Copia_de_01_Intro_to_Pyhon_with_Colab.ipynb

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      "display_name": "Python 3",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/JoseEliasDuranRoa/Bio-bio-Coal-mining-municipality-MAP/blob/main/Copia_de_01_Intro_to_Pyhon_with_Colab.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rYLQROQqpfk5"
      },
      "source": [
        "---\n",
        "# Important: before you start\n",
        "\n",
        "* **To open this file:** when you double-click on the file in Drive, you must choose \"Connect to an external application: Collaboratory\"\n",
        "\n",
        "\n",
        "* **To use your own version of this file:** you must access the menu 'File / Save a copy in Drive...`. Once you have saved the copy in your Drive you can edit and modify it.\n",
        "\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xcGRfKP2VeiX"
      },
      "source": [
        "# 1 Main programming languages for Data analysis\n",
        "\n",
        "* [R](https://cran.r-project.org/): an interpreted programming language for statistical computing and graphics\n",
        "\n",
        "* [python](https://www.python.org/): a general-purpose interpreted, interactive, and high-level programming language.\n",
        "\n",
        "<!--\n",
        "We will mainly focus on python, but R is also highly recommened.\n",
        "-->\n",
        "\n",
        "Several other choices exist, either as \"similary\" equivalent alternatives or as more specifically oriented:  Stata, Matlab/Octave, Julia, etc.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tE_Bzup5n2Ha"
      },
      "source": [
        "\n",
        "## Python and R\n",
        "\n",
        "<!-- https://datasciencetut.com/difference-between-r-and-python/ -->\n",
        "\n",
        " **Feature**                  | **R**                                                 | **Python**                                                                                 \n",
        "--------------------------------|-------------------------------------------------------|--------------------------------------------------------------------------------------------\n",
        " Objective                      | Data analysis and statistics                          | Deployment and production                                                                  \n",
        " Primary Users                  | Scholar and R&D                                       | Programmers and developers                                                                 \n",
        " Flexibility                    | Easy to use available library                         | Simple to build new models from scratch.\n",
        " Learning curve                 | Difficult at the beginning                            | Difficult at the beginning, then linear and smooth                                         \n",
        " Task                           | Easy to get primary results                           | Good to deploy the algorithm                                                               \n",
        " Database size                  | Handle huge size                                      | Handle huge size                                                                           \n",
        " IDE                            | Posit (Rstudio), VS Code, PyCharm                     | Spyder, pyCharm, VS Code, Jupyter Notebook                                                                   \n",
        " Important Packages and library | tidyverse, ggplot2, caret, zoo, tidymodels, datatable | pandas, scipy, scikit-learn, TensorFlow, caret                                             \n",
        " Disadvantages                  | Slow                                                  | Not as many libraries as R                                                                 \n",
        "                                | Dependencies between library                          |                                                                                            \n",
        " Advantages                     | Graphs are made to talk.                              |  Readability. Speed. Function in Python                                                    \n",
        "                                | Large catalog for data analysis                       | Mathematical computation-deployment code.                                                  \n",
        "                                | Quarto/RMarkdown. Shiny                               | Jupyter notebook.                                                                          \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ULsgQcxRn2Hi"
      },
      "source": [
        "# 1.1 Starting with R & Python"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tSDoWsNfn2Hm"
      },
      "source": [
        "## Using R\n",
        "\n",
        "* In your local computer:\n",
        "\n",
        "  * Download and install in your computer [R](https://cran.r-project.org/)\n",
        "\n",
        "  * It is highly recommended to use [Posit](https://posit.co/), previously known as RStudio (or any other good editor)\n",
        "\n",
        "* Alternatively, use [Posit cloud](https://posit.cloud/)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "## Using Python on a local machine\n",
        "\n",
        "### Alternative 1\n",
        "\n",
        "* Download from <https://www.python.org/>\n",
        "\n",
        "* Install a text editor: [Spyder](https://github.com/spyder-ide/), [pyCharm](https://www.jetbrains.com/pycharm/)\n",
        "  \n",
        "  - OR any good text editor (VS Code, emacs, Vim, etc.)\n",
        "  \n",
        "  - Also [Posit](https://posit.co/)\n",
        "\n",
        "* Installing packages and Virtual Environment\n",
        "\n",
        "  - You need to create a virtual environment (see [here](https://docs.python.org/3/library/venv.html) or [here](https://realpython.com/python-virtual-environments-a-primer/), among others)\n",
        "\n",
        "  - To install new package, you can use `pip`\n",
        "\n",
        "      `pip install pip -U`\n",
        "\n",
        "      `pip install jupyter`\n",
        "\n",
        "\n",
        "### Alternative 2: [anaconda](https://www.anaconda.com/)\n",
        "\n",
        "- It is full-feature platform\n",
        "\n",
        "- Automatic install of Python and Spyder\n",
        "\n",
        "- Optionally you can install pyCharm and R\n",
        "\n",
        "- Automatic setting of a virtual enviroment\n",
        "\n",
        "- Easier package management\n",
        "\n",
        "### A comment on notebooks\n",
        "\n",
        " - A Jupyter notebook lets you write and execute Python code locally in your web browser.\n",
        "\n",
        "- It makes very easy to execute code in bits, so they are widely used in scientific computing.\n"
      ],
      "metadata": {
        "id": "XE6xD_ZwfY2W"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y7RrbCr8n2Hy"
      },
      "source": [
        "# 1.2 Cloud Computing wiht Google Colab (online)\n",
        "\n",
        "<!--\n",
        "<center><img src=\"https://miro.medium.com/max/1050/1*Lad06lrjlU9UZgSTHUoyfA.png\" height=\"200\"></center>\n",
        "-->\n",
        "\n",
        "- [Colab](https://colab.research.google.com/) is Google’s flavor of Jupyter notebooks aimed to foster machine learning in eduation and research.\n",
        "\n",
        "- Colab runs entirely in the cloud.\n",
        "\n",
        "- It’s free, requires no setup, comes preinstalled with many packages and is easy to share with the world\n",
        "\n",
        "- Additionaly, we benefit from free access to hardware accelerators like GPUs and TPUs (with some restrictions: eg. Colab will disconnect after 12 hours or ~30 min of idling and unsaved data will be lost.)\n",
        "\n",
        "- More information in [FAQ](https://research.google.com/colaboratory/faq.html)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V5lxo-v91qeE"
      },
      "source": [
        "You can write Jupyter notebooks in a markup language named [Markdown](https://en.wikipedia.org/wiki/Markdown). You know about another markup language, $\\LaTeX$, but Markdown is simpler.\n",
        "\n",
        "You can also can write $\\LaTeX$ in Markdown\n",
        "\n",
        " $y_i=\\beta_0+\\beta_1 x_i + \\varepsilon_i$\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DX0WgI35z5p5"
      },
      "source": [
        "## How to move around a notebook\n",
        "\n",
        "+ You can write text combined with chunks of code in a notebook\n",
        "\n",
        "+ Both types of cells can be easily inserted with the menu bar or moving your mouse at the end of previous cell\n",
        "\n",
        "+ Text cells a markup language known as Markdown. It allows to insert $LaTeX$ fragments\n",
        "\n",
        "+ Cell codes are run in a cloud machine. Colab can run Python code, but also R code."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E3-6zF8On2H2"
      },
      "source": [
        "## How to install additional packages\n",
        "Google Colab has a number of basic packages installed:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y2Mv6TFWWT3u",
        "outputId": "2f97823e-238d-4444-cea5-90ce8f639814",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "!pip list"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Package                          Version\n",
            "-------------------------------- ---------------------\n",
            "absl-py                          1.4.0\n",
            "accelerate                       0.33.0\n",
            "aiohappyeyeballs                 2.4.0\n",
            "aiohttp                          3.10.5\n",
            "aiosignal                        1.3.1\n",
            "alabaster                        0.7.16\n",
            "albucore                         0.0.14\n",
            "albumentations                   1.4.14\n",
            "altair                           4.2.2\n",
            "annotated-types                  0.7.0\n",
            "anyio                            3.7.1\n",
            "argon2-cffi                      23.1.0\n",
            "argon2-cffi-bindings             21.2.0\n",
            "array_record                     0.5.1\n",
            "arviz                            0.18.0\n",
            "asn1crypto                       1.5.1\n",
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            "bigquery-magics                  0.2.0\n",
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            "build                            1.2.1\n",
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            "charset-normalizer               3.3.2\n",
            "chex                             0.1.86\n",
            "clarabel                         0.9.0\n",
            "click                            8.1.7\n",
            "click-plugins                    1.1.1\n",
            "cligj                            0.7.2\n",
            "cloudpathlib                     0.19.0\n",
            "cloudpickle                      2.2.1\n",
            "cmake                            3.30.2\n",
            "cmdstanpy                        1.2.4\n",
            "colorcet                         3.1.0\n",
            "colorlover                       0.3.0\n",
            "colour                           0.1.5\n",
            "community                        1.0.0b1\n",
            "confection                       0.1.5\n",
            "cons                             0.4.6\n",
            "contextlib2                      21.6.0\n",
            "contourpy                        1.3.0\n",
            "cryptography                     43.0.0\n",
            "cuda-python                      12.2.1\n",
            "cudf-cu12                        24.4.1\n",
            "cufflinks                        0.17.3\n",
            "cupy-cuda12x                     12.2.0\n",
            "cvxopt                           1.3.2\n",
            "cvxpy                            1.5.3\n",
            "cycler                           0.12.1\n",
            "cymem                            2.0.8\n",
            "Cython                           3.0.11\n",
            "dask                             2024.7.1\n",
            "datascience                      0.17.6\n",
            "db-dtypes                        1.3.0\n",
            "dbus-python                      1.2.18\n",
            "debugpy                          1.6.6\n",
            "decorator                        4.4.2\n",
            "defusedxml                       0.7.1\n",
            "distributed                      2024.7.1\n",
            "distro                           1.7.0\n",
            "dlib                             19.24.2\n",
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            "docstring_parser                 0.16\n",
            "docutils                         0.18.1\n",
            "dopamine_rl                      4.0.9\n",
            "duckdb                           0.10.3\n",
            "earthengine-api                  0.1.418\n",
            "easydict                         1.13\n",
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            "einops                           0.8.0\n",
            "en-core-web-sm                   3.7.1\n",
            "entrypoints                      0.4\n",
            "et-xmlfile                       1.1.0\n",
            "etils                            1.7.0\n",
            "etuples                          0.3.9\n",
            "eval_type_backport               0.2.0\n",
            "exceptiongroup                   1.2.2\n",
            "fastai                           2.7.17\n",
            "fastcore                         1.7.1\n",
            "fastdownload                     0.0.7\n",
            "fastjsonschema                   2.20.0\n",
            "fastprogress                     1.0.3\n",
            "fastrlock                        0.8.2\n",
            "filelock                         3.15.4\n",
            "fiona                            1.9.6\n",
            "firebase-admin                   6.5.0\n",
            "Flask                            2.2.5\n",
            "flatbuffers                      24.3.25\n",
            "flax                             0.8.4\n",
            "folium                           0.17.0\n",
            "fonttools                        4.53.1\n",
            "frozendict                       2.4.4\n",
            "frozenlist                       1.4.1\n",
            "fsspec                           2024.6.1\n",
            "future                           1.0.0\n",
            "gast                             0.6.0\n",
            "gcsfs                            2024.6.1\n",
            "GDAL                             3.6.4\n",
            "gdown                            5.1.0\n",
            "geemap                           0.34.0\n",
            "gensim                           4.3.3\n",
            "geocoder                         1.38.1\n",
            "geographiclib                    2.0\n",
            "geopandas                        0.14.4\n",
            "geopy                            2.4.1\n",
            "gin-config                       0.5.0\n",
            "glob2                            0.7\n",
            "google                           2.0.3\n",
            "google-ai-generativelanguage     0.6.6\n",
            "google-api-core                  2.19.2\n",
            "google-api-python-client         2.137.0\n",
            "google-auth                      2.27.0\n",
            "google-auth-httplib2             0.2.0\n",
            "google-auth-oauthlib             1.2.1\n",
            "google-cloud-aiplatform          1.64.0\n",
            "google-cloud-bigquery            3.25.0\n",
            "google-cloud-bigquery-connection 1.15.5\n",
            "google-cloud-bigquery-storage    2.25.0\n",
            "google-cloud-bigtable            2.26.0\n",
            "google-cloud-core                2.4.1\n",
            "google-cloud-datastore           2.19.0\n",
            "google-cloud-firestore           2.16.1\n",
            "google-cloud-functions           1.16.5\n",
            "google-cloud-iam                 2.15.2\n",
            "google-cloud-language            2.13.4\n",
            "google-cloud-pubsub              2.23.0\n",
            "google-cloud-resource-manager    1.12.5\n",
            "google-cloud-storage             2.8.0\n",
            "google-cloud-translate           3.15.5\n",
            "google-colab                     1.0.0\n",
            "google-crc32c                    1.5.0\n",
            "google-generativeai              0.7.2\n",
            "google-pasta                     0.2.0\n",
            "google-resumable-media           2.7.2\n",
            "googleapis-common-protos         1.65.0\n",
            "googledrivedownloader            0.4\n",
            "graphviz                         0.20.3\n",
            "greenlet                         3.0.3\n",
            "grpc-google-iam-v1               0.13.1\n",
            "grpcio                           1.64.1\n",
            "grpcio-status                    1.48.2\n",
            "gspread                          6.0.2\n",
            "gspread-dataframe                3.3.1\n",
            "gym                              0.25.2\n",
            "gym-notices                      0.0.8\n",
            "h5netcdf                         1.3.0\n",
            "h5py                             3.11.0\n",
            "holidays                         0.55\n",
            "holoviews                        1.18.3\n",
            "html5lib                         1.1\n",
            "httpimport                       1.3.1\n",
            "httplib2                         0.22.0\n",
            "huggingface-hub                  0.24.6\n",
            "humanize                         4.10.0\n",
            "hyperopt                         0.2.7\n",
            "ibis-framework                   8.0.0\n",
            "idna                             3.8\n",
            "imageio                          2.34.2\n",
            "imageio-ffmpeg                   0.5.1\n",
            "imagesize                        1.4.1\n",
            "imbalanced-learn                 0.12.3\n",
            "imgaug                           0.4.0\n",
            "immutabledict                    4.2.0\n",
            "importlib_metadata               8.4.0\n",
            "importlib_resources              6.4.4\n",
            "imutils                          0.5.4\n",
            "inflect                          7.3.1\n",
            "iniconfig                        2.0.0\n",
            "intel-cmplr-lib-ur               2024.2.1\n",
            "intel-openmp                     2024.2.1\n",
            "ipyevents                        2.0.2\n",
            "ipyfilechooser                   0.6.0\n",
            "ipykernel                        5.5.6\n",
            "ipyleaflet                       0.18.2\n",
            "ipyparallel                      8.8.0\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                     2.2.0\n",
            "jax                              0.4.26\n",
            "jaxlib                           0.4.26+cuda12.cudnn89\n",
            "jeepney                          0.7.1\n",
            "jellyfish                        1.1.0\n",
            "jieba                            0.42.1\n",
            "Jinja2                           3.1.4\n",
            "joblib                           1.4.2\n",
            "jsonpickle                       3.2.2\n",
            "jsonschema                       4.23.0\n",
            "jsonschema-specifications        2023.12.1\n",
            "jupyter-client                   6.1.12\n",
            "jupyter-console                  6.1.0\n",
            "jupyter_core                     5.7.2\n",
            "jupyter-server                   1.24.0\n",
            "jupyterlab_pygments              0.3.0\n",
            "jupyterlab_widgets               3.0.13\n",
            "kaggle                           1.6.17\n",
            "kagglehub                        0.2.9\n",
            "keras                            3.4.1\n",
            "keyring                          23.5.0\n",
            "kiwisolver                       1.4.5\n",
            "langcodes                        3.4.0\n",
            "language_data                    1.2.0\n",
            "launchpadlib                     1.10.16\n",
            "lazr.restfulclient               0.14.4\n",
            "lazr.uri                         1.0.6\n",
            "lazy_loader                      0.4\n",
            "libclang                         18.1.1\n",
            "librosa                          0.10.2.post1\n",
            "lightgbm                         4.4.0\n",
            "linkify-it-py                    2.0.3\n",
            "llvmlite                         0.43.0\n",
            "locket                           1.0.0\n",
            "logical-unification              0.4.6\n",
            "lxml                             4.9.4\n",
            "malloy                           2024.1091\n",
            "marisa-trie                      1.2.0\n",
            "Markdown                         3.7\n",
            "markdown-it-py                   3.0.0\n",
            "MarkupSafe                       2.1.5\n",
            "matplotlib                       3.7.1\n",
            "matplotlib-inline                0.1.7\n",
            "matplotlib-venn                  0.11.10\n",
            "mdit-py-plugins                  0.4.1\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                              2024.2.1\n",
            "ml-dtypes                        0.4.0\n",
            "mlxtend                          0.23.1\n",
            "more-itertools                   10.3.0\n",
            "moviepy                          1.0.3\n",
            "mpmath                           1.3.0\n",
            "msgpack                          1.0.8\n",
            "multidict                        6.0.5\n",
            "multipledispatch                 1.0.0\n",
            "multitasking                     0.0.11\n",
            "murmurhash                       1.0.10\n",
            "music21                          9.1.0\n",
            "namex                            0.0.8\n",
            "natsort                          8.4.0\n",
            "nbclassic                        1.1.0\n",
            "nbclient                         0.10.0\n",
            "nbconvert                        6.5.4\n",
            "nbformat                         5.10.4\n",
            "nest-asyncio                     1.6.0\n",
            "networkx                         3.3\n",
            "nibabel                          5.0.1\n",
            "nltk                             3.8.1\n",
            "notebook                         6.5.5\n",
            "notebook_shim                    0.2.4\n",
            "numba                            0.60.0\n",
            "numexpr                          2.10.1\n",
            "numpy                            1.26.4\n",
            "nvidia-nccl-cu12                 2.22.3\n",
            "nvtx                             0.2.10\n",
            "oauth2client                     4.1.3\n",
            "oauthlib                         3.2.2\n",
            "opencv-contrib-python            4.10.0.84\n",
            "opencv-python                    4.10.0.84\n",
            "opencv-python-headless           4.10.0.84\n",
            "openpyxl                         3.1.5\n",
            "opt-einsum                       3.3.0\n",
            "optax                            0.2.2\n",
            "optree                           0.12.1\n",
            "orbax-checkpoint                 0.6.1\n",
            "osqp                             0.6.7.post0\n",
            "packaging                        24.1\n",
            "pandas                           2.1.4\n",
            "pandas-datareader                0.10.0\n",
            "pandas-gbq                       0.23.1\n",
            "pandas-stubs                     2.1.4.231227\n",
            "pandocfilters                    1.5.1\n",
            "panel                            1.4.5\n",
            "param                            2.1.1\n",
            "parso                            0.8.4\n",
            "parsy                            2.1\n",
            "partd                            1.4.2\n",
            "pathlib                          1.0.1\n",
            "patsy                            0.5.6\n",
            "peewee                           3.17.6\n",
            "pexpect                          4.9.0\n",
            "pickleshare                      0.7.5\n",
            "Pillow                           9.4.0\n",
            "pip                              24.1.2\n",
            "pip-tools                        7.4.1\n",
            "platformdirs                     4.2.2\n",
            "plotly                           5.15.0\n",
            "plotnine                         0.12.4\n",
            "pluggy                           1.5.0\n",
            "polars                           0.20.2\n",
            "pooch                            1.8.2\n",
            "portpicker                       1.5.2\n",
            "prefetch_generator               1.0.3\n",
            "preshed                          3.0.9\n",
            "prettytable                      3.11.0\n",
            "proglog                          0.1.10\n",
            "progressbar2                     4.2.0\n",
            "prometheus_client                0.20.0\n",
            "promise                          2.3\n",
            "prompt_toolkit                   3.0.47\n",
            "prophet                          1.1.5\n",
            "proto-plus                       1.24.0\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                          14.0.2\n",
            "pyarrow-hotfix                   0.6\n",
            "pyasn1                           0.6.0\n",
            "pyasn1_modules                   0.4.0\n",
            "pycocotools                      2.0.8\n",
            "pycparser                        2.22\n",
            "pydantic                         2.8.2\n",
            "pydantic_core                    2.20.1\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                           2.0.1.4\n",
            "pygame                           2.6.0\n",
            "Pygments                         2.16.1\n",
            "PyGObject                        3.42.1\n",
            "PyJWT                            2.9.0\n",
            "pymc                             5.10.4\n",
            "pymystem3                        0.2.0\n",
            "pynvjitlink-cu12                 0.3.0\n",
            "PyOpenGL                         3.1.7\n",
            "pyOpenSSL                        24.2.1\n",
            "pyparsing                        3.1.4\n",
            "pyperclip                        1.9.0\n",
            "pyproj                           3.6.1\n",
            "pyproject_hooks                  1.1.0\n",
            "pyshp                            2.3.1\n",
            "PySocks                          1.7.1\n",
            "pytensor                         2.18.6\n",
            "pytest                           7.4.4\n",
            "python-apt                       2.4.0\n",
            "python-box                       7.2.0\n",
            "python-dateutil                  2.8.2\n",
            "python-louvain                   0.16\n",
            "python-slugify                   8.0.4\n",
            "python-utils                     3.8.2\n",
            "pytz                             2024.1\n",
            "pyviz_comms                      3.0.3\n",
            "PyYAML                           6.0.2\n",
            "pyzmq                            24.0.1\n",
            "qdldl                            0.1.7.post4\n",
            "ratelim                          0.1.6\n",
            "referencing                      0.35.1\n",
            "regex                            2024.5.15\n",
            "requests                         2.32.3\n",
            "requests-oauthlib                1.3.1\n",
            "requirements-parser              0.9.0\n",
            "rich                             13.8.0\n",
            "rmm-cu12                         24.4.0\n",
            "rpds-py                          0.20.0\n",
            "rpy2                             3.4.2\n",
            "rsa                              4.9\n",
            "safetensors                      0.4.4\n",
            "scikit-image                     0.23.2\n",
            "scikit-learn                     1.3.2\n",
            "scipy                            1.13.1\n",
            "scooby                           0.10.0\n",
            "scs                              3.2.7\n",
            "seaborn                          0.13.1\n",
            "SecretStorage                    3.3.1\n",
            "Send2Trash                       1.8.3\n",
            "sentencepiece                    0.1.99\n",
            "setuptools                       71.0.4\n",
            "shapely                          2.0.6\n",
            "shellingham                      1.5.4\n",
            "simple_parsing                   0.1.5\n",
            "six                              1.16.0\n",
            "sklearn-pandas                   2.2.0\n",
            "smart-open                       7.0.4\n",
            "sniffio                          1.3.1\n",
            "snowballstemmer                  2.2.0\n",
            "snowflake-connector-python       3.12.1\n",
            "sortedcontainers                 2.4.0\n",
            "soundfile                        0.12.1\n",
            "soupsieve                        2.6\n",
            "soxr                             0.5.0\n",
            "spacy                            3.7.6\n",
            "spacy-legacy                     3.0.12\n",
            "spacy-loggers                    1.0.5\n",
            "Sphinx                           5.0.2\n",
            "sphinxcontrib-applehelp          2.0.0\n",
            "sphinxcontrib-devhelp            2.0.0\n",
            "sphinxcontrib-htmlhelp           2.1.0\n",
            "sphinxcontrib-jsmath             1.0.1\n",
            "sphinxcontrib-qthelp             2.0.0\n",
            "sphinxcontrib-serializinghtml    2.0.0\n",
            "SQLAlchemy                       2.0.32\n",
            "sqlglot                          20.11.0\n",
            "sqlparse                         0.5.1\n",
            "srsly                            2.4.8\n",
            "stanio                           0.5.1\n",
            "statsmodels                      0.14.2\n",
            "StrEnum                          0.4.15\n",
            "sympy                            1.13.2\n",
            "tables                           3.8.0\n",
            "tabulate                         0.9.0\n",
            "tbb                              2021.13.1\n",
            "tblib                            3.0.0\n",
            "tenacity                         9.0.0\n",
            "tensorboard                      2.17.0\n",
            "tensorboard-data-server          0.7.2\n",
            "tensorflow                       2.17.0\n",
            "tensorflow-datasets              4.9.6\n",
            "tensorflow-hub                   0.16.1\n",
            "tensorflow-io-gcs-filesystem     0.37.1\n",
            "tensorflow-metadata              1.15.0\n",
            "tensorflow-probability           0.24.0\n",
            "tensorstore                      0.1.64\n",
            "termcolor                        2.4.0\n",
            "terminado                        0.18.1\n",
            "text-unidecode                   1.3\n",
            "textblob                         0.17.1\n",
            "tf_keras                         2.17.0\n",
            "tf-slim                          1.1.0\n",
            "thinc                            8.2.5\n",
            "threadpoolctl                    3.5.0\n",
            "tifffile                         2024.8.28\n",
            "tinycss2                         1.3.0\n",
            "tokenizers                       0.19.1\n",
            "toml                             0.10.2\n",
            "tomli                            2.0.1\n",
            "tomlkit                          0.13.2\n",
            "toolz                            0.12.1\n",
            "torch                            2.4.0+cu121\n",
            "torchaudio                       2.4.0+cu121\n",
            "torchsummary                     1.5.1\n",
            "torchvision                      0.19.0+cu121\n",
            "tornado                          6.3.3\n",
            "tqdm                             4.66.5\n",
            "traitlets                        5.7.1\n",
            "traittypes                       0.2.1\n",
            "transformers                     4.44.2\n",
            "tweepy                           4.14.0\n",
            "typeguard                        4.3.0\n",
            "typer                            0.12.5\n",
            "types-pytz                       2024.1.0.20240417\n",
            "types-setuptools                 74.0.0.20240831\n",
            "typing_extensions                4.12.2\n",
            "tzdata                           2024.1\n",
            "tzlocal                          5.2\n",
            "uc-micro-py                      1.0.3\n",
            "uritemplate                      4.1.1\n",
            "urllib3                          2.0.7\n",
            "vega-datasets                    0.9.0\n",
            "wadllib                          1.3.6\n",
            "wasabi                           1.1.3\n",
            "wcwidth                          0.2.13\n",
            "weasel                           0.4.1\n",
            "webcolors                        24.8.0\n",
            "webencodings                     0.5.1\n",
            "websocket-client                 1.8.0\n",
            "Werkzeug                         3.0.4\n",
            "wheel                            0.44.0\n",
            "widgetsnbextension               3.6.8\n",
            "wordcloud                        1.9.3\n",
            "wrapt                            1.16.0\n",
            "xarray                           2024.6.0\n",
            "xarray-einstats                  0.7.0\n",
            "xgboost                          2.1.1\n",
            "xlrd                             2.0.1\n",
            "xyzservices                      2024.6.0\n",
            "yarl                             1.9.4\n",
            "yellowbrick                      1.5\n",
            "yfinance                         0.2.43\n",
            "zict                             3.0.0\n",
            "zipp                             3.20.1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CKy19YxMWMgn"
      },
      "source": [
        "We can install additional packages with:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OVkZ5Yf8n2H4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "067a015b-f185-47e7-f03f-b79759cb0029"
      },
      "source": [
        "!pip install -q numpy pandas scikit-learn -U"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\u001b[K     |████████████████████████████████| 14.8MB 292kB/s \n",
            "\u001b[K     |████████████████████████████████| 22.2MB 1.5MB/s \n",
            "\u001b[31mERROR: datascience 0.10.6 has requirement folium==0.2.1, but you'll have folium 0.8.3 which is incompatible.\u001b[0m\n",
            "\u001b[31mERROR: albumentations 0.1.12 has requirement imgaug<0.2.7,>=0.2.5, but you'll have imgaug 0.2.9 which is incompatible.\u001b[0m\n",
            "\u001b[?25h"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dcvKnPFHyeUo"
      },
      "source": [
        "Note: the symbol `!` means that you are calling the terminal of the Operating System."
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 1.3 Using R and Python together in Colab\n",
        "\n",
        "\n",
        "* Colab provides by default notebooks to write and run Python\n",
        "\n",
        "* To use the notebook directly with R, go to\n",
        "\n",
        "    https://colab.research.google.com/#create=true&language=r  \n",
        "\n",
        "  - In the menu \"Runtime\" and then \"Change runtime type\", you can check to already be in R runtime.\n",
        "\n",
        "\n",
        "* Alternatively you can run R code in the cells of a regular python notebook\n",
        "\n",
        "  1. Load `rpy2` package in the Python runtime\n",
        "\n",
        "    `%load_ext rpy2.ipython`\n",
        "\n",
        "  2. Then, use `%%R` at the beginning of the cell with R code\n"
      ],
      "metadata": {
        "id": "JzGsO85ZhnS7"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XQD4xTu6n2Io"
      },
      "source": [
        "# 2 Python Basics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pxJ41yD_S9vt"
      },
      "source": [
        "Python Version:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "22WQ8kJHmcgT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8106a5d5-6212-4ad5-a187-d09937250d6c"
      },
      "source": [
        "!python -V"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Python 3.8.16\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LZ93RI4IPZEQ"
      },
      "source": [
        "### Using cloud machine\n",
        "\n",
        "* You can connect to a cloud machine by clicking on `Connect`, a button in the right part of the upper bar.\n",
        "\n",
        "* Or directly runnign a cell.\n",
        "\n",
        "* You can also run several cell a time"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sTA1n0pNHIeV"
      },
      "source": [
        "#2.1 Basic Data Types\n",
        "\n",
        "Python has five standard data types\n",
        "\n",
        "* Numbers\n",
        "* String\n",
        "* List\n",
        "* Tuple\n",
        "* Dictionary\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KO5qvCgQMirn"
      },
      "source": [
        "### Assigning Values to Variables\n",
        "\n",
        "The equal sign (=) is used to assign values to variables.\n",
        "\n",
        "The command `print()` show the value stored."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-75yeniDMyOH",
        "outputId": "e26335d8-b19c-4b4a-a600-2d404ad3b4d9"
      },
      "source": [
        "counter = 100          # An integer assignment\n",
        "miles   = 1000.0       # A floating point\n",
        "name    = \"John\"       # A string\n",
        "\n",
        "print(counter)\n",
        "print(miles)\n",
        "print(name)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "100\n",
            "1000.0\n",
            "John\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bYE-ELJJSoDH"
      },
      "source": [
        "**Note** that comments in Python are preceded by the hash symbol: `#`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I632mEySNUkE"
      },
      "source": [
        "#### Multiple Assignment\n",
        "\n",
        "Python allows you to assign a single value to several variables simultaneously.\n",
        "\n",
        "`a = b = c = 1`\n",
        "\n",
        "`a,b,c = 1,2,\"john\"`\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KLboRZ159F3O",
        "outputId": "9f880b80-fc85-4529-8d3b-91c6a54c3fac"
      },
      "source": [
        "a = b = c = [1,2,3]\n",
        "a[1]=20\n",
        "print(a,b)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1, 20, 3] [1, 20, 3]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5ddV_OoJHLsJ"
      },
      "source": [
        "## Numbers\n",
        "\n",
        "Python supports four different numerical types\n",
        "\n",
        "  - int (signed integers)\n",
        "  - long (long integers, they can also be represented in octal and hexadecimal)\n",
        "  - float (floating point real values)\n",
        "  - complex (complex numbers)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I4JUFuGiHu8o",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "be12e75e-82a6-45ec-f54d-c6ec40a3180f"
      },
      "source": [
        "x = int(3.2)\n",
        "print(x, type(x))\n",
        "y=float(x)\n",
        "print(y, type(y))\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "3 <class 'int'>\n",
            "3.0 <class 'float'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I7LY1PO9OJIP"
      },
      "source": [
        "Basic operations work as you would expect from other languages.\n",
        "\n",
        "You can use Python as a basic calculator."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TgjISEUeH2Oy"
      },
      "source": [
        "print(x + 1)   # Addition\n",
        "print(x - 1)   # Subtraction\n",
        "print(x * 2)   # Multiplication\n",
        "print(x ** 2)  # Exponentiation"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LRx94Q5aIHVo"
      },
      "source": [
        "### Addition and Subtraction\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ufpNjubF_Var",
        "outputId": "5decb76d-13ad-4ab2-cd7b-5029b79865d7"
      },
      "source": [
        "2+float('inf')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "inf"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FdMtfDWNn2Iq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9ebc7fd0-f504-4d26-edb4-2e13164c6c3d"
      },
      "source": [
        "float('inf')-float('inf')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "nan"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6M8TVi-gn2I-"
      },
      "source": [
        "### Multiplication and division\n",
        "\n",
        "```\n",
        "2*2\n",
        "2*0\n",
        "2*float('inf')\n",
        "float('inf')*float('inf')\n",
        "float('inf')*0\n",
        "0/0\n",
        "0/2\n",
        "2/0\n",
        "float('inf')/float('inf')\n",
        "float('inf')/0\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LBsdEYPfn2JG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "54fe6d9b-6410-42a4-a956-2ecd9aff57a6"
      },
      "source": [
        "2*2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "nan"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "2/3"
      ],
      "metadata": {
        "id": "QLm74A055qJS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "float('inf')*0"
      ],
      "metadata": {
        "id": "xk0tuqMY5qna"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QgyllwofOXnD"
      },
      "source": [
        "y = 2.5\n",
        "print(type(y))\n",
        "print(y, y + 1, y * 2, y ** 2)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BrD_UiUFn2Jm"
      },
      "source": [
        "### A Special feature in Python\n",
        "\n",
        "- *Python* (also *R*) works with undefined **nan** (Not a Number) numbers or not available **NA** (Not Available) values in their operations and functions\n",
        "\n",
        "- Most of the usual programming languages would stop and show an error message.\n",
        "\n",
        "```\n",
        "sum([2,3])\n",
        "sum([2,float('nan')))\n",
        "```\n",
        "\n",
        "- How to deal with missing values (\"absence of data\") is important for data analysis."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n3dxNhMjR3Xb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4e57f4d0-641f-4520-acd4-f1987b4f97e0"
      },
      "source": [
        "sum([2,float('nan')])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "nan"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZTfU0B6Gn2JS"
      },
      "source": [
        "### Other operations\n",
        "\n",
        "* Floor Division and Modulus\n",
        "\n",
        "`5 // 2`\n",
        "\n",
        "`5 % 2`\n",
        "\n",
        "*  Exponents\n",
        "\n",
        "`2**3`\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P7ZfhyTun2JW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cd6f7cc2-f332-4faf-e7ec-1d534cb71945"
      },
      "source": [
        "2**3"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pUqAZWKfoVdY"
      },
      "source": [
        "### Incremental assignment\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9TqwuVYJH_k7"
      },
      "source": [
        "x += 1\n",
        "print(x)\n",
        "x *= 2\n",
        "print(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vzRAFJFTcLPx"
      },
      "source": [
        "## Type conversion\n",
        "\n",
        "Note that you can convert between different types with `int()`, `long()`, `float()`, etc. but also to `list()`, `tuple()`, etc."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lMuLxhV3T6iu"
      },
      "source": [
        "## Booleans"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nv_LIVOJL9fD"
      },
      "source": [
        "Python implements all of the usual operators for Boolean logic, but uses English words rather than symbols (`&&`, `||`, etc.):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RvoImwgGL9fE",
        "outputId": "d82e448f-245d-475c-e4ed-87473297d3e1"
      },
      "source": [
        "t, f = True, False\n",
        "print(type(t))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'bool'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YQgmQfOgL9fI"
      },
      "source": [
        "Now we let's look at the operations:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6zYm7WzCL9fK",
        "outputId": "3517a141-cd10-4084-d419-66ab3e288142"
      },
      "source": [
        "print(t and f) # Logical AND;\n",
        "print(t or f)  # Logical OR;\n",
        "print(not t)   # Logical NOT;\n",
        "print(t != f)  # Logical XOR;"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "False\n",
            "True\n",
            "False\n",
            "True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nteHGMs_lS2e"
      },
      "source": [
        "## Strings"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9wSx5vbilWMI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8226db45-8daf-41b0-8dbb-8a29b47bea85"
      },
      "source": [
        "hello = 'hello'   # String literals can use single quotes\n",
        "world = \"world\"   # or double quotes; it does not matter\n",
        "print(hello)\n",
        "print(world, len(hello))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "hello\n",
            "world 5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SbB30QIjTJjG",
        "outputId": "df18f7db-8512-4fcf-acd8-5d9c7869310b"
      },
      "source": [
        "hw = hello + ' ' + world  # String concatenation\n",
        "print(hw)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "hello world\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LJTrjzOLS1EB"
      },
      "source": [
        "### A first brief note on print formating"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nfZu7X6RTL3C",
        "outputId": "d90f5fc0-d6cf-425f-a174-4fda6b400136"
      },
      "source": [
        "hw12 = '{} {} {}'.format(hello, world, 12)  # string formatting\n",
        "print(hw12)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "hello world 12\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T0nA_uUNn2Js",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e5b0eb9b-b920-49b8-901e-cca72ea176d2"
      },
      "source": [
        "a = 2*4+7-4\n",
        "print('a: {a}')\n",
        "print(f'a: {a}')\n",
        "\n",
        "\n",
        "b = 5/2+a\n",
        "print(f'b: {b}')\n",
        "\n",
        "print(b)\n",
        "print(\"b:\",b)\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "a: {a}\n",
            "a: 11\n",
            "b: 13.5\n",
            "13.5\n",
            "b: 13.5\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bUpl35bIL9fc"
      },
      "source": [
        "### Methods for strings objects"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VOxGatlsL9fd",
        "outputId": "1c026422-a43f-40d0-eea6-c2b8a326bf56"
      },
      "source": [
        "s = \"hello\"\n",
        "\n",
        "#print(capitalize(s))\n",
        "\n",
        "print(s.capitalize())  # Capitalize a string\n",
        "print(s.upper())       # Convert a string to uppercase; prints \"HELLO\"\n",
        "print(s.rjust(7))      # Right-justify a string, padding with spaces\n",
        "print(s.center(7))     # Center a string, padding with spaces\n",
        "print(s.replace('l', '(ell)'))  # Replace all instances of one substring with another\n",
        "print('  world '.strip())  # Strip leading and trailing whitespace"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Hello\n",
            "HELLO\n",
            "  hello\n",
            " hello \n",
            "he(ell)(ell)o\n",
            "world\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "06cayXLtL9fi"
      },
      "source": [
        "\n",
        "You can find a list of all string methods in the [documentation](https://docs.python.org/3.7/library/stdtypes.html#string-methods).\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LQOaEOAPXBXD"
      },
      "source": [
        "\n",
        "## A note on help in Colab\n",
        "\n",
        "* As you may have noticed, Colab help you to write Python code by providing syntax highlighting.\n",
        "\n",
        "* On-the-fly help is also provided: when writing a method (function/command), you can see its expected arguments and how it works. Also you can see the type and value of variable when mouse pointer passes over it."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p-6hClFjL9fk"
      },
      "source": [
        "## Containers"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FD9H18eQL9fk"
      },
      "source": [
        "Python includes several built-in container types: lists, dictionaries, sets, and tuples."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UsIWOe0LL9fn"
      },
      "source": [
        "###Lists"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wzxX7rgWL9fn"
      },
      "source": [
        "A list is the Python equivalent of an array, but is resizeable and can contain elements of different types:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hk3A8pPcL9fp",
        "outputId": "38149bfa-9505-4e8d-b13f-0458202d3fa9"
      },
      "source": [
        "xs = [3, 1, 2]   # Create a list\n",
        "\n",
        "print(xs, xs[2])  # IMPORTANT: index start at 0  (from the left)\n",
        "\n",
        "print(xs[-1])     # Negative indices count from the end of the list; prints \"2\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3, 1, 2] 2\n",
            "2\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YCjCy_0_L9ft",
        "outputId": "a4947e5d-0cc2-4295-9ef7-e33610ddbd82"
      },
      "source": [
        "xs[2] = 'foo'    # Lists can contain elements of different types\n",
        "print(xs)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3, 1, 'foo']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vJ0x5cF-L9fx",
        "outputId": "d5fd682d-3ce0-4000-98ff-c4e7821f882c"
      },
      "source": [
        "xs.append('bar') # Add a new element to the end of the list\n",
        "print(xs)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3, 1, 'foo', 'bar']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "z_70AHkqWAJ7",
        "outputId": "3d615abe-ccff-4e25-c508-b6a95bb628a0"
      },
      "source": [
        "xs.remove('foo')  # Remove an element\n",
        "print(xs)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[3, 1, 'bar']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cxVCNRTNL9f1",
        "outputId": "2b39ff87-705a-4044-82b4-02c018e001ec"
      },
      "source": [
        "x = xs.pop()     # Remove and return the last element of the list\n",
        "print(x, xs)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "bar [3, 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ilyoyO34L9f4"
      },
      "source": [
        "As usual, you can find all the gory details about lists in the [documentation](https://docs.python.org/3.7/tutorial/datastructures.html#more-on-lists)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ovahhxd_L9f5"
      },
      "source": [
        "####Slicing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YeSYKhv9L9f6"
      },
      "source": [
        "In addition to accessing list elements one at a time, Python provides concise syntax to access sublists.\n",
        "\n",
        "This is known as slicing:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ninq666bL9f6",
        "outputId": "fcf2ca67-abf9-454c-fb0c-e619ee974a12"
      },
      "source": [
        "nums = list(range(5))    # range is a built-in function that creates a list of integers\n",
        "print(nums)         # Prints \"[0, 1, 2, 3, 4]\"\n",
        "print(nums[2:4])    # Get a slice from index 2 to 4 (exclusive); prints \"[2, 3]\"\n",
        "print(nums[2:])     # Get a slice from index 2 to the end; prints \"[2, 3, 4]\"\n",
        "print(nums[:2])     # Get a slice from the start to index 2 (exclusive); prints \"[0, 1]\"\n",
        "print(nums[:])      # Get a slice of the whole list; prints [\"0, 1, 2, 3, 4]\"\n",
        "print(nums[:-1])    # Slice indices can be negative; prints [\"0, 1, 2, 3]\"\n",
        "nums[2:4] = [8, 9] # Assign a new sublist to a slice\n",
        "print(nums)         # Prints \"[0, 1, 8, 9, 4]\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 2, 3, 4]\n",
            "[2, 3]\n",
            "[2, 3, 4]\n",
            "[0, 1]\n",
            "[0, 1, 2, 3, 4]\n",
            "[0, 1, 2, 3]\n",
            "[0, 1, 8, 9, 4]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UONpMhF4L9f_"
      },
      "source": [
        "####Loops"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_DYz1j6QL9f_"
      },
      "source": [
        "You can loop over the elements of a list:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4cCOysfWL9gA",
        "outputId": "d5029c8f-e540-4a2c-d1cb-b1550ac6a14d"
      },
      "source": [
        "animals = ['cat', 'dog', 'monkey']\n",
        "for i in animals:\n",
        "    print(i)\n",
        "    print(i+\"hola\")\n",
        "print(i)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "cat\n",
            "cathola\n",
            "dog\n",
            "doghola\n",
            "monkey\n",
            "monkeyhola\n",
            "monkey\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AQYeTfgQZoi-"
      },
      "source": [
        "Unlike many other programming languages, Python does NOT use markup symbol like curly brackets (`for () { ... }`, `for () ... endfor`) to indicate the beginning and ending of loop block. In Python, loops blocks are recognized by **indentation**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KxIaQs7pL9gE"
      },
      "source": [
        "If you want access to the index of each element within the body of a loop, use the built-in `enumerate` function:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JjGnDluWL9gF",
        "outputId": "03f9e026-d5df-45e0-8196-190853a0d6d6"
      },
      "source": [
        "animals = ['cat', 'dog', 'monkey']\n",
        "for idx, animal in enumerate(animals):\n",
        "   #print('#{}: {}'.format(idx + 1, animal))   # old more complex syntax for print formating\n",
        "   print(f'#{idx+1}: {animal}')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "#1: cat\n",
            "#2: dog\n",
            "#3: monkey\n",
            "<enumerate object at 0x7fa87fa0a120>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sNkiuXTbt3kQ"
      },
      "source": [
        "##### while loop"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zgHR5yW-t9FA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0880b5f4-061c-443c-aa46-1816d032106f"
      },
      "source": [
        "i = 0\n",
        "while i < 5:\n",
        "    print(i)\n",
        "    i += 1"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0\n",
            "1\n",
            "2\n",
            "3\n",
            "4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "arrLCcMyL9gK"
      },
      "source": [
        "####List comprehensions:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Qn2jU_pL9gL"
      },
      "source": [
        "When programming, frequently we want to transform one type of data into another. As a simple example, consider the following code that computes square numbers:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "IVNEwoMXL9gL",
        "outputId": "d571445b-055d-45f0-f800-24fd76ceec5a"
      },
      "source": [
        "nums = [0, 1, 2, 3, 4]\n",
        "squares = []\n",
        "for x in nums:\n",
        "    squares.append(x ** 2)\n",
        "print(squares)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 4, 9, 16]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7DmKVUFaL9gQ"
      },
      "source": [
        "You can make this code simpler using a list comprehension:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "kZxsUfV6L9gR",
        "outputId": "4254a7d4-58ba-4f70-a963-20c46b485b72"
      },
      "source": [
        "nums = [0, 1, 2, 3, 4]\n",
        "squares = [x ** 2 for x in nums]\n",
        "print(squares)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 4, 9, 16]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-D8ARK7tL9gV"
      },
      "source": [
        "List comprehensions can also contain conditions:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "yUtgOyyYL9gV",
        "outputId": "1ae7ab58-8119-44dc-8e57-fda09197d026"
      },
      "source": [
        "nums = [0, 1, 2, 3, 4]\n",
        "even_squares = [x ** 2 for x in nums if x % 2 == 0]\n",
        "print(even_squares)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 4, 16]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nuxA3IoHdnXc"
      },
      "source": [
        "### Dictionaries"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gLXwPHO-dewL"
      },
      "source": [
        "A dictionary stores (key, value) pairs. You can use it like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9cMHffVxdewN",
        "outputId": "33f75fd8-54f0-4bac-fbdc-639685c3d492"
      },
      "source": [
        "d = {'cat': 'cute', 'dog': 'furry'}  # Create a new dictionary with some data\n",
        "print(d['cat'])       # Get an entry from a dictionary; prints \"cute\"\n",
        "print('cat' in d)     # Check if a dictionary has a given key; prints \"True\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cute\n",
            "True\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7bde5G0gdewP",
        "outputId": "f2aef6e4-1253-4a26-f234-9a83fcb445dd"
      },
      "source": [
        "d['fish'] = 'wet'    # Set an entry in a dictionary\n",
        "print(d['fish'])      # Prints \"wet\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "wet\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 166
        },
        "id": "YESB2uRRdewR",
        "outputId": "5359f0a0-2551-4218-e9ed-d13c196f6870"
      },
      "source": [
        "print(d['monkey'])  # KeyError: 'monkey' not a key of d"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "KeyError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-8-78fc9745d9cf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'monkey'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# KeyError: 'monkey' not a key of d\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mKeyError\u001b[0m: 'monkey'"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "v-BJ0mopdewT",
        "outputId": "a76f7645-d534-4a02-877b-17026dfecec1"
      },
      "source": [
        "print(d.get('monkey', 'N/A'))  # Get an element with a default; prints \"N/A\"\n",
        "print(d.get('fish', 'N/A'))    # Get an element with a default; prints \"wet\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "N/A\n",
            "wet\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "hUT-7FWjdewT",
        "outputId": "652a950f-b0c2-4623-98bd-0191b300cd57"
      },
      "source": [
        "del d['fish']        # Remove an element from a dictionary\n",
        "print(d.get('fish', 'N/A')) # \"fish\" is no longer a key; prints \"N/A\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "N/A\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JVESgi6wdewW"
      },
      "source": [
        "You can find all you need to know about dictionaries in the [documentation](https://docs.python.org/2/library/stdtypes.html#dict)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7HGncqIudewX"
      },
      "source": [
        "It is easy to iterate over the keys in a dictionary:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "W2b6HYFndewX",
        "outputId": "155bdb17-3179-4292-c832-8166e955e942"
      },
      "source": [
        "d = {'person': 2, 'cat': 4, 'spider': 8}\n",
        "for animal, legs in d.items():\n",
        "    print('A {} has {} legs'.format(animal, legs))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "A person has 2 legs\n",
            "A cat has 4 legs\n",
            "A spider has 8 legs\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TSbmjZsYdewZ"
      },
      "source": [
        "Dictionary comprehensions: These are similar to list comprehensions, but allow you to easily construct dictionaries. For example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "iTQHlKAzdewb",
        "outputId": "e9ddf886-39ed-4f35-dd80-64a19d2eec9b"
      },
      "source": [
        "nums = [0, 1, 2, 3, 4]\n",
        "even_num_to_square = {x: x ** 2 for x in nums if x % 2 == 0}\n",
        "print(even_num_to_square)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{0: 0, 2: 4, 4: 16}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V9MHfUdvL9g2"
      },
      "source": [
        "### Sets"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Rpm4UtNpL9g2"
      },
      "source": [
        "A set is an **unordered** collection of distinct elements. As a simple example, consider the following:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 253
        },
        "id": "MmyaniLsL9g2",
        "outputId": "3bed1086-9070-4496-bc27-f59758819f34"
      },
      "source": [
        "animals = {'cat', 'dog'}\n",
        "print('cat' in animals)   # Check if an element is in a set; prints \"True\"\n",
        "print('fish' in animals)  # prints \"False\"\n",
        "\n",
        "print(animals)\n",
        "\n",
        "animals[1]\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True\n",
            "False\n",
            "{'dog', 'cat'}\n"
          ]
        },
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-3-f91fff98751e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manimals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0manimals\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m: 'set' object is not subscriptable"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "ElJEyK86L9g6",
        "outputId": "b9d7dab9-5a98-41cd-efbc-786d0c4377f7"
      },
      "source": [
        "animals.add('fish')      # Add an element to a set\n",
        "print('fish' in animals)\n",
        "print(len(animals))       # Number of elements in a set;"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "True\n",
            "3\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "5uGmrxdPL9g9",
        "outputId": "e644d24c-26c6-4b43-ab15-8aa81fe884d4"
      },
      "source": [
        "animals.add('cat')       # Adding an element that is already in the set does nothing\n",
        "print(len(animals))\n",
        "animals.remove('cat')    # Remove an element from a set\n",
        "print(len(animals))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "3\n",
            "2\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GD_OpdRufDJJ"
      },
      "source": [
        "It is usually simpler to generate a set from a list:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qEeaLdxLfAbt",
        "outputId": "732d7e8d-d33b-4779-967f-4d68e039b1e1"
      },
      "source": [
        "mylist = ['one','two','three','three']\n",
        "myset = set(mylist)\n",
        "print(myset)\n",
        "\n",
        "print('\\'one\\' belongs to set {}'.format('one' in myset))\n",
        "print('\\'four\\' belongs to set {}'.format('four' in myset))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'three', 'one', 'two'}\n",
            "'one' belongs to set True\n",
            "'four' belongs to set False\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zk2DbvLKL9g_"
      },
      "source": [
        "_Loops_: Iterating over a set has the same syntax as iterating over a list; however since sets are unordered, you cannot make assumptions about the order in which you visit the elements of the set:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "K47KYNGyL9hA",
        "outputId": "4477f897-4355-4816-b39b-b93ffbac4bf0"
      },
      "source": [
        "animals = {'cat', 'dog', 'fish'}\n",
        "for idx, animal in enumerate(animals):\n",
        "    print('#{}: {}'.format(idx + 1, animal))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "#1: dog\n",
            "#2: cat\n",
            "#3: fish\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "puq4S8buL9hC"
      },
      "source": [
        "Set comprehensions: Like lists and dictionaries, we can easily construct sets using set comprehensions:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "iw7k90k3L9hC",
        "outputId": "72d6b824-6d31-47b2-f929-4cf434590ee5"
      },
      "source": [
        "from math import sqrt\n",
        "print({int(sqrt(x)) for x in range(30)})"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{0, 1, 2, 3, 4, 5}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qPsHSKB1L9hF"
      },
      "source": [
        "### Tuples"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kucc0LKVL9hG"
      },
      "source": [
        "A tuple is an (immutable) ordered list of values. A tuple is in many ways similar to a list; one of the most important differences is that tuples can be used as keys in dictionaries and as elements of sets, while lists cannot. Here is a trivial example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "9wHUyTKxL9hH",
        "outputId": "cdc5f620-04fe-4b0b-df7a-55b061d23d88"
      },
      "source": [
        "d = {(x, x + 1): x for x in range(10)}  # Create a dictionary with tuple keys\n",
        "t = (5, 6)       # Create a tuple\n",
        "print(type(t))\n",
        "print(d[t])\n",
        "print(d[(1, 2)])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'tuple'>\n",
            "5\n",
            "1\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ks9RI5pGkHpt"
      },
      "source": [
        "# 2.2 If-Conditions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2ZMRddW5kKb0"
      },
      "source": [
        "a = 1\n",
        "if a>1:\n",
        "  print('\"a\" is greater than 1')\n",
        "else:\n",
        "  print('\"a\" is NOT greater than 1')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DgmTLP-ZklFA"
      },
      "source": [
        "a = 1\n",
        "b = 2\n",
        "if a>1 and b>1:\n",
        "  print('{} y {} are greater than 1'.format(a,b))\n",
        "else:\n",
        "  print('{} y {} are NOT greater than 1'.format(a,b))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p7MVfc11lBCB"
      },
      "source": [
        "a = 1\n",
        "b = 2\n",
        "if a>1 or b>1:\n",
        "  print('{} or {} are greater than 1'.format(a,b))\n",
        "else:\n",
        "  print('Neither {}, nor {} are greater than 1'.format(a,b))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AXA4jrEOL9hM"
      },
      "source": [
        "# 2.3 Functions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WaRms-QfL9hN"
      },
      "source": [
        "Python functions are defined using the `def` keyword. For example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "kiMDUr58L9hN",
        "outputId": "9f53bf9a-7b2a-4c51-9def-398e4677cd6c"
      },
      "source": [
        "def sign(x):\n",
        "    if x > 0:\n",
        "        return 'positive'\n",
        "    elif x < 0:\n",
        "        return 'negative'\n",
        "    else:\n",
        "        return 'zero'\n",
        "\n",
        "for x in [-1, 0, 1]:\n",
        "    print(sign(x))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "negative\n",
            "zero\n",
            "positive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U-QJFt8TL9hR"
      },
      "source": [
        "We will often define functions to take optional keyword arguments, like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "PfsZ3DazL9hR",
        "outputId": "6e6af832-67d8-4d8c-949b-335927684ae3"
      },
      "source": [
        "def hello(name, loud=False):\n",
        "    if loud:\n",
        "        print('HELLO, {}'.format(name.upper()))\n",
        "    else:\n",
        "        print('Hello, {}!'.format(name))\n",
        "\n",
        "hello('Bob')\n",
        "hello('Fred', loud=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Hello, Bob!\n",
            "HELLO, FRED\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3cfrOV4dL9hW"
      },
      "source": [
        "# 3 Numpy"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fY12nHhyL9hX"
      },
      "source": [
        "Numpy is the core library for scientific computing in Python. Many other libraries depends on it.\n",
        "\n",
        "It provides a high-performance multidimensional array object, and tools for working with these arrays.\n",
        "\n",
        "If you are already familiar with MATLAB, you might find this [tutorial](http://wiki.scipy.org/NumPy_for_Matlab_Users) useful to get started with Numpy.\n",
        "\n",
        "- Documentation <https://docs.scipy.org/doc/numpy/user/>\n",
        "- Quick tutorial <https://docs.scipy.org/doc/numpy/user/quickstart.html>\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PYQyE_RcUD-l"
      },
      "source": [
        "If not yet installed, you must install `numpy` with\n",
        "\n",
        "`pip install numpy`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7NPTGMPiFR0Z"
      },
      "source": [
        "!pip list\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lZMyAdqhL9hY"
      },
      "source": [
        "To use Numpy, we first need to import the `numpy` package:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "58QdX8BLL9hZ"
      },
      "source": [
        "import numpy as np"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DDx6v1EdL9hb"
      },
      "source": [
        "# 3.1 Arrays"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f-Zv3f7LL9hc"
      },
      "source": [
        "* A numpy array is a grid of values all of the same type.\n",
        "\n",
        "* It is indexed by a tuple of nonnegative integers.\n",
        "\n",
        "The number of dimensions is the rank of the array; the shape of an array is a tuple of integers giving the size of the array along each dimension.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n2sct6yyWF0-"
      },
      "source": [
        "##  Vectors (1D arrays)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_eMTRnZRL9hc"
      },
      "source": [
        "We can initialize numpy arrays from nested Python lists, and access elements using square brackets:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-l3JrGxCL9hc",
        "outputId": "aa888c1d-f6de-4c3f-d165-0041c3a0fc9e"
      },
      "source": [
        "a = np.array([1, 2, 3])  # Create a rank 1 array\n",
        "print(type(a), a.shape, a[0], a[1], a[2])\n",
        "a[0] = 5                 # Change an element of the array\n",
        "print(a)\n",
        "\n",
        "b = [1,2,3]\n",
        "type(b)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'numpy.ndarray'> (3,) 1 2 3\n",
            "[5 2 3]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "list"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F9tyMSmUVQ3U",
        "outputId": "0e33b4a3-1dc3-4e94-ac24-88d0b6db6183"
      },
      "source": [
        "c = np.array(['good','morning'])\n",
        "print(f'String array: {c}; its type: {type(c)}')\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "String array: ['good' 'morning']; its type: <class 'numpy.ndarray'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8_RNTNdOYYVR",
        "outputId": "243acbca-2a6b-426e-e56b-c2a7efe0763e"
      },
      "source": [
        "print(f'dimension with len: {len(a)}; its type: {type(len(a))}')\n",
        "\n",
        "print(f'dimension with shape: {a.shape}; its type: {type(a.shape)}')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "dimension with len: 3; its type: <class 'int'>\n",
            "dimension with shape: (3,); its type: <class 'tuple'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iWlw1mDbWsbQ"
      },
      "source": [
        "## Matrices (2D arrays)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ma6mk-kdL9hh",
        "outputId": "54f200a0-6226-4537-e619-3e7c321c4599"
      },
      "source": [
        "b = np.array([[1,2,3],[4,5,6]])   # Create a rank 2 array\n",
        "print(b)\n",
        "\n",
        "print(b.shape)\n",
        "print(b[0, 0], b[0, 1], b[1, 0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1 2 3]\n",
            " [4 5 6]]\n",
            "(2, 3)\n",
            "1 2 4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FaXucD1EeTfC",
        "outputId": "4426cbcd-89d4-4419-c9bb-a00d275e3fee"
      },
      "source": [
        "print(f'dimension with len: {len(b)}; its type: {type(len(b))}')\n",
        "\n",
        "print(f'dimension with shape: {b.shape}; its type: {type(b.shape)}')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "dimension with len: 2; its type: <class 'int'>\n",
            "dimension with shape: (2, 3); its type: <class 'tuple'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CO45t9i3XHS5"
      },
      "source": [
        "## Functions to create arrays"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qxi0JH85ekac",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "21bd8477-8014-4ce9-b3fd-d23014c7c4f9"
      },
      "source": [
        "# Using reshape\n",
        "\n",
        "mat1 = np.arange(1,7).reshape((3,2))\n",
        "mat1"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [3, 4],\n",
              "       [5, 6]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vIqNcJhfeuil"
      },
      "source": [
        "* **Exercise** Look for information on `arange` and `reshape`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mVTN_EBqL9hn",
        "outputId": "28b6db3a-ac78-44b1-fa5b-4744eade96ac"
      },
      "source": [
        "a = np.zeros((2,2))  # Create an array of all zeros\n",
        "print(a)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0. 0.]\n",
            " [0. 0.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "skiKlNmlL9h5",
        "outputId": "3626b538-f92c-4ce4-e305-c6896899349d"
      },
      "source": [
        "b = np.ones((1,2))   # Create an array of all ones\n",
        "print(b)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1. 1.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HtFsr03bL9h7",
        "outputId": "286452aa-968a-46cc-f251-83cf5df42695"
      },
      "source": [
        "c = np.full((2,2), 7) # Create a constant array\n",
        "print(c)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[7 7]\n",
            " [7 7]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-QcALHvkL9h9",
        "outputId": "84d526ba-6ddd-44f6-b305-71088040c30c"
      },
      "source": [
        "d = np.eye(2)        # Create a 2x2 identity matrix\n",
        "print(d)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1. 0.]\n",
            " [0. 1.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RCpaYg9qL9iA",
        "outputId": "4180901b-d395-4e75-f8ef-5a9fd851c97c"
      },
      "source": [
        "np.random.seed(1000)\n",
        "\n",
        "e = np.random.random((2,2)) # Create an array filled with random values\n",
        "print(e)\n",
        "\n",
        "f = np.random.normal(size=100)\n",
        "print(f)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.65358959 0.11500694]\n",
            " [0.95028286 0.4821914 ]]\n",
            "[-0.30079667  0.38947455 -0.1074373  -0.47998308  0.5950355  -0.46466753\n",
            "  0.66728131 -0.80611561 -1.19606983 -0.40596016 -0.18237734  0.10319289\n",
            " -0.13842199  0.70569237  1.27179528 -0.98674733 -0.33483545 -0.0994817\n",
            "  0.4071921   0.91938754  0.31211801  1.53316107 -0.55017387 -0.38314741\n",
            " -0.82294096  1.60008337 -0.0692813   0.08320949 -0.32692468 -0.04579719\n",
            " -0.30446006  1.92301013 -0.078659   -0.58206572 -1.61798224  0.86726082\n",
            " -1.04043709  0.65042142  2.69964586  0.80202451 -1.09692126 -0.17805445\n",
            " -0.42287048 -0.33040055 -1.11116278 -0.74200575  2.57475919  1.07321332\n",
            " -1.86613451 -0.64717693  1.08224081  0.17667032 -0.83532823 -1.69499832\n",
            "  1.13341723  1.04853072 -2.12832537 -1.43713939  0.17793711  1.39442275\n",
            "  0.29132019 -0.08200619  0.64424261  0.32807995  0.85743275 -0.93696928\n",
            "  0.18007496 -1.42337059 -0.36775578 -1.52328799 -0.6347717   0.98740384\n",
            " -1.01601962  2.04572375  0.24999852  0.65116253 -1.26602354  1.3741556\n",
            " -0.60990513  0.03075795  0.81965668  1.45431373 -0.58367645  0.41534745\n",
            "  0.66702578  0.8694953  -1.20270333  2.86176918 -2.68159245 -1.16881176\n",
            " -0.58416422  0.8182497   1.59043723 -0.25828823  0.44702904  1.93841974\n",
            " -0.39031935 -0.58069634  1.94898697 -1.86255134]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jI5qcSDfL9iC"
      },
      "source": [
        "## Array indexing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M-E4MUeVL9iC"
      },
      "source": [
        "Numpy offers several ways to index into arrays."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QYv4JyIEL9iD"
      },
      "source": [
        "**Slicing:** Similar to Python lists, numpy arrays can be sliced.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QNO_wpcDgs1f",
        "outputId": "be6c019d-061b-4a6b-db92-48dcc9489b95"
      },
      "source": [
        "print(f'Full Vector a={a}')\n",
        "print(f'Access to ONE element a[0]={a[0]}')\n",
        "print(f'Access from start to a given position a[:2]={a[:2]}')\n",
        "print(f'Access from a position to the end     a[2:]={a[2:]}')\n",
        "print(f'Access from one position to another   a[1:2]={a[1:2]}')\n",
        "print(f'Access al último elemento             a[-1]={a[-1]}')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Full Vector a=[[0. 0.]\n",
            " [0. 0.]]\n",
            "Access to ONE element a[0]=[0. 0.]\n",
            "Access from start to a given position a[:2]=[[0. 0.]\n",
            " [0. 0.]]\n",
            "Access from a position to the end     a[2:]=[]\n",
            "Access from one position to another   a[1:2]=[[0. 0.]]\n",
            "Access al último elemento             a[-1]=[0. 0.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ajtsCrVBgxP9"
      },
      "source": [
        "\n",
        "Since arrays may be multidimensional, you must specify a slice for each dimension of the array:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wLWA0udwL9iD",
        "outputId": "06ea568c-0d28-42a8-99ae-9f62bbde5e4d"
      },
      "source": [
        "# Create the following rank 2 array with shape (3, 4)\n",
        "# [[ 1  2  3  4]\n",
        "#  [ 5  6  7  8]\n",
        "#  [ 9 10 11 12]]\n",
        "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
        "\n",
        "# Use slicing to pull out the subarray consisting of the first 2 rows\n",
        "# and columns 1 and 2; b is the following array of shape (2, 2):\n",
        "# [[2 3]\n",
        "#  [6 7]]\n",
        "b = a[:2, 1:3]\n",
        "print(b)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[2 3]\n",
            " [6 7]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KahhtZKYL9iF"
      },
      "source": [
        "A slice of an array is a view into the same data, so modifying it will modify the original array."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1kmtaFHuL9iG",
        "outputId": "509dde11-8571-467a-e0ac-a7aaa44992b9"
      },
      "source": [
        "print(a[0, 1])\n",
        "b[0, 0] = 77    # b[0, 0] is the same piece of data as a[0, 1]\n",
        "print(a[0, 1])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2\n",
            "77\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_Zcf3zi-L9iI"
      },
      "source": [
        "You can also **mix integer indexing with slice indexing**. However, doing so will yield an array of lower rank than the original array. Note that this is quite different from the way that MATLAB handles array slicing:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G6lfbPuxL9iJ",
        "outputId": "b5688816-c2eb-4c9e-c892-3a538db60353"
      },
      "source": [
        "# Create the following rank 2 array with shape (3, 4)\n",
        "a = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])\n",
        "print(a)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 1  2  3  4]\n",
            " [ 5  6  7  8]\n",
            " [ 9 10 11 12]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NCye3NXhL9iL"
      },
      "source": [
        "Two ways of accessing the data in the middle row of the array.\n",
        "Mixing integer indexing with slices yields an array of lower rank,\n",
        "while using only slices yields an array of the same rank as the\n",
        "original array:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EOiEMsmNL9iL",
        "outputId": "3854f3a5-8902-4229-aa98-5cd8fb7c370e"
      },
      "source": [
        "row_r1 = a[1, :]    # Rank 1 view of the second row of a\n",
        "row_r2 = a[1:2, :]  # Rank 2 view of the second row of a\n",
        "row_r3 = a[[1], :]  # Rank 2 view of the second row of a\n",
        "print(row_r1, row_r1.shape)\n",
        "print(row_r2, row_r2.shape)\n",
        "print(row_r3, row_r3.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[5 6 7 8] (4,)\n",
            "[[5 6 7 8]] (1, 4)\n",
            "[[5 6 7 8]] (1, 4)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 254
        },
        "id": "pi6g3vgSMFtm",
        "outputId": "82a6929f-4c05-41f3-e5da-1af78f084f22"
      },
      "source": [
        "row_r1 = a[1, :]    # Rank 1 view of the second row of a\n",
        "row_r2 = a[1:2, :]\n",
        "\n",
        "print(row_r1[1])\n",
        "\n",
        "print(row_r2[1])\n",
        "\n",
        "print(row_r2[0,1])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "error",
          "ename": "IndexError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-20-78266ba2bd08>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrow_r1\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrow_r2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\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      7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrow_r2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mIndexError\u001b[0m: index 1 is out of bounds for axis 0 with size 1"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JXu73pfDL9iN"
      },
      "source": [
        "# We can make the same distinction when accessing columns of an array:\n",
        "col_r1 = a[:, 1]\n",
        "col_r2 = a[:, 1:2]\n",
        "print(col_r1, col_r1.shape)\n",
        "print()\n",
        "print(col_r2, col_r2.shape)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VP3916bOL9iP"
      },
      "source": [
        "**Integer array indexing:** When you index into numpy arrays using slicing, the resulting array view will always be a subarray of the original array. In contrast, integer array indexing allows you to construct arbitrary arrays using the data from another array. Here is an example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TBnWonIDL9iP"
      },
      "source": [
        "a = np.array([[1,2], [3, 4], [5, 6]])\n",
        "\n",
        "# An example of integer array indexing.\n",
        "# The returned array will have shape (3,) and\n",
        "print(a[[0, 1, 2], [0, 1, 0]])\n",
        "\n",
        "# The above example of integer array indexing is equivalent to this:\n",
        "print(np.array([a[0, 0], a[1, 1], a[2, 0]]))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n7vuati-L9iR"
      },
      "source": [
        "# When using integer array indexing, you can reuse the same\n",
        "# element from the source array:\n",
        "print(a[[0, 0], [1, 1]])\n",
        "\n",
        "# Equivalent to the previous integer array indexing example\n",
        "print(np.array([a[0, 1], a[0, 1]]))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kaE8dBGgL9id"
      },
      "source": [
        "**Boolean array indexing:** Boolean array indexing lets you pick out arbitrary elements of an array. Frequently this type of indexing is used to select the elements of an array that satisfy some condition. Here is an example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "32PusjtKL9id"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "a = np.array([[1,2], [3, 4], [5, 6]])\n",
        "\n",
        "bool_idx = (a > 2)  # Find the elements of a that are bigger than 2;\n",
        "                    # this returns a numpy array of Booleans of the same\n",
        "                    # shape as a, where each slot of bool_idx tells\n",
        "                    # whether that element of a is > 2.\n",
        "\n",
        "print(bool_idx)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cb2IRMXaL9if"
      },
      "source": [
        "# We use boolean array indexing to construct a rank 1 array\n",
        "# consisting of the elements of a corresponding to the True values\n",
        "# of bool_idx\n",
        "print(a[bool_idx])\n",
        "\n",
        "# We can do all of the above in a single concise statement:\n",
        "print(a[a > 2])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CdofMonAL9ih"
      },
      "source": [
        "For brevity we have left out a lot of details about numpy array indexing; if you want to know more you should read the documentation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jTctwqdQL9ih"
      },
      "source": [
        "##Datatypes"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kSZQ1WkIL9ih"
      },
      "source": [
        "Every numpy array is a grid of elements of the same type. Numpy provides a large set of numeric datatypes that you can use to construct arrays. Numpy tries to guess a datatype when you create an array, but functions that construct arrays usually also include an optional argument to explicitly specify the datatype. Here is an example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4za4O0m5L9ih"
      },
      "source": [
        "x = np.array([1, 2])  # Let numpy choose the datatype\n",
        "y = np.array([1.0, 2.0])  # Let numpy choose the datatype\n",
        "z = np.array([1, 2], dtype=np.int64)  # Force a particular datatype\n",
        "\n",
        "print(x.dtype, y.dtype, z.dtype)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RLVIsZQpL9ik"
      },
      "source": [
        "You can read all about numpy datatypes in the [documentation](http://docs.scipy.org/doc/numpy/reference/arrays.dtypes.html)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TuB-fdhIL9ik"
      },
      "source": [
        "##Array math"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "18e8V8elL9ik"
      },
      "source": [
        "Basic mathematical functions operate elementwise on arrays, and are available both as operator overloads and as functions in the numpy module:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gHKvBrSKL9il"
      },
      "source": [
        "x = np.array([[1,2],[3,4]], dtype=np.float64)\n",
        "y = np.array([[5,6],[7,8]], dtype=np.float64)\n",
        "\n",
        "# Elementwise sum; both produce the array\n",
        "print(x + y)\n",
        "print(np.add(x, y))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1fZtIAMxL9in"
      },
      "source": [
        "# Elementwise difference; both produce the array\n",
        "print(x - y)\n",
        "print(np.subtract(x, y))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nil4AScML9io"
      },
      "source": [
        "# Elementwise product; both produce the array\n",
        "print(x * y)\n",
        "print(np.multiply(x, y))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0JoA4lH6L9ip"
      },
      "source": [
        "# Elementwise division; both produce the array\n",
        "# [[ 0.2         0.33333333]\n",
        "#  [ 0.42857143  0.5       ]]\n",
        "print(x / y)\n",
        "print(np.divide(x, y))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g0iZuA6bL9ir"
      },
      "source": [
        "# Elementwise square root; produces the array\n",
        "# [[ 1.          1.41421356]\n",
        "#  [ 1.73205081  2.        ]]\n",
        "print(np.sqrt(x))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KDRjuTpAjdtm"
      },
      "source": [
        "Remember: when using lists, the symbol `+` does NOT add, but concatenates two lists"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-YMyNq8jk3AE"
      },
      "source": [
        "b = [1,2,3]\n",
        "print(f'b+b: {b+b}')\n",
        "#print(f'b*b: {b*b}')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a5d_uujuL9it"
      },
      "source": [
        "Note that unlike MATLAB, `*` is elementwise multiplication, not matrix multiplication. We instead use the dot function to compute inner products of vectors, to multiply a vector by a matrix, and to multiply matrices. dot is available both as a function in the numpy module and as an instance method of array objects:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I3FnmoSeL9iu"
      },
      "source": [
        "x = np.array([[1,2],[3,4]])\n",
        "y = np.array([[5,6],[7,8]])\n",
        "\n",
        "v = np.array([9,10])\n",
        "w = np.array([11, 12])\n",
        "\n",
        "# Inner product of vectors; both produce 219\n",
        "print(v.dot(w))\n",
        "print(np.dot(v, w))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vmxPbrHASVeA"
      },
      "source": [
        "You can also use the `@` operator which is equivalent to numpy's `dot` operator."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vyrWA-mXSdtt"
      },
      "source": [
        "print(v @ w)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zvUODeTxL9iw"
      },
      "source": [
        "# Matrix / vector product; both produce the rank 1 array [29 67]\n",
        "print(x.dot(v))\n",
        "print(np.dot(x, v))\n",
        "print(x @ v)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3V_3NzNEL9iy"
      },
      "source": [
        "# Matrix / matrix product; both produce the rank 2 array\n",
        "# [[19 22]\n",
        "#  [43 50]]\n",
        "print(x.dot(y))\n",
        "print(np.dot(x, y))\n",
        "print(x @ y)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FbE-1If_L9i0"
      },
      "source": [
        "Numpy provides many useful functions for performing computations on arrays; one of the most useful is `sum`:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DZUdZvPrL9i0"
      },
      "source": [
        "x = np.array([[1,2],[3,4]])\n",
        "\n",
        "print(np.sum(x))  # Compute sum of all elements; prints \"10\"\n",
        "print(np.sum(x, axis=0))  # Compute sum of each column; prints \"[4 6]\"\n",
        "print(np.sum(x, axis=1))  # Compute sum of each row; prints \"[3 7]\""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ahdVW4iUL9i3"
      },
      "source": [
        "You can find the full list of mathematical functions provided by numpy in the [documentation](http://docs.scipy.org/doc/numpy/reference/routines.math.html).\n",
        "\n",
        "Apart from computing mathematical functions using arrays, we frequently need to reshape or otherwise manipulate data in arrays. The simplest example of this type of operation is transposing a matrix; to transpose a matrix, simply use the T attribute of an array object:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "63Yl1f3oL9i3"
      },
      "source": [
        "print(x)\n",
        "print(\"transpose\\n\", x.T)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mkk03eNIL9i4"
      },
      "source": [
        "v = np.array([[1,2,3]])\n",
        "print(v )\n",
        "print(\"transpose\\n\", v.T)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yLXvF7mLmZXc"
      },
      "source": [
        "## String vectors methods"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QXH0W6MXm8-S"
      },
      "source": [
        "b = np.array([\"hello\",\"world\"])\n",
        "print(f'b+b: {np.core.defchararray.add(b, b)}')\n",
        "print(f'\\'hello\\'*3: {\"hello\"*3}')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ldAhwIWLnjaD"
      },
      "source": [
        "## Vector Operations with `nan`"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "reOl4Gnnn2K-"
      },
      "source": [
        "You can find help on functions:\n",
        "\n",
        "- `np.sum?`\n",
        "- `np.mean?`\n",
        "- `np.std?`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9Tgl4kVbn19m",
        "outputId": "28bde998-9f39-499d-d128-7700f86f5eae"
      },
      "source": [
        "a = np.array([1,2,float('nan')])\n",
        "print(f'a.sum: {a.sum()}')\n",
        "print(f'a.mean: {a.mean()}')\n",
        "print(f'a.std: {a.std():.2f}')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "a.sum: nan\n",
            "a.mean: nan\n",
            "a.std: nan\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bTYKlaZpn6NR",
        "outputId": "9d7f50d8-b8f0-4dba-b87c-4440a663869d"
      },
      "source": [
        "print(f'np.nansum(a): {np.nansum(a)}')\n",
        "print(f'np.nanmean(a): {np.nanmean(a)}')\n",
        "print(f'np.nanstd(a): {np.nanstd(a):.2f}')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "np.nansum(a): 3.0\n",
            "np.nanmean(a): 1.5\n",
            "np.nanstd(a): 0.50\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "REfLrUTcL9i7"
      },
      "source": [
        "##Broadcasting"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EygGAMWqL9i7"
      },
      "source": [
        "Broadcasting is a powerful mechanism that allows numpy to work with arrays of different shapes when performing arithmetic operations. Frequently we have a smaller array and a larger array, and we want to use the smaller array multiple times to perform some operation on the larger array.\n",
        "\n",
        "For example, suppose that we want to add a constant vector to each row of a matrix. We could do it like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WEEvkV1ZL9i7",
        "outputId": "f2e6f936-2459-462c-830c-0db49dbd2e0a"
      },
      "source": [
        "# We will add the vector v to each row of the matrix x,\n",
        "# storing the result in the matrix y\n",
        "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
        "v = np.array([1, 0, 1])\n",
        "y = np.empty_like(x)   # Create an empty matrix with the same shape as x\n",
        "\n",
        "# Add the vector v to each row of the matrix x with an explicit loop\n",
        "for i in range(4):\n",
        "    y[i, :] = x[i, :] + v\n",
        "\n",
        "print(y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 2  2  4]\n",
            " [ 5  5  7]\n",
            " [ 8  8 10]\n",
            " [11 11 13]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2OlXXupEL9i-"
      },
      "source": [
        "This works; however when the matrix `x` is very large, computing an explicit loop in Python could be slow. Note that adding the vector v to each row of the matrix `x` is equivalent to forming a matrix `vv` by stacking multiple copies of `v` vertically, then performing elementwise summation of `x` and `vv`. We could implement this approach like this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vS7UwAQQL9i-",
        "outputId": "169cd6a0-0a80-4fb2-8a29-623c931b122e"
      },
      "source": [
        "vv = np.tile(v, (4, 1))  # Stack 4 copies of v on top of each other\n",
        "print(vv)                # Prints \"[[1 0 1]\n",
        "                         #          [1 0 1]\n",
        "                         #          [1 0 1]\n",
        "                         #          [1 0 1]]\""
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[1 0 1]\n",
            " [1 0 1]\n",
            " [1 0 1]\n",
            " [1 0 1]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "d6fvsZigKCMQ",
        "outputId": "572c8c62-e0b7-4cd6-859c-279e4844d723"
      },
      "source": [
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3],\n",
              "       [ 4,  5,  6],\n",
              "       [ 7,  8,  9],\n",
              "       [10, 11, 12]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rmYm7qajKGSg",
        "outputId": "a9270408-23f5-430b-9ddc-835e0dada6df",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "v"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 0, 1])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 86
        },
        "id": "N0hJphSIL9jA",
        "outputId": "def6a757-170c-43bf-8728-732dfb133273"
      },
      "source": [
        "y = x + vv  # Add x and vv elementwise\n",
        "print(y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 2  2  4]\n",
            " [ 5  5  7]\n",
            " [ 8  8 10]\n",
            " [11 11 13]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zHos6RJnL9jB"
      },
      "source": [
        "Numpy broadcasting allows us to perform this computation without actually creating multiple copies of v. Consider this version, using broadcasting:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 86
        },
        "id": "vnYFb-gYL9jC",
        "outputId": "df3bea8a-ad72-4a83-90bb-306b55c6fb93"
      },
      "source": [
        "# We will add the vector v to each row of the matrix x,\n",
        "# storing the result in the matrix y\n",
        "x = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
        "v = np.array([1, 0, 1])\n",
        "y = x + v  # Add v to each row of x using broadcasting\n",
        "print(y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 2  2  4]\n",
            " [ 5  5  7]\n",
            " [ 8  8 10]\n",
            " [11 11 13]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "08YyIURKL9jH"
      },
      "source": [
        "The line `y = x + v` works even though `x` has shape `(4, 3)` and `v` has shape `(3,)` due to broadcasting; this line works as if v actually had shape `(4, 3)`, where each row was a copy of `v`, and the sum was performed elementwise.\n",
        "\n",
        "Broadcasting follows difficult rules: try reading the explanation from the [documentation](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html) or this [explanation](http://wiki.scipy.org/EricsBroadcastingDoc).\n",
        "\n",
        "Functions that support broadcasting are known as universal functions. You can find the list of all universal functions in the [documentation](http://docs.scipy.org/doc/numpy/reference/ufuncs.html#available-ufuncs).\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "89e2FXxFL9jQ"
      },
      "source": [
        "Broadcasting typically makes your code more concise and faster, so you should strive to use it where possible."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iF3ZtwVNL9jQ"
      },
      "source": [
        "This brief overview has touched on many of the important things that you need to know about numpy, but is far from complete. Check out the [numpy reference](http://docs.scipy.org/doc/numpy/reference/) to find out much more about numpy."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tEINf4bEL9jR"
      },
      "source": [
        "# 4 Visualization libraries\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "* Matplotlib\n",
        "\n",
        "  - MatPlotLib is a flexible graphics display package.\n",
        "\n",
        "  - It is powerful but somewhat difficult for novice users.\n",
        "  - Documentation <https://matplotlib.org/contents.html>\n",
        "  - Quick Start Tutorial <https://matplotlib.org/users/pyplot_tutorial.html>\n",
        "\n",
        "* Plotnine\n",
        "\n",
        "  - Plotnine makes it much easier to visualize the most common data.\n",
        "  - It is built on top of Matplotlib and offers high-level facilities\n",
        "  - It is similar to the well-known and widely used `ggplot2` package from `R`.\n",
        "  - Documentation <https://plotnine.readthedocs.io/en/stable/index.html>\n",
        "  - Quick Start Tutorials <https://plotnine.readthedocs.io/en/stable/tutorials.html>\n",
        "\n",
        "\n",
        "> Note:\n",
        "> In Python there are a wide variety of packages for graphical data representation. Some examples are [Seaborn](https://seaborn.pydata.org/), [Bokeh](https://bokeh.org/), [Altair](https://altair-viz.github.io/) and for interactive graphics [Plotly](https://plotly.com/).\n",
        "> Each of them have special characteristics, and pros and cons. It is difficult to recommend one over the other for every situation.\n",
        "> For 2D graphics that are not interactive my recommendation is [Plotnine](https://plotnine.readthedocs.io/en/stable/) or Seaborn.\n"
      ],
      "metadata": {
        "id": "MBaUJBZfz9s6"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0hgVWLaXL9jR"
      },
      "source": [
        "## (Brief) Intro to Matplotlib\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cmh_7c6KL9jR"
      },
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jOsaA5hGL9jS"
      },
      "source": [
        "By running this special iPython command, we will be displaying plots inline:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ijpsmwGnL9jT"
      },
      "source": [
        "%matplotlib inline"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U5Z_oMoLL9jV"
      },
      "source": [
        "###Plotting"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6QyFJ7dhL9jV"
      },
      "source": [
        "The most important function in `matplotlib` is plot, which allows you to plot 2D data. Here is a simple example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "pua52BGeL9jW",
        "outputId": "9ac3ee0f-7ff7-463b-b901-c33d21a2b10c"
      },
      "source": [
        "# Compute the x and y coordinates for points on a sine curve\n",
        "x = np.arange(0, 3 * np.pi, 0.1)\n",
        "y = np.sin(x)\n",
        "\n",
        "# Plot the points using matplotlib\n",
        "plt.plot(x, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f0f3a0b4208>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 105
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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UlImgpa2dNTsrmDEq2cpCDhiWHMOQpOgeP8sxnrGqoAKx1kKOmZOVyqHqenaW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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9W2VAcLiL9jX"
      },
      "source": [
        "With just a little bit of extra work we can easily plot multiple lines at once, and add a title, legend, and axis labels:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "TfCQHJ5AL9jY",
        "outputId": "fdb9c033-0f06-4041-a69d-a0f3a54c7206"
      },
      "source": [
        "y_sin = np.sin(x)\n",
        "y_cos = np.cos(x)\n",
        "\n",
        "# Plot the points using matplotlib\n",
        "plt.plot(x, y_sin)\n",
        "plt.plot(x, y_cos)\n",
        "plt.xlabel('x axis label')\n",
        "plt.ylabel('y axis label')\n",
        "plt.title('Sine and Cosine')\n",
        "plt.legend(['Sine', 'Cosine'])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f0f39c04780>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 106
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3W4qrWZieQFCAl/mmgyOMaq0la203lpU5sAm6O3wi+2qTw33l8UKj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\nhJOkqACmAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R5IeAY03L9ja"
      },
      "source": [
        "###Subplots"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CfUzwJg0L9ja"
      },
      "source": [
        "You can plot different things in the same figure using the subplot function. Here is an example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "dM23yGH9L9ja",
        "outputId": "14dfa5ea-f453-4da5-a2ee-fea0de8f72d9"
      },
      "source": [
        "# Compute the x and y coordinates for points on sine and cosine curves\n",
        "x = np.arange(0, 3 * np.pi, 0.1)\n",
        "y_sin = np.sin(x)\n",
        "y_cos = np.cos(x)\n",
        "\n",
        "# Set up a subplot grid that has height 2 and width 1,\n",
        "# and set the first such subplot as active.\n",
        "plt.subplot(2, 1, 1)\n",
        "\n",
        "# Make the first plot\n",
        "plt.plot(x, y_sin)\n",
        "plt.title('Sine')\n",
        "\n",
        "# Set the second subplot as active, and make the second plot.\n",
        "plt.subplot(2, 1, 2)\n",
        "plt.plot(x, y_cos)\n",
        "plt.title('Cosine')\n",
        "\n",
        "# Show the figure.\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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LIAx4BxhqZC4hLMGmilwpNVAptUcplamUetToPJaklGqjlFqrlNqllNqplLrX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\nTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gLtsST5SL9jc"
      },
      "source": [
        "You can read much more about the `subplot` function in the [documentation](http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.subplot)."
      ]
    }
  ]
}