Rethinking_2/Chp_10.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:37.225938Z",
     "iopub.status.busy": "2022-06-01T19:06:37.225403Z",
     "iopub.status.idle": "2022-06-01T19:06:38.707838Z",
     "shell.execute_reply": "2022-06-01T19:06:38.707085Z"
    }
   },
   "outputs": [],
   "source": [
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:38.711822Z",
     "iopub.status.busy": "2022-06-01T19:06:38.711433Z",
     "iopub.status.idle": "2022-06-01T19:06:38.721678Z",
     "shell.execute_reply": "2022-06-01T19:06:38.721081Z"
    }
   },
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:38.725307Z",
     "iopub.status.busy": "2022-06-01T19:06:38.725036Z",
     "iopub.status.idle": "2022-06-01T19:06:38.729046Z",
     "shell.execute_reply": "2022-06-01T19:06:38.728572Z"
    }
   },
   "outputs": [],
   "source": [
    "d = {\n",
    "    \"A\": [0, 0, 10, 0, 0],\n",
    "    \"B\": [0, 1, 8, 1, 0],\n",
    "    \"C\": [0, 2, 6, 2, 0],\n",
    "    \"D\": [1, 2, 4, 2, 1],\n",
    "    \"E\": [2, 2, 2, 2, 2],\n",
    "}\n",
    "p = pd.DataFrame(data=d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:38.731951Z",
     "iopub.status.busy": "2022-06-01T19:06:38.731721Z",
     "iopub.status.idle": "2022-06-01T19:06:38.735958Z",
     "shell.execute_reply": "2022-06-01T19:06:38.735119Z"
    }
   },
   "outputs": [],
   "source": [
    "p_norm = p / p.sum(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:38.739367Z",
     "iopub.status.busy": "2022-06-01T19:06:38.739024Z",
     "iopub.status.idle": "2022-06-01T19:06:38.753598Z",
     "shell.execute_reply": "2022-06-01T19:06:38.752694Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A   -0.000000\n",
       "B    0.639032\n",
       "C    0.950271\n",
       "D    1.470808\n",
       "E    1.609438\n",
       "dtype: float64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def entropy(x):\n",
    "    y = [0 if i == 0 else i * np.log(i) for i in x]\n",
    "    return -sum(y)\n",
    "\n",
    "\n",
    "H = p_norm.apply(entropy, axis=0)\n",
    "H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:38.777658Z",
     "iopub.status.busy": "2022-06-01T19:06:38.777261Z",
     "iopub.status.idle": "2022-06-01T19:06:39.006026Z",
     "shell.execute_reply": "2022-06-01T19:06:39.005142Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 296,
       "width": 440
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ways = [1, 90, 1260, 37800, 113400]\n",
    "logwayspp = np.log(ways) / 10\n",
    "plt.plot(logwayspp, H, \"o\")\n",
    "plt.plot([0.0, max(logwayspp)], [0.0, max(H)], \"--k\")\n",
    "plt.ylabel(\"entropy\")\n",
    "plt.xlabel(\"log(ways) per pebble\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:39.009631Z",
     "iopub.status.busy": "2022-06-01T19:06:39.009344Z",
     "iopub.status.idle": "2022-06-01T19:06:39.015084Z",
     "shell.execute_reply": "2022-06-01T19:06:39.014527Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0, 1.0, 1.0, 1.0]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Build list of the candidate distributions.\n",
    "p = [\n",
    "    [1 / 4, 1 / 4, 1 / 4, 1 / 4],\n",
    "    [2 / 6, 1 / 6, 1 / 6, 2 / 6],\n",
    "    [1 / 6, 2 / 6, 2 / 6, 1 / 6],\n",
    "    [1 / 8, 4 / 8, 2 / 8, 1 / 8],\n",
    "]\n",
    "\n",
    "# Compute expected value of each. The sum of the multiplied entries is just a dot product.\n",
    "p_ev = [np.dot(i, [0, 1, 1, 2]) for i in p]\n",
    "p_ev"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:39.018160Z",
     "iopub.status.busy": "2022-06-01T19:06:39.017836Z",
     "iopub.status.idle": "2022-06-01T19:06:39.022174Z",
     "shell.execute_reply": "2022-06-01T19:06:39.021667Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.3862943611198906,\n",
       " 1.3296613488547582,\n",
       " 1.3296613488547582,\n",
       " 1.2130075659799042]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the entropy of each distribution\n",
    "p_ent = [entropy(i) for i in p]\n",
    "p_ent"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:39.025094Z",
     "iopub.status.busy": "2022-06-01T19:06:39.024843Z",
     "iopub.status.idle": "2022-06-01T19:06:39.029641Z",
     "shell.execute_reply": "2022-06-01T19:06:39.028983Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.09000000000000002,\n",
       " 0.21000000000000002,\n",
       " 0.21000000000000002,\n",
       " 0.48999999999999994]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = 0.7\n",
    "A = [(1 - p) ** 2, p * (1 - p), (1 - p) * p, p**2]\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:39.032382Z",
     "iopub.status.busy": "2022-06-01T19:06:39.032097Z",
     "iopub.status.idle": "2022-06-01T19:06:39.036669Z",
     "shell.execute_reply": "2022-06-01T19:06:39.036178Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.221728604109787"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-np.sum(A * np.log(A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:39.040119Z",
     "iopub.status.busy": "2022-06-01T19:06:39.039827Z",
     "iopub.status.idle": "2022-06-01T19:06:39.044636Z",
     "shell.execute_reply": "2022-06-01T19:06:39.043874Z"
    }
   },
   "outputs": [],
   "source": [
    "def sim_p(G=1.4):\n",
    "    x123 = np.random.uniform(size=3)\n",
    "    x4 = (G * np.sum(x123) - x123[1] - x123[2]) / (2 - G)\n",
    "    x1234 = np.concatenate((x123, [x4]))\n",
    "    z = np.sum(x1234)\n",
    "    p = x1234 / z\n",
    "    return -np.sum(p * np.log(p)), p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:39.051312Z",
     "iopub.status.busy": "2022-06-01T19:06:39.050734Z",
     "iopub.status.idle": "2022-06-01T19:06:41.211310Z",
     "shell.execute_reply": "2022-06-01T19:06:41.210195Z"
    }
   },
   "outputs": [],
   "source": [
    "H = np.zeros(10**5)\n",
    "p = np.zeros((10**5, 4))\n",
    "for rep in range(10**5):\n",
    "    h, p_ = sim_p()\n",
    "    H[rep] = h\n",
    "    p[rep] = p_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:41.215082Z",
     "iopub.status.busy": "2022-06-01T19:06:41.214809Z",
     "iopub.status.idle": "2022-06-01T19:06:41.425036Z",
     "shell.execute_reply": "2022-06-01T19:06:41.424391Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 296,
       "width": 440
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_kde(H)\n",
    "plt.xlabel(\"Entropy\")\n",
    "plt.ylabel(\"Density\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:41.427950Z",
     "iopub.status.busy": "2022-06-01T19:06:41.427691Z",
     "iopub.status.idle": "2022-06-01T19:06:41.431664Z",
     "shell.execute_reply": "2022-06-01T19:06:41.431185Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2217247113399679"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code 10.13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:41.434410Z",
     "iopub.status.busy": "2022-06-01T19:06:41.434155Z",
     "iopub.status.idle": "2022-06-01T19:06:41.439527Z",
     "shell.execute_reply": "2022-06-01T19:06:41.438584Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.09050856, 0.20904247, 0.20994041, 0.49050856])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p[np.argmax(H)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-06-01T19:06:41.443835Z",
     "iopub.status.busy": "2022-06-01T19:06:41.443516Z",
     "iopub.status.idle": "2022-06-01T19:06:41.455648Z",
     "shell.execute_reply": "2022-06-01T19:06:41.454886Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.10.4\n",
      "IPython version      : 8.4.0\n",
      "\n",
      "numpy     : 1.22.4\n",
      "matplotlib: 3.5.2\n",
      "arviz     : 0.12.1\n",
      "pandas    : 1.4.2\n",
      "\n",
      "Watermark: 2.3.1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -iv -w"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}