Practice_Lab_Math_AI_ML.ipynb

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 "cells": [
  {
   "cell_type": "markdown",
   "id": "5258daf2-273f-452d-9ea8-7515b5997452",
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   "source": [
    "# Mathematical Foundation for AI and Machine Learning\n",
    "# Practice Lab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "06977fd8-8062-4548-9e95-a393ede2af72",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Numpy: 2.0.1\n",
      "Pandas: 2.2.2\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "print(\"Numpy: {}\".format(np.__version__))\n",
    "print(\"Pandas: {}\".format(pd.__version__))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b3686e74-8a21-45da-9fcd-d00ee5033662",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2ca4f61d-6116-4f9b-aa10-1f32761ebecc",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining a scalar\n",
    "x = 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "bbf2e7ab-0716-4a26-9225-7d35e05614ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# defining a vector\n",
    "x = np.array((1,2,3))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6759f02d-fa66-41ce-be36-0fc9a47388be",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " dimension of vector (3,)\n",
      " size of vector 3\n"
     ]
    }
   ],
   "source": [
    "print(f' dimension of vector {x.shape}')\n",
    "print(f' size of vector {x.size}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "1d2868b5-72ea-4240-a9d5-93128f8ca81e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 2, 3],\n",
       "        [4, 5, 6],\n",
       "        [7, 8, 9]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x= np.matrix([[1,2,3],[4,5,6],[7,8,9]])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "55cd3127-824d-414b-b689-a57dc9638928",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " dimension of vector (3, 3)\n",
      " size of vector 9\n"
     ]
    }
   ],
   "source": [
    "print(f' dimension of vector {x.shape}')\n",
    "print(f' size of vector {x.size}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c6aa3581-964d-4c9f-ae67-60ccbb704a26",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.ones((3,3))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "664b6e35-27d3-4578-8323-253f4203b996",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]],\n",
       "\n",
       "       [[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]],\n",
       "\n",
       "       [[1., 1., 1.],\n",
       "        [1., 1., 1.],\n",
       "        [1., 1., 1.]]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.ones((3,3,3))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "68e0e2b0-de09-41fd-838b-a1648155b96e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " dimension of vector (3, 3, 3)\n",
      " size of vector 27\n"
     ]
    }
   ],
   "source": [
    "print(f' dimension of vector {x.shape}')\n",
    "print(f' size of vector {x.size}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "76fd59da-69d1-4863-a0ef-c18f99b46572",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# indexing\n",
    "A = np.ones((5,5), dtype = int)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c3db6a00-cf17-4452-ac67-0e1659c1f8db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1],\n",
       "       [1, 1, 1, 1, 1]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Indexing starts at 0\n",
    "A[0,1] = 2\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "947a748b-e7c4-4dec-9817-0ef4780a5085",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4, 2, 1, 1, 1],\n",
       "       [5, 1, 1, 1, 5],\n",
       "       [4, 1, 1, 1, 1],\n",
       "       [4, 1, 1, 1, 1],\n",
       "       [4, 1, 1, 1, 1]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1,4] = 5\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "dd5ec397-94e7-423e-a50f-8baee517c3ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Matrix Operations\n",
    "A = np.matrix([[1,2],[3,4]])\n",
    "B = np.ones([2,2], dtype = int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f852b5bc-8e6e-40f0-bfbc-1873720ba591",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[1, 2],\n",
       "        [3, 4]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "1c1aad55-7a55-49ef-ad91-88abb6ed9743",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1],\n",
       "       [1, 1]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "f357d63c-9c03-4dae-8e38-3af9295d21f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[2, 3],\n",
       "        [4, 5]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Addition or Sum\n",
    "C = A + B\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d70283af-8acb-45d1-9446-2adfede17235",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0, 1],\n",
       "        [2, 3]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Subtraction\n",
    "C = A - B\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4f0bd62d-e911-44ac-b5fb-46a49e46bf8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[3, 3],\n",
       "        [7, 7]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Multiplication\n",
    "C = A*B\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "b7da0023-42ed-4936-b93e-9484729963ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[3, 3],\n",
       "        [7, 7]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Dot Product same as Multiplication\n",
    "D  = A.dot(B)\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "ef88d81d-b5ba-4a5a-88e9-8dfc0d92adca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Matrix transpose\n",
    "A = np.array(range(9))\n",
    "A = A.reshape(3,3)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "9d0767ad-00df-47a7-a334-3f35fae1c559",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 3, 6],\n",
       "       [1, 4, 7],\n",
       "       [2, 5, 8]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = A.T\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "b90404ec-2a61-49b3-aabf-2820c4b2db9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " dimension of vector (3, 3, 3, 3, 3, 3, 3, 3, 3, 3)\n",
      " size of vector 59049\n"
     ]
    }
   ],
   "source": [
    "# Tensors\n",
    "A  = np.ones([3 for x in range(10)])\n",
    "print(f' dimension of vector {A.shape}')\n",
    "print(f' size of vector {A.size}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "650c9845-13d7-484a-899f-ae97c566dc60",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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