Numpy (1).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2]\n",
      "[[0]\n",
      " [1]\n",
      " [2]]\n"
     ]
    }
   ],
   "source": [
    "a = np.arange(3)\n",
    "b = np.arange(3)[:, np.newaxis]\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [1, 2, 3],\n",
       "       [2, 3, 4]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.  1.]\n",
      " [ 1.  1.  1.]]\n",
      "[0 1 2]\n"
     ]
    }
   ],
   "source": [
    "#example 1\n",
    "M = np.ones((2,3))\n",
    "a = np.arange(3)\n",
    "print(M)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2.,  3.],\n",
       "       [ 1.,  2.,  3.]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0]\n",
      " [1]\n",
      " [2]]\n",
      "[0 1 2]\n"
     ]
    }
   ],
   "source": [
    "#example 2, both arrays need broadcasting\n",
    "a = np.arange(3).reshape((3,1))\n",
    "b = np.arange(3)\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [1, 2, 3],\n",
       "       [2, 3, 4]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.]\n",
      " [ 1.  1.]\n",
      " [ 1.  1.]]\n",
      "[0 1 2]\n"
     ]
    }
   ],
   "source": [
    "#example 3, two arrays are not compatible\n",
    "M = np.ones((3,2))\n",
    "a = np.arange(3)\n",
    "print(M)\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (3,2) (3,) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-9e16e9f98da6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mM\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (3,2) (3,) "
     ]
    }
   ],
   "source": [
    "M + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M_transposed = M.reshape(2,3)\n",
    "M_transposed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2.,  3.],\n",
       "       [ 1.,  2.,  3.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M_transposed + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1],\n",
       "       [2]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#or \n",
    "a[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.],\n",
       "       [ 1.,  1.],\n",
       "       [ 1.,  1.]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.],\n",
       "       [ 2.,  2.],\n",
       "       [ 3.,  3.]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M + a[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.42018313,  0.12159042,  0.66713412],\n",
       "       [ 0.87872015,  0.72984238,  0.03229245],\n",
       "       [ 0.45284011,  0.83872328,  0.01890434],\n",
       "       [ 0.193342  ,  0.86088328,  0.51583931],\n",
       "       [ 0.56127677,  0.23531122,  0.91229955],\n",
       "       [ 0.07741292,  0.7812319 ,  0.62819586],\n",
       "       [ 0.12405475,  0.53199737,  0.19088382],\n",
       "       [ 0.77323554,  0.84945991,  0.0080845 ],\n",
       "       [ 0.09121972,  0.00631892,  0.14465718],\n",
       "       [ 0.48550814,  0.38278739,  0.60365558]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#broadcasting in practice\n",
    "#centering an array\n",
    "X = np.random.random((10,3))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.42018313,  0.12159042,  0.66713412])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.40577932,  0.53381461,  0.37219467])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xmean = X.mean(0)\n",
    "Xmean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#now we can center the array by subtracting the mean\n",
    "#broadcasting operation\n",
    "X_centered = X- Xmean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  5.55111512e-18,  -3.33066907e-17,  -1.11022302e-17])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_centered.mean(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#mean is  zero, it just looks weird because\n",
    "#machine is so precise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Plotting a two-dimensional function\n",
    "#z=f(x,y)\n",
    "#x and y have 50 steps from 0 to 5\n",
    "x = np.linspace(0,5,50)\n",
    "y = np.linspace(0,5,50)[:, np.newaxis]\n",
    "#print(x)\n",
    "#print(y)\n",
    "z = np.sin(x) ** 10 + np.cos(10 + y*x) * np.cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
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p1BpEzyWyYpOeTADshILuf6iyVbEsD7iu0JSPrZH5IElBe0YlFOXYiuQcywmF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\nDh/YHMcZOHxgcxxn4PCBzXGcgeP/A7LhrxdHzOurAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f45a72c6cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "plt.imshow(z, origin='lower', extent=[0, 5, 0, 5],\n",
    "           cmap='viridis')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([1,2,3,4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x < 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True, False,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x != 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True, False, False], dtype=bool)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x == 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#It is also possible to do an \n",
    "#element-wise comparison of two arrays\n",
    "(2 * x) == (x ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 0, 3, 3],\n",
       "       [7, 9, 3, 5],\n",
       "       [2, 4, 7, 6]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = np.random.RandomState(0)\n",
    "x = rng.randint(10, size=(3,4))\n",
    "x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True,  True],\n",
       "       [False, False,  True,  True],\n",
       "       [ True,  True, False, False]], dtype=bool)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x < 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5 0 3 3]\n",
      " [7 9 3 5]\n",
      " [2 4 7 6]]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(x < 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(x < 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 2, 2])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how many values less than 6 in each row?\n",
    "np.sum(x < 6, axis =1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#are there any values greater than 8?\n",
    "np.any(x > 8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any(x < 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 0, 3, 3],\n",
       "       [7, 9, 3, 5],\n",
       "       [2, 4, 7, 6]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 3, 3, 2, 4])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[x < 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'str' object cannot be interpreted as an integer",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-59-6edf144c59d5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mbin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'I'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'str' object cannot be interpreted as an integer"
     ]
    }
   ],
   "source": [
    "bin('I')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b11000'"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(24)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[51 92 14 71 60 20 82 86 74 74]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "rand = np.random.RandomState(42)\n",
    "\n",
    "x = rand.randint(100, size = 10)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[71, 86, 14]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#accessing three different elements in array\n",
    "[x[3], x[7], x[2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([71, 86, 60])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#alternatively, we can pass a single list or array\n",
    "#of indices to obtain the same result\n",
    "ind = [3,7,4]\n",
    "x[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[71, 86],\n",
       "       [60, 20]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind = np.array([[3, 7],\n",
    "                [4, 5]])\n",
    "x[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "data type not understood",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-296393729f2b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m ind = np.array([3, 7],\n\u001b[0;32m----> 2\u001b[0;31m                 [4, 5])\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mind\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: data type not understood"
     ]
    }
   ],
   "source": [
    "ind = np.array([3, 7],\n",
    "                [4, 5])\n",
    "x[ind]\n",
    "#python does not recognize the data type as array\n",
    "#Unless we place double brackets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#fancy indexing also works in multiple dimensions\n",
    "X = np.arange(12).reshape((3,4))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# first index refers to the row, second to the column\n",
    "row_index = np.array([0,1,2])\n",
    "col_index = np.array([2,1,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2]\n",
      "[2 1 3]\n"
     ]
    }
   ],
   "source": [
    "print(row_index)\n",
    "print(col_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  5, 11])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Like with standard indexing, the first index \n",
    "#refers to the row, and the second to the column:\n",
    "X[row_index, col_index]\n",
    "#first value = X[0,2]\n",
    "#second value = X[1,1]\n",
    "#third value = X[2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  1,  3],\n",
       "       [ 6,  5,  7],\n",
       "       [10,  9, 11]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#broadcasting example\n",
    "#combine column vector and a row vector within indices\n",
    "X[row_index[:, np.newaxis], col_index]\n",
    "#newaxis expans dimensions of tuple by 1\n",
    "#the added dimension is the position of the newaxis\n",
    "#object in the selection tuple\n",
    "#think of broadcasting like legos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3]],\n",
       "\n",
       "       [[ 4,  5,  6,  7]],\n",
       "\n",
       "       [[ 8,  9, 10, 11]]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row_index[:, np.newaxis]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  5, 11])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row_index, col_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 3])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "col_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [2, 1, 3],\n",
       "       [4, 2, 6]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_index[:, np.newaxis] * col_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1],\n",
       "       [2]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_index[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6, 4, 5])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#We can combine fancy and simple indices:\n",
    "X[1,[2,0,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[2,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6,  4,  5],\n",
       "       [10,  8,  9]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#We can also combine fancy indexing with slicing:\n",
    "#slicing is like broadcasting but it slices out anything\n",
    "#above the explcit selection\n",
    "X[1:, [2, 0, 1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3]],\n",
       "\n",
       "       [[ 4,  5,  6,  7]],\n",
       "\n",
       "       [[ 8,  9, 10, 11]]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row_index[:, np.newaxis]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3],\n",
       "       [ 7],\n",
       "       [11]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row_index[:, np.newaxis], 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  7, 11])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[row_index, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  2],\n",
       "       [ 4,  6],\n",
       "       [ 8, 10]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = np.array([1,0,1,0], dtype = bool)\n",
    "X[row_index[:, np.newaxis], mask]\n",
    "#only returns 1st and 3rd column from matrix X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Selecting random points\n",
    "#common use of fancy indexing is selecting subsets of rows \n",
    "#from a matrix\n",
    "rand = np.random.RandomState(42)\n",
    "mean = [0, 0]\n",
    "cov = [[1, 2],\n",
    "       [2, 5]]\n",
    "X = rand.multivariate_normal(mean, cov, 100)\n",
    "X.shape\n",
    "#shape of this matrix is 100 rows and 2 columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda/2.7/envs/fodl/lib/python3.6/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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Wqa0N3dp2ziRhebio5HaWAMKHrmkPZJNn9B4ZUP/pMVeSaoQxfWWYunSjmEgF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\n8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0784cf59b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set()  # for plot styling\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([72, 55, 29, 40, 92, 10,  0, 95, 33, 46, 68, 86, 13, 67,  3,  4, 88,\n",
       "       48, 83, 98])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let's use fancy indexing to select 20 random points. \n",
    "#We'll do this by first choosing 20 random indices with \n",
    "#no repeats, and use these indices to select a portion \n",
    "#of the original array:\n",
    "\n",
    "indices = np.random.choice(X.shape[0], 20, replace=False)\n",
    "indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 2)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selection = X[indices] #fancy indexing here\n",
    "selection.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.53929105, -0.4557248 ],\n",
       "       [ 1.78285987,  4.27550608],\n",
       "       [-0.67937246, -0.58422777],\n",
       "       [ 0.0662893 ,  0.54657238],\n",
       "       [-0.06678347,  0.61159902],\n",
       "       [-1.26768205, -3.3048337 ],\n",
       "       [-0.40599258, -1.129809  ],\n",
       "       [ 0.0847964 ,  1.13167598],\n",
       "       [-0.31750674,  0.31968711],\n",
       "       [ 0.77400336,  1.51395046],\n",
       "       [ 0.84687929,  1.6959506 ],\n",
       "       [-0.05932052,  0.22604784],\n",
       "       [ 0.919606  ,  2.62677788],\n",
       "       [ 0.25630301,  2.29640712],\n",
       "       [-1.75268695, -3.40069525],\n",
       "       [ 0.22610904,  1.13313826],\n",
       "       [-0.56825559,  0.20140359],\n",
       "       [-0.37348099, -0.61909868],\n",
       "       [-1.48535581, -1.5328922 ],\n",
       "       [ 0.75774974,  1.99576056]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -4.05992582e-01,  -1.12980900e+00],\n",
       "       [ -1.18122448e+00,  -1.20321251e+00],\n",
       "       [  3.05929845e-01,   4.85151964e-01],\n",
       "       [ -1.75268695e+00,  -3.40069525e+00],\n",
       "       [  2.26109036e-01,   1.13313826e+00],\n",
       "       [  6.06369182e-01,   9.59802450e-01],\n",
       "       [  5.08636661e-01,  -8.42962089e-01],\n",
       "       [  1.80879440e+00,   3.75820034e+00],\n",
       "       [  8.15476694e-01,   2.30887376e+00],\n",
       "       [  1.37937009e+00,   1.80142746e+00],\n",
       "       [ -1.26768205e+00,  -3.30483370e+00],\n",
       "       [  4.82839600e-01,  -3.76458413e-01],\n",
       "       [  4.60495820e-01,   1.23179700e+00],\n",
       "       [  9.19606001e-01,   2.62677788e+00],\n",
       "       [  6.66544157e-01,   1.29345291e+00],\n",
       "       [ -1.52931750e-01,   1.63568156e+00],\n",
       "       [  4.17238258e-01,  -1.37555797e-01],\n",
       "       [ -2.92735771e-01,  -2.02815831e+00],\n",
       "       [  5.56968489e-01,  -7.76490778e-01],\n",
       "       [  1.15174837e+00,   2.99364761e+00],\n",
       "       [ -7.47833961e-01,  -1.61994320e+00],\n",
       "       [  2.22072477e-01,   2.10218094e-01],\n",
       "       [  1.64144866e+00,   3.18365385e+00],\n",
       "       [  2.10315704e-02,   1.19499555e+00],\n",
       "       [  3.57224353e-01,  -1.04588503e+00],\n",
       "       [ -1.52049937e-01,  -7.83891078e-01],\n",
       "       [  3.91315999e-01,   1.60679404e+00],\n",
       "       [ -1.30890483e+00,  -2.15196545e+00],\n",
       "       [  8.93666346e-01,   1.82281235e+00],\n",
       "       [ -6.79372462e-01,  -5.84227775e-01],\n",
       "       [  5.13747885e-01,   1.03934128e+00],\n",
       "       [  1.47988870e+00,   2.27800264e+00],\n",
       "       [ -1.26968657e+00,  -1.59731090e+00],\n",
       "       [ -3.17506736e-01,   3.19687112e-01],\n",
       "       [ -8.72314798e-02,  -9.08868012e-01],\n",
       "       [ -9.22467115e-01,  -5.62273838e-01],\n",
       "       [ -5.65664260e-01,   3.27923760e-01],\n",
       "       [  2.10580041e+00,   5.97347277e+00],\n",
       "       [  3.40041545e-02,  -2.41549933e-01],\n",
       "       [  6.75833791e-01,  -5.19721987e-01],\n",
       "       [  6.62892964e-02,   5.46572381e-01],\n",
       "       [ -1.16706263e+00,  -3.37851008e+00],\n",
       "       [  9.38964800e-01,   1.72376364e+00],\n",
       "       [ -9.71528884e-01,  -1.98964057e+00],\n",
       "       [  2.93015666e-01,   1.26295906e+00],\n",
       "       [ -4.60372351e-01,  -6.29833900e-02],\n",
       "       [  7.74003359e-01,   1.51395046e+00],\n",
       "       [  9.22323621e-01,   6.42589030e-01],\n",
       "       [ -3.73480991e-01,  -6.19098683e-01],\n",
       "       [  8.50483915e-02,  -4.85903033e-02],\n",
       "       [  1.46860606e+00,   3.09022544e+00],\n",
       "       [  6.23645146e-01,   6.37233912e-01],\n",
       "       [ -5.61500084e-03,   4.23785685e-01],\n",
       "       [ -1.80941659e+00,  -4.17935640e+00],\n",
       "       [ -2.09456316e-01,  -5.86251957e-01],\n",
       "       [  1.78285987e+00,   4.27550608e+00],\n",
       "       [ -9.98287405e-01,   2.56115059e-01],\n",
       "       [  6.23211862e-02,   4.76849144e-01],\n",
       "       [  4.79303216e-01,  -1.07827667e-01],\n",
       "       [ -1.34358292e+00,  -2.42980966e+00],\n",
       "       [ -3.82810713e-01,  -1.90850070e+00],\n",
       "       [ -7.59547776e-01,  -3.35106320e+00],\n",
       "       [ -1.38043633e+00,  -9.61736037e-01],\n",
       "       [  1.13184900e+00,   2.11956895e+00],\n",
       "       [  1.00605935e-01,  -3.02073909e-01],\n",
       "       [  1.40638829e+00,   3.46953372e+00],\n",
       "       [  8.00204682e-01,   2.44447775e+00],\n",
       "       [  2.56303014e-01,   2.29640712e+00],\n",
       "       [  8.46879292e-01,   1.69595060e+00],\n",
       "       [ -2.80560525e-01,  -2.00961096e+00],\n",
       "       [ -7.10367454e-01,  -3.00137619e-01],\n",
       "       [  1.41446454e+00,   3.61466573e+00],\n",
       "       [ -5.39291055e-01,  -4.55724799e-01],\n",
       "       [  1.64811031e+00,   2.54963833e+00],\n",
       "       [ -5.95862244e-01,  -1.11708482e+00],\n",
       "       [ -3.64005207e-01,  -5.03793469e-01],\n",
       "       [  5.39381280e-01,   1.55357119e+00],\n",
       "       [  2.60679294e-03,  -7.66915048e-01],\n",
       "       [ -1.90507889e+00,  -4.08639424e+00],\n",
       "       [  8.49368730e-01,   2.76120601e+00],\n",
       "       [  5.99284208e-01,   2.29873430e+00],\n",
       "       [ -7.56341215e-01,  -2.71426936e+00],\n",
       "       [ -1.04800791e+00,  -2.08332405e+00],\n",
       "       [ -1.48535581e+00,  -1.53289220e+00],\n",
       "       [  5.15151400e-01,   4.27847352e-01],\n",
       "       [  1.13400126e+00,   1.85469452e+00],\n",
       "       [ -5.93205174e-02,   2.26047839e-01],\n",
       "       [ -5.72178291e-01,  -4.86023894e-01],\n",
       "       [ -5.68255591e-01,   2.01403592e-01],\n",
       "       [ -7.96452642e-01,   1.02148312e+00],\n",
       "       [ -2.50021261e-01,  -1.53138537e+00],\n",
       "       [  8.04741461e-01,   2.46504213e+00],\n",
       "       [ -6.67834661e-02,   6.11599016e-01],\n",
       "       [ -4.09344137e-01,  -1.06707361e+00],\n",
       "       [  1.36204232e+00,   1.64860222e+00],\n",
       "       [  8.47963951e-02,   1.13167598e+00],\n",
       "       [  2.78926763e-01,  -6.74989163e-01],\n",
       "       [ -3.07452890e-01,  -3.25192411e-01],\n",
       "       [  7.57749744e-01,   1.99576056e+00],\n",
       "       [  3.83617953e-01,  -3.11006470e-01]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f0772488f60>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda/2.7/envs/fodl/lib/python3.6/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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EXtLmjQTYsB8XGIWROwjEQKDieqNstl+pVKKtWQKvafOwB1ivojByB4EYCFRcb5TN9ivR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\n/j+8SWcPy6ibrwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0772576b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#lets see which were selected\n",
    "plt.scatter(X[:,0], X[:,1], alpha = 0.3)\n",
    "plt.scatter(selection[:, 0], selection[:,1],\n",
    "           facecolor='none', s=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#modifying values with fancy indexing\n",
    "x = np.arange(10)\n",
    "i = np.array([2,1,8,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 8, 4])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x[i] = 99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0 99 99  3 99  5  6  7 99  9]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0 89 89  3 89  5  6  7 89  9]\n"
     ]
    }
   ],
   "source": [
    "#We can use any assignment-type operator for this. For example:\n",
    "x[i] -= 10\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Notice, though, that repeated indices with these operations \n",
    "#can cause some potentially unexpected results. Consider \n",
    "#the following\n",
    "x = np.zeros(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x[[0,0]] = [4,6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 6.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Where did the 4 go? The result of this operation is to \n",
    "#first assign x[0] = 4, followed by x[0] = 6. \n",
    "#The result, of course, is that x[0] contains the value 6.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.,  0.,  1.,  1.,  1.,  0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = [2, 3, 3, 4, 4, 4]\n",
    "x[i] += 1\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.  0.  1.  2.  3.  0.  0.  0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "x= np.zeros(10)\n",
    "np.add.at(x,i,1)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#binning data\n",
    "np.random.seed(42)\n",
    "x = np.random.randn(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.        , -4.47368421, -3.94736842, -3.42105263, -2.89473684,\n",
       "       -2.36842105, -1.84210526, -1.31578947, -0.78947368, -0.26315789,\n",
       "        0.26315789,  0.78947368,  1.31578947,  1.84210526,  2.36842105,\n",
       "        2.89473684,  3.42105263,  3.94736842,  4.47368421,  5.        ])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#compute a histogram by hand\n",
    "bins= np.linspace(-5,5,20)\n",
    "bins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,\n",
       "        0.,  0.,  0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts = np.zeros_like(bins)\n",
    "counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11, 10, 11, 13, 10, 10, 13, 11,  9, 11,  9,  9, 10,  6,  7,  9,  8,\n",
       "       11,  8,  7, 13, 10, 10,  7,  9, 10,  8, 11,  9,  9,  9, 14, 10,  8,\n",
       "       12,  8, 10,  6,  7, 10, 11, 10, 10,  9,  7,  9,  9, 12, 11,  7, 11,\n",
       "        9,  9, 11, 12, 12,  8,  9, 11, 12,  9, 10,  8,  8, 12, 13, 10, 12,\n",
       "       11,  9, 11, 13, 10, 13,  5, 12, 10,  9, 10,  6, 10, 11, 13,  9,  8,\n",
       "        9, 12, 11,  9, 11, 10, 12,  9,  9,  9,  7, 11, 10, 10, 10])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#find the apppropriate bin for each x\n",
    "i = np.searchsorted(bins,x)\n",
    "i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# add 1 to each of these bins\n",
    "np.add.at(counts, i, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f0772401048>]"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda/2.7/envs/fodl/lib/python3.6/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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T5GwA0LTG/RF0a2tr3HfffXH77bdHo9GIm266KRYvXlzkbADQtCb0PeBly5bFsmXLipoF\nAGYMV8ICgAQCDAAJBBgAEggwACQQYABIIMAAkECAASCBAANAgpbR0dHp/f+GAoAm5AQMAAkEGAAS\nCDAAJBBgAEggwACQQIABIIEAT6GdO3fGpz/96fjb3/6WPUrp/PSnP42vfOUrsWbNmrjjjjvi73//\ne/ZIpXHo0KFYuXJlLF++PPr6+rLHKZ1Tp07Ft771rfjqV78aq1atit27d2ePVFqNRiPWrVsX3/3u\nd7NHmRYEeIqcOnUqDh8+HFdccUX2KKV0ww03xN69e+P3v/99fPKTn4xHH300e6RSaDQasX379tix\nY0fs27cv9u7dGydOnMgeq1QqlUrcfffd8dxzz8UTTzwRjz/+uD0cp1//+tfxqU99KnuMaUOAp8j9\n998fW7dujZaWluxRSumLX/xitLa2RkTE5z73uTh9+nTyROVw7NixuPrqq2PBggVx6aWXxqpVq+LA\ngQPZY5VKrVaLa6+9NiIi5syZEwsXLoz+/v7kqcrn9OnT8cILL8TNN9+cPcq0IcBTYP/+/VGr1aKz\nszN7lKbw29/+NpYuXZo9Rin09/fH5ZdffvbnHR0d4jEBJ0+ejFdffTWWLFmSPUrp/OQnP4mtW7fG\nJZfIzr+0Zg/QLG677bZ44403PnD7nXfeGY8++mjs3LkzYapyudAefvnLX46IiF/96ldRqVTia1/7\n2lSPxwz3zjvvxObNm+Oee+6JOXPmZI9TKn/4wx9i3rx58ZnPfCZefPHF7HGmDQEuyK5du857+2uv\nvRYnT56MtWvXRsQ/P4ZZv359PPXUU1GtVqdwwunvw/bwX5555pl44YUXYteuXT7Kv0gdHR3nfFzf\n398fHR0diROV03vvvRebN2+ONWvWxIoVK7LHKZ1XXnklDh48GIcOHYqRkZF4++2344c//GH87Gc/\nyx4tlf8ZwxTr6emJp59+OubNm5c9SqkcOnQoHnjggXjsscfs3Ufwj3/8I1auXBm7du2Kjo6OuPnm\nm+PnP/95LF68OHu00hgdHY277ror5s6dG/fee2/2OKX34osvxs6dO/1FynACpiR+/OMfx7vvvhu9\nvb0REbFkyZLYvn178lTTX2tra9x3331x++23R6PRiJtuukl8P6KXX345nn322bjmmmvOfpK1ZcuW\nWLZsWfJklJ0TMAAk8NfRACCBAANAAgEGgAQCDAAJBBgAEggwACQQYABIIMAAkOD/Ad4TwJ7VXEnT\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f07724a1828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the results\n",
    "plt.plot(bins,counts,linestyle='steps')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  0.,   0.,   0.,   0.,   1.,   3.,   7.,   9.,  23.,  22.,  17.,\n",
       "         10.,   7.,   1.,   0.,   0.,   0.,   0.,   0.]),\n",
       " array([-5.        , -4.47368421, -3.94736842, -3.42105263, -2.89473684,\n",
       "        -2.36842105, -1.84210526, -1.31578947, -0.78947368, -0.26315789,\n",
       "         0.26315789,  0.78947368,  1.31578947,  1.84210526,  2.36842105,\n",
       "         2.89473684,  3.42105263,  3.94736842,  4.47368421,  5.        ]),\n",
       " <a list of 1 Patch objects>)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda/2.7/envs/fodl/lib/python3.6/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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///7skQprbm4uRkZG4rvf/W72KIuCALfJyZMn49ixY3HTTTdlj1JIn/vc5+LQoUPxhz/8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f077243cac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x, bins, histtype='step')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def selection_sort(x):\n",
    "    for i in range(len(x)):\n",
    "        swap = i + np.argmin(x[i:])\n",
    "        (x[i], x[swap]) = (x[swap], x[i])\n",
    "    return x\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([4,3,2,1,5])\n",
    "#selection_sort(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 5)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i_length = range(len(x))\n",
    "i_length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 3, 2, 1, 5])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[0:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 3, 5])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmin(x[0:]) # returns the indices of min values in along axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0 + np.argmin(x[0:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "swap = 0 + np.argmin(x[0:])\n",
    "swap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x[0], x[swap]) #actual values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(x[0], x[swap]) = (x[swap], x[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 2, 4, 5])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "swap = 1 + np.argmin(x[1:])\n",
    "swap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(x[1], x[swap]) = (x[swap], x[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 4, 3, 5])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "swap = 2 + np.argmin(x[2:])\n",
    "swap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(x[2], x[swap]) = (x[swap], x[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6 3 7 4 6 9]\n",
      " [2 6 7 4 3 7]\n",
      " [7 2 5 4 1 7]\n",
      " [5 1 4 0 9 5]]\n"
     ]
    }
   ],
   "source": [
    "#sorting along rows or columns\n",
    "import numpy as np\n",
    "rand = np.random.RandomState(42)\n",
    "X = rand.randint(0,10,(4,6))\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 4, 0, 1, 5],\n",
       "       [5, 2, 5, 4, 3, 7],\n",
       "       [6, 3, 7, 4, 6, 7],\n",
       "       [7, 6, 7, 4, 9, 9]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sort each column of X\n",
    "np.sort(X, axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4, 6, 6, 7, 9],\n",
       "       [2, 3, 4, 6, 7, 7],\n",
       "       [1, 2, 4, 5, 7, 7],\n",
       "       [0, 1, 4, 5, 5, 9]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sort each row of X\n",
    "np.sort(X, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 3, 4, 6, 5, 7])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#partial sorts: partitioning\n",
    "x = np.array([7,2,3,1,6,5,4])\n",
    "np.partition(x,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 4, 6, 7, 6, 9],\n",
       "       [2, 3, 4, 7, 6, 7],\n",
       "       [1, 2, 4, 5, 7, 7],\n",
       "       [0, 1, 4, 5, 9, 5]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.partition(X, 2, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.23089383,  0.24102547],\n",
       "       [ 0.68326352,  0.60999666],\n",
       "       [ 0.83319491,  0.17336465],\n",
       "       [ 0.39106061,  0.18223609],\n",
       "       [ 0.75536141,  0.42515587],\n",
       "       [ 0.20794166,  0.56770033],\n",
       "       [ 0.03131329,  0.84228477],\n",
       "       [ 0.44975413,  0.39515024],\n",
       "       [ 0.92665887,  0.727272  ],\n",
       "       [ 0.32654077,  0.57044397]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#example: k-Nearest Neighbors\n",
    "X = rand.rand(10,2)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda/2.7/envs/fodl/lib/python3.6/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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YAwBgGGEMAIBhhDEAAIYRxgAAGEYYAwBgGGEMAIBhlukGAACpdeKzCfUNhDR5IaLVuZaq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\njDAGAMCw/weMoJ45CpXJ8gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f38802f0be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn; seaborn.set() # Plot styling\n",
    "plt.scatter(X[:, 0], X[:, 1], s = 100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#using broadcasting and math we can compute the squared difference between points\n",
    "#or k nearest neighbors\n",
    "dis_sq = np.sum((X[:, np.newaxis, :] - X[np.newaxis, :, :]) **2, axis = -1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.23089383,  0.24102547]],\n",
       "\n",
       "       [[ 0.68326352,  0.60999666]],\n",
       "\n",
       "       [[ 0.83319491,  0.17336465]],\n",
       "\n",
       "       [[ 0.39106061,  0.18223609]],\n",
       "\n",
       "       [[ 0.75536141,  0.42515587]],\n",
       "\n",
       "       [[ 0.20794166,  0.56770033]],\n",
       "\n",
       "       [[ 0.03131329,  0.84228477]],\n",
       "\n",
       "       [[ 0.44975413,  0.39515024]],\n",
       "\n",
       "       [[ 0.92665887,  0.727272  ]],\n",
       "\n",
       "       [[ 0.32654077,  0.57044397]]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#breaking down the operation above\n",
    "X[:, np.newaxis, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.23089383,  0.24102547],\n",
       "        [ 0.68326352,  0.60999666],\n",
       "        [ 0.83319491,  0.17336465],\n",
       "        [ 0.39106061,  0.18223609],\n",
       "        [ 0.75536141,  0.42515587],\n",
       "        [ 0.20794166,  0.56770033],\n",
       "        [ 0.03131329,  0.84228477],\n",
       "        [ 0.44975413,  0.39515024],\n",
       "        [ 0.92665887,  0.727272  ],\n",
       "        [ 0.32654077,  0.57044397]]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[np.newaxis, :, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10, 2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# for each pair of points, compute differences in their coordinates\n",
    "differences = X[:, np.newaxis, :] - X[np.newaxis, :, :]\n",
    "differences.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.        ,  0.        ],\n",
       "        [-0.45236969, -0.36897119],\n",
       "        [-0.60230109,  0.06766081],\n",
       "        [-0.16016678,  0.05878938],\n",
       "        [-0.52446758, -0.18413041],\n",
       "        [ 0.02295216, -0.32667486],\n",
       "        [ 0.19958053, -0.60125931],\n",
       "        [-0.21886031, -0.15412477],\n",
       "        [-0.69576504, -0.48624653],\n",
       "        [-0.09564694, -0.32941851]],\n",
       "\n",
       "       [[ 0.45236969,  0.36897119],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [-0.14993139,  0.436632  ],\n",
       "        [ 0.29220291,  0.42776057],\n",
       "        [-0.07209789,  0.18484078],\n",
       "        [ 0.47532186,  0.04229633],\n",
       "        [ 0.65195023, -0.23228812],\n",
       "        [ 0.23350939,  0.21484642],\n",
       "        [-0.24339535, -0.11727534],\n",
       "        [ 0.35672275,  0.03955268]],\n",
       "\n",
       "       [[ 0.60230109, -0.06766081],\n",
       "        [ 0.14993139, -0.436632  ],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [ 0.4421343 , -0.00887143],\n",
       "        [ 0.0778335 , -0.25179122],\n",
       "        [ 0.62525325, -0.39433567],\n",
       "        [ 0.80188162, -0.66892012],\n",
       "        [ 0.38344078, -0.22178558],\n",
       "        [-0.09346395, -0.55390734],\n",
       "        [ 0.50665414, -0.39707932]],\n",
       "\n",
       "       [[ 0.16016678, -0.05878938],\n",
       "        [-0.29220291, -0.42776057],\n",
       "        [-0.4421343 ,  0.00887143],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [-0.3643008 , -0.24291979],\n",
       "        [ 0.18311894, -0.38546424],\n",
       "        [ 0.35974732, -0.66004869],\n",
       "        [-0.05869353, -0.21291415],\n",
       "        [-0.53559826, -0.54503591],\n",
       "        [ 0.06451984, -0.38820789]],\n",
       "\n",
       "       [[ 0.52446758,  0.18413041],\n",
       "        [ 0.07209789, -0.18484078],\n",
       "        [-0.0778335 ,  0.25179122],\n",
       "        [ 0.3643008 ,  0.24291979],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [ 0.54741975, -0.14254445],\n",
       "        [ 0.72404812, -0.4171289 ],\n",
       "        [ 0.30560728,  0.03000564],\n",
       "        [-0.17129746, -0.30211612],\n",
       "        [ 0.42882064, -0.1452881 ]],\n",
       "\n",
       "       [[-0.02295216,  0.32667486],\n",
       "        [-0.47532186, -0.04229633],\n",
       "        [-0.62525325,  0.39433567],\n",
       "        [-0.18311894,  0.38546424],\n",
       "        [-0.54741975,  0.14254445],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [ 0.17662837, -0.27458445],\n",
       "        [-0.24181247,  0.17255009],\n",
       "        [-0.7187172 , -0.15957167],\n",
       "        [-0.11859911, -0.00274365]],\n",
       "\n",
       "       [[-0.19958053,  0.60125931],\n",
       "        [-0.65195023,  0.23228812],\n",
       "        [-0.80188162,  0.66892012],\n",
       "        [-0.35974732,  0.66004869],\n",
       "        [-0.72404812,  0.4171289 ],\n",
       "        [-0.17662837,  0.27458445],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [-0.41844084,  0.44713454],\n",
       "        [-0.89534557,  0.11501278],\n",
       "        [-0.29522748,  0.2718408 ]],\n",
       "\n",
       "       [[ 0.21886031,  0.15412477],\n",
       "        [-0.23350939, -0.21484642],\n",
       "        [-0.38344078,  0.22178558],\n",
       "        [ 0.05869353,  0.21291415],\n",
       "        [-0.30560728, -0.03000564],\n",
       "        [ 0.24181247, -0.17255009],\n",
       "        [ 0.41844084, -0.44713454],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [-0.47690473, -0.33212176],\n",
       "        [ 0.12321336, -0.17529374]],\n",
       "\n",
       "       [[ 0.69576504,  0.48624653],\n",
       "        [ 0.24339535,  0.11727534],\n",
       "        [ 0.09346395,  0.55390734],\n",
       "        [ 0.53559826,  0.54503591],\n",
       "        [ 0.17129746,  0.30211612],\n",
       "        [ 0.7187172 ,  0.15957167],\n",
       "        [ 0.89534557, -0.11501278],\n",
       "        [ 0.47690473,  0.33212176],\n",
       "        [ 0.        ,  0.        ],\n",
       "        [ 0.6001181 ,  0.15682802]],\n",
       "\n",
       "       [[ 0.09564694,  0.32941851],\n",
       "        [-0.35672275, -0.03955268],\n",
       "        [-0.50665414,  0.39707932],\n",
       "        [-0.06451984,  0.38820789],\n",
       "        [-0.42882064,  0.1452881 ],\n",
       "        [ 0.11859911,  0.00274365],\n",
       "        [ 0.29522748, -0.2718408 ],\n",
       "        [-0.12321336,  0.17529374],\n",
       "        [-0.6001181 , -0.15682802],\n",
       "        [ 0.        ,  0.        ]]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "differences\n",
    "#this makes sense, each dot will have 9 points it will calculate distance from,\n",
    "#in addition to itself which has a distance of 0 \n",
    "#notice there is repition here though\n",
    "# non repetitive distance would be = 10!\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10, 2)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# square the coordinate differences \n",
    "sq_differences = differences ** 2\n",
    "sq_differences.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sum of cordinate differences to get the squared distance\n",
    "dist_sq = sq_differences.sum(-1)\n",
    "dis_sq.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  0.34077808,  0.36734458,  0.02910959,  0.30897025,\n",
       "         0.10724327,  0.40134515,  0.07165428,  0.72052468,  0.11766489],\n",
       "       [ 0.34077808,  0.        ,  0.21312693,  0.26836165,  0.03936422,\n",
       "         0.22771985,  0.47899687,  0.10068562,  0.0729948 ,  0.12881554],\n",
       "       [ 0.36734458,  0.21312693,  0.        ,  0.19556145,  0.06945687,\n",
       "         0.54644225,  1.09046826,  0.19621568,  0.31554885,  0.41437041],\n",
       "       [ 0.02910959,  0.26836165,  0.19556145,  0.        ,  0.1917251 ,\n",
       "         0.18211523,  0.5650824 ,  0.04877736,  0.58392964,  0.15486817],\n",
       "       [ 0.30897025,  0.03936422,  0.06945687,  0.1917251 ,  0.        ,\n",
       "         0.3199873 ,  0.6982422 ,  0.09429615,  0.12061697,  0.20499577],\n",
       "       [ 0.10724327,  0.22771985,  0.54644225,  0.18211523,  0.3199873 ,\n",
       "         0.        ,  0.1065942 ,  0.08824681,  0.54201754,  0.01407328],\n",
       "       [ 0.40134515,  0.47899687,  1.09046826,  0.5650824 ,  0.6982422 ,\n",
       "         0.1065942 ,  0.        ,  0.37502203,  0.81487163,  0.16105668],\n",
       "       [ 0.07165428,  0.10068562,  0.19621568,  0.04877736,  0.09429615,\n",
       "         0.08824681,  0.37502203,  0.        ,  0.33774299,  0.04590943],\n",
       "       [ 0.72052468,  0.0729948 ,  0.31554885,  0.58392964,  0.12061697,\n",
       "         0.54201754,  0.81487163,  0.33774299,  0.        ,  0.38473676],\n",
       "       [ 0.11766489,  0.12881554,  0.41437041,  0.15486817,  0.20499577,\n",
       "         0.01407328,  0.16105668,  0.04590943,  0.38473676,  0.        ]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dis_sq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_sq.diagonal()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 3 7 5 9 4 1 2 6 8]\n",
      " [1 4 8 7 9 2 5 3 0 6]\n",
      " [2 4 3 7 1 8 0 9 5 6]\n",
      " [3 0 7 9 5 4 2 1 6 8]\n",
      " [4 1 2 7 8 3 9 0 5 6]\n",
      " [5 9 7 6 0 3 1 4 8 2]\n",
      " [6 5 9 7 0 1 3 4 8 2]\n",
      " [7 9 3 0 5 4 1 2 8 6]\n",
      " [8 1 4 2 7 9 5 3 0 6]\n",
      " [9 5 7 0 1 3 6 4 8 2]]\n"
     ]
    }
   ],
   "source": [
    "nearest = np.argsort(dist_sq, axis=1)\n",
    "print(nearest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Notice that the first column gives the numbers 0 through 9 in order: \n",
    "#this is due to the fact that each point's closest neighbor is itself, \n",
    "#as we would expect.\n",
    "\n",
    "K = 2\n",
    "nearest_partition = np.argpartition(dist_sq, K + 1, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda/2.7/envs/fodl/lib/python3.6/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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TNcWySjE2MJVKxcyZXhQsWIgFC7wIDAzQ6/FtbW3Zvt2Pzp27c+XKJRwda3Hs2BG99iGE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\n0oyFEEIIhUkzFkIIIRQmzVgIIYRQ2P8AX60UPeqf9jAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3849eb8d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], s=100)\n",
    "K =2\n",
    "for i in range(X.shape[0]):\n",
    "    for j in nearest_partition[i, : K+1]:\n",
    "        # plot a line from X[i] to X[j]\n",
    "        # use some zip magic to make it happen:\n",
    "        plt.plot(*zip(X[j], X[i]), color = 'black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 8])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nearest_partition[1,: 2+1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#structured data: numpy\n",
    "name = ['Alice', 'Bob', 'Cathy', 'Doug']\n",
    "age = [25, 45, 37, 19]\n",
    "weight = [55.0, 85.5, 68.0, 61.5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#creating a structured array using a compound data type\n",
    "x = np.zeros(4, dtype=int)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('name', '<U10'), ('age', '<i4'), ('weight', '<f8')]\n"
     ]
    }
   ],
   "source": [
    "# Use a compound data type for structured arrays\n",
    "data = np.zeros(4, dtype = {'names':('name', 'age', 'weight'),\n",
    "                           'formats': ('U10', 'i4', 'f8')})\n",
    "print(data.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([('', 0,  0.), ('', 0,  0.), ('', 0,  0.), ('', 0,  0.)], \n",
       "      dtype=[('name', '<U10'), ('age', '<i4'), ('weight', '<f8')])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " #Now that we've created an empty container array, \n",
    "#we can fill the array with our lists of values:\n",
    "\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('Alice', 25,  55. ) ('Bob', 45,  85.5) ('Cathy', 37,  68. )\n",
      " ('Doug', 19,  61.5)]\n"
     ]
    }
   ],
   "source": [
    "data['name'] = name\n",
    "data['age'] = age\n",
    "data['weight'] = weight\n",
    "print(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Alice', 'Bob', 'Cathy', 'Doug'], \n",
       "      dtype='<U10')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The handy thing with structured arrays is that you can now refer \n",
    "#to values either by index or by name:\n",
    "data['name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('Alice', 25,  55.)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#get first row of data\n",
    "data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('Bob', 45,  85.5)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Doug'"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the name from the last row\n",
    "data[-1]['name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Alice', 'Doug'], \n",
       "      dtype='<U10')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Using Boolean masking, this even allows you to do some more \n",
    "#sophisticated operations such as filtering on age:\n",
    "\n",
    "#get names where age is under 30\n",
    "data[data['age'] < 30]['name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25, 45, 37, 19], dtype=int32)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['age']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True], dtype=bool)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#let's break this down\n",
    "data['age'] <30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([('Alice', 25,  55. ), ('Doug', 19,  61.5)], \n",
       "      dtype=[('name', '<U10'), ('age', '<i4'), ('weight', '<f8')])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data['age'] <30]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Alice', 'Doug'], \n",
       "      dtype='<U10')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data['age'] < 30]['name']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])\n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "#more advanced compound types\n",
    "\n",
    "tp = np.dtype([('id', 'i8' ), ('mat', 'f8', (3,3))])\n",
    "X = np.zeros(1, dtype =tp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([(0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])], \n",
       "      dtype=[('id', '<i8'), ('mat', '<f8', (3, 3))])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.],\n",
       "        [ 0.,  0.,  0.]]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X['mat']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X['mat'][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0, [[ 0.,  0.,  0.], [ 0.,  0.,  0.], [ 0.,  0.,  0.]])\n",
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "print(X[0])\n",
    "print(X['mat'][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#RecordArrays: structured Arrays with a Twist\n",
    "data_rec = data.view(np.recarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "rec.array([('Alice', 25,  55. ), ('Bob', 45,  85.5), ('Cathy', 37,  68. ),\n",
       " ('Doug', 19,  61.5)], \n",
       "          dtype=[('name', '<U10'), ('age', '<i4'), ('weight', '<f8')])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_rec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25, 45, 37, 19], dtype=int32)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data['age']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([25, 45, 37, 19], dtype=int32)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_rec.age"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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