numpy experiences.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3/1/2019\n",
    "\n",
    "## N-dimensional arrays (ndarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3], [4, 5, 6]]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lst = [\n",
    "    [1, 2, 3],\n",
    "    [4, 5, 6]\n",
    "]\n",
    "\n",
    "lst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1d = np.array(lst)\n",
    "\n",
    "ary1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'list'>\n",
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "print(type(lst))\n",
    "print(type(ary1d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1d.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [4., 5., 6.]], dtype=float32)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float32_ary = ary1d.astype(np.float32)\n",
    "\n",
    "float32_ary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float32')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float32_ary.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1d.itemsize #returns the size of a single array element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1d.size #returns number of elements in an array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1d.ndim #number of dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1d.shape #the ndarray is 2 rows and 3 columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1, 2, 3]).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(5)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar = np.array(5)\n",
    "scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "()"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scalar.ndim #scalar is 0 dimension"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## array construction routines"
   ]
  },
  {
   "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": [
    "def generator():\n",
    "    for i in range(10):\n",
    "        if i % 2:\n",
    "            yield i\n",
    "            \n",
    "gen = generator()\n",
    "np.fromiter(gen, dtype = int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7, 9])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "generator_expression = (i for i in range(10) if i % 2)\n",
    "np.fromiter(generator_expression, dtype = int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "generator"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(generator_expression)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1.],\n",
       "       [1., 1.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.empty((3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0.],\n",
       "       [0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 0],\n",
       "       [0, 4]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag((4,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#np.arange() is same as Python's range()\n",
    "\n",
    "np.arange(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5, 6, 7, 8])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(4,9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 3.33333333, 5.66666667, 8.        ])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(1, 8, num = 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## arrary indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n"
     ]
    }
   ],
   "source": [
    "ary = np.array([1, 2, 3])\n",
    "print(ary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2]\n",
      "[1 2]\n"
     ]
    }
   ],
   "source": [
    "print(ary[0:2])\n",
    "print(ary[:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "\n",
    "ary[0, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[0, 1] #first row, second column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[0] #first row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[ : , 0] #first column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [4, 5]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[: ,  :2] #first two columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## array math and universal functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "lst = [\n",
    "    [1, 2, 3],\n",
    "    [4, 5, 6]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "[1, 2, 3]\n",
      "1\n",
      "[4, 5, 6]\n"
     ]
    }
   ],
   "source": [
    "for a, b in enumerate(lst):\n",
    "    print(a)\n",
    "    print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[2, 3, 4], [5, 6, 7]]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for row_index, row_val in enumerate(lst):\n",
    "    for col_index, col_val in enumerate(row_val):\n",
    "        lst[row_index][col_index] += 1\n",
    "lst"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[2, 3, 4], [5, 6, 7]]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lst = [\n",
    "    [1, 2, 3],\n",
    "    [4, 5, 6]\n",
    "]\n",
    "\n",
    "#list comprehension\n",
    "[[cell + 1 for cell in row] for row in lst]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# now let's see how numpy makes this super easy\n",
    "ary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4],\n",
       "       [5, 6, 7]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add(ary, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3, 4],\n",
       "       [5, 6, 7]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6],\n",
       "       [ 8, 10, 12]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 7, 9])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.reduce(ary, axis = 0) #sum the value of rows(axis = 0), column total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6, 15])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add.reduce(ary, axis = 1) #sum the value of columns(axis =1), row total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 7, 9])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary.sum(axis =0) #column totals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6, 15])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary.sum(axis =1) #row totals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "ary1 = np.array([1, 2, 3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "ary2 = np.array([4, 5, 6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 7, 9])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1 + ary2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "ary3 = np.array([[4, 5, 6], [7, 8, 9]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  7,  9],\n",
       "       [ 8, 10, 12]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary3 + ary1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  7,  9],\n",
       "       [ 8, 10, 12]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1 + ary3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this is to say, when arrays are added up, they automatically fill themselves to match the max dimensions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ValueError: operands could not be broadcast together with shapes (2,3) (2,) \n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    ary3 + np.array([1, 2])\n",
    "except ValueError as e:\n",
    "    print('ValueError:', e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  6,  7],\n",
       "       [ 9, 10, 11]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary3 + np.array([[1], [2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## advanced indexing - memory views and copies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_row = ary[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "first_row += 99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([100, 101, 102])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[100, 101, 102],\n",
       "       [  4,   5,   6]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note that the first row of ary has been changed.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "ary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 5])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "center_col = ary[:, 1]\n",
    "center_col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1, 101,   3],\n",
       "       [  4, 104,   6]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "center_col += 99\n",
    "ary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary = np.array([[1, 2, 3], [4, 5, 6]])\n",
    "ary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5, 6])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second_row = ary[1].copy()\n",
    "second_row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([103, 104, 105])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second_row += 99\n",
    "second_row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**That is, slicing arrays create memory views, which means that two arrays share memory. Modifying one will change the other.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_row = ary[:1]\n",
    "first_row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.may_share_memory(first_row, ary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second_row = ary[1].copy()\n",
    "np.may_share_memory(second_row, ary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fancy indexing always return a copy.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3],\n",
       "       [4, 6]])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[:, [0, 2]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "this_is_a_copy = ary[:, [0,2]]\n",
    "this_is_a_copy += 99\n",
    "ary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Boolean masks for indexing, also returns a copy**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False],\n",
       "       [ True,  True,  True]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "greater3_mask = ary > 3\n",
    "greater3_mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5, 6])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[greater3_mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 6])"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary[(ary > 3) & (ary % 2 == 0)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## comparison operators and mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "ary = np.array([1, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True,  True])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = ary > 2\n",
    "mask"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2, 3]),)"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask.nonzero() #gives the index positions of array elements that meet certain condition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([2, 3]),)"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(ary > 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**np.where(condition, x, y):\n",
    "if condition is True, yield x, otherwise yield y.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 1])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(ary > 2, 1, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## random number generators in numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.69646919, 0.28613933, 0.22685145])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "np.random.rand(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng2 = np.random.RandomState(seed = 123)\n",
    "z_scores = rng2.randn(100, 2)\n",
    "#z_scores is an array of 100 rows and 2 columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(z_scores[:, 0], z_scores[:, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## reshaping arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1d = np.array([1,2,3,4,5,6])\n",
    "ary2d_view = ary1d.reshape(2,3)\n",
    "ary2d_view"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.may_share_memory(ary1d, ary2d_view)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary2d_view.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary2d_view.flatten() #flatten does the same thing as ravel, but flattern returns a copy instead of a view"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.may_share_memory(ary2d_view.flatten(), ary2d_view)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "ary = np.array([[1,2,3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [1, 2, 3]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate((ary,ary), axis = 0) # stack along rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3, 1, 2, 3]])"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate((ary,ary), axis = 1) # stack along columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## linear algebra with numpy arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_vector = np.array([1, 2, 3])\n",
    "row_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "column_vector = np.array([1, 2, 3]).reshape(-1, 1)\n",
    "column_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_vector[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_vector[:, None]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix = np.array([[1,2,3],\n",
    "                  [4,5,6]])\n",
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4],\n",
       "       [2, 5],\n",
       "       [3, 6]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4],\n",
       "       [2, 5],\n",
       "       [3, 6]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## set operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "ary = np.array([1,1,2,3,1,5])\n",
    "ary_set = np.unique(ary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 5])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary_set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## serializing numpy arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### np.save"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ary1 = np.array([1,2,3])\n",
    "np.save('ary-data.npy', ary1)\n",
    "np.load('ary-data.npy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### np.savez\n",
    "this will generate an archive to save more .npy files\n",
    "the saved object is .npz, which can be accessed like a dictionary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n"
     ]
    }
   ],
   "source": [
    "print(ary1)\n",
    "\n",
    "ary2 = np.array([4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.savez('ary-data.npz', ary1, ary2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'arr_0': array([1, 2, 3]), 'arr_1': array([4, 5, 6])}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d = np.load('ary-data.npz')\n",
    "dict(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3/3/2019\n",
    "## pandas fundamentals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "create a **Series** by passing a list, letting panda create a default integer index."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    3.0\n",
       "2    NaN\n",
       "3    4.0\n",
       "4    5.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "s = pd.Series([1, 3, np.NaN, 4, 5])\n",
    "s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "create a **DataFrame** by passing a NumPy array, with a datetime index and labeled columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04',\n",
       "               '2013-01-05', '2013-01-06'],\n",
       "              dtype='datetime64[ns]', freq='D')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dates = pd.date_range('20130101', periods = 6)\n",
    "dates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.70608915, -0.58038837,  0.41746011,  0.14396383],\n",
       "       [-0.37594357, -0.40275928,  1.70905992, -0.88590318],\n",
       "       [ 1.03816534, -0.38639004,  0.06794504,  1.16432843],\n",
       "       [ 0.25979039,  0.71274923, -0.53375317,  0.34829114],\n",
       "       [-1.08677957,  0.39724045,  3.19274214,  0.07114987],\n",
       "       [-0.51630058, -0.33398263, -0.60813685,  2.02388353]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn(6, 4) #generate a sample from standard normal distribution having 6 rows and 4 columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A', 'B', 'C', 'D']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list('ABCD')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-01-01</th>\n",
       "      <td>0.169786</td>\n",
       "      <td>0.414946</td>\n",
       "      <td>0.531851</td>\n",
       "      <td>0.443999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-02</th>\n",
       "      <td>0.739269</td>\n",
       "      <td>0.802684</td>\n",
       "      <td>0.201066</td>\n",
       "      <td>0.769266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-03</th>\n",
       "      <td>0.509956</td>\n",
       "      <td>0.485647</td>\n",
       "      <td>0.209849</td>\n",
       "      <td>0.294387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-04</th>\n",
       "      <td>0.471555</td>\n",
       "      <td>0.570203</td>\n",
       "      <td>0.456042</td>\n",
       "      <td>0.854817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-05</th>\n",
       "      <td>0.692286</td>\n",
       "      <td>0.249153</td>\n",
       "      <td>0.331672</td>\n",
       "      <td>0.329096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-06</th>\n",
       "      <td>0.842882</td>\n",
       "      <td>0.967027</td>\n",
       "      <td>0.949670</td>\n",
       "      <td>0.441215</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   A         B         C         D\n",
       "2013-01-01  0.169786  0.414946  0.531851  0.443999\n",
       "2013-01-02  0.739269  0.802684  0.201066  0.769266\n",
       "2013-01-03  0.509956  0.485647  0.209849  0.294387\n",
       "2013-01-04  0.471555  0.570203  0.456042  0.854817\n",
       "2013-01-05  0.692286  0.249153  0.331672  0.329096\n",
       "2013-01-06  0.842882  0.967027  0.949670  0.441215"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(np.random.rand(6,4), index = dates, columns = list('ABCD'))\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "create a **DataFrame** by passing a dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2013-01-02</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3</td>\n",
       "      <td>test</td>\n",
       "      <td>foo</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2013-01-02</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3</td>\n",
       "      <td>train</td>\n",
       "      <td>foo</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2013-01-02</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3</td>\n",
       "      <td>test</td>\n",
       "      <td>foo</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2013-01-02</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3</td>\n",
       "      <td>train</td>\n",
       "      <td>foo</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     A          B    C  D      E    F\n",
       "0  1.0 2013-01-02  1.0  3   test  foo\n",
       "1  1.0 2013-01-02  1.0  3  train  foo\n",
       "2  1.0 2013-01-02  1.0  3   test  foo\n",
       "3  1.0 2013-01-02  1.0  3  train  foo"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2 = pd.DataFrame({'A': 1. ,\n",
    "                    'B': pd.Timestamp('20130102'),\n",
    "                    'C': pd.Series(1, index = list(range(4)), dtype = 'float32'),\n",
    "                    'D': np.array([3]*4, dtype = 'int32'),\n",
    "                    'E': pd.Categorical([\"test\", \"train\", \"test\", \"train\"]),\n",
    "                    'F': 'foo'})\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A           float64\n",
       "B    datetime64[ns]\n",
       "C           float32\n",
       "D             int32\n",
       "E          category\n",
       "F            object\n",
       "dtype: object"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2013-01-01', '2013-01-02', '2013-01-03', '2013-01-04',\n",
       "               '2013-01-05', '2013-01-06'],\n",
       "              dtype='datetime64[ns]', freq='D')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Int64Index([0, 1, 2, 3], dtype='int64')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>6.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.570956</td>\n",
       "      <td>0.581610</td>\n",
       "      <td>0.446692</td>\n",
       "      <td>0.522130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.241468</td>\n",
       "      <td>0.262703</td>\n",
       "      <td>0.279278</td>\n",
       "      <td>0.233897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.169786</td>\n",
       "      <td>0.249153</td>\n",
       "      <td>0.201066</td>\n",
       "      <td>0.294387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.481155</td>\n",
       "      <td>0.432621</td>\n",
       "      <td>0.240305</td>\n",
       "      <td>0.357126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.601121</td>\n",
       "      <td>0.527925</td>\n",
       "      <td>0.393857</td>\n",
       "      <td>0.442607</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.727524</td>\n",
       "      <td>0.744564</td>\n",
       "      <td>0.512898</td>\n",
       "      <td>0.687949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.842882</td>\n",
       "      <td>0.967027</td>\n",
       "      <td>0.949670</td>\n",
       "      <td>0.854817</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              A         B         C         D\n",
       "count  6.000000  6.000000  6.000000  6.000000\n",
       "mean   0.570956  0.581610  0.446692  0.522130\n",
       "std    0.241468  0.262703  0.279278  0.233897\n",
       "min    0.169786  0.249153  0.201066  0.294387\n",
       "25%    0.481155  0.432621  0.240305  0.357126\n",
       "50%    0.601121  0.527925  0.393857  0.442607\n",
       "75%    0.727524  0.744564  0.512898  0.687949\n",
       "max    0.842882  0.967027  0.949670  0.854817"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         A    C    D\n",
       "count  4.0  4.0  4.0\n",
       "mean   1.0  1.0  3.0\n",
       "std    0.0  0.0  0.0\n",
       "min    1.0  1.0  3.0\n",
       "25%    1.0  1.0  3.0\n",
       "50%    1.0  1.0  3.0\n",
       "75%    1.0  1.0  3.0\n",
       "max    1.0  1.0  3.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2.describe() #gives a summary for numeric columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2013-01-01 00:00:00</th>\n",
       "      <th>2013-01-02 00:00:00</th>\n",
       "      <th>2013-01-03 00:00:00</th>\n",
       "      <th>2013-01-04 00:00:00</th>\n",
       "      <th>2013-01-05 00:00:00</th>\n",
       "      <th>2013-01-06 00:00:00</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>A</th>\n",
       "      <td>0.169786</td>\n",
       "      <td>0.739269</td>\n",
       "      <td>0.509956</td>\n",
       "      <td>0.471555</td>\n",
       "      <td>0.692286</td>\n",
       "      <td>0.842882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>B</th>\n",
       "      <td>0.414946</td>\n",
       "      <td>0.802684</td>\n",
       "      <td>0.485647</td>\n",
       "      <td>0.570203</td>\n",
       "      <td>0.249153</td>\n",
       "      <td>0.967027</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>C</th>\n",
       "      <td>0.531851</td>\n",
       "      <td>0.201066</td>\n",
       "      <td>0.209849</td>\n",
       "      <td>0.456042</td>\n",
       "      <td>0.331672</td>\n",
       "      <td>0.949670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>D</th>\n",
       "      <td>0.443999</td>\n",
       "      <td>0.769266</td>\n",
       "      <td>0.294387</td>\n",
       "      <td>0.854817</td>\n",
       "      <td>0.329096</td>\n",
       "      <td>0.441215</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   2013-01-01  2013-01-02  2013-01-03  2013-01-04  2013-01-05  2013-01-06\n",
       "A    0.169786    0.739269    0.509956    0.471555    0.692286    0.842882\n",
       "B    0.414946    0.802684    0.485647    0.570203    0.249153    0.967027\n",
       "C    0.531851    0.201066    0.209849    0.456042    0.331672    0.949670\n",
       "D    0.443999    0.769266    0.294387    0.854817    0.329096    0.441215"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-01-06</th>\n",
       "      <td>0.842882</td>\n",
       "      <td>0.967027</td>\n",
       "      <td>0.949670</td>\n",
       "      <td>0.441215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-05</th>\n",
       "      <td>0.692286</td>\n",
       "      <td>0.249153</td>\n",
       "      <td>0.331672</td>\n",
       "      <td>0.329096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-04</th>\n",
       "      <td>0.471555</td>\n",
       "      <td>0.570203</td>\n",
       "      <td>0.456042</td>\n",
       "      <td>0.854817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-03</th>\n",
       "      <td>0.509956</td>\n",
       "      <td>0.485647</td>\n",
       "      <td>0.209849</td>\n",
       "      <td>0.294387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-02</th>\n",
       "      <td>0.739269</td>\n",
       "      <td>0.802684</td>\n",
       "      <td>0.201066</td>\n",
       "      <td>0.769266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-01</th>\n",
       "      <td>0.169786</td>\n",
       "      <td>0.414946</td>\n",
       "      <td>0.531851</td>\n",
       "      <td>0.443999</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   A         B         C         D\n",
       "2013-01-06  0.842882  0.967027  0.949670  0.441215\n",
       "2013-01-05  0.692286  0.249153  0.331672  0.329096\n",
       "2013-01-04  0.471555  0.570203  0.456042  0.854817\n",
       "2013-01-03  0.509956  0.485647  0.209849  0.294387\n",
       "2013-01-02  0.739269  0.802684  0.201066  0.769266\n",
       "2013-01-01  0.169786  0.414946  0.531851  0.443999"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sort_index(axis = 0, ascending = False) #axis = 0, sort rows by descending order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>D</th>\n",
       "      <th>C</th>\n",
       "      <th>B</th>\n",
       "      <th>A</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-01-01</th>\n",
       "      <td>0.443999</td>\n",
       "      <td>0.531851</td>\n",
       "      <td>0.414946</td>\n",
       "      <td>0.169786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-02</th>\n",
       "      <td>0.769266</td>\n",
       "      <td>0.201066</td>\n",
       "      <td>0.802684</td>\n",
       "      <td>0.739269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-03</th>\n",
       "      <td>0.294387</td>\n",
       "      <td>0.209849</td>\n",
       "      <td>0.485647</td>\n",
       "      <td>0.509956</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-04</th>\n",
       "      <td>0.854817</td>\n",
       "      <td>0.456042</td>\n",
       "      <td>0.570203</td>\n",
       "      <td>0.471555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-05</th>\n",
       "      <td>0.329096</td>\n",
       "      <td>0.331672</td>\n",
       "      <td>0.249153</td>\n",
       "      <td>0.692286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-06</th>\n",
       "      <td>0.441215</td>\n",
       "      <td>0.949670</td>\n",
       "      <td>0.967027</td>\n",
       "      <td>0.842882</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   D         C         B         A\n",
       "2013-01-01  0.443999  0.531851  0.414946  0.169786\n",
       "2013-01-02  0.769266  0.201066  0.802684  0.739269\n",
       "2013-01-03  0.294387  0.209849  0.485647  0.509956\n",
       "2013-01-04  0.854817  0.456042  0.570203  0.471555\n",
       "2013-01-05  0.329096  0.331672  0.249153  0.692286\n",
       "2013-01-06  0.441215  0.949670  0.967027  0.842882"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sort_index(axis = 1, ascending = False) #axis = 1, sort columns by descending order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2013-01-05</th>\n",
       "      <td>0.692286</td>\n",
       "      <td>0.249153</td>\n",
       "      <td>0.331672</td>\n",
       "      <td>0.329096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-01</th>\n",
       "      <td>0.169786</td>\n",
       "      <td>0.414946</td>\n",
       "      <td>0.531851</td>\n",
       "      <td>0.443999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-03</th>\n",
       "      <td>0.509956</td>\n",
       "      <td>0.485647</td>\n",
       "      <td>0.209849</td>\n",
       "      <td>0.294387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-04</th>\n",
       "      <td>0.471555</td>\n",
       "      <td>0.570203</td>\n",
       "      <td>0.456042</td>\n",
       "      <td>0.854817</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-02</th>\n",
       "      <td>0.739269</td>\n",
       "      <td>0.802684</td>\n",
       "      <td>0.201066</td>\n",
       "      <td>0.769266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-01-06</th>\n",
       "      <td>0.842882</td>\n",
       "      <td>0.967027</td>\n",
       "      <td>0.949670</td>\n",
       "      <td>0.441215</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   A         B         C         D\n",
       "2013-01-05  0.692286  0.249153  0.331672  0.329096\n",
       "2013-01-01  0.169786  0.414946  0.531851  0.443999\n",
       "2013-01-03  0.509956  0.485647  0.209849  0.294387\n",
       "2013-01-04  0.471555  0.570203  0.456042  0.854817\n",
       "2013-01-02  0.739269  0.802684  0.201066  0.769266\n",
       "2013-01-06  0.842882  0.967027  0.949670  0.441215"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sort_values(by = 'B')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2013-01-01    0.169786\n",
       "2013-01-02    0.739269\n",
       "2013-01-03    0.509956\n",
       "2013-01-04    0.471555\n",
       "2013-01-05    0.692286\n",
       "2013-01-06    0.842882\n",
       "Freq: D, Name: A, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['A']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2013-01-01    0.169786\n",
       "2013-01-02    0.739269\n",
       "2013-01-03    0.509956\n",
       "2013-01-04    0.471555\n",
       "2013-01-05    0.692286\n",
       "2013-01-06    0.842882\n",
       "Freq: D, Name: A, dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2013-01-01 00:00:00', freq='D')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dates[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "A    0.169786\n",
       "B    0.414946\n",
       "C    0.531851\n",
       "D    0.443999\n",
       "Name: 2013-01-01 00:00:00, dtype: float64"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.loc[dates[0]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# np.argmax return the index of the largest value in the list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "lst = [1,2,3,4]\n",
    "import numpy as np\n",
    "np.argmax(lst)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# np.argsort return the sorted index "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "lst = [1,3,2,4]\n",
    "arr = np.array(lst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 2, 4])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 1, 3])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argsort(lst)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 1, 3])"
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