Numpy.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello World\n"
     ]
    }
   ],
   "source": [
    "print(\"Hello World\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Creating Numpy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "L=[1,2,3,4,5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "L1=[1,True, \"Hello\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, True, 'Hello']"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(L1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bool"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# a. Using np.array()\n",
    "\n",
    "arr1=np.array([1,2,3,4,5])\n",
    "arr1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2=np.array([[1,2,3],[4,5,6]])\n",
    "arr2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1, 2],\n",
       "        [3, 4]],\n",
       "\n",
       "       [[5, 6],\n",
       "        [7, 8]]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3=np.array([[[1,2],[3,4]],[[5,6],[7,8]]])\n",
    "arr3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(arr3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr4=np.zeros((2,3))\n",
    "arr4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr5=np.ones((2,3))\n",
    "arr5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7, 9])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr6=np.arange(1,10,2)\n",
    "arr6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.51907364, 0.32775468, 0.33993041],\n",
       "       [0.13241128, 0.15838664, 0.43028503]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.random((2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10.        ,  -7.77777778,  -5.55555556,  -3.33333333,\n",
       "        -1.11111111,   1.11111111,   3.33333333,   5.55555556,\n",
       "         7.77777778,  10.        ])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr7=np.linspace(-10,10,10)\n",
    "arr7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr8=arr7.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10.        ,  -7.77777778,  -5.55555556,  -3.33333333,\n",
       "        -1.11111111,   1.11111111,   3.33333333,   5.55555556,\n",
       "         7.77777778,  10.        ])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr8=np.copy(arr7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10.        ,  -7.77777778,  -5.55555556,  -3.33333333,\n",
       "        -1.11111111,   1.11111111,   3.33333333,   5.55555556,\n",
       "         7.77777778,  10.        ])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr9=np.identity(3)\n",
    "arr9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Properties/Attributes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2, 2)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3.itemsize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1., 2.],\n",
       "        [3., 4.]],\n",
       "\n",
       "       [[5., 6.],\n",
       "        [7., 8.]]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3.astype('float')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Arrays V Lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# In terms of memory\n",
    "L=range(100)\n",
    "A=np.arange(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2400"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.getsizeof(L[0])*len(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "400"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.itemsize*A.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "# In terms of execution time\n",
    "x=range(1000000)\n",
    "y=range(1000000,2000000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "start_time=time.time()\n",
    "z=[(x+y) for x,y in zip(x,y)]\n",
    "t1=time.time()-start_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1577079563.5617762"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time.time()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "a=np.arange(1000000)\n",
    "b=np.arange(1000000,2000000)\n",
    "\n",
    "start_time=time.time()\n",
    "c=a+b\n",
    "t2=time.time()-start_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "54.49407420642011"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1/t2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Array Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4,  5],\n",
       "       [ 6,  7,  8,  9, 10, 11],\n",
       "       [12, 13, 14, 15, 16, 17],\n",
       "       [18, 19, 20, 21, 22, 23]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=np.arange(24).reshape(4,6)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[24, 25, 26, 27, 28, 29],\n",
       "       [30, 31, 32, 33, 34, 35],\n",
       "       [36, 37, 38, 39, 40, 41],\n",
       "       [42, 43, 44, 45, 46, 47]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b=np.arange(24,48).reshape(4,6)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[          0,           1,    67108864,  2030534587,           0,\n",
       "         1804648021],\n",
       "       [ 1073741824,   265001655,           0,  1165272329,           0,\n",
       "          223731123],\n",
       "       [          0, -1053241123,           0,  1119702383,           0,\n",
       "         -946637167],\n",
       "       [          0,   764714667,           0,   101251813,           0,\n",
       "         1016499751]], dtype=int32)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a**b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False, False, False],\n",
       "       [False, False, False, False, False, False],\n",
       "       [False, False, False, False,  True,  True],\n",
       "       [ True,  True,  True,  True,  True,  True]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a>15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  3,  6,  9, 12, 15],\n",
       "       [18, 21, 24, 27, 30, 33],\n",
       "       [36, 39, 42, 45, 48, 51],\n",
       "       [54, 57, 60, 63, 66, 69]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a*3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 415,  505,  595,  685],\n",
       "       [1369, 1675, 1981, 2287],\n",
       "       [2323, 2845, 3367, 3889],\n",
       "       [3277, 4015, 4753, 5491]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.dot(np.transpose(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "a+=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11, 12, 13],\n",
       "       [14, 15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24, 25]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.5, 10.5, 16.5, 22.5])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.mean(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 27,  63,  99, 135])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.90929743,  0.14112001, -0.7568025 , -0.95892427, -0.2794155 ,\n",
       "         0.6569866 ],\n",
       "       [ 0.98935825,  0.41211849, -0.54402111, -0.99999021, -0.53657292,\n",
       "         0.42016704],\n",
       "       [ 0.99060736,  0.65028784, -0.28790332, -0.96139749, -0.75098725,\n",
       "         0.14987721],\n",
       "       [ 0.91294525,  0.83665564, -0.00885131, -0.8462204 , -0.90557836,\n",
       "        -0.13235175]])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.5"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Indexing and Slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=np.arange(10)\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 5])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[3:6:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4],\n",
       "       [ 8, 10]])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0:2,0:3:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1, 2],\n",
       "        [3, 4]],\n",
       "\n",
       "       [[5, 6],\n",
       "        [7, 8]]])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11, 12, 13],\n",
       "       [14, 15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24, 25]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 4 5 6 7]\n",
      "[ 8  9 10 11 12 13]\n",
      "[14 15 16 17 18 19]\n",
      "[20 21 22 23 24 25]\n"
     ]
    }
   ],
   "source": [
    "for i in a:\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 8,  9, 10, 11, 12, 13])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "for i in np.nditer(arr3):\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11, 12, 13],\n",
       "       [14, 15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24, 25]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4,  5,  6,  7],\n",
       "       [14, 15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24, 25]])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[0,2,3]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11, 12, 13],\n",
       "       [14, 15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24, 25]])"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11, 12, 13],\n",
       "       [14, 15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24, 25]])"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "d=a>15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False, False, False],\n",
       "       [False, False, False, False, False, False],\n",
       "       [False, False,  True,  True,  True,  True],\n",
       "       [ True,  True,  True,  True,  True,  True]])"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[d]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16, 17, 18, 19, 20, 21, 22, 23, 24, 25])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[d]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.linspace(-50,50,50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [],
   "source": [
    "y=x*x + 2*x + 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x75bdf89278>]"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  3,  4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11, 12, 13],\n",
       "       [14, 15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24, 25]])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[14, 16],\n",
       "       [20, 22]])"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2:,0:3:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}