logistic-regressors/logistic-regressor.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "03f8827e-7e96-494f-8f87-4eb8a2a03ff9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data',\n",
       " 'target',\n",
       " 'frame',\n",
       " 'target_names',\n",
       " 'DESCR',\n",
       " 'feature_names',\n",
       " 'filename',\n",
       " 'data_module']"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "df29211b-b8ae-4d64-a903-de8ba22daa5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'data': array([[5.1, 3.5, 1.4, 0.2],\n",
       "        [4.9, 3. , 1.4, 0.2],\n",
       "        [4.7, 3.2, 1.3, 0.2],\n",
       "        [4.6, 3.1, 1.5, 0.2],\n",
       "        [5. , 3.6, 1.4, 0.2],\n",
       "        [5.4, 3.9, 1.7, 0.4],\n",
       "        [4.6, 3.4, 1.4, 0.3],\n",
       "        [5. , 3.4, 1.5, 0.2],\n",
       "        [4.4, 2.9, 1.4, 0.2],\n",
       "        [4.9, 3.1, 1.5, 0.1],\n",
       "        [5.4, 3.7, 1.5, 0.2],\n",
       "        [4.8, 3.4, 1.6, 0.2],\n",
       "        [4.8, 3. , 1.4, 0.1],\n",
       "        [4.3, 3. , 1.1, 0.1],\n",
       "        [5.8, 4. , 1.2, 0.2],\n",
       "        [5.7, 4.4, 1.5, 0.4],\n",
       "        [5.4, 3.9, 1.3, 0.4],\n",
       "        [5.1, 3.5, 1.4, 0.3],\n",
       "        [5.7, 3.8, 1.7, 0.3],\n",
       "        [5.1, 3.8, 1.5, 0.3],\n",
       "        [5.4, 3.4, 1.7, 0.2],\n",
       "        [5.1, 3.7, 1.5, 0.4],\n",
       "        [4.6, 3.6, 1. , 0.2],\n",
       "        [5.1, 3.3, 1.7, 0.5],\n",
       "        [4.8, 3.4, 1.9, 0.2],\n",
       "        [5. , 3. , 1.6, 0.2],\n",
       "        [5. , 3.4, 1.6, 0.4],\n",
       "        [5.2, 3.5, 1.5, 0.2],\n",
       "        [5.2, 3.4, 1.4, 0.2],\n",
       "        [4.7, 3.2, 1.6, 0.2],\n",
       "        [4.8, 3.1, 1.6, 0.2],\n",
       "        [5.4, 3.4, 1.5, 0.4],\n",
       "        [5.2, 4.1, 1.5, 0.1],\n",
       "        [5.5, 4.2, 1.4, 0.2],\n",
       "        [4.9, 3.1, 1.5, 0.2],\n",
       "        [5. , 3.2, 1.2, 0.2],\n",
       "        [5.5, 3.5, 1.3, 0.2],\n",
       "        [4.9, 3.6, 1.4, 0.1],\n",
       "        [4.4, 3. , 1.3, 0.2],\n",
       "        [5.1, 3.4, 1.5, 0.2],\n",
       "        [5. , 3.5, 1.3, 0.3],\n",
       "        [4.5, 2.3, 1.3, 0.3],\n",
       "        [4.4, 3.2, 1.3, 0.2],\n",
       "        [5. , 3.5, 1.6, 0.6],\n",
       "        [5.1, 3.8, 1.9, 0.4],\n",
       "        [4.8, 3. , 1.4, 0.3],\n",
       "        [5.1, 3.8, 1.6, 0.2],\n",
       "        [4.6, 3.2, 1.4, 0.2],\n",
       "        [5.3, 3.7, 1.5, 0.2],\n",
       "        [5. , 3.3, 1.4, 0.2],\n",
       "        [7. , 3.2, 4.7, 1.4],\n",
       "        [6.4, 3.2, 4.5, 1.5],\n",
       "        [6.9, 3.1, 4.9, 1.5],\n",
       "        [5.5, 2.3, 4. , 1.3],\n",
       "        [6.5, 2.8, 4.6, 1.5],\n",
       "        [5.7, 2.8, 4.5, 1.3],\n",
       "        [6.3, 3.3, 4.7, 1.6],\n",
       "        [4.9, 2.4, 3.3, 1. ],\n",
       "        [6.6, 2.9, 4.6, 1.3],\n",
       "        [5.2, 2.7, 3.9, 1.4],\n",
       "        [5. , 2. , 3.5, 1. ],\n",
       "        [5.9, 3. , 4.2, 1.5],\n",
       "        [6. , 2.2, 4. , 1. ],\n",
       "        [6.1, 2.9, 4.7, 1.4],\n",
       "        [5.6, 2.9, 3.6, 1.3],\n",
       "        [6.7, 3.1, 4.4, 1.4],\n",
       "        [5.6, 3. , 4.5, 1.5],\n",
       "        [5.8, 2.7, 4.1, 1. ],\n",
       "        [6.2, 2.2, 4.5, 1.5],\n",
       "        [5.6, 2.5, 3.9, 1.1],\n",
       "        [5.9, 3.2, 4.8, 1.8],\n",
       "        [6.1, 2.8, 4. , 1.3],\n",
       "        [6.3, 2.5, 4.9, 1.5],\n",
       "        [6.1, 2.8, 4.7, 1.2],\n",
       "        [6.4, 2.9, 4.3, 1.3],\n",
       "        [6.6, 3. , 4.4, 1.4],\n",
       "        [6.8, 2.8, 4.8, 1.4],\n",
       "        [6.7, 3. , 5. , 1.7],\n",
       "        [6. , 2.9, 4.5, 1.5],\n",
       "        [5.7, 2.6, 3.5, 1. ],\n",
       "        [5.5, 2.4, 3.8, 1.1],\n",
       "        [5.5, 2.4, 3.7, 1. ],\n",
       "        [5.8, 2.7, 3.9, 1.2],\n",
       "        [6. , 2.7, 5.1, 1.6],\n",
       "        [5.4, 3. , 4.5, 1.5],\n",
       "        [6. , 3.4, 4.5, 1.6],\n",
       "        [6.7, 3.1, 4.7, 1.5],\n",
       "        [6.3, 2.3, 4.4, 1.3],\n",
       "        [5.6, 3. , 4.1, 1.3],\n",
       "        [5.5, 2.5, 4. , 1.3],\n",
       "        [5.5, 2.6, 4.4, 1.2],\n",
       "        [6.1, 3. , 4.6, 1.4],\n",
       "        [5.8, 2.6, 4. , 1.2],\n",
       "        [5. , 2.3, 3.3, 1. ],\n",
       "        [5.6, 2.7, 4.2, 1.3],\n",
       "        [5.7, 3. , 4.2, 1.2],\n",
       "        [5.7, 2.9, 4.2, 1.3],\n",
       "        [6.2, 2.9, 4.3, 1.3],\n",
       "        [5.1, 2.5, 3. , 1.1],\n",
       "        [5.7, 2.8, 4.1, 1.3],\n",
       "        [6.3, 3.3, 6. , 2.5],\n",
       "        [5.8, 2.7, 5.1, 1.9],\n",
       "        [7.1, 3. , 5.9, 2.1],\n",
       "        [6.3, 2.9, 5.6, 1.8],\n",
       "        [6.5, 3. , 5.8, 2.2],\n",
       "        [7.6, 3. , 6.6, 2.1],\n",
       "        [4.9, 2.5, 4.5, 1.7],\n",
       "        [7.3, 2.9, 6.3, 1.8],\n",
       "        [6.7, 2.5, 5.8, 1.8],\n",
       "        [7.2, 3.6, 6.1, 2.5],\n",
       "        [6.5, 3.2, 5.1, 2. ],\n",
       "        [6.4, 2.7, 5.3, 1.9],\n",
       "        [6.8, 3. , 5.5, 2.1],\n",
       "        [5.7, 2.5, 5. , 2. ],\n",
       "        [5.8, 2.8, 5.1, 2.4],\n",
       "        [6.4, 3.2, 5.3, 2.3],\n",
       "        [6.5, 3. , 5.5, 1.8],\n",
       "        [7.7, 3.8, 6.7, 2.2],\n",
       "        [7.7, 2.6, 6.9, 2.3],\n",
       "        [6. , 2.2, 5. , 1.5],\n",
       "        [6.9, 3.2, 5.7, 2.3],\n",
       "        [5.6, 2.8, 4.9, 2. ],\n",
       "        [7.7, 2.8, 6.7, 2. ],\n",
       "        [6.3, 2.7, 4.9, 1.8],\n",
       "        [6.7, 3.3, 5.7, 2.1],\n",
       "        [7.2, 3.2, 6. , 1.8],\n",
       "        [6.2, 2.8, 4.8, 1.8],\n",
       "        [6.1, 3. , 4.9, 1.8],\n",
       "        [6.4, 2.8, 5.6, 2.1],\n",
       "        [7.2, 3. , 5.8, 1.6],\n",
       "        [7.4, 2.8, 6.1, 1.9],\n",
       "        [7.9, 3.8, 6.4, 2. ],\n",
       "        [6.4, 2.8, 5.6, 2.2],\n",
       "        [6.3, 2.8, 5.1, 1.5],\n",
       "        [6.1, 2.6, 5.6, 1.4],\n",
       "        [7.7, 3. , 6.1, 2.3],\n",
       "        [6.3, 3.4, 5.6, 2.4],\n",
       "        [6.4, 3.1, 5.5, 1.8],\n",
       "        [6. , 3. , 4.8, 1.8],\n",
       "        [6.9, 3.1, 5.4, 2.1],\n",
       "        [6.7, 3.1, 5.6, 2.4],\n",
       "        [6.9, 3.1, 5.1, 2.3],\n",
       "        [5.8, 2.7, 5.1, 1.9],\n",
       "        [6.8, 3.2, 5.9, 2.3],\n",
       "        [6.7, 3.3, 5.7, 2.5],\n",
       "        [6.7, 3. , 5.2, 2.3],\n",
       "        [6.3, 2.5, 5. , 1.9],\n",
       "        [6.5, 3. , 5.2, 2. ],\n",
       "        [6.2, 3.4, 5.4, 2.3],\n",
       "        [5.9, 3. , 5.1, 1.8]]),\n",
       " 'target': array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]),\n",
       " 'frame': None,\n",
       " 'target_names': array(['setosa', 'versicolor', 'virginica'], dtype='<U10'),\n",
       " 'DESCR': '.. _iris_dataset:\\n\\nIris plants dataset\\n--------------------\\n\\n**Data Set Characteristics:**\\n\\n    :Number of Instances: 150 (50 in each of three classes)\\n    :Number of Attributes: 4 numeric, predictive attributes and the class\\n    :Attribute Information:\\n        - sepal length in cm\\n        - sepal width in cm\\n        - petal length in cm\\n        - petal width in cm\\n        - class:\\n                - Iris-Setosa\\n                - Iris-Versicolour\\n                - Iris-Virginica\\n                \\n    :Summary Statistics:\\n\\n    ============== ==== ==== ======= ===== ====================\\n                    Min  Max   Mean    SD   Class Correlation\\n    ============== ==== ==== ======= ===== ====================\\n    sepal length:   4.3  7.9   5.84   0.83    0.7826\\n    sepal width:    2.0  4.4   3.05   0.43   -0.4194\\n    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\\n    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\\n    ============== ==== ==== ======= ===== ====================\\n\\n    :Missing Attribute Values: None\\n    :Class Distribution: 33.3% for each of 3 classes.\\n    :Creator: R.A. Fisher\\n    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\\n    :Date: July, 1988\\n\\nThe famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\\nfrom Fisher\\'s paper. Note that it\\'s the same as in R, but not as in the UCI\\nMachine Learning Repository, which has two wrong data points.\\n\\nThis is perhaps the best known database to be found in the\\npattern recognition literature.  Fisher\\'s paper is a classic in the field and\\nis referenced frequently to this day.  (See Duda & Hart, for example.)  The\\ndata set contains 3 classes of 50 instances each, where each class refers to a\\ntype of iris plant.  One class is linearly separable from the other 2; the\\nlatter are NOT linearly separable from each other.\\n\\n.. topic:: References\\n\\n   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\\n     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\\n     Mathematical Statistics\" (John Wiley, NY, 1950).\\n   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\\n     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\\n   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\\n     Structure and Classification Rule for Recognition in Partially Exposed\\n     Environments\".  IEEE Transactions on Pattern Analysis and Machine\\n     Intelligence, Vol. PAMI-2, No. 1, 67-71.\\n   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\\n     on Information Theory, May 1972, 431-433.\\n   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\\n     conceptual clustering system finds 3 classes in the data.\\n   - Many, many more ...',\n",
       " 'feature_names': ['sepal length (cm)',\n",
       "  'sepal width (cm)',\n",
       "  'petal length (cm)',\n",
       "  'petal width (cm)'],\n",
       " 'filename': 'iris.csv',\n",
       " 'data_module': 'sklearn.datasets.data'}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b8d7e32c-5ed5-411e-b411-e4304f47c087",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1a602ea1-efee-4b93-aa9d-1bff49564e2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "29679ab5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xffff81b97610>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lp=iris.data[:,0:1]\n",
    "wp=iris.data[:,1:2]\n",
    "plt.plot(lp,wp,'.k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2874984a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xffff81298d00>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lp,'.k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "68274907",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.target"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6120b70a",
   "metadata": {},
   "source": [
    "# Logistic regressor\n",
    "## Decision boudaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a75ea97f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xffff65ac3e80>]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "t=np.linspace(-100, 100, 1000)\n",
    "sig=1/(1+np.exp(-t+3))\n",
    "plt.plot(t,sig, '.b', label=r\"$\\sigma=\\frac{1}{1+e^{-t}}$\")\n",
    "plt.legend(loc='upper left', fontsize=20)\n",
    "plt.axis([-5, 5, -0.1, 1])\n",
    "plt.plot([0,0], [0,1], 'r--')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2be6077b",
   "metadata": {},
   "source": [
    "# Iris-Setosa Classifier based on petal width"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f59aa9ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "X=iris.data[:,1:2]\n",
    "y=(iris.target==0).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "25839b5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\
      ],
      "text/plain": [
       "LogisticRegression(random_state=42)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "mylr=LogisticRegression(solver='lbfgs', random_state=42)\n",
    "mylr.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "4539a843",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xffff538572e0>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy89olMNAAAACXBIWXMAAA9hAAAPYQGoP6dpAABAKElEQVR4nO3de3xU1b3///ckkAQEEjhAAiQmiICIAnIRIlVRU6P1WNFyROUHaOOlFC+Ueo5wVMLFilKlVlGxiIJHKyBV66kWixgEkeMFDCJQFAuSKAnwbUkQJIFk/f4YM5AwezJ7bnsur+fjMY/Anr1m7+zZ2fOZtT7rs13GGCMAAACHJDm9AwAAILERjAAAAEcRjAAAAEcRjAAAAEcRjAAAAEcRjAAAAEcRjAAAAEcRjAAAAEe1cHoH/FFfX69vv/1Wbdu2lcvlcnp3AACAH4wxOnjwoLp27aqkJOv+j5gIRr799lvl5OQ4vRsAACAAZWVlys7Otnw+JoKRtm3bSnL/Mu3atXN4bwAAgD+qq6uVk5Pj+Ry3EhPBSMPQTLt27QhGAACIMc2lWJDACgAAHEUwAgAAHEUwAgAAHEUwAgAAHEUwAgAAHEUwAgAAHEUwAgAAHEUwAgAAHEUwAgAAHGU7GFmzZo2uvPJKde3aVS6XS6+//nqzbVavXq2BAwcqNTVVp59+uhYtWhTArkKSPvn2E128+GJ98u0nTu9K3AvmWI9YNEKuGS6NWDTCdttb//dWuWa4dOv/3mq77dVLrpZrhktXL7nadtsXNr2g9g+31wubXrDdNu+xPLlmuJT3WJ7ttsEcqxmrZ6jFzBaasXpGRNsG8x4Fc5yDOSedahsMrneJw3YwcujQIfXv319PPvmkX+vv3LlTV1xxhS666CKVlpZq0qRJuvnmm/X222/b3lm4L2Qlu0r0P5v+x+ldiXvBHOs1X69p9NOOhu0Fst3//eJ/G/2049H1j+rAkQOau36u7bZfV33d6KcdwRyrJz56QnWmTvM+mhfRtsG8R8Ec52DOSafaBoPrXeKwfW+ayy+/XJdffrnf68+fP1/du3fXo48+Kknq06eP3n//ff3ud79TYWGh3c0npK8PfK39h/fL5XJp6ZalkqQlW5Zo/IDxMsaoY+uOys3IdXgv40Mwx/ruv92tT/d8KpdcMjKSJCOjgsUFMjI6p8s5euTSR7y2nf/xfG2q3CSXy6UjdUckSUfqjuiXb/5Sxhj1z+yvXwz5hde2v1nzG/d2XS7VmTpJUp2p038s+w8Z497uvRfc67Xtut3rtPNfO+VKcmlz5WZJ0meVn+mlzS/J1Bt1b99dw08d7rXtT//4U23et1kuNb7nxGm/P01GRmd3Oltv3PBGyI/Vn7b+SVv3bZXL5dL/+/7/SZL2f79fD6x5QMYYndnpTP3szJ+FvG0w71EwxzmYc9KptsHgepeYXMYYE3Bjl0uvvfaaRo4cabnOBRdcoIEDB+qxxx7zLHv++ec1adIkVVVVeW1TU1Ojmpoaz/8b7vpXVVWVkDfKc804frFvuHifeBGXJFMc8NuIEwRzrE9sa4W2tA2mbTDnZCTbBoPrXfiUl0tffin17CllZze/PBSqq6uVnp7e7Od32BNYKyoqlJmZ2WhZZmamqqur9f3333ttM3v2bKWnp3seOTk54d7NqPbi1S+qRZK7E+vEb5GS1CKphV68+kXH9i3eBHOs26e19/navp7v26mvz7a+nu/WtpvPtr6enzB4gs+2vp5PdiX7bOvr+WCO1SXdL/HZ1tfzwbQN5j0K5jgHc0461TYYXO+OKy+XSkrcP/19zmr5woVSbq508cXunwsX+l4eaVE5m2bq1KmqqqryPMrKypzeJUeN6TdGH978odfnPrz5Q43pNybCexS/gjnW/7znn7okz/uH2SV5l+if9/zTsu3nv/zc8gNpwuAJ+vyXn1u2LZ9crlF9Rnl9blSfUSqf7OVK9oOnrnhKL17j/eL+4jUv6qkrnrJse2zaMXXP6O71ue4Z3XVs2jHLtsEcq3fGvaNZF83y+tysi2bpnXHvhKVtMO9RMMc5mHPSqbbBiNfrnd3AwleQYDewKC+Xbr1Vqq93/7++XrrtNunjj70v97aP4Rb2YCQrK0uVlZWNllVWVqpdu3Zq1aqV1zapqalq165do0dY+Do7olTSD29ZUnTGkXGFY41oE8w56VTbYETr32CoeiWsnrMKHsrLAwssvvzy+PIGdXXS++97X75jR3DHJxBhf4fz8/O1atWqRstWrlyp/Pz8cG/at+b6puyebWHW+ZTOymqTpUFdB2n+FfM1qOsgZbXJUudTOkd0PxJBMMf6vFPP8/y7dYvWXpdbObfbuZ5/56bnel1uJT/n+N9Th7QOXpdb6dWhl5JcSWrdsrVuOOsGtW7ZWkmuJPXq0Kv5fe56fN9OTGQ9cbmVYI7VgKwBnm0O6TrEs+2G5eFqG8x7FMxxDuacdKptMKLheheq4Y5AAosPPrAOEgIJLHr2lJKafNonJ0s/+pH35aef7v9xChlj08GDB82nn35qPv30UyPJzJ0713z66afm66+/NsYYM2XKFDN27FjP+v/4xz9M69atzX/+53+abdu2mSeffNIkJyebFStW+L3NqqoqI8lUVVXZ3V3vysqMSUoyRjr+SE52LzfGmGefPf58UpL7/76Wn/i67757/HVC7MjRI6a+vt4YY0x9fb05cvRIWLaD4I71lootpqamxhhjTE1NjdlSscXvtmX/KjNHjx41xhhz9OhRU/Yv/8+lHft2mNraWmOMMbW1tWbHvh1+t636vsrU1dUZY4ypq6szVd/7/7e2dudac/jwYWOMMYcPHzZrd671u20wx2rvwb3m2LFjxhhjjh07ZvYe3BuRtsG8R8Ec52DOSafaBiNS2/V22ba61Ft9dHz0kfVHyrvvNl7e8CgpsX5u2TLr1wtkHxp+p+Tk48tP/FjztjxU/P38th2MlJSUGEknPcaPH2+MMWb8+PHmwgsvPKnNgAEDTEpKijnttNPM888/b2ubIQ9GfJ0dwbzTVoFKmIMUAIA1q0uwt8u2r++qVh8dc+fa/0jxFViUlfkOEgINLMrKju+TP8tDIWzBiBMi2jMS6rPN4d4UAEgUoejlWLo0PN9V7QYWDftoFSQ4EVgEgmCkOVZnQCj74Xz1tTXsg69ABQDQSLh7Ofy5bIeyV6K552IdwYg/rM4Au2dbKEPshn2hxwQAGolEL0dzQyQN24uFXolo4O/nd1AVWCPF3wpuIVVe7k5DPv30k0vVeVu+cKE7Dbquzp2O/MwzUmGhO636xBTn5GRp1y53SvTFF5+83ZIS6auvjqdYJyVJf/iDVFTUeB/CVS4PAKJA08tcebn9y+myZdJ113lvk53t/bLdcKm1utTDHn8/vwlGQsnb2Wt1tlv9Za1fLw0b5vuvx1egAgAxwup7lbfL3GmnWX9/O/1060Dl7betA46GfSDoCB+CkWhipzcl0L+4htel1wRADLD6XhXM9zR6OaIPwUisaPpXEkhfZEmJNGIEvSYAolIohlwaRrDp5YgtBCOxzO7Qzq5d7n/76jWhxwSAA0I55NJwKSPgiB1Rc9deBKCoyP2XV1Li/tkQ+mdnu/+Sk3+4G2pDoJKdbV0jeMeO6LktI4C45a18ulW58zZtrMuQ+7rMSe6fI0YQiMQbekZikbevBoEOtDa0pdcEQICsRohLShhySXQM0yQiuwmx5JkACFKwo8cEHPGNYZpE5G14x+p2jaef7vt2kpJjdygGEL2aXhZ8jRAz5AJ/EYzEm6Z/3eSZAAgRb5cFX993JOsUOOBEDNMkilDnmQCIW97SyHwNxzRXWAyJi2EaNOatP9Sq1+S776x7TBowhAPEJatOUV8dqfR+IFj0jMBe4TVK0gNxK5hkVMAbekbgPzt5Js0lvQKICd46N4NJRgWCQTAC76z6XX1drSSGb4AYYDUUQzIqnEIwAmve8kx8Xa2YgQNEPV+dm/70fjAdF+FAMAJ7rK5WEsM3QAxornOT3g84oYXTO4AYVFQkFRY2TnotKfE92AzAEU2n6TZ0bjZNRG0YipHc6/F
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xnew=np.linspace(2,5,70).reshape(-1,1)\n",
    "yPred=mylr.predict_proba(Xnew)\n",
    "plt.plot(Xnew,yPred[:,0],'.r', label='No Iris-Set')\n",
    "plt.plot(Xnew,yPred[:,1],'.b', label='Iris-Set')\n",
    "plt.legend()\n",
    "plt.plot(X,y,'*g')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7474195c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "0196eda3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xffff536c56d0>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Iris-Setosa Classifier based on petal width\n",
    "\n",
    "X=iris.data[:,0:1]\n",
    "y=(iris.target==0).astype(int)\n",
    "\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "mylr=LogisticRegression(solver='lbfgs', random_state=42)\n",
    "mylr.fit(X,y)\n",
    "\n",
    "Xnew=np.linspace(2,8,70).reshape(-1,1)\n",
    "yPred=mylr.predict_proba(Xnew)\n",
    "#plt.plot(Xnew,yPred[:,0],'.r', label='No Iris-Set')\n",
    "plt.plot(Xnew,yPred[:,1],'.b', label='Iris-Set')\n",
    "plt.legend()\n",
    "plt.plot(X,y,'*g')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d56c901",
   "metadata": {},
   "source": [
    "# Session 2: Softmax regression\n",
    "## multiple features class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "00ba053b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0xffff67a417f0>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "pl=iris.data[:,2:3]\n",
    "pw=iris.data[:,3:]\n",
    "plt.plot(pl,pw,'sb')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "b3849a04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-4 {color: black;background-color: white;}#sk-container-id-4 pre{padding: 0;}#sk-container-id-4 div.sk-toggleable {background-color: white;}#sk-container-id-4 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-4 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-4 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-4 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-4 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-4 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-4 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-4 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-4 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-4 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-4 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-4 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-4 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-4 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-4 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-4 div.sk-item {position: relative;z-index: 1;}#sk-container-id-4 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-4 div.sk-item::before, #sk-container-id-4 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-4 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-4 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-4 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-4 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-4 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-4 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-4 div.sk-label-container {text-align: center;}#sk-container-id-4 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-4 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-4\" class=\"sk-top-container\
      ],
      "text/plain": [
       "LogisticRegression(C=10, random_state=42)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "X=iris.data[:,2:]\n",
    "y=(iris.target==2).astype(int)\n",
    "\n",
    "lrmi=LogisticRegression(solver='lbfgs',\n",
    "                       C=10,\n",
    "                       random_state=42)\n",
    "lrmi.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "3fa13847",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "x0, x1=np.meshgrid(\n",
    "    np.linspace(1,6.9,500).reshape(-1,1),\n",
    "    np.linspace(0.1,2.5,200).reshape(-1,1))\n",
    "Xnew=np.c_[x0.ravel(), x1.ravel()]\n",
    "yProb=lrmi.predict_proba(Xnew)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "f34d82b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xffff3def9c10>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(X[y==0,0], X[y==0,1],'bs',label='No Virg')\n",
    "plt.plot(X[y==1,0], X[y==1,1],'g^',label='Virginica')\n",
    "zz=yProb[:,1].reshape(x0.shape)\n",
    "contour=plt.contour(x0,x1,zz)\n",
    "plt.clabel(contour, inline=1,fontsize=15)\n",
    "plt.xlabel(\"Petal Length\")\n",
    "plt.ylabel(\"Petal Width\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b566781b",
   "metadata": {},
   "source": [
    "# Multiclass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "090c8abc",
   "metadata": {},
   "outputs": [],
   "source": [
    "X=iris.data[:,2:]\n",
    "y=iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "aa59ee97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0xffff3d208c40>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lrmi2=LogisticRegression(multi_class='multinomial',\n",
    "                        solver='lbfgs',\n",
    "                        C=10,\n",
    "                        random_state=42)\n",
    "lrmi2.fit(X,y)\n",
    "x0,x1=np.meshgrid(\n",
    "        np.linspace(0,8,500).reshape(-1,1),\n",
    "    np.linspace(0,3.5,200).reshape(-1,1))\n",
    "Xnew=np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "yProba=lrmi2.predict_proba(Xnew)\n",
    "yPred=lrmi2.predict(Xnew)\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "customc=ListedColormap(['#fafab0', '#9898ff', '#a0faa0'])\n",
    "zz1=yProba[:,1].reshape(x0.shape)\n",
    "zz=yPred.reshape(x0.shape)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(X[y==2,0], X[y==2,1],'g^',label='Virg')\n",
    "plt.plot(X[y==1,0], X[y==1,1],'bs',label='Versic')\n",
    "plt.plot(X[y==0,0], X[y==0,1],'yo',label='Setos')\n",
    "contour=plt.contour(x0,x1,zz1,cmap=plt.cm.brg)\n",
    "plt.clabel(contour,inline=1,fontsize=12)\n",
    "plt.contourf(x0,x1,zz,cmap=customc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "01ed7f9b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "X=iris.data[:,2:]\n",
    "y=(iris.target==2).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "9f90fa65",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-5 {color: black;background-color: white;}#sk-container-id-5 pre{padding: 0;}#sk-container-id-5 div.sk-toggleable {background-color: white;}#sk-container-id-5 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-5 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-5 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-5 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-5 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-5 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-5 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-5 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-5 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-5 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-5 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-5 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-5 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-5 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-5 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-5 div.sk-item {position: relative;z-index: 1;}#sk-container-id-5 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-5 div.sk-item::before, #sk-container-id-5 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-5 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-5 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-5 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-5 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-5 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-5 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-5 div.sk-label-container {text-align: center;}#sk-container-id-5 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-5 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-5\" class=\"sk-top-container\
      ],
      "text/plain": [
       "LogisticRegression(C=100000000000000000000, random_state=80)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mlr2=LogisticRegression(solver='lbfgs', C=100**10, \n",
    "                       random_state=80)\n",
    "mlr2.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "c84364aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "x0,x1=np.meshgrid(\n",
    "    np.linspace(1,7,500).reshape(-1,1),\n",
    "    np.linspace(0,3,200).reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "c97642ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "Xnew=np.c_[x0.ravel(), x1.ravel()]\n",
    "yPred=mlr2.predict_proba(Xnew)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "080dd993",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.0, 7.0, 0.7, 3.0)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[y==0, 0], X[y==0,1],'bs')\n",
    "plt.plot(X[y==1, 0], X[y==1,1],'g^')\n",
    "zz=yPred[:,1].reshape(x0.shape)\n",
    "contour=plt.contour(x0,x1,zz)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.axis([3,7,0.7,3])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29f23df4",
   "metadata": {},
   "source": [
    "## Multiclass classifer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "0dc5a275",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-8 {color: black;background-color: white;}#sk-container-id-8 pre{padding: 0;}#sk-container-id-8 div.sk-toggleable {background-color: white;}#sk-container-id-8 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-8 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-8 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-8 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-8 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-8 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-8 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-8 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-8 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-8 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-8 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-8 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-8 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-8 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-8 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-8 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-8 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-8 div.sk-item {position: relative;z-index: 1;}#sk-container-id-8 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-8 div.sk-item::before, #sk-container-id-8 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-8 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-8 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-8 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-8 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-8 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-8 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-8 div.sk-label-container {text-align: center;}#sk-container-id-8 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-8 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-8\" class=\"sk-top-container\
      ],
      "text/plain": [
       "LogisticRegression(C=10, multi_class='multinomial', random_state=42)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=iris.data[:,2:]\n",
    "y=iris.target\n",
    "mlr3=LogisticRegression(\n",
    "    multi_class='multinomial',\n",
    "    solver='lbfgs',\n",
    "    C=10,\n",
    "    random_state=42)\n",
    "mlr3.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a0bd6104",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "ae96a421",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "x0,x1=np.meshgrid(\n",
    "    np.linspace(1,7,500).reshape(-1,1),\n",
    "    np.linspace(0,3,200).reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "7efb4dbf",
   "metadata": {},
   "outputs": [],
   "source": [
    "Xnew=np.c_[x0.ravel(), x1.ravel()]\n",
    "yPred=mlr3.predict_proba(Xnew)\n",
    "yProba=mlr3.predict(Xnew)\n",
    "zz=yProba.reshape(x0.shape)\n",
    "zz1=yPred[:,1].reshape(x0.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "2d63e529",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xffff23600220>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAj8AAAG6CAYAAADnOSfBAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy89olMNAAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOydd3hUVfrHP+feaZn0kEZLQgktdCnSe7MAIkVQQLGLa/25u6hr211117bquq6uIljoUhSR3psivbcAoaSSXqbe+/tjkpBIykwyCQHu53nmSTJzzrnn3pnMfOc973m/QlVVFQ0NDQ0NDQ2NmwTpWk9AQ0NDQ0NDQ6M20cSPhoaGhoaGxk2FJn40NDQ0NDQ0bio08aOhoaGhoaFxU6GJHw0NDQ0NDY2bCk38aGhoaGhoaNxUaOJHQ0NDQ0ND46ZCEz8aGhoaGhoaNxWa+NHQ0NDQ0NC4qdDEj4aGhoaGhsZNRZ0SP59++int27cnICCAgIAAevTowc8//1xhn4ULF9KqVStMJhPt2rVjxYoVtTRbDQ0NDQ0NjeuROiV+GjVqxNtvv83u3bv57bffGDhwIKNGjeLw4cNltt++fTsTJ07kwQcfZO/evYwePZrRo0dz6NChWp65hoaGhoaGxvWCqOvGpiEhIbzzzjs8+OCDVz02YcIE8vLyWL58efF9t956Kx07duS///1vbU5TQ0NDQ0ND4zpBd60nUB5Op5OFCxeSl5dHjx49ymyzY8cOnnvuuVL3DRs2jKVLl5Y7rtVqxWq1Fv+tKArp6enUq1cPIYRX5q6hoaGhoaFRs6iqSk5ODg0aNECSPFvIqnPi5+DBg/To0QOLxYKfnx9LliyhTZs2ZbZNSkoiIiKi1H0REREkJSWVO/5bb73F66+/7tU5a2hoaGhoaFwbzp8/T6NGjTzqU+fET8uWLdm3bx9ZWVksWrSIqVOnsmnTpnIFkKfMmDGjVLQoKyuLqKgozpz5An9/s1eOoVF1zh4Q/HmgnuAI+PSwrUpjbHv+BMdmJ9L5j9F0+mOMR32/+eZ2AEIOb6btF88iUEhv2ZMTE17GGly/zD7Bx7YTuXMpoQc2IKkOADKaduHC563I71h2n4pwbMwmf+oZyFOR2pkwz2+GFK73eJzcszJbxgSRnyBhjlLoszgTvxinx+NoaGho1EUKcgp4rslz+Pv7e9y3zokfg8FA8+bNAbjlllvYtWsXH374IZ999tlVbSMjI0lOTi51X3JyMpGRkeWObzQaMRqNV93v728mIEATP9caPz+BDgN6SSUgoGovT12ejA8GQiL9PX5OfXwCMGQm02XuG+gRJPYYx6nJbyJJEj7l9LF0Gs7ZTsNJTE8kas2XNNgyD7/4vTQevJfkqe059+ZAHGG+7k9ipA/m9f7k33ES9aAD5c4EfH6KRWp69eu2wnNpD8M2WNgwLJjcUzq2jzQzYGUGAa00AaShoXHjUJWUlTq126ssFEUplaNTkh49erBu3bpS961Zs6bcHCGNmwNrliv6YqiieIpd9Bb6vEyyo+I4du8b4OZasjWkPicnvMzON1aT2H0UABGzD9Cp3WeEfX0APNhbIHcy47upJaKJAfW0lbz+x3AeyPf4XHwbKwxal0FgGwcFl2TWDQ4m82Cd+86joaGhUavUKfEzY8YMNm/ezNmzZzl48CAzZsxg48aN3HvvvQBMmTKFGTNmFLd/+umnWblyJe+99x7Hjh3jtdde47fffuPJJ5+8VqegUQewFYmfIM8/5H0vniDiN1etqGNT3kTVGTwewxrSgKMPvMNvf5xPTsOW6NMLiH3oR1qPmo/hYrbb40jNTfhubIXU1gc1yUHeoBM4tuZ4PB+f+goD16YT1MGONUVm/ZBg0vdoAkhDQ+PmpU6Jn5SUFKZMmULLli0ZNGgQu3btYtWqVQwZMgSAhIQEEhMTi9v37NmTOXPm8Pnnn9OhQwcWLVrE0qVLadu27bU6BY06gD27UPz4yx73jVrzJQDJnUeQ26h1teaR3bQTv724mNOjn8epMxC88jQdOv+Pet8fdXsMqb4e3/UtkHv5QZaT/NtOYv8p0+O5GENVBq7JoF53G7Z0iQ3Dgknb4XkekYaGhsaNQJ2v81PTZGdnExgYSFranArzQ5xOgcMhe7JycdMiBOh0TmTZ84t1Zr/g6a4GQuqrzDpXtYTnb5ttJfe8lTHbuxLeJcDtfkqOhTP130S2FfDbH+eT3bRTlY5fFubEU7T56o8EJLgKcCY/0IEz7w9F8XUvsqTmKxRMisexIgtkMH0Rg+Heeh7Pw54j2Dw6iNQtBnS+Cn2WZhLRz+7xOBoaGhrXmoLsAh4PfZysrCwCAtx/r4c6mPBc11BVSEnxJzvbnzoWKKvjKAQE5BAenkNVyidVR2Tac10JvTqzZ89X/g+HkW0F5EU0IbtJx6pPoKyx6zdn95/m0+THj4le9V8ivtqP/46LHJ87hoK4sEr7C7OEz8JmWB45i/27dCwPnEXNcGJ8Mtyjeej9Vfr9mMHWcUEkrTGy+c5gei/MpP6wqglNDQ0NjesRTfxUgkv4BBMWForZbNAKIbqBqqrk59tITXW9vCIiPMhTEUVjVP34jnwFAL2fZy/v/J9cy1GpnYdTJcVWCaqsJ370c+Q+l0OLqcswH0ujfa+vOP2f20ibVPlSrdALTF/GIIJ12P6dgvW585DpwPBSfY9elzoz9Pk+k233BHFphZEtY4LoNS+LhneWvbFAQ0ND40ZDEz8V4HQKsrP9CQsLpV49z+sI3Mz4+Li2ZaemOggNzXV7CUxUU/yoiorT6hI/Oh/3Iz+qomBZfxKAtLb9qnZwN0mJf5WMZ5+k3apJBK07Q4v7l+H/ywXOvjME1VBxnpKQBMb3GiFCZKxvJGJ9I9EVAXqnEUJyXwDJJui1IJOdUwI5v9jE1vGB9JidRdR4TQBpaGjc+GjrOBXgcMiAhNns+Y4fDQqvm1R4Hd2jOIBRRfHjKFCKf9eZ3T+u/UgKSno+DqOZnJh2VTu4B9gD6nFk+T2cf7E3APU/3U3c0G/RJ1YeJRNCYHy5AaYPGgNg+zgFyyPnUB2eXTTZAD2+zSJ6YgGqU7BjSiBnvjF5fjIaGhoa1xma+KmAouiDttRVNYqumydRnOpGfhwFVwr4ySb3X97WHWcAyG7SAVWunV1QltkPcDJqJkeXjMcRYCRg+wXa95iJ32+X3OpvmB6OaWYMyGD/+jIFE+NRrUql/Uoi6aD7zGyaTstHVQS/PBjIqf+VV85RQ0ND48ZAEz8adYtqip+iJS9JJ5Bk90Wrdc9FALKjaz7q83sSk//Gge0PkN8qFOOlXNoO+JrQuYfc6mu4rx4+85uBQeBYlkn+XadQ8zyr4CzJ0PU/OcROdxVR/G16AMc/1gSQhobGjYsmfm5SXn/9bTp37nOtp3EV1V32UqyujpLRs5e27aCrflRuY+94yHlK5tbnOLj1ftJvj0WyOmkxdRlRf9kASuUXQj8yCPOPzcFXwrk2h/wRJ1EzHR4dX0jQ+f0cWj2XB8De5wM48k/N7kVDQ+PGRBM/NyAjR97DiBFjy3xsy5btyHIwd911B2vWLKvlmVWOKHxFKp6t3hRTFPmRje5HfVRVxX7U5RGX1yC2agf2AnmLHuHYorFc+D+XPUujf2yn5cTFSPmV1+HRDQjAvDIWgmScO/PIG3ICJcWz+j1CQIe3col7KReAAy/7c/ANX622lYaGxg2HJn5qkZycvezfP5KcnL01epxp0yazdu0GLly4eNVjs2bNoUuXTrRv35Z69ULKHcNmuzZ1X6ob+XHaCpe99O6/tJ2J2ag5VpAE+eHRVTuwl7DMfoCENwdy8os7UfQS9ZYcI27wN+iTcivtq+vuh+/aFohwHcr+AvIHHEc579nzKAS0ezWP9n9zJV4f/psf+1/00wSQhobGDYUmfmqR5OR5ZGVtITl5fo0e5447hhEWFsrs2XNL3Z+bm8uiRct44IH7rlr2euCBJ7jrrnt58813adSoNa1bdwVg+/Zf6Ny5D2ZzJN26DWDp0p+Q5WD27TtYI3MXkutTtqqRH8Xu6i8b3I/8OE5fBkAXE1w
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "plt.plot(X[y==2,0], X[y==2,1],'y*', label='Virg')\n",
    "plt.plot(X[y==1,0], X[y==1,1],'g^', label='Vers')\n",
    "plt.plot(X[y==0,0], X[y==0,1],'bs', label='Set')\n",
    "contour=plt.contour(x0,x1,zz1, cmap=plt.cm.brg)\n",
    "ccmap=ListedColormap(['#fafab0', '#9898ff', '#a0faa0'])\n",
    "plt.contourf(x0,x1,zz,cmap=ccmap)\n",
    "plt.clabel(contour, inline=1,fontsize=12)\n",
    "plt.xlabel('Petal Width', fontsize=12)\n",
    "plt.ylabel('Petal Length', fontsize=12)\n",
    "#plt.axis([0,7,0,3.5])\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9531c07",
   "metadata": {},
   "source": [
    "## Sepal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "d99ec4da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-9 {color: black;background-color: white;}#sk-container-id-9 pre{padding: 0;}#sk-container-id-9 div.sk-toggleable {background-color: white;}#sk-container-id-9 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-9 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-9 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-9 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-9 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-9 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-9 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-9 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-9 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-9 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-9 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-9 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-9 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-9 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-9 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-9 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-9 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-9 div.sk-item {position: relative;z-index: 1;}#sk-container-id-9 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-9 div.sk-item::before, #sk-container-id-9 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-9 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-9 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-9 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-9 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-9 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-9 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-9 div.sk-label-container {text-align: center;}#sk-container-id-9 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-9 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-9\" class=\"sk-top-container\
      ],
      "text/plain": [
       "LogisticRegression(C=10, multi_class='multinomial', random_state=42)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X=iris.data[:,0:2]\n",
    "y=iris.target\n",
    "mlr3=LogisticRegression(\n",
    "    multi_class='multinomial',\n",
    "    solver='lbfgs',\n",
    "    C=10,\n",
    "    random_state=42)\n",
    "mlr3.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "7c28a9a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "x0,x1=np.meshgrid(\n",
    "    np.linspace(0,9,500).reshape(-1,1),\n",
    "    np.linspace(0,7,200).reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "258b2dd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "Xnew=np.c_[x0.ravel(), x1.ravel()]\n",
    "yPred=mlr3.predict_proba(Xnew)\n",
    "yProba=mlr3.predict(Xnew)\n",
    "zz=yProba.reshape(x0.shape)\n",
    "zz1=yPred[:,1].reshape(x0.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "2d1cc5a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0xffff23370a00>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.colors import ListedColormap\n",
    "plt.plot(X[y==2,0], X[y==2,1],'y*', label='Virg')\n",
    "plt.plot(X[y==1,0], X[y==1,1],'g^', label='Vers')\n",
    "plt.plot(X[y==0,0], X[y==0,1],'bs', label='Set')\n",
    "contour=plt.contour(x0,x1,zz1, cmap=plt.cm.brg)\n",
    "ccmap=ListedColormap(['#fafab0', '#9898ff', '#a0faa0'])\n",
    "plt.contourf(x0,x1,zz,cmap=ccmap)\n",
    "plt.clabel(contour, inline=1,fontsize=12)\n",
    "plt.xlabel('Sepal Width', fontsize=12)\n",
    "plt.ylabel('Sepal Length', fontsize=12)\n",
    "#plt.axis([0,7,0,3.5])\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "37b5eb33",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "840fcc9a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}