Section 6 exercises are done

section_6_appendix/28_exercise_1.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A = np.array([[0.3, 0.6, 0.1],\n",
+    "     [0.5, 0.2, 0.3],\n",
+    "     [0.4, 0.1, 0.5]])\n",
+    "v = np.array([0.33, 0.33, 0.33])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "dist = []"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 67,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 0\n",
+      "[0.33 0.33 0.33]\n",
+      "[0.396 0.297 0.297]\n",
+      "Iteration 1\n",
+      "[0.396 0.297 0.297]\n",
+      "[0.3861 0.3267 0.2772]\n",
+      "Iteration 2\n",
+      "[0.3861 0.3267 0.2772]\n",
+      "[0.39006 0.32472 0.27522]\n",
+      "Iteration 3\n",
+      "[0.39006 0.32472 0.27522]\n",
+      "[0.389466 0.326502 0.274032]\n",
+      "Iteration 4\n",
+      "[0.389466 0.326502 0.274032]\n",
+      "[0.3897036 0.3263832 0.2739132]\n",
+      "Iteration 5\n",
+      "[0.3897036 0.3263832 0.2739132]\n",
+      "[0.38966796 0.32649012 0.27384192]\n",
+      "Iteration 6\n",
+      "[0.38966796 0.32649012 0.27384192]\n",
+      "[0.38968222 0.32648299 0.27383479]\n",
+      "Iteration 7\n",
+      "[0.38968222 0.32648299 0.27383479]\n",
+      "[0.38968008 0.32648941 0.27383052]\n",
+      "Iteration 8\n",
+      "[0.38968008 0.32648941 0.27383052]\n",
+      "[0.38968093 0.32648898 0.27383009]\n",
+      "Iteration 9\n",
+      "[0.38968093 0.32648898 0.27383009]\n",
+      "[0.3896808  0.32648936 0.27382983]\n",
+      "Iteration 10\n",
+      "[0.3896808  0.32648936 0.27382983]\n",
+      "[0.38968086 0.32648934 0.27382981]\n",
+      "Iteration 11\n",
+      "[0.38968086 0.32648934 0.27382981]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 12\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 13\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 14\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 15\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 16\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 17\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 18\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 19\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 20\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 21\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 22\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 23\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "Iteration 24\n",
+      "[0.38968085 0.32648936 0.27382979]\n",
+      "[0.38968085 0.32648936 0.27382979]\n"
+     ]
+    }
+   ],
+   "source": [
+    "for i in range(25):\n",
+    "    _v = v.dot(A)\n",
+    "    print(\"Iteration %i\" % i)\n",
+    "    print(v)\n",
+    "    print(_v)\n",
+    "    diff = _v - v\n",
+    "    dist.append(np.linalg.norm(diff))\n",
+    "    v = _v"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[0.08083316151184486,\n",
+       " 0.03704240812906204,\n",
+       " 0.004849989690710693,\n",
+       " 0.002222544487743674,\n",
+       " 0.00029099938144264706,\n",
+       " 0.00013335266926457683,\n",
+       " 1.7459962886455936e-05,\n",
+       " 8.001160155840784e-06,\n",
+       " 1.0475977731887158e-06,\n",
+       " 4.800696093667666e-07,\n",
+       " 6.285586635460998e-08,\n",
+       " 2.8804176523432448e-08,\n",
+       " 3.77135205560905e-09,\n",
+       " 1.728250651936743e-09,\n",
+       " 2.2628112469628292e-10,\n",
+       " 1.0369503822604577e-10,\n",
+       " 1.3576844819538952e-11,\n",
+       " 6.221705260970853e-12,\n",
+       " 8.145748833116578e-13,\n",
+       " 3.7327324007457455e-13,\n",
+       " 4.886006264695781e-14,\n",
+       " 2.2357835448669304e-14,\n",
+       " 2.9691980252969e-15,\n",
+       " 1.3799853365199569e-15,\n",
+       " 1.8410966031475738e-16]"
+      ]
+     },
+     "execution_count": 68,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dist"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(dist)\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_6_appendix/28_exercise_2.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from random import randrange\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "X = np.random.random(1000)\n",
+    "Y = [0]*1000"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for i in range(1000):\n",
+    "    for j in range(1000):\n",
+    "        Y[i] += X[randrange(1000)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.hist(Y, bins=100)\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_6_appendix/28_exercise_3.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "mnist = pd.read_csv(\"train.csv\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "C:\\Users\\litak\\Anaconda3\\envs\\tensorflow-cpu\\lib\\site-packages\\ipykernel_launcher.py:1: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  \"\"\"Entry point for launching an IPython kernel.\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "numpy.ndarray"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mnist_7 = mnist[mnist['label'] == 7].as_matrix()\n",
+    "type(mnist_7)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "M7_mean = np.array([np.mean(mnist_7[:,i]) for i in range(784)])\n",
+    "M7_mean = M7_mean.reshape(28, 28)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.imshow(255-M7_mean, cmap='gray')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "C:\\Users\\litak\\Anaconda3\\envs\\tensorflow-cpu\\lib\\site-packages\\ipykernel_launcher.py:1: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  \"\"\"Entry point for launching an IPython kernel.\n"
+     ]
+    }
+   ],
+   "source": [
+    "M_3 = mnist[mnist['label'] == 3].as_matrix()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "M3_mean = np.array([np.mean(M_3[:,i]) for i in range(784)])\n",
+    "M3_mean = M3_mean.reshape(28, 28)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.imshow(255-M3_mean, cmap='gray')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "C:\\Users\\litak\\Anaconda3\\envs\\tensorflow-cpu\\lib\\site-packages\\ipykernel_launcher.py:2: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  \n"
+     ]
+    }
+   ],
+   "source": [
+    "mnist = pd.read_csv(\"train.csv\")\n",
+    "M1 = mnist[mnist['label'] == 1].as_matrix()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "M1_mean = np.array([np.mean(M1[:,i]) for i in range(784)])\n",
+    "M1_mean = M1_mean.reshape(28, 28)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.imshow(255 - M1_mean, cmap='gray')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "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",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_6_appendix/28_exercise_4.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "C:\\Users\\litak\\Anaconda3\\envs\\tensorflow-cpu\\lib\\site-packages\\ipykernel_launcher.py:2: FutureWarning: Method .as_matrix will be removed in a future version. Use .values instead.\n",
+      "  \n"
+     ]
+    }
+   ],
+   "source": [
+    "mnist = pd.read_csv(\"train.csv\")\n",
+    "M6 = mnist[mnist['label'] == 6].as_matrix()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "M6_mean = np.array([np.mean(M6[:,i]) for i in range(784)])\n",
+    "M6_mean = M6_mean.reshape(28, 28)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "'''Manual rotation'''\n",
+    "# creating empty array\n",
+    "rotated = np.array([[0]*29]*28)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "for i in range(28):\n",
+    "    rotated[:,27-i] = M6_mean[i,:]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.imshow(255 - rotated, cmap='gray')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(28, 28)"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "'''Rotation with numpy function'''\n",
+    "\n",
+    "M6_rotated = np.rot90(M6_mean, k=3)\n",
+    "M6_rotated.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.imshow(255 - M6_rotated, cmap='gray')\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_6_appendix/28_exercise_5.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[1., 0., 0.],\n",
+       "       [0., 1., 0.],\n",
+       "       [0., 0., 1.]])"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "I3 = np.eye(3)\n",
+    "I3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A = np.array([[0.3, 0.6, 0.1],\n",
+    "              [0.5, 0.2, 0.3],\n",
+    "              [0.4, 0.1, 0.5]])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def is_symmetric_automatic(matrix):\n",
+    "    return (matrix == matrix.T).all()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 7,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_symmetric_automatic(A)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_symmetric_automatic(I3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def is_symmetric_manual(matrix):\n",
+    "    matrix_T = np.zeros((len(matrix), len(matrix[0])))\n",
+    "    for i in range(len(matrix)):\n",
+    "        for j in range(len(matrix[i])):\n",
+    "            matrix_T[i,j] = matrix[j,i]\n",
+    "    return(matrix_T == matrix).all()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_symmetric_manual(A)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "is_symmetric_automatic(I3)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_6_appendix/28_exercise_7.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "theta = np.linspace(-np.pi, np.pi, 200)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for t in theta:\n",
+    "    plt.scatter(10*np.sin(t) + 2*np.random.random(1), 10*np.cos(t) + 2*np.random.random(1), color='blue')\n",
+    "    plt.scatter(20*np.sin(t) + 2*np.random.random(1), 20*np.cos(t) + 2*np.random.random(1), color='red')\n",
+    "plt.axis('equal')\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

section_6_appendix/28_exercise_9.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "b = np.random.uniform(-1, 1, (1000, 2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>0</th>\n",
+       "      <th>1</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>-0.131156</td>\n",
+       "      <td>-0.189478</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>-0.016687</td>\n",
+       "      <td>0.727200</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>-0.647184</td>\n",
+       "      <td>0.910890</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>-0.492190</td>\n",
+       "      <td>0.149369</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>-0.576105</td>\n",
+       "      <td>0.550543</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "          0         1\n",
+       "0 -0.131156 -0.189478\n",
+       "1 -0.016687  0.727200\n",
+       "2 -0.647184  0.910890\n",
+       "3 -0.492190  0.149369\n",
+       "4 -0.576105  0.550543"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.DataFrame(b)\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "csv = df.to_csv(path_or_buf=\"data.csv\")"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}