introduction-to-numpy.ipynb

{
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   "cell_type": "code",
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   "id": "d0ae2b18-18f0-4e11-ae1d-ef09a1aca4bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "097f28fa-9beb-4fe4-b595-7b341cdd3ea6",
   "metadata": {},
   "source": [
    "## DataTypes & Attributes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "01547f79-d414-40f1-8a22-0cb313ff199c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# NumPy's main datatypes is ndarray\n",
    "a1=np.array([1,2,3])\n",
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1bb2032b-e206-4df4-9533-5a0d010f7b9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(a1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b16dcc18-dd2d-429c-85f1-58e512eba2d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "a2=np.array([[1,2.0,3.3],\n",
    "             [4,5  ,6.5]])\n",
    "a3=np.array([[[1,2,3],\n",
    "             [4,5,6],\n",
    "             [7,8,9]],\n",
    "            [[10,11,12],\n",
    "             [13,14,15],\n",
    "             [16,17,18]]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2fd59b5f-b1da-4d94-bfb9-249c7465ccad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 2. , 3.3],\n",
       "       [4. , 5. , 6.5]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "432af675-0d84-468a-bde7-7f88b9ce2153",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6],\n",
       "        [ 7,  8,  9]],\n",
       "\n",
       "       [[10, 11, 12],\n",
       "        [13, 14, 15],\n",
       "        [16, 17, 18]]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0f225eb4-0107-468d-a880-6344e59ee3e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "db095119-ef02-4c04-9c72-f478be7cb33c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "07ea8d59-7f46-4db3-8652-0dc36d3b5912",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3, 3)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "0701d75e-a684-41a7-a046-59dc8f2e1cdf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 2, 3)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1.ndim,a2.ndim,a3.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0e35dcb9-304f-42ab-a189-b35cb997ee21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(dtype('int32'), dtype('float64'), dtype('int32'))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1.dtype,a2.dtype,a3.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d0accbf7-fdd5-4816-bf74-e6f479790259",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 6, 18)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1.size,a2.size,a3.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ce7b699b-e55b-4391-90e7-5bb4409d9a6d",
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     0    1    2\n",
       "0  1.0  2.0  3.3\n",
       "1  4.0  5.0  6.5"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a DataFrame from a NumPy array\n",
    "import pandas as pd\n",
    "\n",
    "df=pd.DataFrame(a2)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b2b282b-7a58-46b6-9bf8-c5e7a54ca836",
   "metadata": {},
   "source": [
    "## 2. Creating arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0f9a20ba-a0eb-40c9-a2e7-a32a5fdd163d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_array=np.array([1,2,3])\n",
    "sample_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d0df6572-481a-4191-ad2e-146bcae5fb23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_array.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ed6ebecc-1f75-461a-aa1a-ed52582bf81c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones=np.ones((2,3))\n",
    "ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "45bc27f7-dcbe-4a14-ae4f-056642ed5d52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "99c90ced-1763-41c9-bb78-095c63ee6dfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zeros=np.zeros((2,3))\n",
    "zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2d3dec17-6671-4699-bce4-caed114dc9c7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 4, 6, 8])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range_array=np.arange(0,10,2)\n",
    "range_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e10c51a3-fc29-4fbd-b754-04a08de43918",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 6, 8, 5, 8],\n",
       "       [0, 1, 8, 1, 6],\n",
       "       [4, 6, 4, 9, 2]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_array=np.random.randint(0, 10, size=(3,5))\n",
    "random_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ac810724-cbf7-4226-a2b9-ed2ea2c9f85e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_array.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "6f5f6e43-511c-4c5e-9c0f-6828ed7466de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 5)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_array.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "07e4b65e-e936-4e54-9c77-62f1281cac92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.33040793, 0.99626144, 0.4501074 ],\n",
       "       [0.98671329, 0.91353231, 0.47117792],\n",
       "       [0.4831306 , 0.58850026, 0.62207192],\n",
       "       [0.67247299, 0.55895526, 0.32199236],\n",
       "       [0.45429125, 0.42638456, 0.61989581]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_array_2=np.random.random((5,3))\n",
    "random_array_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "366bb247-1438-43a0-9336-c717982491a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 3)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_array_2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "cbed6a35-c8b5-4f94-bed3-01a9f71aa199",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.03715221, 0.32709038, 0.16975319],\n",
       "       [0.99018352, 0.72690708, 0.11146663],\n",
       "       [0.17248054, 0.58536896, 0.63739384],\n",
       "       [0.82503801, 0.39789665, 0.44339355],\n",
       "       [0.02586375, 0.89728388, 0.00658609]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_array_3=np.random.rand(5,3)\n",
    "random_array_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "62c207bc-9d11-474e-ba9a-a2a5af526f51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 0, 3],\n",
       "       [3, 7, 9],\n",
       "       [3, 5, 2],\n",
       "       [4, 7, 6],\n",
       "       [8, 8, 1]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pseudo-random numbers\n",
    "np.random.seed(seed=0)\n",
    "random_array_4=np.random.randint(10,size=(5,3))\n",
    "random_array_4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "fff3b30a-87f3-4fd3-bad3-32c8333b8a7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, 3)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_array_4.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05a541f4-1957-42ef-8d07-10fa6a0ac04b",
   "metadata": {},
   "source": [
    "## 3.Viewing array and matrices "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ff78e7fe-20fb-4f5a-baa0-f315de6ddfe2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.unique(random_array_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "bd0e9691-fe78-4d0a-a8f6-621604aa3f97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9243c812-de0e-4d8e-8ff2-71df297d1e38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 2. , 3.3],\n",
       "       [4. , 5. , 6.5]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "09390a30-c678-4157-ad1a-4f8f5e2cceb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6],\n",
       "        [ 7,  8,  9]],\n",
       "\n",
       "       [[10, 11, 12],\n",
       "        [13, 14, 15],\n",
       "        [16, 17, 18]]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "66b3e691-ba2a-44b1-9af4-f5043aacc3da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "5616691b-6e06-4c69-a53f-1362a6693f06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1. , 2. , 3.3])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "ab71b1cb-61f2-4bd2-8279-7b2e2f709b00",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " a3[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "5cbe93ea-f66f-4031-aade-f7192a2cfb66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2],\n",
       "        [ 4,  5]],\n",
       "\n",
       "       [[10, 11],\n",
       "        [13, 14]]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3[:2,:2,:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "4f346f05-7ba9-4bbf-9998-b02e01aaa898",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[8, 8, 2, 3, 2],\n",
       "         [0, 8, 8, 3, 8],\n",
       "         [2, 8, 4, 3, 0],\n",
       "         [4, 3, 6, 9, 8]],\n",
       "\n",
       "        [[0, 8, 5, 9, 0],\n",
       "         [9, 6, 5, 3, 1],\n",
       "         [8, 0, 4, 9, 6],\n",
       "         [5, 7, 8, 8, 9]],\n",
       "\n",
       "        [[2, 8, 6, 6, 9],\n",
       "         [1, 6, 8, 8, 3],\n",
       "         [2, 3, 6, 3, 6],\n",
       "         [5, 7, 0, 8, 4]]],\n",
       "\n",
       "\n",
       "       [[[6, 5, 8, 2, 3],\n",
       "         [9, 7, 5, 3, 4],\n",
       "         [5, 3, 3, 7, 9],\n",
       "         [9, 9, 7, 3, 2]],\n",
       "\n",
       "        [[3, 9, 7, 7, 5],\n",
       "         [1, 2, 2, 8, 1],\n",
       "         [5, 8, 4, 0, 2],\n",
       "         [5, 5, 0, 8, 1]],\n",
       "\n",
       "        [[1, 0, 3, 8, 8],\n",
       "         [4, 4, 0, 9, 3],\n",
       "         [7, 3, 2, 1, 1],\n",
       "         [2, 1, 4, 2, 5]]]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a4=np.random.randint(10,size=(2,3,4,5))\n",
    "a4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "a81617b7-aa4d-4bf5-90e2-d73033088645",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((2, 3, 4, 5), 4)"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a4.shape, a4.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "f854de52-231b-4b82-818c-7e0c259a84a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[8, 8, 2, 3],\n",
       "         [0, 8, 8, 3],\n",
       "         [2, 8, 4, 3],\n",
       "         [4, 3, 6, 9]],\n",
       "\n",
       "        [[0, 8, 5, 9],\n",
       "         [9, 6, 5, 3],\n",
       "         [8, 0, 4, 9],\n",
       "         [5, 7, 8, 8]],\n",
       "\n",
       "        [[2, 8, 6, 6],\n",
       "         [1, 6, 8, 8],\n",
       "         [2, 3, 6, 3],\n",
       "         [5, 7, 0, 8]]],\n",
       "\n",
       "\n",
       "       [[[6, 5, 8, 2],\n",
       "         [9, 7, 5, 3],\n",
       "         [5, 3, 3, 7],\n",
       "         [9, 9, 7, 3]],\n",
       "\n",
       "        [[3, 9, 7, 7],\n",
       "         [1, 2, 2, 8],\n",
       "         [5, 8, 4, 0],\n",
       "         [5, 5, 0, 8]],\n",
       "\n",
       "        [[1, 0, 3, 8],\n",
       "         [4, 4, 0, 9],\n",
       "         [7, 3, 2, 1],\n",
       "         [2, 1, 4, 2]]]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the first 4 numbers of the inner most arrays\n",
    "a4[:,:,:,:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32416cb2-e66f-47f9-be69-91bc06efa404",
   "metadata": {},
   "source": [
    "## 4. Manipulating and comparing arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "641985fb-a3d5-4c9f-a5ab-04c60e9dab8e",
   "metadata": {},
   "source": [
    "#### Arithmetic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "451a6fcc-04fc-466b-be2e-5a9662ac62f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "b2872608-2582-42d1-9a3b-4afafd579767",
   "metadata": {},
   "outputs": [],
   "source": [
    "ones=np.ones(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "831effad-4ee0-485b-a3a4-451f84bf118a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1.])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "70fefddd-47f7-445b-882a-15a5ae872535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 3., 4.])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1+ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "8e9293df-2b18-437c-8b67-17ea61be8530",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 3., 4.])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add(a1,ones)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "baba3138-3ec6-4d17-9e58-0edf9853a39f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2.])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1-ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "7b94567d-d130-4eed-afa1-c5477860361d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3.])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1*ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "d1689836-9726-4ec1-bf63-bfc397247a2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 2. , 3.3],\n",
       "       [4. , 5. , 6.5]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "1724f4e1-6267-4279-a529-c08d1000b4ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  4. ,  9.9],\n",
       "       [ 4. , 10. , 19.5]])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1*a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "93358cea-bb9b-45bb-87ec-f69efd2ef706",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "cannot reshape array of size 18 into shape (2,3)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[59], line 3\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;66;03m# How can you reshape a2 to be compatible with a3?\u001b[39;00m\n\u001b[0;32m      2\u001b[0m \u001b[38;5;66;03m# Search: \"How to reshape numpy array\"\u001b[39;00m\n\u001b[1;32m----> 3\u001b[0m new_a3\u001b[38;5;241m=\u001b[39ma3\u001b[38;5;241m.\u001b[39mreshape((\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m3\u001b[39m))\n\u001b[0;32m      4\u001b[0m a2\u001b[38;5;241m*\u001b[39ma3\n",
      "\u001b[1;31mValueError\u001b[0m: cannot reshape array of size 18 into shape (2,3)"
     ]
    }
   ],
   "source": [
    "# How can you reshape a2 to be compatible with a3?\n",
    "# Search: \"How to reshape numpy array\"\n",
    "new_a3=a3.reshape((2,3))\n",
    "a2*a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "4b6d4a08-9f30-4610-ae99-41d66efd7271",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3.])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1/ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "2de0958c-1b97-4ac8-a395-f88281509c7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 1.        , 1.1       ],\n",
       "       [4.        , 2.5       , 2.16666667]])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2/a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "3d9f7559-ed34-4512-81ee-fafa3d9478b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [4., 2., 2.]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# floor division removes the decimals\n",
    "a2//a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "fdde1748-15b3-422d-bb24-26a73db489a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  4.  , 10.89],\n",
       "       [16.  , 25.  , 42.25]])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "8cb572ee-9a64-41d7-8877-b52dd7d90e38",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.  ,  4.  , 10.89],\n",
       "       [16.  , 25.  , 42.25]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.square(a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "bf001491-b0d5-442e-94e0-3d3b001d4109",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1], dtype=int32)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1%2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "99279e34-67ac-4a4a-8b52-83a26e185758",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5, 1. , 1.5])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "d8048950-61eb-4168-8034-cdc51e0a7c95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.71828183,  7.3890561 , 20.08553692])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(a1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "b0da2fe6-bd75-40ec-98e1-6453c79d0f0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 0.69314718, 1.09861229])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(a1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8dbb9a40-63c7-4b18-b6e2-0c93f44c0f71",
   "metadata": {},
   "source": [
    "#### Aggregation\n",
    "Aggregation = performig the same operation on a number of things"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "d771c6b8-f491-4ad0-a85a-5f85b936d1d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "listy_list=[1,2,3]\n",
    "listy_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "e29acef0-5c2b-4f51-9ea6-20a7b99eac4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(listy_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "00f9728b-5502-444a-8d9c-abf63a55e4bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(a1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "071747eb-886a-46a9-875b-fca23eb8a9a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(a1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4a39706-6b96-4bd8-a1e4-c1c4d86d96e7",
   "metadata": {},
   "source": [
    "Use Python's methods (`sum()`) on Python datatypes and use Numpy's methods on numpy arrays (`np.sum()`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "bea5e4fa-4ffd-4b86-8df8-1da6425670ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100000"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#creating a massive numpy array\n",
    "massive_array=np.random.random(100000)\n",
    "massive_array.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "3c0b094d-5261-4f7d-b434-8dd75fa59a2a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.21874937, 0.56957353, 0.45210904, 0.97023668, 0.68054469,\n",
       "       0.08529557, 0.05641833, 0.4878377 , 0.88100456, 0.97640439])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "massive_array[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "cf83a107-7e00-4aa6-954c-05732cefbda9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "29.4 ms ± 4.74 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n",
      "127 µs ± 26.3 µs per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit sum(massive_array) #Python's sum()\n",
    "%timeit np.sum(massive_array) #NumPy's np.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "7e019236-521f-41d0-8ad7-4fbf1721879f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.6333333333333333"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "650a48ba-f360-4a2a-985e-4ad92ca4e355",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.5"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "a36f5d14-aaee-4bd9-a0a9-0d63d80e00d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "a769845d-6d0a-47ca-91f6-5e3eb3f224d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8226964152656422"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Standard deviation = a measure of how spread out a group of numbers is from the mean\n",
    "np.std(a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "f2a3f254-ea25-4035-875f-c4781a304bcc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.3222222222222224"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# variance = measure of the averae degree to which each numbe ris different from the mean\n",
    "# higher variance = wider range of numbers\n",
    "# lower variance = lower range of numbers\n",
    "np.var(a2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "67921840-3a7e-4e6f-a95d-1bba314185fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.8226964152656422"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#SD = sqrt of var\n",
    "np.sqrt(np.var(a2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "8bb49870-cd30-4c92-b240-8b89a36436f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# demo of std and var\n",
    "high_var_array=np.array([1,100,200,300,4000,5000])\n",
    "low_var_array=np.array([2,4,6,8,10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "3378a925-5c21-41ab-ad8e-c9ec140669aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4296133.472222221, 8.0)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(high_var_array), np.var(low_var_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "57d043fb-9cac-42d5-aa1f-984c59ed0ca4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2072.711623024829, 2.8284271247461903)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(high_var_array), np.std(low_var_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "d155c3f5-8339-467b-bf2f-6000bf038b1b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1600.1666666666667, 6.0)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(high_var_array), np.mean(low_var_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "e4d23f30-3ff6-4c90-8b7a-d0b8ccb81048",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.hist(high_var_array)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "cbd3f97a-2858-4b45-a161-4fcab0ad08e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(low_var_array)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13a6389c-a159-4d0e-a283-2e6baf0073ed",
   "metadata": {},
   "source": [
    "#### Reshaping and Transposing "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "8de36e35-c86a-476d-8df1-5043f0f259be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 2. , 3.3],\n",
       "       [4. , 5. , 6.5]])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "b866edb9-0c6c-49a2-92be-13c8d2f1f682",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "d3809e8f-e643-465d-b96f-82a1c79cb1cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1,  2,  3],\n",
       "        [ 4,  5,  6],\n",
       "        [ 7,  8,  9]],\n",
       "\n",
       "       [[10, 11, 12],\n",
       "        [13, 14, 15],\n",
       "        [16, 17, 18]]])"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "cf649c35-86ba-402e-8d2f-786beb77ddcb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3, 3)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "63a3200a-e18d-4547-b368-17266e006458",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1. ],\n",
       "        [2. ],\n",
       "        [3.3]],\n",
       "\n",
       "       [[4. ],\n",
       "        [5. ],\n",
       "        [6.5]]])"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2_reshape=a2.reshape(2,3,1)\n",
    "a2_reshape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "47235077-8bd4-4242-8320-e1a76ff4e246",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  1. ,   2. ,   3. ],\n",
       "        [  8. ,  10. ,  12. ],\n",
       "        [ 23.1,  26.4,  29.7]],\n",
       "\n",
       "       [[ 40. ,  44. ,  48. ],\n",
       "        [ 65. ,  70. ,  75. ],\n",
       "        [104. , 110.5, 117. ]]])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2_reshape*a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "10e9f519-3de6-4c45-a711-3052d85b1cce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 2. , 3.3],\n",
       "       [4. , 5. , 6.5]])"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "ec7a4606-ed64-43e5-b3e4-13bee97ce603",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 4. ],\n",
       "       [2. , 5. ],\n",
       "       [3.3, 6.5]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Transpose\n",
    "a2.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "5fb55809-91fa-42ed-b49f-9db442518e7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1, 10],\n",
       "        [ 4, 13],\n",
       "        [ 7, 16]],\n",
       "\n",
       "       [[ 2, 11],\n",
       "        [ 5, 14],\n",
       "        [ 8, 17]],\n",
       "\n",
       "       [[ 3, 12],\n",
       "        [ 6, 15],\n",
       "        [ 9, 18]]])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3.T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39052fbb-a85f-428e-95f1-ad6318e0ff08",
   "metadata": {},
   "source": [
    "## Dot Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "96b9e46d-7805-4e82-9df7-4e62be23ef0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 0, 3],\n",
       "       [3, 7, 9],\n",
       "       [3, 5, 2],\n",
       "       [4, 7, 6],\n",
       "       [8, 8, 1]])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "\n",
    "mat1=np.random.randint(10,size=(5,3))\n",
    "mat2=np.random.randint(10,size=(5,3))\n",
    "\n",
    "mat1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "0164d17d-9ff8-4d38-ae77-5e6c349b149c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 7, 7],\n",
       "       [8, 1, 5],\n",
       "       [9, 8, 9],\n",
       "       [4, 3, 0],\n",
       "       [3, 5, 0]])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "a16a0f12-aa55-4dc5-9029-40d227ab386c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5, 3), (5, 3))"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat1.shape,mat2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "d1dd3e26-0172-41ba-ba9e-0b962dec6fb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[30,  0, 21],\n",
       "       [24,  7, 45],\n",
       "       [27, 40, 18],\n",
       "       [16, 21,  0],\n",
       "       [24, 40,  0]])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#element vise\n",
    "mat1 * mat2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "51b5dac3-ffc9-49ee-98cf-f2eafd67ac83",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "shapes (5,3) and (5,3) not aligned: 3 (dim 1) != 5 (dim 0)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[114], line 2\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[38;5;66;03m# dot product\u001b[39;00m\n\u001b[1;32m----> 2\u001b[0m np\u001b[38;5;241m.\u001b[39mdot(mat1,mat2)\n",
      "\u001b[1;31mValueError\u001b[0m: shapes (5,3) and (5,3) not aligned: 3 (dim 1) != 5 (dim 0)"
     ]
    }
   ],
   "source": [
    "# dot product\n",
    "np.dot(mat1,mat2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "f7a3de67-3446-4ce4-b864-23f4d75b2471",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 51,  55,  72,  20,  15],\n",
       "       [130,  76, 164,  33,  44],\n",
       "       [ 67,  39,  85,  27,  34],\n",
       "       [115,  69, 146,  37,  47],\n",
       "       [111,  77, 145,  56,  64]])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(mat1,mat2.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d876c97d-e5da-4c36-a6f1-f10ac3a9441d",
   "metadata": {},
   "source": [
    "## Dot product example (nut butter sales)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "4c387178-53ab-4b60-8d2f-1fc3ee65d61a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12, 15,  0],\n",
       "       [ 3,  3,  7],\n",
       "       [ 9, 19, 18],\n",
       "       [ 4,  6, 12],\n",
       "       [ 1,  6,  7]])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "# number of jars sold\n",
    "sales_amounts=np.random.randint(20,size=(5,3))\n",
    "sales_amounts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "a0e133c7-877b-4f81-8c0d-c11a93fa82c5",
   "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>Almond butter</th>\n",
       "      <th>Peanut butter</th>\n",
       "      <th>Cashew butter</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Mon</th>\n",
       "      <td>12</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tues</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wed</th>\n",
       "      <td>9</td>\n",
       "      <td>19</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>thur</th>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fri</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Almond butter  Peanut butter  Cashew butter\n",
       "Mon              12             15              0\n",
       "Tues              3              3              7\n",
       "Wed               9             19             18\n",
       "thur              4              6             12\n",
       "Fri               1              6              7"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# creating a dataframe for weekly_sales\n",
    "weekly_sales=pd.DataFrame(sales_amounts,\n",
    "                          index=[\"Mon\",\"Tues\",\"Wed\",\"thur\",\"Fri\"],\n",
    "                          columns=[\"Almond butter\",\"Peanut butter\", \"Cashew butter\"])\n",
    "weekly_sales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "17858c8d-8062-4c1d-a4b2-6c2d475a22e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10,  8, 12])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create prices array\n",
    "prices=np.array([10,8,12])\n",
    "prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "704666ee-ea5a-4717-86f3-32223dcf58f2",
   "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>Almond butter</th>\n",
       "      <th>Peanut butter</th>\n",
       "      <th>Cashew butter</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Price</th>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Almond butter  Peanut butter  Cashew butter\n",
       "Price             10              8             12"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#creating a dataframe for butter prices\n",
    "butter_prices=pd.DataFrame(prices.reshape(1,3),\n",
    "                           index=[\"Price\"],\n",
    "                           columns=[\"Almond butter\",\"Peanut butter\", \"Cashew butter\"])\n",
    "butter_prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "e3904d78-709e-41e3-832a-793f4920737c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([240, 138, 458, 232, 142])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_sales=prices.dot(sales_amounts.T)\n",
    "total_sales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "321e9995-bbd9-4765-b84b-7d91091d4b2b",
   "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>Mon</th>\n",
       "      <th>Tues</th>\n",
       "      <th>Wed</th>\n",
       "      <th>thur</th>\n",
       "      <th>Fri</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Price</th>\n",
       "      <td>240</td>\n",
       "      <td>138</td>\n",
       "      <td>458</td>\n",
       "      <td>232</td>\n",
       "      <td>142</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Mon  Tues  Wed  thur  Fri\n",
       "Price  240   138  458   232  142"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Create daily_sales\n",
    "daily_sales=butter_prices.dot(weekly_sales.T)\n",
    "daily_sales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "ba5d4e2e-0ad1-45de-90da-31c624f43179",
   "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>Almond butter</th>\n",
       "      <th>Peanut butter</th>\n",
       "      <th>Cashew butter</th>\n",
       "      <th>Total ($)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Mon</th>\n",
       "      <td>12</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tues</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wed</th>\n",
       "      <td>9</td>\n",
       "      <td>19</td>\n",
       "      <td>18</td>\n",
       "      <td>458</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>thur</th>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>12</td>\n",
       "      <td>232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Fri</th>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>142</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Almond butter  Peanut butter  Cashew butter  Total ($)\n",
       "Mon              12             15              0        240\n",
       "Tues              3              3              7        138\n",
       "Wed               9             19             18        458\n",
       "thur              4              6             12        232\n",
       "Fri               1              6              7        142"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weekly_sales[\"Total ($)\"]=daily_sales.T\n",
    "weekly_sales"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2ec3167-8d3b-4dbe-b44b-81b668b926c0",
   "metadata": {},
   "source": [
    "#### Comparison operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "37fba8a1-6e68-4adb-a52e-fc5fe27da404",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "80eee95e-5d43-43ee-9101-4e28fb4a92f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1. , 2. , 3.3],\n",
       "       [4. , 5. , 6.5]])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "7cd93886-71da-4ef8-be57-bd2d00c6ff5a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False],\n",
       "       [False, False, False]])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1>a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "d2123cad-399e-4977-ac3a-55ac635ecd0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False,  True],\n",
       "       [ True,  True,  True]])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1<a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "57530ec1-1746-4546-a0fe-150689fb6ad9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True,  True, False],\n",
       "       [False, False, False]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1==a2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa9b7f4e-e315-42c6-91e2-839b602d467f",
   "metadata": {},
   "source": [
    "## 5. Sorting arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "9d8d6d41-4db3-4e5c-96c2-49d6a7116b0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 6, 8, 5, 8],\n",
       "       [0, 1, 8, 1, 6],\n",
       "       [4, 6, 4, 9, 2]])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "0784ac0b-d6a3-463f-aeb8-47d14f075372",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 5, 6, 8, 8],\n",
       "       [0, 1, 1, 6, 8],\n",
       "       [2, 4, 4, 6, 9]])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(random_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "eca301a2-dccf-4832-b624-6d9a1515ecf7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 3, 1, 2, 4],\n",
       "       [0, 1, 3, 4, 2],\n",
       "       [4, 0, 2, 1, 3]], dtype=int64)"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argsort(random_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "86f31e22-3a50-4257-a44b-7cabd552a6c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 2)"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmin(a1),np.argmax(a1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "3abea94a-4c46-4fe7-b63d-0bff7ef4326b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 0, 0, 2, 0], dtype=int64)"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(random_array,axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71dda847-89b2-4dc7-9c31-aa57b1a54ba7",
   "metadata": {},
   "source": [
    "## 6. Practical Example - NumPy in Action!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5172a01b-5d02-4ee6-98bd-0a3889881a54",
   "metadata": {},
   "source": [
    "<img src=\"numpy-images/panda.png\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "616b4acc-168f-4d15-b6fa-cb7973bfe8c2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "# turn an image into a numpy array\n",
    "from matplotlib.image import imread\n",
    "\n",
    "panda = imread(\"numpy-images/panda.png\")\n",
    "print(type(panda))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "21595ee2-63d3-4e3a-bd2f-cbe5f7def24b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        ...,\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765]],\n",
       "\n",
       "       [[0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        ...,\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765]],\n",
       "\n",
       "       [[0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        ...,\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[0.13333334, 0.07450981, 0.05490196],\n",
       "        [0.12156863, 0.0627451 , 0.04313726],\n",
       "        [0.10980392, 0.05098039, 0.03137255],\n",
       "        ...,\n",
       "        [0.02745098, 0.02745098, 0.03529412],\n",
       "        [0.02745098, 0.02745098, 0.03529412],\n",
       "        [0.02745098, 0.02745098, 0.03529412]],\n",
       "\n",
       "       [[0.13333334, 0.07450981, 0.05490196],\n",
       "        [0.12156863, 0.0627451 , 0.04313726],\n",
       "        [0.12156863, 0.0627451 , 0.04313726],\n",
       "        ...,\n",
       "        [0.02352941, 0.02352941, 0.03137255],\n",
       "        [0.02352941, 0.02352941, 0.03137255],\n",
       "        [0.02352941, 0.02352941, 0.03137255]],\n",
       "\n",
       "       [[0.13333334, 0.07450981, 0.05490196],\n",
       "        [0.12156863, 0.0627451 , 0.04313726],\n",
       "        [0.12156863, 0.0627451 , 0.04313726],\n",
       "        ...,\n",
       "        [0.02352941, 0.02352941, 0.03137255],\n",
       "        [0.02352941, 0.02352941, 0.03137255],\n",
       "        [0.02352941, 0.02352941, 0.03137255]]], dtype=float32)"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "panda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "504e1d78-fe02-4c74-b3b3-0f69dc4cf3c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(24465000, (2330, 3500, 3), 3)"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "panda.size,panda.shape,panda.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "3bfd1044-bbae-4694-81a4-c385dd0332d4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        ...,\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765]],\n",
       "\n",
       "       [[0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        ...,\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765]],\n",
       "\n",
       "       [[0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        ...,\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765],\n",
       "        [0.16470589, 0.12941177, 0.09411765]],\n",
       "\n",
       "       [[0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        ...,\n",
       "        [0.16862746, 0.13333334, 0.09803922],\n",
       "        [0.16862746, 0.13333334, 0.09803922],\n",
       "        [0.16862746, 0.13333334, 0.09803922]],\n",
       "\n",
       "       [[0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        [0.05490196, 0.10588235, 0.06666667],\n",
       "        ...,\n",
       "        [0.16862746, 0.13333334, 0.09803922],\n",
       "        [0.16862746, 0.13333334, 0.09803922],\n",
       "        [0.16862746, 0.13333334, 0.09803922]]], dtype=float32)"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "panda[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f52aaed2-7cd5-4ad4-9c1a-431da8f698c5",
   "metadata": {},
   "source": [
    "<img src=\"numpy-images/car-photo.png\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "ca78aca4-9c93-4961-9858-cbc250164878",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "car=imread(\"numpy-images/car-photo.png\")\n",
    "print(type(car))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "f30acdfc-9910-4203-9991-6699b2757c60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0.5019608 , 0.50980395, 0.4862745 , 1.        ],\n",
       "        [0.3372549 , 0.34509805, 0.30588236, 1.        ],\n",
       "        [0.20392157, 0.21568628, 0.14901961, 1.        ],\n",
       "        ...,\n",
       "        [0.64705884, 0.7058824 , 0.54901963, 1.        ],\n",
       "        [0.59607846, 0.63529414, 0.45882353, 1.        ],\n",
       "        [0.44705883, 0.47058824, 0.3372549 , 1.        ]]], dtype=float32)"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "car[:1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e3114ec-11d6-41fc-9990-f99e0cd203c2",
   "metadata": {},
   "source": [
    "<img src=\"numpy-images/dog-photo.png\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "29ade308-af5c-4085-81bb-929ed7ab68fe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "dog=imread(\"numpy-images/car-photo.png\")\n",
    "print(type(dog))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3af513b4-447b-41f6-ae17-c111daf55cbb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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