Numpy/Numpy Revision.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lFF783PD7ypT"
   },
   "source": [
    "### What is numpy?\n",
    "\n",
    "NumPy is the fundamental package for scientific computing in Python. It is a Python library that provides a multidimensional array object, various derived objects (such as masked arrays and matrices), and an assortment of routines for fast operations on arrays, including mathematical, logical, shape manipulation, sorting, selecting, I/O, discrete Fourier transforms, basic linear algebra, basic statistical operations, random simulation and much more.\n",
    "\n",
    "\n",
    "At the core of the NumPy package, is the ndarray object. This encapsulates n-dimensional arrays of homogeneous data types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HPRzhmwiZkOP"
   },
   "source": [
    "### Numpy Arrays Vs Python Sequences\n",
    "\n",
    "- NumPy arrays have a fixed size at creation, unlike Python lists (which can grow dynamically). Changing the size of an ndarray will create a new array and delete the original.\n",
    "\n",
    "- The elements in a NumPy array are all required to be of the same data type, and thus will be the same size in memory.\n",
    "\n",
    "- NumPy arrays facilitate advanced mathematical and other types of operations on large numbers of data. Typically, such operations are executed more efficiently and with less code than is possible using Python’s built-in sequences.\n",
    "\n",
    "- A growing plethora of scientific and mathematical Python-based packages are using NumPy arrays; though these typically support Python-sequence input, they convert such input to NumPy arrays prior to processing, and they often output NumPy arrays."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import Numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install numpy\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0PyrZ724szaG"
   },
   "source": [
    "### Creating Numpy Arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
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    "id": "V4AVNXrts3sL",
    "outputId": "5efc2800-7099-4f1a-c548-df46c157de27"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n"
     ]
    }
   ],
   "source": [
    "# np.array\n",
    "a = np.array([1,2,3])\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7, 9])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds = np.array([1,3,5,7,9])\n",
    "odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "odds.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
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    "id": "AAfxD1kCs6R5",
    "outputId": "e71d27eb-3106-43fd-8147-5a33b645f8b0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]]\n"
     ]
    }
   ],
   "source": [
    "# 2D and 3D\n",
    "b = np.array([[1,2,3],[4,5,6]])\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6],\n",
       "       [ 8, 10, 12],\n",
       "       [14, 16, 18]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "even = np.array([[2,4,6],[8,10,12],[14,16,18]])\n",
    "even"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "even.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "MyrHdd6J6CrF",
    "outputId": "2d7750a8-6e28-424d-bac4-7e61e7e73e9f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1 2]\n",
      "  [3 4]]\n",
      "\n",
      " [[5 6]\n",
      "  [7 8]]]\n"
     ]
    }
   ],
   "source": [
    "#  3D array / tensor\n",
    "c = np.array([[[1,2],[3,4]],[[5,6],[7,8]]])\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "FM8AwUOdFqC7",
    "outputId": "63ee85e6-449e-4e1f-e5a3-563bfae4dc9e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dtype\n",
    "np.array([1,2,3],dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array([1,2,3],dtype=bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ZY187Au_s8vm",
    "outputId": "cb13d451-a431-446f-f3a3-245315da6775"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 3., 5., 7., 9.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.arange\n",
    "np.arange(1,11,2,dtype = float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 3, 5, 7, 9])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(1,11,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14, 15, 16, 17, 18],\n",
       "       [19, 20, 21, 22, 23, 24, 25, 26, 27],\n",
       "       [28, 29, 30, 31, 32, 33, 34, 35, 36]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(1,37).reshape(4,9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "3Gc7BaJZwl7e",
    "outputId": "c1e4173a-80d6-449b-9cbc-ae4a6fba5d20"
   },
   "outputs": [],
   "source": [
    "# with reshape\n",
    "x = np.arange(16).reshape(2,2,2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.ndim # 4D array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "R2BYpYcGs-9l",
    "outputId": "992ba3c5-532b-4229-997b-b584de7d36d8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.ones \n",
    "np.ones((3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeros = np.zeros((4,5))\n",
    "zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 5)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeros.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True],\n",
       "       [ True,  True]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((2,2),dtype = bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vOjv_Euj8HGR",
    "outputId": "85fb7d62-e57f-4935-f33b-0c47a8bca4b3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.zeros\n",
    "np.zeros((3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "fYEeYi7itCRM",
    "outputId": "6a5ead6b-3dbb-45f5-a495-b7d78c2683ba"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.67119034, 0.51287857, 0.70717218, 0.73419688],\n",
       "       [0.12812082, 0.76489271, 0.74626886, 0.99438811],\n",
       "       [0.41579397, 0.42262405, 0.10283957, 0.70723241]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.random\n",
    "np.random.random((3,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.40831777],\n",
       "        [0.10836947],\n",
       "        [0.78932147],\n",
       "        [0.36725868],\n",
       "        [0.25149549],\n",
       "        [0.42977365],\n",
       "        [0.79975425],\n",
       "        [0.21801435],\n",
       "        [0.1075131 ],\n",
       "        [0.72273827]]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.random((1,10,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vel7WrgltE3P",
    "outputId": "21b993d2-c91c-42fa-f97c-030b87cc292a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10,  -8,  -6,  -4,  -2,   1,   3,   5,   7,  10])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.linspace\n",
    "np.linspace(-10,10,10,dtype=int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-10.        ,  -8.57142857,  -7.14285714,  -5.71428571,\n",
       "        -4.28571429,  -2.85714286,  -1.42857143,   0.        ,\n",
       "         1.42857143,   2.85714286,   4.28571429,   5.71428571,\n",
       "         7.14285714,   8.57142857,  10.        ])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(-10,10,15)\n",
    "# 1. Lower Range 2. Upper Range 3. Number of items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ewyMuXh1tJzi",
    "outputId": "921cf302-94d7-4d44-d696-881b839ced04"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# np.identity\n",
    "np.identity(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0.],\n",
       "       [0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.identity(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LphXpjZJtNyI"
   },
   "source": [
    "### Array Attributes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "UXnB5dIEFOgD",
    "outputId": "d6261278-40ee-4caa-cf15-946552e4e7c0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0, 1],\n",
       "        [2, 3]],\n",
       "\n",
       "       [[4, 5],\n",
       "        [6, 7]]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = np.arange(10,dtype=np.int32)\n",
    "A2 = np.arange(12,dtype=float).reshape(3,4)\n",
    "A3 = np.arange(8).reshape(2,2,2)\n",
    "A3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "qib4oDFptRKN",
    "outputId": "b70741e8-d727-4c59-b6ed-b8fd922501b8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ndim\n",
    "A1.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A3.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "InUvH8KGtSRv",
    "outputId": "d567d4cb-a533-4419-e4de-677dc5dd87bb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# shape\n",
    "print(A1.shape)\n",
    "A1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 4)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  2.,  3.],\n",
       "       [ 4.,  5.,  6.,  7.],\n",
       "       [ 8.,  9., 10., 11.]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(A2.shape)\n",
    "A2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 2, 2)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[[0, 1],\n",
       "        [2, 3]],\n",
       "\n",
       "       [[4, 5],\n",
       "        [6, 7]]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(A3.shape)\n",
    "A3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "9Dko5610tT-Z",
    "outputId": "5e8fdaa5-d444-4867-8ad0-3acf299c391e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  1.,  2.,  3.],\n",
       "       [ 4.,  5.,  6.,  7.],\n",
       "       [ 8.,  9., 10., 11.]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# size\n",
    "print(A2.size)\n",
    "A2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "wDFdHtH3tV1Z",
    "outputId": "dd8bf2cd-bc17-4d6c-ae17-06ae052ab711"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "8\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "# itemsize\n",
    "print(A1.itemsize)\n",
    "print(A2.itemsize)\n",
    "print(A3.itemsize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Pik7FgEVtXDj",
    "outputId": "00b7b1ad-d200-4c7c-e440-ba3c05928073"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int32\n",
      "float64\n",
      "int32\n"
     ]
    }
   ],
   "source": [
    "# dtype\n",
    "print(A1.dtype)\n",
    "print(A2.dtype)\n",
    "print(A3.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7Ase0eFWtcFl"
   },
   "source": [
    "### Changing Datatype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "DZPEFqhotbFS",
    "outputId": "848bd55f-1d69-4443-c832-d2735f4611f3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# astype\n",
    "A1.astype(float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2.astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "k-y-aaV9u52l"
   },
   "source": [
    "### Array Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "mIk8tk53HnOW",
    "outputId": "eba6d5cf-f698-494c-ea3c-c38541421cb4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = np.arange(12).reshape(3,4)\n",
    "A2 = np.arange(12,24).reshape(3,4)\n",
    "\n",
    "A2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Scalar operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vtQrWQKD87Fn",
    "outputId": "632feb6a-d00e-481f-806c-7b8589742bd2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# arithmetic\n",
    "A1 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2, -1,  0,  1],\n",
       "       [ 2,  3,  4,  5],\n",
       "       [ 6,  7,  8,  9]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 - 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  2,  4,  6],\n",
       "       [ 8, 10, 12, 14],\n",
       "       [16, 18, 20, 22]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   1,   4,   9],\n",
       "       [ 16,  25,  36,  49],\n",
       "       [ 64,  81, 100, 121]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "mCgPxTzQrtte",
    "outputId": "14a8bbd7-363d-42a7-bc28-984d37c6de07"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [False,  True, False, False],\n",
       "       [False, False, False, False]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# relational\n",
    "A1 == 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False],\n",
       "       [False,  True,  True,  True],\n",
       "       [ True,  True,  True,  True]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2 > 16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 14, 16, 18],\n",
       "       [20, 22, 24, 26],\n",
       "       [28, 30, 32, 34]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 + A2 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Vector operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "E2S3xDRxrt5D",
    "outputId": "2dfc1e18-65f7-4131-aed8-67bcc7b0996b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[          0,           1,       16384,    14348907],\n",
       "       [          0, -1564725563,  1159987200,   442181591],\n",
       "       [          0,  1914644777, -1304428544,  -122979837]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# arithmetic\n",
    "A1 ** A2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AQZgntYTu8ot"
   },
   "source": [
    "### Array Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "CHUj0a_dIP4F",
    "outputId": "a4e84b6e-e80f-4612-b9ae-9b64c87de269"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[33.,  3., 90.],\n",
       "       [94., 73., 30.],\n",
       "       [ 8., 10.,  9.]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = np.random.random((3,3))\n",
    "A1 = np.round(A1*100)\n",
    "A1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "94.0"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "350.0"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1320633072000.0"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1.prod()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15, 19, 23])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(A2,axis=1) # 0 -> col and 1 -> row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 16, 20])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(A2,axis=1) # 0 -> col and 1 -> row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "J1EWNET29Urx",
    "outputId": "34e6d72b-35f5-4dc3-f107-289bb0396c39"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([24816.,  2190., 24300.])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 0 -> col and 1 -> row\n",
    "np.prod(A1,axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "JAlMLFkds9KC",
    "outputId": "63636deb-3321-4714-d5a4-388445e1c492"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13.5, 17.5, 21.5])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2.mean()\n",
    "np.mean(A2,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16., 17., 18., 19.])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2.mean()\n",
    "np.mean(A2,axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13.5, 17.5, 21.5])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(A2,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.25, 1.25, 1.25])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(A2,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "vwLoQQVqs-m-",
    "outputId": "128781c4-4e3d-4748-c619-cdb874c99d9b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.99991186,  0.14112001,  0.89399666],\n",
       "       [-0.24525199, -0.67677196, -0.98803162],\n",
       "       [ 0.98935825, -0.54402111,  0.41211849]])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# trigonomoetric functions\n",
    "np.sin(A1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "RoEtYuiytFm1",
    "outputId": "7ab0e6f1-820d-4deb-c7a3-b3301eed9ec4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[114, 120, 126],\n",
       "       [378, 400, 422],\n",
       "       [642, 680, 718]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# dot product\n",
    "a2 = np.arange(12).reshape(3,4)\n",
    "a3 = np.arange(12,24).reshape(4,3)\n",
    "np.dot(a2,a3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "qd7GmrgEtH6i",
    "outputId": "85a52de0-68b1-4838-c462-f28a7e00d4db"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.49650756, 1.09861229, 4.49980967],\n",
       "       [4.54329478, 4.29045944, 3.40119738],\n",
       "       [2.07944154, 2.30258509, 2.19722458]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# log and exponents\n",
    "np.log(A1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.14643580e+14, 2.00855369e+01, 1.22040329e+39],\n",
       "       [6.66317622e+40, 5.05239363e+31, 1.06864746e+13],\n",
       "       [2.98095799e+03, 2.20264658e+04, 8.10308393e+03]])"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(A1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "EOXnVCZhtKk1",
    "outputId": "3be37070-696a-46e9-b5e7-6298bf2cdbb9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[79., 51., 25.],\n",
       "       [68., 37.,  0.]])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# round/floor/ceil\n",
    "np.round(np.random.random((2,3))*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[63., 77., 23.],\n",
       "       [52.,  9., 21.]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.floor(np.random.random((2,3))*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[33., 35., 93.],\n",
       "       [69., 27., 83.]])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ceil(np.random.random((2,3))*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2pYZJMrAuvuv"
   },
   "source": [
    "### Indexing and Slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "v1LynzX9u2R-",
    "outputId": "38bb09f7-c353-4da7-8f65-29126e81e742"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0, 1],\n",
       "        [2, 3]],\n",
       "\n",
       "       [[4, 5],\n",
       "        [6, 7]]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1 = np.arange(10)\n",
    "a2 = np.arange(12).reshape(3,4)\n",
    "a3 = np.arange(8).reshape(2,2,2)\n",
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "qyFbwR9Ku2YE",
    "outputId": "ee0795d0-a9e0-4494-dcf1-25278cdd3ef6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Q2IbBdEXu2a5",
    "outputId": "27f37180-6151-4b88-a4a7-b6b943a1a79f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "GIR5YhVzu2dc",
    "outputId": "5827789b-c94c-4343-f4bf-c37c0e55ae7b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[2,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "IbM-KNY3HP9-",
    "outputId": "b1ef95eb-dba8-4a19-f8d2-28505beffbff"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0, 1],\n",
       "        [2, 3]],\n",
       "\n",
       "       [[4, 5],\n",
       "        [6, 7]]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "xG7HU0RgHQD-",
    "outputId": "c0c15e95-2b15-4167-aeea-a2e9751aedb8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3[0,1,1] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3[1,0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "3EhcikSWHQKO",
    "outputId": "1a3fe02e-8b8f-4182-9a6d-0bb023be5b8c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3[1,1,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "_cgU2A52HQO0",
    "outputId": "eed00cc5-cefc-48de-bdc4-f28946b3131e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "HnFM0Wa5IMw2",
    "outputId": "312df828-b754-46e8-e47c-b6f3f2d11ad8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 4])"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1[2:5:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "SDWOK56EIM3n",
    "outputId": "682830f3-6c21-43c3-9b05-df473541570c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 183,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5, 6, 7])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[1,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  6, 10])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  3],\n",
       "       [ 9, 11]])"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[::2,1::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  6],\n",
       "       [ 8, 10]])"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[1::,::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 7])"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[1,0::3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "u7dQcPKpINDS",
    "outputId": "dd032bf5-8e11-4f23-9ec7-5e1807fda319"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2,  6, 10])"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "GYjyXNKnINTA",
    "outputId": "d1214ff7-d55d-43e4-94bb-8a6153a07a8a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  6],\n",
       "       [ 9, 10]])"
      ]
     },
     "execution_count": 186,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[1:,1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Z-24y62tK7KO",
    "outputId": "41eb67f0-d6f2-4c25-e64f-0482607c4d27"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2],\n",
       "        [ 3,  4,  5],\n",
       "        [ 6,  7,  8]],\n",
       "\n",
       "       [[ 9, 10, 11],\n",
       "        [12, 13, 14],\n",
       "        [15, 16, 17]],\n",
       "\n",
       "       [[18, 19, 20],\n",
       "        [21, 22, 23],\n",
       "        [24, 25, 26]]])"
      ]
     },
     "execution_count": 187,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3 = np.arange(27).reshape(3,3,3)\n",
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "DB1bM8NCMTub",
    "outputId": "9d8f91b7-3074-4788-e464-5529082cf4ba"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2],\n",
       "        [ 3,  4,  5],\n",
       "        [ 6,  7,  8]],\n",
       "\n",
       "       [[18, 19, 20],\n",
       "        [21, 22, 23],\n",
       "        [24, 25, 26]]])"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3[0::2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4, 5])"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3[0,1,::]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[22, 23],\n",
       "       [25, 26]])"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3[2,1:3,1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "mi2B5NN9IM-B",
    "outputId": "673febf9-b6ed-4fb7-d12d-32e9b3a9938a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  2],\n",
       "       [18, 20]])"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3[::2,0,::2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dUv9qM1yuIKJ"
   },
   "source": [
    "### Iterating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "lNgaCad6uKhm",
    "outputId": "b841e6c6-2d41-4a11-c9c1-7af7bb5dc72c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "a1\n",
    "for i in a1:\n",
    "  print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jNIsE0YFM6ZN",
    "outputId": "54433740-b3db-4467-a002-c447b8e8ebd7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "B2Hk-zAONHTY",
    "outputId": "793c2607-7b52-4556-cda0-fd82e60905c8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3]\n",
      "[4 5 6 7]\n",
      "[ 8  9 10 11]\n"
     ]
    }
   ],
   "source": [
    "for i in a2:\n",
    "  print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "8hfuC98qM-hC",
    "outputId": "0fb1ef2e-f8fd-4701-ba34-28c54527e2ce"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2],\n",
       "        [ 3,  4,  5],\n",
       "        [ 6,  7,  8]],\n",
       "\n",
       "       [[ 9, 10, 11],\n",
       "        [12, 13, 14],\n",
       "        [15, 16, 17]],\n",
       "\n",
       "       [[18, 19, 20],\n",
       "        [21, 22, 23],\n",
       "        [24, 25, 26]]])"
      ]
     },
     "execution_count": 210,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "DsYEnw2ONOIy",
    "outputId": "e1b309f4-0101-4991-8663-06e5f60597a1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]\n",
      " [6 7 8]]\n",
      "[[ 9 10 11]\n",
      " [12 13 14]\n",
      " [15 16 17]]\n",
      "[[18 19 20]\n",
      " [21 22 23]\n",
      " [24 25 26]]\n"
     ]
    }
   ],
   "source": [
    "for i in a3:\n",
    "  print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "IuRJ1QiRNZRM",
    "outputId": "438cbd63-6e58-49a8-b8c7-313e40addfce"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n"
     ]
    }
   ],
   "source": [
    "for i in np.nditer(a2):\n",
    "  print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZSS6AF_luNc-"
   },
   "source": [
    "### Reshaping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "DBIaUE8duQDz",
    "outputId": "ea99f6b4-b3ef-4cd7-dfee-63f1bcb3f6a3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  4,  8],\n",
       "       [ 1,  5,  9],\n",
       "       [ 2,  6, 10],\n",
       "       [ 3,  7, 11]])"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Transpose\n",
    "np.transpose(a2)\n",
    "a2.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  9, 18],\n",
       "        [ 3, 12, 21],\n",
       "        [ 6, 15, 24]],\n",
       "\n",
       "       [[ 1, 10, 19],\n",
       "        [ 4, 13, 22],\n",
       "        [ 7, 16, 25]],\n",
       "\n",
       "       [[ 2, 11, 20],\n",
       "        [ 5, 14, 23],\n",
       "        [ 8, 17, 26]]])"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "IULUNn5OuQMT",
    "outputId": "0588ea26-7e91-4f04-c291-e650892551da"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26])"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ravel\n",
    "a3.ravel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ouKcJQ5EuUQC"
   },
   "source": [
    "### Stacking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "HHSY1njTuXLi",
    "outputId": "a059eb6d-0f0c-48a3-c992-f513cbeabc70"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23]])"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# horizontal stacking\n",
    "a4 = np.arange(12).reshape(3,4)\n",
    "a5 = np.arange(12,24).reshape(3,4)\n",
    "a5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ne9uXt3yPKez",
    "outputId": "a7a04092-8889-4628-9966-85b7ef7f5b99"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3,  0,  1,  2,  3, 12, 13, 14, 15],\n",
       "       [ 4,  5,  6,  7,  4,  5,  6,  7, 16, 17, 18, 19],\n",
       "       [ 8,  9, 10, 11,  8,  9, 10, 11, 20, 21, 22, 23]])"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hstack((a2,a4,a5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "F6bFFNKuuZW5",
    "outputId": "14145606-ead6-417d-ae7f-f9ff5ec78394"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23]])"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Vertical stacking\n",
    "np.vstack((a4,a5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kaY006uXucF5"
   },
   "source": [
    "### Splitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kgbl6wkD9ll6",
    "outputId": "cb3ca012-8b56-426f-b3c8-eb919a4b89d8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# horizontal splitting\n",
    "a4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 390
    },
    "id": "FIfZM5BsQE5l",
    "outputId": "5d220f04-bf07-480c-9f51-d360c77f3635"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[0, 1],\n",
       "        [4, 5],\n",
       "        [8, 9]]),\n",
       " array([[ 2,  3],\n",
       "        [ 6,  7],\n",
       "        [10, 11]])]"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.hsplit(a4,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "nfhKoruOuhK-"
   },
   "outputs": [],
   "source": [
    "# vertical splitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "qJ2xEBFUuieB",
    "outputId": "d8395819-f098-4caa-9501-281d0722d593"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 13, 14, 15],\n",
       "       [16, 17, 18, 19],\n",
       "       [20, 21, 22, 23]])"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 390
    },
    "id": "1wxcLLR_QWVu",
    "outputId": "29ed6135-282d-4ed2-ddde-24c3b7fe750b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[12, 13, 14, 15]]),\n",
       " array([[16, 17, 18, 19]]),\n",
       " array([[20, 21, 22, 23]])]"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vsplit(a5,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "E_EVrYA7QadG"
   },
   "outputs": [],
   "source": [
    "\n"
   ]
  }
 ],
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