Homework_02_Solution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d7ea4a05-3a9d-4cc0-a2eb-ed18ca6df2b9",
   "metadata": {},
   "source": [
    "Question 1:"
   ]
  },
  {
   "attachments": {
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     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "931bb98b-9901-44ec-9d1d-b78c2f2d0442",
   "metadata": {},
   "source": [
    "![image.png](attachment:55912518-e42c-40c9-aaee-8fa6657f2bd0.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdca89b1-2edc-4259-8c7b-1a3a5215dcf3",
   "metadata": {},
   "source": [
    "Question 2:"
   ]
  },
  {
   "attachments": {
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    }
   },
   "cell_type": "markdown",
   "id": "65535c9a-d70d-4953-b425-d0c56adabd97",
   "metadata": {},
   "source": [
    "![image.png](attachment:598e7169-256b-469d-a03a-2ea374568e3b.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b893af8-bada-4898-b438-a2f06f58c070",
   "metadata": {},
   "source": [
    "Question 3:"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "52a43627-858f-4c89-a741-ff680cab252f",
   "metadata": {},
   "source": [
    "![image.png](attachment:60c99b4c-e861-4e09-9304-f9a24f3f8021.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79334580",
   "metadata": {},
   "source": [
    "Question 4:"
   ]
  },
  {
   "attachments": {
    "e094236a-4b91-461c-8f84-f6d79bc79576.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "8efa6f54-dece-4a7e-91fd-d609d6ea72ef",
   "metadata": {},
   "source": [
    "![image.png](attachment:e094236a-4b91-461c-8f84-f6d79bc79576.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "06206b3b-54a5-43e7-9b0b-fbc5bf2c78e4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "506fab2a-a50c-42bd-a106-c83a9d2828ea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2024-07-09 22:50:29--  https://raw.githubusercontent.com/alexeygrigorev/minsearch/main/minsearch.py\n",
      "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.111.133, 185.199.109.133, 185.199.108.133, ...\n",
      "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.111.133|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 3832 (3.7K) [text/plain]\n",
      "Saving to: ‘minsearch.py’\n",
      "\n",
      "minsearch.py        100%[===================>]   3.74K  --.-KB/s    in 0s      \n",
      "\n",
      "2024-07-09 22:50:29 (23.4 MB/s) - ‘minsearch.py’ saved [3832/3832]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!rm -f minsearch.py\n",
    "!wget https://raw.githubusercontent.com/alexeygrigorev/minsearch/main/minsearch.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1bd061c0-4e3e-4caa-9f89-760c3f85a9d8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3ac947de-effd-4b61-8792-a6d7a133f347",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<minsearch.Index at 0x792b8fd8a5f0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import requests \n",
    "import minsearch\n",
    "\n",
    "docs_url = 'https://github.com/DataTalksClub/llm-zoomcamp/blob/main/01-intro/documents.json?raw=1'\n",
    "docs_response = requests.get(docs_url)\n",
    "documents_raw = docs_response.json()\n",
    "\n",
    "documents = []\n",
    "\n",
    "for course in documents_raw:\n",
    "    course_name = course['course']\n",
    "\n",
    "    for doc in course['documents']:\n",
    "        doc['course'] = course_name\n",
    "        documents.append(doc)\n",
    "\n",
    "index = minsearch.Index(\n",
    "    text_fields=[\"question\", \"text\", \"section\"],\n",
    "    keyword_fields=[\"course\"]\n",
    ")\n",
    "\n",
    "index.fit(documents)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8f087272-b44d-4738-9ea2-175ec63a058b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def search(query):\n",
    "    boost = {'question': 3.0, 'section': 0.5}\n",
    "\n",
    "    results = index.search(\n",
    "        query=query,\n",
    "        filter_dict={'course': 'data-engineering-zoomcamp'},\n",
    "        boost_dict=boost,\n",
    "        num_results=5\n",
    "    )\n",
    "\n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "742ab881-499a-4675-83c4-2013ea1377b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_prompt(query, search_results):\n",
    "    prompt_template = \"\"\"\n",
    "You're a course teaching assistant. Answer the QUESTION based on the CONTEXT from the FAQ database.\n",
    "Use only the facts from the CONTEXT when answering the QUESTION.\n",
    "\n",
    "QUESTION: {question}\n",
    "\n",
    "CONTEXT: \n",
    "{context}\n",
    "\"\"\".strip()\n",
    "\n",
    "    context = \"\"\n",
    "    \n",
    "    for doc in search_results:\n",
    "        context = context + f\"section: {doc['section']}\\nquestion: {doc['question']}\\nanswer: {doc['text']}\\n\\n\"\n",
    "    \n",
    "    prompt = prompt_template.format(question=query, context=context).strip()\n",
    "    return prompt\n",
    "\n",
    "def llm(prompt):\n",
    "    response = client.chat.completions.create(\n",
    "        model='gemma:2b',\n",
    "        messages=[{\"role\": \"user\", \"content\": prompt}]\n",
    "    )\n",
    "    \n",
    "    return response.choices[0].message.content"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fe8bff3e-b672-42be-866b-f2d9bb217106",
   "metadata": {},
   "outputs": [],
   "source": [
    "def rag(query):\n",
    "    search_results = search(query)\n",
    "    prompt = build_prompt(query, search_results)\n",
    "    answer = llm(prompt)\n",
    "    return answer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "988ece59-951a-4b32-ba3f-cb8efb66a9bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from openai import OpenAI\n",
    "\n",
    "client = OpenAI(\n",
    "    base_url='http://localhost:11434/v1/',\n",
    "    api_key='ollama',\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a1ec7d72-37af-443c-9646-561eb446983c",
   "metadata": {},
   "outputs": [],
   "source": [
    "prompt = \"What's the formula for energy?\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d396bb33-4489-492d-a342-0843a622c31e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"Sure. Here's the formula for the energy of an object:\\n\\n**E = K + U**\\n\\nwhere:\\n\\n* **E** is the energy\\n* **K** is the kinetic energy\\n* **U** is the potential energy\\n\\n**Kinetic energy** (K) is the energy an object possesses when it moves. It is calculated as half the mass of an object multiplied by its velocity squared:\\n\\n**K = 1/2 * m * v^2**\\n\\nwhere:\\n\\n* **m** is the mass of the object\\n* **v** is its velocity\\n\\n**Potential energy** (U) is the energy an object possesses when it is in a specific position or state. It is calculated as the product of the force acting on the object and its position.\\n\\n**Force** is the interaction between two objects, and it can be calculated as the product of the masses of the objects and their gravitational constant.\\n\\n**Position** can refer to the height of an object, the distance from a reference point, or any other relevant measure of its position.\\n\\nThe energy of an object is a measure of its ability to do work. The total energy of an object is always conserved, meaning that it remains constant regardless of its motion. This means that the total energy of a system can only change through external work done on the system.\""
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "llm(prompt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "655c6306-2679-4868-8c30-8bcdc5a0b916",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sure. Here's the formula for the energy of an object:\n",
      "\n",
      "**E = K + U**\n",
      "\n",
      "where:\n",
      "\n",
      "* **E** is the energy\n",
      "* **K** is the kinetic energy\n",
      "* **U** is the potential energy\n",
      "\n",
      "**Kinetic energy** (K) is the energy an object possesses when it moves. It is calculated as half the mass of an object multiplied by its velocity squared:\n",
      "\n",
      "**K = 1/2 * m * v^2**\n",
      "\n",
      "where:\n",
      "\n",
      "* **m** is the mass of the object\n",
      "* **v** is its velocity\n",
      "\n",
      "**Potential energy** (U) is the energy an object possesses when it is in a specific position or state. It is calculated as the product of the force acting on the object and its position.\n",
      "\n",
      "**Force** is the interaction between two objects, and it can be calculated as the product of the masses of the objects and their gravitational constant.\n",
      "\n",
      "**Position** can refer to the height of an object, the distance from a reference point, or any other relevant measure of its position.\n",
      "\n",
      "The energy of an object is a measure of its ability to do work. The total energy of an object is always conserved, meaning that it remains constant regardless of its motion. This means that the total energy of a system can only change through external work done on the system.\n"
     ]
    }
   ],
   "source": [
    "print(_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c93f2200-9125-4ba9-9385-6bc7e7c98287",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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