "intercept = -w0/w2\n",
    "\n",
    "print(\"z =\", z)\n",
    "print(\"slope =\",slope)\n",
    "print(\"intercept =\",intercept)\n",
    "\n",
    "\n",
    "def abline(slope, intercept):\n",
    "     # Plot a line from slope and intercept\n",
    "     ax = plt.gca()\n",
    "     x_value = np.array(ax.get_xlim())\n",
    "     y_value = intercept + slope * x_value\n",
    "     plt.plot(x_value, y_value, '--')\n",
    "        \n",
    "abline(slope,intercept)         \n",
    "\n",
    "\n",
    "top,bottom = generatedata(rad,thk,sep,1000)\n",
    "\n",
    "X1 = [i[0] for i in top]\n",
    "Y1 = [i[1] for i in top]\n",
    "\n",
    "X2 = [i[0] for i in bottom]\n",
    "Y2 = [i[1] for i in bottom]\n",
    "\n",
    "\n",
    "plt.scatter(X1,Y1,s = 1)\n",
    "plt.scatter(X2,Y2,s = 1)\n",
    "\n",
    "#plt.plot(slope,'bx')\n",
    "#plt.plot(intercept,'rx')\n",
    "\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3(d) Use the linear regression algorithm to obtain the weights w, and compare this result with the pocket algorithm in terms of computation time and quality of the solution ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time_elapsed 3.096163436566712e-05\n",
      "X: (1000, 3)\n",
      "X_trans (3, 1000)\n",
      "z = [-0.12059439 -0.02219944  0.10219446]\n",
      "slope = 0.217227474790305\n",
      "intercept = 1.1800482002336878\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import time\n",
    "\n",
    "time_start = time.clock()\n",
    "#run your code\n",
    "time_elapsed = (time.clock() - time_start)\n",
    "print('time_elapsed', time_elapsed)\n",
    "\n",
    "#parameters\n",
    "rad = 10\n",
    "thk = 5\n",
    "sep = -5\n",
    "\n",
    "#n data points,(x1,y1) are the coordinates of the top semi-circle\n",
    "def generatedata(rad,thk,sep,n,x1=0,y1=0):\n",
    "    # center of the top semi-circle\n",
    "    X1 = x1\n",
    "    Y1 = y1\n",
    "\n",
    "    # center of the bottom semi-circle\n",
    "    X2 = X1 + rad + thk / 2\n",
    "    Y2 = Y1 - sep\n",
    "    \n",
    "    # data points in the top semi-circle\n",
    "    top = []\n",
    "    # data points in the bottom semi-circle\n",
    "    bottom = []\n",
    "    \n",
    "    # parameters\n",
    "    r1 = rad + thk\n",
    "    r2 = rad\n",
    "    \n",
    "    cnt = 1\n",
    "    while(cnt <= n):\n",
    "        #uniformed generated points\n",
    "        x = np.random.uniform(-r1,r1)\n",
    "        y = np.random.uniform(-r1,r1)\n",
    "        \n",
    "        d = x**2 + y**2\n",
    "        if(d >= r2**2 and d <= r1**2):\n",
    "            if (y > 0):\n",
    "                top.append([X1 + x,Y1 + y])\n",
    "                cnt += 1\n",
    "            else:\n",
    "                bottom.append([X2 + x,Y2 + y])\n",
    "                cnt += 1\n",
    "        else:\n",
    "            continue\n",
    "\n",
    "    return top,bottom\n",
    "\n",
    "top,bottom = generatedata(rad,thk,sep,1000)\n",
    "\n",
    "X1 = [i[0] for i in top]\n",
    "Y1 = [i[1] for i in top]\n",
    "\n",
    "X2 = [i[0] for i in bottom]\n",
    "Y2 = [i[1] for i in bottom]\n",
    "\n",
    "\n",
    "plt.scatter(X1,Y1,s = 1)\n",
    "plt.scatter(X2,Y2,s = 1)\n",
    "\n",
    "# pre-processing the data for (a)\n",
    "x1 = [[1] + i + [1] for i in top]\n",
    "x2 = [[1] + i + [-1] for i in bottom]\n",
    "data = x1 + x2\n",
    "\n",
    "X = []\n",
    "Y = []\n",
    "\n",
    "for i in range(1000):\n",
    "    Y.append(data[i][3])\n",
    "#print(Y)\n",
    "\n",
    "for i in range(1000):\n",
    "    X.append(data[i][:3])\n",
    "\n",
    "\n",
    "def linear_reg(X,Y):\n",
    "    \n",
    "    print(\"X:\",np.shape(X))\n",
    "    \n",
    "    X_trans = np.transpose(X)\n",
    "    print(\"X_trans\",np.shape(X_trans))\n",
    "    \n",
    "    X_1 = (np.matmul(X_trans,X)) \n",
    "    X_inverse = np.linalg.inv(X_1)\n",
    "    #print(\"X_inverse:\",np.shape(X_inverse))\n",
    "    \n",
    "    X_pseudoinverse = np.matmul(X_inverse,X_trans)\n",
    "    #print(\"X_pseudoinverse\",np.shape(X_pseudoinverse))\n",
    "    #print(\"Y:\",np.shape(Y))\n",
    "    \n",
    "    w_lin = np.matmul(X_pseudoinverse, Y )\n",
    "    #print(\"w_lin\",np.shape(w_lin))   \n",
    "    return (w_lin)\n",
    "    \n",
    "z = linear_reg(X,Y)\n",
    "\n",
    "\n",
    "\n",
    "w0 = z[0]\n",
    "w1 = z[1]\n",
    "w2 = z[2]\n",
    "\n",
    "slope = -w1/w2\n",
    "intercept = -w0/w2\n",
    "\n",
    "print(\"z =\", z)\n",
    "print(\"slope =\",slope)\n",
    "print(\"intercept =\",intercept)\n",
    "\n",
    "\n",
    "def abline(slope, intercept):\n",
    "     # Plot a line from slope and intercept\n",
    "     ax = plt.gca()\n",
    "     x_value = np.array(ax.get_xlim())\n",
    "     y_value = intercept + slope * x_value\n",
    "     plt.plot(x_value, y_value, '--')\n",
    "        \n",
    "abline(slope,intercept)         \n",
    "\n",
    "\n",
    "top,bottom = generatedata(rad,thk,sep,1000)\n",
    "\n",
    "X1 = [i[0] for i in top]\n",
    "Y1 = [i[1] for i in top]\n",
    "\n",
    "X2 = [i[0] for i in bottom]\n",
    "Y2 = [i[1] for i in bottom]\n",
    "\n",
    "\n",
    "plt.scatter(X1,Y1,s = 1)\n",
    "plt.scatter(X2,Y2,s = 1)\n",
    "\n",
    "#plt.plot(slope,'bx')\n",
    "#plt.plot(intercept,'rx')\n",
    "\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### From the above pocket and linear algorithms we observe that the computaion of pocket is more when compared to linear but when comparing the quality of solution, pocket performs better. \n",
    "#### Note : Due the very long computation time  and system speed constraints for 100,000 iterations, I'm considering only 100 iterations as a sample and testing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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",
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