Chapter2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numpy version:  1.11.3\n",
      "Python 3.6.0 :: Anaconda custom (x86_64)\r\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "print(\"numpy version: \",numpy.__version__)\n",
    "!python --version"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Python lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], list, int)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# python list holds many python objects\n",
    "L = list(range(10))\n",
    "L, type(L), type(L[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(['0', '1', '2', '3', '4', '5', '6', '7', '8', '9'], list, str)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L2 = list(str(i) for i in L)\n",
    "L2, type(L2), type(L2[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[bool, str, float, int]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#because of python's dynamic typing, it can hold heterogenous lists\n",
    "L3 = [True, \"2\", 3.0, 4]\n",
    "[type(item) for item in L3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array('i', [0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#built-in array module in ptyhon since 3.3\n",
    "import array\n",
    "L  = list(range(10))\n",
    "A = array.array('i', L)\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Creating Numpy arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.np.array to create numpy array from python list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "Pylist = [1, 2, 3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "NumpyList = np.array(Pylist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NumpyList"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(list, numpy.ndarray)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(Pylist) , type(NumpyList)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  2.,  3.,  4.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# declare the type of list \n",
    "np.array([1,2,3,4], dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4],\n",
       "       [4, 5, 6],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# multidimensional numpy array\n",
    "np.array([range(i, i+3) for i in [2,4,6]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2.from scratch "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create zeros\n",
    "np.zeros(3, dtype=int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.,  1.,  1.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create 3x5 array filled with 1s\n",
    "np.ones((3,5), dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.,  5.,  5.,  5.],\n",
       "       [ 5.,  5.,  5.,  5.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create an array of 5s \n",
    "np.full((2,4), 5, dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 6, 8])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#array of linear sequence from 4 to 10 \n",
    "np.arange(4, 10, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.  ,  0.25,  0.5 ,  0.75,  1.  ])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# array of evenly spaced values\n",
    "np.linspace(0, 1, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.78772728,  0.43475258,  0.80173387,  0.36467609],\n",
       "       [ 0.90600859,  0.69279576,  0.63677792,  0.58005333],\n",
       "       [ 0.29011891,  0.63721852,  0.00373535,  0.36661782]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# uniformly distributed random values between 0 and 1\n",
    "np.random.random((3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.06895387,  1.33122329,  0.40084701],\n",
       "       [-0.45159799, -1.480771  ,  0.11710757]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# normally distributed values mean=0, std= 1\n",
    "np.random.normal(0,1, (2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 6, 2],\n",
       "       [4, 2, 2, 3, 5]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# random integer, interval [0, 10)\n",
    "np.random.randint(0, 10, (2,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.,  0.],\n",
       "       [ 0.,  1.,  0.],\n",
       "       [ 0.,  0.,  1.]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# identity matrix\n",
    "np.eye(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.41257038,  0.70840527,  0.55898304,  0.96145733],\n",
       "       [ 0.79404544,  0.83858273,  0.9691193 ,  0.23643289],\n",
       "       [ 0.76567086,  0.8344795 ,  0.54639659,  0.37024142]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.random_sample((3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  1.,  1.])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#creare an uninitialized array of three integers. the values will be whatever happens\n",
    "#already exists in that memory location\n",
    "np.empty(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basics of Numpy Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "a. Attributes of arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(0) #to generate the same random array each time this code run\n",
    "x1 = np.random.randint(10, size=6) #one dimensional array\n",
    "x2 = np.random.randint(10, size=(3,4)) #two dimensional array\n",
    "x3 = np.random.randint(10, size=(3,4,5)) #three dimensional array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 3, 3, 7, 9])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2, 4],\n",
       "       [7, 6, 8, 8],\n",
       "       [1, 6, 7, 7]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[8, 1, 5, 9, 8],\n",
       "        [9, 4, 3, 0, 3],\n",
       "        [5, 0, 2, 3, 8],\n",
       "        [1, 3, 3, 3, 7]],\n",
       "\n",
       "       [[0, 1, 9, 9, 0],\n",
       "        [4, 7, 3, 2, 7],\n",
       "        [2, 0, 0, 4, 5],\n",
       "        [5, 6, 8, 4, 1]],\n",
       "\n",
       "       [[4, 9, 8, 1, 1],\n",
       "        [7, 9, 9, 3, 6],\n",
       "        [7, 2, 0, 3, 5],\n",
       "        [9, 4, 4, 6, 4]]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x3 ndim: 3\n",
      "x3 shape: (3, 4, 5)\n",
      "x3 size: 60\n",
      "x3 data: <memory at 0x10db8bb88>\n",
      "x3 dtype: int64\n",
      "x3 item: <built-in method item of numpy.ndarray object at 0x112f9f260>\n",
      "x3 itemsize: 8 bytes\n",
      "x3 nbytes: 480 bytes\n"
     ]
    }
   ],
   "source": [
    "print(\"x3 ndim:\", x3.ndim)\n",
    "print(\"x3 shape:\", x3.shape)\n",
    "print(\"x3 size:\", x3.size)\n",
    "print(\"x3 data:\", x3.data)\n",
    "print(\"x3 dtype:\", x3.dtype)\n",
    "print(\"x3 item:\", x3.item)\n",
    "print(\"x3 itemsize:\", x3.itemsize, \"bytes\")\n",
    "print(\"x3 nbytes:\", x3.nbytes, \"bytes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "b. Array indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 3, 3, 7, 9])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2, 4],\n",
       "       [7, 6, 8, 8],\n",
       "       [1, 6, 7, 7]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2, 4]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# colon is for slicing. see the difference above and below.\n",
    "x2[0:1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[1,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[2,-3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# change the values in the array\n",
    "x2[2,0] = 7\n",
    "x2[2,1] = 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2, 4],\n",
       "       [7, 6, 8, 8],\n",
       "       [7, 7, 7, 7]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "c. Array slicing x[start : stop : step] default values 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(10)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:5] #first 5 elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6, 8])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[::2] #every other element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7, 9])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[1::2] #every other element starting from 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7, 9])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(1,10, 2) #example of arange method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[::-1] #all elements, reversed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5, 2, 4],\n",
       "       [7, 6, 8, 8],\n",
       "       [7, 7, 7, 7]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Multidimensional subarrays\n",
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 5, 2, 4])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[0] #first row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 7, 7, 7])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[2] #third row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True,  True]], dtype=bool)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[2:] == x2[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 8]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[1:2, 1:3] #second row intersection between second and third column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7, 7, 7, 7],\n",
       "       [8, 8, 6, 7],\n",
       "       [4, 2, 5, 3]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[::-1, ::-1] #can be reversed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 7, 7])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2[:,0] #first column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 5],\n",
       "       [7, 6]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# copying feature \n",
    "x2_sub = x2[:2 , :2]\n",
    "x2_sub"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[61,  5],\n",
       "       [ 7,  6]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2_sub[0,0] = 61\n",
    "x2_sub"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[61,  5,  2,  4],\n",
       "       [ 7,  6,  8,  8],\n",
       "       [ 7,  7,  7,  7]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# modifying subarray affects the original array as well\n",
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[61,  5],\n",
       "       [ 7,  6]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#use copy method to keep the original array not updated\n",
    "x2_sub_copy = x2[:2, :2].copy()\n",
    "x2_sub_copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[99,  5],\n",
       "       [ 7,  6]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2_sub_copy[0,0] = 99\n",
    "x2_sub_copy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[61,  5,  2,  4],\n",
       "       [ 7,  6,  8,  8],\n",
       "       [ 7,  7,  7,  7]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d. Reshaping of arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use reshape method \n",
    "grid = np.arange(1,10).reshape((3,3))\n",
    "grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# convert one dimensional array into two dimensional row or column matrix\n",
    "y = np.array([1,2,3])\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# row vector via reshape\n",
    "y.reshape((1,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#row vector via newaxis  \n",
    "y[np.newaxis, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# column vector via reshape\n",
    "y.reshape((3,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#column vector via newaxis \n",
    "y[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "e. Array concatination and splitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.array([1,2,3])\n",
    "y = np.array([1,2,3])\n",
    "z = np.array([61,61,61])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  1,  2,  3, 61, 61, 61])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use np.concatinate\n",
    "np.concatenate([x,y,z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# concat two dimensional arrays\n",
    "grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9],\n",
       "       [1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate([grid, grid])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 1, 2, 3],\n",
       "       [4, 5, 6, 4, 5, 6],\n",
       "       [7, 8, 9, 7, 8, 9]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate([grid, grid], axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# vertical stack with vstack\n",
    "np.vstack([x, grid])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[99],\n",
       "       [99],\n",
       "       [99]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = np.array([[99], [99], [99]])\n",
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[99,  1,  2,  3],\n",
       "       [99,  4,  5,  6],\n",
       "       [99,  7,  8,  9]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# horizontal stack with hstack\n",
    "np.hstack([k, grid])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# splitting of arrays\n",
    "sp = np.arange(10)\n",
    "sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0]), array([1, 2]), array([3, 4, 5, 6, 7, 8, 9]))"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x1, x2, x3 = np.split(sp, [1, 3])\n",
    "x1 , x2, x3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "four = np.arange(16).reshape((4,4))\n",
    "four"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0, 1, 2, 3],\n",
       "        [4, 5, 6, 7]]), array([[ 8,  9, 10, 11],\n",
       "        [12, 13, 14, 15]]))"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1, f2 = np.vsplit(four,[2] )\n",
    "f1, f2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introducing Ufuncs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "np.random.seed(0)\n",
    "\n",
    "def compute_reciprocal(values):\n",
    "    output = np.empty(len(values))\n",
    "    for i in range(len(values)):\n",
    "        output[i] = 1.0 / values[i]\n",
    "    return output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.16666667,  1.        ,  0.25      ,  0.25      ,  0.125     ])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values = np.random.randint(1,10, size=5)\n",
    "compute_reciprocal(values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.22 s ± 31.5 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "big_array = np.random.randint(1, 100 , size=1000000)\n",
    "%timeit compute_reciprocal(big_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.16666667  1.          0.25        0.25        0.125     ]\n",
      "[ 0.16666667  1.          0.25        0.25        0.125     ]\n"
     ]
    }
   ],
   "source": [
    "print(compute_reciprocal(values))\n",
    "print(1.0 / values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.78 µs ± 22.1 ns per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit (1.0 / values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x     =  [0 1 2 3 4 5 6]\n",
      "x + 2 =  [2 3 4 5 6 7 8]\n",
      "x * 2 =  [ 0  2  4  6  8 10 12]\n",
      "x / 2 =  [ 0.   0.5  1.   1.5  2.   2.5  3. ]\n",
      "x //2 = [0 0 1 1 2 2 3]\n"
     ]
    }
   ],
   "source": [
    "# array arithmetic\n",
    "x = np.arange(7)\n",
    "print(\"x     = \", x)\n",
    "print(\"x + 2 = \", x +2)\n",
    "print(\"x * 2 = \", x * 2)\n",
    "print(\"x / 2 = \", x / 2)\n",
    "print(\"x //2 =\", x // 2) #floor devision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0,   -3,  -12,  -33,  -72, -135, -228])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# more operations\n",
    "((x ** 2) + 2 ) * (-x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0,   -3,  -12,  -33,  -72, -135, -228])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# arithmetic operations implemented in numpy\n",
    "np.multiply(np.add( np.power(x, 2), 2 ), np.negative(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 2, 0, 1])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# absolute value\n",
    "z = np.array([-5, -2, 0, 1])\n",
    "abs(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 2, 0, 1])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.absolute(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 2, 0, 1])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.absolute(z) == np.abs(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  1.57079633,  3.14159265])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# trigonometric functions\n",
    "theta = np.linspace(0, np.pi, 3)\n",
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.00000000e+00   1.00000000e+00   1.22464680e-16]\n",
      "[  0.00000000e+00   1.63312394e+16  -1.22464680e-16]\n"
     ]
    }
   ],
   "source": [
    "print(np.sin(theta))\n",
    "print(np.tan(theta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6]\n",
      "[ 0.          0.84147098  0.90929743  0.14112001 -0.7568025  -0.95892427\n",
      " -0.2794155 ]\n",
      "[ 1.          0.54030231 -0.41614684 -0.9899925  -0.65364362  0.28366219\n",
      "  0.96017029]\n"
     ]
    }
   ],
   "source": [
    "print(x)\n",
    "print(np.sin(x))\n",
    "print(np.cos(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6]\n",
      "[ 0  1  4  9 16 25 36]\n",
      "[  0   1   8  27  64 125 216]\n"
     ]
    }
   ],
   "source": [
    "# Exponents and logarithms\n",
    "print(x)\n",
    "print(np.power(x, 2))\n",
    "print(np.power(x, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gamma(x) =  [  1.00000000e+00   2.40000000e+01   3.62880000e+05]\n",
      "ln|gamma(x) = [  0.           3.17805383  12.80182748]\n"
     ]
    }
   ],
   "source": [
    "from scipy import special\n",
    "#gamma functions\n",
    "x = [1, 5, 10]\n",
    "print(\"gamma(x) = \", special.gamma(x))\n",
    "print(\"ln|gamma(x) =\", special.gammaln(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Advanced Ufunc features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(4)\n",
    "np.multiply(x, 2, out=x)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  2.,  4.,  6.,  8.])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# x and y has to have same amount of elements\n",
    "x = np.arange(5)\n",
    "y = np.empty(5)\n",
    "np.multiply(x, 2, out=y)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.,   0.,   2.,   0.,   4.,   0.,   8.,   0.,  16.,   0.])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = np.zeros(10)\n",
    "np.power(2, x, out=k[::2])\n",
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15\n",
      "120\n"
     ]
    }
   ],
   "source": [
    "# aggregate\n",
    "x = np.arange(1, 6)\n",
    "print(np.add.reduce(x))\n",
    "print(np.multiply.reduce(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  6, 10, 15])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.accumulate(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Aggregations: Min. Max. Std. Median. Mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.random.randint(1, 1000, size=10000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "938 ms ± 61 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "6.35 ms ± 95.8 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "# summing all values in an array\n",
    "%timeit sum(x)   #python code\n",
    "%timeit np.sum(x)  #numpy code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 999\n",
      "1 999\n"
     ]
    }
   ],
   "source": [
    "# min and max\n",
    "print(min(x), max(x) ) # python code\n",
    "print(np.min(x) , np.max(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.28 s ± 22.3 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n",
      "15.4 ms ± 207 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "# again numpy operates much more quickly\n",
    "%timeit (min(x), max(x))\n",
    "%timeit (np.min(x) , np.max(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 2, 4, 2],\n",
       "       [4, 1, 4, 4],\n",
       "       [1, 4, 3, 3]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Multidimensional aggregation\n",
    "M = np.random.randint(1,5, size=(3,4))\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sum of all values\n",
    "M.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 3, 2])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# min of each column\n",
    "np.min(M, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 4, 4])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# max of each column\n",
    "np.max(M, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 13, 11])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sum of each row\n",
    "np.sum(M, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Other aggreagation functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n = [1,3,4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#product of elements\n",
    "np.prod(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.247219128924647"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 4)"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(n), np.max(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 2)"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# index of min and max\n",
    "np.argmin(n), np.argmax(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.0, 2.6666666666666665)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(n), np.mean(n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "order,name,height(cm)\r\n",
      "1,George Washington,189\r\n",
      "2,John Adams,170\r\n",
      "3,Thomas Jefferson,189\r\n"
     ]
    }
   ],
   "source": [
    "!head -4 data/president_heights.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>name</th>\n",
       "      <th>height(cm)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>order</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>George Washington</td>\n",
       "      <td>189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>John Adams</td>\n",
       "      <td>170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Thomas Jefferson</td>\n",
       "      <td>189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>James Madison</td>\n",
       "      <td>163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>James Monroe</td>\n",
       "      <td>183</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    name  height(cm)\n",
       "order                               \n",
       "1      George Washington         189\n",
       "2             John Adams         170\n",
       "3       Thomas Jefferson         189\n",
       "4          James Madison         163\n",
       "5           James Monroe         183"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "data = pd.read_csv('data/president_heights.csv', index_col='order')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 42 entries, 1 to 44\n",
      "Data columns (total 2 columns):\n",
      "name          42 non-null object\n",
      "height(cm)    42 non-null int64\n",
      "dtypes: int64(1), object(1)\n",
      "memory usage: 1008.0+ bytes\n"
     ]
    }
   ],
   "source": [
    "data.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>height(cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>42.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>179.738095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>7.015869</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>163.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>174.250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>182.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>183.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>193.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       height(cm)\n",
       "count   42.000000\n",
       "mean   179.738095\n",
       "std      7.015869\n",
       "min    163.000000\n",
       "25%    174.250000\n",
       "50%    182.000000\n",
       "75%    183.000000\n",
       "max    193.000000"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "heights = np.array(data['height(cm)'])\n",
    "len(heights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean height: 179.738095238\n",
      "Std of heigth: 7.01586885536\n",
      "min of height: 163\n",
      "max of heights: 193\n",
      "median of heights: 182.0\n"
     ]
    }
   ],
   "source": [
    "print(\"Mean height:\", np.mean(heights))\n",
    "print(\"Std of heigth:\",np.std(heights, ddof=1))\n",
    "print('min of height:', np.min(heights))\n",
    "print('max of heights:', np.max(heights))\n",
    "print('median of heights:', np.median(heights))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bG6vBgwdr5MiRie4TERHhwgoBAM5UbZenu0tIdwdr33V3CYDhlChRIsn1hp4S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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ca643c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,5) )\n",
    "plt.hist(heights)\n",
    "plt.title('Height distribution of US Presidents')\n",
    "plt.xlabel('height (cm)')\n",
    "plt.ylabel('number')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([0, 1, 2])\n",
    "b = np.array([5, 5, 5])\n",
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.]])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = np.ones((3, 3))\n",
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  2.,  3.],\n",
       "       [ 1.,  2.,  3.],\n",
       "       [ 1.,  2.,  3.]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(3)\n",
    "y = np.arange(3)[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2]\n",
      "[[0]\n",
      " [1]\n",
      " [2]]\n"
     ]
    }
   ],
   "source": [
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [1, 2, 3],\n",
       "       [2, 3, 4]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of M: (2, 3)\n",
      "[[ 1.  1.  1.]\n",
      " [ 1.  1.  1.]]\n",
      " \n",
      "shape of a: (3,)\n",
      "[0 1 2]\n",
      "\n",
      "shape of M + a: (2, 3)\n",
      "[[ 1.  2.  3.]\n",
      " [ 1.  2.  3.]]\n"
     ]
    }
   ],
   "source": [
    "#Broadcasting example 1\n",
    "M = np.ones((2,3))\n",
    "a = np.arange(3)\n",
    "\n",
    "print(\"Shape of M:\", M.shape)\n",
    "print(M)\n",
    "print(' ')\n",
    "print(\"shape of a:\",a.shape) \n",
    "print(a)\n",
    "print('')\n",
    "print(\"shape of M + a:\", (M+a).shape) \n",
    "print(M + a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0]\n",
      " [1]\n",
      " [2]]\n",
      "Shape of a: (3, 1)\n",
      " \n",
      "[0 1 2]\n",
      "Shape of b: (3,)\n",
      " \n",
      "[[0 1 2]\n",
      " [1 2 3]\n",
      " [2 3 4]]\n",
      "Shape of a + b: (3, 3)\n"
     ]
    }
   ],
   "source": [
    "# Broadcasting example 2\n",
    "a = np.arange(3).reshape((3,1))\n",
    "print(a)\n",
    "print('Shape of a:', a.shape)\n",
    "print(' ')\n",
    "b= np.arange(3)\n",
    "print(b)\n",
    "print('Shape of b:',b.shape)\n",
    "print(' ')\n",
    "print(a + b)\n",
    "print('Shape of a + b:',(a+b).shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.]\n",
      " [ 1.  1.]\n",
      " [ 1.  1.]]\n",
      "Shape of M: (3, 2)\n",
      "\n",
      "[0 1 2]\n",
      "Shape of a: (3,)\n",
      "\n",
      "M + a throws an error. These arrays are incompatible.\n"
     ]
    }
   ],
   "source": [
    "# Broadcasting example 3\n",
    "M = np.ones((3,2))\n",
    "print(M)\n",
    "print('Shape of M:', M.shape)\n",
    "print('')\n",
    "a = np.arange(3)\n",
    "print(a)\n",
    "print('Shape of a:', a.shape)\n",
    "print('')\n",
    "print(\"M + a throws an error. These arrays are incompatible.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 2, 2],\n",
       "       [1, 2, 3],\n",
       "       [0, 4, 0]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Broadcasting in practice\n",
    "X = np.random.randint(0, 5,size=(3, 3))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.33333333,  2.66666667,  1.66666667])"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#mean of each feature (row)\n",
    "Xmean = X.mean(axis=0)\n",
    "Xmean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.66666667,  0.66666667, -0.33333333],\n",
       "       [ 0.33333333,  0.66666667, -1.33333333],\n",
       "       [ 1.33333333, -1.33333333,  1.66666667]])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xcentered = Xmean - X\n",
    "Xcentered"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -7.40148683e-17,  -1.48029737e-16,   7.40148683e-17])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Xcentered.mean(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RVFQEAHj44Yfxj3/8A+vXr1f2W7NmDZxOJ2688UZyzJUrVyI7OxsjRoyA2+1GeXk5Nm7c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\nCGHy/wO+6Rbx5HnptwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11feae9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting two dimensional function z = f(x, y)\n",
    "x = np.linspace(0, 5, 50)\n",
    "y = np.linspace(0, 5, 50)[:,np.newaxis]\n",
    "\n",
    "z = np.sin(x) ** 10 + np.cos(10 + y * x) * np.cos(x)\n",
    "\n",
    "#plot the function\n",
    "plt.imshow(z, origin='lower', extent=[0,5,0,5], cmap='viridis')\n",
    "plt.colorbar();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(365,)"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rainfall = pd.read_csv('data/Seattle2014.csv')['PRCP']\n",
    "inches = rainfall / 254 #1/10mm = 1 inch\n",
    "inches.shape  # 365 days in a year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAgAYgUACABiBQAIAGIFAAgAYgUACABiBQAIAGIFAAgAYgUACABiBQAIAGIFAAgAYgUAC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\nAAAjEEgAACMQSAAAI/wbG+tq5lvDyosAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112fbd8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(inches, bins=40); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 4, 9, 2],\n",
       "       [2, 4, 1, 2],\n",
       "       [7, 4, 4, 1]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#working with 2-dimensional array\n",
    "f = np.random.randint(10, size=(3,4))\n",
    "f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(f < 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this code and cod above result the same. in this case, True=1 , False =0\n",
    "np.sum(f < 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 1])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# how many values less than 3 for each row\n",
    "np.sum( f < 3, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(False, False)"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.any() , np.all()\n",
    "np.any(f == 0 ) , np.all(f==0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True], dtype=bool)"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any(f > 5 , axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "29"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# go back to Seattlle rainy days data\n",
    "\n",
    "# how many days rained less than 4 inches and greater than 1 inch\n",
    "np.sum((inches > 0.5) & (inches < 1)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of days without rain: 215\n",
      "Number of days with rain: 150\n",
      "Days with more than 0.5 inches: 37\n",
      "Rainy days with < 0.1 inches: 75\n"
     ]
    }
   ],
   "source": [
    "# Other examples\n",
    "print(\"Number of days without rain:\", np.sum(inches == 0))\n",
    "print(\"Number of days with rain:\", np.sum(inches != 0))\n",
    "print(\"Days with more than 0.5 inches:\", np.sum(inches > 0.5) )\n",
    "print(\"Rainy days with < 0.1 inches:\", np.sum((inches < 0.2) & (inches != 0))) \n",
    "#0.2 equals 0.1 inches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 2, 2],\n",
       "       [1, 2, 3],\n",
       "       [0, 4, 0]])"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[False  True  True]\n",
      " [ True  True False]\n",
      " [ True False  True]]\n",
      "Return is one dimensional array\n",
      "[2 2 1 2 0 0]\n"
     ]
    }
   ],
   "source": [
    "# less than 3 of all values\n",
    "print(X < 3)\n",
    "print('Return is one dimensional array')\n",
    "print(X[X < 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 2, 1, 2, 0, 0])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lessThan3 = X[X < 3]\n",
    "lessThan3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1666666666666667, 0)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can do statisctics on this new array\n",
    "np.mean(lessThan3), np.min(lessThan3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# go back to Seattle rain data. \n",
    "# rainy days mask\n",
    "rainy = inches > 0\n",
    "#summer days june 21th 172. day\n",
    "summer = (np.arange(365) - 172 < 90) & (np.arange(365) - 172 > 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Median precip on rainy days: 0.194881889764\n",
      "Median precip on summer days: 0.0\n",
      "Max precip on rainy days: 1.83858267717\n",
      "Max precip on summer days: 0.850393700787\n",
      "Median precip on non-summer rainy days: 0.200787401575\n"
     ]
    }
   ],
   "source": [
    "print(\"Median precip on rainy days:\", np.median(inches[rainy]))\n",
    "print(\"Median precip on summer days:\", np.median(inches[summer]))\n",
    "print(\"Max precip on rainy days:\", np.max(inches[rainy]))\n",
    "print(\"Max precip on summer days:\", np.max(inches[summer]))\n",
    "print(\"Median precip on non-summer rainy days:\", np.median(inches[rainy & ~summer]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = np.arange(10)\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t[(t > 3 ) & (t < 6)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fancy Indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([51, 92, 14, 71, 60, 20, 82, 86, 74, 74])"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rand = np.random.RandomState(42)\n",
    "r = rand.randint(100, size=10)\n",
    "r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(14, 20, 86)"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# instead of using \n",
    "r[2], r[5], r[7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([14, 20, 86])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# pass a single list or array of indices  \n",
    "ind= [2, 5, 7]\n",
    "r[ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[71, 86],\n",
       "       [60, 20]])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ind2 = np.array([[3,7],\n",
    "                [4,5]])\n",
    "r[ind2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# combined indexing\n",
    "Y = np.arange(12).reshape(3,4)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  8,  9])"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fancy and simple indices\n",
    "Y[2, [2, 0, 1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  6],\n",
       "       [ 9, 10]])"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# fancy indexing with slicing\n",
    "Y[1:,[1,2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Selecting random points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 2)"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean=[0,0]\n",
    "cov=[[1,2],\n",
    "     [2,5]]\n",
    "X = rand.multivariate_normal(mean, cov, 100)\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.644508  , -0.46220608],\n",
       "       [ 0.7376352 ,  1.21236921],\n",
       "       [ 0.88151763,  1.12795177],\n",
       "       [ 2.04998983,  5.97778598],\n",
       "       [-0.1711348 , -2.06258746]])"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RUjzwdHR04MSJE1iyZInf9enTp+PIkSNKF0eU8IR2p+4bLKQeHR0s6DEjjZSieOBxOp3w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\niEhT/x9uN7L8YevBQAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ca642e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:, 1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([41, 24, 79, 26, 38, 18,  2, 64, 67, 25, 13, 17, 14, 37, 31, 91, 80,\n",
       "       98, 66, 92])"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# select 20 random points \n",
    "indices = np.random.choice(X.shape[0], 20, replace=False)\n",
    "indices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-1.33461668, -3.03203218],\n",
       "        [ 0.4299908 ,  0.36324254],\n",
       "        [-0.31332021, -1.7895623 ],\n",
       "        [ 0.32124996,  0.33137032],\n",
       "        [ 0.35936721,  0.40554974],\n",
       "        [ 1.53817376,  1.99973464],\n",
       "        [ 0.88151763,  1.12795177],\n",
       "        [ 0.13143756, -0.07833855],\n",
       "        [-0.51172373, -1.40960773],\n",
       "        [ 0.97253528,  3.53815717],\n",
       "        [ 0.49514263,  1.18939673],\n",
       "        [-0.53943081, -0.3478899 ],\n",
       "        [ 0.0629872 ,  0.57349278],\n",
       "        [ 0.44457363,  1.87828298],\n",
       "        [-1.51101746, -3.2818741 ],\n",
       "        [-0.16863279,  0.39422355],\n",
       "        [ 1.12659538,  1.49627535],\n",
       "        [-0.99658689, -2.35038099],\n",
       "        [-0.14547282, -1.34125678],\n",
       "        [ 0.12065651,  1.13236323]]), (20, 2))"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selection = X[indices] #fancy indexing here\n",
    "selection, selection.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAF33a4JtGo43qfikMZxB1jmtunMa9TXFzu4DW/u5PO9+XIvybb/BoDPHIarh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\nAVr/VNkhay23AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1204e2710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], alpha=0.3)\n",
    "plt.scatter(selection[:,0], selection[:,1], s=200,facecolor=None);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 99, 99,  3, 99,  5,  6,  7, 99,  9])"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# modifying values with fancy indexing\n",
    "x = np.arange(10)\n",
    "i = np.array([2,1,8,4])\n",
    "x[i] = 99\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 89, 89,  3, 89,  5,  6,  7, 89,  9])"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[i] -=10\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  1.,  1.,  0.,  1.,  0.,  0.,  0.,  1.,  0.])"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# to fix the nonintuitive result use at() ufunc\n",
    "n = np.zeros(10)\n",
    "i = np.array([2,1,8,4])\n",
    "np.add.at(n, i, 1)\n",
    "n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GnfHqnyv/b5bfhRsXRnrBXqqgP4aKtE92ZXFj2Viyfp86EjajR4/WnXfeqdbWVi1ZsmRw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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12071e278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bining Data\n",
    "np.random.seed(42)\n",
    "x = np.random.randn(100)\n",
    "\n",
    "#compute hist by hand\n",
    "bins = np.linspace(-5, 5, 20)\n",
    "counts = np.zeros_like(bins)\n",
    "\n",
    "#find appropreate bin for each x\n",
    "i = np.searchsorted(bins, x)\n",
    "\n",
    "#add 1 each of these bins\n",
    "np.add.at(counts, i, 1)\n",
    "\n",
    "#plot the result\n",
    "plt.plot(bins, counts, linestyle= 'steps');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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l9XqVn5/v9iimHH2DwMKFC/XLL7/o6tWr+vHHH/Xcc885ufuE8Mknn6hVq5b9vosrV67o\nypUr+uCDD3Ts2DFt3bpVx44d04IFC9weLW74kPN/HDlyRAsWLNC+ffu0Z88epaamatq0abp+/brb\no7nu5MmT+vzzz5Wdne32KOYc+ZwN/vLzzz/r5Zdf1uHDhxUIBLRjxw7l5eW5PVazsH//fs2ePVsX\nL15Up07Jf/mDcePGKTs7W5s3b67f9uyzzyovL0/vv/++i5O5LxqNqmfPniouLtakSZPcHsc1f/75\np0aPHq3Nmzdrw4YNysrKUkFBgdtjmWnZfwV3UE1NjRYuXKiPP/74ns8b4a/1adu2rTp06OD2KObu\n3Lmj06dPa+zYsQ22jx07VidOnHBpquYjGo3q7t278nq9bo/iqqVLlyovL0+jRo1ye5S44OJpDlm2\nbJnGjRunCRMmuD1KsxOJRLRu3Tq98sorSk1N/qccH3J+uFWrVmnQoEHKzc11exTX7NixQ+fPn9en\nn37q9ihxk/z/5zfB2rVrtXHjxofeZ+/evfr999/166+/3vPW72TT2PUYOXJk/c/RaFRz585Vt27d\ntGbNGusR0cytXr1aZWVlKi0tVUpKitvjuCIcDmvNmjUqLS1V69at3R4nbnjN5iGqqqpUVVX10Pv0\n6NFDy5cv15dfftngjQF1dXVq1aqVcnNzVVpaaj1qXDR2Pf59qiwajWrWrFmSpK+//lodO3Y0n7E5\n4LsC7y8YDKqkpER79+5Vv3793B7HNcXFxVq8eHGD2NbV1cnj8ahVq1YqLy9X27ZtXZzQBrFxQHl5\nuSKRSINtI0aM0Lp16zR58mT17t3bncFcVFNTo1mzZikWi2n37t1KT7//9eiT1bhx4/TUU09p06ZN\n9dtycnI0derUFvkGgZUrV+rbb7/V3r171b9/f7fHcVUkElF5eXmDbYsXL1afPn20bNkyDRw4UB6P\nx6Xp7HAazQHdu3dX9+7d79neo0ePFhuaGTNmqKamRsXFxbp165Zu3bolScrIyFCbNm1cntAeH3L+\njxUrVmjXrl3auXOnvF6vKioqJElpaWkt5rfdv/N6vfe8OaJDhw7KyMhQVlaWS1PZIzZw3OnTp3Xy\n5ElJf/1t/u/+/2s6yWrGjBmqrq5WQUGBKioqNHDgwBb5IWfprw+3SrrnYwArV65UMBh0YyS4gNNo\nAABzfM4GAGCO2AAAzBEbAIA5YgMAMEdsAADmiA0AwByxAQCYIzYAAHPEBgBg7v8AMrifAWZpMFgA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12072ff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# this deos the same above. \n",
    "plt.hist(x, bins, histtype='step');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NumPy routine:\n",
      "87.5 µs ± 17.7 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n",
      "\n",
      "Custom routine:\n",
      "17.7 µs ± 757 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# matplotlib uses np.histogram function to create this chart. \n",
    "#lets compare both\n",
    "print(\"NumPy routine:\")\n",
    "%timeit counts, edges = np.histogram(x, bins)\n",
    "print('')\n",
    "print('Custom routine:')\n",
    "%timeit np.add.at(counts, np.searchsorted(bins,x), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# np.histogram?? ##for more information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sorting Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  3,  7,  8,  9, 11])"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1,7,8,3,9,11])\n",
    "np.sort(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x before: [ 1  7  8  3  9 11]\n",
      "x after sorted in place: [ 1  3  7  8  9 11]\n"
     ]
    }
   ],
   "source": [
    "# if you prefer to sort array in-place, use .sort method  \n",
    "print(\"x before:\", x)\n",
    "x.sort()\n",
    "print(\"x after sorted in place:\", x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 0, 1, 4, 2])"
      ]
     },
     "execution_count": 176,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# argsort returns indicies for the sorted elements\n",
    "y = np.array([3,5,8,1,6])\n",
    "i = np.argsort(y)\n",
    "i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 6, 8])"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# you  may use fancy  indexing alter\n",
    "y[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[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]])"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sorting along rows and columns\n",
    "rand = np.random.RandomState(42)\n",
    "X = rand.randint(0, 10, (4,6))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "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": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#sort each column of X\n",
    "np.sort(X, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "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": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# sort each row of X\n",
    "np.sort(X, axis =1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 3,  1,  4,  6, 11, 70, 99])"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# partial sorting\n",
    "# find the 3 smallest values in the array\n",
    "x = np.array([11,3,6,70,4,1, 99])\n",
    "np.partition(x, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: k-Nearest Neighbors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 7],\n",
       "       [6, 8],\n",
       "       [7, 4],\n",
       "       [1, 4],\n",
       "       [7, 9],\n",
       "       [8, 8],\n",
       "       [0, 8],\n",
       "       [6, 8],\n",
       "       [7, 0],\n",
       "       [7, 7]])"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#create random 10 points on a two dimensional array\n",
    "X = rand.randint(0, 11,(10,2))\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IAABGKBIAgBGKBABghCIBABihSAAARigSAIARigQAYIQiAQAYoUgAAEYoEgCAEYoEAGCE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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120deabe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1], s=100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  0],\n",
       "        [-3, -1],\n",
       "        [-4,  3],\n",
       "        [ 2,  3],\n",
       "        [-4, -2],\n",
       "        [-5, -1],\n",
       "        [ 3, -1],\n",
       "        [-3, -1],\n",
       "        [-4,  7],\n",
       "        [-4,  0]],\n",
       "\n",
       "       [[ 3,  1],\n",
       "        [ 0,  0],\n",
       "        [-1,  4],\n",
       "        [ 5,  4],\n",
       "        [-1, -1],\n",
       "        [-2,  0],\n",
       "        [ 6,  0],\n",
       "        [ 0,  0],\n",
       "        [-1,  8],\n",
       "        [-1,  1]],\n",
       "\n",
       "       [[ 4, -3],\n",
       "        [ 1, -4],\n",
       "        [ 0,  0],\n",
       "        [ 6,  0],\n",
       "        [ 0, -5],\n",
       "        [-1, -4],\n",
       "        [ 7, -4],\n",
       "        [ 1, -4],\n",
       "        [ 0,  4],\n",
       "        [ 0, -3]],\n",
       "\n",
       "       [[-2, -3],\n",
       "        [-5, -4],\n",
       "        [-6,  0],\n",
       "        [ 0,  0],\n",
       "        [-6, -5],\n",
       "        [-7, -4],\n",
       "        [ 1, -4],\n",
       "        [-5, -4],\n",
       "        [-6,  4],\n",
       "        [-6, -3]],\n",
       "\n",
       "       [[ 4,  2],\n",
       "        [ 1,  1],\n",
       "        [ 0,  5],\n",
       "        [ 6,  5],\n",
       "        [ 0,  0],\n",
       "        [-1,  1],\n",
       "        [ 7,  1],\n",
       "        [ 1,  1],\n",
       "        [ 0,  9],\n",
       "        [ 0,  2]],\n",
       "\n",
       "       [[ 5,  1],\n",
       "        [ 2,  0],\n",
       "        [ 1,  4],\n",
       "        [ 7,  4],\n",
       "        [ 1, -1],\n",
       "        [ 0,  0],\n",
       "        [ 8,  0],\n",
       "        [ 2,  0],\n",
       "        [ 1,  8],\n",
       "        [ 1,  1]],\n",
       "\n",
       "       [[-3,  1],\n",
       "        [-6,  0],\n",
       "        [-7,  4],\n",
       "        [-1,  4],\n",
       "        [-7, -1],\n",
       "        [-8,  0],\n",
       "        [ 0,  0],\n",
       "        [-6,  0],\n",
       "        [-7,  8],\n",
       "        [-7,  1]],\n",
       "\n",
       "       [[ 3,  1],\n",
       "        [ 0,  0],\n",
       "        [-1,  4],\n",
       "        [ 5,  4],\n",
       "        [-1, -1],\n",
       "        [-2,  0],\n",
       "        [ 6,  0],\n",
       "        [ 0,  0],\n",
       "        [-1,  8],\n",
       "        [-1,  1]],\n",
       "\n",
       "       [[ 4, -7],\n",
       "        [ 1, -8],\n",
       "        [ 0, -4],\n",
       "        [ 6, -4],\n",
       "        [ 0, -9],\n",
       "        [-1, -8],\n",
       "        [ 7, -8],\n",
       "        [ 1, -8],\n",
       "        [ 0,  0],\n",
       "        [ 0, -7]],\n",
       "\n",
       "       [[ 4,  0],\n",
       "        [ 1, -1],\n",
       "        [ 0,  3],\n",
       "        [ 6,  3],\n",
       "        [ 0, -2],\n",
       "        [-1, -1],\n",
       "        [ 7, -1],\n",
       "        [ 1, -1],\n",
       "        [ 0,  7],\n",
       "        [ 0,  0]]])"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:, np.newaxis,:] - X[np.newaxis, :, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}