NumPy_101.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true,
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/hussain0048/Python-Notes/blob/master/NumPy_101.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Table of Content- Main**"
      ],
      "metadata": {
        "id": "MSvNuUgwU2k2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "1.   📚 *_[Introduction](#introduction)_*\n",
        "2.   📚 *_[Array Creation](#array_creation)_*\n",
        "3.   📚 *_[Arthimetic Operations](#arthimetic_operations)_*\n",
        "4.   📚 *_[Basic Mathematic Operations](#basic_mathematic_operations)_*\n",
        "5.   📚 *_[Statistical Analysis](#statistical_analysis)_*\n",
        "6.   📚 *_[Linear Algebra](#linear_algebra)_*\n",
        "7.   📚 *_[Data Cleaning](#data_cleaning)_*\n",
        "\n"
      ],
      "metadata": {
        "id": "mAKrScvfVQ67"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Section 1- Introduction<a name='introduction'></a>**"
      ],
      "metadata": {
        "id": "AvgSpC5aLpUB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Installing Packages from Requirements Files**"
      ],
      "metadata": {
        "id": "LHlVINhLL_xY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Checking pip is installed or not ?**\n",
        "\n"
      ],
      "metadata": {
        "id": "SeDGYhhb-Y_b"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# In command line type\n",
        "!pip --version"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7vJShQvX-eLy",
        "outputId": "0be9e12b-4dcf-41bd-9daa-035a7eefac7b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "pip 23.1.2 from /usr/local/lib/python3.10/dist-packages/pip (python 3.10)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Updating the pip :-**"
      ],
      "metadata": {
        "id": "C1bmd9nm-wID"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install --upgrade pip"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xR-86VvM-yR6",
        "outputId": "4ad1c2d7-12ad-4075-e6e0-eafda458868a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: pip in /usr/local/lib/python3.10/dist-packages (23.1.2)\n",
            "Collecting pip\n",
            "  Downloading pip-23.3-py3-none-any.whl (2.1 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.1/2.1 MB\u001b[0m \u001b[31m22.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hInstalling collected packages: pip\n",
            "  Attempting uninstall: pip\n",
            "    Found existing installation: pip 23.1.2\n",
            "    Uninstalling pip-23.1.2:\n",
            "      Successfully uninstalled pip-23.1.2\n",
            "Successfully installed pip-23.3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**How to get help from pip ?**\n",
        "\n"
      ],
      "metadata": {
        "id": "hwIm69qF-7lK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip help"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WTr9iJGm_AOq",
        "outputId": "09b527f0-2dde-4e53-f69e-04b08cdcac19"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Usage:   \n",
            "  pip <command> [options]\n",
            "\n",
            "Commands:\n",
            "  install                     Install packages.\n",
            "  download                    Download packages.\n",
            "  uninstall                   Uninstall packages.\n",
            "  freeze                      Output installed packages in requirements format.\n",
            "  inspect                     Inspect the python environment.\n",
            "  list                        List installed packages.\n",
            "  show                        Show information about installed packages.\n",
            "  check                       Verify installed packages have compatible dependencies.\n",
            "  config                      Manage local and global configuration.\n",
            "  search                      Search PyPI for packages.\n",
            "  cache                       Inspect and manage pip's wheel cache.\n",
            "  index                       Inspect information available from package indexes.\n",
            "  wheel                       Build wheels from your requirements.\n",
            "  hash                        Compute hashes of package archives.\n",
            "  completion                  A helper command used for command completion.\n",
            "  debug                       Show information useful for debugging.\n",
            "  help                        Show help for commands.\n",
            "\n",
            "General Options:\n",
            "  -h, --help                  Show help.\n",
            "  --debug                     Let unhandled exceptions propagate outside the main subroutine,\n",
            "                              instead of logging them to stderr.\n",
            "  --isolated                  Run pip in an isolated mode, ignoring environment variables and user\n",
            "                              configuration.\n",
            "  --require-virtualenv        Allow pip to only run in a virtual environment; exit with an error\n",
            "                              otherwise.\n",
            "  --python <python>           Run pip with the specified Python interpreter.\n",
            "  -v, --verbose               Give more output. Option is additive, and can be used up to 3 times.\n",
            "  -V, --version               Show version and exit.\n",
            "  -q, --quiet                 Give less output. Option is additive, and can be used up to 3 times\n",
            "                              (corresponding to WARNING, ERROR, and CRITICAL logging levels).\n",
            "  --log <path>                Path to a verbose appending log.\n",
            "  --no-input                  Disable prompting for input.\n",
            "  --keyring-provider <keyring_provider>\n",
            "                              Enable the credential lookup via the keyring library if user input\n",
            "                              is allowed. Specify which mechanism to use [disabled, import,\n",
            "                              subprocess]. (default: disabled)\n",
            "  --proxy <proxy>             Specify a proxy in the form\n",
            "                              scheme://[user:passwd@]proxy.server:port.\n",
            "  --retries <retries>         Maximum number of retries each connection should attempt (default 5\n",
            "                              times).\n",
            "  --timeout <sec>             Set the socket timeout (default 15 seconds).\n",
            "  --exists-action <action>    Default action when a path already exists: (s)witch, (i)gnore,\n",
            "                              (w)ipe, (b)ackup, (a)bort.\n",
            "  --trusted-host <hostname>   Mark this host or host:port pair as trusted, even though it does not\n",
            "                              have valid or any HTTPS.\n",
            "  --cert <path>               Path to PEM-encoded CA certificate bundle. If provided, overrides\n",
            "                              the default. See 'SSL Certificate Verification' in pip documentation\n",
            "                              for more information.\n",
            "  --client-cert <path>        Path to SSL client certificate, a single file containing the private\n",
            "                              key and the certificate in PEM format.\n",
            "  --cache-dir <dir>           Store the cache data in <dir>.\n",
            "  --no-cache-dir              Disable the cache.\n",
            "  --disable-pip-version-check\n",
            "                              Don't periodically check PyPI to determine whether a new version of\n",
            "                              pip is available for download. Implied with --no-index.\n",
            "  --no-color                  Suppress colored output.\n",
            "  --no-python-version-warning\n",
            "                              Silence deprecation warnings for upcoming unsupported Pythons.\n",
            "  --use-feature <feature>     Enable new functionality, that may be backward incompatible.\n",
            "  --use-deprecated <feature>  Enable deprecated functionality, that will be removed in the future.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**pip show command :**\n",
        "\n"
      ],
      "metadata": {
        "id": "SKx8tN3g_Hf5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip show <package name>"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6ufeRJ95_Mmq",
        "outputId": "b1fcc108-5d56-4fe6-c9f1-a027515b34fb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "/bin/bash: -c: line 1: syntax error near unexpected token `newline'\n",
            "/bin/bash: -c: line 1: `pip show <package name>'\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Create a virtual environment.**"
      ],
      "metadata": {
        "id": "7ok_kcU8MRsU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "python -m venv new_project"
      ],
      "metadata": {
        "id": "iir97aX7MWPH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Windows\n",
        "new_project\\Scripts\\activate\n",
        "#macOS/Linux\n",
        "source new_project/bin/activate"
      ],
      "metadata": {
        "id": "-ixvysd1McKR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "And to finish up, you can run the deactivate command in the command prompt."
      ],
      "metadata": {
        "id": "I8zefqrdMjJX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Install Python Package**"
      ],
      "metadata": {
        "id": "wm_tXBiZMoBo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pip install package_name"
      ],
      "metadata": {
        "id": "E5UkWcq0MsPe"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Install Python Package Specific Version**\n",
        "\n"
      ],
      "metadata": {
        "id": "6TSfi0oDMuw5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pip install package_name==1.2.3"
      ],
      "metadata": {
        "id": "9k0asodyMy1X"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Install Python Package from the Requirements file**\n",
        "\n"
      ],
      "metadata": {
        "id": "vC1eCS8tM9q_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pip install -r requirements.txt"
      ],
      "metadata": {
        "id": "PFamBXqNNG5q"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Make sure the text file is in the directory you were intended to. Usually in the project root. You can use the following command to have a requirements file from one environment to the other."
      ],
      "metadata": {
        "id": "EaxL0lh5NLl3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Installing Packages from Online repo :**\n",
        "\n"
      ],
      "metadata": {
        "id": "hDi43J0P_WGa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "1pip install Github repository URL"
      ],
      "metadata": {
        "id": "uqWt_oDl_ccy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "pip freeze > requirements.txt"
      ],
      "metadata": {
        "id": "vBflW86VNO4i"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Install Python Package From the URL**\n",
        "\n"
      ],
      "metadata": {
        "id": "EBJz5ZCv_jrt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "1pip install git+https://github.com/username/repo_name.git"
      ],
      "metadata": {
        "id": "cBkj-E2b_tPx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Get Installed Package Information**\n",
        "\n"
      ],
      "metadata": {
        "id": "-zWRIfNZ_3Ly"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip show package_name"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7bcJkENy_7Ip",
        "outputId": "687cc1ce-0d2b-4a65-846d-dd534e075c59"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[33mWARNING: Package(s) not found: package_name\u001b[0m\u001b[33m\n",
            "\u001b[0m"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Get the List of All the Installed Packages**"
      ],
      "metadata": {
        "id": "jJAVunSrABfq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip list"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SIp1e0RxAF8R",
        "outputId": "25eeea13-896e-43e3-8ab5-2fb28ca691cb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Package                          Version\n",
            "-------------------------------- ---------------------\n",
            "absl-py                          1.4.0\n",
            "aiohttp                          3.8.6\n",
            "aiosignal                        1.3.1\n",
            "alabaster                        0.7.13\n",
            "albumentations                   1.3.1\n",
            "altair                           4.2.2\n",
            "anyio                            3.7.1\n",
            "appdirs                          1.4.4\n",
            "argon2-cffi                      23.1.0\n",
            "argon2-cffi-bindings             21.2.0\n",
            "array-record                     0.4.1\n",
            "arviz                            0.15.1\n",
            "astropy                          5.3.4\n",
            "astunparse                       1.6.3\n",
            "async-timeout                    4.0.3\n",
            "atpublic                         4.0\n",
            "attrs                            23.1.0\n",
            "audioread                        3.0.1\n",
            "autograd                         1.6.2\n",
            "Babel                            2.13.0\n",
            "backcall                         0.2.0\n",
            "beautifulsoup4                   4.11.2\n",
            "bidict                           0.22.1\n",
            "bigframes                        0.8.0\n",
            "bleach                           6.1.0\n",
            "blinker                          1.4\n",
            "blis                             0.7.11\n",
            "blosc2                           2.0.0\n",
            "bokeh                            3.2.2\n",
            "bqplot                           0.12.40\n",
            "branca                           0.6.0\n",
            "build                            1.0.3\n",
            "CacheControl                     0.13.1\n",
            "cachetools                       5.3.1\n",
            "catalogue                        2.0.10\n",
            "certifi                          2023.7.22\n",
            "cffi                             1.16.0\n",
            "chardet                          5.2.0\n",
            "charset-normalizer               3.3.0\n",
            "chex                             0.1.7\n",
            "click                            8.1.7\n",
            "click-plugins                    1.1.1\n",
            "cligj                            0.7.2\n",
            "cloudpickle                      2.2.1\n",
            "cmake                            3.27.7\n",
            "cmdstanpy                        1.2.0\n",
            "colorcet                         3.0.1\n",
            "colorlover                       0.3.0\n",
            "colour                           0.1.5\n",
            "community                        1.0.0b1\n",
            "confection                       0.1.3\n",
            "cons                             0.4.6\n",
            "contextlib2                      21.6.0\n",
            "contourpy                        1.1.1\n",
            "cryptography                     41.0.4\n",
            "cufflinks                        0.17.3\n",
            "cupy-cuda11x                     11.0.0\n",
            "cvxopt                           1.3.2\n",
            "cvxpy                            1.3.2\n",
            "cycler                           0.12.1\n",
            "cymem                            2.0.8\n",
            "Cython                           3.0.3\n",
            "dask                             2023.8.1\n",
            "datascience                      0.17.6\n",
            "db-dtypes                        1.1.1\n",
            "dbus-python                      1.2.18\n",
            "debugpy                          1.6.6\n",
            "decorator                        4.4.2\n",
            "defusedxml                       0.7.1\n",
            "diskcache                        5.6.3\n",
            "distributed                      2023.8.1\n",
            "distro                           1.7.0\n",
            "dlib                             19.24.2\n",
            "dm-tree                          0.1.8\n",
            "docutils                         0.18.1\n",
            "dopamine-rl                      4.0.6\n",
            "duckdb                           0.8.1\n",
            "earthengine-api                  0.1.374\n",
            "easydict                         1.10\n",
            "ecos                             2.0.12\n",
            "editdistance                     0.6.2\n",
            "eerepr                           0.0.4\n",
            "en-core-web-sm                   3.6.0\n",
            "entrypoints                      0.4\n",
            "et-xmlfile                       1.1.0\n",
            "etils                            1.5.1\n",
            "etuples                          0.3.9\n",
            "exceptiongroup                   1.1.3\n",
            "fastai                           2.7.13\n",
            "fastcore                         1.5.29\n",
            "fastdownload                     0.0.7\n",
            "fastjsonschema                   2.18.1\n",
            "fastprogress                     1.0.3\n",
            "fastrlock                        0.8.2\n",
            "filelock                         3.12.4\n",
            "fiona                            1.9.5\n",
            "firebase-admin                   5.3.0\n",
            "Flask                            2.2.5\n",
            "flatbuffers                      23.5.26\n",
            "flax                             0.7.4\n",
            "folium                           0.14.0\n",
            "fonttools                        4.43.1\n",
            "frozendict                       2.3.8\n",
            "frozenlist                       1.4.0\n",
            "fsspec                           2023.6.0\n",
            "future                           0.18.3\n",
            "gast                             0.4.0\n",
            "gcsfs                            2023.6.0\n",
            "GDAL                             3.4.3\n",
            "gdown                            4.6.6\n",
            "geemap                           0.28.2\n",
            "gensim                           4.3.2\n",
            "geocoder                         1.38.1\n",
            "geographiclib                    2.0\n",
            "geopandas                        0.13.2\n",
            "geopy                            2.3.0\n",
            "gin-config                       0.5.0\n",
            "glob2                            0.7\n",
            "google                           2.0.3\n",
            "google-api-core                  2.11.1\n",
            "google-api-python-client         2.84.0\n",
            "google-auth                      2.17.3\n",
            "google-auth-httplib2             0.1.1\n",
            "google-auth-oauthlib             1.0.0\n",
            "google-cloud-bigquery            3.10.0\n",
            "google-cloud-bigquery-connection 1.12.1\n",
            "google-cloud-bigquery-storage    2.22.0\n",
            "google-cloud-core                2.3.3\n",
            "google-cloud-datastore           2.15.2\n",
            "google-cloud-firestore           2.11.1\n",
            "google-cloud-functions           1.13.3\n",
            "google-cloud-iam                 2.12.2\n",
            "google-cloud-language            2.9.1\n",
            "google-cloud-resource-manager    1.10.4\n",
            "google-cloud-storage             2.8.0\n",
            "google-cloud-translate           3.11.3\n",
            "google-colab                     1.0.0\n",
            "google-crc32c                    1.5.0\n",
            "google-pasta                     0.2.0\n",
            "google-resumable-media           2.6.0\n",
            "googleapis-common-protos         1.61.0\n",
            "googledrivedownloader            0.4\n",
            "graphviz                         0.20.1\n",
            "greenlet                         3.0.0\n",
            "grpc-google-iam-v1               0.12.6\n",
            "grpcio                           1.59.0\n",
            "grpcio-status                    1.48.2\n",
            "gspread                          3.4.2\n",
            "gspread-dataframe                3.3.1\n",
            "gym                              0.25.2\n",
            "gym-notices                      0.0.8\n",
            "h5netcdf                         1.2.0\n",
            "h5py                             3.9.0\n",
            "holidays                         0.35\n",
            "holoviews                        1.17.1\n",
            "html5lib                         1.1\n",
            "httpimport                       1.3.1\n",
            "httplib2                         0.22.0\n",
            "humanize                         4.7.0\n",
            "hyperopt                         0.2.7\n",
            "ibis-framework                   6.2.0\n",
            "idna                             3.4\n",
            "imageio                          2.31.5\n",
            "imageio-ffmpeg                   0.4.9\n",
            "imagesize                        1.4.1\n",
            "imbalanced-learn                 0.10.1\n",
            "imgaug                           0.4.0\n",
            "importlib-metadata               6.8.0\n",
            "importlib-resources              6.1.0\n",
            "imutils                          0.5.4\n",
            "inflect                          7.0.0\n",
            "iniconfig                        2.0.0\n",
            "install                          1.3.5\n",
            "intel-openmp                     2023.2.0\n",
            "ipyevents                        2.0.2\n",
            "ipyfilechooser                   0.6.0\n",
            "ipykernel                        5.5.6\n",
            "ipyleaflet                       0.17.4\n",
            "ipython                          7.34.0\n",
            "ipython-genutils                 0.2.0\n",
            "ipython-sql                      0.5.0\n",
            "ipytree                          0.2.2\n",
            "ipywidgets                       7.7.1\n",
            "itsdangerous                     2.1.2\n",
            "jax                              0.4.16\n",
            "jaxlib                           0.4.16+cuda11.cudnn86\n",
            "jeepney                          0.7.1\n",
            "jieba                            0.42.1\n",
            "Jinja2                           3.1.2\n",
            "joblib                           1.3.2\n",
            "jsonpickle                       3.0.2\n",
            "jsonschema                       4.19.1\n",
            "jsonschema-specifications        2023.7.1\n",
            "jupyter-client                   6.1.12\n",
            "jupyter-console                  6.1.0\n",
            "jupyter_core                     5.4.0\n",
            "jupyter-server                   1.24.0\n",
            "jupyterlab-pygments              0.2.2\n",
            "jupyterlab-widgets               3.0.9\n",
            "kaggle                           1.5.16\n",
            "keras                            2.13.1\n",
            "keyring                          23.5.0\n",
            "kiwisolver                       1.4.5\n",
            "langcodes                        3.3.0\n",
            "launchpadlib                     1.10.16\n",
            "lazr.restfulclient               0.14.4\n",
            "lazr.uri                         1.0.6\n",
            "lazy_loader                      0.3\n",
            "libclang                         16.0.6\n",
            "librosa                          0.10.1\n",
            "lida                             0.0.10\n",
            "lightgbm                         4.0.0\n",
            "linkify-it-py                    2.0.2\n",
            "lit                              17.0.2\n",
            "llmx                             0.0.15a0\n",
            "llvmlite                         0.39.1\n",
            "locket                           1.0.0\n",
            "logical-unification              0.4.6\n",
            "lxml                             4.9.3\n",
            "malloy                           2023.1056\n",
            "Markdown                         3.5\n",
            "markdown-it-py                   3.0.0\n",
            "MarkupSafe                       2.1.3\n",
            "matplotlib                       3.7.1\n",
            "matplotlib-inline                0.1.6\n",
            "matplotlib-venn                  0.11.9\n",
            "mdit-py-plugins                  0.4.0\n",
            "mdurl                            0.1.2\n",
            "miniKanren                       1.0.3\n",
            "missingno                        0.5.2\n",
            "mistune                          0.8.4\n",
            "mizani                           0.9.3\n",
            "mkl                              2023.2.0\n",
            "ml-dtypes                        0.3.1\n",
            "mlxtend                          0.22.0\n",
            "more-itertools                   10.1.0\n",
            "moviepy                          1.0.3\n",
            "mpmath                           1.3.0\n",
            "msgpack                          1.0.7\n",
            "multidict                        6.0.4\n",
            "multipledispatch                 1.0.0\n",
            "multitasking                     0.0.11\n",
            "murmurhash                       1.0.10\n",
            "music21                          9.1.0\n",
            "natsort                          8.4.0\n",
            "nbclassic                        1.0.0\n",
            "nbclient                         0.8.0\n",
            "nbconvert                        6.5.4\n",
            "nbformat                         5.9.2\n",
            "nest-asyncio                     1.5.8\n",
            "networkx                         3.1\n",
            "nibabel                          4.0.2\n",
            "nltk                             3.8.1\n",
            "notebook                         6.5.5\n",
            "notebook_shim                    0.2.3\n",
            "numba                            0.56.4\n",
            "numexpr                          2.8.7\n",
            "numpy                            1.23.5\n",
            "oauth2client                     4.1.3\n",
            "oauthlib                         3.2.2\n",
            "opencv-contrib-python            4.8.0.76\n",
            "opencv-python                    4.8.0.76\n",
            "opencv-python-headless           4.8.1.78\n",
            "openpyxl                         3.1.2\n",
            "opt-einsum                       3.3.0\n",
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            "orbax-checkpoint                 0.4.1\n",
            "osqp                             0.6.2.post8\n",
            "packaging                        23.2\n",
            "pandas                           1.5.3\n",
            "pandas-datareader                0.10.0\n",
            "pandas-gbq                       0.17.9\n",
            "pandas-stubs                     1.5.3.230304\n",
            "pandocfilters                    1.5.0\n",
            "panel                            1.2.3\n",
            "param                            1.13.0\n",
            "parso                            0.8.3\n",
            "parsy                            2.1\n",
            "partd                            1.4.1\n",
            "pathlib                          1.0.1\n",
            "pathy                            0.10.2\n",
            "patsy                            0.5.3\n",
            "peewee                           3.17.0\n",
            "pexpect                          4.8.0\n",
            "pickleshare                      0.7.5\n",
            "Pillow                           9.4.0\n",
            "pip                              23.3\n",
            "pip-tools                        6.13.0\n",
            "platformdirs                     3.11.0\n",
            "plotly                           5.15.0\n",
            "plotnine                         0.12.3\n",
            "pluggy                           1.3.0\n",
            "polars                           0.17.3\n",
            "pooch                            1.7.0\n",
            "portpicker                       1.5.2\n",
            "prefetch-generator               1.0.3\n",
            "preshed                          3.0.9\n",
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            "progressbar2                     4.2.0\n",
            "prometheus-client                0.17.1\n",
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            "prompt-toolkit                   3.0.39\n",
            "prophet                          1.1.5\n",
            "proto-plus                       1.22.3\n",
            "protobuf                         3.20.3\n",
            "psutil                           5.9.5\n",
            "psycopg2                         2.9.9\n",
            "ptyprocess                       0.7.0\n",
            "py-cpuinfo                       9.0.0\n",
            "py4j                             0.10.9.7\n",
            "pyarrow                          9.0.0\n",
            "pyasn1                           0.5.0\n",
            "pyasn1-modules                   0.3.0\n",
            "pycocotools                      2.0.7\n",
            "pycparser                        2.21\n",
            "pyct                             0.5.0\n",
            "pydantic                         1.10.13\n",
            "pydata-google-auth               1.8.2\n",
            "pydot                            1.4.2\n",
            "pydot-ng                         2.0.0\n",
            "pydotplus                        2.0.2\n",
            "PyDrive                          1.3.1\n",
            "PyDrive2                         1.6.3\n",
            "pyerfa                           2.0.1\n",
            "pygame                           2.5.2\n",
            "Pygments                         2.16.1\n",
            "PyGObject                        3.42.1\n",
            "PyJWT                            2.3.0\n",
            "pymc                             5.7.2\n",
            "pymystem3                        0.2.0\n",
            "PyOpenGL                         3.1.7\n",
            "pyOpenSSL                        23.2.0\n",
            "pyparsing                        3.1.1\n",
            "pyperclip                        1.8.2\n",
            "pyproj                           3.6.1\n",
            "pyproject_hooks                  1.0.0\n",
            "pyshp                            2.3.1\n",
            "PySocks                          1.7.1\n",
            "pytensor                         2.14.2\n",
            "pytest                           7.4.2\n",
            "python-apt                       0.0.0\n",
            "python-box                       7.1.1\n",
            "python-dateutil                  2.8.2\n",
            "python-louvain                   0.16\n",
            "python-slugify                   8.0.1\n",
            "python-utils                     3.8.1\n",
            "pytz                             2023.3.post1\n",
            "pyviz_comms                      3.0.0\n",
            "PyWavelets                       1.4.1\n",
            "PyYAML                           6.0.1\n",
            "pyzmq                            23.2.1\n",
            "qdldl                            0.1.7.post0\n",
            "qudida                           0.0.4\n",
            "ratelim                          0.1.6\n",
            "referencing                      0.30.2\n",
            "regex                            2023.6.3\n",
            "requests                         2.31.0\n",
            "requests-oauthlib                1.3.1\n",
            "requirements-parser              0.5.0\n",
            "rich                             13.6.0\n",
            "rpds-py                          0.10.6\n",
            "rpy2                             3.4.2\n",
            "rsa                              4.9\n",
            "scikit-image                     0.19.3\n",
            "scikit-learn                     1.2.2\n",
            "scipy                            1.11.3\n",
            "scooby                           0.7.4\n",
            "scs                              3.2.3\n",
            "seaborn                          0.12.2\n",
            "SecretStorage                    3.3.1\n",
            "Send2Trash                       1.8.2\n",
            "setuptools                       67.7.2\n",
            "shapely                          2.0.2\n",
            "six                              1.16.0\n",
            "sklearn-pandas                   2.2.0\n",
            "smart-open                       6.4.0\n",
            "sniffio                          1.3.0\n",
            "snowballstemmer                  2.2.0\n",
            "sortedcontainers                 2.4.0\n",
            "soundfile                        0.12.1\n",
            "soupsieve                        2.5\n",
            "soxr                             0.3.7\n",
            "spacy                            3.6.1\n",
            "spacy-legacy                     3.0.12\n",
            "spacy-loggers                    1.0.5\n",
            "Sphinx                           5.0.2\n",
            "sphinxcontrib-applehelp          1.0.7\n",
            "sphinxcontrib-devhelp            1.0.5\n",
            "sphinxcontrib-htmlhelp           2.0.4\n",
            "sphinxcontrib-jsmath             1.0.1\n",
            "sphinxcontrib-qthelp             1.0.6\n",
            "sphinxcontrib-serializinghtml    1.1.9\n",
            "SQLAlchemy                       2.0.22\n",
            "sqlglot                          17.16.2\n",
            "sqlparse                         0.4.4\n",
            "srsly                            2.4.8\n",
            "stanio                           0.3.0\n",
            "statsmodels                      0.14.0\n",
            "sympy                            1.12\n",
            "tables                           3.8.0\n",
            "tabulate                         0.9.0\n",
            "tbb                              2021.10.0\n",
            "tblib                            2.0.0\n",
            "tenacity                         8.2.3\n",
            "tensorboard                      2.13.0\n",
            "tensorboard-data-server          0.7.1\n",
            "tensorflow                       2.13.0\n",
            "tensorflow-datasets              4.9.3\n",
            "tensorflow-estimator             2.13.0\n",
            "tensorflow-gcs-config            2.13.0\n",
            "tensorflow-hub                   0.15.0\n",
            "tensorflow-io-gcs-filesystem     0.34.0\n",
            "tensorflow-metadata              1.14.0\n",
            "tensorflow-probability           0.20.1\n",
            "tensorstore                      0.1.45\n",
            "termcolor                        2.3.0\n",
            "terminado                        0.17.1\n",
            "text-unidecode                   1.3\n",
            "textblob                         0.17.1\n",
            "tf-slim                          1.1.0\n",
            "thinc                            8.1.12\n",
            "threadpoolctl                    3.2.0\n",
            "tifffile                         2023.9.26\n",
            "tinycss2                         1.2.1\n",
            "toml                             0.10.2\n",
            "tomli                            2.0.1\n",
            "toolz                            0.12.0\n",
            "torch                            2.0.1+cu118\n",
            "torchaudio                       2.0.2+cu118\n",
            "torchdata                        0.6.1\n",
            "torchsummary                     1.5.1\n",
            "torchtext                        0.15.2\n",
            "torchvision                      0.15.2+cu118\n",
            "tornado                          6.3.2\n",
            "tqdm                             4.66.1\n",
            "traitlets                        5.7.1\n",
            "traittypes                       0.2.1\n",
            "triton                           2.0.0\n",
            "tweepy                           4.13.0\n",
            "typer                            0.9.0\n",
            "types-pytz                       2023.3.1.1\n",
            "types-setuptools                 68.2.0.0\n",
            "typing_extensions                4.5.0\n",
            "tzlocal                          5.1\n",
            "uc-micro-py                      1.0.2\n",
            "uritemplate                      4.1.1\n",
            "urllib3                          2.0.6\n",
            "vega-datasets                    0.9.0\n",
            "wadllib                          1.3.6\n",
            "wasabi                           1.1.2\n",
            "wcwidth                          0.2.8\n",
            "webcolors                        1.13\n",
            "webencodings                     0.5.1\n",
            "websocket-client                 1.6.4\n",
            "Werkzeug                         3.0.0\n",
            "wheel                            0.41.2\n",
            "widgetsnbextension               3.6.6\n",
            "wordcloud                        1.9.2\n",
            "wrapt                            1.15.0\n",
            "xarray                           2023.7.0\n",
            "xarray-einstats                  0.6.0\n",
            "xgboost                          2.0.0\n",
            "xlrd                             2.0.1\n",
            "xxhash                           3.4.1\n",
            "xyzservices                      2023.10.0\n",
            "yarl                             1.9.2\n",
            "yellowbrick                      1.5\n",
            "yfinance                         0.2.31\n",
            "zict                             3.0.0\n",
            "zipp                             3.17.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Uninstall Python Package**\n",
        "\n"
      ],
      "metadata": {
        "id": "JdC6vUloNWU_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pip install --upgrade package_name"
      ],
      "metadata": {
        "id": "jcB8VBWPNaSg"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "pip uninstall package_name"
      ],
      "metadata": {
        "id": "uTwp2FzLNgDa"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Get Installed Package Information**\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "U4DP_jbLNjRe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pip show package_name"
      ],
      "metadata": {
        "id": "DkXeHaWtNnNe"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Get the List of All the Installed Packages**\n",
        "\n"
      ],
      "metadata": {
        "id": "h2KiQyKINptG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip list"
      ],
      "metadata": {
        "id": "uduUCBOBNtpW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**outdated or not the current version.**"
      ],
      "metadata": {
        "id": "sT_s86QkN2Sk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pip list --outdated"
      ],
      "metadata": {
        "id": "zaMKEZmoN85S"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "344x1LzWyd8K"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**📚Section 2-Array Creation<a name='array_creation'></a>**\n",
        "\n",
        "NumPy stands for ‘Numerical Python’. It is an open-source Python library used to perform various mathematical and scientific tasks.NumPy is one of the very first libraries in Python that makes your numerical computations easy and efficient. This course will get you acquainted (familiarize) with NumPy. It contains multi-dimensional arrays and matrices, along with many high-level [link text](https://)"
      ],
      "metadata": {
        "id": "RLwXpfoFfD69"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Table of Content**"
      ],
      "metadata": {
        "id": "tPpT7aOfz2x0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "1.   📚 Installing NumPy\n",
        "2.   📚 Creating NumPy\n",
        "\n",
        " 2.1 📚 Creating Numpy with Array Method\n",
        "\n",
        " 2.2 📚 Conversion from other Python structures\n",
        "\n",
        " 2.3 📚 Use of Special Library Functions\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "X6wU6Dtsz-Ga"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##**2.1: Installing NumPy**"
      ],
      "metadata": {
        "id": "hU2fTryOGEEV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**How to Install Numpy?**"
      ],
      "metadata": {
        "id": "1Em_GmIwfQZ1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install numpy"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cGZRkk99fS3i",
        "outputId": "3216a85f-1fac-439d-f2b1-03d0d72caa6f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (1.23.5)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"Hello to the Numpy\")"
      ],
      "metadata": {
        "id": "GudkkJrRt46h",
        "outputId": "39b7aac2-607f-45d6-cd57-fd1966061163",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Hello to the Numpy\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Importing NumPy**"
      ],
      "metadata": {
        "id": "-nX8kBByBWPz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "# Here we are importing numpy as np and np is an alias for numpy\n",
        "# Aliases are alternative names for existing Python modules or objects.\n",
        "# Assigning aliases can make Python programs easier to read and write."
      ],
      "metadata": {
        "id": "HQ7JdzuMfmT7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "conda install numpy"
      ],
      "metadata": {
        "id": "RWjkLehNGa46"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Virtual environment**"
      ],
      "metadata": {
        "id": "0WrsV1yFGfA3"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# create the virtual environment\n",
        "python3 -m venv venv\n",
        "\n",
        "# activate the virtual environment\n",
        "source venv/bin/activate\n",
        "\n",
        "# upgrade pip package manager\n",
        "pip3 install --upgrade pip\n",
        "\n",
        "#install numpy\n",
        "pip3 install numpy"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "id": "hk20wKnbGkM3",
        "outputId": "1e3ea504-2f0e-44de-d506-947289331e7e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "SyntaxError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-9-3559d4d58963>\"\u001b[0;36m, line \u001b[0;32m2\u001b[0m\n\u001b[0;31m    python3 -m venv venv\u001b[0m\n\u001b[0m               ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **2.2- Creating NumPy Array**"
      ],
      "metadata": {
        "id": "J5fkbewyHJfR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Creating NumPy Array with Array method**"
      ],
      "metadata": {
        "id": "WJXg9RVihY4b"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Single Dimension Array**"
      ],
      "metadata": {
        "id": "hbZwY4KUHzbA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "a = np.array([2,3,4])\n",
        "b = np.array([2.0,3.5,4.4])"
      ],
      "metadata": {
        "id": "xeR1LIuDIfPk"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"The data type of a is:\",a.dtype)\n",
        "print(\"The data type of b is:\",b.dtype)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6jCTdbj6IiUo",
        "outputId": "8dcf6609-3b29-4025-fdc9-252a6d3ab1e9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The data type of a is: int64\n",
            "The data type of b is: float64\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Creating 2D Array or Matrices**\n"
      ],
      "metadata": {
        "id": "SOwe3s1Hhis2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Create a 2D NumPy array with 2 rows and 2 columns\n",
        "arr2D = np.array([[1, 2], [4, 5]])\n",
        "\n",
        "# Print the array\n",
        "print(arr2D)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PGoAZegdimyu",
        "outputId": "a993492c-d9d5-428c-fcda-9419a1014363"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2]\n",
            " [4 5]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#complex 2D Array\n",
        "c=np.array([[1,2],[3,4]], dtype= complex)\n",
        "print(c)"
      ],
      "metadata": {
        "id": "pL-bH-AYk-uU",
        "outputId": "b974f13e-742d-480b-dacf-dc81ae1b1f4b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1.+0.j 2.+0.j]\n",
            " [3.+0.j 4.+0.j]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Array full of zero and full of ones and Random numbers**"
      ],
      "metadata": {
        "id": "TxBN5TJVj0qe"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "oArray = np.zeros((3,4))\n",
        "oneArray = np.ones((3,4))\n",
        "print(oArray)\n",
        "print(oneArray)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QjOcEiL-j4jO",
        "outputId": "14ffea87-9416-42e8-d43d-3d4bc893bd0a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0. 0. 0. 0.]\n",
            " [0. 0. 0. 0.]\n",
            " [0. 0. 0. 0.]]\n",
            "[[1. 1. 1. 1.]\n",
            " [1. 1. 1. 1.]\n",
            " [1. 1. 1. 1.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "Arrrand = np.random.random(3)\n",
        "print(Arrrand)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Q6kpoKqMjs06",
        "outputId": "6a54c789-86f8-4626-ab83-2293318f0b0e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.07721194 0.81039761 0.80214133]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Empty Array in Numpy**\n"
      ],
      "metadata": {
        "id": "sJytidlukGvO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "oArray = np.zeros((3,4))\n",
        "oneArray = np.ones((3,4))\n",
        "print(oArray)\n",
        "print(oneArray)"
      ],
      "metadata": {
        "id": "esKPc6hZkxMF",
        "outputId": "b4ddbbbd-3de2-4be3-9107-d1d19ef1d3ff",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0. 0. 0. 0.]\n",
            " [0. 0. 0. 0.]\n",
            " [0. 0. 0. 0.]]\n",
            "[[1. 1. 1. 1.]\n",
            " [1. 1. 1. 1.]\n",
            " [1. 1. 1. 1.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "emptyArray=np.empty"
      ],
      "metadata": {
        "id": "XIwuvMRRk27c"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Conversion from other Python structures**"
      ],
      "metadata": {
        "id": "_cfI9S0m42WO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "array_list = np.array([1, 2, 3])\n",
        "array_tuple = np.array(((1, 2, 3), (4, 5, 6)))\n",
        "array_set = np.array({\"pikachu\", \"snorlax\", \"charizard\"})"
      ],
      "metadata": {
        "id": "Cg9H2HOZ4-RR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Use of Special Library Function**"
      ],
      "metadata": {
        "id": "c31k5YNO04VY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "NumPy has a large list of special cases functions that generate arrays, which are too large and seemingly disconnected to enumerate. Here are a few examples:"
      ],
      "metadata": {
        "id": "nF-wtQxN1Eft"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# diagonal array\n",
        "diagonal = np.diag([1, 2, 3], k=0)\n",
        "\n",
        "# identity\n",
        "identity = np.identity(3)\n",
        "\n",
        "# eye\n",
        "eye = np.eye(4, k=1)\n",
        "\n",
        "# rand\n",
        "rand = np.random.rand(3,2)\n"
      ],
      "metadata": {
        "collapsed": true,
        "id": "Jc1o1Dky1Bxa"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f'Diagonal matrix from array-like structure:\\n{diagonal}\\n')\n",
        "print(f'Identity matrix:\\n{identity}\\n')\n",
        "print(f'Diagonal matrix with ones and zeros elsewhere:\\n{eye}\\n')\n",
        "print(f'Array of random numbers sampled from a uniform distribution:\\n{rand}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5-K0b3DM2pkJ",
        "outputId": "b567e6c1-9124-4ab2-a9bd-6630d3d09ab8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Diagonal matrix from array-like structure:\n",
            "[[1 0 0]\n",
            " [0 2 0]\n",
            " [0 0 3]]\n",
            "\n",
            "Identity matrix:\n",
            "[[1. 0. 0.]\n",
            " [0. 1. 0.]\n",
            " [0. 0. 1.]]\n",
            "\n",
            "Diagonal matrix with ones and zeros elsewhere:\n",
            "[[0. 1. 0. 0.]\n",
            " [0. 0. 1. 0.]\n",
            " [0. 0. 0. 1.]\n",
            " [0. 0. 0. 0.]]\n",
            "\n",
            "Array of random numbers sampled from a uniform distribution:\n",
            "[[0.33434968 0.65584555]\n",
            " [0.00968158 0.92594849]\n",
            " [0.16759017 0.57404106]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **An array with a constant**"
      ],
      "metadata": {
        "id": "dWUjFJuJ2yeX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating a constant array\n",
        "arr_c = np.full((2,2), 7)\n",
        "print(arr_c)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RRF25D4j22ro",
        "outputId": "b70a08e3-65bf-4721-bd9f-9f4f81036ed0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[7 7]\n",
            " [7 7]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Creating an array with start value, end value and number of values**"
      ],
      "metadata": {
        "id": "dWGTfE9E2-PO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "arr_L = np.linspace(0, 5,7)\n",
        "print(arr_L)\n",
        "#observe here dtype('float64')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jPygfRbR3Anb",
        "outputId": "ed0bcc3a-3219-42ed-cf1e-e5ace2e40e41"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.         0.83333333 1.66666667 2.5        3.33333333 4.16666667\n",
            " 5.        ]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Creating an array with start value, end value and number of values(datatypes int)**"
      ],
      "metadata": {
        "id": "_hjG31If3Su6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "arr_a=np.arange(1, 10,1)\n",
        "print(arr_a)\n",
        "#here dtype('int32')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Y0D_IzMr3U_L",
        "outputId": "9d0f269f-0929-44e0-b446-0f179ca5b75f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 2 3 4 5 6 7 8 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **An array filled with random integers**\n"
      ],
      "metadata": {
        "id": "nhodryLG3hpA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "arr_1= np.random.randint(10,100,7)\n",
        "print(arr_1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2L0EFb1Z3j-3",
        "outputId": "a0675128-8c8c-4e18-94da-16380614e465"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[43 60 13 63 46 95 54]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **An array filled with random values(which follows Normal Distribution)**\n"
      ],
      "metadata": {
        "id": "KWLHnxWq3p1v"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "arr_n= np.random.randn(10)\n",
        "print(arr_n)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pF6u3NXP3t6m",
        "outputId": "12af04b8-92e4-4a87-d908-abd493069e26"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[-1.52378948 -0.1743775   1.479895    0.10271934  0.90654494 -0.42533973\n",
            "  0.06759782  1.26611259 -1.27700556 -1.86179845]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Creating a 2x2 identity matrix**\n"
      ],
      "metadata": {
        "id": "Y3buA1DV32j4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#  Create a 2x2 identity matrix\n",
        "arr_I = np.eye(2)\n",
        "print(arr_I)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YHsIhtbl36fV",
        "outputId": "d567558e-c356-4917-c2ed-ce60c7e2ede5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1. 0.]\n",
            " [0. 1.]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Creating Arrays from existing data**\n",
        "This is useful for converting Python sequence into ndarray. numpy.asarray(a, dtype=None ,order = None)"
      ],
      "metadata": {
        "id": "W8S_5DMS4HKH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#converting list to ndarray\n",
        "import numpy as np\n",
        "x = [1,2,3]\n",
        "a = np.asarray(x)\n",
        "print (a)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n5NmgnxGO0Ja",
        "outputId": "8ea4b7ce-398b-4621-d662-2fbff543c728"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 2 3]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ndarray from tuple\n",
        "x_1 = (1,2,3)\n",
        "a_1 = np.asarray(x_1)\n",
        "print (a_1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "T5n0rrvdO2ky",
        "outputId": "4b63adac-2239-4e48-d9d2-2a87e139697b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 2 3]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# ndarray from list of tuples\n",
        "import numpy as np\n",
        "x_2 = [(1,2,3),(4,5)]\n",
        "a_2 = np.asarray(x_2)\n",
        "print (a_2)"
      ],
      "metadata": {
        "id": "aO2sO90BO44j"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "arr = np.array([[1,2,3],[4,5,6]])\n",
        "print (arr.shape)"
      ],
      "metadata": {
        "id": "UepLP1ojO8_6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#resizing the above array\n",
        "a = np.array([[1,2,3],[4,5,6]])\n",
        "a.shape = (3,2)\n",
        "print (a"
      ],
      "metadata": {
        "id": "Ca6Txmj0O-g3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array([[1,2,3],[4,5,6]])\n",
        "b = a.reshape(3,2)\n",
        "print (b)"
      ],
      "metadata": {
        "id": "9thagH9WO_ur"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**📚Section 3- Arthimetic Operations<a name='arthimetic_operations'></a>**"
      ],
      "metadata": {
        "id": "3gtbL5POocfK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **3.1- Addition**"
      ],
      "metadata": {
        "id": "JhpWU1dio2Rt"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 1**"
      ],
      "metadata": {
        "id": "7GjX7UxFpOYh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "A = np.arange(12).reshape(3,4)\n",
        "A"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FALoUIz9orON",
        "outputId": "91267341-08a7-4e22-de30-f94c2fda20c4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "B = np.arange(12).reshape(3,4)\n",
        "B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8tvy_1d9o1Cs",
        "outputId": "a5355714-745b-4ebe-8875-fdc077d7cec5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A+B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pwqDdqpVo5t9",
        "outputId": "5765af8e-5875-4cb9-8229-36b34727db23"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  2,  4,  6],\n",
              "       [ 8, 10, 12, 14],\n",
              "       [16, 18, 20, 22]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 2**"
      ],
      "metadata": {
        "id": "9ztVb7-4pSOQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data=np.array([1,2])\n",
        "ones= np.ones(2)\n",
        "addition = data + ones\n",
        "print(f'Addition of data and ones:\\n{addition}\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9ZJNqMmupV4o",
        "outputId": "cab7db32-2964-4d81-c1be-658ce7fb0be6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Addition of data and ones:\n",
            "[2. 3.]\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data=np.array([[1,2],[2,4]])\n",
        "ones= np.ones(2)\n",
        "addition = data + ones\n",
        "print(f'Addition of data and ones:\\n{addition}\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HQo6BZippeM_",
        "outputId": "22e9dbaa-c90e-4d53-a87f-5ac12baa8b2c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Addition of data and ones:\n",
            "[[2. 3.]\n",
            " [3. 5.]]\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **3.2-Substraction , multiplication and Division**"
      ],
      "metadata": {
        "id": "GxhK8Z3qpmbV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Substraction**"
      ],
      "metadata": {
        "id": "Zm7VDIM2pwqA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 1**"
      ],
      "metadata": {
        "id": "Dg8YQJBbp4bR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A-B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kN-er8eTo9ft",
        "outputId": "e74053ce-6d6c-45b0-d6a5-23dd3a2ad3ee"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 0, 0, 0],\n",
              "       [0, 0, 0, 0],\n",
              "       [0, 0, 0, 0]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 2**"
      ],
      "metadata": {
        "id": "oynd7ZF9p7w5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data=np.array([[1,2]])\n",
        "ones= np.ones(1)\n",
        "subtraction = data - ones\n",
        "print(f'Subtraction of data and ones:\\n{subtraction}\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f7h2UI6op-fY",
        "outputId": "fa9d28fb-0ef3-4956-cbd9-ee2cb8396364"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Subtraction of data and ones:\n",
            "[[0. 1.]]\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Multiplication**"
      ],
      "metadata": {
        "id": "0YyZxogRuenH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 1-**"
      ],
      "metadata": {
        "id": "9DOBdmGLuiOw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A*B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iOX3p32xo-6F",
        "outputId": "32553e4f-5c94-4bc7-9339-37a3d3169b3c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  0,   1,   4,   9],\n",
              "       [ 16,  25,  36,  49],\n",
              "       [ 64,  81, 100, 121]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 2**"
      ],
      "metadata": {
        "id": "OeUpdsDAumog"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data=np.array([[1,2]])\n",
        "multiplication = data * data\n",
        "print(f'Subtraction of data and ones:\\n{subtraction}\\n')\n",
        "print(f'Multiplication of data and data:\\n{multiplication}\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8aZ-uxwIupix",
        "outputId": "aca08471-5fa9-42e8-c240-2e5fa5845992"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Subtraction of data and ones:\n",
            "[[0. 1.]]\n",
            "\n",
            "Multiplication of data and data:\n",
            "[[1 4]]\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Division**"
      ],
      "metadata": {
        "id": "UGK-XfL21GiH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example**"
      ],
      "metadata": {
        "id": "osWR3sHR1NTl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A/B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZeYGP9xbpAxt",
        "outputId": "fcf2f799-20a9-4e39-a0df-b505de3c9294"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-11-5d618eb3152c>:1: RuntimeWarning: invalid value encountered in divide\n",
            "  A/B\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[nan,  1.,  1.,  1.],\n",
              "       [ 1.,  1.,  1.,  1.],\n",
              "       [ 1.,  1.,  1.,  1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Example 2**"
      ],
      "metadata": {
        "id": "NFXjChbC1Rv1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data=np.array([[1,2]])\n",
        "true_division = data / data\n",
        "print(f'True divition of data and data:\\n{true_division}\\n')"
      ],
      "metadata": {
        "id": "8xrzcP_dpB_l",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c100aa27-7e63-41f5-f6a2-560f834bf55c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True divition of data and data:\n",
            "[[1. 1.]]\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.arange(1, 10).reshape((3,3))\n",
        "b = np.arange(10,19).reshape((3,3))\n"
      ],
      "metadata": {
        "id": "9c6YfobX1cXN"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "subtraction = a - b\n",
        "multiplication = a * b\n",
        "true_division = a / b\n",
        "floor_division = a // b\n",
        "remainder = np.remainder(a, b)"
      ],
      "metadata": {
        "id": "fMfuisYQ1g63"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f'Array a:\\n{a}\\n')\n",
        "print(f'Array b:\\n{b}\\n')\n",
        "print(f'Subtraction of a and b:\\n{subtraction}\\n')\n",
        "print(f'Multiplication of a and b:\\n{multiplication}\\n')\n",
        "print(f'True divition of a and b:\\n{true_division}\\n')\n",
        "print(f'Floor division of a and b:\\n{floor_division}\\n')\n",
        "print(f'Remainder of a and b:\\n{remainder}')"
      ],
      "metadata": {
        "id": "cbkoO68a1kds",
        "outputId": "a5066c97-daa5-42fa-b4f8-6f1eba739e15",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Array a:\n",
            "[[1 2 3]\n",
            " [4 5 6]\n",
            " [7 8 9]]\n",
            "\n",
            "Array b:\n",
            "[[10 11 12]\n",
            " [13 14 15]\n",
            " [16 17 18]]\n",
            "\n",
            "Subtraction of a and b:\n",
            "[[-9 -9 -9]\n",
            " [-9 -9 -9]\n",
            " [-9 -9 -9]]\n",
            "\n",
            "Multiplication of a and b:\n",
            "[[ 10  22  36]\n",
            " [ 52  70  90]\n",
            " [112 136 162]]\n",
            "\n",
            "True divition of a and b:\n",
            "[[0.1        0.18181818 0.25      ]\n",
            " [0.30769231 0.35714286 0.4       ]\n",
            " [0.4375     0.47058824 0.5       ]]\n",
            "\n",
            "Floor division of a and b:\n",
            "[[0 0 0]\n",
            " [0 0 0]\n",
            " [0 0 0]]\n",
            "\n",
            "Remainder of a and b:\n",
            "[[1 2 3]\n",
            " [4 5 6]\n",
            " [7 8 9]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **3.3- Dot Product**"
      ],
      "metadata": {
        "id": "E6-TpjeM1q-h"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "dot product is a mathematical operation that calculates the sum of the products of corresponding elements of two vectors. In NumPy, you can calculate the dot product using the dot() function."
      ],
      "metadata": {
        "id": "N6Gc8LRWL0Jg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "a = np.array([1, 2, 3])\n",
        "b = np.array([4, 5, 6])\n",
        "dot_product = np.dot(a, b)\n",
        "print(dot_product)\n",
        "a = np.array([[1, 2], [3, 4]])\n",
        "b = np.array([[5, 6], [7, 8]])\n",
        "dot_product = np.dot(a, b)\n",
        "print(dot_product)"
      ],
      "metadata": {
        "id": "qVU9H318120d",
        "outputId": "50550999-49b1-4b1c-b296-5c5998f49302",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "32\n",
            "[[19 22]\n",
            " [43 50]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **3.4-Broadcasting**"
      ],
      "metadata": {
        "id": "i1SmHC7g17EZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "NumPy’s broadcasting feature enables operations between arrays of different shapes and sizes"
      ],
      "metadata": {
        "id": "jdzvBvwZL8Rx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "arr = np.array([[1, 2, 3], [4, 5, 6]])\n",
        "scalar = 2\n",
        "result_broadcast = arr * scalar\n",
        "print(\"Broadcasting Result:\", result_broadcast)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TLMtTQabODat",
        "outputId": "7c55509d-a9a5-4459-968b-27aab5fec21a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Broadcasting Result: [[ 2  4  6]\n",
            " [ 8 10 12]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating 1D NumPy arrays\n",
        "arr1 = np.array([1, 2, 3])\n",
        "arr2 = np.array([4, 5, 6])\n",
        "scalar = 2\n",
        "# Actual Matrix Multiplication using np.dot\n",
        "matrix_multiplication = np.dot(arr,arr*2)"
      ],
      "metadata": {
        "id": "SvG691A_OMSC"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "# Creating 1D NumPy arrays\n",
        "arr1 = np.array([1, 2, 3])\n",
        "arr2 = np.array([4, 5, 6])\n",
        "scalar = 2\n",
        "\n",
        "# Creating a 1D array (Vector)\n",
        "arr_1d = np.array([1, 2, 3])\n",
        "# Dimesion: 1 , Shape: (3,), Size: 3\n",
        "print(f\"Dimension: {arr_1d.ndim}, Shape: {arr_1d.shape}, size: {arr_1d.size}\")\n",
        "\n",
        "# Creating a 2D array (Matrix) # Dimension: 2 , Shape: (2, 3)\n",
        "arr_2d = np.array([[1, 2, 3], [4, 5, 6]])\n",
        "\n",
        "# Creating a 3D array (Tensor) # Dimension: 3 , Shape: (2, 2, 2)\n",
        "arr_3d = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])"
      ],
      "metadata": {
        "id": "1cEVPg0wObme"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#**📚Section 4-The Basics operations on Numpy Array<a name='basic_mathematic_operations'></a>**\n",
        "NumPy’s main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the\n",
        "same type, indexed by a tuple of non-negative integers. In NumPy dimensions are called axes.\n",
        "For example, the array for the coordinates of a point in 3D space, [1, 2, 1], has one axis. That axis has 3 elements\n",
        "in it, so we say it has a length of 3. In the example pictured below, the array has 2 axes. The first axis has a length of 2,\n",
        "the second axis has a length of 3.\n",
        "[[1., 0., 0.],\n",
        "[0., 1., 2.]]\n",
        "NumPy’s array class is called ndarray. It is also known by the alias array. Note that numpy.array is not the\n",
        "same as the Standard Python Library class array.array, which only"
      ],
      "metadata": {
        "id": "TuIFR11HiUmK"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **4.1-Array Shape and Size:**"
      ],
      "metadata": {
        "id": "3Ctq8hE5K0gN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "**1-  ndarray.ndim**\n",
        "\n",
        "the number of axes (dimensions) of the array.\n",
        "\n",
        "**2-  ndarray.shape**\n",
        "\n",
        "the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a\n",
        "matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the number of axes, ndim.\n",
        "\n",
        "**3-  ndarray.size**\n",
        "\n",
        "the total number of elements of the array. This is equal to the product of the elements of shape.\n",
        "\n",
        "**4-  ndarray.dtype**\n",
        "\n",
        "an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python\n",
        "types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some\n",
        "examples.\n",
        "\n",
        "**5-  ndarray.itemsize**\n",
        "\n",
        "the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize\n",
        "8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.\n",
        "\n",
        "**6-  itemsize.**\n",
        "\n",
        "ndarray.data\n",
        "the buffer containing the actual elements of the array. Normally, we won’t need to use this attribute because we\n",
        "will access the elements in an array using indexing facilities.\n"
      ],
      "metadata": {
        "id": "DMQHKx5ig_TD"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**An example**\n"
      ],
      "metadata": {
        "id": "zGCRH2O7g_gr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "arr = np.arange(15).reshape(3, 5)\n",
        "# Arange function will create 15 points from 0 to 14 and then reshape will reshape it accordingly\n"
      ],
      "metadata": {
        "id": "G1kxfmaijN7a"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "arr"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RSbQiIVRgAxQ",
        "outputId": "363dfed4-e85b-4e60-9470-35bdd6526245"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3,  4],\n",
              "       [ 5,  6,  7,  8,  9],\n",
              "       [10, 11, 12, 13, 14]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(arr.shape)"
      ],
      "metadata": {
        "id": "F3ClKsPphVYX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a7b3fcc8-4e8f-45e9-b670-d37d325c82e2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "(3, 5)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(arr.ndim)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YJEwJExEj6G5",
        "outputId": "746c0d45-c21c-48d6-8ba2-5237203f7092"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(arr.dtype.name)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TvyxWmNjj_Oo",
        "outputId": "90e96b79-bbcf-4c95-9010-14545b733944"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "int64\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(arr.size)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3Vi0y_23kGWY",
        "outputId": "327a1393-bc91-4308-fba2-5bb896f03426"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "15\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(type(arr))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VNAPiinlkJoI",
        "outputId": "58934a42-629c-4882-b193-5daaf3cfa5a5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'numpy.ndarray'>\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###  **4.2-Indexing and Slicing**"
      ],
      "metadata": {
        "id": "K27e_ucuVEBr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "NumPy supports powerful indexing and slicing operations for extracting specific elements or subarrays from an array: Array indexing Refers to accessing individual elements within a NumPy array,.Array Slicing: This allows you to extract specific portions of an array, creating new arrays with the selected elements."
      ],
      "metadata": {
        "id": "WlzfbbBvEflz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Accessing a specific element\n",
        "specific_element = arr[1, 2]"
      ],
      "metadata": {
        "id": "yaxh1EWCkcKh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating a NumPy array\n",
        "arr = np.array([10, 20, 30, 40, 50])\n",
        "# Accessing individual elements\n",
        "first_element = arr[0] # Access the first element (10)\n",
        "# Accessing elements using negative indices\n",
        "last_element = arr[-1] # Access the last element (50)\n",
        "# Creating a 2D NumPy array\n",
        "arr_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
        "# Slicing along rows and columns\n",
        "sliced_array = arr_2d[0,1] # Element at row 0, column 1 (value: 2)"
      ],
      "metadata": {
        "id": "3IR-q0XiVaE8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Slicing the array to create a new array\n",
        "sliced_array = arr[1:4] # Slice from index 1 to 3 (exclusive) [20,30,40]\n",
        "# Slicing with a step of 2\n",
        "sliced_array = arr[0::2] # Start at index 0, step by 2 [10,30,50]\n",
        "# Slicing with negative index\n",
        "second_to_last = arr[-2::] # Access the last two elements [40,50]\n",
        "# Conditional slicing: Select elements greater than 30\n",
        "sliced_array = arr[arr > 30] # Result: [40, 50]\n",
        "# Creating a 2D NumPy array\n",
        "arr_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
        "# Slicing along rows and columns\n",
        "sliced_array = arr_2d[1:3, 0:2] # Slice a 2x2 subarray: [[4, 5], [7, 8]]"
      ],
      "metadata": {
        "id": "HqaK4SKIVe_M"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **4.3-Aggregation Functions**"
      ],
      "metadata": {
        "id": "4vVz0czgVzNq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "NumPy provides functions for aggregating data, such as calculating the sum, mean, minimum, and maximum:"
      ],
      "metadata": {
        "id": "Xqo8ohyjE1XK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculating the sum of an array\n",
        "sum_of_array = np.sum(arr_2d)\n",
        "# Calculating the mean of an array\n",
        "mean_of_array = np.mean(arr_1d)\n",
        "# Finding the minimum and maximum values in an array\n",
        "min_value = np.min(arr_2d)\n",
        "max_value = np.max(arr_1d)"
      ],
      "metadata": {
        "id": "tWlgroQ8V7iV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**1- Sum Calculation**"
      ],
      "metadata": {
        "id": "q4O6aWQbXDry"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating a 2D array\n",
        "matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
        "print(matrix)\n",
        "# Sum of all elements\n",
        "total_sum = np.sum(matrix)\n",
        "print(\"Total Sum:\", total_sum)\n",
        "# Sum along each column (axis=0)\n",
        "column_sums = np.sum(matrix, axis=0)\n",
        "print(\"Column Sums:\", column_sums)\n",
        "# Sum along each row (axis=1)\n",
        "row_sums = np.sum(matrix, axis=1)\n",
        "print(\"Row Sums:\", row_sums)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DYATECK1WId0",
        "outputId": "b3cd7d15-4834-4f09-cbcf-7abc2b26cd99"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]\n",
            " [7 8 9]]\n",
            "Total Sum: 45\n",
            "Column Sums: [12 15 18]\n",
            "Row Sums: [ 6 15 24]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**2- Mean and Average:**"
      ],
      "metadata": {
        "id": "V1vEea--XLix"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Mean of all elements\n",
        "mean_value = np.mean(matrix)\n",
        "print(\"Mean:\", mean_value)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CNPwZWuxXPKx",
        "outputId": "07ff92cc-298b-49a0-e013-5c8ae72db53d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean: 5.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Mean along each column\n",
        "column_means = np.mean(matrix, axis=0)\n",
        "print(\"Column Means:\", column_means)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7n4V9cEAXTOh",
        "outputId": "1ef7222d-1fc8-480e-8f07-88b0401b0ab9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Column Means: [4. 5. 6.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Mean along each row\n",
        "row_means = np.mean(matrix, axis=1)\n",
        "print(\"Row Means:\", row_means)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z110nS5bXWz5",
        "outputId": "fce7be89-4821-494f-e522-45b623a7584d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Row Means: [2. 5. 8.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**3- Maximum and Minimum:**"
      ],
      "metadata": {
        "id": "670x61eubA9_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Maximum element\n",
        "max_value = np.max(matrix)\n",
        "print(\"Maximum Value:\", max_value)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e6bzdesxbFY3",
        "outputId": "f1864fdd-9898-4a9e-9800-d449d3f19cf1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Maximum Value: 9\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Maximum along each column\n",
        "column_max = np.max(matrix, axis=0)\n",
        "print(\"Column Max Values:\", column_max)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BKQsohz2bJQt",
        "outputId": "da23193c-a274-4ca1-c181-8083ed4a84e2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Column Max Values: [7 8 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Maximum along each row\n",
        "row_max = np.max(matrix, axis=1)\n",
        "print(\"Row Max Values:\", row_max)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cFzkJBxHbNnU",
        "outputId": "b928cfc7-962d-43cf-cb8b-910175392882"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Row Max Values: [3 6 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Minimum element\n",
        "min_value = np.min(matrix)\n",
        "print(\"Minimum Value:\", min_value)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XCp08VdGbR48",
        "outputId": "f94e797c-7837-4174-860b-11068e2fa3af"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Minimum Value: 1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We aggregate all the values in a matrix, but we can also aggregate across the rows or columns by using the axis parameter."
      ],
      "metadata": {
        "id": "lBGp3vYOFW71"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **4.4- Reshaping and Transposing**"
      ],
      "metadata": {
        "id": "eHqXOpTrbbAj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating Arrays\n",
        "array_1 = np.arange(-9,9, 2)\n",
        "array_2 = np.arange(-9,9, 2).reshape((3,3))\n",
        "\n",
        "data = np.array([10, 20, 30, 40, 50])"
      ],
      "metadata": {
        "id": "Z6B6igqLsrV7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**1- Reshaping 1D Array to 2D Array:**"
      ],
      "metadata": {
        "id": "JFl2XYskEGjs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Creating a 1D array\n",
        "original_array = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
        "\n",
        "# Reshaping the 1D array to a 2D array with 3 rows and 3 columns\n",
        "reshaped_array = original_array.reshape(3, 3)\n",
        "\n",
        "# Printing the original and reshaped arrays\n",
        "print(\"Original 1D array:\")\n",
        "print(original_array)\n",
        "print(\"\\nReshaped 2D array:\")\n",
        "print(reshaped_array)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XeARIW_wbxCS",
        "outputId": "efe8128c-fbf0-4297-e538-a7a2328f80d6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original 1D array:\n",
            "[1 2 3 4 5 6 7 8 9]\n",
            "\n",
            "Reshaped 2D array:\n",
            "[[1 2 3]\n",
            " [4 5 6]\n",
            " [7 8 9]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**2- Reshaping 1D Array to 3D Array:**"
      ],
      "metadata": {
        "id": "KSPyjfXkFX-b"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Creating a 1D array\n",
        "original_array = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])\n",
        "\n",
        "# Reshaping the 1D array to a 3D array with 2 blocks, 2 rows, and 3 columns\n",
        "reshaped_array = original_array.reshape(2, 2, 3)\n",
        "\n",
        "# Printing the original and reshaped arrays\n",
        "print(\"Original 1D array:\")\n",
        "print(original_array)\n",
        "print(\"\\nReshaped 3D array:\")\n",
        "print(reshaped_array)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NXPxSsNtFUKs",
        "outputId": "029ab8fa-f992-4ea5-e3ca-b0f3a866061a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original 1D array:\n",
            "[ 1  2  3  4  5  6  7  8  9 10 11 12]\n",
            "\n",
            "Reshaped 3D array:\n",
            "[[[ 1  2  3]\n",
            "  [ 4  5  6]]\n",
            "\n",
            " [[ 7  8  9]\n",
            "  [10 11 12]]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**3- Reshaping with -1:**"
      ],
      "metadata": {
        "id": "V3p3gbQpHBQJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Creating a 1D array with 12 elements\n",
        "original_array = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12])\n",
        "\n",
        "# Reshaping the 1D array to a 2D array with 4 rows and an automatically calculated number of columns\n",
        "reshaped_array = original_array.reshape(-1, 4)\n",
        "\n",
        "# Printing the original and reshaped arrays\n",
        "print(\"Original 1D array:\")\n",
        "print(original_array)\n",
        "print(\"\\nReshaped 2D array with -1:\")\n",
        "print(reshaped_array)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oT5aUS8mG0Fi",
        "outputId": "683d38d3-675d-463f-c6a7-a4ae7a2ca12a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original 1D array:\n",
            "[ 1  2  3  4  5  6  7  8  9 10 11 12]\n",
            "\n",
            "Reshaped 2D array with -1:\n",
            "[[ 1  2  3  4]\n",
            " [ 5  6  7  8]\n",
            " [ 9 10 11 12]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**4- Flattening a 2D or 3D Array:**"
      ],
      "metadata": {
        "id": "brLiT8h4bkHO"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Flattening is the process of converting a multi-dimensional array into a 1D array. The flatten method achieves this:"
      ],
      "metadata": {
        "id": "aPvTxeXFGAFw"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Creating a 2D array\n",
        "original_2d_array = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
        "\n",
        "# Flattening the 2D array using flatten()\n",
        "flattened_array = original_2d_array.flatten()\n",
        "\n",
        "# Printing the original and flattened arrays\n",
        "print(\"Original 2D array:\")\n",
        "print(original_2d_array)\n",
        "print(\"\\nFlattened 1D array:\")\n",
        "print(flattened_array)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0x-0DRk6bzX9",
        "outputId": "b031f7a3-3648-4b84-ac3f-1dd8a5b48a6c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original 2D array:\n",
            "[[1 2 3]\n",
            " [4 5 6]\n",
            " [7 8 9]]\n",
            "\n",
            "Flattened 1D array:\n",
            "[1 2 3 4 5 6 7 8 9]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Creating a 3D array\n",
        "original_3d_array = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]], [[9, 10], [11, 12]]])\n",
        "\n",
        "# Flattening the 3D array using flatten()\n",
        "flattened_array_3d = original_3d_array.flatten()\n",
        "\n",
        "# Printing the original and flattened arrays\n",
        "print(\"Original 3D array:\")\n",
        "print(original_3d_array)\n",
        "print(\"\\nFlattened 1D array:\")\n",
        "print(flattened_array_3d)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Fuw9L2XXcRzd",
        "outputId": "1e511016-78b5-4c72-8faa-06965b565d6d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original 3D array:\n",
            "[[[ 1  2]\n",
            "  [ 3  4]]\n",
            "\n",
            " [[ 5  6]\n",
            "  [ 7  8]]\n",
            "\n",
            " [[ 9 10]\n",
            "  [11 12]]]\n",
            "\n",
            "Flattened 1D array:\n",
            "[ 1  2  3  4  5  6  7  8  9 10 11 12]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**5- Transpose operations**"
      ],
      "metadata": {
        "id": "WsPlfZqIdKZb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "matrix3x2 = np.array([[1, 2], [3, 4], [5, 6]]) # Define a 3x2 matrix\n",
        "print('Original matrix 3 x 2')\n",
        "print(matrix3x2)\n",
        "print('Transposed matrix 2 x 3')\n",
        "print(matrix3x2.T)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kw34XEbCdSj6",
        "outputId": "0d99a4f0-7f33-4c8d-c391-27dc197391ed"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original matrix 3 x 2\n",
            "[[1 2]\n",
            " [3 4]\n",
            " [5 6]]\n",
            "Transposed matrix 2 x 3\n",
            "[[1 3 5]\n",
            " [2 4 6]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **4.5- Append and Delete**"
      ],
      "metadata": {
        "id": "Fp176_MAfv0z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create an array\n",
        "original_array = np.array([1, 2, 3])\n",
        "# Append elements in-place\n",
        "original_array = np.append(original_array, [4, 5, 6])\n",
        "# Create a NumPy array\n",
        "arr = np.array([1, 2, 3, 4, 5])\n",
        "# Remove the item at index 2 (value 3)\n",
        "new_arr = np.delete(arr, 2)\n",
        "# Create a 2D NumPy array\n",
        "arr = np.array([[1, 2, 3], [4,5, 6], [7, 8, 9]])\n",
        "# Remove the second row (index 1)\n",
        "new_arr = np.delete(arr, 1, axis=0)"
      ],
      "metadata": {
        "id": "wWJma5Chf6qF"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "nparray = np.array([[1, 2, 3, 4]]) # Define a 1 x 4 matrix. Note the 2 level of square brackets\n",
        "print('Original array')\n",
        "print(nparray)\n",
        "print('Transposed array')\n",
        "print(nparray.T)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W1E1FHHUdYXc",
        "outputId": "638a28fe-caaa-4085-c15a-e6e197ff38b1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original array\n",
            "[[1 2 3 4]]\n",
            "Transposed array\n",
            "[[1]\n",
            " [2]\n",
            " [3]\n",
            " [4]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# sum over\n",
        "sum_1, sum_2, sum_3 = np.sum(array_1), np.sum(array_2, axis=0), np.sum(array_2, axis=1)\n",
        "# take product\n",
        "prod_1, prod_2, prod_3 = np.prod(array_1), np.prod(array_2, axis=0), np.prod(array_2, axis=1)\n",
        "# cumulative sum\n",
        "cumsum_1, cumsum_2, cumsum_3 = np.cumsum(array_1), np.cumsum(array_2, axis=0), np.cumsum(array_2, axis=1)\n",
        "# clip values\n",
        "clip_1, clip_2 = np.clip(array_1, 2, 8), np.clip(array_2, 2, 8)\n",
        "# take absolute value\n",
        "absolute_1, absolute_2 = np.absolute(array_1), np.absolute(array_2)\n",
        "# take square root\n",
        "sqrt_1, sqrt_2 = np.sqrt(np.absolute(array_1)), np.sqrt(np.absolute(array_2))\n",
        "# take the square power\n",
        "square_1, square_2 =  np.square(array_1), np.square(array_2)\n",
        "# sign function\n",
        "sign_1, sign_2 = np.sign(array_1), np.sign(array_2)\n",
        "# n power\n",
        "power = np.power(np.absolute(array_1), np.absolute(array_1))"
      ],
      "metadata": {
        "id": "DVpjwLBTbpdS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#converting list to ndarray\n",
        "import numpy as np\n",
        "x = [1,2,3]\n",
        "a = np.asarray(x)\n",
        "print (a)\n",
        "\n",
        "\n",
        "# ndarray from tuple\n",
        "x_1 = (1,2,3)\n",
        "a_1 = np.asarray(x_1)\n",
        "print (a_1)\n",
        "\n",
        "# ndarray from list of tuples\n",
        "import numpy as np\n",
        "x_2 = [(1,2,3),(4,5,6)]\n",
        "a_2 = np.asarray(x_2)\n",
        "print (a_2)\n",
        "\n",
        "#  .Important Arrays attributes\n",
        "# arr.shape :It returns a tuple listing the length of the array along each dimension.\n",
        "import numpy as np\n",
        "arr = np.array([[1,2,3],[4,5,6]])\n",
        "print (arr.shape)\n",
        "\n",
        "\n",
        "#resizing the above array\n",
        "a = np.array([[1,2,3],[4,5,6]])\n",
        "a.shape = (3,2)\n",
        "print (a)\n",
        "\n",
        "\n",
        "a = np.array([[1,2,3],[4,5,6]])\n",
        "b = a.reshape(3,2)\n",
        "print (b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mxdJ-uNE4M80",
        "outputId": "66eba020-bd32-4172-fb98-79e5f4e4e03a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 2 3]\n",
            "[1 2 3]\n",
            "[[1 2 3]\n",
            " [4 5 6]]\n",
            "(2, 3)\n",
            "[[1 2]\n",
            " [3 4]\n",
            " [5 6]]\n",
            "[[1 2]\n",
            " [3 4]\n",
            " [5 6]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **📚Section 5-Statistical Analysis<a name='statistical_analysis'></a>**"
      ],
      "metadata": {
        "id": "5FOpljH3dSOH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **5.1-Descriptive Statistics**"
      ],
      "metadata": {
        "id": "KaX_Xx6Tdhdu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Although NumPy is not a library for statistical analysis, it does provide several descriptive statistics functions. In NumPy documentation these are presented as “order”, “average and variances”, “correlating” and “histograms”, but all of those are just descriptive statistics."
      ],
      "metadata": {
        "id": "94UvDR57SYok"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "# Creating a NumPy array\n",
        "data = np.array([1, 2, 3, 4, 5])\n",
        "# Calculate mean and median\n",
        "mean_value = np.mean(data)\n",
        "median_value = np.median(data)\n",
        "# Calculate variance and standard deviation\n",
        "variance_value = np.var(data)\n",
        "std_deviation_value = np.std(data)"
      ],
      "metadata": {
        "id": "k0gmRhrEdvJo"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **5.2- Working with Distributions**"
      ],
      "metadata": {
        "id": "JY6lRf-1d34v"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "NumPy supports various probability distributions, making it easier to model and simulate data."
      ],
      "metadata": {
        "id": "LyncJvJmShS7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "# Generating random samples from a normal distribution\n",
        "random_samples = np.random.normal(loc=0, scale=1, size=1000)"
      ],
      "metadata": {
        "id": "qdeN8LNYenie"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **5-3-Hypothesis Testing**"
      ],
      "metadata": {
        "id": "VK0Fukmje9FF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# One-sample t-test\n",
        "from scipy.stats import ttest_1samp\n",
        "t_statistic, p_value = ttest_1samp(data, popmean=3)"
      ],
      "metadata": {
        "id": "HlPRsFKtfIhm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "p_value"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tOu7qyuKfMCG",
        "outputId": "cc2c0419-9f2f-4811-efa1-eaf4c1896591"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **5.4-Correlation and Regression**"
      ],
      "metadata": {
        "id": "vRfJRGg-iA7S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data1 = np.array([3, 1, 5, 2, 4])\n",
        "data2 = np.array([3, 1, 6, 7, 4])\n",
        "\n",
        "# Calculate correlation coefficient\n",
        "correlation_coefficient = np.corrcoef(data1, data2)[0, 1]\n",
        "# Linear regression\n",
        "slope, intercept = np.polyfit(data1, data2, 1)"
      ],
      "metadata": {
        "id": "cR0SIeN6iKRr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "intercept"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2Rjm5bcJi2va",
        "outputId": "b0d0ae82-7ba1-4190-cb4f-8a5b95c32fb6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.100000000000001"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **5.5-Data Transformation**"
      ],
      "metadata": {
        "id": "PDOD9GibjHzr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Data Centering\n",
        "data = np.array([10, 20, 30, 40, 50])\n",
        "mean = np.mean(data)\n",
        "centered_data = data - mean"
      ],
      "metadata": {
        "id": "zze2HHs6jTS3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Standardization\n",
        "std_dev = np.std(data)\n",
        "standardized_data = (data - mean) / std_dev"
      ],
      "metadata": {
        "id": "p5ALLsWNjZSP"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Log Transformation\n",
        "log_transformed_data = np.log(data)"
      ],
      "metadata": {
        "id": "ySeIGaYZjdu8"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **5.6-Random Sampling**"
      ],
      "metadata": {
        "id": "ftggyIB9mFYo"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Random sampling involves selecting a subset of data points from a larger dataset. NumPy also provides tools for generating random numbers from various probability distributions."
      ],
      "metadata": {
        "id": "fhIGDaRhSqxV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Simple Random Sampling Without replacement\n",
        "data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])\n",
        "random_samples = np.random.choice(data, size=5, replace=False)"
      ],
      "metadata": {
        "id": "-_c0HTtimPMq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Bootstrap Sampling\n",
        "num_samples = 1000\n",
        "bootstrap_samples = np.random.choice(data, size=(num_samples, len(data)), replace=True)"
      ],
      "metadata": {
        "id": "s_Ex7uiqmT4g"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **5.7-Measures of central tendency**"
      ],
      "metadata": {
        "id": "-IR2MMDjpviq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import random as rg"
      ],
      "metadata": {
        "id": "8fJw7ZkvVwhK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install scipy"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Mekmi3ivV5GF",
        "outputId": "364a985f-f33c-4cb0-d427-768ce24f26da"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (1.11.4)\n",
            "Requirement already satisfied: numpy<1.28.0,>=1.21.6 in /usr/local/lib/python3.10/dist-packages (from scipy) (1.25.2)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import scipy.stats as sp"
      ],
      "metadata": {
        "id": "DDVBdZGIV-Ci"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "poisson1 = sp.poisson(5).rvs(1000)\n",
        "poisson2 = sp.poisson(50).rvs(1000)"
      ],
      "metadata": {
        "id": "xtaWe9vhWD8b"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "fig, (ax1, ax2) = plt.subplots(1, 2, constrained_layout=True)\n",
        "fig.suptitle('Sampling from poisson distribution')\n",
        "ax1.hist(poisson1, bins=10)\n",
        "ax1.set_title(\"Expectation of interval: 5\")\n",
        "ax2.hist(poisson2, bins=10)\n",
        "ax2.set_title(\"Expectation of interval: 50\");"
      ],
      "metadata": {
        "id": "_ffGzzbiqBwb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 508
        },
        "outputId": "aaeecdfe-9d84-4674-a946-70e7011c6657"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "# Sample data\n",
        "data = np.array([10, 20, 30, 40, 50, 20, 30, 40, 60])\n",
        "# Mean\n",
        "mean = np.mean(data)\n",
        "print(\"Mean:\", mean)\n",
        "# Median\n",
        "median = np.median(data)\n",
        "print(\"Median:\", median)\n",
        "# Mode\n",
        "mode = np.argmax(np.bincount(data))\n",
        "print(\"Mode:\", mode)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DKfq-wjSZWoz",
        "outputId": "ae0ec52c-2dc7-43da-9a4e-f82bfa1e7f10"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean: 33.333333333333336\n",
            "Median: 30.0\n",
            "Mode: 20\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **5.8-Measures of dispersion**"
      ],
      "metadata": {
        "id": "Yyu6Oe7QaSuZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Measures of dispersion are indicators of the extent to which data distributions are stretched or squeezed."
      ],
      "metadata": {
        "id": "ihyV_tBaTCH_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "rand_matrix = np.random.rand(5,5)\n",
        "print(f\"Pearson product-moment correlation coefficient:\\n{np.corrcoef(poisson1,poisson2)}\\n\")\n",
        "print(f\"Cross-correlation coefficient:\\n{np.correlate(poisson1,poisson2)}\\n\")\n",
        "print(f\"Covariance matrix coefficients:\\n{np.cov(poisson1,poisson2)}\\n\")\n",
        "print(f\"Pearson product-moment correlation coefficient:\\n{np.corrcoef(rand_matrix)}\\n\")\n",
        "print(f\"Covariance matrix coefficients:\\n{np.cov(rand_matrix)}\")"
      ],
      "metadata": {
        "id": "1tB7ju9Gvgtw",
        "outputId": "073421fa-93e8-4e1b-8669-0634722facbb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Pearson product-moment correlation coefficient:\n",
            "[[1.         0.02471646]\n",
            " [0.02471646 1.        ]]\n",
            "\n",
            "Cross-correlation coefficient:\n",
            "[196340]\n",
            "\n",
            "Covariance matrix coefficients:\n",
            "[[ 4.02855255  0.35443443]\n",
            " [ 0.35443443 51.04464464]]\n",
            "\n",
            "Pearson product-moment correlation coefficient:\n",
            "[[ 1.          0.504974   -0.54775987 -0.77002384  0.65395575]\n",
            " [ 0.504974    1.         -0.06140124  0.04098833  0.49868676]\n",
            " [-0.54775987 -0.06140124  1.          0.82810519 -0.61496475]\n",
            " [-0.77002384  0.04098833  0.82810519  1.         -0.65675892]\n",
            " [ 0.65395575  0.49868676 -0.61496475 -0.65675892  1.        ]]\n",
            "\n",
            "Covariance matrix coefficients:\n",
            "[[ 0.01566542  0.02304319 -0.01449566 -0.02600132  0.02909508]\n",
            " [ 0.02304319  0.13292455 -0.00473322  0.00403165  0.06462947]\n",
            " [-0.01449566 -0.00473322  0.04470474  0.04723702 -0.0462197 ]\n",
            " [-0.02600132  0.00403165  0.04723702  0.07278476 -0.06298344]\n",
            " [ 0.02909508  0.06462947 -0.0462197  -0.06298344  0.12635729]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **📚Section 6 -Linear Algebra<a name='linear_algebra'></a>**"
      ],
      "metadata": {
        "id": "9ac_XaU4Ubv_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##**6.1-Basic Linear Algebra Operations with NumPy**"
      ],
      "metadata": {
        "id": "jtvjoelXVINB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating Arrays and Matrices:\n",
        "import numpy as np\n",
        "# Create a 1D array\n",
        "array_1d = np.array([1, 2, 3, 4, 5])\n",
        "# Create a 2D array (matrix)\n",
        "matrix_2d = np.array([[1, 2], [3, 4]])"
      ],
      "metadata": {
        "id": "H2gx6f3rVdf0"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Matrix Multiplication:\n",
        "result = np.dot(matrix_2d, array_1d)\n",
        "\n",
        "narray = np.array([1, 2, 3, 4]) # Define a numpy array\n",
        "print(narray * 3)\n",
        "print(alist * 3)"
      ],
      "metadata": {
        "id": "A4CZm4STVh-A"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Matrix Inversion:\n",
        "inverse_matrix = np.linalg.inv(matrix_2d)"
      ],
      "metadata": {
        "id": "MV0At4huVuOQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Eigenvalue decomposition\n",
        "eigenvalues, eigenvectors = np.linalg.eig(matrix_2d)"
      ],
      "metadata": {
        "id": "nllQV8b2V2tL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Singular value decomposition (SVD)\n",
        "u, s, vh = np.linalg.svd(matrix_2d)"
      ],
      "metadata": {
        "id": "i09xl-xUV5Pq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Transpose a Matrix\n",
        "matrix3x2 = np.array([[1, 2], [3, 4], [5, 6]]) # Define a 3x2 matrix\n",
        "print('Original matrix 3 x 2')\n",
        "print(matrix3x2)\n",
        "print('Transposed matrix 2 x 3')\n",
        "print(matrix3x2.T)"
      ],
      "metadata": {
        "id": "OxSUYFlHV8h1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# note that the transpose operation does not affect 1D arrays.\n",
        "nparray = np.array([1, 2, 3, 4]) # Define an array\n",
        "print('Original array')\n",
        "print(nparray)\n",
        "print('Transposed array')\n",
        "print(nparray.T)"
      ],
      "metadata": {
        "id": "2hp-WgWMWHD3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "nparray = np.array([[1, 2, 3, 4]]) # Define a 1 x 4 matrix. Note the 2 level of square brackets\n",
        "print('Original array')\n",
        "print(nparray)\n",
        "print('Transposed array')\n",
        "print(nparray.T)"
      ],
      "metadata": {
        "id": "O6VUPQrgWKdh"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# dot product\n",
        "nparray1 = np.array([0, 1, 2, 3]) # Define an array\n",
        "nparray2 = np.array([4, 5, 6, 7]) # Define an array\n",
        "flavor1 = np.dot(nparray1, nparray2) # Recommended way\n",
        "print(flavor1)\n",
        "flavor2 = np.sum(nparray1 * nparray2) # Ok way\n",
        "print(flavor2)\n",
        "flavor3 = nparray1 @ nparray2         # Geeks way\n",
        "print(flavor3)\n",
        "# As you never should do:             # Noobs way\n",
        "flavor4 = 0\n",
        "for a, b in zip(nparray1, nparray2):\n",
        "    flavor4 += a * b\n",
        "print(flavor4)\n",
        "\n",
        "norm1 = np.dot(np.array([1, 2]), np.array([3, 4])) # Dot product on nparrays\n",
        "norm2 = np.dot([1, 2], [3, 4]) # Dot product on python lists\n",
        "print(norm1, '=', norm2 )"
      ],
      "metadata": {
        "id": "I1GVbBPxWN4_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Sums by rows and columns\n",
        "nparray2 = np.array([[1, -1], [2, -2], [3, -3]]) # Define a 3 x 2 matrix.\n",
        "sumByCols = np.sum(nparray2, axis=0) # Get the sum for each column. Returns 2 elements\n",
        "sumByRows = np.sum(nparray2, axis=1) # get the sum for each row. Returns 3 elements\n",
        "print('Matrix mean: ')\n",
        "print(mean)\n",
        "print('Mean by columns: ')\n",
        "print(meanByCols)\n",
        "print('Mean by rows:')\n",
        "print(meanByRows)"
      ],
      "metadata": {
        "id": "vAnTXcBWWT0r"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##**6.2-Advanced Linear Algebra Techniques with NumPy**"
      ],
      "metadata": {
        "id": "uNk6Hc9VWZGa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Solving Linear Systems:**"
      ],
      "metadata": {
        "id": "zFoFF138XGVn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Solve linear equations\n",
        "coefficients = np.array([[2, 3], [1, -1]])\n",
        "constants = np.array([8, 1])\n",
        "solution = np.linalg.solve(coefficients, constants)"
      ],
      "metadata": {
        "id": "Td7XmEDlXUim"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Least Squares Fitting**"
      ],
      "metadata": {
        "id": "0Uy1vKIjXX-m"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Fit a line to data using least squares\n",
        "x = np.array([0, 1, 2, 3])\n",
        "y = np.array([0, 0.9, 2.1, 2.8])\n",
        "coefficients = np.polyfit(x, y, deg=1)"
      ],
      "metadata": {
        "id": "FddjOrQ_Xd6e"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Princial Component Analysis (PCA)**"
      ],
      "metadata": {
        "id": "EF7mojZhXsOu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Perform PCA\n",
        "data = np.random.rand(100, 3) # Sample data\n",
        "mean = np.mean(data, axis=0)\n",
        "centered_data = data - mean\n",
        "covariance_matrix = np.cov(centered_data, rowvar=False)\n",
        "eigenvalues, eigenvectors = np.linalg.eig(covariance_matrix)"
      ],
      "metadata": {
        "id": "4ef5CfMiX1x-"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **📚Section 7 -Data Cleaning<a name='data_cleaning'></a>**"
      ],
      "metadata": {
        "id": "Ph4nunOxYNLN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **7.1-Identifying Missing Values**"
      ],
      "metadata": {
        "id": "pOWkZiDAYctQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a NumPy array with missing values\n",
        "data = np.array([1, 2, np.nan, 4, np.nan, 6])\n",
        "# Check for missing values\n",
        "has_missing = np.isnan(data)\n",
        "print(has_missing)"
      ],
      "metadata": {
        "id": "Erq0fabkYsn7",
        "outputId": "d7be023e-3def-49a7-da61-2419a7132d02",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[False False  True False  True False]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **7.2-Removing Rows or Columns with Missing Values**"
      ],
      "metadata": {
        "id": "QtXF8_DVYyXK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a 2D array with missing values\n",
        "data = np.array([[1, 2, 3], [4, np.nan, 6], [7, 8, 9]])\n",
        "# Remove rows with any missing values\n",
        "cleaned_data = data[~np.any(np.isnan(data), axis=1)]\n",
        "print(cleaned_data) # Result: [[1,2,3],[7,8,9]]"
      ],
      "metadata": {
        "id": "KwfwO7WhY6Zj"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **7.3-Removing Outliers**"
      ],
      "metadata": {
        "id": "CB75ZdyxY9Tz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data = np.array([1, 2, 3, 100, 101, 102])\n",
        "threshold = np.percentile(data, 95) # Get 95th percentile\n",
        "cleaned_data = data[data <= threshold] # Remove outliers above threshold"
      ],
      "metadata": {
        "id": "eN7U5f33ZAr6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **7.4-Removing Duplicates**"
      ],
      "metadata": {
        "id": "P_TZjeqmZrhc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "data = np.array([1, 2, 3, 2, 4, 5, 1])\n",
        "unique_values = np.unique(data) # Get unique values"
      ],
      "metadata": {
        "id": "HidXyEwNZxIx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **7-9-Histograms**"
      ],
      "metadata": {
        "id": "N9AxjVUIvxvd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Generate random data\n",
        "np.random.seed(0)  # For reproducibility\n",
        "data = np.random.normal(loc=0, scale=1, size=1000)  # Generate 1000 random numbers from a normal distribution\n",
        "\n",
        "# Create histogram\n",
        "plt.hist(data, bins=30, color='blue', edgecolor='black', alpha=0.7)\n",
        "plt.title('Histogram of Random Data')\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Frequency')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "pzB4jFPrxN-1",
        "outputId": "0ed28372-5f2e-4f3f-ebdb-cb5b76525570",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "chisquare1 = rg.chisquare(5,1000)"
      ],
      "metadata": {
        "id": "ZXmUx7-hwUL0",
        "outputId": "39ac7729-59df-448e-d29f-eec6f18f7656",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 339
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "For each axis slice, the sum of the observed frequencies must agree with the sum of the expected frequencies to a relative tolerance of 1e-08, but the percent differences are:\n199.0",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-25-3b2f424fd326>\u001b[0m in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mchisquare1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchisquare\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/scipy/stats/_stats_py.py\u001b[0m in \u001b[0;36mchisquare\u001b[0;34m(f_obs, f_exp, ddof, axis)\u001b[0m\n\u001b[1;32m   8252\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   8253\u001b[0m     \"\"\"  # noqa\n\u001b[0;32m-> 8254\u001b[0;31m     return power_divergence(f_obs, f_exp=f_exp, ddof=ddof, axis=axis,\n\u001b[0m\u001b[1;32m   8255\u001b[0m                             lambda_=\"pearson\")\n\u001b[1;32m   8256\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/scipy/stats/_stats_py.py\u001b[0m in \u001b[0;36mpower_divergence\u001b[0;34m(f_obs, f_exp, ddof, axis, lambda_)\u001b[0m\n\u001b[1;32m   8049\u001b[0m                    \u001b[0;34mf\"of {rtol}, but the percent differences are:\\n\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   8050\u001b[0m                    f\"{relative_diff}\")\n\u001b[0;32m-> 8051\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   8052\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   8053\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: For each axis slice, the sum of the observed frequencies must agree with the sum of the expected frequencies to a relative tolerance of 1e-08, but the percent differences are:\n199.0"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Universal Functions**"
      ],
      "metadata": {
        "id": "sEiIJgEopSCp"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "NumPy provides familiar mathematical functions such as sin, cos, and exp. In NumPy, these are called “universal functions” (ufunc). Within NumPy, these functions operate elementwise on an array, producing an array as output."
      ],
      "metadata": {
        "id": "L3uchx6EpWff"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "B = np.arange(3)\n",
        "print(B)\n",
        "print(np.exp(B))\n",
        "print(np.sqrt(B))\n",
        "C = np.array([2., -1., 4.])\n",
        "print(np.add(B, C))\n"
      ],
      "metadata": {
        "id": "jnjIg_gjpTOt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Trigonometric functions**"
      ],
      "metadata": {
        "id": "BHniR_53R_FY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "x = np.linspace(-4, 4, 200)\n",
        "\n",
        "# sin function\n",
        "sin = np.sin(x)\n",
        "# cosine function\n",
        "cos = np.cos(x)\n",
        "# tangent function\n",
        "tan = np.tan(x)"
      ],
      "metadata": {
        "id": "HEJ_QyFgSGgx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pylab as plt\n",
        "plt.style.use('dark_background')\n",
        "%config InlineBackend.figure_format = 'retina' # to get high resolution images"
      ],
      "metadata": {
        "id": "H354vn9aSJ4J"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, (ax1, ax2, ax3) = plt.subplots(3, 1)\n",
        "ax1.plot(x, sin)\n",
        "ax1.set_title(\"sin\")\n",
        "ax2.plot(x, cos)\n",
        "ax2.set_title(\"cos\")\n",
        "ax3.plot(x, tan)\n",
        "ax3.set_title(\"tan\")\n",
        "plt.tight_layout()"
      ],
      "metadata": {
        "id": "xCPEWcr4SM8h"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Hyperbolic functions**"
      ],
      "metadata": {
        "id": "HdVbj7D8Sang"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y = np.linspace(-4, 4, 200)\n",
        "\n",
        "# sin function\n",
        "sinh = np.sinh(y)\n",
        "# cosine function\n",
        "cosh = np.cosh(y)\n",
        "# tangent function\n",
        "tanh = np.tanh(y)"
      ],
      "metadata": {
        "id": "TlyJcTDPSnqw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, (ax1, ax2, ax3) = plt.subplots(3, 1)\n",
        "ax1.plot(y, sin)\n",
        "ax1.set_title(\"sinh\")\n",
        "ax2.plot(y, cos)\n",
        "ax2.set_title(\"cosh\")\n",
        "ax3.plot(y, tan)\n",
        "ax3.set_title(\"tanh\")\n",
        "plt.tight_layout()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "zE56HoV-SrNZ",
        "outputId": "13b595d9-5fe2-4847-842f-0958d4711b86"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 424,
              "height": 279
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Rounding**"
      ],
      "metadata": {
        "id": "bjEqeR_3pn6J"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "decimals = np.linspace(0.11111111, 0.99999999, 10)\n",
        "\n",
        "# rounding\n",
        "around = np.around(decimals, 3)\n",
        "# rounding\n",
        "round_ = np.round(decimals, 3)\n",
        "# rounding to integer\n",
        "rint = np.rint(decimals)\n",
        "# rounding integer towards zero\n",
        "fix = np.fix(decimals)\n",
        "# round to the floor\n",
        "floor = np.floor(decimals)\n",
        "# round to the ceiling\n",
        "ceil = np.ceil(decimals)"
      ],
      "metadata": {
        "id": "uzaTBpVSpuGS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"Array of decimals:\\n{decimals}\\n\")\n",
        "print(f\"'around' round to the given number of decimals:\\n{around}\\n\")\n",
        "print(f\"'round' yields identical results than 'around':\\n{round_}\\n\")\n",
        "print(f\"'rint' round to the nearest integer:\\n{rint}\\n\")\n",
        "print(f\"'fix' round to the nearest integer towars zero:\\n{fix}\\n\")\n",
        "print(f\"'floor' round to the floor of the input:\\n{floor}\\n\")\n",
        "print(f\"'ceil' round to the ceiling of the input:\\n{ceil}\")"
      ],
      "metadata": {
        "id": "-3b6uzyLp1Lx"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Exponents and logarithms**\n"
      ],
      "metadata": {
        "id": "6NY03FWyrwmO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "z = np.array([0.1, 1, np.e, np.pi])\n",
        "\n",
        "# exponent\n",
        "exp = np.exp(z)\n",
        "# exponent(x) -1\n",
        "expm1 = np.expm1(z)\n",
        "# 2^P\n",
        "exp2 = np.exp2(z)\n",
        "# natural log\n",
        "log = np.log(z)\n",
        "# log base 10\n",
        "log10 = np.log10(z)\n",
        "# log base 2\n",
        "log2 = np.log2(z)"
      ],
      "metadata": {
        "id": "RPVbw-KWr2BH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f'Compute exponential element-wise:\\n{exp}\\n')\n",
        "print(f\"Compute 'exp(x) - 1' with greater precision for small values:\\n{expm1}\\n\")\n",
        "print(f\"Compute '2**p' for all elements p in the array:\\n{exp2}\\n\")\n",
        "print(f'Compute natural logarithm element-wise:\\n{log}\\n')\n",
        "print(f'Compute base 10 logarithm element-wise:\\n{log10}\\n')\n",
        "print(f'Compute base 2 logarithm element-wise:\\n{log2}\\n')"
      ],
      "metadata": {
        "id": "xEs7NsDHr7pW"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Indexing, Slicing and Iterating"
      ],
      "metadata": {
        "id": "akjQC01bp-Bw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences"
      ],
      "metadata": {
        "id": "XXCuukCTqIHr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.arange(10)**3 # create 10 elements and multiply 3 times with itself"
      ],
      "metadata": {
        "id": "Rm_hn2BDqBI_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0RlJsuLHqLxR",
        "outputId": "e1d42c75-8298-433d-8e75-607007c3f00d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([  0,   1,   8,  27,  64, 125, 216, 343, 512, 729])"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a[2:5] # this will print the elements from 2 to 5-1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nY_sVc8_qMf3",
        "outputId": "624c78aa-6559-4a2c-992a-1158ae2ef35b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 8, 27, 64])"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a[:6:2] = 1000 # store the value 1000 from 0 to 6 with jumps of 2\n",
        "a\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jTqfEiZrqPYv",
        "outputId": "fb3c7005-a123-43e5-d9ec-f4c5afeae280"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1000,    1, 1000,   27, 1000,  125,  216,  343,  512,  729])"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a[::-1] # Reverse the array a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c1y5GiDAqrzw",
        "outputId": "52597f1b-77a1-4e7a-ae1b-15d13b118023"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 729,  512,  343,  216,  125, 1000,   27, 1000,    1, 1000])"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o8XsZa1trAXx",
        "outputId": "78559797-594b-495a-dc1e-e67182567cb2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1000,    1, 1000,   27, 1000,  125,  216,  343,  512,  729])"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "1P8KW0SHrBqQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Iterating over multidimensional arrays"
      ],
      "metadata": {
        "id": "77PY9AO_sAYq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "arr = np.arange(24).reshape(2,3,4)\n",
        "arr"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KKKycTxhsB33",
        "outputId": "730f75ea-9360-4c30-f3e9-3cb329ff41a4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[[ 0,  1,  2,  3],\n",
              "        [ 4,  5,  6,  7],\n",
              "        [ 8,  9, 10, 11]],\n",
              "\n",
              "       [[12, 13, 14, 15],\n",
              "        [16, 17, 18, 19],\n",
              "        [20, 21, 22, 23]]])"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for row in arr:\n",
        "    print(row)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "t2tang7hsa3J",
        "outputId": "32bf4640-b8a6-49c6-d583-a5771729a82d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 0  1  2  3]\n",
            " [ 4  5  6  7]\n",
            " [ 8  9 10 11]]\n",
            "[[12 13 14 15]\n",
            " [16 17 18 19]\n",
            " [20 21 22 23]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for row in arr:\n",
        "  for ro in row:\n",
        "    print(ro)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Px6nqp6gsgro",
        "outputId": "43e887d4-c004-4565-b42c-8d05fe4b8565"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0 1 2 3]\n",
            "[4 5 6 7]\n",
            "[ 8  9 10 11]\n",
            "[12 13 14 15]\n",
            "[16 17 18 19]\n",
            "[20 21 22 23]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for ele in arr.flat:\n",
        "  print(ele)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-L6vLOapsqvZ",
        "outputId": "df91a3d7-fa09-4643-dc65-4633c3e99f4a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0\n",
            "1\n",
            "2\n",
            "3\n",
            "4\n",
            "5\n",
            "6\n",
            "7\n",
            "8\n",
            "9\n",
            "10\n",
            "11\n",
            "12\n",
            "13\n",
            "14\n",
            "15\n",
            "16\n",
            "17\n",
            "18\n",
            "19\n",
            "20\n",
            "21\n",
            "22\n",
            "23\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Copies and Views"
      ],
      "metadata": {
        "id": "pXtKcyg-67WJ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**No Copy at All**\n",
        "Simple assignments make no copy of objects or their data\n"
      ],
      "metadata": {
        "id": "c2gQBvP67Gf_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = np.array([[ 0, 1, 2, 3],\n",
        "[ 4, 5, 6, 7],[ 8, 9, 10, 11]])"
      ],
      "metadata": {
        "id": "gxH5G_mzxCcu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bpCrdFTv6h7r",
        "outputId": "8102b035-3f7f-4a8a-cb7e-af3ec3542335"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = a # No Copy at all but pointing to the same addsress\n",
        "b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XLrhEASW7SKL",
        "outputId": "818b137d-f951-4182-ec2d-bcf128d29bf3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 75
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b is a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0kkgRIqm7UcE",
        "outputId": "3dab01aa-4230-42ee-f33c-e4aaef940db6"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a is b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fjj-U-zp7cQi",
        "outputId": "416e84f8-2c7b-423b-abec-b3b5d7675262"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "####**View or Shallow Copy**\n"
      ],
      "metadata": {
        "id": "qaV7hOa67rnN"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "c = a.view()"
      ],
      "metadata": {
        "id": "Nr7Dj6yr7dKS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "c"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KIWzInyF7zQS",
        "outputId": "d27d60c4-c5e0-420e-c735-07107f4192d5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "c is a # will be false b/c c is not a but a shallow copy of it"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6iwwiqGf70r6",
        "outputId": "cede99fe-8c8f-40cb-c326-dcad3fa34b3d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {},
          "execution_count": 79
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "c.flags.owndata # will be false b/c c copied data from a"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HjVKF9pl72HS",
        "outputId": "493c0cfb-af8c-41c1-ac99-893928b35395"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "c = c.reshape((2, 6)) # c matrix data will be changed after executing this cell but Matrix a will remain the same"
      ],
      "metadata": {
        "id": "RVv1TfiY8EDy"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "c"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XqxQ609J8NRa",
        "outputId": "198b679b-bd22-4de2-c70b-6f239a13a8b8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3,  4,  5],\n",
              "       [ 6,  7,  8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 83
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a # a will be 3 x 4"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "InRw7TWb8OFK",
        "outputId": "0a7dd677-8b61-4d4f-8349-b4b1db30187d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "####**Deep Copy**"
      ],
      "metadata": {
        "id": "Jv7ePAIg8nzd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The copy method makes a complete copy of the array and its data."
      ],
      "metadata": {
        "id": "75k-vLTd8usc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "d = a.copy() # a new array object with new data is created"
      ],
      "metadata": {
        "id": "iPAJuI5D8q01"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "d"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RgQj7dDa9ITq",
        "outputId": "b2d3696c-3070-4cec-9475-fdd438f3fdf4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11]])"
            ]
          },
          "metadata": {},
          "execution_count": 88
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "d is a # will be false b/c d is stand alone matrix now"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_szLPQx39JU3",
        "outputId": "07eea849-61e8-4cc7-edad-899c4e029a02"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "d is c # will be false b/c c is another matrix of a which is shallow copy"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6yqyYV5D9K8_",
        "outputId": "7cc235a4-5198-4517-b48c-48b47a529705"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "d[1:2] = 100\n",
        "d"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tCR5FGlD9SRA",
        "outputId": "1d61bb9c-bec5-4a33-f22e-47bb112147c1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  0,   1,   2,   3],\n",
              "       [100, 100, 100, 100],\n",
              "       [  8,   9,  10,  11]])"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "1kMUsG-s9hGw"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Functions and Methods Overview"
      ],
      "metadata": {
        "id": "Nyba22my9srh"
      }
    }
  ]
}