Introduction.ipynb

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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ZohebAbai/mobile_sensing_robotics/blob/main/Introduction.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "12gvwJpvRmRq"
      },
      "source": [
        "# **Python Tutorial - Exercise**\n",
        "This Jupyter-Notebook script is a collection of exercises for the [introduction to python](https://www.ipb.uni-bonn.de/python-intro/).\n",
        "\n",
        "For the submission make sure to...\n",
        "- rename this file (ex-00-yourLastname.ipynb)\n",
        "- answer all questions in this file. \n",
        "- run the script from the beginning to the end (restart kernel and run whole notebook: '>>'-Button)\n",
        "- submit all necessary files to run this script (e.g. .zip/.tar)\n",
        "\n",
        "#### **Points: [40]**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x6RBJTXxRmRz"
      },
      "source": [
        "## **A. Variables [2]**\n",
        "\n",
        "A variable is a container for a value, which can be of various types, e.g., int, float, str..."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7iCIsKz4RmR0"
      },
      "source": [
        "**Task**: Define two variables $x$ and $y$ and compute their divsion and sum. Let $x = 10$ and $y=3$. **Print out** the **type** of $x$, $y$, $\\frac{x}{y}$ and $x+y$ as well as the **result** of their divsion and sum. **[2]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Kb1w4jLGRmR1"
      },
      "source": [
        "# Define the variables in this cell\n",
        "x, y = 10, 3"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fRkAM9b0RmR1"
      },
      "source": [
        "# Compute the divsion of both variables\n",
        "division = x/y"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pa2vlC4uRmR2"
      },
      "source": [
        "# Compute the sum of both variables\n",
        "summation = x+y"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uQJNpLRmRmR2",
        "outputId": "1a1a993a-edf2-48d2-c5d7-efd56da63cb7"
      },
      "source": [
        "# Print out the data types in this cell\n",
        "print(f\"Data type of x: {type(x)}, y: {type(y)}, division: {type(division)}, summation: {type(summation)}\")"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Data type of x: <class 'int'>, y: <class 'int'>, division: <class 'float'>, summation: <class 'int'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0FpbNsT4RmR3",
        "outputId": "335f1ba6-dc24-4f60-ba5a-92d33d36d90a"
      },
      "source": [
        "# Print out the result of the divison and sum in this cell\n",
        "print(f\"Result Divsion: {division}, Result Sum: {summation}\")"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Result Divsion: 3.3333333333333335, Result Sum: 13\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AGKHHfAcRmR4"
      },
      "source": [
        "## **B. Data Structures [7]**\n",
        "Python has several data structures for efficient data organization. We will now look a little bit closer to the most important ones: \n",
        "- A List is a collection which is *ordered* and *changeable (mutable)*. It allows for *duplicate members*.\n",
        "- A Tuple is a collection which is *ordered* and *unchangeable (immutable)*. It allows for *duplicate members*.\n",
        "- A Dictionary is a collection which is *unordered*, *changeable (mutable)* and *indexed*. *No duplicate* keys allowed"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YL3X9NcQRmR4"
      },
      "source": [
        "#### **B1. Lists**\n",
        "**Tasks**:\n",
        "1. Create a list which contains the values 1 to 9. **Print out** the **length** of the list and compute the **sum** of the first and last entry. Use *indexing* to access these entries **[1.5]**\n",
        "2. Set the first entry of this list to 100 and append the value of 99 to the list. Again **print out** the **length** of this and compute the **sum** of the first and last entry by using *indexing*. **[1.5]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nkFkeVpTRmR5"
      },
      "source": [
        "# Create your list here\n",
        "ls  = [i for i in range(1,10)]"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3kEOvSilRmR5"
      },
      "source": [
        "# Compute the length of the list\n",
        "size = len(ls)"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CppLTmmsRmR5"
      },
      "source": [
        "# Compute the sum of the first and last entry by using indexing.\n",
        "summ = ls[0] + ls[-1]"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mve-2FOhRmR5",
        "outputId": "1403a83d-a333-4f3a-d8af-aa41bae84bc7"
      },
      "source": [
        "# Print out the length of the list this cell\n",
        "print(f\"length of the list: {size}\")"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "length of the list: 9\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zoHGkoXeRmR6",
        "outputId": "f10e45b9-7a46-4810-e6d5-29087b2f195c"
      },
      "source": [
        "# Print out the sum of first and last entry in this cell\n",
        "print(f\"sum of first and last entry: {summ}\")"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "sum of first and last entry: 10\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mpE9JtAQRmR6"
      },
      "source": [
        "# Modify the elements of your list in this cell\n",
        "ls[0] = 100\n",
        "ls.append(int(99))"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zqDB_eshRmR6"
      },
      "source": [
        "# Compute the length of the list\n",
        "size =  len(ls)"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZsngUHwlRmR7"
      },
      "source": [
        "# Compute the sum of the first and last entry by using indexing.\n",
        "summ = ls[0] + ls[-1]"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F-rNOWBiRmR7",
        "outputId": "2acd34cc-b9e3-4fe1-9392-5e3c65e30aef"
      },
      "source": [
        "# Print out the length of the list in this cell\n",
        "print(f\"length of the list: {size}\")"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "length of the list: 10\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vKAt3bNjRmR7",
        "outputId": "052c683b-323e-455c-e124-883a5c5c58e3"
      },
      "source": [
        "# Print out the sum of first and last entry in this cell\n",
        "print(f\"sum of first and last entry: {summ}\")"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "sum of first and last entry: 199\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wl_7_2kYRmR7"
      },
      "source": [
        "#### **B2. Tuples**\n",
        "\n",
        "**Task**:\n",
        "1. Create a tuple which contains the same values as the previously defined list. **[0.5]**\n",
        "2. Try to change the second element of this tuple to 77 and run the script. Describe which error occurs and why. Make sure to comment this line of code afterwards otherwise cells below will not be executed! **[1]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jGM3pChPRmR8",
        "outputId": "8c87b7f2-3c0b-45ab-8caa-8412e56a6a7f"
      },
      "source": [
        "# Create the tuple in this cell\n",
        "tup = tuple(ls)\n",
        "\n",
        "print(tup)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(100, 2, 3, 4, 5, 6, 7, 8, 9, 99)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9Qyx0koFRmR8"
      },
      "source": [
        "# Try to change the 2nd element of this tuple\n",
        "#tup[1] = 101\n",
        "# First execute the code (Cell > Run All) and inspect the error.\n",
        "# Afterwards make sure to comment all code within this cell - otherwise cells below will not be executed!"
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pqZVOEdERmR8"
      },
      "source": [
        "Write your **answer** about which error occurs and why **here**:\n",
        "\n",
        "==> TypeError: 'tuple' object does not support item assignment.\n",
        "**A tuple object is immutable**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DnrIYNjmRmR9"
      },
      "source": [
        "#### **B3. Dictionaries**\n",
        "\n",
        "**Tasks**:\n",
        "1. Create a dictionary which contains the following *key-value* pairs: *City* - *Bonn*, *Street* - *Nussallee*, *HouseNumber* - 15.<br /> Get the value of *HouseNumber* and **print it out**. **[1]**\n",
        "2. Add the key-value pair *LectureRoom* : *14* to this dictionary. Finally **print out** all **keys** and **values** of this dictionary. **[1.5]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i-uwJKOjRmR9"
      },
      "source": [
        "# Create the dictionary here\n",
        "dic = {\"City\":\"Bonn\",\"Street\":\"Nussalee\",\"HouseNumber\":\"15\"}"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7MprGLqtRmR9",
        "outputId": "3ff808fb-0bbd-460e-8a1f-7c78de23b001"
      },
      "source": [
        "# Get the value of 'HouseNumber' and print it in this cell\n",
        "val =  dic.get(\"HouseNumber\")\n",
        "print(val)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "15\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v_SodOTnRmR9"
      },
      "source": [
        "# Add key-value pair\n",
        "dic[\"LectureRoom\"] = \"14\""
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_Ja_foIGRmR-",
        "outputId": "257722d6-ca36-4e9a-cea0-a12c4bef5da8"
      },
      "source": [
        "# Print out all keys of the dict\n",
        "print(dic.keys())"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "dict_keys(['City', 'Street', 'HouseNumber', 'LectureRoom'])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kMt8xXNSRmR-",
        "outputId": "aa246ec5-2839-4b70-97bf-8ee5d0f8f9e4"
      },
      "source": [
        "# Print out all values of the dict\n",
        "print(dic.values())"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "dict_values(['Bonn', 'Nussalee', '15', '14'])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t87MU7pRRmR-"
      },
      "source": [
        "## **C. Conditionals and Loops [4]**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8JkmKYa8RmR-"
      },
      "source": [
        "**Tasks:**\n",
        "1. You are given a list which contains multiple lists itself which we assign to the variable called *nested_list*. **Print out** the length of *nested_list* and write a *for loop* which **prints** the **length** of each individual list within the *nested_list*. **[2]**\n",
        "2. Sum up all entries in the nested list by using nested *for loops*. If a entry is equal to zero **print** the string *'Found zero element**. Finally **print out** the result of the **sum**. **[2]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4XXqRHtuRmR_",
        "outputId": "d9d4a3ee-1eaa-42ec-8969-eb2d6abc2559"
      },
      "source": [
        "# Python is picky with tabs! All code you want to run within a loop or condition needs to be indented by 4 spaces.\n",
        "# In case the loop or condition in nested within another loop or condition it needs to be indented by \n",
        "# 8 spaces and so on.\n",
        "\n",
        "# Example\n",
        "for i in range(1):\n",
        "    print(i)             # -> 4 spaces before the print statement\n",
        "    for j in range(1):   # -> 4 spaces before for begins\n",
        "        print(j)         # -> 8 spaces before the print statement"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0\n",
            "0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nVm7DLX1RmR_"
      },
      "source": [
        "# You are a given a nested list\n",
        "nested_list = [[1,2,3,0],\n",
        "               [4,5,0,6, 5],\n",
        "               [7,0,9,0,10, -10]]"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "A9u0-97GRmSA",
        "outputId": "7d27f93b-5e9a-4c6d-826e-6568328b62e7"
      },
      "source": [
        "# Print out the length of nested_list in this cell\n",
        "print(len(nested_list))"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9sh-F1k_RmSA",
        "outputId": "26b89034-45eb-4ddf-e690-c839c574022e"
      },
      "source": [
        "# Write the code to print the length of each individual list within the nested_list in this cell by using a loop\n",
        "for i in range(len(nested_list)):\n",
        "    print(len(nested_list[i]))"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "4\n",
            "5\n",
            "6\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D7I5QnH2RmSA"
      },
      "source": [
        "# Write the code to sum up all entries in nested_list in this cell\n",
        "summ = 0\n",
        "\n",
        "for i in range(len(nested_list)):\n",
        "    for j in range(len(nested_list[i])):\n",
        "        summ += nested_list[i][j]"
      ],
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cJTSwXhERmSA",
        "outputId": "6a8eaeb6-ca28-4d57-bbbd-b55279f693e7"
      },
      "source": [
        "# Print out the result of the sum in this cell\n",
        "print(f\"Sum of elements in nested list: {summ}\")"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Sum of elements in nested list: 42\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KW4dCwSdRmSB"
      },
      "source": [
        "## **D. Functions [3]**\n",
        "Functions can help you to organize and structure your code, while keeping the effort for redundant tasks low. For an even better organization (especially for bigger projects), it usually makes sense to distribute parts of your code to multiple files (so called modules). \n",
        "\n",
        "**Hint:** Whenever you have to write the same code at least twice: make a function for it!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rm2zTcccRmSB"
      },
      "source": [
        "**Tasks**:\n",
        "1. Create a python file 'utilities.py'. Write in there a function called ```sum_nested_list(...)``` which takes as input parameter a nested list and returns the sum of all entries **[2]**\n",
        "2. Import the the previously created module and pass the given variable *another_nested_list* to your function and **print** the **result**. **[1]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NOq1LoZgRmSB"
      },
      "source": [
        "# Given variable another_nested_list \n",
        "another_nested_list = [[22, -22, 33], [-33, 44, 55], [-55, -44, 1, -2]]"
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VgVwhtTtdWfL"
      },
      "source": [
        "**Pasting the utilities.py file content**\n",
        "\n",
        "```\n",
        "from typing import List\n",
        "\n",
        "def sum_nested_list(nested_list: List):\n",
        "    summ = 0\n",
        "\n",
        "    for i in range(len(nested_list)):\n",
        "        for j in range(len(nested_list[i])):\n",
        "            summ += nested_list[i][j] \n",
        "    \n",
        "    return summ\n",
        "``` "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jHNJz9T6RmSC"
      },
      "source": [
        "# Call your function here\n",
        "from utilities import sum_nested_list"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pbJLsQeCRmSC",
        "outputId": "88b09655-042a-4b8d-84c4-39e17f6b02df"
      },
      "source": [
        "# Print out the sum of all entries here\n",
        "summ = sum_nested_list(another_nested_list)\n",
        "\n",
        "print(summ)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HSWTcaYyRmSC"
      },
      "source": [
        "## **E. Numpy [16.5]**\n",
        "#### **E1. Initialization**\n",
        "Numpy is the most used module for numerical applications in python. It handles matrices very efficiently and has a big library for linear algebra.\n",
        "<br>**Tasks:**\n",
        "1. import numpy **[0.5]**\n",
        "2. create and print a ... **[1]**\n",
        "   - ... 3x4 matrix with zeros\n",
        "   - ... 4x3x3 matrix with ones\n",
        "   - ... 3x3 identity matrix\n",
        "   - ... array with the values from 0 to 4 (integer)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j_qWeOgYRmSC"
      },
      "source": [
        "# Import numpy here as np\n",
        "import numpy as np"
      ],
      "execution_count": 39,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_fhP9T7aRmSC",
        "outputId": "1277cd60-140f-45da-a014-e95c9fbf57af"
      },
      "source": [
        "# Zero matrix\n",
        "zeros = np.zeros((3,4))\n",
        "print(zeros)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0. 0. 0. 0.]\n",
            " [0. 0. 0. 0.]\n",
            " [0. 0. 0. 0.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xBwKTKrdRmSD",
        "outputId": "172740d8-ed36-420a-afbb-bccad5cd7208"
      },
      "source": [
        "# Ones: 3 dimensional matrix\n",
        "ones = np.ones((3,4,3))\n",
        "print(ones)"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[[1. 1. 1.]\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.]\n",
            "  [1. 1. 1.]]\n",
            "\n",
            " [[1. 1. 1.]\n",
            "  [1. 1. 1.]\n",
            "  [1. 1. 1.]\n",
            "  [1. 1. 1.]]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ksA5pHPZRmSD",
        "outputId": "2f423ac9-a870-47f0-e322-0c2fc0b5fab8"
      },
      "source": [
        "# Identity Matrix\n",
        "idn = np.identity(3)\n",
        "print(idn)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1. 0. 0.]\n",
            " [0. 1. 0.]\n",
            " [0. 0. 1.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nr6AHDVuRmSD",
        "outputId": "8585469a-1bd3-4d70-83ca-fd25b887d445"
      },
      "source": [
        "# arange\n",
        "arr = np.arange(5)\n",
        "print(arr)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0 1 2 3 4]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0jBifnjIRmSD"
      },
      "source": [
        "#### **E2. Random numbers**\n",
        "\n",
        "Random sampling is essential in probabilistic robotics theory.\n",
        "\n",
        "**Tasks:**\n",
        "1. Randomly sample 1000 values according to a **uninform distribution** defined in the range between -10 and 10.  **[0.5]**\n",
        "2. Randomly sample 1000 values according to a **normal distribution** with mean 0 and standard deviation 3. **[0.5]**\n",
        "3. Plot histograms of the sampled values for both sets of values. **Hint:** Use matplotlib for the visualization. See *matplotlib.pyplot.hist*. **[1]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9fZpKqG2RmSE"
      },
      "source": [
        "# Uniform sampling\n",
        "rand_uni = np.random.uniform(-10,10,1000)"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QKgTx58dRmSE"
      },
      "source": [
        "# Normal distributed sampling\n",
        "rand_nor = np.random.normal(0,3,1000)"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 517
        },
        "id": "ruw9jhtGRmSE",
        "outputId": "d04745e3-0eed-4fb4-f1b1-de6c7d05b8b1"
      },
      "source": [
        "# Visualization\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.hist(rand_uni)\n",
        "plt.show()\n",
        "plt.hist(rand_nor)\n",
        "plt.show()"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dA3ma39eRmSE"
      },
      "source": [
        "4. Compute and print mean and standard deviations for both sets of values."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ct6SfGGfRmSE",
        "outputId": "f4ff10de-f9a0-4c08-9c4a-548941ab38ee"
      },
      "source": [
        "# uniform\n",
        "print(f\"Uniform Standard Deviation: {np.std(rand_uni)}\")\n",
        "print(f\"Uniform Mean: {np.mean(rand_uni)}\")\n",
        "\n",
        "# normal\n",
        "print(f\"Normal Standard Deviation: {np.std(rand_nor)}\")\n",
        "print(f\"Normal Mean: {np.mean(rand_nor)}\")"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Uniform Standard Deviation: 5.766905919252697\n",
            "Uniform Mean: -0.04405338975640923\n",
            "Normal Standard Deviation: 3.039665497524387\n",
            "Normal Mean: 0.0792982348946494\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n72WOZdORmSF"
      },
      "source": [
        "#### **E3. Images: Cube Slicing**\n",
        "Images are one of the most important data types in photogrammetry, so that the handling of these should feel quite familiar to you.\n",
        "An image in python is typically represented as a 3 dimensional numpy array *(rows, cols, channel)*. We will use matplotlib for the visualization and skimage for reading and writing to disk. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z3Dvbnd7RmSF"
      },
      "source": [
        "**Tasks:**\n",
        "1. Load and visualize the image: *data/cube.jpg*, **Hint:** use ```skimage.io.imread(...)``` for loading the image, and ```plt.imshow()``` for plotting. **[1]**\n",
        "2. print the shape of the image as well as the underlying data type. **[0.5]**\n",
        "3. create two variables which hold the left and the right half of the image, respectively. Make sure that both parts have the same size and plot both images. **Hint:** use subplots. **[1]**\n",
        "4. flip the right image along a vertical axis, plot the result. **[1]**\n",
        "5. Convert the left and the right flipped image to float for later computations. **[0.5]**\n",
        "6. Compute the absolute difference between the left and the right flipped image. **[0.5]**\n",
        "7. Convert the difference image back to uint8, visualize the resulting image. What can you see? Explain the colors you can see. **[3]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F7cD3YkiRmSF"
      },
      "source": [
        "# Import necessary modules here:\n",
        "from skimage import io\n",
        "from skimage.util import compare_images"
      ],
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "mhaISJBJRmSF",
        "outputId": "225a852d-ce70-4de1-dca9-aacc1157b763"
      },
      "source": [
        "# Load and visualize image\n",
        "img = io.imread(\"data/cube.jpg\")\n",
        "plt.imshow(img)"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f9514ad8610>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "afk7sIhmRmSG",
        "outputId": "f7a9b7e1-b7ce-460c-ae35-cd5c4498d646"
      },
      "source": [
        "# print the shape and underlying data type\n",
        "print(\"Shape: \",img.shape,\"Data Type :\",type(img))"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Shape:  (950, 950, 3) Data Type : <class 'numpy.ndarray'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vDrgvvp0RmSG",
        "outputId": "0adbaa03-3daf-4f95-e3fb-79ddc3451420"
      },
      "source": [
        "# Split image in left and right half:\n",
        "img_left = img[:,:475,:]\n",
        "img_right = img[:,475:,:]\n",
        "\n",
        "# print shapes:\n",
        "print(img_left.shape, img_right.shape)"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(950, 475, 3) (950, 475, 3)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "9nmHsmoyRmSG",
        "outputId": "92b97a98-b670-43e4-c337-0f742c63083a"
      },
      "source": [
        "# Plotting left and right image\n",
        "fig,a= plt.subplots(1,2)\n",
        "\n",
        "a[0].set_title(\"Left Image\")\n",
        "a[0].imshow(img_left)\n",
        "\n",
        "a[1].set_title(\"Right Image\")\n",
        "a[1].imshow(img_right)"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f950a6dbd50>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "FdBQBHA5RmSG",
        "outputId": "338cb852-8865-48e4-eeb4-5390f8d3f3df"
      },
      "source": [
        "# flip right image and plot the result:\n",
        "img_flip_right =  np.flip(img_right, axis=1)\n",
        "plt.imshow(img_flip_right)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f950a6586d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3WpbDzKyRmSG",
        "outputId": "81142615-1a0c-4ab2-895e-261f16922b7a"
      },
      "source": [
        "# Convert to float \n",
        "img_left.astype(float)\n",
        "img_flip_right.astype(float)"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        ...,\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.]],\n",
              "\n",
              "       [[255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        ...,\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.]],\n",
              "\n",
              "       [[255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        ...,\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.]],\n",
              "\n",
              "       ...,\n",
              "\n",
              "       [[255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        ...,\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.]],\n",
              "\n",
              "       [[255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        ...,\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.]],\n",
              "\n",
              "       [[255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        ...,\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.],\n",
              "        [255., 255., 255.]]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vEPYbI5aRmSH"
      },
      "source": [
        "# compute difference here:\n",
        "img_diff = compare_images(img_left, img_flip_right, method='diff')"
      ],
      "execution_count": 62,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "ObteFm0rRmSH",
        "outputId": "11ea6d48-62e6-47d6-9d1f-6a798980b6d7"
      },
      "source": [
        "# Convert to uint8:\n",
        "img_diff.astype(dtype='uint8')\n",
        "\n",
        "# Plot differences:\n",
        "plt.imshow(img_diff)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f950a63a1d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CHi996DsRmSH"
      },
      "source": [
        "7. Write your answer here:\n",
        "==> Each color represents different intensity value assigned as we take difference between two images.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ryf2ZEyXRmSH"
      },
      "source": [
        "#### **E4. Point Transformation** \n",
        "Point clouds are a common data type in various areas (surveying, photogrammetry, data analysis...). \n",
        "In the following we have given an L-shaped point cloud [2xn] (*n=200*), on which we want to apply some transformations and visualize the results with matplotlib. \n",
        "\n",
        "**Tasks:**\n",
        "1. Visualize the point cloud. **[0.5]**\n",
        "1. Write a function angle2rotMat(...) that returns the rotation matrix [2x2] for a given rotation angle (in degree). **[0.5]**\n",
        "2. Write for the function a header which describes what the function is doing, as well as the input and output parameter. **[0.5]**\n",
        "3. Create the 2 rotation matrices *R1* and *R2*: the first with an angle of 30[degree] and the second with an angle of 60[degree]. Print both matrices. **[0.5]**\n",
        "4. Rotate the given point cloud by *R1* and save the result in *points_r1*. Be aware of the difference between a matrix multiplication and an elementwise multiplication. **[0.5]**\n",
        "5. Rotate *points_r1* by *R2* and save the result in *points_r2*. **[0.5]**\n",
        "6. Shift points_r2 by the *translation=(3,4)^T* and save the result in *points_t*. **[0.5]**\n",
        "7. Create a figure with 4 subplots. Plot *points*, *points_r1*, *points_r2* and *points_t* in the created subplots, respectively. **[2]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "v-Tgkb5eRmSI",
        "outputId": "a5004320-115b-47ee-f782-774949b1334b"
      },
      "source": [
        "# generating an L-shaped point cloud.\n",
        "import numpy as np\n",
        "np.random.seed(0) # For reproducable results\n",
        "points = np.hstack([np.array([[5,0.5]]).T* np.random.rand(2,100), np.array([[0.5,5]]).T*np.random.rand(2,100)])\n",
        "print('Point cloud dimension:',points.shape)"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Point cloud dimension: (2, 200)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "id": "tw1TjZImRmSI",
        "outputId": "07fdcba2-42ad-42d4-a355-d933c3493da9"
      },
      "source": [
        "# Plot points here\n",
        "plt.plot(points[0,:], points[1,:], 'ro')\n",
        "plt.show()"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hgr9TP6pRmSI"
      },
      "source": [
        "# write angle2rotMat(...):\n",
        "import math\n",
        "\n",
        "def angle2rotMat(angle):\n",
        "\n",
        "  rotMat = np.array([[math.cos(math.radians(angle)),-(math.sin(math.radians(angle)))],\n",
        "                     [math.sin(math.radians(angle)), math.cos(math.radians(angle))]])\n",
        "\n",
        "  return rotMat"
      ],
      "execution_count": 70,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2wJHKlu5RmSJ",
        "outputId": "21f1f0dc-7317-483f-808d-9e6fa3712009"
      },
      "source": [
        "# create rotation matrices\n",
        "R1 = angle2rotMat(30)\n",
        "R2 = angle2rotMat(60)\n",
        "\n",
        "print(f\"R1: {R1}\")\n",
        "print(f\"R2: {R2}\")"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "R1: [[ 0.8660254 -0.5      ]\n",
            " [ 0.5        0.8660254]]\n",
            "R2: [[ 0.5       -0.8660254]\n",
            " [ 0.8660254  0.5      ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w-ABHcSQRmSJ",
        "outputId": "97c64c19-827a-4686-9f9a-200a759167f1"
      },
      "source": [
        "# create translation vector\n",
        "T1 = np.array([[3,4]])\n",
        "\n",
        "# apply Transformations \n",
        "points_r1 = np.dot(R1, points)\n",
        "points_r2 = np.dot(R2, points_r1)\n",
        "points_t = np.add(points_r2.transpose(), T1)\n",
        "\n",
        "print(points_t.shape)"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(200, 2)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "9z9Lw0caRmSJ",
        "outputId": "3f1bf269-3266-4dca-81ae-a090ca0f4003"
      },
      "source": [
        "# create subplots and plot results\n",
        "fig, a= plt.subplots(2,2)\n",
        "\n",
        "\n",
        "a[0][0].set_title(\"Original Points\")\n",
        "a[0][0].plot(points[0,:], points[1,:], 'ro')\n",
        "\n",
        "a[0][1].set_title(\"After R1 transformation\")\n",
        "a[0][1].plot(points_r1[0,:],points_r1[1,:],\"ro\")\n",
        "\n",
        "a[1][0].set_title(\"After R2 transformation\")\n",
        "a[1][0].plot(points_r2[0,:],points_r2[1,:],\"ro\")\n",
        "\n",
        "a[1][1].set_title(\"After R1 and R2 transformation and T1 translation\")\n",
        "a[1][1].plot(points_t[:,0],points_t[:,1],\"ro\")\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ],
      "execution_count": 80,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Qk2HMHGSRmSJ"
      },
      "source": [
        "## **F. Robotic Applications [7.5]**\n",
        "#### **F1. Plot trajectory**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KDlluR4rRmSK"
      },
      "source": [
        "**Tasks:**\n",
        "1. Read robot's odometry data from **odom.data** file. **[0.5]**\n",
        "    - Measurements are stored in rows in the following format: \n",
        "        [*hours*, *minutes*, *seconds*, $\\delta x_i$, $\\delta y_i$], \n",
        "        where *hours*, *minutes*, *seconds* indicate the time when the measurement was acquired. \n",
        "    - The first row contains the first position of the robot in world coordinates ($x_0$, $y_0$).\n",
        "2. Plot the trajectory of the robot in world coordinates. **[2]**\n",
        "    - The trajectory is computed by iteratively applying the measured odometry to the previous position:\n",
        "$$ x_{i+1} = x_{i} + \\delta x_{i},\\qquad y_{i+1} = y_{i} + \\delta y_{i}$$\n",
        "3. Plot the trajectory of the robot in world coordinates from 07:30:00 to 8:00:00. **[1]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uP02SIoYRmSK"
      },
      "source": [
        "# 1.\n",
        "filename = \"data/odom.data\"\n",
        "f = open(filename,\"r\")\n",
        "f1 = f.readlines()\n",
        "\n",
        "x0 = f1[0].split(\",\")[3]\n",
        "y0 = f1[0].split(\",\")[4]"
      ],
      "execution_count": 81,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "bSaIUgJbRmSK",
        "outputId": "40efd657-226c-4bcf-b8e6-8f98ae4cd4ef"
      },
      "source": [
        "# 2.\n",
        "X = []\n",
        "Y = []\n",
        "\n",
        "x = float(x0)\n",
        "y = float(y0)\n",
        "count = 0\n",
        "\n",
        "for lines in f1[1:]:\n",
        "    line = lines.split(\",\")\n",
        "    x = x + float(line[3])\n",
        "    y = y + float(line[4])\n",
        "    X.append(x)\n",
        "    Y.append(y)\n",
        "\n",
        "plt.plot(X,Y,\"ro\")\n",
        "print(x,y)"
      ],
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "197.884812 353.595486\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        },
        "id": "neSj2n1ORmSK",
        "outputId": "60aa32e8-db50-445b-826b-77112e5c30ee"
      },
      "source": [
        "# 3.\n",
        "X_alt = []\n",
        "Y_alt = []\n",
        "\n",
        "\n",
        "x_alt = float(x0)\n",
        "y_alt = float(y0)\n",
        "\n",
        "for lines in f1[1:]:\n",
        "    line =  lines.split(\",\")\n",
        "    x_alt = x_alt + float(line[3])\n",
        "    y_alt = y_alt + float(line[4])\n",
        "\n",
        "    if float(line[0]) == 7.0 and float(line[1]) >= 30.0:\n",
        "        X_alt.append(x_alt)\n",
        "        Y_alt.append(y_alt)\n",
        "\n",
        "    elif float(line[0]) == 8.0:\n",
        "        X_alt.append(x_alt)\n",
        "        Y_alt.append(y_alt)\n",
        "        break;\n",
        "\n",
        "plt.plot(X_alt,Y_alt,\"ro\")"
      ],
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f94fd979410>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 86
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VonHjeTnRmSK"
      },
      "source": [
        "#### **F2. Robot navigation in grid world**\n",
        "Lets assume we have given a robot which is moving in a 2D grid world. We want to visualize the parts of the map which got explored by the robot."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VVSjCPhdRmSL"
      },
      "source": [
        "**Tasks:**\n",
        "1. Generate a 5x5 grid world by using a numpy matrix where each cell is initially zero. **[0.5]**\n",
        "2. A point robot navigates on this grid world starting from cell (0,0) that is in the top-left corner of the grid. Implement the navigation actions of the robot and execute the following sequence of commands: *down*, *right*, *up*, *up*, *right*, *right*, *down*, *down*, *down*, *left*. Print the final position of the robot. **[3.0]**\n",
        "3. Mark the cells visited by the robot in 2. on the grid world by setting their value to $1$ and plot the grid world by using `matplotlib`. **[1.5]**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UrSn4zA1RmSL"
      },
      "source": [
        "# 1.\n",
        "world = np.zeros((5,5))"
      ],
      "execution_count": 88,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Iwx6kTO5RmSL",
        "outputId": "48f2c01a-3f98-442f-92a1-99856013229e"
      },
      "source": [
        "# 2.\n",
        "robot = np.array([0,0]) # origin is in top left\n",
        "\n",
        "up = np.array([-1,0]) \n",
        "down = np.array([1,0])\n",
        "left = np.array([0,-1])\n",
        "right = np.array([0,1])\n",
        "\n",
        "\n",
        "actions =[down,right,up,up,right,right,down,down,down,left]\n",
        "\n",
        "for action in actions:\n",
        "    \n",
        "    if (action+robot)[0] < 0 or (action + robot)[0] > 4 or (action+robot)[1] < 0 or (action + robot)[1] > 4:\n",
        "        continue;\n",
        "    robot += action\n",
        "    world[robot[0]][robot[1]] = 1\n",
        "\n",
        "print(robot)"
      ],
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3 2]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "usEob6vsRmSL",
        "outputId": "720c4793-cab0-4101-d4e2-fe6ea836ac7a"
      },
      "source": [
        "# 3.\n",
        "plt.imshow(world)"
      ],
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f94fd8ebc10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 90
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}