TD5_A_Simple_NN_for_a_Simple_LR.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 435,
   "metadata": {},
   "outputs": [],
   "source": [
    "!git add \"td5_ressources/\"\n",
    "!git add \"TD5_A_Simple_NN_for_a_Simple_LR.ipynb\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[master 9a4bba6] reshaping TD5\n",
      " 1 file changed, 27 insertions(+), 12 deletions(-)\n",
      "Enumerating objects: 5, done.\n",
      "Counting objects: 100% (5/5), done.\n",
      "Delta compression using up to 8 threads\n",
      "Compressing objects: 100% (3/3), done.\n",
      "Writing objects: 100% (3/3), 550 bytes | 550.00 KiB/s, done.\n",
      "Total 3 (delta 2), reused 0 (delta 0)\n",
      "remote: Resolving deltas: 100% (2/2), completed with 2 local objects.\u001b[K\n",
      "To https://github.com/Luc-Bertin/TDs_ESILV.git\n",
      "   7e147bb..9a4bba6  master -> master\n"
     ]
    }
   ],
   "source": [
    "!git commit -m \"reshaping TD5\"\n",
    "!git push origin master"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TD5 • Coding a simple perceptron with Backprop"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Un <a href=\"http://playground.tensorflow.org/#activation=linear&regularization=L1&batchSize=29&dataset=gauss&regDataset=reg-plane&learningRate=0.001&regularizationRate=0.003&noise=15&networkShape=1&seed=0.37334&showTestData=true&discretize=false&percTrainData=50&x=false&y=false&xTimesY=true&xSquared=true&ySquared=true&cosX=false&sinX=false&cosY=false&sinY=false&collectStats=false&problem=classification&initZero=false&hideText=false\">lien sympathique</a> pour s'amuser avec différentes architectures de réseau de neurones </h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, array(4), ())"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar = 4\n",
    "scalar2 = np.array(4)\n",
    "scalar, scalar2, scalar2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4] [1 2 3 4 5 6]\n",
      "(1,) (6,)\n",
      "1 1\n",
      "1 6\n"
     ]
    }
   ],
   "source": [
    "vector_1D = np.array([4])\n",
    "vector_1D_of_multiple_elements = np.array([1,2,3,4,5,6])\n",
    "\n",
    "print(vector_1D, vector_1D_of_multiple_elements)\n",
    "print(vector_1D.shape, vector_1D_of_multiple_elements.shape)\n",
    "print(vector_1D.ndim, vector_1D_of_multiple_elements.ndim)\n",
    "\n",
    "# Number of elements in the array\n",
    "print(vector_1D.size, vector_1D_of_multiple_elements.size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transpose vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1, 2, 3, 4, 5, 6]), (6,))"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(vector_1D_of_multiple_elements.T,\n",
    " vector_1D_of_multiple_elements.T.shape) # same thing (in terms of representation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1, 2, 3, 4, 5, 6]), (6,), 1)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(vector_1D_of_multiple_elements, \n",
    "vector_1D_of_multiple_elements.shape,\n",
    "vector_1D_of_multiple_elements.ndim)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## creation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "matrix = np.array( [ \n",
    "            [ 1,2,3], \n",
    "            [ 4,5,6]\n",
    "          ])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1, 2, 3],\n",
       "        [4, 5, 6]]),\n",
       " (2, 3),\n",
       " 2,\n",
       " 6)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix, matrix.shape, matrix.ndim, matrix.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## transpose matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1, 4],\n",
       "        [2, 5],\n",
       "        [3, 6]]),\n",
       " (3, 2),\n",
       " 2,\n",
       " 6)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.T, matrix.T.shape, matrix.T.ndim, matrix.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Re-shape a vector or matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_1D.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_1D.reshape((1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[4]]])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_1D.reshape((1,1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_1D_of_multiple_elements.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_1D_of_multiple_elements.reshape(3,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector_1D_of_multiple_elements.reshape(2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## pd.DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
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       "0  4"
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     "execution_count": 91,
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   "source": [
    "pd.DataFrame(vector_1D)"
   ]
  },
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   "execution_count": 92,
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    "pd.DataFrame(vector_1D_of_multiple_elements)"
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     "execution_count": 94,
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   "source": [
    "pd.DataFrame(vector_1D_of_multiple_elements) "
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   "cell_type": "code",
   "execution_count": 95,
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  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 1)"
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     "execution_count": 96,
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    "pd.DataFrame(vector_1D_of_multiple_elements).shape"
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   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
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    "pd.DataFrame(vector_1D_of_multiple_elements).T"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vector \"as\" matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In linear algebra, a **column vector** or **column matrix** is an **m × 1 matrix**, that is, a **matrix consisting of a single column of m elements**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "as_matrix = vector_1D_of_multiple_elements.reshape(6, 1) # 6 rows, 1 column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
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       "2  3\n",
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       "5  6"
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     },
     "execution_count": 121,
     "metadata": {},
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   ],
   "source": [
    "pd.DataFrame(as_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, a row vector or row matrix is a 1 × m matrix, that is, a matrix consisting of a single row of m elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "as_matrix = vector_1D_of_multiple_elements.reshape(1, 6) # 1 column, 6 rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
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       "   0  1  2  3  4  5\n",
       "0  1  2  3  4  5  6"
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     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(as_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dot Product (produit scalaire)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "vector1 = np.array([1,2,3,4,5])\n",
    "vector2 = np.array([2,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Not the same number of elements to perform a dot product (must be aligned)\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    np.dot( vector1, vector2 )\n",
    "except:\n",
    "    print(\"Not the same number of elements to perform a dot product (must be aligned)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "vector2 = np.array([2,4,1,1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(vector1, vector2) # 1*2 + 2*4 + 3*1 + 4*1 + 5*1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Again, not aligned because in maths you do the transpose of the vector1 \n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    np.dot(vector1.reshape(1,5), vector2.reshape(1,5))\n",
    "except:\n",
    "    print(\"Again, not aligned because in maths you do the transpose of the vector1 \")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"td5_ressources/dot product.png\" width=\"100%\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[22]]), array([[22]]))"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this works\n",
    "result_dot_product = np.dot(vector1.reshape(1,5), vector2.reshape(1,5).T)\n",
    "# this works\n",
    "result_matrix_product = np.matmul(vector1.reshape(1,5), vector2.reshape(1,5).T)\n",
    "# same result\n",
    "result_dot_product, result_matrix_product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# elementwise multiplication (Hadamard Product on Matrices (or column/row vector)\n",
    "To not confuse with dot product:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 8, 3, 4, 5])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 * vector2 # vector of element multiplications"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 8, 3, 4, 5])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# same result\n",
    "np.multiply(vector1, vector2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 8, 3, 4, 5]])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.multiply(vector1.reshape(1,5), vector2.reshape(1,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Broadcasting rules numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "refers to how numpy **treats arrays** with **different shapes** during **arithmetic operations**.<br>\n",
    "Subject to certain constraints, the **smaller array is “broadcast” across the larger array** so that they have compatible shapes!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Same shapes, no problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4, 6])"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 = np.array([1,2,3])\n",
    "vector2 = np.array([1,2,3])\n",
    "\n",
    "vector1 + vector2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* different shapes, what to do ? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<u>**Example1:**</u>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1,), (3,))"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 = np.array([1])\n",
    "vector2 = np.array([1,2,3])\n",
    "vector1.shape, vector2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4])"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 + vector2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the same thing as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 1 1]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4]])"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1_transformed = np.tile(vector1, reps=(1,3))\n",
    "print( vector1_transformed )\n",
    "\n",
    "vector1_transformed + vector2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"td5_ressources/broadcoast1.png\" width=\"100%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> from https://cs231n.github.io/python-numpy-tutorial/#numpy-broadcasting:\n",
    "* If the arrays do not have the same rank (number of dimensions), **prepend the shape of the lower rank array** with **1s until both shapes have the same length**.\n",
    "* The two arrays **are said to be compatible** in **a** dimension if they have the **same size** in the dimension, or if one of the arrays **has size 1** in **that** dimension.\n",
    "* The arrays can be broadcast together if they **are compatible in all dimensions**.\n",
    "\n",
    "\n",
    "After broadcasting:\n",
    "* After broadcasting, each array **behaves as if it had shape equal to the elementwise maximum of shapes** of the two input arrays.\n",
    "* In any dimension where one array had size 1 and the other array had size greater than 1, the first array behaves **as if it were copied along that dimension**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((1, 1), (3,))"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 = np.array([[1]])\n",
    "vector2 = np.array([1,2,3])\n",
    "vector1.shape, vector2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "prepending ones, the last dimension of the array will be \"strecthed\" so the number of elements match with the one of the first array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4]])"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 + vector2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<u>**Example2:**</u>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2, 1), (3,))"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 = np.array([[1], [2]]) # 2 rows, 1 column\n",
    "vector2 = np.array([1,2,3]) # 1D vector\n",
    "vector1.shape, vector2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. 2 rows in `vector1`, `vector2` does not have \"rows dimension\", prepended a 1 to create a new dimension\n",
    "2. then `vector2` is stretched on its new dim so to have 2 elements, as `vector1` \n",
    "3. while `vector1` has last dimensions (columns) strecthed to have 3 elements, as `vector2`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 + vector2 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the same as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [1, 2, 3]])"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tile(vector2, reps=(2, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [2, 2, 2]])"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tile(vector1, reps=(1, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<u>**Example3:**</u>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 260,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2, 3), (2,))"
      ]
     },
     "execution_count": 260,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vector1 = np.array([[1, 4, 5], [2, 2, 5]]) # 2 rows, 1 column\n",
    "vector2 = np.array([1, 2]) # 1D vector\n",
    "vector1.shape, vector2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After prepending with 1 the vector2, impossible to match 2 to 3:\n",
      "operands could not be broadcast together with shapes (2,3) (2,) \n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    vector1 + vector2\n",
    "except Exception as e:\n",
    "    print(\"After prepending with 1 the vector2, impossible to match 2 to 3:\\n{}\".format(e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding the parameters in a simple linear regression case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 100, 100)\n",
    "y = 8*x + np.random.normal(x, 100) # y = 8*x + epsilon with epsilon ~ N(0,1)\n",
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How to find the coefficient $\\beta$s (here the intercept $\\beta$0 and the slope $\\beta$1) in order to have the best fitting (simple) linear model ? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The plotting function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotting(beta0, beta1):\n",
    "    plt.scatter(x_scaled_and_centered, y)\n",
    "    plt.plot(x_scaled_and_centered, lm.intercept_ + lm.coef_ * x_scaled_and_centered, color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using OLS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(37.18580177143173, array([8.22801749]))"
      ]
     },
     "execution_count": 281,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "# adding one dimension to the x (to have a feature matrix notation,\n",
    "# although x is only 1 feature,\n",
    "# which then can be apparented as a column vector\n",
    "lm = LinearRegression().fit(x[:, np.newaxis], y)\n",
    "lm.intercept_, lm.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With standardization before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 293,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(448.5866764712714, array([239.90962559]))"
      ]
     },
     "execution_count": 293,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "x_scaled_and_centered = StandardScaler().fit_transform(x[:, np.newaxis])\n",
    "lm = LinearRegression(fit_intercept=True).fit(x_scaled_and_centerd, y)\n",
    "lm.intercept_, lm.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotting(lm.intercept_, lm.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using a self-made (definitely non-optimised) algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "metadata": {},
   "outputs": [],
   "source": [
    "def algo_simple_linreg(x, y):\n",
    "    \"\"\"A self-made, definitely non-optimised algorithm to find the best alpha and beta values:\"\"\"\n",
    "    from sklearn.metrics import mean_squared_error\n",
    "    MSE = {}\n",
    "    for beta0 in np.linspace(-5000, 5000, 100):\n",
    "        for beta1 in np.linspace(-5000, 5000, 100):\n",
    "            model = lambda x: beta0 + beta1*x\n",
    "            mse = mean_squared_error( model(x), y)\n",
    "            MSE[(beta0, beta1)] = mse\n",
    "    return MSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [],
   "source": [
    "MSE = algo_simple_linreg(x_scaled_and_centered, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = pd.Series(MSE).unstack()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 391,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "ax = plt.subplot(111)\n",
    "sns.heatmap(params, cmap=\"coolwarm\", ax=ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(454.54545454545496, 252.52525252525265)"
      ]
     },
     "execution_count": 400,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.stack().idxmin()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotting(*params.stack().idxmin())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using One neuron 🤓"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Definition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2 nice definitions i like, just stolen from [there](https://people.minesparis.psl.eu/fabien.moutarde/ES_MachineLearning/Slides/MLP-NeuralNetworks_course_2pp.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> A **processing “unit”** applying a **simple operation to its inputs**, and which can be **“connected” to others** to build a **network** able to realize any input-output function "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> “Usual” definition: a “unit” computing a **weighted sum of its inputs**, that can add a constant term, and **apply some non-linearity (sigmoïd, ReLU, ...)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"td4_ressources/img_perceptron_towards_data_science.png\" width=500>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Behavior formulas\n",
    "\n",
    "From the last definition of what a neuron is we get:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the last definition of what a neuron is we get:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. <span style=\"color: red;\">Weighted sum of its inputs</span> and <span style=\"color: blue;\">can add a constant term<span>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ f(x_i) =  \\color{red}{\\sum_{i=1}^{p}{w_i x_i}}   + \\color{blue}{cst}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Apply some <span style=\"color: green;\">non-linearity function g</span>:<br>\n",
    "    Example: sigmoid function (g is Sigmoid)\n",
    "    $$ g(z) = Sigmoid(z) = \\color{green}{\\frac{1}{1+e^{-z}}} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Then the output of the neuron is:**\n",
    "$$ y_i = ( g \\circ f ) (x) = g(f(x)) = \\color{green}{\\frac{1}{1+e^{-\\color{red}{\\sum_{i=1}^{p}{w_i x_i}}   + \\color{blue}{cst}}}} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seems that **<span style='color: red;'><u>1.</u></span>** look very similar to a simple linear regression formula !<br>\n",
    "- The **weights** $w_i$ can be seen as the **coefficients** of a linear regression.\n",
    "- The $x_i$ as the **features** of **one** data point (one **row vector** then i.e. **one line of a matrix** or one observation in a **dataframe** !). There is $p$ features for one input vector here using the former notation.\n",
    "- The output $y_i$ is a scalar, that is, the output for one input vector of features $i$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can rewrite this formula in **vector notation**, so we could scale this to **multiple input vectors**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$  Y = (g \\circ f) (X) = g( X W + B ) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or maybe using the indices so it is a little bit clearer\n",
    "\n",
    "$$  Y_{k,1} = (g \\circ f) (X_{k,p}) = g( X_{k,p} W_{p,k} + B_{k,1} ) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Where $X$ is a **row vector of p features** (or a **matrix of n row vectors of p features**).<br>\n",
    "This notation is useful as it could be used for one single input, or many.\n",
    "- if **one input row vector** is passed, then, it is a **simple dot product** between this vector and a column **weights vector** occur, forming one scalar output $Y_{1,1}$.\n",
    "- if multiple inputs are being passed (size $k x p$), then W is a matrix of size $p x k$, so that Y has k output (one for each input) and that each feature of x is multiplied by its corresponding feature in W, forming finally a vector of outputs $Y_{k,1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see the simple linear regression as a specification of multiple linear regression: $W_{k,p}$ for k inputs of p features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = x[:, np.newaxis] # to set x as a matrix of row vectors of 1 feature "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = np.random.random(size=tuple(reversed(x.shape))) # all are between 0 and 1 for stability at first"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the bias term:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = np.random.random(size=(x.shape[0], 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loss and Risk function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remembered the cost function ?<br>\n",
    "Let's take a **quadratic loss** as it is **nicely differentiable**,<br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's write: $$ z = (g \\circ f) $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "then:\n",
    "\n",
    "$$ L(y_i, \\hat{y}_i) = L(y_i, z(x_i)) = (y_i - z(x_i))^2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then in matrix notation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ L(Y_{k,1}, \\hat{Y}_{k,1}) = L(Y_{k,1}, z(X_{k,p}) =  (Y_{k,1} - z(X_{k,p}))^2 $$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence the result is a vector of loss for each output."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cost function is the **expected loss value**, if we use the quadratic loss it then becomes the **Mean Squared error**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ MSE = \\sum_{i=1}^{n}{ ( y_i - z(x_i) )^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and in matrix notation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ MSE = E[L(Y_{k,1}, \\hat{Y}_{k,1})]= E[ (Y_{k,1} - z(X_{k,p}))^2 ) ] $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backpropagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At first the weights (coefficients for a linear regression here) are chosen **randomly**.<br>\n",
    "Of course, if we knew them before, why would we use an algorithm ? :P"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to use **Gradient descent**: a **first-order** iterative optimization algorithm for **finding a local minimum of a differentiable function**. We want to minimize the errors produces, we will perform the gradient descent of the loss function. It implies computing the derivative of the loss function w.r.t. the weights. The **quadratic loss function** is then a good choice here as it is differentiable.\n",
    "\n",
    "Computing the gradient of the **loss function** with respect to the **weights** enable us to later find the direction in the weight/parameter space that **minimizes the loss**.\n",
    "\n",
    "This derivative can be done in 2 different ways:\n",
    "- each iteration can use **one input vector**. Each of the weights will be updated computing the derivative on the loss function w.r.t. the weights for **that single input vector** that had been passed forward to compute the output and so the errors, this is named: **stochastic gradient descent**.\n",
    "- or each iteration can use a **batch of multiple vectors** (extreme case is using a bach equaling to the training set, the whole data available, that is, **k row vectors**) to compute the **expected loss value for that batch of inputs**, this is named: **batch gradient descent**. This means that each weight will be updating by the same quantity **meaned** over the grouped information from the predictions errors drawn from passing **k input vectors**.  \n",
    "\n",
    "Once computed, the gradient points **uphill** (maximize the loss), so we need to update the weights taking the opposite direction. Also we will carefully take each update a **little step in this same direction** by using the (negation of the) derivative by a coefficient also called **learning rate**: since it influences to what extent **newly acquired information overrides old information** (wikipedia always gives the best quote).\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"td5_ressources/batch_gradient_formula.png\" width=\"100%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"td5_ressources/stochastic_gradient_formula.png\" width=\"100%\" >"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"td5_ressources/gradient_descent.png\" width=\"100%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How to compute such gradient w.r.t. to the weights ? We use the **chain rule** !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> from wikipedia: Intuitively, the chain rule states that knowing the instantaneous rate of change of z relative to y and that of y relative to x allows one to calculate the instantaneous rate of change of z relative to x.<br> As put by George F. Simmons: \"if a car travels twice as fast as a bicycle and the bicycle is four times as fast as a walking man, then the car travels 2 × 4 = 8 times as fast as the man.\"m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to see how vary the **prediction errors** by making a **change in the weight space** (w.r.t. to each weight = gradient).<br>\n",
    "Here we face a **composite function**, as computing such derivative w.r.t one weight implies (using the chain rule):\n",
    "- to first derive w.r.t the output of the activation function,\n",
    "- then see how the output of the activation function changes w.r.t. the variable before the activation function (weighted inputs sum)\n",
    "- then w.r.t. to the weight itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"td4_ressources/img_formula_gradient_descent_backprop_mattmazur.png\" width=600>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recap "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"td5_ressources/img_explanations_Bertin_Luc.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time to implement it "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which activation are we going to use ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "x = np.linspace(0, 100, 800)\n",
    "y = 8*x + np.random.normal(x, 200) # y = 8*x + epsilon with epsilon ~ N(0,1)\n",
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = x[:, np.newaxis] # to set x as a matrix of row vectors of 1 feature b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {},
   "outputs": [],
   "source": [
    "def split_n_batch_indexes(X, nb_chunks=5):\n",
    "    import numpy as np\n",
    "    indexes = np.arange(len(X))\n",
    "    shuffled_indexes = np.random.shuffle(indexes)\n",
    "    return np.array_split(indexes, nb_chunks)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Neuron:\n",
    "    \"\"\" Implementation of a single Neuron accepting multiple inputs \"\"\"\n",
    "    def __init__(self, X, y, nb_epochs=100, nb_batches=5, \n",
    "                 learning_rate=0.01, activation=\"linear\"):\n",
    "        self.X, self.y = X, y\n",
    "        # random weights\n",
    "        self.W = np.random.random(size=(X.shape[1], 1))\n",
    "        # random bias (only one as only one output)\n",
    "        self.B = np.random.random(size=(1, 1))\n",
    "        # number of epochs\n",
    "        self.nb_epochs = nb_epochs\n",
    "        # number of batches \n",
    "        self.nb_batches = nb_batches\n",
    "        # learning rate\n",
    "        self.learning_rate = learning_rate\n",
    "        # activation\n",
    "        if activation==\"linear\":\n",
    "            self.activation = lambda x: x\n",
    "            self.derivative = lambda x: 1\n",
    "        # records\n",
    "        self.records = {}\n",
    "                \n",
    "    def forward_pass(self, is_batch):\n",
    "        \"\"\" a single forward pass to compute a prediction \"\"\"\n",
    "        self.y_pred_batch = self.activation( self.X[is_batch] @ self.W + self.B)\n",
    "        self.y_pred = self.activation( self.X @ self.W + self.B)\n",
    "        \n",
    "    def compute_mse_on_whole_dataset(self):\n",
    "        \"\"\" return the mean squared errors on whole training set\"\"\"\n",
    "        self.mse = np.mean((self.y - self.y_pred)**2)\n",
    "        \n",
    "    def backpropagation(self, is_batch):\n",
    "        \"\"\" compute the gradient of the errors with respect to \n",
    "        the weights using the chain rule \"\"\"\n",
    "        # gradient of the errors w.r.t the output/prediction\n",
    "        dE_dout = 2*(self.y_pred_batch - self.y[is_batch, np.newaxis])\n",
    "        # gradient of the prediction w.r.t before the activ. func\n",
    "        dout_dz = self.derivative(self.X[is_batch]) #1 for linear\n",
    "        # gradient of z w.r.t the weight\n",
    "        dz_dw = self.X[is_batch]\n",
    "        # final gradient w.r.t the weights:\n",
    "        self.dE_dw = dE_dout * dout_dz * dz_dw\n",
    "        # for the biases (only last part change)\n",
    "        self.dE_db = dE_dout * dout_dz * 1        \n",
    "    \n",
    "    def update_weights_and_biases(self):\n",
    "        dE_dw = self.dE_dw.mean(axis=0)[:, np.newaxis]\n",
    "        dE_db = self.dE_db.mean(axis=0)[:, np.newaxis]\n",
    "        \n",
    "        self.W = self.W - self.learning_rate * dE_dw\n",
    "        self.B = self.B - self.learning_rate * dE_db\n",
    "\n",
    "\n",
    "    def predict(self, X_test):\n",
    "        \"\"\" same as forward pass, just provide our own X\"\"\"\n",
    "        return self.activation( X_test @ self.W + self.B)\n",
    "    \n",
    "    def run(self):\n",
    "        \"\"\" learn iteratively:\n",
    "            - an iteration is a single forward and backward pass\n",
    "            - an epoch is consumed when all the inputs from the \n",
    "              dataset have been used for updating the weight and \n",
    "              biases \"\"\"\n",
    "        # epochs\n",
    "        for i in range(1, self.nb_epochs):\n",
    "            # batches: \n",
    "            for batch_i, indices in enumerate(\n",
    "                    split_n_batch_indexes(self.X, self.nb_batches)):\n",
    "                self.forward_pass(indices)\n",
    "                self.compute_mse_on_whole_dataset()\n",
    "                self.backpropagation(indices)\n",
    "                self.update_weights_and_biases()\n",
    "                self.records[(i, batch_i)] = [self.W, self.B, self.mse]\n",
    "        return self.records"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(x, y)\n",
    "scaler = StandardScaler().fit(X_train)\n",
    "X_train = scaler.transform(X_train)\n",
    "X_test = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<__main__.Neuron at 0x12d97f9a0>"
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "neuron = Neuron(X_train, y_train)\n",
    "neuron"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {},
   "outputs": [],
   "source": [
    "records = neuron.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>weights</th>\n",
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       "                     weights                    bias      mse_train\n",
       "1  0   [[4.443509449033136]]   [[9.644383787235665]]  316078.087993\n",
       "   1   [[10.21384857348198]]  [[18.956325297600568]]  307829.453673\n",
       "   2  [[13.829465261075233]]  [[27.481262123908465]]  299653.437801\n",
       "   3  [[18.483634718716814]]   [[35.58832870180558]]  292329.983030\n",
       "   4  [[24.778160591422168]]   [[44.41565823450879]]  285568.062128\n",
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       "\n",
       "[495 rows x 3 columns]"
      ]
     },
     "execution_count": 445,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "index = pd.MultiIndex.from_tuples(records.keys())\n",
    "records = pd.DataFrame(records.values(), \n",
    "            index=index,\n",
    "            columns=['weights', 'bias', 'mse_train'])\n",
    "records"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_weights = records.weights.apply(np.ravel).apply(pd.Series)\n",
    "df_bias = records.bias.apply(np.ravel).apply(pd.Series)\n",
    "df_bias.rename(columns = lambda x: \"bias_{}\".format(x), inplace=True)\n",
    "df_weights.rename(columns = lambda x: \"weights_{}\".format(x), inplace=True)\n",
    "df = pd.concat([df_weights, df_bias], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {},
   "outputs": [
    {
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>495 rows × 2 columns</p>\n",
       "</div>"
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       "       weights_0      bias_0\n",
       "1  0    4.443509    9.644384\n",
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     },
     "execution_count": 447,
     "metadata": {},
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    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lucbertin/.pyenv/versions/3.8.4/lib/python3.8/site-packages/pandas/plotting/_matplotlib/core.py:1235: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
      "  ax.set_xticklabels(xticklabels)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 448,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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o+rrc+FoIEdEk3LtjzSKwx8Hkr4W7EiGEOC0J964K+GHLYhh9OST1ww9dCSFiioR7V5V8ZEZ/HP8v4a5ECCE6JeHeVVtfgbgkeSNVCNEvSLh3ha8Ftr8Ooy4FZ3y4qxFCiE5JuHfFlpehpUbeSBVC9BsS7l2x4a+QOQIKLgh3JUII0SUS7p2pK4X9K2DCl+WGHEKIfkPCvTObrZtNnX3t6dcTIsyCwd4bfNXrD1DX4uu1/QN4fAHaDiDblcFktdYEg/r4uh1to7Um0Mlz0347jy+AxxfoStmd8geCpz1uZ7X1VFdGhYxtmxdDbhFkDA93JeIMaK2pbPDijrOT4naedl1fIEhNUyv1Hh+7KxoZMSCZIRnx7K9u5lBtC3aboqbZR5xdsbeqiewkF37rF7S8toVkt5OA1rS0BhiSkYDDpkhPjGN7eT01za1U1HkozEni2O98vceHPxCkuTWAUuCw20iNdxLvtNPo9VPT1Mr+6mZyUlwkxNlx2G34A0H2VTVR2eAlPzORygYvuyoaGD0wmVEDkklw2WlpDdLg8ZGV7KKmqRWbTYGG0ppmlFJ4fAGyklykJTgZnBZPVaOXPZVNtLT68fiCtPgC5KbFE++0s/1wPbXNPnKSXYwamMyInGQ8/gBby+ooq20BFEMy4slOclFe56Gp1c9Z2UnsrWykrsWH1x8kPyOBBo+flHgHafFxtPqDeANBUtwOio80crjew6AUN0opGr1+Gr1+sq36appbaW4N0OoPMiQjgUSXg5qmVsrrWghqyEyMQyk40uAlMc7BoFQ3Aa2pbfbR6PUTCGryMxIYMygZr888d8luB82tAQ7XefD4A4wemMLheg9eX4Dm1gBBrRmY4iY1IY76Fh++QJA4h41kt5PDdS1oIN5px+20EwhqfAHznNmUIt5px25TBIKastoW0hKcpMU7yUl2U9HgITvJRXpiHJtL67j78jFcOXFwyH/mVSQMtV5UVKTXrl0b7jJOdmQ7PD4D5j5g7pMq+lwwqAlqjcNuIxjUlNd7qGrwclZOEodqW1DAzooGympacDls5KS4qW/xcajOQ6PHT4svQEurn/UHajlwtBmAvPR46lt8jBmUQnmdh+ZWP15/kEBQ47TbzqiFqpS5b/qpOO2KhDjHCcdw2k0YxDns2BQEgpp6jw9fQONy2LDbFPkZCbT4AjR5TevWZlMUZCaS7HZQ0eAhI9HFyJwkNpXWcbCmmSavnziHnRS3g6PNrWQluQgGNf6gZkhGPDalcDnsVDZ6OVTbQnWjl4Q4B+MGp5CeEEd8nB2nXbH7SCNOm43sFBejByRTUt3MrooGdh9pwB/QTB+eQX5GAvUtfkprW6hrbmVIRgIJcXZ2VzSSmx7PgBQ3TrtiX1UTmUkuWloD1Da3EtCQ5LLT4PEzNDORJJeduhYf8U4HyW4HbqedfVWNtPiCZCbGkZbgRGv47GAtiXF2MpNcZCe5cNoVlQ1elFIMTHXR0hpkX1UjQQ0DUlykJcQBsLeyiZ0V9ThsNkYNSOZoUytxDhuFOUkEtWbn4QZy080fM5fDTnycjZKqZqoaveSmxxNn/Wx4/UEGprpx2BQtrQE8/iB2BU67jTiHDX9A02K1+g/XeRg1MJmA1hyp99Do9ZOZ6GJvVROBYJARA5L51xlDmT78pDuRdvHnTa3TWhd1tExa7qezeTEoG4y/JtyVRJ3qRi9rSmqoqPdwVnYSZbXNVNR7SXKZsHI77FQ1ennlszJafAFS453UNncvdBPj7MTHOUiIszMwxc3Cc4fx7rbDOO028tLj2VbewNhBKWQkxeFy2LApRas/SGZSHJlJLtPiToijyevnYE0zWUkuCrISiXPYSIt30twaYHBaPPUeHw6bwqYUg1LdNHj8KAVBDQ0e0+KrbmylMCeJ1HgndpvC6w/itNvwBcwflUTXyb+KvkAQh03RF/eX9weCOOxd76UNBjVef5D4OBljKVJJuJ+K1rD57zD8IkjKCXc1/UowqKlo8BDUsKWsjuIjjZTVtmBTUN3YSmWDl01ldbT6O+6LdNoV/qDGabMxb9Jgcq0ugxZfgDi7jQtGZrOrooFhmYn4AkHGDEohJ8XFgWrT3ZCVFEdeegJ228mheMv5BSE/3+xk1wmP0xPjjk9nWNOF7X6E3E4TivbTDEDn7EbYnqnuBDuAzaYk2COchPuplK6B2v1w0Z3hriRiaa0prWlhS1kdB44289mBWo42tVJc2cjRptYT1s1MjEMDCXF2klwOrp86hLnjBjIkI4GS6iayk10My0ykuTVAeoITrz+ILxAk+RT945edPeikeTnJcqNyIY6RcD+VzX8HhxtGXxHuSsLuUG0L/9xcTkl1Ey6HncP1HqobvWw7VE+9x398vUGpbganxfOFUTkMz04E4LzCLApzkkjqoNvhmCEZCcenj7Vo3dYbVUKInpFw70jAbz6VOnIuuFPCXU2f8geCbCuv57MDtZTWNLNq31E2ldYBptXtD2gGpblJS4jjiomDGT84lXGDUxhmvbln66ArRAjR9yTcO1LyETRXxcS17Y1eP2tKjrJq71E+3FVJZYOHqkbTpRJntzFpSBo/uHgkV04cTH5GwvErV4QQkU3CvSM73wRHfNSOAHmgupmnPinhkz1V7KxoQGuwKZicn84FI7K5cFQ2U/LTGZDiJs5xYpDbkJa5EP2BhHt7WsOut8xVMlE0AmST18/zaw7y7KcllFQ3Y7cpioam852LzmLqsAxmDM+UPm4hooiEe3tHtkPtAZj1g3BXckY+O1DDM5/uZ03JUY7Ue/EHgwQ1TBuWwVem5nP15FwGpsrVJUJEKwn39na9Zb6PuCS8dfRAZYOX51YdoLyuhSUbDuF22phekMmwCYnE2RUXjsrmnKEZ4S5TCNEHJNzb2/U2DJoIKSdfRx2pDh5tZvG6Uv6ycj/V1keq544byH9eMUau/RYiRkm4t9V8FEpXw6wfhruSLimva+E3b+/klc/KAJhekMFz88YzPDuxTz/dKISIPBLubRUvBR2EkZHdJbO25CjPrT7Akg2HsCvFrRcMZ8G0oeRnJnS+sRAiJki4t7X7bUjIgsFTwl3JSbTWfLS7ikeX7WZNSQ1KwddmDOWbs4af8AlPIYQACffPBQNQ/J75VKotsro0Nh6s5YG3dvDJnmoGp7q558qxXD059/hQpkII0Z6E+zGla8xNsEd8KdyVHHeotoX739zBaxsPkZEYxz1XjmXB9KEnfbBICCHak3A/ZtdbYHPAWbPDXQlaa/60ooQH3txBQGtun13IrReeddrBt4QQoi1Ji2N2vQ35MyE+LaxlLN9dyWPvF7Ny71G+OCaHn10xTt4oFUJ0m4Q7QM1+OLINvnRf2Epo8Pi457WtvLy+jJxkF7+6ajxfnZ7fJ3fhEUJEHwl3MK12gFGX9vmhtda8teUw//3mdspqWrh9zgi++4VC6VcXQpwRCXeAPUshvQAyz+rTw7b6g/z6ze38eUUJQzMTePHfZlI0TIYHEEKcuU6bh0qpIUqp95VS25RSW5VSd1jzM5RS7yqldlvf0635Sin1iFKqWCm1SSkVeReNtxXww/5PzCiQfajVH+T7L27gzytKWDhzKMt+cJEEuxAiZLryv78f+IHWeiwwA7hNKTUWuBNYqrUeASy1HgNcCoywvm4F/i/kVYdS+Ubw1kPBBX12yJV7q7nif5fzj03l/PTS0fxi/vgOb+YshBA91Wm4a63LtdbrrekGYDuQC8wHnrZWexq4ypqeDzyjjZVAmlIqckfh2veh+T5sVp8c7v99uIfrn1hJkzfAooVF/NuFfdsVJISIDd3qc1dKDQMmA6uAAVrrcmvRYWCANZ0LHGyzWak1r7zNPJRSt2Ja9uTn53e37tDZ9xHkjIWk7F4/1DtbD3P/Wzu4/OxBPHjdROLj5OYYQoje0eVLMpRSScBLwL9rrevbLtNaa0B358Ba6ye01kVa66Ls7N4P1g55G2H/Chj+hV49jMcX4O5XNvOtv6xj/OBUCXYhRK/rUstdKeXEBPtftdYvW7MrlFKDtNblVrfLEWt+GTCkzeZ51rzIs+9DCLTCqLm9doja5lZufWYdq0uOctO5w/jRJaMk2IUQva4rV8soYBGwXWv9UJtFrwELremFwJI28//VumpmBlDXpvsmsuz9EJwJMGRGr+y+wePjhj+uYsPBWh65YTI/nzeORBlCQAjRB7qSNOcBXwM2K6U2WPPuAu4HXlRK3QLsB75sLfsncBlQDDQDXw9lwSG1/xMYMg0coR9dsdUf5KtPrmJXRQOLFhZx0aickB9DCCFOpdNw11p/DJzqOr05HayvgdvOsK7e11IDFVvgC3f3yu6f+mQfG0vreOSGyRLsQog+F7t9BAdWAhqGnhvS3foCQR5dVszvl+5m9ugcrpwQuVeBCiGiV+yG+/4VYHdB7jkh26XXH+DWZ9bx4a5Krpmcy6//5WwZ+EsIERYxHO6fQF4RON0h2V0wqPnx4k18uKuS/776bG6cHsZr94UQMS82hx70NsChDSHtknnwnZ0s2XCIH88dJcEuhAi72Az3g6tBB0IW7n9ZuZ/HP9jDjdPz+bYMJyCEiACxGe77PwFlh7xpZ7yrt7aU819LtjBndA6/nDdO+tiFEBEhRsN9BQyeDK6kM9pNvcfHT17azIS8NB69cQoOe2w+nUKIyBN7aeRrgbJ1IemS+c1bO6lr8XHfVeNlSAEhRESJvXAvW2fGkxl63hnt5g8f7uHZlfv5xvkFjM9NDVFxQggRGrEX7iXWB27zez6ezDtbD3P/mzu4cuJgfnrZmNDVJoQQIRJ74V78HuROgfi0Hm3e0hrgF69vY9SAZB768kS5g5IQIiLFVrg3H4XStVB4cY938T9v76CstoVfXTUep7yBKoSIULGVTsfGkxl+YY82/+fmcv68ooSbzh3GtAK5mbUQInLFVrgfXAU2p7kMspv2Vjby48WbmDQkjbukn10IEeFiL9wHTQRnfLc2a2kN8J2/rsdpVzy2YApxjth62oQQ/U/spJS/FcrWd/sqGa01//nqFnZWNPC76yeTm9a9PwxCCBEOsRPu5Rsh4IUh07u12bIdR3hpfSnfmz2CC0eG6UbeQgjRTbET7qVrzPchXR9PxhcI8us3d1CQlcj3Zhf2UmFCCBF6sRPuZesgJQ+SB3Z5kz+v2EfxkUbuvmyMXPYohOhXYiexytaZDy910dGmVn7/3m7mjM7hi2MH9GJhQggRerER7s1HoWZft26p98RHe2n2BfjpZaN7sTAhhOgdsRHuZevN9y623LeU1fHk8r1cPTmXwpzkXixMCCF6R4yE+zpAwaBJna4aDGp+tHgTGYlx3HPFuF4vTQghekNshPvBVZA9Gtwpna76zrYKtpfXc9dlY0hNcPZBcUIIEXrRH+7BgLln6tCZna8a1PzuvV0UZCVyxYRBfVCcEEL0jugP94ot0NoA+Z2H+1tbD7PjcAN3zBkht8wTQvRr0Z9ghz4z3/OKTrtaMKj5/Xu7OSs7kSsnDu6DwoQQovfERri7UyG94LSrvbPtMDsrGrh9zgi5AYcQot+LjXAfPBnUqQM7ENQ8srTY6muXVrsQov+L7nD3e6FiW6eXQD77aQnbyuv5/sUjpdUuhIgK0R3uFVsh6DvtzTk8vgCPvr+HmcMzuVKukBFCRInoDvfyDeb74EmnXOWFNQepavRyxxdHoE7TdSOEEP1JdId76TpIyIK0oR0ubvUH+X8f7qFoaDrT5Z6oQogoEuXhvsZcAnmKFvmrG8o4VOfhu7MLpdUuhIgqnYa7UupPSqkjSqktbeZlKKXeVUrttr6nW/OVUuoRpVSxUmqTUqrrY+yGmqcOqnZBbsfXt2uteXL5XkYPTJY7LAkhok5XWu5PAXPbzbsTWKq1HgEstR4DXAqMsL5uBf4vNGX2QNl6QENex8P8flxcxa6KRr4xa7i02oUQUafTcNdafwQcbTd7PvC0Nf00cFWb+c9oYyWQppQKzyUoZWsBdcox3J9cvo+sJBdXTpQrZIQQ0aenfe4DtNbl1vRh4NitinKBg23WK7XmnUQpdatSaq1Sam1lZWUPyziNsvWQNcJ8OrWd3RUNfLirkoUzh+Jy2EN/bCGECLMzfkNVa60B3YPtntBaF2mti7Kze6HP+/BmGDihw0V/WrEPl8PGghkdX0UjhBD9XU/DveJYd4v1/Yg1vwwY0ma9PGte32qpgbqDMPDskxZVN3p5eX0Z10zJIyMxrs9LE0KIvtDTcH8NWGhNLwSWtJn/r9ZVMzOAujbdN32nYqv5PnD8SYueW3UArz/ILecP69uahBCiDzk6W0Ep9TfgIiBLKVUK3APcD7yolLoF2A982Vr9n8BlQDHQDHy9F2ru3OHN5nu7bhl/IMhzqw8wa0SW3BtVCBHVOg13rfUNp1g0p4N1NXDbmRZ1xso3QdIASMo5YfbSHUcor/Pw83lyb1QhRHSLzk+oHt7cYX/7X1buZ1CqmzmjczrYSAghokf0hbu/FSp3nBTu+6qaWL67ihum5cst9IQQUS/6Uq5yhxnmt11/+yNLd+Ny2Lh+6pBTbCiEENEj+sL98CbzvU24VzZ4eXVDGQvPHUZOijtMhQkhRN+JwnDfDM5EyPj8nqnvbqtAa7h6cocflhVCiKgTneE+YBzYPh9W4K2thxmamcDogXL5oxAiNnR6KWS/EgyacJ/w5eOz6lp8fFJcxS3nF8joj0L0AZ/PR2lpKR6PJ9ylRA23201eXh5Op7PL20RXuNfuB289DPj8k6kvry/FH9RcLvdHFaJPlJaWkpyczLBhw6RBFQJaa6qrqyktLaWgoKDzDSzR1S1zZLv5boW71ppnPt3PlPw0JuSlha8uIWKIx+MhMzNTgj1ElFJkZmZ2+z+hKAt3a0yZnNEArCmpYV9VEwumy+iPQvQlCfbQ6snzGWXhvh3S8sFl3jj9+9qDJLkcXHr2wDAXJoQQfSu6wr1iG+SMBaDJ6+cfm8u5YsIgEuKi660FIYToTPSEu78VqncfD/d/bC6nuTXAdUV5YS5MCNEffOMb32Dbtm2nXeemm25i8eLFJ80vKSnhueee69Fx33rrLUaNGkVhYSH3339/j/bRkehp0lYXQ9B/PNz/vvYgw7MTmZKfHubChIhdv3h9K9sO1Yd0n2MHp3DPlaEf2fXJJ5/s8bbHwv3GG2/s1naBQIDbbruNd999l7y8PKZOncq8efMYO3Zsj2s5Jnpa7kesv7g5Y9hX1cSakhquO2eIvLEjRIz5zW9+wyOPPALA97//fWbPng3AsmXLWLBgAe+88w4zZ85kypQpXHfddTQ2NgJw0UUXsXbtWgAWLVrEyJEjmTZtGt/85jf57ne/e3z/H330Eeeeey7Dhw8/3oq/8847Wb58OZMmTeLhhx9m69atTJs2jUmTJjFhwgR2797dYa2rV6+msLCQ4cOHExcXx/XXX8+SJUs6XLe7oqflfmQ7KDtkjWDpp+bOfvMmDQ5zUULEtt5oYXdm1qxZ/Pa3v+X2229n7dq1eL1efD4fy5cvZ8KECdx777289957JCYm8sADD/DQQw/xs5/97Pj2hw4d4le/+hXr168nOTmZ2bNnM3HixOPLy8vL+fjjj9mxYwfz5s3j2muv5f777+fBBx/kjTfeAOB73/sed9xxBwsWLKC1tZVAINBhrWVlZQwZ8vlghnl5eaxatSokz0P0hHvlDsgYDg4XHxdXcVZ2Irlp8eGuSgjRx8455xzWrVtHfX09LpeLKVOmsHbtWpYvX868efPYtm0b5513HgCtra3MnDnzhO1Xr17NhRdeSEZGBgDXXXcdu3btOr78qquuwmazMXbsWCoqKjqsYebMmdx3332UlpZyzTXXMGLEiF4621OLnm6Zyp2QPYoGj49P91Qza0R2uCsSQoSB0+mkoKCAp556inPPPZdZs2bx/vvvU1xcTEFBARdffDEbNmxgw4YNbNu2jUWLFnVr/y6X6/i0ufncyW688UZee+014uPjueyyy1i2bFmH6+Xm5nLw4MHjj0tLS8nNDc0Ah9ER7n4vHN0LOWN4e2sFXn+QKydKl4wQsWrWrFk8+OCDXHDBBcyaNYs//OEPTJ48mRkzZrBixQqKi4sBaGpqOqFVDjB16lQ+/PBDampq8Pv9vPTSS50eLzk5mYaGhuOP9+7dy/Dhw7n99tuZP38+mzZt6nC7qVOnsnv3bvbt20drayvPP/888+bNO4Mz/1x0dMtUF4MOQPZo3lxXTl56PFPy08JdlRAiTGbNmsV9993HzJkzSUxMxO12M2vWLLKzs3nqqae44YYb8Hq9ANx7772MHDny+La5ubncddddTJs2jYyMDEaPHk1qauppjzdhwgTsdjsTJ07kpptuwuv18uyzz+J0Ohk4cCB33XVXh9s5HA4effRRLrnkEgKBADfffDPjxoXmfQp1qn8r+lJRUZE+9i51j2xeDC/dQss3PmLSHw5x4/T8sLyRI4SA7du3M2bMmHCXcUYaGxtJSkrC7/dz9dVXc/PNN3P11VeHtaaOnlel1DqtdVFH60dHt0zlTlA2llen4fUHuXjMgHBXJITox37+858zadIkxo8fT0FBAVdddVW4S+q26OiWqdwOGcN5e2ctKW4HUwsywl2REKIfe/DBB0O6v+rqaubMmXPS/KVLl5KZmRnSYx0TJeG+k2DWKJbtqGD26Byc9uj4h0QIER0yMzPZsGFDnx6z/6eg3wvVeyiPG0ZNs4+Lx8oIkEII0f/DvXoP6ABrmrJx2hUXjMwKd0VCCBF2/T/cq3YC8MahFGaelUWyu+v3GBRCiGjV/8O9chcaxce16Vw0Uj6VKoQQEA3hXrWTloTBeHBRNEyG9xVCmCF4x48ff9L8rozZ3lVer5evfOUrFBYWMn36dEpKSkKy31Dp/1fLVO2izJGP22ljzKCUcFcjhGjrzTvh8ObQ7nPg2XBpz25qcSZjtre3aNEi0tPTKS4u5vnnn+cnP/kJL7zwQsj2f6b6d8s9GERXFfNZczbTCzLlEkghxHF+v58FCxYwZswYrr32Wpqbm08Ys/3b3/42RUVFjBs3jnvuuef4dnfeeSdjx45lwoQJ/PCHPzzl/pcsWcLChQsBuPbaa1m6dOkpBxILh/7dcq87gPK3sN6XwxfHyqdShYg4PWxhh8LOnTtZtGgR5513HjfffDOPP/74Ccvvu+8+MjIyCAQCzJkzh02bNpGbm8srr7zCjh07UEpRW1t7yv23HYvd4XCQmppKdXU1WVmRccVe/27qVprR3PaRy9xxcn27EOJzQ4YMOT5u+1e/+lU+/vjjE5a/+OKLTJkyhcmTJ7N161a2bdtGamoqbrebW265hZdffpmEhIRwlB4S/TrctXUZ5ODCiWQnuzpZWwgRS9rfYrPt43379vHggw+ydOlSNm3axOWXX47H48HhcLB69WquvfZa3njjDebOnXvK/bcdi93v91NXV9drQwn0RL8O9/LMmfzMt5ApYwrDXYoQIsIcOHCATz/9FIDnnnuO888///iy+vp6EhMTSU1NpaKigjfffBMwo0HW1dVx2WWX8fDDD7Nx48ZT7n/evHk8/fTTACxevJjZs2dH1D2be6XPXSk1F/g9YAee1Fr3Ssfbxw0DeCZwCe/IQGFCiHZGjRrFY489xs0338zYsWP59re/zeuvvw7AxIkTmTx5MqNHjz6h+6ahoYH58+fj8XjQWvPQQw+dcv+33HILX/va1ygsLCQjI4Pnn3++T86rq0Ie7kopO/AYcDFQCqxRSr2mtQ7NxaVtpCfEcfHYAYzISQr1roUQ/diwYcPYsWPHSfM/+OCD49NPPfVUh9uuXr26S8dwu938/e9/70l5faI3Wu7TgGKt9V4ApdTzwHwg5OF+8dgBXCxXyQghxEl6I9xzgYNtHpcC09uvpJS6FbgVID8/vxfKEEKIM3ffffed1EK/7rrruPvuu8NUUdeE7Tp3rfUTwBNgbrMXrjqEEKGntY6oNxfPxN133x32IO/Jh6N642qZMmBIm8d51jwhRAxwu91UV1dH1Kc1+zOtNdXV1bjd7m5t1xst9zXACKVUASbUrwdu7IXjCCEiUF5eHqWlpVRWVoa7lKjhdrvJy8vr1jYhD3ettV8p9V3gbcylkH/SWm8N9XGEEJHJ6XRSUFAQ7jJiXq/0uWut/wn8szf2LYQQonP9+hOqQgghOibhLoQQUUhFwjvaSqlKYH8PN88CqkJYTn8h5x07YvGcITbPu7vnPFRr3eH9RSMi3M+EUmqt1roo3HX0NTnv2BGL5wyxed6hPGfplhFCiCgk4S6EEFEoGsL9iXAXECZy3rEjFs8ZYvO8Q3bO/b7PXQghxMmioeUuhBCiHQl3IYSIQhEX7kqpeKXUh9YdnVBKvaWUqlVKvdHF7V1KqReUUsVKqVVKqWHW/LOVUk/1XuXd0/Y8lVKTlFKfKqW2KqU2KaW+0ma971rnopVSWV3c90Kl1G7ra2Gb+e8ppdJ743y6qv3ra81LUUqVKqUebTPvPqXUQaVUYzf2/VPrudqplLrEmhenlPpIKRW24a2tOtr/XOcrpd5RSm1XSm1r83MaNa93B+f8P9bP+Hal1CPKGhM42l7riKG1jqgv4DbgjjaP5wBXAm90cfvvAH+wpq8HXmiz7D0gP9zn2P48gZHACGt6MFAOpFmPJwPDgBIgqwv7zQD2Wt/Trel0a9lC4O5IOe82834PPAc82mbeDGAQ0NjF/Y4FNgIuoADYA9itZfcACyLpvIEPgIut6SQgIdpe73Y/4+cCKzCDCdqBT4GLovG1jpSviGu5AwuAJcceaK2XAg3d2H4+8LQ1vRiYc6yFALyOCfxIcPw8tda7tNa7relDwBEg23r8mda6pBv7vQR4V2t9VGtdA7wLzLWWvQbcEJrye+yE11cpdQ4wAHin7Upa65Va6/Ju7Hc+8LzW2qu13gcUY275CPCqddxwOn7eSqmxgENr/S6A1rpRa91sTUfT6932tdaAG4jDhLITqICofK0jQkSFu1IqDhjezR/u9o7f5k9r7QfqgExr2Vpg1pnUGAqnO0+l1DTML8CeHu6+o9sc5gJYv/wupVRmRxv2tvbnrZSyAb8FfhiC3Z/yvIEtwNQQHKNHOni9RwK1SqmXlVKfKaV+07abqpsi8vVuf85a60+B9zH/lZYDb2utt/dw9xH7WkeSiAp3zLgKtb24/yOYbo9w6/A8lVKDgGeBr2utg7107HA+B+3P+zvAP7XWpb15UK11AGhVSiX35nFOo/15OzCNjB9igmg4cFMvHTtcr/cJ56yUKgTGYO7MlgvMVkqFvKEVAa91xIi0cG/B/Ot2Jo7f5s96YyUVqLaWua1jhNtJ56mUSgH+gekjXXkG++7sNofhfA7an/dM4LtKqRLgQeBflVL393DfnZ23C/D0cN9nqv15lwIbtNZ7rf8uXwWm9HDfkfp6tz/nq4GVVhdUI/Am5vXviUh+rSNGRIW79W+kXSnVacArpX6tlLq6g0WvYd5IArgWWKatd1ow/w5vCUmxZ6D9eVr/wr4CPKO1XtyVfSilpimlnulg0dvAl5RS6daVEl+y5mG99zAQ82Zdn2t/3lrrBVrrfK31MEwr9hmt9Z2n24dS6mql1K87WPQacL11tVQBMAJYbW2TCVRprX0hPJ0u6+Dneg2QppQ6NprfbGDb6fbR317vDs75AHChUsqhlHICFwKn7Zbpj691JImocLe8A5x/7IFSajnwd8wbo6XHLnsCzgYOd7D9IiBTKVUM/AfQNiy+gGkdR4K25/ll4ALgJqXUButrEoBS6nalVCmmdbJJKfWktU0+HbTItNZHgV9hAmQN8EtrHsA5mNaTv5fOqStOeH1PxbpsrhRIsF73n1uLzgLq26+vza0cX8SE5FvAbda/6BAZr/vx87bq+iGwVCm1GVDAHyHqXu+2r/VizPtImzFXumzUWr8OUflaR4ZwX67T/gvz7+mzXVjv7W7u1wWsxFyl0G/O8zTb/waY0M1tfg/M6efn/Rcgu5vbvAyM7Ofn3e9e71h9rSPlK+Iu9tdar1dKva+UsuvP/xp3tN4lp1p2CvnAnTq8rdbjunqep9n+Rz047BZtLi0NmxCc91e7s77V5fWq1npXd48VSrH4esfqax0pZOAwIYSIQpHY5y6EEOIMSbgLIUQUknAXQogoJOEuhBBRSMJdCCGi0P8Ha6Gxw3INbS8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind=\"line\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12df02610>]"
      ]
     },
     "execution_count": 449,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_test, y_test)\n",
    "plt.plot(X_test, neuron.predict(X_test), color='green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_dpi_ratio', { dpi_ratio: fig.ratio });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    var resizeObserver = new ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
       "        case 1:\n",
       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
       "        case 3:\n",
       "            cursor = 'move';\n",
       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = 'image/png';\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data']);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.one(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<img src=\"data:,\" width=\"0\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "\n",
    "import matplotlib.animation as animation\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "# Initial plot\n",
    "x_ = np.linspace(-2, 2, 100).reshape((100,1))\n",
    "# y_ = weight*x_ + bias\n",
    "y_ = float(df.iloc[0, 0])*x_ + float(df.iloc[0, 1])\n",
    "\n",
    "line, = ax.plot(x_, y_, label=\"Fit from the neuron\")\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (4,2)\n",
    "plt.ylabel(\"y\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.scatter(X_train, y_train, color='red', label=\"Training data\")\n",
    "plt.scatter(X_test, y_test, color='green', label=\"Test data\")\n",
    "plt.xlim(-2, 2)\n",
    "plt.legend()\n",
    "plt.title(\"Linear regression training fit using a single neuron | perceptron\")\n",
    "\n",
    "def animate(i):\n",
    "    line.set_label(\"Fit from the perceptron : epoch {}\".format(i))\n",
    "    plt.legend()\n",
    "    x_ = np.linspace(-2, 2, 100).reshape((100,1))\n",
    "    line.set_xdata(x_)  # update the data\n",
    "    line.set_ydata( float(df.iloc[i, 0])*x_ \n",
    "                   + float(df.iloc[i, 1]))# update the data\n",
    "    return line,\n",
    "\n",
    "ani = animation.FuncAnimation(fig, animate, frames=np.arange(1, len(df)), interval=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's try with multiple features ;-)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "linear regression coefficients [-0.72097319  1.32905744  0.14098068  0.31901842 -1.9611038   2.39122944\n",
      "  0.02842854 -3.10284546  2.2339583  -1.52408631 -1.94909087  1.18566169\n",
      " -3.79786679]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "X, y = load_boston(return_X_y=True)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)\n",
    "scaler  = StandardScaler()\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "X_test  = scaler.transform(X_test)\n",
    "lm = LinearRegression().fit(X_train, y_train)\n",
    "print( \"linear regression coefficients {}\".format(lm.coef_) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {},
   "outputs": [],
   "source": [
    "neuron_on_boston = Neuron(X_train, y_train, \n",
    "                          learning_rate=0.1, \n",
    "                          nb_batches=1)\n",
    "records_on_boston = neuron_on_boston.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "index = pd.MultiIndex.from_tuples(records_on_boston.keys())\n",
    "df_boston = pd.DataFrame(records_on_boston.values(), \n",
    "            index=index, columns=['weights', 'bias', 'mse_train'])\n",
    "df_weights = df_boston.weights.apply(np.ravel).apply(pd.Series)\n",
    "df_bias = df_boston.bias.apply(np.ravel).apply(pd.Series)\n",
    "df_bias.rename(columns = lambda x: \"bias_{}\".format(x), inplace=True)\n",
    "df_weights.rename(columns = lambda x: \"weights_{}\".format(x), inplace=True)\n",
    "df = pd.concat([df_weights, df_bias], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "execution_count": 456,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig = plt.Figure(figsize=(10,6))\n",
    "ax = fig.gca()\n",
    "save = df.drop(\"bias_0\", axis=1).stack().unstack(level=0).loc[0].T\n",
    "save.plot(ax=ax)\n",
    "ax.legend().remove()\n",
    "fig.legend(loc='center', bbox_to_anchor=(1,0.5))\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "metadata": {},
   "outputs": [],
   "source": [
    "at_10  = save.iloc[10]\n",
    "at_50 = save.iloc[50]\n",
    "at_98 = save.iloc[98]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 13 artists>"
      ]
     },
     "execution_count": 458,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(x=np.arange(len(lm.coef_)), height=lm.coef_, color='red')\n",
    "plt.bar(x=np.arange(len(lm.coef_)), height=at_10, color='white', alpha = 0.5)\n",
    "plt.bar(x=np.arange(len(lm.coef_)), height=at_50, color='white', alpha = 0.5)\n",
    "plt.bar(x=np.arange(len(lm.coef_)), height=at_98, color='white', alpha = 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In Keras ? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    "from keras import optimizers\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(1, input_shape=(X.shape[1],), activation='linear'))\n",
    "sgd = optimizers.SGD(lr=0.02)\n",
    "model.compile(loss='mean_squared_error', optimizer=sgd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A callback to store weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.callbacks import LambdaCallback\n",
    "\n",
    "weights = {}\n",
    "def save_weights(epoch, logs):\n",
    "    weights[epoch] = model.layers[0].get_weights()\n",
    "    \n",
    "keep_weights = LambdaCallback(on_epoch_end=save_weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "metadata": {},
   "outputs": [],
   "source": [
    "history = model.fit(x=X_train, y=y_train, \n",
    "                    batch_size=X_train.shape[0], epochs=99, \n",
    "                    validation_data=(X_test, y_test), \n",
    "                    verbose=0, callbacks=[keep_weights])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'verbose': 0, 'epochs': 99, 'steps': 1}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 464,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Y2/cYUwams6pkH3WnXWq9W7Xkc6dDUkqpTnXC5C4ilwIVxphlnfnBIjJLRIpEpKiysrIzD31C5wxKwxj4kDPA7YO1r3Xr5yulVFdrz537RGCaiGwDXsJqjnkUSBQRj71NNlBqL5cCOQB2fQKw9/CDGmOeMMYUGmMK09LSTukkOmp4VgLJMREs/LLeappZ97o2zSilQsoJk7sx5j+NMdnGmFzgm8D7xpjrgUXAVfZmM4HX7eV59jp2/fvG9Ky3Y7hcwqSCVBZv2kNgyHSo3QUlS50OSymlOs2p9HO/H7hHRLZgtak/bZc/DaTY5fcAD5xaiF1jysA09tQ1siF+otU0s+41p0NSSqlO4znxJm2MMR8AH9jLxcC4o2zTAFzdCbF1qUkFVlPQom0NDMk/32qauejX4Aqr57qUUiEqbDNZWpyPkdkJLFhXDkMuh/2lUFrkdFhKKdUpwja5A1w0NJMVO/dR0fdccEfA2n86HZJSSnWK8E7uQzIAeHfrQci/ENa8CgG/w1EppdSpC+vknp8eS15qDO+uK4cRV0NdGWz7yOmwlFLqlIV1chcRLhqSwadb97C/3/kQEQer5jgdllJKnbKwTu4AFw3NoNlv+KC4DoZMg3XzoPmg02EppdQpCfvkPionidRYH++uLYMR10BTLWzUl2crpXq3sE/ubpdw4ZB0PthYSWP2BIjNhNUvOx2WUkqdkrBP7gAXDcmkrrGFT7/cB8Ovgs0LoL7K6bCUUuqkaXIHzjothZgIN/PXlltNM4Fm7fOulOrVNLkDkV43552ewfy1ZTSnDYPUQbBqttNhKaXUSdPkbrtsRB+qDjTx7+IqGDUDdi6BPZudDksppU6KJnfblEFpxEV6+NfKXTByBogbvvi702EppdRJ0eRu83ncTB2ayfw1ZTRGpUHBhbDyH+BvOfHOSinVw2hyD3LZyL7UNrbw4cZKGP0fUFcOW95zOiyllOowTe5BJpyWQnJMBP9atRsGToWYNPjib06HpZRSHabJPYjX7eLiYZm8t66cer/AiGth0ztQ170v8FZKqVOlyf0w00b25WCzn4XrK2D0tyDQot0ilVK9jib3w4zNTSYj3se8lbsg/XTIKrSaZnrWO76VUuq4NLkfxuUSpo/KYtGGCvbWNcIZN0LlBtj+b6dDU0qpdtPkfhRXjsmmJWB4fcUuGHYlRCZA0dNOh6WUUu2myf0oBmXGMSI7gZeXlUBENIy63hrnva7C6dCUUqpdNLkfw9VnZLN+937W7qqBwm9bg4ktf97psJRSql00uR/DZSP7EuF28XJRCaQWQN4UWPasvkBbKdUraHI/hsToCC4cmsHrK0ppagnA2JuhZidsftfp0JRS6oROmNxFJFJEPheRlSKyVkR+YZfnicgSEdkiIrNFJMIu99nrW+z63C4+hy5z1RnZVNc38/6GChh0CcT1gaVPOR2WUkqdUHvu3BuB84wxI4FRwNdEZDzwO+ARY0w+UA3cbG9/M1Btlz9ib9crTcpPJT3Ox9xlO8HttbpFbnlPhwJWSvV4J0zuxlJnr3rtyQDnAXPt8ueAy+3l6fY6dv35IiKdFXB38rhdXHlGNu9vqGB3zUHrh1V3BHz2mNOhKaXUcbWrzV1E3CKyAqgAFgBbgX3GmNbxcEuALHs5C9gJYNfXACmdGHO3um5cPwzwj893Qmy69Rq+FS/qO1aVUj1au5K7McZvjBkFZAPjgMGn+sEiMktEikSkqLKy5w7MlZMczTkD03jp8x00+wMw/nZoOQjL/up0aEopdUwd6i1jjNkHLALOAhJFxGNXZQOl9nIpkANg1ycAe49yrCeMMYXGmMK0tLSTi76bfGt8fypqG1mwrhwyhsKAc2HJE9DS5HRoSil1VO3pLZMmIon2chRwIbAeK8lfZW82E3jdXp5nr2PXv29M7x5165xB6WQlRvH3z7ZbBWd9D+rKYO0/nQ1MKaWOoT137n2ARSKyClgKLDDGvAHcD9wjIluw2tRbB195Gkixy+8BHuj8sLuX2yVcd2Y//r11L1sq6iD/fEgdBJ/+SUeLVEr1SO3pLbPKGDPaGDPCGDPMGPNLu7zYGDPOGJNvjLnaGNNolzfY6/l2fXFXn0R3uHZsDl638MKS7SACZ90OZaugeJHToSml1BH0CdV2So318bVhfZi7rIQDjS0wcob1UNNHDzsdmlJKHUGTewfcOCGX2oYWXi7aCR4fTLgTtn0EO5Y4HZpSSh1Ck3sHnNE/iTH9Ennmk234A8Z6YjUqGT76g9OhKaXUITS5d9Ctkwawo6qeBevKICLG6ve+eT7sXuV0aEop9RVN7h100dBMcpKjePKjL62CcbdARBx8rG3vSqmeQ5N7B7ldwrcn5rFsezXLd1RDVJKV4Ne+BpWbnA5PKaUATe4n5ZrCHOIjPTz1kd3Lc/wd4I2GDx90NjCllLJpcj8JMT4P153Zn3fWlLF97wGITYPx34U1r0DZGqfDU0opTe4n69sTc/G4Xfy/RVutggl3gi8BPvits4EppRSa3E9aenwkM8bm8MryEkqq66229wnfgw1vQOlyp8NTSoU5Te6n4DtTTkME/vKh3fZ+5netfu+Lfu1sYEqpsKfJ/RT0TYziqjOymV20k/L9DRAZD2d/33oV37ZPnA5PKRXGNLmfotum5OMPmLa797G3QlxfePfHEAg4G5xSKmxpcj9F/VKiuXxUFi9+vp3K2kaIiIbzfwK7lsPaV50OTykVpjS5d4LvnZdPs9/w50VbrIIR34TM4fDeL6C5wdnglFJhSZN7J8hLjeGawmxeWLKdnVX14HLBRb+Gmh3w+V+cDk8pFYY0uXeSu84vwCXC/7632SoYMAUKpsLiP8CBI14hq5RSXUqTeyfpkxDFzAm5vPpFCZvKa63Ci/4bmurg/f92NjilVNjR5N6JbptyGrERHn4/f6NVkDbI6vu+7FkoXeZobEqp8KLJvRMlxUQwa/IA3l1XzrLt1VbhOQ9AbDq8eS8E/M4GqJQKG5rcO9m3z84jI97HL99YRyBgrAebLvo17PoClj/vdHhKqTChyb2Txfg8/HDqYFbu3MdrK0qtwuFXQf+zYeEv9MdVpVS30OTeBb4xOouROYk8+PYGDjS2gAh8/ffQWAsLfuJ0eEqpMKDJvQu4XMJPLx1CRW0jj31gDwmcfjpMuAtWvABb33c2QKVUyNPk3kXO6J/E9FF9eeKjYuvBJoAp90NKAcy7GxrrnA1QKRXSTpjcRSRHRBaJyDoRWSsid9vlySKyQEQ22/Mku1xE5I8iskVEVonImK4+iZ7qgYsH4xbh5/PWYowBbyRM/xPU7NS+70qpLtWeO/cW4F5jzBBgPHCHiAwBHgAWGmMKgIX2OsDFQIE9zQIe6/Soe4k+CVHcc+FAFm6oYP7aMquw33gYdyss+Qvs+MzZAJVSIeuEyd0Ys9sYs9xergXWA1nAdOA5e7PngMvt5enA88byGZAoIn06O/De4qaJuZzeJ56fzVtLbUOzVXj+zyAhB167TZtnlFJdokNt7iKSC4wGlgAZxpjddlUZkGEvZwE7g3YrscsOP9YsESkSkaLKysqOxt1reNwufnvFcCpqG/nDu5usQl8sfOMxqPoS3v2RswEqpUJSu5O7iMQCrwDfN8bsD64zxhjAdOSDjTFPGGMKjTGFaWlpHdm11xmVk8gN4/vz3KfbWLFzn1WYezZMvNsammDDW06Gp5QKQe1K7iLixUrsLxhjWt9AUd7a3GLPK+zyUiAnaPdsuyys/Z+pg8iIi+SHc1fS0GwPQ3Duj6xx3+d9D2rLnQ1QKRVS2tNbRoCngfXGmIeDquYBM+3lmcDrQeU32L1mxgM1Qc03YSsu0suDVw5nU3kdj7xnN894IuCKp6DpgNX+rq/lU0p1kvbcuU8E/gM4T0RW2NMlwIPAhSKyGbjAXgd4CygGtgBPArd3fti90zmD0pkxLocnFhezbHuVVZg+GKb+BrYuhI//4GyASqmQIVZzubMKCwtNUVGR02F0i7rGFqY+shivW3jr7klER3jAGHjlFuudqze8DnmTnQ5TKdULiMgyY0zh0er0CdVuFuvz8NDVI9i2t57fvrXBKhSByx6FlHyYezPUljkbpFKq19Pk7oAJp6Vyy9l5/O2z7byzxk7kvli45nnrzU0v3wQtTc4GqZTq1TS5O+SHXxvMiOwEfjh3JSXV9tgz6afDZX+EHf+Gd+53NkClVK+myd0hER4X/3fGaAIG7vrHFzT77Z4yI66Gid+Homfg8ycdjVEp1XtpcndQ/5QYfnPFcJbv2Nf29CrA+T+FgV+Dt++H4g+dC1Ap1WtpcnfYtJF9mTGuH49/uJW3V9uPA7jccMWT1g+sc26Ayk3HP4hSSh1Gk3sP8PNpQxiVk8i9L69kU3mtVRgZD9fNBrcX/n6l9qBRSnWIJvcewOdx8/i3ziDG52HW80XUHLRHj0zOg+tfhvq98MJV0LD/+AdSSimbJvceIjMhkseuH0NJ9UHu+scXtLT+wNp3tNVFsmI9zPkPaGl0NlClVK+gyb0HKcxN5pfTh/Hhpkp+1vr2JoCCC2Dan6D4A6sPvL/Z0TiVUj2fJvce5roz+/GdKQN4YckOnvyouK1i1Ay45Pew8U149VYI+J0LUinV43mcDkAd6f6pgympPshv3tpAVmI0Xx9hv8hq3K3QfBAW/AQ8kTD9z1bPGqWUOowm9x7I5RL+cPVIymoa+MGcFSRGe5mYn2pVTrwLWhpg0a+tu/fLHwO3Xkal1KG0WaaHivS6eXpmIXkpMdz6fBHLd1S3VU75IZz3Y1g9B+bqODRKqSNpcu/BEqMj+NvN40iL83HjM5+zbldQV8jJ98HU38L6eTD7equ5RimlbJrce7j0+Ej+fvOZREd4uOGZJW0POQGcdTtc+ghsXgDPT4f6KucCVUr1KJrce4Gc5Gj+fsuZuESY8cRnrN8ddAdf+G24+lnYtQKevgiqtzkUpVKqJ9Hk3kvkp8fy0qzxeN0uZjz5GWtKa9oqh14ON7wGByrhqQuhdJlTYSqleghN7r3IgLRYZn9nPDERHq578rO297AC9J8AN78L3kh45mJYNce5QJVSjtPk3sv0T4nhpVnjSYn1cf1TS3hvXXlbZdoguHURZI+1HnRa8FN92EmpMKXJvRfKSY5m7nfPYlBGHN/5+zLmLN3ZVhmTajXRFN4MnzwKf78C6iodi1Up5QxN7r1USqyPF28dz8T8VH74yip+P38jgYA9Fo3bC5c+bL+y7zP4yyTY/m9nA1ZKdStN7r1YjM/D0zML+ebYHP60aAu3vbCM+qaWtg3OmAm3vAfeaHj2Ulj8kDbTKBUmNLn3cl63i99eMZyfXjqEBevKueqxT9teuA2QORxmfWD1qHn/V/DXS6DqS6fCVUp1E03uIUBE+PbZeTxz41h2Vtfz9T9+zKINFW0bRMbDlU9br+6rWA+Pnw3LnoXWIYWVUiHnhMldRJ4RkQoRWRNUliwiC0Rksz1PsstFRP4oIltEZJWIjOnK4NWhzhmUzr++dzZ9E6O46dml/H7+Rvyt7fAiMOIauO0T6wUg/7obnp8GVcXHP6hSqldqz537s8DXDit7AFhojCkAFtrrABcDBfY0C3isc8JU7ZWbGsM/b5/AtYVWO/w3n/iUnVVBzTSJOXDDPGvYgl0r4P9NsHrV6AtAlAopJ0zuxpjFwOGDlkwHnrOXnwMuDyp/3lg+AxJFpE8nxaraKdLr5ndXjeDha0ayfnctlzz6Ef/8oqTtzU4ulzVswR1L4LRzrf7wj02E4g+dDVwp1WlOts09wxiz214uAzLs5SwgqNM1JXbZEURklogUiUhRZaX2w+4KV4zJ5u27JzEoM44fzF7JHS8up7I26B2s8X1hxj9gxkvWGPHPT4M5M/UHV6VCwCn/oGqs28EO/zJnjHnCGFNojClMS0s71TDUMeQkR/PSrPHcN3UQ762r4IKHP+SVZUF38QCDLrbu4s/5L9j8LvxpLLzznzrKpFK92Mkm9/LW5hZ73to1oxTICdou2y5TDvK4Xdxxbj5v3T2J/PRY7n15JTc88znFlXVtG3mj4Jz74c7lMPKbsORxeHQUfPA7aNh/zGMrpXqmk03u84CZ9vJM4PWg8hvsXjPjgZqg5hvlsPz0WOZ85yx+MW0oK3bsY+r/Luah+RsOffApvg9M/xN89xPImwQf/AYeHQEf/UGTvFK9iJgT9HUWkX8A5wCpQDnwM+A1YA7QD9gOXGOMqRIRAf6E1bumHrjJGFN0oiAKCwtNUdEJN1OdqKK2gQff3sCry0vJjI/k/0wdxDdGZ+F2yaEb7voCPngQNr0DvgQYdwuceRvEalOaUk4TkWXGmMKj1p0ouXcHTe7OWbqtil+9sY6VJTWc3iee/7x4MJMKUrG+p4Ps+gI+fgTWzQOPz+ozf+ZtkDHEmcCVUprc1fEFAoY3Vu/mf97ZQEn1QcblJnPPRQMZPyDlyI33bIZ//19YNdvqYZM3BcbeYv0o6/Z2f/BKhTFN7qpdGlv8zF66kz+9v4WK2kbOGpDCHefmMzE/5cg7+foqawiDpU/B/lKIzYDR/wGjr4fkAY7Er1S40eSuOqSh2c/fP9vOE4uLqahtZER2At+dchpTh2Ye2Sbvb4EtC6Dor1Y3Sgz0mwCjZsCQ6RCZ4Mg5KBUONLmrk9LQ7OefX5Tylw+3sm1vPVmJUcyc0J9rC/uREH2UJpiaEqu5ZsWLsHcLuH1QcCEMuxIGToWImO4/CaVCmCZ3dUr8AcOCdWU888k2Pv+yiiivm2kj+zLjzH6MzE44ssnGGCgpgjWvwNp/Ql0ZeKIg/3wYfKmV6KOTnTkZpUKIJnfVadaU1vC3T7czb+UuDjb7GdInnqsLs5k2si8psb4jdwj4rbdArZ8H69+A2l0gLsg500ryBRdB+hBr1EqlVIdocledrrahmddX7OKlpTtYU7ofj0s4Z1Aa00Zlcf7gdGJ8niN3CgSsLpWb3oZN86FslVUem2kNYDbgHMidBAlHHY5IKXUYTe6qS20sq+XVL0p47YtSyvc3Eul1cd7gdC4e1odzBqURF3mMLpI1pbD1fSheBFsXwUF7LJvkAdB/IvSfAP3GQ1Ke3tkrdRSa3FW3CAQMS7dV8caq3by9Zjd76pqIcLuYkJ/CBadncM6gNLKToo+1M5SvgW0fw7aPYPsn0FBj1cWkQ3YhZJ1hzfuMgqjE7jotpXosTe6q2/kDhuU7qpm/pox315Wzw35hyMCMWKYMTOPsgjTG5SYTFeE++gECAdizEXZ8CjuWQGmR1QOnVfIAK8lnDofMEZA5zOprr3f4KoxocleOMsawtfIAH2ys4P0NFRRtq6bJHyDC7WJUv0TG5yVz5oAUxvRLOnayBzhYDaXLrDdI7V4Bu1ZCzY62+qhk68fZ9MGQNhhSB1pTXKYmfRWSNLmrHuVgk5+l26r4eMsePt26l7W7aggY8LiEoX3jGdM/iTH9khiVk0h2UtSRXS0POVg1lK+FsjVQsc56AXjlBmgMGsEyIg5SBkBKvnXHn5QHyXmQlGv9mOvS98Sr3kmTu+rR9jc0s2x7NUu/rGLZ9mpWluyjoTkAQHJMBMOzEhiWFc+wvgkM7ZtAdlIUrsOflA1mDNSWWc06lZus5pyqrda4ODU7wQTatnVHQEI2JORY75dNyIH4LOstVa2TL17v/FWPpMld9SrN/gAbdteysmQfq0r2sXJnDVsq6/AHrP9WY30eBmbEMrhPPAPTYynIiKMgPZa0ON/x7/LBehH4vh1Qvc2a9u1om/aXWl8Kh79YzBNlNe3EZVrt+rEZ1pDHMekQk2ZN0ckQk6pfBKpbaXJXvV5Ds5+NZbWs3bWfjWX7WV9Wy4bd+9nf0PaikTifh7y0GAakxpCXGktuajT9U2LolxxNUrT3xIkfoKXJetBq/24r2e/fBXXlULvbSvx1FdbUWHP0/V1eiEqykn1UsjWPTLR690QlWsuRCdbki4fIeGvui7Mm13F+c1DqMJrcVUgyxlBZ18jm8jo2l9dSvOcAxZUHKK6sY1dNwyHbxkS4yUmOJjspiqzEKPp+NUWSmRBFepwPr7sDbe/NDVC/Bw5UQl0l1O+1pz3W/GA11Fdb84PV0LAPmutPfFxvNETEgi/WnsdZY/JExIA3BiKi7W1irFcjeqOs9da5J9Ja/mrus/7y8PisMrdX/7IIIcdL7kd5jFCp3kFESI+LJD0ukon5qYfUNTT72VlVz7a99eyoqmdnVT0l1fWUVB9kyZdV1Abd8VvHgpQYHxnxPtLjfKTHRZIW5yM1NoLUOB8pMdZyckwEidERuL2Rdlt9dvsDbmm0XlXYUGNNjTXWeuN+aKw9dGqqg8Y66wvhQCVUfWktNx2wpkDzyf/DeSKtQd08Edbc7bWSv9trr0fYdRHWXyJue3J5we0JKvdYc5fHrne3rbs89rrnsHU3iPso60Fzl8e6IF+Vu6xlcdnrh9e5graRw8qCJzl0OcRpclchKdLrttriM+KOWr+/oZnd+xrYXXOQspoGdtU0UFnbQPn+Rsr3N7B21372Hmj6qp0/mAgkRnlJio4gMbp1HkFClNeePMTby3GRXuIiPfbkJTY6FXdnvKLQ3wzNB62E33ywbWo5aP1V0Tr3N1ovVflq2V5vaWpb9ze1zf3N1rypHgI11pDO/ibry6S1LtBilbeWncoXjaPk0KQfvH7Eshy27GpbPu6c49cDnPMADL+q089Ok7sKS/GRXuIzvQzKPHryB+tBrOr6JvbWNbG3rpHKukaqDzRRdaCJvQea2FffzL6DTeyuaWBDWS01B5upa2w55vFaRUe4ifF5iPV5vlqOiXAT7fMQ7XUTHeEmKsKqi45wE+ltm0d6Xfbcjc/jItIbS6Q3AV+MC5/HRYTHRYTb1b7fFzqLMdYAcYGWwya/lfi/Wra3Mf62deNvqz+kPNC2bgKHTq3bHlFm2vY76rIBTNB+QcuHl8NR9mldNkH7mMPmHKP8aHN72y4aIVWTu1LH4HYJqbE+UmN9wLG/BII1+wPUNrRQc7CZmoPN1DY0U9vQ8tX8QKOfukbrS6Cu0c+BxhbqGlvYU9fEgap66hv91De1cLDZT7P/5H8Pi/C48LntZB+U9L12mdcteO311mWP24XXJXjcErTswuMWvC4XbpfgdQtulwuPvZ3bZU9izT1uwSWCx+XC7QK3y4vb5cUlbdtJ67ILq9wtuDxWmbWd1eTmFmtdBFyu1nWr7mhzV9D2ErxO64136DfFBNPkrlQn8rpdJMdYbfOnqtkfoKHZz8FmPweb/DQ0B9qWW/w0NgdoDJo3NAdo8gdobLHWm1oCbZM/QLM/QFOLockfoMVeP9DYQrPf0BII0Ow3NPsDtLTOA8baLmDw21Nv1/plIHDIF4Egh9QhQfW0lYtd2VZu7Ru8Ha3lx6qz/6f1q+buCwYybWTfTj9XTe5K9VCtd9bHHFWzmwUChpaAIWDMV4m/Nem3BH0BBC+3btu63DoPBMBvDIHWbY3BGEPA0LaNMfgD2OX2MtY2gUDb9saO7as6Y6yWk6B9WtcNQfUcuq0x2Mc7dHsTXEZri0rrNkfWGbt5xloPPoaltcxasX6/6Qqa3JVS7eJyCRHHezJY9Sg6qIZSSoUgTe5KKRWCuiS5i8jXRGSjiGwRkQe64jOUUkodW6cndxFxA38GLgaGADNEZEhnf45SSqlj64o793HAFmNMsTGmCXgJmN4Fn6OUUuoYuiK5ZwE7g9ZL7LJDiMgsESkSkaLKysouCEMppcKXYz+oGmOeMMYUGmMK09I6YawNpZRSX+mK5F4K5AStZ9tlSimlukmnj+cuIh5gE3A+VlJfClxnjFl7nH0qge0n+ZGpwJ6T3Lc3C9fzhvA9dz3v8NKe8+5vjDlq00enP6FqjGkRke8B8wE38MzxEru9z0m3y4hI0bEGqw9l4XreEL7nrucdXk71vLtk+AFjzFvAW11xbKWUUiemT6gqpVQICoXk/oTTATgkXM8bwvfc9bzDyymdd494QbZSSqnOFQp37koppQ6jyV0ppUJQr07u4TL6pIjkiMgiEVknImtF5G67PFlEFojIZnue5HSsXUFE3CLyhYi8Ya/nicgS+7rPFpFTf6ddDyMiiSIyV0Q2iMh6ETkrHK63iPzA/m98jYj8Q0QiQ/V6i8gzIlIhImuCyo56jcXyR/vfYJWIjDnR8Xttcg+z0SdbgHuNMUOA8cAd9rk+ACw0xhQAC+31UHQ3sD5o/XfAI8aYfKAauNmRqLrWo8A7xpjBwEis8w/p6y0iWcBdQKExZhjWczLfJHSv97PA1w4rO9Y1vhgosKdZwGMnOnivTe6E0eiTxpjdxpjl9nIt1v/Rs7DO9zl7s+eAyx0JsAuJSDbwdeApe12A84C59iYhd94ikgBMBp4GMMY0GWP2EQbXG+vZmyj7SfdoYDcher2NMYuBqsOKj3WNpwPPG8tnQKKI9Dne8Xtzcm/X6JOhRkRygdHAEiDDGLPbrioDMpyKqwv9L/BDIGCvpwD7jDEt9nooXvc8oBL4q90c9ZSIxBDi19sYUwr8HtiBldRrgGWE/vUOdqxr3OF815uTe9gRkVjgFeD7xpj9wXXG6tMaUv1aReRSoMIYs8zpWLqZBxgDPGaMGQ0c4LAmmBC93klYd6h5QF8ghiObLcLGqV7j3pzcw2r0SRHxYiX2F4wxr9rF5a1/mtnzCqfi6yITgWkisg2r2e08rLboRPvPdgjN614ClBhjltjrc7GSfahf7wuAL40xlcaYZuBVrP8GQv16BzvWNe5wvuvNyX0pUGD/kh6B9cPLPIdj6hJ2O/PTwHpjzMNBVfOAmfbyTOD17o6tKxlj/tMYk22MycW6vu8bY64HFgFX2ZuF4nmXATtFZJBddD6wjhC/3ljNMeNFJNr+b771vEP6eh/mWNd4HnCD3WtmPFAT1HxzdMaYXjsBl2ANL7wV+JHT8XTheZ6N9efZKmCFPV2C1f68ENgMvAckOx1rF/4bnAO8YS8PAD4HtgAvAz6n4+uC8x0FFNnX/DUgKRyuN/ALYAOwBvgb4AvV6w38A+u3hWasv9ZuPtY1BgSrd+BWYDVWj6LjHl+HH1BKqRDUm5tllFJKHYMmd6WUCkGa3JVSKgRpcldKqRCkyV0ppUKQJnellApBmtyVUioE/X+oNezKFF9mUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(history.params)\n",
    "losses_ = pd.DataFrame(history.history)\n",
    "losses_.plot(kind=\"line\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'weight_0': -0.720973185445283,\n",
       " 'weight_1': 1.3290574386023888,\n",
       " 'weight_2': 0.14098068438146516,\n",
       " 'weight_3': 0.3190184199461178,\n",
       " 'weight_4': -1.9611038002705747,\n",
       " 'weight_5': 2.3912294381194052,\n",
       " 'weight_6': 0.028428542130489065,\n",
       " 'weight_7': -3.1028454604117153,\n",
       " 'weight_8': 2.2339582985686506,\n",
       " 'weight_9': -1.5240863072636608,\n",
       " 'weight_10': -1.949090868280713,\n",
       " 'weight_11': 1.1856616926433907,\n",
       " 'weight_12': -3.797866790151385}"
      ]
     },
     "execution_count": 465,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_weights = pd.DataFrame(weights).T\n",
    "coefs_linear_reg = dict(zip(\n",
    "    [\"weight_{}\".format(_) for _ in range(len(lm.coef_))], \n",
    "    lm.coef_ \n",
    "))\n",
    "coefs_linear_reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x14e6d2be0>"
      ]
     },
     "execution_count": 466,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "( df_weights[0]\n",
    "     .apply(np.ravel)\n",
    "     .apply(pd.Series)\n",
    "     .rename(columns = lambda x: \"weight_{}\".format(x))\n",
    "     .plot(kind='line', ax=ax) )\n",
    "ax.set_xlim(0,100)\n",
    "ax.legend().remove()\n",
    "fig.legend(loc='center', bbox_to_anchor=(1, 0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 13 artists>"
      ]
     },
     "execution_count": 467,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "at_98  = df_weights.iloc[98,0].reshape(-1)\n",
    "plt.bar(x=np.arange(len(lm.coef_)), height=lm.coef_, color='red')\n",
    "plt.bar(x=np.arange(len(lm.coef_)), height=at_98, color='white', alpha = 0.8)\n",
    "#history.model.get_weights()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fin."
   ]
  }
 ],
 "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": "3.8.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}