Lecture 10 - Array Transposition.ipynb

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   "source": [
    "import numpy as np"
   ]
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   "cell_type": "code",
   "execution_count": 4,
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   "source": [
    "# create an arrange of 50 elements, reshape to 10 rows of 5 elements\n",
    "arr = np.arange(50).reshape((10,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14],\n",
       "       [15, 16, 17, 18, 19],\n",
       "       [20, 21, 22, 23, 24],\n",
       "       [25, 26, 27, 28, 29],\n",
       "       [30, 31, 32, 33, 34],\n",
       "       [35, 36, 37, 38, 39],\n",
       "       [40, 41, 42, 43, 44],\n",
       "       [45, 46, 47, 48, 49]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  5, 10, 15, 20, 25, 30, 35, 40, 45],\n",
       "       [ 1,  6, 11, 16, 21, 26, 31, 36, 41, 46],\n",
       "       [ 2,  7, 12, 17, 22, 27, 32, 37, 42, 47],\n",
       "       [ 3,  8, 13, 18, 23, 28, 33, 38, 43, 48],\n",
       "       [ 4,  9, 14, 19, 24, 29, 34, 39, 44, 49]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# transpose is easy, call the .T method\n",
    "arr.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7125, 7350, 7575, 7800, 8025],\n",
       "       [7350, 7585, 7820, 8055, 8290],\n",
       "       [7575, 7820, 8065, 8310, 8555],\n",
       "       [7800, 8055, 8310, 8565, 8820],\n",
       "       [8025, 8290, 8555, 8820, 9085]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can take the \"dot\" product (google it, he didn't explain)\n",
    "np.dot(arr.T, arr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The \"dot product\" of an array is the sum of the multiple of two arrays:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "def dot(v1, v2):\n",
    "...     return sum(x*y for x,y in zip(v1,v2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "dot([1,2,3], [4,5,6]) = 32"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1],\n",
       "        [ 2,  3],\n",
       "        [ 4,  5],\n",
       "        [ 6,  7],\n",
       "        [ 8,  9]],\n",
       "\n",
       "       [[10, 11],\n",
       "        [12, 13],\n",
       "        [14, 15],\n",
       "        [16, 17],\n",
       "        [18, 19]],\n",
       "\n",
       "       [[20, 21],\n",
       "        [22, 23],\n",
       "        [24, 25],\n",
       "        [26, 27],\n",
       "        [28, 29]],\n",
       "\n",
       "       [[30, 31],\n",
       "        [32, 33],\n",
       "        [34, 35],\n",
       "        [36, 37],\n",
       "        [38, 39]],\n",
       "\n",
       "       [[40, 41],\n",
       "        [42, 43],\n",
       "        [44, 45],\n",
       "        [46, 47],\n",
       "        [48, 49]]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a 3d matrix -> 5 sets, 5 rows, 2 columns\n",
    "arr3d = np.arange(50).reshape((5,5,2))\n",
    "arr3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = np.array([[1,2,3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# we can swap axes\n",
    "arr.swapaxes(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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