NumPy_LinearAlgerba.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1b6326a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "68c95348",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello\n"
     ]
    }
   ],
   "source": [
    "print(\"Hello\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3f559b3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0, 0],\n",
       "       [0, 2, 0, 0, 0],\n",
       "       [0, 0, 3, 0, 0],\n",
       "       [0, 0, 0, 4, 0],\n",
       "       [0, 0, 0, 0, 5]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.diag([1,2,3,4,5])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8df4685b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1f551a23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.42170277, 0.63298336, 0.61082744, 0.83532549, 0.87040838])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.random.rand(5)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e6be466e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.78855027,  0.08388371, -0.07318452, -0.97266004, -0.03870472])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.random.randn(5)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cdf4558e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10)\n",
    "a.dtype\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "235fb6ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(10,dtype=\"float64\")\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5bb0e6fc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]\n",
      " [0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((3,4))\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "094d8cfd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.+2.j, 2.+4.j])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.array([1+2j,2+4j])\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "132f6e2a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "complex128\n"
     ]
    }
   ],
   "source": [
    "print(d.dtype)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "944cbc7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True, False])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([True,False,True,False])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "93eeacb9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "# indexing slicing\n",
    "\n",
    "a = np.arange(10)\n",
    "print(a[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ff2fdabd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2ba764fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0],\n",
       "       [0, 2, 0, 0],\n",
       "       [0, 0, 3, 0],\n",
       "       [0, 0, 0, 4]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.diag([1,2,3,4])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ed609038",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "62d22b7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[3,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "644f7116",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0],\n",
       "       [0, 2, 0, 0],\n",
       "       [0, 0, 3, 5],\n",
       "       [0, 0, 0, 4]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2,3]=5\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "679d0b42",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.arange(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4ccc1398",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2ba9d490",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:8:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "a29c2418",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c11e220f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[5:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "20938c29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 7])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[4::3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "4c10fb51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "70e5b1bb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 0])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[2::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f1b81450",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 8, 7, 6, 5, 4, 3])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:2:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9c3c7747",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:5:1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "af8e2eec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Copy & Views\n",
    "a = np.arange(10)\n",
    "\n",
    "a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "96bdb464",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = a[:4]\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "e44c3fba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shares_memory(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "5dc44dad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  1,  2,  3])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[0]=10\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "08120c2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  1,  2,  3,  4,  5,  6,  7,  8,  9])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "406f3d2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.copy(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "771bbc04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  1,  2,  3,  4,  5,  6,  7,  8,  9])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "2e0209d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shares_memory(a,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "e7196262",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11,  1,  2,  3,  4,  5,  6,  7,  8,  9])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[0]=11\n",
    "c\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "8a9c267d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  1,  2,  3,  4,  5,  6,  7,  8,  9])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "21b4bf16",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = a.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "a7fab085",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  1,  2,  3,  4,  5,  6,  7,  8,  9])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "10f4a42a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shares_memory(a,d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "41319bcd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  9,  6,  8,  6, 13,  1,  0, 11,  7, 13,  9,  7,  0, 15])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fancy Indexing\n",
    "\n",
    "a = np.random.randint(0,20,15)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "92c80a7e",
   "metadata": {},
   "outputs": [],
   "source": [
    "mask = (a % 2 == 0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "1d728fad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  6,  8,  6,  0,  0])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "extract_from_a = a[mask]\n",
    "extract_from_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "ecfc6443",
   "metadata": {},
   "outputs": [],
   "source": [
    "a[mask]=-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "3d44f87f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1,  9, -1, -1, -1, 13,  1, -1, 11,  7, 13,  9,  7, -1, 15])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "3a0ff678",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 10, 20, 30, 40, 50, 60, 70, 80, 90])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(0,100,10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "74e29c06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 30, 40, 20, 60, 40])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[2,3,4,2,6,4]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "63c108f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "a[[2,6,7]]=-100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "b60e3d28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0,   10, -100,   30,   40,   50, -100, -100,   80,   90])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "509eb426",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Elementwise Operations\n",
    "\n",
    "a = np.array([1,2,3,4,5])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "e971ec5c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "d6c5b7c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6,  7,  8,  9, 10])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a+5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "c5b5ce8f",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = a+10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "f5401ea3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([11, 12, 13, 14, 15])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "c308482e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.shares_memory(a,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "6b91c0c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "d = a **2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "dae3ce2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  4,  9, 16, 25], dtype=int32)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "f565d7d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 2., 2., 2.])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.ones(4)+1\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "30d8babe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0.])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "5d6e0f98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 1, 2, 3]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [1,2,3,4]\n",
    "b = [1,2,3]\n",
    "a+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "0ee80aa5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "d18f66be",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.diag([3,4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "b459615a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 0, 0, 0],\n",
       "       [0, 4, 0, 0],\n",
       "       [0, 0, 5, 0],\n",
       "       [0, 0, 0, 6]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "364ffac1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9,  0,  0,  0],\n",
       "       [ 0, 16,  0,  0],\n",
       "       [ 0,  0, 25,  0],\n",
       "       [ 0,  0,  0, 36]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c*c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "106f1132",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9,  0,  0,  0],\n",
       "       [ 0, 16,  0,  0],\n",
       "       [ 0,  0, 25,  0],\n",
       "       [ 0,  0,  0, 36]])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.dot(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "fe0ed157",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True,  True,  True],\n",
       "       [ True,  True,  True,  True],\n",
       "       [ True,  True,  True,  True],\n",
       "       [ True,  True,  True,  True]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c == c\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "8a8f55fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [False, False, False, False],\n",
       "       [False, False, False, False],\n",
       "       [False, False, False, False]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a == c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "89cabd14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [1,2,3,4]\n",
    "b=[3,1,4,1]\n",
    "a == b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "192e7c11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False,  True, False])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1,2,3,4])\n",
    "b = np.array([1,1,3,5])\n",
    "a ==b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "ee66f943",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False, False])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a > b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "da73ea8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array_equal(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "a64ab23a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_and(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "6b2bfc1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_or(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "5dd5bb3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = np.array([1,0,0,1])\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "51552ab2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False,  True])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_and(a,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "47406cfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.logical_or(a,c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "74c209a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Transcendental function\n",
    "\n",
    "a = np.arange(5)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "242de4e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.84147098,  0.90929743,  0.14112001, -0.7568025 ])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sin(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "28ac75b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-91-89b6b8e53c58>:1: RuntimeWarning: divide by zero encountered in log\n",
      "  np.log(a)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([      -inf, 0.        , 0.69314718, 1.09861229, 1.38629436])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "dfb19e1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  2.71828183,  7.3890561 , 20.08553692, 54.59815003])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "c9b84fb1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# shape Mismatch\n",
    "\n",
    "a = np.arange(4)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "4a210f42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + np.array([1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "f2411e1d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Basic Reductions\n",
    "\n",
    "x = np.array([1,2,3,4])\n",
    "np.sum(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "c72cac1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([[1,2],[3,4]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "088f2c47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 6])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum(axis = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "e420bc01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 7])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "21a2f595",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "b609eff1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "01640e6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.argmin()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "2e8ea3ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.argmax()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "c72a3807",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# logical Operation\n",
    "np.all([True,True,False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "243070d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any([True,False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "753bfb19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.any([False,False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "e128b0c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1,2,3,2])\n",
    "b= np.array([2,2,3,2])\n",
    "c = np.array([6,4,4,5])\n",
    "((a <= b) & ( b <=c)).all()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "ce5786f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.75"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1,2,3,1])\n",
    "y = np.array([[1,2,3],[5,6,1]])\n",
    "x.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "f443f005",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "cd3ffe51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 5.])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(y,axis=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "75fbd94f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.82915619758885"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "e0d50bbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# load data into numpy array object\n",
    "\n",
    "data = np.loadtxt(\"demo.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "74b9ab49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.23  ,   2.334 ,   0.2321, 123.    ])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "65eda93e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.23\n",
      "2.334\n",
      "0.2321\n",
      "123.0\n"
     ]
    }
   ],
   "source": [
    "first,second,third,forth = data.T\n",
    "print(first)\n",
    "print(second)\n",
    "print(third)\n",
    "print(forth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "ef92b356",
   "metadata": {},
   "outputs": [],
   "source": [
    "data1 = data[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "accb2fa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1.23  ,   2.334 ,   0.2321, 123.    ])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "70969aa6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "52.71788496944727"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1.std(axis=0) # column wise std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "0dc96028",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data1.argmax() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "be894a24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0, 10, 20, 30],\n",
       "       [ 0, 10, 20, 30],\n",
       "       [ 0, 10, 20, 30],\n",
       "       [ 0, 10, 20, 30]])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Broadcasting\n",
    "\n",
    "a = np.tile(np.arange(0,40,10),(4,1))\n",
    "a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "id": "5b3c5987",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = a.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "81acf0b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  1,  2])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([10,1,2])\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "9ff95452",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 4)"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "6a7077dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 1)"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.arange(0,20,10)\n",
    "b.shape\n",
    "b = b[:,np.newaxis]\n",
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "9344079b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Array Shape Manipulation\n",
    "\n",
    "# Flattering\n",
    "\n",
    "a = np.array([[1,2,3],[4,5,6]])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "8f175e11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "a6603d0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4],\n",
       "       [2, 5],\n",
       "       [3, 6]])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "b1103749",
   "metadata": {},
   "outputs": [],
   "source": [
    "b = a.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "ae0fe198",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "6103e625",
   "metadata": {},
   "outputs": [],
   "source": [
    "b = b.reshape((2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "edde7f3c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "8c6fa014",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[100,   2,   3],\n",
       "       [  4,   5,   6]])"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[0,0]=100\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "cadc777d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([1,2,3])\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "0b6eae72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[:,np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "c118c9bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "02343b79",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 2, 1],\n",
       "       [1, 0, 2]], dtype=int64)"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[1,4,2],[3,2,5]])\n",
    "b = np.argsort(a)\n",
    "a = np.sort(a,axis=1)\n",
    "a\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "486192e4",
   "metadata": {},
   "source": [
    "a[b]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "5c46346a",
   "metadata": {},
   "outputs": [],
   "source": [
    "########################################"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "658a6f91",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}