{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "In this introduction to our `sklearn` tutorial, we will investigate the basic tools that will be needed for the more machine-learning oriented sections that will follow.\n",
    "\n",
    "## NumPy\n",
    "\n",
    "### Basics of `ndarray` type\n",
    "\n",
    "First, we will present the `numpy` library and its `ndarray` object.\n",
    "\n",
    "Let us first import this library. As it will be used very often in our code, it is usual to rename it `np` while importing:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, we can create a first array and manipulate it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1]\n",
      " [2 3]\n",
      " [4 5]]\n"
     ]
    }
   ],
   "source": [
    "arr = np.array([[0, 1], [2, 3], [4, 5]])\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0.    2.5]\n",
      " [  5.    7.5]\n",
      " [ 10.   12.5]]\n"
     ]
    }
   ],
   "source": [
    "print(2.5 * arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  2]\n",
      " [ 4  6]\n",
      " [ 8 10]]\n"
     ]
    }
   ],
   "source": [
    "print(arr + arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int64\n"
     ]
    }
   ],
   "source": [
    "print(arr.dtype)  # Data type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 2)\n"
     ]
    }
   ],
   "source": [
    "print(arr.shape)  # 3 rows, 2 columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "print(arr.ndim)  # Our array is a matrix and hence has 2 dimensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial, we will always consider vectors (`ndim = 1`) or matrices (`ndim = 2`), but `numpy` can be used to manipulate arrays with any number of dimensions.\n",
    "\n",
    "### Element-wise operations _vs_ matrix products\n",
    "\n",
    "One important thing to understand with `numpy` is that the usual product between two arrays is an element-wise product, not matrix/vector product:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1]\n",
      " [2 3]]\n",
      "[[1 0]\n",
      " [0 1]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[0, 1], [2, 3]])\n",
    "I = np.array([[1, 0], [0, 1]])\n",
    "print(A)\n",
    "print(I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0]\n",
      " [0 3]]\n",
      "[[0 1]\n",
      " [2 3]]\n"
     ]
    }
   ],
   "source": [
    "print(A * I)\n",
    "print(np.dot(A, I))  # np.dot is the matrix product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, in `numpy`, `A ** 2` is the element-wise square of matrix `A`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1]\n",
      " [4 9]]\n",
      "[[ 2  3]\n",
      " [ 6 11]]\n"
     ]
    }
   ],
   "source": [
    "print(A ** 2)\n",
    "print(np.dot(A, A))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quite easily, we can transpose an array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 2 4]\n",
      " [1 3 5]]\n"
     ]
    }
   ],
   "source": [
    "print(arr.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building usual arrays\n",
    "\n",
    "`numpy` also offers routines to build typical matrices / vectors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.zeros((2, 3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.  1.]\n",
      " [ 1.  1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.ones((2, 3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.]\n",
      " [ 0.  1.  0.]\n",
      " [ 0.  0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.eye(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print(np.arange(10))  # Returns a vector (ie. an array made of only one dimension)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.   0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1. ]\n"
     ]
    }
   ],
   "source": [
    "print(np.linspace(0, 1, 11))  # Vector of 11 equally spaced values between 0 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.76405235  0.40015721  0.97873798  2.2408932   1.86755799]\n",
      " [-0.97727788  0.95008842 -0.15135721 -0.10321885  0.4105985 ]]\n",
      "[[ 0.79172504  0.52889492  0.56804456  0.92559664  0.07103606]\n",
      " [ 0.0871293   0.0202184   0.83261985  0.77815675  0.87001215]]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)             # Set the seed of the random generator to get reproducible results\n",
    "print(np.random.randn(2, 5))  # randn returns samples drawn from N(0,1)\n",
    "print(np.random.rand(2, 5))   # rand returns samples drawn uniformly in [0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Array slicing and boolean indexing\n",
    "\n",
    "As for lists, `numpy` arrays can be accessed by slice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]])\n",
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[3 4]\n",
      " [8 9]]\n"
     ]
    }
   ],
   "source": [
    "print(M[:2, 3:])  # Row indices up to 2 (excluded), Column indices strating from 3 (included)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5  6  7  8  9]\n",
      " [10 11 12 13 14]]\n"
     ]
    }
   ],
   "source": [
    "print(M[1:3, :])  # Row indices 1 (included) to 3 (excluded), All columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to get a subset of a matrix is to use boolean indexing.\n",
    "\n",
    "Let us assume, for example, that we want to keep only positive components in a vector v:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10  5 -1  4  0  3]\n",
      "[10  5  4  3]\n"
     ]
    }
   ],
   "source": [
    "v = np.array([10, 5, -1, 4, 0, 3])\n",
    "print(v)\n",
    "v2 = v[v > 0]  # Keep only strictly positive components from v\n",
    "print(v2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operations on arrays\n",
    "\n",
    "`numpy` offers facilities to compute basic statistics from arrays (sum of their elements, minimum/maximum values, mean, standard deviation, ...). We present some of them in the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n"
     ]
    }
   ],
   "source": [
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19\n"
     ]
    }
   ],
   "source": [
    "print(np.max(M))  # Could also be written M.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "print(np.min(M))  # Could also be written M.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.5\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(M))  # Could also be written M.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.76628129734\n"
     ]
    }
   ],
   "source": [
    "print(np.std(M))  # Could also be written M.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49.6990945592\n"
     ]
    }
   ],
   "source": [
    "print(np.linalg.norm(M))  # L2-norm by default"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "190\n"
     ]
    }
   ],
   "source": [
    "print(np.sum(M))  # Could also be written M.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[30 34 38 42 46]\n"
     ]
    }
   ],
   "source": [
    "print(np.sum(M, axis=0))  # Column marginals, could also be written M.sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The latter can also be used on binary vectors, in which cases it corresponds to the number of `True` entries in the array: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n"
     ]
    }
   ],
   "source": [
    "v = np.array([10, 5, -1, 4, 0, 3])\n",
    "print(np.sum(v > 0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Element-wise operations\n",
    "\n",
    "`numpy` also offers many vectorized versions of standard mathematical operations. For these functions, element-wise operations are performed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n",
      "[[ 0.          1.          1.41421356  1.73205081  2.        ]\n",
      " [ 2.23606798  2.44948974  2.64575131  2.82842712  3.        ]\n",
      " [ 3.16227766  3.31662479  3.46410162  3.60555128  3.74165739]\n",
      " [ 3.87298335  4.          4.12310563  4.24264069  4.35889894]]\n"
     ]
    }
   ],
   "source": [
    "print(M)\n",
    "print(np.sqrt(M))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  2.20264658e+04   1.48413159e+02   3.67879441e-01   5.45981500e+01\n",
      "   1.00000000e+00   2.00855369e+01]\n"
     ]
    }
   ],
   "source": [
    "print(np.exp(v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10  5  1  4  0  3]\n"
     ]
    }
   ],
   "source": [
    "print(np.abs(v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.83907153  0.28366219  0.54030231 -0.65364362  1.         -0.9899925 ]\n"
     ]
    }
   ],
   "source": [
    "print(np.cos(v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concatenating and reshaping arrays\n",
    "\n",
    "We can get a reshaped version of an array, as soon as the number of elements is unchanged:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[10  5]\n",
      " [-1  4]\n",
      " [ 0  3]]\n"
     ]
    }
   ],
   "source": [
    "print(v.reshape((3, 2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this does not change the shape of `v` but rather returns a new array with the required shape.\n",
    "\n",
    "One can also concatenate several arrays to create new ones. There exists two modes of concatenation:\n",
    "* horizontal concatenation stacks columns;\n",
    "* vertical concatenation stacks rows.\n",
    "\n",
    "Of course, these operations require that corresponding dimensions match."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  0.  1.  1.  1.  1.  1.]\n",
      " [ 0.  0.  0.  1.  1.  1.  1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.hstack((np.zeros((2, 3)), np.ones((2, 5)))))  # Same number of rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.]\n",
      " [ 1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.]\n",
      " [ 1.  1.  1.  1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "print(np.vstack((np.zeros((2, 5)), np.ones((3, 5)))))  # Same number of columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting with `matplotlib`\n",
    "\n",
    "`matplotlib` is a library dedicated to plotting data. It features a huge number of plotting facilities. Here, we will only detail a few functions that will be used later in this tutorial.\n",
    "\n",
    "### Scatter plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1081c78d0>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1075bc2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "# You don't need to write the previous line in your scripts, it just means\n",
    "# \"Render matplotlib figures in the notebook\"\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = np.random.randn(100, 2)\n",
    "y = np.array([0] * 50 + [1] * 50)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1])  # Takes 2 vectors as inputs: x-coordinates and y-coordinates\n",
    "\n",
    "# NB: if you are coding in a standard Python script (ie. not a notebook as this one),\n",
    "# you will have to enter the following command for the plot to show up in a new window:\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might want to draw larger dots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x108260da0>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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egYHVbN48wsTEMlTdZ7k2gojwwQ+uBz5K7cSq/UxPb7TszBbCBNzwhIhw9913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\n/kJ5dgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1075a67f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might also want to change the color of the dots or use different colors depending on the class label of each data point:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10832d160>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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f/GROkk8tglrJVmZTHsbd04KXFfLU1BTL+vsZWbeOhZOT7FcNNf1eRFj50Y/y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1075bc1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=100, c=\"r\")  # \"r\" means red"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1083e8390>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jOQYALYIgR6/3XofTG/ny5cMuk+EtScBFmYw3XuBygKkWcFEU24uiGCyKokoU\nxQKiKM5JC8MkUs4nn3QhMNCCIKwkEM/xJYFAbkTgP0AFFCBv3vx0796d4GBvD5aZw6ZNm/jll6kY\njZ1wPU88chepgKqYTO346KOuXLx4MVXjCILAsmUL8fWNwLVcmzB1lSBE4ue3i6VLU17/svbbb/Of\nl6iVf4DquAQ7KUoDhaxWZr1ERZSzZ88BeCs4bEAUnWmyD8DHx4fOXboQ6SE01Qoc0Wjo9/nnqR4v\nvZBcKC8Rfn5+jB37LaJ4jsJYvbYvhA24D4BafYIOHTK2SEJKGTXqBwyG6rjmo0kRiMNRjkmTfk31\nWBUqVODff3fw5psG1OrJ+Pmtxs/vT9TqSdSoYSEycjdlypRBFEW2b9/OwIFf0L17byZMmOAx+VPf\nzz7jsI8P7uaQDuAsrmLJnihvMjFr2rTnvLoXj08++RC1OspjG5nsKC1avJNmBTMGf/UVN3PlYpdc\nnuipyAis0mqp07jxC71QL+VCecmoW7cRW7deoiqnaIznz/1P5BzhbSAErXYJGzeuY+3q1Vw4cwb/\nHDlo3b499erVQyZL3X3e6XSydetWoqOjkcvlhIWF8frrr6eoD5PJRLZs2bHbB+GqbuiOGwQHb+ba\ntfOpsvlpzp49y6FDhwBXXvBHiatOnDhBs2bvcutWPEZjcURRhUZzF6fzFH379mHs2O+T/OyGDRnC\n3IkTaWo0EvTU+w+Av1UqTlqtDPPyndEDs3x9uR8fn0ZXmbncunWLYsVKEx/fGJJMn3YLrXYxu3Zt\n5Y033kizca9evUrrFi04e+oUpcxm1E4nMWo1p4APPvyQCZMnZ1qFpQzbyOPFiHQR8AcPHrBw4UL2\n7TuEQqGgXr3avPPOO5m+/TUzcTqd+PiocDg6oWEhg7C5fcSyAz+gwEJ11OojVCxXghPR0ZS32chp\nt2MCTvr64pMzJ2s3baJkyZLPZdPatWvp3a0bgl5PfqsVpyDwn0zGa8WKMXfxYkqXLp2sfu7du0e+\nfIWwWAZ6aRlH9uwLiYnxnpY2NZw/f56KFUN58KAmovg6CbMn6tFqV/Hxx02ZPHlConNFUWTqlCl8\n+/XXaK1WcjmdGGUyLtvtdOjYkdlz5zLAbveYqfsGsDEoiIvJLLbw33//MWP6dM6cOIGvnx8t27Sh\nRYsWKY6iSU92795No0bNsFhKY7W+DuQE9MjlR1GpDjNz5lTat2+XLmMfOXKEP1at4kFsLCFFitCh\nQ4dMzwGBgUQBAAAgAElEQVTz0gr4hAkTGTJkGDLZaxgMwYADP7+LyGT3WLx4Po0aNUrT8bIKVqsV\njUaL0zkMJVOpyx2quZmF7wZ2CDJq1mmAIfY25uPHaWI2J5jbisARQWBP9uwciopKcZX5FStW0O3D\nD2luNFKIJxLneNSvnx+7IiOTdXOw2+34+eXAbO4GeFpcPUvJksc4efJIimx9mvj4eObPn8/0iRO5\nduMGOq2Wd1u3pk///hQt6podtmrVjj//vIPTGeamFxNq9TSOHTvw+Jykrmnbtm1cvXqVbNmyUa9e\nPbJly8a7zZph/usvQj18bzarVIT178/osWM9XovFYqHLBx+wbu1aytvtBNhsmIEzfn48UKlY/ddf\nL1QFoatXrzJx4mRmzZpLbOxdtFo/2rRpw+ef90/2zf5l4aUU8IkTJzFkyPcPc1TkfOboJbTaP1i7\ndiV16tRJszGzEjlzBhAT8x6gQMEMamChGuLj2ZwRV8jQPpmMPfv2ERsby4ctW9JZr0+ysBbAFoWC\n8p078+v06cm2w2w2E5QnD631etyVkI0UBExvvsm23buT1Wfnzt2YP/8sDsdbbtvodKv48cee9OjR\nI9m2Ps25c+eoXbMmOeLjed1gIADXZ3ZcqeSoQsHk6dNp1Lgx+fMXwmzuBbgvLKFUbqVnz0pMmPBz\nimzYu3cvTerW5X2jMdFfOLgCRVfqdESdPEmBAu6WOl20eecdTmzaRAuTKdH+3FPAJl9fdu/bl2UK\nUbxKvHRb6ePj4xk8+CuMxtYkFm+AEIzGBnTr1jfDi96+KHTv3hWV6jCQCzvd2U0JfkLBNFRMRcXP\nKDgg8+err7+mUqVKTPr5Z173IN4Ale12Fi5ciNlsTrYdy5cvJxjcije4CkIcOnSIs2fPJqvPIUMG\noVYfBs4leVwmO4CfXwzvv/98WQLNZjN1w8Iof/s27xoMvIYrB0xeoI7NRkeTib7du7NixQpUqrx4\nEm8Am60AkZEpj9euVq0a3//0Ewu1WvYKAqaH78cDO+RyVmi1/L58uVfxPnjwIBGbN9MyCfEGKAlU\nNhj4esiQFNso8WKQpQR8yZIlyGSFgVweWpXg5s177N+/P6PMeqHo378vOt15BCEKyIGddtj5lJu0\n5RZtcQhh5AzMzqeffgrAiehoCnrpMzugEgSPxW1NJhMbNmxg8eLFREREsGPbNgp6iddVAq8pFOzb\nty9Z11asWDHWr1+Nn99faLVrcAn5LeAkvr7LyJs3ip07tz53mNmKFSvQPnhAFWfSG3gCgJomE/Nn\nzkQUvUVzAzifewG4e48erN+6Fd9mzfhFoWCMUslUlYoinTrx74EDyXIT/jphAq8/4xZ7loqiyIZN\nm7JM2TSJhGSpgg4HDx7BYAjy0koGhBAdHf1C+fYyisDAQHbu3Ebt2vUxGk+g15fG5TN+gJ9fNDlz\nCkRERDzepKNUKvG2r00EbE5nkgteNpuN4V99xbSpU8krk6ETRe4BMVYrNZJhrwApeloKCwvj0qWz\nzJ49h9mzF/HgQRyBgYH07fslbdq0Qa32VNHeMzMmT6asl5tOeWB8VBSiXAXEgoeSFxrNORo2fP7S\nXqGhoSxfvRqHw4HRaESn06XohnA8KopSbm5Gj20EcqtUnD9/nly5PE2MJF5EspSAu8J5kjPzsWdq\nHuPMpnTp0ly+fI5Vq1bx22/zuHv3EkFBgfTq9QNNmzZNEBZVv3FjDk6bRn6bzW1/lwH/7NnJly+h\nQ8Rut9OySRMu7trFByZTAqfWFuA0EOrBTjtwweFIcVhYjhw5+PzzAXz++YAUneeNmzdv4s0T7ANk\n8/HhrSbN+OOPPVitjd20vI8onqB79zWptksul+Pnl1RCX8+ofHxw/1t9gtXpfKWjt7IyWcqFUq9e\nHfz8LnhpZcPhOEutWrUyxKa04uLFi/zyyy98/fXXTJ8+nfv376eqP5VKRfv27dm2bSPHjh1g8+Z1\ntGzZMlFMa+9+/TgqlxPrph8nsEerpf/AgYlmf/PmzeP07t20eka8AcKA63iuMR8FlCxV6oWJLsju\n7+92g80jHIDeZmPEiP8RFHQfpXILrgS7jxCBy2i1i/nhhzHkzZs33ez1RqOWLTmj8RSM6HJAWeXy\nF+Z3IJEyslQUit1uJyioAHfvvk3Swf4gk+2hZk0n27f/nSZjpjcxMTF06PAhERHbEcVSWCxqtNoH\nOJ1n6Ny5MxMm/ITT6WTlypVsWrcOq9XK65Uq8XHnzmkWp/rzjz8y9uuvafRMuF8MsFWjIXelSmz8\n558EszRRFClXvDgVzp6lmJt+DwNbgQ6QYMOKCJwA/tbp+GfHjhTnE0kNt2/f5sKFC6hUKsqUKZPA\nLTRx4kTmDBlCS6PR7fnHgctvvMHeQ4e4e/cuXbr0YNOmTSiVRXE6fZDLb6HVOvnppzF07NghA67I\nPXfu3OG1kBA6mUyJagqB6+b8h1pNy88/Z+R332W0eRJeeCnDCCMiImjSpCVG49u4skI8cpVYkcn2\n4+9/lAMH/n28W+5FRq/XU7lydS5c8MVqrU3CQgx6tNp1VKyYl1PHjpDb6aRIfDwK4IZazUmg/6ef\n8u3336dJyafFv//O/wYPxhQTQ4BMhhG45XDQtWtXvhszJlFdxAcPHhCQKxdf2u0eH+N2AjsEgSK+\nvgTFx+MQBM7rdKhz5uT35cszbJ0iKiqKL78cxrZt21CrA3A6rcjlFvr27cXQoYNRq9XExcXxWsGC\nNHjwgOJJ9KEHFmi1TP/9d1q0aPH4/Rs3brBlyxbMZjNFihShdu3aKV68fHq3qlKpJCwsjHLlEhW4\nSjGLFi6kb7duNDCZKM6TR+5YIEKtRl26NFt37ULjZaYukfG8lAIOsGfPHrp378f58xeRyQoBDuz2\nc7z5ZnVmzZpK4cKF03S89GLs2HF8881CTKZ3Icm08hfwYR4dIFEKUj2wXKvl/X79+G706DSxRxRF\n9u3bx5UrV/Dz86NWrVqP08k6HA42btzI/PmLuXcvhsDAPPyx7He+8OA7B9csfknOnEyYMoVjUVEo\nlEreeustwsPDM6zW4K5du2jYsBkGQzXgDVzJrwBuodHspFy57EREbGbRot8ZNuxr7t+6ThVEquJa\norQC0cBerZaeAwYw4ttv09S+devW0btbN4iPJ7/NhkMQOCMIFCtZkrm///7cu2AfsXHjRgYPGMC1\nS5cIUiiw4Lo5f/Txx3w/dmyClMESLw4vrYA/IioqiqioKORyOdWrV89SdQRFUSQoKIRbtxoASe9w\n9GEaTbmJuyzJemCqSsW5S5fS1dd6+vRp6tVrTGysSHx8KUCHINxDIW7jE0Q8jXwUiK1Rg627dqWb\nfZ4wm80EBRUgNrYhSbvdnKhUf1CypIozZ25hNNYB/JGzG5f1Tpw48VWp+WnSRLp27Zqm9nnarXpI\nENjr58fuffsoUaJEqsc6duwY58+fR6vVUqNGDUm4X3BeegHPyty/f5+goIJYrQNJevZ9GzW/MQi7\nx00269VqWgwbxtCvvkoXO2/cuEHZsm8QExOKKCb0VQtsoSy7aeVmu74TWODryy8LFyZwOWQkCxcu\npGfP0ej1nqrHHwB2AD0hQQYSJ675txGYiVYrZ8+enSlOxOUOs9lMcEAArePj3VaG2SsI2GrWZMuO\nHUkeF0WRGzducPXqVQIDAylQoECKnmzsdjuxsbHodDrJjfKC8dLtxHz58HRju0sQco/iDRBkNnPs\nYaa89OCHH35Gry+SSLwBRN7kFFp2kfhK7MB6lYoCZcumqGZkWrNkyR/o9Ul5tB/hxLXcWgcSpY+S\n4aoXmhOohtGYmzZt3k+zXb7Lli0jSBQ9lvWqJIrs37+f8+cTZld0OByMGjWKgGzZKJgvH7VCQyka\nEkJA9uz89JNr4dsTZ8+epXuXLuTw86Nw/vxkz5aNujVrprhIs0TmIgl4JpEjRw5y5crNoxJoiZF5\n3WADLqFUPhPDa7fbOXLkCHv37uXWrVvPbaPD4WDmzFlYre6yU+uw0ZXt+DFBJmOnILgiTxQKftVo\nCAwP56+//860dJwAer2BJz7vZ7kITMAV8FjGS09lgbtcu3YnzUq37di6lZDk7FZVKhPsVrXZbITX\nqMHkYcNoqNfzFTAU6AYUfPCArwYOpFnDhm5FfOfOnVSpUIH/5s2jm9nMQIuFQXY72Xbv5sNWrRie\nTk9zEmmPJOCZhCAIDBjQD40mkqRn4gW4gR33AW0uzvv5Uf/hDNdisTByxAjyBQTQNCyMjg0bUqxQ\nIZo1aMCRIynPznf//n1sNgeeUxdkx8bHOH2zU6JbN7StWhHavz+7Dx5k7caNaVI9JTWULl0MuTyp\nm9hlYBnQENfXwFtaVRVgx2IpyrY0KnLrdDrdVkR/GuFh20cMGzqUq5GRfILLq//oS5wHaA7UBiK2\nbGH8z4mTaMXExNCySROaGQyEOxyP8zoqgQrAh0YjMyZMYPXq1c99XRIZhyTgmUivXj0pWlSNSrWB\nhJtBABzIZWp2evBnXgJuCQKtW7fGYrHQoHZtlo0bx7sxMXSNj+eDuDj6mM04Nm8mvEYNIiIiUmSf\nj48PDocVz8V9AexotX78Om0av69Ywbgff3xhstv16tUdH5+jJCyLJgIbgCa4Ujpp8LzlCFwZuHPg\ncMjTpKguQGiNGlzV6Ty2sQMX7PbHu1XNZjNTJk+mGe63UYcCGlFkzPffJ5qFz50zhxCHw23tdx1Q\n02BgzMiRKbgSicxCEvBMRKvVsmvXVho3LoRa/Sta7Trk8n/w9V2FRjODzt0/5npQEP8olY8z0oEr\nQiEaV8mn35ctQ6VSMXLECO4dOUIrk4nAp9qqcH2hWxiNtGrRApPp6Z484+/vT9GiJXAV+XKPXH6S\nJk0aJrvfjKRs2bLUr18XjWYNPHZKXQdMQClc89uKgDe3yD6gIr6+NylTxpu7JXl07NiRC6LIHQ9t\nooCSpUs/viHu2LEDf5vN4zORgCtY0hwfz7FjCQsz/z5nDmU8bFQC1y3tWHQ0d+54skziRUAS8Ewm\nW7ZsrFq1lHPnTvHjj5357rvG/Prr59y6dY0pUyYReegQwc2a8atazcps2fgzWzamaLVcLF+etRs3\n0qBBA6xWK9OnTOEtk8ntL7QIEOR0snTp0hTZN3jwAHS6PeA2q0YcPj6H+eyzvinqN6U4HA5u3brF\nnTt3vC7QPcuSJQuoW7coWu10ZLJduKrNh/Dkz78qcAZIajFYBLbjimjPg1weQ7NmzZ77Op7G19eX\nn8aPZ5lWy7NOnke7VXfodEz+7bfH78fFxaFNxiKqL64ZevwzJddi4+LcVhR9hALw9fEhLs5bkWGJ\nzCZLJbN6mQkODqZnz56J3s+bNy9LVq7k9u3b7NmzB6vVSunSpSlbtuzjNgcPHsQXz1XoAYrr9axa\nsoSPPvoo2Xa9//77rFq1lr//XobRWBcez++dwAW02k0MHz40zWalzxIXF8fPP49n8uSpGI0mRFF8\nmMyqH71790pW6JtarWbt2lUcOHCAiROnEBGxnWvXdDy5D/gCnYDFwBFc81c/XKK9D9fXpBFa7Vom\nTRqfpmXIunbtilwuZ9Cnn5IXCIyPxwGc9/VF6e/PsjlzqFChwuP2QUFBxMhkiF785/cAkygmqqIU\nFBTE/StXEjylPYsFiLdayZ079/NfmESGIMWBvwRs3bqV3u++SzsvM6bTwO2aNdmyc2eK+nc4HIwZ\nM46ffhqPw6FBEHyx2++SJ092Ro8eQbt26VOn8Pbt24SG1uTGDV8sllBcNw8RuIpGs5fixV0uqJQu\nlB4/fpwqVWphMvWBBIGaDlyfUjQuF8tdIC9arQa4xKRJv9C5c+e0uLREWCwWVq1axeFDhzgaFcWh\nQ1HExcUiCHL8/f3p3783/fr1RafTEZwnD03u33ebx90O/AIUL1OGQ9HRCY4tWLCA73v1op2H6Jf9\ngNCgAWulkMJMRdrI84pw4cIF3ihdmr5ms8dHqh1yOcU//pipM2Y81zh2u529e/cSFxdHcHAwFSpU\nSNft8LVq1SUy0oHNVjuJo05Uqg20bFmCJUsWpLjvSpXe5PDhPIhiJTctLuLjs5xWrVrx1lvV6dix\nY7pH1BgMBsLC3ubkyThMpmpAQVwe7Wuo1fsIDrYQGbmT1X/+yaDu3enidCZyhziBtcApQWDdli2J\nSguazWZKvvYaZW/eTLJwxU1giUbDhq1bqVatWrpcp0TySI6ASy6Ul4DChQtTrlw5ju/fj7s9gnbg\niErFT717J3j/+vXrXLp0CY1GQ9myZT3GbN+9exelUkmBAgUoU6ZMuor3yZMnOXjwEDZbn2eO3MG1\nCAkWSwVWr17M7du3U5yZcd68GVSv/hYuF3EFnszEReAMWu16Vq5cQcOGGbc4261bL06csGE2tybh\n8lQ+zOaWXL26jffea09ExN+cOX2aST/9RBVRpCyuL/JlXPVOYwAEgdUrVxIWFpbgd6pWq9m6cye1\na9bk8oMHvG4wkIeHdT99fIiSy/ltzhxJvLMKoiim68s1hER6s2PHDjG7RiN2BXHEM69hIL6uVost\nmzR53D4yMlKsHx4u+qnV4mv+/mKwn5+YN2dO8dtvvhGtVmuCvvft2yfWqdNQVKl8RX//IqKvb5CY\nO3eQOGrU94naPo3ZbBaXLVsmjh49Whw/frx4+vTpZF/PqFGjRIWiuggjHr66ixAigq8IZR++dKJM\nll0cOXJkyj8wURSjoqLE8uWriFptTlGjCRXV6jdFX99gMSSkmLhly5bn6vN5uX37tqhS6UT44qlr\nfvY1TNRo/MVTp06JoiiKW7ZsEXVKpagGUQWiL4hlQPwUxEEgltBqxY5t24pOpzPRePHx8eK0adPE\nCqVKiXmyZxcLBweLgz7/XLxw4UKGXreEex5qp0d9lVwoLxGrV6/mgw4dKAoUNxrxAW7IZBzVaKgW\nFsaSlSvRaDRs3LiR9q1aUdNopDxPktjeAHZoNOSrWpX1f/+NUqlk8+bNtGzZBpOpJvD6U62vo9Hs\noFq1EDZtWptgYU8URSZNmMA3w4cTAOQxGrEqlZwSBCpVqsT8JUsSVfdxOBz8+eefjB83jqjoaGw2\nG3abLzaa4IrTXgS8jauo2aMZpR04hEq1g/379zx3+tWoqCh2796Nw+Hg9ddfp2bNmhmWKfERc+bM\noW/fSRgMnnPGKBSb+OabpgwdOpRBn3/OzsmTaWS1JtnWCszU6Vjzzz+EhnqqjSTxIiL5wF9BYmNj\nmTtnDmuWL8dkMlGybFl69etHlSpVAFce74LBwbQyGJJcBHMAKzQaOg4dSt9+/ciXLwS9/l1w01qj\nWc6wYR8wdOiTyubffvMN08aN4x2jMUFkjB34V6Hgv9y52X/kyOMMiiaTiWYNGnDu0CEqGQwUweXL\n/Q/YgRIDAnaaAe4E+jBlylwmOjr9csKkN+PHj+fLL5djtdb30nInn39eke+//47A3Ll5Pz7eY0z4\nHpmM3K1asWjZsrQ0VyIDyJBkVoIgNBQE4ZQgCGcEQfgytf1JpI7s2bPz6WefsXXPHv49fJg5CxY8\nFm+A+fPnU5ik5RhcnuAwk4nJ48czd+5cRLGQx9YmUxi//DIJh8NVq/Ty5cv8MGYM7Z8Rb3DNm2vZ\n7RS4e5fhQ4c+fr/rRx9xb/9+OhkMlMO1G9APqAT0xkZerMi44eGqX+fChSscPHjQQ5sXm6CgIFQq\nd4XtnqBWx1GgQD6uXr2Kwun0KN4AhZ1ODu7fnzZGSrxwpErABUGQA5NxJZQoDbQXBOHF2EMtkSR/\nLl1KcYPBY5sgQGa1Mnv2IgwGb3mogzGbBaIfhqtNmTyZck4nnkrwhtrtLF68GL1ez9WrV1m9ejWN\nzOYkMy/6AK4lvf24nAJJIcNuL8YONylXswLNmjXD6bzGwyVIN5iAU7Rr1w6ZTIYzGU+2TkCWwe4g\niYwjtTPwqsBZURQviqJoA5YAmZP4WSJZGA0G1Mlop5bJMBo9ZfJ7glyuebxFf9e2bRRx45N9hD+Q\nS6nk5MmTLF26lNJeRskOBCPgitFOGlFMuxwlnnjw4AG//vorHdu0oWObNkydOjXRbsfnQavV8tln\nn6LVriVxXhwAOxrNOtq3b0/evHnJnz8/CrXa43MJwFm5nFq1kwrDlHgZSK2A5yNhPtSrD9+TeEEp\nVqoUN73Ua7QCdywWSpcuiSDc9NKjFYvl9pNqSMlc73i0SHj92jX8LBav7XPjANw/OajV1xLsTk0P\nfps+nfyBgcz88kv0y5cTv3w50wcNIl9gIHPnzEl1/998M5y2beui1c5GEPbi2k95HziATjeH2rWL\nMm3aZAAUCgW9+vVjr1rtNqu8ATji40Pfzz5LtW0SLyapjQNP1rd1xIgRj38ODw8nPDw8lcNKPC89\n+/al5erVhBoMbotFRAHV33yTL7/8nC1b3sVgCAUPrd98szpBQa6682+GhRF57BhFPczC44G7Visl\nSpQgd548GJVK8FJbMxaBxAUXHnEJjcZG/freFgCfnzlz5jBswAA+NJl4eoN5JYOB28DAPn1QqVS0\n7/D8lehlMhmzZk2nS5cP+fHHCezevQpRdPLGGxUZNGgOb7/9doLomM8HDmTV0qVsPH+ecIslwadz\nB1ij09GtZ890v7FJpA0REREpzhiaqigUQRCqASNEUWz48P9DAKcoimOfaiNFobxAiKJI43r1uL17\nN02S8DtfxpXlcHNEBJUrV6ZOnYb8++89LJbGJBbxy2i1q9i2bdPj6vIHDx6kRpUq9BVFt0mTtigU\nlOjYkZlz53L27FkqlStHX7PZbUZuPTAesNOZxAuq19FqV7Bo0SxatmyZ7M/hEefOnePYsWPI5XKq\nVKlCYGDiLCFWq5V8AQG8FxfnNofIVWBdrlxcuXkz0Wao+/fvM3vWLGZNncqde/fw9/Ojw4cf0qNX\nr0ThlCnlwIEDNKpTh7j4eF7DtQB8E1dy3AaNG7N67VpkSTxx2e121q5dy6ZNW7BabbzxRjk6depE\n9uzZU2WPRNqR7mGEgiAocDkm6+LaHrcPaC+K4smn2kgCnkxiYmL4559/MBgMhISEEBYWluSXL7UY\nDAbea96cw5GRlDeZCHQ6sQD/6XRcAJauXEmDBg0A0Ov1NG36LgcOHMNoLI8oBgIWdLrTwAWWL19M\no0aNAFelmKoVKhBz8iRmUaQtrmJkj3Dg2il4PFcuDkZFERzsKibWpH59YrZvp77VmihBkwNYo9GQ\nq0oVIg8eRRAKoNcXAER8fS8D15k5cxpt27ZN0Wdw5MgRevf+jEOHDuPjEwI4sVguUr9+faZMmZAg\nCdSKFSsY1rkz7b34uhf4+fHLokUJshUePnyYBnXrUtBsprzJRA5cN6TDCgXRgkC7999n2LBhFClS\nJEX2gyuFQmjFioTGxVFcFDmHy/2VDVcJjtVaLd0GDWL4U0/AANu3b+e999phsfgSH18YUKDV3sTp\nPMPw4cMYPPiLZMfBnzt3junTZ3DixH/4+upo0+YdmjdvnqlVmF4WMiQOXBCERrgmSHJgliiKo585\nLgm4F/R6Pb1792fZsmUolYUQRTWCcBudTmTs2O/44IMP0nxMURTZt28fUydO5MypU2g0Gt5p355O\nnTqRLVu2RG337t3LhAlTOH36LBqNhvbt3+GDDz7A39//cbulS5cy7JNP6KDX8y+wCyiAKwWVBVd6\nVKUg0OKDD5g9d+7j82JjY6ldowa2ixepYjQSgss3dxaI1GrxL1qU7r174+PjQ0xMDMePuxYz33qr\nBq1bt0atTs6y7BMiIyOpW7chBsOjzUmP5v4m5PJIcuQ4zcGDeylY0DXbHzlyJP+MGEEdL3/HWxQK\nmo0axRdffAHAvXv3KFW0KOGxsUkWbLuMa3uSwseHOnXqsGDJkgSfpzfavvsud1evJsxNet144De1\nmlPnzj2+WUZGRlKnTgOMxma46vk8TSw63XKGDOnDV18N9ji21Wqlc+durFz5Bw5HeWy2AMCCn99/\nqFR6/vrrz8dPZRLPh7SRJwtgNBqpVi2MM2cEzOZweOx4EIEraLV/8c03XzBw4IDMMzKZ1AoNJWjf\nvsdiZQVO4gqMUwDFcIUFztXpuBMTk2D3ptFoZPbs2Uz44QcuXL2KKIoUCArCbDKhtNkIEkWsMhnn\nbDYaN2rElBkzyJXLWxR0YpxOJ/nzF+HGjWq4CjokRi7fRa1aMrZt2wTA999/z4bhw3n7Yay7Ozb5\n+NB6zBg+e7hoOHbMGJaPHEkzD0U0tuESWh+VCmuxYuzaty9ZKXLv3r1L4QIF6G02u10ZANikUlFv\n0CC++fZbACpWrMbhw8HgNmtOHGr1DK5du0TOnDndtIHWrdvz119RmEwtebI79xGn8PXdRGTkLkqX\nLu31WiSSRqpKnwUYM2YcZ87YMJubQAKvsQAUxGhsz//+N4KLFy9mjoEp4Nz58wQ99X8fXDIRDtQE\n8gI5ABwO7t+/n+BcrVZLnz59OHPpEkaTiWnTpqGPiaFhTAxd9HqaGAy8Ex9Pb7OZa+vW8Wblyon6\nSA5///03rkyqJd22cTiqsnfvXi5cuABAnTp1OKNWeyws5wD+UygSLNDPmjaN171UQKqEK3ltfYsF\n0/nzzH3qycQT0dHRBKtUHsUboKDFwt6H8fEnT57k1KkzuAo0u8MfQSjBnDnu7Thy5Ajr1/+NyfQO\nicUboCQGQxUGD/6fF+skUosk4JmI3W5n8uSpmM3VwW16/uw4neWZPHlKRpr2XKh9fNxutXmEA7A4\nHB7dHg8ePGBA//60M5koTMJPRgPUs9nIef06w4YMcdODezZt2kx8/Gu4/7wBfJDLi7F9+3YAQkND\nyZMvH1EezjgsCBR67bXHtSsBbt+9i/s5rItsuJ61bEAVo5EJ48Yl6zqE/7d353E2lu8Dxz/3mXNm\nzjJjMLaxjC2TJUtEtjShbJWlJEK2X0JCClFRadEeylIhKhJtCn2FYSzJMJaxG2JsM3Yzc9Y55/79\ncS4ttMMAACAASURBVMY+55zZN/f79fJ6GeeZ57mO5fKc+7nu6xIiQyVgEhBpz1F2796NVhuG54oi\nN4ulAv/+G+Px9alTv8Rma4C3QdBS3suqVf/j3LlzGYhSySqVwPNRXFwcDocAr/NRwG6vwYoVq/Mm\nqGzo+Pjj7PMxreYQUPvuu72u9b737rtUtlq9Thhqbrfz3YIFJHsZTJAem81BRqpnpfTDnlYKKYTg\nhyVLWB8UxBYhbhouZwc2C8HmoCAW3DKurlhgIL6is+DeLakDqgCHjh3L0IakevXqcdpm83n+o3o9\nrdq2Bdy140JkZBydE53O8+9RTMxunE5f1TMGAgLKEBcXl4HrKVmlEng+cjqduAt5fPHD6cz9XYbZ\n9eKoUezQaj1uBrcDq4WgRNlQDhxIf1elw+Hgq+lfev2QD+7dnKX9/dm1y9t98e3q1auDyXTrBMpb\nSTSaE9cGCQPUrVuXDVu24HjgAabp9fxSrBg/FyvGdL0eIiLYtHXrTccDPN27N7v901tiuG4n7pV4\nDdc3VWSkAqREiRJ07dqVLV6qPS7ifgYx6P/+D4BmzZphtx8l/Z2e1wUGHqFdu9YeXw8I8MfzjNTr\nXC47/j7ev5I9KoHno8qVK5Oaehm44vU4jeY4DRt6euiU+6SUWCwWn8OEw8PDeeeDD/jOYGA/XFsz\ndj+OhW/QcFH6sXr1QerXb8LYseO59QH3b7/9htMpfHzId/ODTG+f79mzJy7XEbz3HImjZEkjdevW\nZdmyZSxevJjo6Ghq1qzJqnXr2LF3L2/MncvEuXPZfeAAK9esITw8/LazDBs+nFitlhMernIBd6XO\n1Uavh4B6tWrh55eRdw/vf/QRcSVKsMHP77Z0egpYZDTyzvvvXxt2ERoaSuvWrfHz2+LlrPFoNAl0\n797d4xFdunTEYDjkI7qzCGHJtVmpiptK4PnIZDLRo8fT+PlFeznKjl6/I1emvvuqDoqPj+flUaMI\nCQ4mOCgIvb8/j7dv77Vp1LAXXqBctXB+EQY+QMsMAvgEf+YTSCIPk8pIwIzN1pQvvviOjz76+Fos\nUkq++WYBVld54nz81bQCpywWatb0/DAyPcWKFWPSpNcxGpcA6c0QPY3B8Afh4XcRGlqJ3r3HMmjQ\n+0REPEr16rX5/fffqVq1Kt26daNbt27XSg3TU7lyZRYsWsQSo5EojebacocV94aJubgf8FbC/Wxg\nq8nEqLEZb+hZvnx5/tm2DWfTpkzX61mu17PK35/vgoL4tUQJ3p02jRdHjLjpe2bNmk6JEvvx81uP\nu7jzKhewD4NhKd9//63XZxSDBg3Evf3D0ycZiV4fxZAhz6k78FymygjzWXx8PPXr38elS/cjZUNu\nfrhmxWj8jQ4d6rNkycIMnS81NZWEhAQ0Gg1ly5a9bSPQli1b+GTKFP5YvhyL3U7ZkiUZNHgww4YP\nv2kXYnR0NO3atKG2xcK9DgchuP+578Jdm/3S+PG8OmHCbdePiYmhZcuHMZuH4r7LTcLdqqoc1+8X\n4oGfgV4EBHxLWFhl4uL2o9H44e8fiNlcHX9iGEWqxyqLDYCjeXMiN27M0O/LjaSUvPvuFCZPfgch\namKxVARcBAYexen8j5CQ0pw9WxKb7UG41lfRBcRhMKzgyy8/oV+/ZzN8vdjYWD587z0WLloELhcS\nuBv3nXcY7o09fxkMlLv/fpavWpWlTTCHDh1i1apVWK1W7rrrLjp06HBTmeaNTpw4wYABg1m/fj06\n3V1IqQXiKV++NDNmfEabNm18Xu+7777nueeGY7G0A8K5/md7Gb1+HeHhGjZvXofRaMz0e1HcVB14\nIXHgwAE6depCQkISKSk1kVJPQMB5hIjl6aefZvbsLz3+Y7zq4sWLfPzhh8yaMQOnzYZTSoKDgxn+\n0ku8MHw4BoOBTz/5hMmvv05ji4V6UmLA3TMjJiCAwwYDq9aupUGDBiQlJVE9LIw2ly6lW2yXBCww\nGpmzeDGdOnW66bXhw0fy5Zc7cbkivEQrgRlAJ+BvoDLue1EX7ju7KPxwUIpk+uLAdMt3xgK/A7+v\nWJGtmZXnzp1jzpy5bN4cjUajoX371sTG7mPWrLXYbJ1Jv1LlLHr9txw/foTSpb09Zr2d1Wpl7Msv\nM3fOHCprtRSz20nW6TiSmkqfPn34dNo0AgJu7su4fft2PvvoI1YsX47NbqdKpUoMe+klevfujclk\n8nCljImPjycqKgqHw0GdOnVo1KhRpiYRrVy5klGjxhIffxo/v1DARmrqafr06cPHH0/Jdnx3OpXA\nCxEpJevXr+enn37mypUkwsOr06/fszdt6fbk9OnTtLz/fkomJtLEZqMM7kR3EthsMGAMD2fCm28y\nqFcvepvNpNftIhaIKlmSw8eOMX/+fGaPGUNXL33DdwMJjRsT9e+/N/364493Z9kyJ543ily1CPd4\ntOO473Jb3PCaA1iIH1YEidwNVCYVG7Adf5Lxo2LVShw54rm9bFbYbDZKly5PUlIvuKll1c0Mhj+Z\nMKELEyaM93iMN8nJySxbtoyEhARCQkJ47LHH0u1BMuXdd5nyzjs0slqp43IRgHtte4fJhK1UKdZu\n3JjtXio5YdeuXRw5cgSDwUCLFi0IDPTUBUfJDJXA7xCtmjZFt20brdJ5oOcCluv1nDaZuP/8eep5\nOc9Sk4lhH3/MvJkzqbZjB7c/lrsuFfgsIIC448dvmgg/cOBg5s49ipQtPH8zAF8DrXEvylQAGt/y\n+iVgJjAY2IuWs7jQ4aISBkMU338/i65du/q4RuZs376diIguJCUN9HHkQZo0iWfLltwbILF06VKG\n9u1Lb7OZYum8HqXVkli9Ojv27s2VfjlK/lM7Me8Au3fvZs/u3bTwUI2hAZparSScP4+vTc33pKTw\n7ezZXLh40etEHXBXUgfqdFy8eHM1R58+PTGZ9uC90/BZ3OvjobiXTGqkc0xx3Ovm24EGpNIK4ReM\n0RjJpEmv5HjyBncJo0bjfanKTYvDkbtlnW9OmEBbD8kboGVqKldOnWLVqlW5GodSsKkEXsgtXbqU\n2jabz7I7I763rwTjXhcuU6YMvqYz2oHzKSn8+OPim5L4gw8+SIUKIV5K1RzActzDnDbgXv9Ov4Wp\nTleKMmXiMBpnUbz4Qnr2rMjGjasZM+YVH9FlzV133YXNloh7e41nfn7xNGzo7bNM9uzfv59T8fG3\ntZq6kQDuSUpizsyZuRaHUvCpBF7IXbpwAYOPJksG3CnJ19aLS0Dp0qUZOHQou32sY8YCyFJMmfIr\nFStW5tdffwXcH/v++msZpUvvwd9/Ge7u1OAulNuHu3hOC5zDPXf+sdvOfZVeb2H69M9ISbnMxYuJ\nLFgwlwYNGvh4F1kXEhJCu3YdEMLbcGQ7/v47GTFiWK7FkZCQQIhO5/MfZwncE42UO5dK4IVc5apV\nueSjnaoJMGo07PVxrtjAQAYMGUKPHj24YjKx3UNFwjngL7Q46ITZ/Dhm89P06tWfqKgod0yVKxMb\nG8O4cY9RvPhSNJp3gHfQaJYREJCC0ZiIn98hoE9adOm5hNMZT8eOHX1EnbOmTHmbwMBtwJ50XrVi\nMPxMly6dqFu3bq7FULJkSS6npvrsdXIFCCnl+WGrUvSph5iF3JkzZ6hRtarXtqLngG8NBvyFoLfZ\n7O4IeItdwOZSpTh87BhGo5EDBw7Q+oEHKJuSQgOzmTKAGYhBsAU/HHQEGt5whp00aXKWLVuibjqv\nlJKkpCScTienT59GCEG1atXo2vUp1qw5g83WntvvIxwYjUt5/vnH+PjjjDV3Ss/FixeZP38+O7dt\nw9/fnzbt2tGlSxefJZnbt2+nY8fOmM3+JCXVAPT4+59Fo9lNz55PM2vWFz7PkR1SSmpUrswD8fFU\n8XLcDMBsNPLiiBGMGDUq02WNSsGmqlDuEM8PHEjUwoV0tVhu6w9nBn40Ghn2+uuYgoKY8MorNLLZ\nqOdyYcQ9emuHXs8xo5HV69bdND/x0qVLzPnmG96ZNInLyWY0+OOiFk6aw7VWU6fREIMflxB+/7Fw\n8UK6du3qs574ypUrREQ8wsGDl0hJaQRU5WoduMkUTdu2jVmyZFGWNrVIKfnw/fd5+623qKHRUN5s\nJhU4EhTEZa2W7xcvpm1agydPnE4nK1asYMmSX0lONlOrVg0GDRpwfXhzOteMjIzk00+ns2fPfvz9\ndTz+eAdeeGEolSpVyvR7+Pqrr3hr5Eh6mc3p/se8DdgIPAVsDwjgZHAw6zdvztJkH6VgykgCv7aF\nObd+uC+h5Ca73S6f6NxZhppMsoMQchjIISDb+vnJkkajHPnCC9Llckkppdy+fbvs26uXLGYySX+t\nVoaVKycnv/22TExM9Hj+Fi1aS+gpYdINP8ZIHZWkAZ18ACG7gIwAWUqvl43r15enTp3yGbfVapXz\n5s2TtWo1kFqtv9TpAmTTpq3kzz//LJ1OZ5Z/P95/5x1ZwWiUI0FOuuXHsyCLG41yw4YNWT7/rVJS\nUuRDDz0iAwPLSyE6SnhOQj8ZENBcGgxBcsaMmZk+p8vlksOHDpWhJpPsAnICyIlpf66NQBYD+cIN\n76ujRiNrVqt27c9ZKfzScqfX/KruwIsIKSVRUVF8/tFHxGzbhhCCByIiePGll2jYsKHvE3jRrt1j\n/O9//nCtityBjtnU5wIdcN5UAeMCNmi1xFeoQPSuXbeNZ8uogwcPsnz5csxmM1WqVKFr164ZmlRz\n8eJFwsqX5/+sVm5tWHsKiAaOAqk6HV2efJIRo0fTqFGjLMV4VadOXVmz5hhW66Pc3mv7PAbDDyxa\nNIfHH388U+eVUrJixQo+evddIjduRIO7mqgRcB83j/+QwJzAQOb88ovPTxdK4aCWUJQcMXfuXF58\n8WOSk692qIuhIssZiMPjWIRfDAb6vv02L40enalrnTp1ih49+rBt2zZcrlo4HDqMxvNIeZLXXpvA\n2LEve12e+ezTT/nutdd4zGy+9msuYCWwH3fiu1qed0SjYYdeT7enn2bGV19laUNMbGwsTZq0wmIZ\nhudCzYPUqLGLAwd2ZWqr+lXr1q2j/2OP0SspycsIBdgMhPbuzdwFCzJ9DaXgURt5lBzRo0cPNJrT\nwBEA/NlEKy/JG+A+i4Vpn3ySqeucPXuW++5rxj//gMUyHJutPS5XG5KTnyIlpS+TJ09j3LjbG2jd\naEd0NKE3JG+AKNx330OAVkD5tB8tXS4Gmc2sXrSI18dnbVv8rFlfY7fXx3uV/V2cOpXI7t27s3SN\nS5cuESiE1+QN7jvyM6qs8I6iErjik9Fo5LfflmI0/gZswckFfD2WqwAcP30ah8N34/+r3njjTc6d\nK09qaituT4ghpKQ8zbRpX3L48GGP59DqdNxYFW8D/gGehHQfBuqBzmYz06ZO5coV733Z03Pw4BGc\nTl+lfBq02jIcO3Ys0+cHKFeuHIl2u8+ywnNAwvnMzwlVCi+VwJUMiYiIYOPGSNq10yJw4msjuQv3\nGu49d9+doak5ZrOZ+fMX4HA09XKUidTUekyb5nk+aNv27TkSdL0RwH7cLVvT3+vpVgyoqtGwdOlS\nn3FeZbVaWbhwIfHxx/C1cxNASkuWmzw1adKEZKeL416OcQFb0XLg8FGcPjZ2KUWHSuBKhjVo0ICV\nK3+nbevW7POxlrsP94zHOkeP8lDLluzfv9/r8QcPHkSrDcZ7qgWHoxrr1nnuAd6tWzfOazRcvde9\nDF5na15V3GwmPj4+A0fCzJmzKFOmPM899zb79jkBzwOA3c4j5UWaN2+eofPfSggB/nqWoiUpnddd\nwB/44SAUp1Ny4YK6C79TqASuZNrY119nm9Ho8b7TjrvLSWPcTWUbJyfz8osv5tj1vT0T9/f35/vF\ni/nZYGAP7mHBZs+HX2P39ycoyFcLL/j886mMHj2RpKSeJCf3ALqlXcHT+rYTg2EtQ4YMvq3Xd2YE\nBRUnmQZ8gY5IBOdw/+e0B5iNjt2UwsHTOJ32bF1HKVxUAlcy7cEHH6R7374sMho5fctricD3uPsM\nXh3x21BK1kdFcdLLA7bw8PC0+aDe22jpdEdp1aqZ12MeeeQRfl+5kkO1a/OvXs8e3P+peOIA9grh\ns8zv4sWLjBs3AbO5B3C1ha4f8DTuOpe1cO0e2T0J1GhczH33leXttyd5PbcvHTu2R6MthpUBbOAe\nZmFkOgH8RnnO0BkHzwEnCA+vleXSTaXwUQlcyTQhBFO/+IJRkyezQKdjBrAYd4fv+bjL9B7n+jyb\nACAsIMBrFYbRaKRPn97odN4G7qag1e7kxRd9N5Jq1aoVMXv2sGbzZurUrcs6rdbjQ8AonY5mzZpR\nvXp1r+ecO3ceGk04UPKWV8oBA3EPR/sC+BiDYSrlyq3izTf/j9WrV2R7NuSoUcPR6bYDRlJ5Agdj\ncPAqdp4D7gFcmEybGTt2VLauoxQuKoErWSKEYMSoUbRp3ZpwoDbwEDAKeIDb/2I5wWed9VtvTSQk\n5ARabRTc9pj0AibTjwwb9jw1aqTXPzx9DRo04H9r13I+LIzfAwJuGsObCCwLCOBMhQos+PFHn+eK\nivoHs9nTEOOSuDsrjsJkCuXzz6dw8uRRXn55dI70Tbnnnnt4441XMRp/wF3OeeN/R2cwGhfz8MON\n6d27d7avpRQeKoEr2dKmQwdSjEbuAapz+z5EcK8Qn7DZfO4ILVOmDNHRm2ncOBWDYTr+/isRYg2B\ngUswGufx6qvP88EH72U6xpCQEP7Zvp1Oo0fzU/HiTDMamWY0sjg4mHajRrElJiZDjaDcm3B8FfMF\n4OfnT7ly5XJ8Us64cWP4+utPqVJlC4GBswgOXkKxYnMpUeJnxo/vz5IlC9V0njtMlndiCiG6A5OA\nmkBjKeV2D8epnZhF2KVLl6hUvjzPWiweqz3W+vkR2qULC5csyfB59+/fz59//onZbKZq1ap069Yt\nRyacp6amXluLL1++fKbujqdPn864cd+QktLFy1FW9PrpHD68P9fmVUop2bFjB6dOnSI4OJimTZtm\nqemXUrDl6lZ6IURN3BVMs4DRKoHfuebMmcOY4cN53GwmjOtr3w5gi58fe0qUYOuOHQViAG92XL58\nmdDQSlgsffFUnKjRbODhhw2sXPl73gaXQVJKzp8/j9VqpXTp0qpipQDL1a30Usr9UsqDWf1+pegY\nMGAAX8yZw6oyZZgXFMRfej1/Go1M0+uRzZuzZfv2Qp+8AYKDg5k+/TOMxkXArTXjycAP6EQkV86d\nYtSIEezcuTMfokyfy+Vi3rx51KtZkyoVKlDv7rspXbIkQ557jv/++y+/w1OyKNvNrIQQa1F34Aru\nJLF69WoOHDhAQEAArVu39lnZURgtXLiIF198CZvNgMVSBuE8hJDn8cfdLKsYcAHYpdNxX9OmLPnt\nN0qUSG+MRt5wuVz0euoptqxcSYuUFKrjvnO7DGzTatljNPL3unW5Oq5OybxsL6EIIVbhrpG61Xgp\n5bK0Y3wm8IkTJ177OiIigoiICN/RK0oB5nQ6+eOPPxg5bBiJJ09yHxDBzR9pncBffn6k1qrFpujo\nfFuu+Pijj5gxcSJPm83pNsTaA2woXZr/TpzIdrmjknWRkZFERkZe+/rNN9/M/Xay6g5cya6YmBj2\n7NmDTqejZcuWubLcEhcXx5fTprFy2TLsDge1atdm+OjRtGnTJsuVG59+8glTxo4lJDWVpzwcI4Ef\nDAZemzmTvn37Zjn+rHI6nVQODaXj2bN4+139ITCQt77+mh49euRZbIp3edIPPC2BvyylTHeUt0rg\niieRkZEMGTKS48dPodGEIYQTh+MwDz4Ywddfz6BixYo5cp2pn3/O6+PGUd/p5G6HAx3uFeydgYGE\n33svv61Ygcnkabhy+lwuF9UqVuTy6dN0w90wy5MDwIE6ddgWG5v1N5FF27Zto/NDD/F/Sel1Ubku\nBqBDB35dvjxP4lJ8y9WHmEKIrkKIeKAp8KcQYkVWz6XceVauXEmnTl3Zv/9uzOYhJCc/RlJSF6zW\n4fz9dwoNG97vdet9Rv30009MHj+e/lYrbRwOKgJlca9V90tO5uLWrfR68slMnzcxMZELFy5wGXy2\n1g0DDsbFZfoaOeHKlSsEZuAThgm4fMl7GwOl4MlOFcovUspKUkqDlLKclLJDTgamFF02m40ePXpj\nNnfFvYfzxr+GATidD3Lhwt0MHjw8W9eRUvL6mDG0N5tJ7xGiH9DRaiVq3Tr27NmTqXM7nU780joy\n+mremgr4+aW3xSn3VahQgbMOh88YzwtBWNWqeRKTknPUti0lzy1ZsgSXqzSQ/oR3AKfzfv7+exWn\nT9/aLivjtm/fzuWzZ/E2p10L1LPb+XrWrEydu0yZMvj5+1MBd89xb/YCrR54IFPnzynh4eFUqVYN\nb/W+LmCzlHR47LG8CkvJISqBK3nur79Wk5zsLa0C6AkIqMamTZuyfJ34+HjK+Pl5Hf0GUMrp5L9M\nLnHodDoGDR6MXqtlA+5NS+mxAFv1ekaNGZOp8+ekSe++yzIhOJ/Oay5gOX5YKMann36R16Ep2aQS\nuJLnbDYH6XdNuZUfqam+Zv94FhQUREoGjjMDwcW9D5JIz8tjxmANCcEPdwvds7e8fgb4VqOhe9++\n+Vo6azAYcOqCmYmW5Wg4iXv82i5gBv7spBQO/o/du2N9Dt7IS4mJiRw4cEANqPBCJXAlzzVu3ACD\nwdfSiJPU1OPcc889gPth3OHDhzl79tY06VmLFi244HKle+d5o31BQXTv1SvD572qVKlSbNq6lXJ1\n63Jep+MbYDawEJgOLPD356V33+WLmTOzNI0+p6xZsxabvT4OhhJNY+YTzGwC+YNKnKVrWi/xIIQI\nZ926dfkW51V//PEH993XnLCw6tx3XwShoZV46KF2REVF5XdoBY5K4Eqe69+/H1Lux70X0JM9hIdX\nx2Kx0KVTJ0JLl6blvfdSrVIlmjZsyC+//OLzOnq9nsFDhrDGYPD4EG+nEFCsGO3bt8/KW6FSpUpE\n79rF6o0bGTZqFPUfeYR63bsz9YcfuJSSwitjx+Zr8gaw2+24V/tL4qIDNkZh52XsDMQ9dsP9acjl\n8svUEOrc8NZb79Cjx0C2bauAzTaS5OTnsdtHEhmpp337zsybNy9f4ytosl0H7vMCqg68UHA6nfz1\n11/s3bsXrVZL69atqVevXq5db/Lk93jvvS8xm7sDwbe8egSj8Xdee20MU95+mxZWK/WkRI+74uMA\nsN5opN+wYbz3wQder2O323n0kUc4tnUrzc1mKuNutnUZiNZq2R8YyNoNG6hTp04uvMuCYf78+Qwb\nNoXkZE/bjQAkgYFz+P33b3nooYfyLLYbRUZG0qlTd8zmZ4H0xtudw2BYwPbt/1CzZs28Di/P5clG\nngwEoRJ4AffTTz8xdOgIbDYDVmt5NJpU/PwOUaNGNRYtmp8r/1iklLz77hQmT34HjaYGZnN5IJWg\noDi02ivMmDGVwQMG0MNspnw6358CLDCZmL1wIY/5qJ5wOBzMmDGDzz74gAsXLuCv0WCVkt69ezNu\nwgTCwrxtwyn8zGYzZcqUJyWlN55HPB+hQoUo4uPj8u0TwyOPPMqqVQJ3lX76tNq1DBxYh5kzs/bA\n1Wq1Epf2wLpatWoYDIYsnScvqASu+LRgwXc8//xIzObO3Lyf0IkQ2ylWbAtbt27K1BSczLh48SLz\n589n27Zd+PvraN++LZ07d2bi66+z7rPPeMRm8/i9u4Bz99/Pun/+ydC1pJScPHkSu91OaGhogf7H\nm9NmzJjJyy9Pwmx+Cgi55dVTGI0/8eOP83n00UfzIzycTicBAXqczldwD+Hz5BwlSy7h/PnMlZde\nuHCBN9+czJw5cxHCCAhcrmSefbYvkya9nqGBHnlNJXDFq+TkZMqWrYDZ/Azu/Ym3E2IzERGwZs3K\nPI0tvHJlHjx+HG+b6VOBj3Q6Es+fz9BE+TvdtGnTGTv2VYS4C7O5Iu5lk6NIeZK5c7+ie/fu+RZb\nSkoKxYuXJDV1vI8jzRiNM0lJ8fb85GYJCQk0btychIRS2O1NuT7T9CI63RZKlTpFdPRmypdP77Ne\n/snVrfRK4ff9998jRBU8JW8AKRuxefMmjh07lldhAZBsNuNr/o4W0Gu1JCcn50VIWZKQkMDhw4dJ\n8tGLJC8MH/4Cp0+fYMqUgfTsWZJnninNtGmvcPbs6XxN3uAeah0QYMDdiNebRMqVy1yi7dXrWc6c\nqYTd3pGbB1KXwOFoz9mzNXjyycxXIRUEKoHfwdau3UBKyq3rvw5gBwHMJoBPCeAbkEGsX78+T2Or\nWL78bXXVt0oGHFJSsuStU+Lzl5SSH3/8kbp1G1G58l3ce29LSpcOpXPn7uzYsSNfYwsODuaFF17g\nhx++5bvv5tKvX78CsZQkhGDgwAHodDFejzMad/Lii89n+LxHjhxh06bNOBwtPR6TmtqMHTt2sm/f\nvgyft6BQCfyOd+MntHPo+JxK/ElnTtGPyzxBApVspxn+/PP8+++/eRbV8yNGsMtHh8AYPz+6P/lk\ngRoLJqVk+PCRDBw4mtjYcGy2USQnD8Fme4Fly5Jo0eIhVqxQfd/SM3r0SPT6PbjrjG4nxDZMpgT6\n9euX4XP++eefuMf2ept9qiU1tSZ//PFHJqItGFQCv4M98EBTTKaro8EsaJlDO5IZiIPaQCgQDjyD\npIPZTIeHH+b48eN5ElvPnj1JKV6cLR466R0FogMCGDthQp7Ek1GLFy9m3rylaRUfNbm+49SAlM0w\nm5+ge/eeJCYmYrVaWbBgAd06deLBZs0Y8OyzBWoMW14LCwvj779XEBy8CpPpV+Ag7v2sewkMXEzZ\nsjvYsGEtwcG3lp16ZjabSU31PaTC4fAv0EtxnqgEfgfr06cPLlcc7o3VMVTD4bGAqyZQ22Lh808+\nyZPYDAYDa6KiOFChAosCA9kLJABHgGUGA78HBvLzsmUFrh548uQPSElpCXhalqiEyxXO+PETWXsu\nNQAADLhJREFUqFi2LC8PHMiq5cvZ9s8//DR/Po0bNKBWjRqcOHEiL8MuMJo0acLx43FMmTKI+vXj\nCAtbTePGp/jii7EcPXqQ8PDwTJ2vcuXK6PW+t+KbTBepUqVKFqPOP6oK5Q43c+YsRo9+g1SzhV4k\nUcXLsReAb00mLiYl5VmtsM1mY8mSJcyaOpVTp05RLCiIXv3703/AAEJCbi2Hy1+JiYmEhVXDZnsJ\n771etqFjGSWAEkAruDYt5zywETgYEMCegweLfI16brNYLJQuHUpKSl9uL5+86hIGwzckJJwsUNVM\nGalC0eZVMErB9Pzzg/H31zF44EDK+Di2JGC2WrFarXn24CsgIIBnnnmGZ555Jk+ulx1JSUlotSZs\nNu+NunTEEIr797MzNz+FCAEeB6JsNjq2bUvsQW+NYBVfDAYDr702gbffnobZ/DTu0RU3MmM0/sro\n0aMLVPLOKLWEojBgwABCSpbE7OM4G+4Zjzc+NJRScuXKFa5cucKd/kmrTJkyOBzJuJvIepKEi5Mk\nAg+Dx1a3LYATR48SHR2d02HeccaOfZlhw55Br5+NTrcG+A84hlYbicEwmwEDOvPmm2/kc5RZoxK4\nAkDXJ54gVuv9A9kuoH3aEGCz2cynn35GpUrVKVWqLCEhZQgLu4vPP/8ci8VbAiu6goKC6NChI0J4\nKxW8iBGowu33gjfSAHVTU1m6ZElOhnhHEkLwwQfvsWPHFgYNqkft2ruoXXsnAwbUIjp6I9OmfZbv\nDceySq2BKwDs27ePZo0a0cdioVQ6rycB3xqN/PTnn9x77720bNmauDgbFsv9XJ8KeRyDYQvh4Sai\nolYXyo+k2bVjxw5atIjAbH6S26dlSjSaFehd/1IT91KJN5uB6oMH88XMmbkSq1KwqZ2YSobVqlWL\nT6ZP53ujke2APe3XU4FYYIHRyMhx44iIiKBPnwEcOuSPxfIk7v4pIu1HZSyWJ9m/X/Dss4Py543k\nswYNGrBkyUJMpiUYDH/iLnhMAGIJDFxIWNglNAYDiRk41zmtlsrVfE0uUu5k6g5cucn69et5Z+JE\nNmzaRDF/f5IdDurVrcurEyfy6KOPEh8fT3h4HazW4YCn+lorev0XxMXtL3D9JfLK2bNn+eqrr1mw\nYDHJyUlUrFiRkSOH0LVrV9547TU++/BD+gPlPHy/FZgWEMDBI0fu2N/DO51qZqVk2fnz5zl37hwl\nSpSgTJnr9Smff/4548b9gNXa0ev3Gwx/8NFH/Rk6dGhuh1roWCwW6oSHc/nECQYAgbe87gCW+Pvz\nQK9efDV3bj5EqBQEqoxQybKQkJB066wvXbqE1ar3+f02m4FLly7lRmiFnsFgIPbAAdpGRDBt61aa\n4J6Lo8G94LJdr+fB9u35cvbs/A1UKfDUGriSKaGhoRiNvjvrGQxXKFfO0wKBYjQa2fTvv2yMjqZE\nx46sLFuWv0JDKda5Mz+vWsXin39Gp/PWv0NR1BKKkkkXLlygQoXKWK1D8FwIl4ReP4szZ05kqm+F\noijXqSoUJceVLFmS/v37YzQuw71aeys7RuMfPPfccyp5K0ouU2vgSoadP3+e+fPnk5SUROnSThIS\nvsZqbQzclXbEIUymGNq3b8XHH0/Jz1AV5Y6gllAUn6SUTJz4Jh9++BFC1MRiKQfYMRhiSU1NQq8P\nQKvV0rhxY155ZQRt2rQptDvbFKWgyNUyQiHEh8CjuPd8xAH9pZS3DapTCbzwGz/+daZOnU9KypNA\nsVtePYjR+Cfr16+mUaNG+RGeohRJuZ3AHwZWSyldQoj3AaSU49I5TiXwQuzMmTNUrVoDq/V5bq9Y\nvmobzZolsWnT2rwMTVGKtFx9iCmlXCWldKV9uQW8DhBXCqmvvvoaqIPn5A1Qj5iYGOLi4vIoKkVR\nIOeqUAYAy3PoXEoB8u+/MVitFXwcpSMgIIy9e/fmSUyKorh5rUIRQqwi/XYN46WUy9KOmQDYpZQ/\n5EJ8Sj7TarW4O4F7J6UTPz/vgwwURclZXhO4lPJhb68LIfoBHYE23o6bNGnStZ9HREQQERGR0fiU\nfNap08P8/fdUkpPv9XKUGbv9OE2aNMmzuBSlqImMjCQyMjJT35Odh5jtgY+BB6WU57wcpx5iFmIp\nKSmULVuBlJSnuD658WZa7Wq6dq3E4sXf521wilKE5XYVyiHc/USvjnzeLKW8rfWcSuCF3y+//MIz\nzwzAYukA1OD6oxMrWu1mSpc+SkzMv5QtWzbd74+NjWXRwoWcS0igfKVK9O7Th2qqz7WieKXaySo5\n5n//+x9Dh47izJkLCFEBIZw4HHG0adOWr7/+Mt3GVefOneOprl3ZsW0b99jtmJxOruh0xPr50aZt\nW+YvXEhgoLfqFkW5c6kEruQoKSXR0dHs378ff39/WrVqRWhoaLrHJicn07RhQ0r+9x8RDgc3Pt50\nACsDAjA0aMCaqCjVdU9R0qESuJJvPv3kE+a+9hrdLJZ0J6+7gO9MJt6bM4ennnoqr8NTlAJPJXAl\n31SrWJGIkyep7OWYWOBko0Zsio7Oq7AUpdBQ7WSVfGG32zl++jRhPo6rCuzdvz8vQlKUIkklcCXH\naTQapJS4fBznBDSqa6GiZJlK4EqO02q11K9dm0M+jjsANG/WLC9CUpQiSSVwJVeMGjuWf00mUj28\nbgO2mUyMGjs2L8NSlCJFJXAlV/Tq1YuazZvzi8HArU3izwOLjUY6PvEErVu3zo/wFKVIUFUoSq6x\n2+28OmYMX82eTZhWi8np5LJWS6KUjBo9mgmvv45Go+4hFCU9qoxQKRCSk5NZuXIlFy5coGzZsrRr\n1w69Xp/fYSlKgaYSuKIoSiGl6sAVRVGKMJXAFUVRCimVwBVFUQoplcAVRVEKKZXAFUVRCimVwBVF\nUQoplcAVRVEKKZXAFUVRCimVwBVFUQoplcAVRVEKKZXAFUVRCimVwBVFUQoplcAVRVEKKZXAFUVR\nCimVwBVFUQoplcAVRVEKKZXAFUVRCqksJ3AhxNtCiJ1CiB1CiNVCiEo5GZiiKIriXXbuwD+QUtaX\nUjYAfgUm5lBMhUpkZGR+h5CrivL7K8rvDdT7uxNkOYFLKZNu+DIQOJf9cAqfov6XqCi/v6L83kC9\nvzuBNjvfLIR4B+gDmIGmORKRoiiKkiFe78CFEKuEELvT+fEYgJRygpQyDJgHfJoH8SqKoihphJQy\n+ycRIgxYLqW8J53Xsn8BRVGUO5CUUnh7PctLKEKIGlLKQ2lfdgZishKAoiiKkjVZvgMXQiwB7gac\nQBwwREqZmIOxKYqiKF7kyBKKoiiKkvfyZCdmUd70I4T4UAixL+39/SyECM7vmHKSEKK7EGKPEMIp\nhGiY3/HkFCFEeyHEfiHEISHE2PyOJycJIeYIIRKEELvzO5bcIISoJIRYm/b3MlYI8WJ+x5RThBB6\nIcSWtFy5Vwjxntfj8+IOXAgRdLVuXAgxHKgvpRyU6xfOA0KIh4HVUkqXEOJ9ACnluHwOK8cIIWoC\nLmAWMFpKuT2fQ8o2IYQfcABoC5wEtgI9pZT78jWwHCKEeABIBuZLKevmdzw5TQhRDignpdwhhAgE\ntgFditCfn1FKaRZCaIENwMtSyg3pHZsnd+BFedOPlHKVlNKV9uUWoGJ+xpPTpJT7pZQH8zuOHNYE\nOCyl/E9K6QAW4X4QXyRIKaOAi/kdR26RUp6RUu5I+3kysA8on79R5RwppTntp/6AH3DB07F51sxK\nCPGOEOI48Czwfl5dN48NAJbndxCKTxWA+Bu+PpH2a0ohI4SoAtyL++apSBBCaIQQO4AEYK2Ucq+n\nY7O1E/OWi64CyqXz0ngp5TIp5QRgghBiHO5NP/1z6tq5zdd7SztmAmCXUv6Qp8HlgIy8vyJGPbkv\nAtKWT5YAI9LuxIuEtE/0DdKep/0lhIiQUkamd2yOJXAp5cMZPPQHCtldqq/3JoToB3QE2uRJQDks\nE392RcVJ4MYH6ZVw34UrhYQQQgcsBb6TUv6a3/HkBinlZSHEn8B9QGR6x+RVFUqNG770uOmnMBJC\ntAdeATpLKa35HU8uKyqbsqKBGkKIKkIIf6AH8Hs+x6RkkBBCAN8Ae6WUn+V3PDlJCFFKCFE87ecG\n4GG85Mu8qkIpspt+hBCHcD9suPqgYbOUcmg+hpSjhBBdgalAKeAyECOl7JC/UWWfEKID8Bnuh0Tf\nSCm9lmsVJkKIhcCDQAiQCLwhpZybv1HlHCFES2A9sIvry2GvSilX5l9UOUMIURf4FvfNtQZYIKX8\n0OPxaiOPoihK4aRGqimKohRSKoEriqIUUiqBK4qiFFIqgSuKohRSKoEriqIUUiqBK4qiFFIqgSuK\nohRSKoEriqIUUv8Pu4RXmEF7uuwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1082a8630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=100, c=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You could also ask for unfilled dots, somewhat transparent dots, or another shape (_ie._ not circles):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1084a56d8>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xXLmEhARYW1vXur+aUC8OnIh+J6IXRFRKRGlENB6MA28QNm3ahEGDBqGwsBCa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1083bf9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=100, facecolors=\"none\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1085619e8>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nTbo8LyiYSU7OhRw82IzWC6MOELEGvkA2TqgNqJ3OnSHXe6M5VrQ73sdyVSDV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\nURLAhRDCoiSACyGERf1/qwhiqhM89ngAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108423cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=100, alpha=0.5)  # alpha should be beetwen 0 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10861cd30>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xcuBAD03SLIeUa2UE2kMPHKXRAweaRw8cADJGAAeARBHAsdKVzxQkfwv0w9o5cNv3Sfp9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10853aef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=100, marker=\"s\")  # \"s\" means square"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Drawing curves\n",
    "\n",
    "If you now want to draw curves instead of scatter plots, you can use `plt.plot`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1086d7d68>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wV0SWiMj9Dq5HAdenDzBqlO0o/ImlHYpXmzbAvn1655yMEqeMRGQOgAuL+Kvf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10859b278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 10, 100)\n",
    "y = np.sin(x)\n",
    "\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x108795860>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5iPzcwfUo6Pr3B8aOtR2FP7G0Q2XVrh1w4IDeOSegxBkjEZkP4MIi/uoPp39i\njDEiUtzZeG2NMf8VkQsAzBeRjcaYIo94Hzp06Pcfp6WlIY2rGMIlLU0bR336KXD55baj8Y/164Ev\nvwTatrUdCQVAzuLFyElNBX71K63xx0lMgueYishGaK3+MxG5CMC7xpgrSvmepwAcNsY8V8TfmURj\noQAZMgQ491zgtDf4yPvDH4DvvgOGDbMdCQXFihVAv37A5s2QcuVgjClzCd1JeScbwF2xj+8CML3w\nA0SkioicHfv4TAA3A8h1cE0Kuttv1xIP3+BVfj4wZgwwYIDtSChImjfXYzSXL4/7W50k/WcBdBaR\nTQA6xD6HiFwsIrNij7kQwBIRWQ3gIwBvGWPmObgmBV2LFproVqywHYk/vP8+cNZZwFVX2Y6EgkRE\n58jGjYv/W/1SUmF5J0KefBI4fBh4/nnbkdh3331A3brA74pb8UxUjA0bgE6dIHv3xlXeYdIn723Y\noF0k8/KivUTx+HHgkkuAlSuB2rVtR0NBNHIk5N57PavpEyWmUSPgwguBnBzbkdg1Zw5w5ZVM+JS4\nQYPi/hYmfbLjzjuBN96wHYVdnMAlC1jeITs+/xxo2FBLPGefbTsa7x08CNSpo101zzvPdjQUYCLC\n8g4FQI0aQPv20W3CNnmyzmsw4ZPHmPTJnnvuAV5/3XYUdowcqf9+Io+xvEP2fPcdUKsW8MEHQP36\ntqPxzoYNun0+L4+988kxlncoOCpW1B26o0eX/tgwGTkSuOsuJnyygiN9smv1aiAjQyc0y0VgDHLi\nBJCaCixaxKZzlBQc6VOwXHMNUL068O67tiPxxqxZQIMGTPhkDZM+2Xf33VryiILXXktoQw1RsrC8\nQ/bt3w/Uqwds2QKcf77taNyzd6/uwM3L0yZrREnA8g4FT/XqWtcP+/LNN94AsrKY8MkqjvTJH5Yu\n1dYMmzaFc0I3P193IL/5JtC6te1oKEQ40qdgatVKR8DvvGM7Ene8/TZwzjn67ySyiEmf/EFEe8uP\nGGE7Ene8/DIweLD+O4ksYnmH/OObb7QJWW6u9pkPi61bdYS/axdQubLtaChkWN6h4Dr7bOC224B/\n/ct2JMk1YoT22WHCJx/gSJ/8JTcXSE/XHboVKtiOxrkjR/SQlI8/Bi691HY0FEIc6VOwNW2qzdem\nTLEdSXKMGwe0acOET77BpE/+8+ijwLBhQNDv/IwBhg/XCVwin2DSJ//p2hX49lttShZkixdreadT\nJ9uREH0zjoY+AAAHbElEQVSPSZ/8p1w54JFHgL/+1XYkzjz7LPDYY+HcbEaBxYlc8qdjx4C6dYGF\nC4HGjW1HE7/Vq4Fu3XS5ZqVKtqOhEONELoXDGWcADzwAPP+87UgS8+yzwJAhTPjkOxzpk3/t36+9\n59evBy680HY0Zbdli/bX2bZN9x4QuYgjfQqP6tX1OMUXXrAdSXyGDQN+9SsmfPIljvTJ33bvBq6+\nWkf7NWvajqZ0e/cCTZoAn34KXHCB7WgoAuId6TPpk/89/LD+98UX7cZRFo88oufgvvSS7UgoIpj0\nKXw++0xPnFq9Wg8V96tdu4BmzYBPPgEuush2NBQRTPoUTr/7HXDwIPCPf9iOpHj33KPdQf/8Z9uR\nUIQw6VM47d8PXH45sGwZcNlltqP5qdxc3Xm7ebMelkLkEa7eoXCqXl172Pzxj7YjKdrvf69/mPDJ\n5zjSp+A4dAi44gogOxto2dJ2ND9YsgQYOBDYuJGbschzHOlTeJ17ru50vf9+4NQp29Go/Hzg8ce1\njs+ETwHApE/BMnCgtmjwy+la//63/rd/f7txEJURyzsUPGvX6qTpunV2N0Dt3Qtcc402hWvSxF4c\nFGlcvUPRMGSIHqReMNK2IStL9w/86U/2YqDIY9KnaPj6a6BRI2DsWKB9e++vP20a8MQTumHsjDO8\nvz5RDCdyKRrOOUfr+nfeqWv4vXToEPDgg3p9JnwKGI70KdgefRTYtAmYMQOQMg92EmcM0Lu3tnp+\n+WX3r0dUCo70KVqeeUZ783jV4OzZZ4E9e4J7uAtFHkf6FHzbtgGtWgFz5gDXXuvedebNA+6+W1tB\n1Krl3nWI4sCRPkXPZZcBI0YAPXvqmbRu2L5d5w/Gj2fCp0BLsR0AUVJkZQFffKHr9xcvTm4L5j17\ngC5dgP/5H+DGG5P3vEQWMOlTeNx3H3D0KNCxoyb+ZJyru3Ur0LmzHn/44IPOn4/IsoTLOyLSR0TW\nicgpEWlewuPSRWSjiGwWkd8mej2iMhkyRFs1dOyobY6dWLdO9wA8/jjw2GPJiY/IMic1/VwAmQAW\nF/cAESkPYDiAdACNAfQXkUYOrhkJOTk5tkPwjYR+Fn/4gzZla9MGGD1al1nGwxit3XfsqKt17rsv\n/hhcwNfFD/izSFzCSd8Ys9EYs6mUh10HYIsxZocx5gSA8QB6JHrNqOAL+gcJ/SxEgAce0J44w4Zp\nM7TPPy/b927ZAtxyiy4FnTYNGDAg/uu7hK+LH/BnkTi3V+9cAiDvtM93x75G5L6mTYGPP9bzahs2\n1E1Vc+b8tC3z119rgv/5z3Xp5803AytWAK1b24mbyEUlJn0RmS8iuUX86V7G5+fCe7KrcmXghReA\nnTt1Zc+TTwJVqwK1a2uztGbN9FzbESOAxo21l86jjwIVKtiOnMgVjjdnici7AB4xxqws4u9aARhq\njEmPff4EgHxjzF+KeCzfIIiIEhDP5qxkLdks7oLLATQQkboA9gLoB6DI0ybiCZqIiBLjZMlmpojk\nAWgFYJaIzIl9/WIRmQUAxpiTAAYDeBvAegATjDEbnIdNRESJ8E3vHSIicp/13jvcvKVEJFVE3o1t\nePtERB6yHZNtIlJeRFaJyEzbsdgkIlVFZLKIbBCR9bG5skgSkSdivyO5IjJWRCJzGr2IjBSRfSKS\ne9rXqsUW3GwSkXkiUrW057Ga9Ll560dOABhijLkSWjJ7IMI/iwK/hpYFo347+jcAs40xjQBcBSCS\nJdLY3ODPATQ3xjQFUB7AbTZj8tgoaK483e8AzDfGNATwTuzzEtke6XPzVowx5jNjzOrYx4ehv9gX\n243KHhGpBaALgH+j+IUCoSci5wK4wRgzEtB5MmPMIcth2fI1dHBURURSAFQBsMduSN4xxiwBcKDQ\nlzMAjI59PBpAz9Kex3bS5+atIsRGNM0AfGQ3EqteAPAYgHzbgVh2KYAvRGSUiKwUkX+JSBXbQdlg\njPkKwHMAdkFXAx40xiywG5V1NY0x+2If7wNQs7RvsJ30o37b/hMichaAyQB+HRvxR46IdAPwuTFm\nFSI8yo9JAdAcwCvGmOYAvkUZbuHDSETqAXgYQF3oXfBZInKH1aB8JHYKVak51XbS3wPg9MbnqdDR\nfiSJSAUAUwD8xxgz3XY8FrUBkCEi2wGMA9BBRN6wHJMtuwHsNsZ8HPt8MvRNIIpaAPjAGLM/thx8\nKvS1EmX7RORCABCRiwCU2mTKdtL/fvOWiFSEbt7KthyTFSIiAF4DsN4Y86LteGwyxvzeGJNqjLkU\nOlG30Bgz0HZcNhhjPgOQJyINY1/qBGCdxZBs2giglYhUjv2+dIJO9EdZNoC7Yh/fBaDUwaLVQ1SM\nMSdFpGDzVnkAr0V481ZbAAMArBWRVbGvPWGMmWsxJr+IehnwQQBjYgOjrQDusRyPFcaYNbE7vuXQ\nuZ6VAP5pNyrviMg4AO0BnB/bGPskgGcBTBSRewHsANC31Ofh5iwiouiwXd4hIiIPMekTEUUIkz4R\nUYQw6RMRRQiTPhFRhDDpExFFCJM+EVGEMOkTEUXI/wNNTdlKtx3QdQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10823e438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, color=\"r\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x108850860>]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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J0BJYGzZS/jjn5gNbdvv2YGB86vZ44Iy6nid00dfirWqkejQ9gFfDJgnqbuBa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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10870bcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, linestyle=\"dashed\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Drawing several items in a single plot\n",
    "\n",
    "Up to now, we have used a single plot command (`plt.scatter` or `plt.plot`) at a time. However, it is often the case that we want to draw several items in the same plot (_eg._ a scatter plot containing raw data and a fitted regression line).\n",
    "\n",
    "To do so, we need to encapsulate our plot calls between the creation of a new figure (`plt.figure()`) and a command to either show the plot in a new window or save the figure to a file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bCPxLnf9EMohKKBnCK5UMA/4HuBc4DDiWCRN2UVi4jocfngloWqBIutCemN3O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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1087aacf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.randn(100)\n",
    "y = 2.3 * x + 0.3 * np.random.randn(100)\n",
    "\n",
    "xx = np.linspace(-2.5, 2.5, 10)\n",
    "yy = 2.3 * xx\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xx, yy)\n",
    "plt.show()\n",
    "# Alternatively, you could use plt.savefig(\"regression.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tuning plots\n",
    "\n",
    "`matplotlib` also makes it easy to set the title of a plot, change x-axis (or y-axis) limits, add a legend, _etc._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10891d8d0>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BX//61+y33/vYeee3MWPG8TzzzDNlvb4kbrnlFl566SUee+wxPve5z3HFFVfw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\nmRXlIGFmZkX9f96EXrgsxCzWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108934c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.scatter(x, y, label=\"Data\")\n",
    "plt.title(\"This is a scatter plot\")\n",
    "plt.xlim(-1, 5)\n",
    "plt.ylim(-2, 2)\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.xlabel(\"x-axis\")\n",
    "plt.ylabel(\"y-axis\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common API for `sklearn` models\n",
    "\n",
    "`sklearn` models share a very simple common API that makes them very easy-to-use. Using a model consists in:\n",
    "1. Building it (at this step, hyper parameters of the models are passed);\n",
    "2. Fitting it to some data;\n",
    "3. Predicting output of the (already fitted) model for some new data.\n",
    "\n",
    "In the following, we give examples of these three steps for some standard models (that will be considered in more details in the following sections of this tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  1.  1.  1.  0.  1.  1.  0.  1.]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "\n",
    "n_samples = 1000\n",
    "d = 20\n",
    "\n",
    "X_train = np.random.randn(n_samples, d)\n",
    "X_test = np.random.randn(10, d)\n",
    "y_train = np.array(np.hstack((np.zeros((n_samples // 2, )), np.ones((n_samples // 2, )))))\n",
    "\n",
    "# Step 1\n",
    "support_vector_classifier = SVC(kernel=\"linear\")\n",
    "# Step 2\n",
    "support_vector_classifier.fit(X_train, y_train)\n",
    "# Step 3\n",
    "y_predicted = support_vector_classifier.predict(X_test)\n",
    "print(y_predicted)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 3 0 2 4 4 3 2 1 4]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "n_samples = 1000\n",
    "d = 20\n",
    "\n",
    "X_train = np.random.randn(n_samples, d)\n",
    "X_test = np.random.randn(10, d)\n",
    "\n",
    "# Step 1\n",
    "kmeans_model = KMeans(n_clusters=5)\n",
    "# Step 2\n",
    "kmeans_model.fit(X_train)  # Unsupervised machine learning: no need to pass y for fitting\n",
    "# Step 3\n",
    "assign_test = kmeans_model.predict(X_test)\n",
    "print(assign_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.33472163  0.79796058]\n",
      " [-0.46399731  0.78611098]\n",
      " [-0.87449232 -1.83561782]\n",
      " [-0.75057156 -1.15396323]\n",
      " [ 0.32040141  0.46079091]\n",
      " [ 1.5839373   0.647358  ]\n",
      " [-0.27961775  0.91918918]\n",
      " [ 1.83052297  0.99542658]\n",
      " [ 1.78791687 -0.28391957]\n",
      " [ 0.94153714  0.06447396]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "n_samples = 1000\n",
    "d = 20\n",
    "\n",
    "X_train = np.random.randn(n_samples, d)\n",
    "X_test = np.random.randn(10, d)\n",
    "\n",
    "# Step 1\n",
    "pca_model = PCA(n_components=2)\n",
    "# Step 2\n",
    "pca_model.fit(X_train)  # Unsupervised machine learning: no need to pass y for fitting\n",
    "# Step 3\n",
    "X_transformed = pca_model.transform(X_test)\n",
    "print(X_transformed)"
   ]
  }
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