python_tutorial/Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "h9OjSt_q0qIp"
   },
   "source": [
    "# Python3 Tutorial: Advanced Machine Learning Fall 2019"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "F7GLlh2D0qI0"
   },
   "source": [
    "Adapted from [Ian Kinsella](http://stat.columbia.edu/department-directory/name/ian-kinsella/), [Volodymyr Kuleshov's](http://web.stanford.edu/~kuleshov/) and [Isaac Caswell's](https://symsys.stanford.edu/viewing/symsysaffiliate/21335) CS228 Python [tutorial](https://github.com/kuleshov/cs228-material/blob/master/tutorials/python/cs228-python-tutorial.ipynb). Most examples are copied explicity, so I would like to thank them for their thorough work and encourage any students interested in learning the equivalent material for Python 2.7 to check it out."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "r6s4oSgB0qI1"
   },
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xszHfSqD0qI2"
   },
   "source": [
    "Python is a general-purpose programming language that prioritizes programmer efficiency, ease of use, and readability. Python's flexibility makes it a powerful tool for a diverse range of applications from web development to scientific computing. As a result, Python has become a standard tool for modern machine learning due to having access to a wide range of cutting-edge libraries. For this reason, we are requiring that you use Python and become familiar with a small number of these libraries. In this tutorial, I will introduce the basic concepts neccessary to make the transition to Python from another high-level programming language (R, Matlab, Julia, ect.)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "5rRzbmHk0qI3"
   },
   "source": [
    "## Your Development Environment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-FFLtRUf0qI3"
   },
   "source": [
    "We highly recommend the use of [Jupyter Notebooks](https://jupyter.readthedocs.io/en/latest/) for scripting reproduceable analyses and generating informal reports. These notebooks provide a convenient development environment to intregrate [Markdown](), [Latex](), plots, and code in a single document. However, for this course we will be having you use Google's [Colab](https://colab.research.google.com/) to create your homeworks and reports. This will avoid the requirement of installing an up to date python distribution, managing environments, and running notebooks on your local machines. Moreover, the results can be published to html to facilitate submission and grading of assignments. The interface is easy to use, so I will introduce features as we progress through the demo and you should be able to get a feel for it by following along.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Nppzh7Zs0qI4"
   },
   "source": [
    "### Colab shortcuts\n",
    "\n",
    "Use Ctrl/Command+M+H to display a menu with all available keyboard shortcuts. Important shortcuts are Ctrl/Command+Enter to run the selected cell, or Alt+Enter to insert a new cell."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Nppzh7Zs0qI4"
   },
   "source": [
    "### The Virtual Machine\n",
    "\n",
    "When you open a notebook in Colab, the resources used are being hosted on a virtual machine. Prefacing lines with the \"!\" character in code cells allows you to execute basic Unix style commands on the command line. For example, we can explore the machine's file system and available resources."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "colab_type": "code",
    "id": "lEJWV7n7vAvt",
    "outputId": "a302f699-a2d5-4432-eb87-29b101e391af"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Filesystem      Size  Used Avail Use% Mounted on\r\n",
      "overlay          40G  5.8G   32G  16% /\r\n",
      "tmpfs           6.4G     0  6.4G   0% /dev\r\n",
      "tmpfs           6.4G     0  6.4G   0% /sys/fs/cgroup\r\n",
      "tmpfs           6.4G     0  6.4G   0% /opt/bin\r\n",
      "/dev/sda1        46G  6.7G   39G  15% /etc/hosts\r\n",
      "shm              64M     0   64M   0% /dev/shm\r\n",
      "tmpfs           6.4G     0  6.4G   0% /sys/firmware\r\n"
     ]
    }
   ],
   "source": [
    "!df -h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 445
    },
    "colab_type": "code",
    "id": "xlWjL8hYv4q0",
    "outputId": "be673ba2-c9ec-41f6-9c48-ff7b3070812a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Architecture:        x86_64\r\n",
      "CPU op-mode(s):      32-bit, 64-bit\r\n",
      "Byte Order:          Little Endian\r\n",
      "CPU(s):              2\r\n",
      "On-line CPU(s) list: 0,1\r\n",
      "Thread(s) per core:  2\r\n",
      "Core(s) per socket:  1\r\n",
      "Socket(s):           1\r\n",
      "NUMA node(s):        1\r\n",
      "Vendor ID:           GenuineIntel\r\n",
      "CPU family:          6\r\n",
      "Model:               63\r\n",
      "Model name:          Intel(R) Xeon(R) CPU @ 2.30GHz\r\n",
      "Stepping:            0\r\n",
      "CPU MHz:             2300.000\r\n",
      "BogoMIPS:            4600.00\r\n",
      "Hypervisor vendor:   KVM\r\n",
      "Virtualization type: full\r\n",
      "L1d cache:           32K\r\n",
      "L1i cache:           32K\r\n",
      "L2 cache:            256K\r\n",
      "L3 cache:            46080K\r\n",
      "NUMA node0 CPU(s):   0,1\r\n",
      "Flags:               fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ss ht syscall nx pdpe1gb rdtscp lm constant_tsc rep_good nopl xtopology nonstop_tsc cpuid pni pclmulqdq ssse3 fma cx16 sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand hypervisor lahf_lm abm pti fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms xsaveopt\r\n"
     ]
    }
   ],
   "source": [
    "!lscpu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "uuEhjrW3v7Pt",
    "outputId": "82bb8dfe-faef-4f97-f828-1295cb6951d6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              total        used        free      shared  buff/cache   available\r\n",
      "Mem:          13022         596         238           0       12187       12169\r\n",
      "Swap:             0           0           0\r\n"
     ]
    }
   ],
   "source": [
    "!free -m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-FvcjAgbw7_K"
   },
   "source": [
    "### Creating A Working Environment On Your Virtual Machine\n",
    "\n",
    "The availability of Unix-style commands means that we can use typical python tools like ```pip``` to manage the packages installed in our python environment. Fortunately, Colab is oriented towards datascience so we can see below that most packages we will need to use in this course come pre-installed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 2074
    },
    "colab_type": "code",
    "id": "N2g2VovTwpOa",
    "outputId": "0a355498-2650-4bf6-c3c2-f039cbb694a5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Package                  Version  \r\n",
      "------------------------ ---------\r\n",
      "absl-py                  0.4.1    \r\n",
      "altair                   2.2.2    \r\n",
      "astor                    0.7.1    \r\n",
      "beautifulsoup4           4.6.3    \r\n",
      "bleach                   2.1.4    \r\n",
      "bokeh                    0.13.0   \r\n",
      "cachetools               2.1.0    \r\n",
      "certifi                  2018.8.24\r\n",
      "chardet                  3.0.4    \r\n",
      "crcmod                   1.7      \r\n",
      "cycler                   0.10.0   \r\n",
      "decorator                4.3.0    \r\n",
      "entrypoints              0.2.3    \r\n",
      "future                   0.16.0   \r\n",
      "gast                     0.2.0    \r\n",
      "google-api-core          1.3.0    \r\n",
      "google-api-python-client 1.6.7    \r\n",
      "google-auth              1.4.2    \r\n",
      "google-auth-httplib2     0.0.3    \r\n",
      "google-auth-oauthlib     0.2.0    \r\n",
      "google-cloud-bigquery    1.1.0    \r\n",
      "google-cloud-core        0.28.1   \r\n",
      "google-cloud-language    1.0.2    \r\n",
      "google-cloud-storage     1.8.0    \r\n",
      "google-cloud-translate   1.3.1    \r\n",
      "google-colab             0.0.1a1  \r\n",
      "google-resumable-media   0.3.1    \r\n",
      "googleapis-common-protos 1.5.3    \r\n",
      "grpcio                   1.14.2   \r\n",
      "h5py                     2.8.0    \r\n",
      "html5lib                 1.0.1    \n",
      "httplib2                 0.11.3   \n",
      "idna                     2.6      \n",
      "ipykernel                4.6.1    \n",
      "ipython                  5.5.0    \n",
      "ipython-genutils         0.2.0    \n",
      "Jinja2                   2.10     \n",
      "joblib                   0.12.3   \n",
      "jsonschema               2.6.0    \n",
      "jupyter-client           5.2.3    \n",
      "jupyter-core             4.4.0    \n",
      "Keras                    2.1.6    \n",
      "Markdown                 2.6.11   \n",
      "MarkupSafe               1.0      \n",
      "matplotlib               2.1.2    \n",
      "mistune                  0.8.3    \n",
      "mpmath                   1.0.0    \n",
      "nbconvert                5.3.1    \n",
      "nbformat                 4.4.0    \n",
      "networkx                 2.1      \n",
      "nltk                     3.2.5    \n",
      "notebook                 5.2.2    \n",
      "numpy                    1.14.5   \n",
      "oauth2client             4.1.2    \n",
      "oauthlib                 2.1.0    \n",
      "olefile                  0.45.1   \n",
      "opencv-python            3.4.2.17 \n",
      "packaging                17.1     \n",
      "pandas                   0.22.0   \n",
      "pandas-gbq               0.4.1    \n",
      "pandocfilters            1.4.2    \n",
      "patsy                    0.5.0    \n",
      "pexpect                  4.6.0    \n",
      "pickleshare              0.7.4    \n",
      "Pillow                   4.0.0    \n",
      "pip                      18.0     \n",
      "plotly                   1.12.12  \n",
      "pluggy                   0.7.1    \n",
      "portpicker               1.2.0    \n",
      "prompt-toolkit           1.0.15   \n",
      "protobuf                 3.6.1    \n",
      "psutil                   5.4.7    \n",
      "ptyprocess               0.6.0    \n",
      "py                       1.6.0    \n",
      "pyasn1                   0.4.4    \n",
      "pyasn1-modules           0.2.2    \n",
      "PyDrive                  1.3.1    \n",
      "Pygments                 2.1.3    \n",
      "pymc3                    3.5      \n",
      "pyparsing                2.2.0    \n",
      "pystache                 0.5.4    \n",
      "python-dateutil          2.5.3    \n",
      "pytz                     2018.5   \n",
      "PyWavelets               0.5.2    \n",
      "PyYAML                   3.13     \n",
      "pyzmq                    16.0.4   \n",
      "requests                 2.18.4   \n",
      "requests-oauthlib        1.0.0    \n",
      "rsa                      3.4.2    \n",
      "scikit-image             0.13.1   \n",
      "scikit-learn             0.19.2   \n",
      "scipy                    0.19.1   \n",
      "seaborn                  0.7.1    \n",
      "setuptools               39.1.0   \n",
      "simplegeneric            0.8.1    \n",
      "six                      1.11.0   \n",
      "statsmodels              0.8.0    \n",
      "sympy                    1.1.1    \n",
      "tensorboard              1.10.0   \n",
      "tensorflow               1.10.1   \n",
      "tensorflow-hub           0.1.1    \n",
      "termcolor                1.1.0    \n",
      "terminado                0.8.1    \n",
      "testpath                 0.3.1    \n",
      "Theano                   1.0.2    \n",
      "toolz                    0.9.0    \n",
      "tornado                  4.5.3    \n",
      "tqdm                     4.25.0   \n",
      "traitlets                4.3.2    \n",
      "typing                   3.6.6    \n",
      "uritemplate              3.0.0    \n",
      "urllib3                  1.22     \n",
      "vega-datasets            0.5.0    \n",
      "virtualenv               16.0.0   \n",
      "wcwidth                  0.1.7    \n",
      "webencodings             0.5.1    \n",
      "Werkzeug                 0.14.1   \n",
      "wheel                    0.31.1   \n",
      "xgboost                  0.7.post4\n"
     ]
    }
   ],
   "source": [
    "!pip list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4NmUz7_byx12"
   },
   "source": [
    "If at any point you need to install a package which is not already available, this can be done from a code cell as follows: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 187
    },
    "colab_type": "code",
    "id": "HHArgpzTwsfy",
    "outputId": "a257445a-a63f-4025-b6cc-838f33da4d7d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: bokeh in /usr/local/lib/python3.6/dist-packages (0.13.0)\r\n",
      "Requirement already satisfied: numpy>=1.7.1 in /usr/local/lib/python3.6/dist-packages (from bokeh) (1.14.5)\r\n",
      "Requirement already satisfied: six>=1.5.2 in /usr/local/lib/python3.6/dist-packages (from bokeh) (1.11.0)\r\n",
      "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from bokeh) (2.5.3)\r\n",
      "Requirement already satisfied: PyYAML>=3.10 in /usr/local/lib/python3.6/dist-packages (from bokeh) (3.13)\r\n",
      "Requirement already satisfied: Jinja2>=2.7 in /usr/local/lib/python3.6/dist-packages (from bokeh) (2.10)\r\n",
      "Requirement already satisfied: packaging>=16.8 in /usr/local/lib/python3.6/dist-packages (from bokeh) (17.1)\n",
      "Requirement already satisfied: tornado>=4.3 in /usr/local/lib/python3.6/dist-packages (from bokeh) (4.5.3)\n",
      "Requirement already satisfied: MarkupSafe>=0.23 in /usr/local/lib/python3.6/dist-packages (from Jinja2>=2.7->bokeh) (1.0)\n",
      "Requirement already satisfied: pyparsing>=2.0.2 in /usr/local/lib/python3.6/dist-packages (from packaging>=16.8->bokeh) (2.2.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install bokeh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7KoB-zQpzizY"
   },
   "source": [
    "An important thing to note is that the VM hosts for the notebooks are ephemeral, meaning any change you make to it's state will not be persisted. For example, if you upload a dataset or save results to your working directory they will NOT neccessarily be there when you return to the notebook later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "N0wpOUVhvaEx",
    "outputId": "492d0638-cad6-48cd-ed56-d5d509ef4473"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample_data\r\n"
     ]
    }
   ],
   "source": [
    "!ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bKqkWeLRvaPi"
   },
   "outputs": [],
   "source": [
    "!touch example.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "Vrqr16p_veiz",
    "outputId": "b7eabaa6-dd2f-46b2-b1b8-910197a30131"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "example.txt  sample_data\r\n"
     ]
    }
   ],
   "source": [
    "!ls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tI5G-kth0ovo"
   },
   "source": [
    "Above, we see that I created a new text file in my working directory. However, if I let this notebook go idle for a period of time or my VM's lifetime expires, it will be recycled and this file will no longer be present in my working directory. As such, it is important to use the tools we introduce at the end of this lecture to manage data used within or created by the notebooks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "EBkqij2W0qI8"
   },
   "source": [
    "## Submitting Your Homework Assignments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pxYl7ABw0qI8"
   },
   "source": [
    "To make sure grading goes off without a hitch, we will require that you submit all code/figures (and optionally math) by downloading your notebook in ```.html``` format. Unfortunately, the notebooks on Colab are missing the feature to convert these easily, so we have written a notebook to do this for you (see submit.ipynb). Will show this in action at the end of the tutorial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "rlvz2zei0qI9"
   },
   "source": [
    "# [Basic Python](https://docs.python.org/3/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "CcrBAVkj0qI-"
   },
   "source": [
    "## Data Types & Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "0fwHq5Fk0qI_"
   },
   "source": [
    "### [Integers & Floats](https://docs.python.org/3/tutorial/introduction.html#numbers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-0_HvrQr0qI_"
   },
   "source": [
    "Python is a dynamically typed language and mathematical operations work exactly as you would expect. $ y = X \\beta + \\epsilon$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "colab_type": "code",
    "id": "AVnZLGeD0qJA",
    "outputId": "afbc0e43-91da-4fe4-ad55-938f58a0617f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 <class 'int'>\n",
      "4\n",
      "2\n",
      "<class 'float'>\n",
      "5.0\n",
      "1.5\n",
      "6.25\n",
      "<class 'float'>\n"
     ]
    }
   ],
   "source": [
    "x = 3\n",
    "print(x, type(x))\n",
    "print(x + 1)   # Addition;\n",
    "print(x - 1)   # Subtraction;\n",
    "y = 2.5\n",
    "print(type(y)) # Prints \"<type 'float'>\"\n",
    "print(y * 2)   # Multiplication;\n",
    "print(x / 2)   # Division;\n",
    "print(y ** 2)  # Exponentiation;\n",
    "print(type(y*x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "d-ti1q2b0qJF"
   },
   "source": [
    "While Python does not provide unary incerement(```++```) and decrement (```--```) operators, however it does provide syntax for incrementation and decrementation which includes other cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "iIpqirtL0qJF",
    "outputId": "3082971c-ce2b-493f-d21f-acf0b1889cf4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "x += 1  # x = x + 1 \n",
    "print(x)\n",
    "x *= 2  # x = x * 2\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "kI8SAbhl0qJK"
   },
   "source": [
    "### [Booleans](https://docs.python.org/3/tutorial/datastructures.html#more-on-conditions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AwbAeY0C0qJK"
   },
   "source": [
    "Python implements all of the standard logical operators for Boolean variables. However, it provides english keywords to enhance readability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "zqbwybbl0qJL",
    "outputId": "93f39033-8e6f-489b-ce25-d8f86c2e2956"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'bool'>\n",
      "False\n",
      "True\n",
      "False\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "t, f = True, False\n",
    "print(type(t)) # Prints \"<type 'bool'>\"\n",
    "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;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zHY7xy-80qJN"
   },
   "source": [
    "### [Strings](https://docs.python.org/3/tutorial/introduction.html#strings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lZgbrIAc0qJO"
   },
   "source": [
    "Strings in python are technically immutable, however string variables in python are easily reassigned making them appear mutable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "JTATYBgo0qJO",
    "outputId": "648f84c3-567a-4c89-8ed3-e7658bfff0a3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FooFoo Foo\n"
     ]
    }
   ],
   "source": [
    "a = \"Foo\"  # the variable 'a' points to the string \"Foo\"\n",
    "b = a  # 'b' points to the same string \"Foo\" that 'a' points to\n",
    "a = a + a  # 'a' now points to the new string \"FooFoo\",\n",
    "print(a, b) # but b still points to the old \"Foo\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9Kiw1uoo0qJR"
   },
   "source": [
    "Strings variables also contain a number of useful methods to which reassign them to new strings based on their current value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 119
    },
    "colab_type": "code",
    "id": "q4Pyb5PG0qJS",
    "outputId": "a7d19d06-1414-4e68-c86f-5162e0175fdb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello\n",
      "HELLO\n",
      "  hello\n",
      " hello \n",
      "he(ell)(ell)o\n",
      "world\n"
     ]
    }
   ],
   "source": [
    "s = \"hello\"\n",
    "print(s.capitalize())  # Capitalize a string;\n",
    "print(s.upper())       # Convert a string to uppercase;\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 \n",
    "                                # substring with another;\n",
    "print('  world '.strip())  # Strip leading and trailing whitespace;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fP7FpKqR0qJU"
   },
   "source": [
    "Additionally, python provides string formatting which can be used to substitute variable values into a string in place of ```{}``` instances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "QbOyrvE90qJW",
    "outputId": "169e01a8-f403-49f6-a221-95cd9905a4a2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The string variable 'a' contains 6 characters.\n",
      "The value of the <class 'int'> variable 'x' is 8\n"
     ]
    }
   ],
   "source": [
    "print(\"The string variable 'a' contains {} characters.\".format(len(a)))\n",
    "print(\"The value of the {} variable 'x' is {}\".format(type(x), x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Dnx7JkRu0qJZ"
   },
   "source": [
    "## Containers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GTVZsuhf0qJa"
   },
   "source": [
    "Python includes several built-in container types including lists, dictionaries, sets, and tuples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GBeYG0h_0qJb"
   },
   "source": [
    "### [Lists](https://docs.python.org/3/tutorial/introduction.html#lists)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DXWgjVXH0qJb"
   },
   "source": [
    "A list is the Python equivalent of an array, but is resizeable and can contain elements of different types. Note that arrays start at zero and negative indexing works differently than in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "ukirQCDb0qJc",
    "outputId": "84b02310-f953-4a24-ecd6-837de3a9b91f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 2\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "xs = [3, 1, 2]   # Create a list\n",
    "print(xs[0], xs[2])\n",
    "print(xs[-1])  # print(xs[len(xs)-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "XI4vOvIn0qJe",
    "outputId": "c71aae04-1e9f-4cae-8f99-da11c97b1f5d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 1, 'foo']\n"
     ]
    }
   ],
   "source": [
    "xs[2] = 'foo'    # Lists can contain elements of different types\n",
    "print(xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "WSMDncN-0qJj",
    "outputId": "40a02129-93a0-4ebe-df15-287eac025b53"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3, 1, 'foo', 'bar']\n"
     ]
    }
   ],
   "source": [
    "xs.append('bar') # Add a new element to the end of the list\n",
    "print(xs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "kc0oLGwv0qJn",
    "outputId": "2a023991-7e10-49ab-f91f-e674d57123f8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bar [3, 1, 'foo']\n"
     ]
    }
   ],
   "source": [
    "x = xs.pop()     # Remove and return the last element of the list\n",
    "print(x, xs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XWRKE0WH0qJr"
   },
   "source": [
    "#### Slicing\n",
    "\n",
    "Indexing sequential elements of an array is referred to as \"sclicing\" and works hwo you would expect after using R or Matlab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 136
    },
    "colab_type": "code",
    "id": "_hjLXPo70qJs",
    "outputId": "0e05d3cd-89be-48bd-f48d-7f5b2b6d4cd3"
   },
   "outputs": [
    {
     "name": "stdout",
     "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"
     ]
    }
   ],
   "source": [
    "nums = list(range(5)) # range is a built-in function that creates a sequence 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);\n",
    "print(nums[2:])       # Get a slice from index 2 to the end;\n",
    "print(nums[:2])       # Get a slice from the start to index 2 (exclusive);\n",
    "print(nums[:])        # Get a slice of the whole list;\n",
    "print(nums[:-1])      # Slice indices can be negative;\n",
    "nums[2:4] = [8, 9]    # Assign a new sublist to a slice\n",
    "print(nums)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6GtJP7Ze0qJt"
   },
   "source": [
    "#### For Loops, & List Comprehensions\n",
    "\n",
    "You can loop over the elements of a list like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "yLJr1yVR0qJu",
    "outputId": "375891e5-e66b-48ad-f87c-fc36e1fe1cec"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cat\n",
      "dog\n",
      "monkey\n"
     ]
    }
   ],
   "source": [
    "animals = ['cat', 'dog', 'monkey']\n",
    "for animal in animals:\n",
    "    print(animal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "agsY0v5f0qJv"
   },
   "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",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "6lQpZgeN0qJw",
    "outputId": "df40bd35-366d-4bbf-8a71-6437f0363fcf"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#1: cat\n",
      "#2: dog\n",
      "#3: monkey\n"
     ]
    }
   ],
   "source": [
    "animals = ['cat', 'dog', 'monkey']\n",
    "for idx, animal in enumerate(animals):\n",
    "    print('#{}: {}'.format(idx + 1, animal))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "B5aC8OFW0qJz"
   },
   "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",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "chLyyDJ50qJz",
    "outputId": "edc74db4-b7f1-42a8-c881-7fc867cc40e1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 4, 9, 16]\n"
     ]
    }
   ],
   "source": [
    "nums = [0, 1, 2, 3, 4]\n",
    "squares = []\n",
    "for x in nums:\n",
    "    squares.append(x ** 2)\n",
    "print(squares)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "p7L8q8KY0qJ1"
   },
   "source": [
    "You can make this code simpler using a list comprehension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "7REmUSwI0qJ1",
    "outputId": "107a6623-8af7-4fb9-8d8b-206dfd9a5ed2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 4, 9, 16]\n"
     ]
    }
   ],
   "source": [
    "squares = [x ** 2 for x in nums]\n",
    "print(squares)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "H9yFl_E90qJ3"
   },
   "source": [
    "List comprehensions can also contain conditions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "JPPOLZsd0qJ4",
    "outputId": "f9b1aef3-af74-4196-92d3-b7c8b911af14"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 4, 16]\n"
     ]
    }
   ],
   "source": [
    "nums = [0, 1, 2, 3, 4]\n",
    "even_squares = [x ** 2 for x in nums if x % 2 == 0]\n",
    "print(even_squares)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mDwM95Mg0qJ7"
   },
   "source": [
    "### [Dictionaries](https://docs.python.org/3/tutorial/datastructures.html#dictionaries)\n",
    "\n",
    "A dictionary stores (key, value) pairs, similar to a Map in Java or an object in Javascript. You can use it like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "Orfp5Gh20qJ7",
    "outputId": "0154f649-455f-4426-9b76-9d839ce6b60b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feline\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "d = {'cat': 'feline', 'dog': 'canine'}  # Create a new dictionary with some data\n",
    "print(d['cat'])                         # Get an entry from a dictionary;\n",
    "print('cat' in d)                       # Check if a dictionary has a given key;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "yckSZo5L0qJ9",
    "outputId": "68e516f8-5863-4b31-b7dc-880ef2fc8a15"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ursa\n"
     ]
    }
   ],
   "source": [
    "d['bear'] = 'ursa'    # Set an entry in a dictionary\n",
    "print(d['bear'])      # Prints \"ursa\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 164
    },
    "colab_type": "code",
    "id": "j_ebJlXN0qKA",
    "outputId": "c32f6b79-0697-46e1-c6b5-95aa0eaafaa0"
   },
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "ignored",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-27-58339d2299e4>\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[0m\n\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m: 'monkey'"
     ]
    }
   ],
   "source": [
    "print(d['monkey'])     # KeyError: 'monkey' not a key of d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "jJXUHJKy0qKC",
    "outputId": "a552d1d0-62a8-4ac7-ca9e-4bf183da9814"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N/A\n",
      "ursa\n"
     ]
    }
   ],
   "source": [
    "print(d.get('monkey', 'N/A'))  # Get an element with a default; prints \"N/A\"\n",
    "print(d.get('bear', 'N/A'))    # Get an element with a default; prints \"ursa\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "GtYbVZnR0qKD",
    "outputId": "5e148875-3aa9-4497-d9d8-5a7a3469033b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N/A\n"
     ]
    }
   ],
   "source": [
    "del d['bear']                # Remove an element from a dictionary\n",
    "print(d.get('bear', 'N/A'))  # \"bear\" is no longer a key; prints \"N/A\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Gq6Apvtp0qKF"
   },
   "source": [
    "#### For Loops, & Dictionary Comprehensions\n",
    "\n",
    "It is easy to iterate over the keys in a dictionary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "ruQ1COBQ0qKF",
    "outputId": "1437a12d-0968-4fc6-ba2d-3d97e6bc3712"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A person has 2 legs\n",
      "A cat has 4 legs\n",
      "A spider has 8 legs\n"
     ]
    }
   ],
   "source": [
    "d = {'person': 2, 'cat': 4, 'spider': 8}\n",
    "for animal in d:\n",
    "    print('A {} has {} legs'.format(animal, d[animal]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DZheFRfT0qKH"
   },
   "source": [
    "If you want access to keys and their corresponding values, use the items method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "RpWQ7U4a0qKI",
    "outputId": "bf115e38-bc9d-4728-9639-2ac9bbf25c3b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A person has 2 legs\n",
      "A cat has 4 legs\n",
      "A spider has 8 legs\n"
     ]
    }
   ],
   "source": [
    "for animal, legs in d.items():\n",
    "    print('A {} has {} legs'.format(animal, legs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "e80Au7kB0qKL"
   },
   "source": [
    "\n",
    "Dictionary comprehensions: These are similar to list comprehensions, but allow you to easily construct dictionaries. For example:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "-5aKnPXJ0qKM",
    "outputId": "7255610b-23b8-422c-8981-4dbb8657dd93"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16\n",
      "{0: 0, 2: 4, 4: 16, 6: 36}\n"
     ]
    }
   ],
   "source": [
    "even_num_to_square = {x: x ** 2 for x in range(7) if x % 2 == 0}\n",
    "print(even_num_to_square[4])\n",
    "print(even_num_to_square)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yMN5YsKS0qKO"
   },
   "source": [
    "### [Sets](https://docs.python.org/3/tutorial/datastructures.html#sets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "a_rA958l0qKO"
   },
   "source": [
    "A set is an unordered collection of distinct elements. As a simple example, consider the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "qbiU0SG80qKP",
    "outputId": "6aae7ec8-e14c-40ef-f372-fcbe565c6eef"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "False\n"
     ]
    }
   ],
   "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\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "0Hhh9ffX0qKQ",
    "outputId": "8b8af907-9cee-4f79-d09d-70c68214822a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "3\n"
     ]
    }
   ],
   "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;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "9vnQgAmD0qKW",
    "outputId": "1c3ecf28-8701-4e8d-8c1b-754aca6700f8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "2\n"
     ]
    }
   ],
   "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))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AhhuEXZi0qKY"
   },
   "source": [
    "#### For Loops & Set Comprehensions\n",
    "\n",
    "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",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "JQBdaVIP0qKZ",
    "outputId": "db93e241-f572-462c-d402-d668eea97c6c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "#1: dog\n",
      "#2: fish\n",
      "#3: cat\n"
     ]
    }
   ],
   "source": [
    "animals = {'cat', 'dog', 'fish'}\n",
    "for idx, animal in enumerate(animals):\n",
    "    print('#{}: {}'.format(idx + 1, animal))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "lciJj_HZ0qKc"
   },
   "source": [
    "Set comprehensions: Like lists and dictionaries, we can easily construct sets using set comprehensions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "bLlkbIy30qKc",
    "outputId": "6d40f460-d55c-403b-df16-1ab92b3c64e5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2, 3, 4, 5}\n"
     ]
    }
   ],
   "source": [
    "from math import sqrt\n",
    "print({int(sqrt(x)) for x in range(30)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GCLELkzr0qKf"
   },
   "source": [
    "### [Tuples](https://docs.python.org/3/tutorial/datastructures.html#tuples-and-sequences)\n",
    "\n",
    "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",
   "execution_count": 38,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "PQ-3j3mc0qKf",
    "outputId": "9498dedc-ad68-4e97-81eb-8efbc043ac95"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'tuple'>\n",
      "5\n",
      "1\n"
     ]
    }
   ],
   "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)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Lrf1cwTg0qKi"
   },
   "source": [
    "Additionally, tuples are immutable setting their behavior apart from lists. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 164
    },
    "colab_type": "code",
    "id": "PVnF2WBL0qKj",
    "outputId": "5c761278-202d-4419-9a70-977db0534934"
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "ignored",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-39-c8aeb8cd20ae>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mt\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: 'tuple' object does not support item assignment"
     ]
    }
   ],
   "source": [
    "t[0] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "E1pFHxtm0qKl"
   },
   "source": [
    "## [Functions](https://docs.python.org/3/tutorial/controlflow.html#defining-functions)\n",
    "\n",
    "Python functions are defined using the def keyword. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "-CYFUUu60qKl",
    "outputId": "035c3cd0-d439-4eac-a9b0-cdbf4cedb9c3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "negative\n",
      "zero\n",
      "positive\n"
     ]
    }
   ],
   "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))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OtSSoPM30qKp"
   },
   "source": [
    "We will often define functions to take optional keyword arguments, like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "YCcgwd5Y0qKq",
    "outputId": "6fb22497-7c66-4c84-cc1b-b580ad4e8bbd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, Bob.\n",
      "HELLO, FRED!\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Vvs5unmi0qKs"
   },
   "source": [
    "## [Classes](https://docs.python.org/3/tutorial/classes.html)\n",
    "\n",
    "Python has been used as an object oriented language since its inception. As such, the syntax for defining and using classes in is straightforward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "4IqSl8vN0qKs",
    "outputId": "092e371c-dfcc-459b-bda4-514b38c2d7a1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, Fred.\n",
      "HELLO, FRED!\n"
     ]
    }
   ],
   "source": [
    "class Greeter:\n",
    "\n",
    "    # Constructor\n",
    "    def __init__(self, name):\n",
    "        self.name = name  # Create an instance variable\n",
    "\n",
    "    # Instance method\n",
    "    def greet(self, loud=False):\n",
    "        if loud:\n",
    "            print('HELLO, {}!'.format(self.name.upper()))\n",
    "        else:\n",
    "            print('Hello, {}.'.format(self.name))\n",
    "\n",
    "g = Greeter('Fred')  # Construct an instance of the Greeter class\n",
    "g.greet()            # Call an instance method\n",
    "g.greet(loud=True)   # Call an instance method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xAiupI-b0qKu"
   },
   "source": [
    "# [Numpy](https://docs.scipy.org/doc/numpy-1.13.0/index.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FmgCd8Xq0qKu"
   },
   "source": [
    "Numpy is the core library for scientific computing in Python. It provides a high-performance multidimensional array object, and tools for working with these arrays. If you are already familiar with MATLAB, you might find [this](http://wiki.scipy.org/NumPy_for_Matlab_Users) tutorial useful to get started with Numpy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9HEvaxwF0qKv"
   },
   "source": [
    "To use Numpy, we first need to import the numpy package. The following commands will all work, but the first is commonly accepted as best practice and we will use that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "NwCS8XEQ0qKv"
   },
   "outputs": [],
   "source": [
    "import numpy as np  # use functions from numpy by calling 'np.func'\n",
    "# import numpy  # use functions from numpy by calling 'numpy.func'\n",
    "# from numpy import func  # imports the function 'numpy.func' into the namespace as 'func'\n",
    "# from numpy import *  # imports the entire numpy namespace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RcXpwULJ0qKx"
   },
   "source": [
    "## Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "9pBDhWRT0qKy"
   },
   "source": [
    "A numpy array is a grid of values, all of the same type, and is indexed by a tuple of nonnegative integers. 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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tOk2s8Eq0qKy"
   },
   "source": [
    "We can initialize numpy arrays from nested Python lists, and access elements using square brackets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "L5q3Tf560qKz",
    "outputId": "cfe4c652-659a-4d27-8dad-61ac06ab33a0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'> (3,) 1 2 3\n",
      "[5 2 3]\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "0vAIwzvN0qK0",
    "outputId": "93711318-48bc-48c3-8d50-215336840f8f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]]\n"
     ]
    }
   ],
   "source": [
    "b = np.array([[1,2,3],[4,5,6]])   # Create a rank 2 array\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "grVhq6vk0qK2",
    "outputId": "310383ee-b183-436f-9e8a-6a3f237ac05a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 3)\n",
      "1 2 4\n"
     ]
    }
   ],
   "source": [
    "print(b.shape)\n",
    "print(b[0, 0], b[0, 1], b[1, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PQETwBea0qK5"
   },
   "source": [
    "Numpy also provides many functions to create arrays:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "T2KMTE9x0qK5",
    "outputId": "fd85a66e-6227-46de-92ff-75fb2c701e7e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0.]\n",
      " [0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((2,2))  # Create an array of all zeros\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "VmPMTu820qK7",
    "outputId": "d5262017-a15e-4064-de51-3d29f3bb1903"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "b = np.ones((1,2))   # Create an array of all ones\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "QzRw891v0qK8",
    "outputId": "f0b126e2-b637-4fc2-c49a-c063e3acd533"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[7 7]\n",
      " [7 7]]\n"
     ]
    }
   ],
   "source": [
    "c = np.full((2,2), 7) # Create a constant array\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "ChBrHucL0qK_",
    "outputId": "9bbd1959-4324-45dd-ecd4-b956f5292ede"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0.]\n",
      " [0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "d = np.eye(2)        # Create a 2x2 identity matrix\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "ImPZpcPb0qLA",
    "outputId": "abd3e8a1-1a2d-4161-bc4c-8512cf2fbf9a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.52250417 0.93409489]\n",
      " [0.55614622 0.94573446]]\n"
     ]
    }
   ],
   "source": [
    "e = np.random.random((2,2)) # Create an array filled with random values\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3ahtXayr0qLC"
   },
   "source": [
    "### Array Indexing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "IZVB-xwD0qLD"
   },
   "source": [
    "Numpy offers several ways to index into arrays.\n",
    "\n",
    "Slicing: Similar to Python lists, numpy arrays can be sliced. Since arrays may be multidimensional, you must specify a slice for each dimension of the array:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "v7ZUZ6M60qLD",
    "outputId": "ffa1a9c3-5355-41ce-858e-8b7d9c725348"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 3]\n",
      " [6 7]]\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-Xt1p8iT0qLF"
   },
   "source": [
    "A slice of an array is a view into the same data, so modifying it will modify the original array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "dAZ7GbSa0qLH",
    "outputId": "4e68fc89-70a7-4c95-ae9b-4870cbcb8738"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "77\n"
     ]
    }
   ],
   "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])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "E0ScQy0N0qLI"
   },
   "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",
   "execution_count": 54,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "RoSyPGsD0qLJ",
    "outputId": "de5b6a10-f567-418c-d2ff-b88e206a15f5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3  4]\n",
      " [ 5  6  7  8]\n",
      " [ 9 10 11 12]]\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fCK-gYQS0qLN"
   },
   "source": [
    "Two ways of accessing the data in the middle row of the array. Mixing integer indexing with slices yields an array of lower rank, while using only slices yields an array of the same rank as the original array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "wkSOeCJI0qLO",
    "outputId": "86edbbaf-ede4-4ceb-c324-f21f449344e8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 6 7 8] (4,)\n",
      "[[5 6 7 8]] (1, 4)\n",
      "[[5 6 7 8]] (1, 4)\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "j56TRvKe0qLQ"
   },
   "source": [
    "We can make the same distinction when accessing columns of an array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 102
    },
    "colab_type": "code",
    "id": "4Ym3AlOm0qLQ",
    "outputId": "098b537d-fd1f-431c-edca-ce598fd94eb5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2  6 10] (3,)\n",
      "\n",
      " [[ 2]\n",
      " [ 6]\n",
      " [10]] (3, 1)\n"
     ]
    }
   ],
   "source": [
    "col_r1 = a[:, 1]\n",
    "col_r2 = a[:, 1:2]\n",
    "print(col_r1, col_r1.shape)\n",
    "print(\"\\n\", col_r2, col_r2.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ZtO7QVKN0qLS"
   },
   "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",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "kyeGzUHy0qLS",
    "outputId": "818cc64b-4e7a-48b6-c9e5-3eaac1506feb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 4 5]\n",
      "[1 4 5]\n"
     ]
    }
   ],
   "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]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "iPHOja4y0qLU",
    "outputId": "f98b65f0-1d0c-4fa0-e94f-dd0820086bf8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 2]\n",
      "[2 2]\n"
     ]
    }
   ],
   "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]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YuwzH6u40qLV"
   },
   "source": [
    "One useful trick with integer array indexing is selecting or mutating one element from each row of a matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "24oNQWHs0qLX",
    "outputId": "e22752c8-0215-4a8b-b4d0-8877463ae4e1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]\n",
      " [10 11 12]]\n"
     ]
    }
   ],
   "source": [
    "# Create a new array from which we will select elements\n",
    "a = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "CqhW3rRH0qLY",
    "outputId": "22b4a523-b252-4392-c839-f204d7b83c33"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  6  7 11]\n"
     ]
    }
   ],
   "source": [
    "# Create an array of indices\n",
    "b = np.array([0, 2, 0, 1])\n",
    "\n",
    "# Select one element from each row of a using the indices in b\n",
    "print(a[np.arange(4), b])  # Prints \"[ 1  6  7 11]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "flMEizlL0qLZ",
    "outputId": "c448b73f-652b-4f42-8399-19885b8dfe40"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[11  2  3]\n",
      " [ 4  5 16]\n",
      " [17  8  9]\n",
      " [10 21 12]]\n"
     ]
    }
   ],
   "source": [
    "# Mutate one element from each row of a using the indices in b\n",
    "a[np.arange(4), b] += 10\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XfX2DLb00qLb"
   },
   "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",
   "execution_count": 62,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "ChC9kbn40qLb",
    "outputId": "aa067bc1-f3c4-4b60-a3d7-98a1f9ae9f9f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[False False]\n",
      " [ True  True]\n",
      " [ True  True]]\n"
     ]
    }
   ],
   "source": [
    "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "yrVm_hpn0qLf",
    "outputId": "8ca84c85-cb30-4b1f-9917-aff00b606469"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 4 5 6]\n",
      "[3 4 5 6]\n"
     ]
    }
   ],
   "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])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gKSwsJOQ0qLi"
   },
   "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": {
    "colab_type": "text",
    "id": "RX93v31J0qLi"
   },
   "source": [
    "## Datatypes\n",
    "\n",
    "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",
   "execution_count": 65,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "UVDuFUNH0qLi",
    "outputId": "a229ceae-4b41-4fef-e91b-ea64d9cfb5a8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int64 float64 int64\n"
     ]
    }
   ],
   "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([1.0, 2.0], dtype=np.int64)  # Force a particular datatype\n",
    "\n",
    "print(x.dtype, y.dtype, z.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TmG0f_Z70qLl"
   },
   "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": {
    "colab_type": "text",
    "id": "V03BlGhn0qLl"
   },
   "source": [
    "## Array Math\n",
    "\n",
    "Basic mathematical functions operate elementwise on arrays, and are available both as operator overloads and as functions in the numpy module:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "7JDbDpoQ0qLl",
    "outputId": "804d5852-ae69-42cc-9aef-d51c095ee86c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 6.  8.]\n",
      " [10. 12.]]\n",
      "[[ 6.  8.]\n",
      " [10. 12.]]\n"
     ]
    }
   ],
   "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))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "cRir9Cs50qLn",
    "outputId": "f2055bad-69f1-456a-a9e0-cd033892e559"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-4. -4.]\n",
      " [-4. -4.]]\n",
      "[[-4. -4.]\n",
      " [-4. -4.]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise difference; both produce the array\n",
    "print(x - y)\n",
    "print(np.subtract(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "1Qs0Q0YW0qLo",
    "outputId": "01f1d4a1-00d5-460b-8fd1-d6dccd7548b3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5. 12.]\n",
      " [21. 32.]]\n",
      "[[ 5. 12.]\n",
      " [21. 32.]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise product; both produce the array\n",
    "print(x * y)\n",
    "print(np.multiply(x, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "mUzYwzCC0qLq",
    "outputId": "c59973f8-4455-4696-d9dc-d5b5cb4f3cdb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.2        0.33333333]\n",
      " [0.42857143 0.5       ]]\n",
      "[[0.2        0.33333333]\n",
      " [0.42857143 0.5       ]]\n"
     ]
    }
   ],
   "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))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "GbqqKEf90qLs",
    "outputId": "749e4ece-c8ec-419f-9529-869781df15b1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.         1.41421356]\n",
      " [1.73205081 2.        ]]\n"
     ]
    }
   ],
   "source": [
    "# Elementwise square root; produces the array\n",
    "# [[ 1.          1.41421356]\n",
    "#  [ 1.73205081  2.        ]]\n",
    "print(np.sqrt(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "yl5jCt6B0qLt"
   },
   "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",
   "execution_count": 71,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "1RaTb8EK0qLt",
    "outputId": "d26f2584-7c71-4519-c92a-1b9633aa0350"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "219\n",
      "219\n"
     ]
    }
   ],
   "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))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "bijNSBk_0qLu",
    "outputId": "5cb151c9-e790-4935-a296-8dc50d7f6857"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[29 67]\n",
      "[29 67]\n"
     ]
    }
   ],
   "source": [
    "# Matrix / vector product; both produce the rank 1 array [29 67]\n",
    "print(x.dot(v))\n",
    "print(np.dot(x, v))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "BGeLWq9U0qLv",
    "outputId": "53bc069a-9540-4b8d-c86f-841f4f88e059"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[19 22]\n",
      " [43 50]]\n",
      "[[19 22]\n",
      " [43 50]]\n"
     ]
    }
   ],
   "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))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fdhrsLq60qLw"
   },
   "source": [
    "Numpy provides many useful functions for performing computations on arrays; one of the most useful is sum:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "NmbarGZZ0qLy",
    "outputId": "02cd4ef4-8a27-4bbf-ab23-195c2d45aa39"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "[4 6]\n",
      "[3 7]\n"
     ]
    }
   ],
   "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]\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "I-jv8Eyy0qLy"
   },
   "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",
   "execution_count": 75,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "_Rgr_wKw0qLz",
    "outputId": "2b919e1d-b732-4b52-ae1a-ed5e50287363"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]]\n",
      "[[1 3]\n",
      " [2 4]]\n"
     ]
    }
   ],
   "source": [
    "print(x)\n",
    "print(x.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "pxzSJ11W0qL0",
    "outputId": "f4306554-6553-4ad9-93bf-004534c41af7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]]\n",
      "[[1]\n",
      " [2]\n",
      " [3]]\n"
     ]
    }
   ],
   "source": [
    "v = np.array([[1,2,3]])\n",
    "print(v) \n",
    "print(v.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BodegtvE0qL1"
   },
   "source": [
    "## Broadcasting\n",
    "\n",
    "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",
   "execution_count": 77,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "colab_type": "code",
    "id": "0FANu-Cn0qL1",
    "outputId": "ea107c70-95bf-4124-9886-195d2d21bbb0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3]\n",
      " [ 4  5  6]\n",
      " [ 7  8  9]\n",
      " [10 11 12]]\n",
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "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",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6F-rqddM0qL3"
   },
   "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",
   "execution_count": 78,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "j5vkq1zK0qL3",
    "outputId": "c285671e-76d9-4c71-b098-3c2c0fee62b9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 1]\n",
      " [1 0 1]\n",
      " [1 0 1]\n",
      " [1 0 1]]\n"
     ]
    }
   ],
   "source": [
    "vv = np.tile(v, (4, 1))  # Stack 4 copies of v on top of each other\n",
    "print(vv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "EqrPw0q50qL4",
    "outputId": "43d134a4-7bd4-4075-840d-f3dbf3d91250"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "source": [
    "y = x + vv  # Add x and vv elementwise\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "HxJEdq3w0qL6"
   },
   "source": [
    "\n",
    "Numpy broadcasting allows us to perform this computation without actually creating multiple copies of v. Consider this version, using broadcasting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "z07elq_e0qL6",
    "outputId": "d9385b64-44af-4a0e-f8fb-03b06fbaca18"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  2  4]\n",
      " [ 5  5  7]\n",
      " [ 8  8 10]\n",
      " [11 11 13]]\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hNyoP7jK0qL8"
   },
   "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 two arrays together follows these rules:\n",
    "\n",
    "1. If the arrays do not have the same rank, prepend the shape of the lower rank array with 1s until both shapes have the same length.\n",
    "2. The two arrays are said to be compatible in a dimension if they have the same size in the dimension, or if one of the arrays has size 1 in that dimension.\n",
    "3. The arrays can be broadcast together if they are compatible in all dimensions.\n",
    "4. After broadcasting, each array behaves as if it had shape equal to the elementwise maximum of shapes of the two input arrays.\n",
    "5. In any dimension where one array had size 1 and the other array had size greater than 1, the first array behaves as if it were copied along that dimension\n",
    "\n",
    "If this explanation does not make sense, try reading the explanation from the [documentation](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html) or this explanation.\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",
    "Here are some applications of broadcasting:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 68
    },
    "colab_type": "code",
    "id": "nupgR3bV0qL9",
    "outputId": "8136eee0-5be1-4894-eaac-81eb0002408e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4  5]\n",
      " [ 8 10]\n",
      " [12 15]]\n"
     ]
    }
   ],
   "source": [
    "# Compute outer product of vectors\n",
    "v = np.array([1,2,3])  # v has shape (3,)\n",
    "w = np.array([4,5])    # w has shape (2,)\n",
    "# To compute an outer product, we first reshape v to be a column\n",
    "# vector of shape (3, 1); we can then broadcast it against w to yield\n",
    "# an output of shape (3, 2), which is the outer product of v and w:\n",
    "\n",
    "print(np.reshape(v, (3, 1)) * w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "cw0rMYW60qL_",
    "outputId": "54acb0de-b89b-4167-e7b7-444a7db3ed77"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 4 6]\n",
      " [5 7 9]]\n"
     ]
    }
   ],
   "source": [
    "# Add a vector to each row of a matrix\n",
    "x = np.array([[1,2,3], [4,5,6]])\n",
    "# x has shape (2, 3) and v has shape (3,) so they broadcast to (2, 3),\n",
    "# giving the following matrix:\n",
    "\n",
    "print(x + v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "wPC1gO0K0qMB",
    "outputId": "7ace62d8-cdcb-4c0b-d0b7-230b2a822602"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5  6  7]\n",
      " [ 9 10 11]]\n"
     ]
    }
   ],
   "source": [
    "# Add a vector to each column of a matrix\n",
    "# x has shape (2, 3) and w has shape (2,).\n",
    "# If we transpose x then it has shape (3, 2) and can be broadcast\n",
    "# against w to yield a result of shape (3, 2); transposing this result\n",
    "# yields the final result of shape (2, 3) which is the matrix x with\n",
    "# the vector w added to each column. Gives the following matrix:\n",
    "\n",
    "print((x.T + w).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "sP4Ipmfl0qMC",
    "outputId": "b4951159-a71b-4b44-b251-2975525a7c6a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5  6  7]\n",
      " [ 9 10 11]]\n"
     ]
    }
   ],
   "source": [
    "# Another solution is to reshape w to be a row vector of shape (2, 1);\n",
    "# we can then broadcast it directly against x to produce the same\n",
    "# output.\n",
    "print(x + np.reshape(w, (2, 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 51
    },
    "colab_type": "code",
    "id": "jlrh_IYj0qMF",
    "outputId": "db6989eb-9cf6-48f1-af0a-2f226b28d935"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 2  4  6]\n",
      " [ 8 10 12]]\n"
     ]
    }
   ],
   "source": [
    "# Multiply a matrix by a constant:\n",
    "# x has shape (2, 3). Numpy treats scalars as arrays of shape ();\n",
    "# these can be broadcast together to shape (2, 3), producing the\n",
    "# following array:\n",
    "print(x * 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "EKeSVugs0qMF"
   },
   "source": [
    "Broadcasting typically makes your code more concise and faster, so you should strive to use it where possible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PJo3zu_g0qMF"
   },
   "source": [
    "# [Matplotlib](https://matplotlib.org/contents.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AQdKZNIU0qMF"
   },
   "source": [
    "Matplotlib is a plotting library similar to that of Matlab (hence the name)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3IGUFygT0qMG"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (12, 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ITUkgjQA0qMH"
   },
   "source": [
    "By running the following \"iPython Magic\" command, we will be displaying plots inline:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9Rk3rrPo0qMH"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LXrtV4eR0qMI"
   },
   "source": [
    "## Standalone Plots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tR94Vezv0qMI"
   },
   "source": [
    "The most important function in matplotlib is plot, which allows you to plot 2D data. Here is a simple example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "colab_type": "code",
    "id": "eo5r7X7T0qMJ",
    "outputId": "c2fa94b9-ce30-41b5-de31-b24d696de555"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0VEnS97dAl3gsk/1ujjeWlktApCTGULgkXUo8IWh8aUeWEA2MQA5+sETSNwyD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffbbe57c048>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "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)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FCeHDTq30qMJ"
   },
   "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",
   "execution_count": 89,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 294
    },
    "colab_type": "code",
    "id": "YLWC5hhx0qMJ",
    "outputId": "7ffa8aa8-0add-46c9-8235-07dc50b4d534"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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T76wKGGxoysLHnG3sx2ZXXDbK5R/k1KgUROIuWsfaGZhWt72/aEcSaYmRVEsL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\nKEqnVLJQFEVROvX/AVNIn8N0md+1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffbbe4fc8d0>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "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'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "04vTQdKd0qMK"
   },
   "source": [
    "## Subplots"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Kwv1Qc_J0qML"
   },
   "source": [
    "You can plot different things in the same figure using the subplot function. Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 280
    },
    "colab_type": "code",
    "id": "sd_HhLuc0qML",
    "outputId": "7c4202ea-4b82-4628-b7a7-e20edbce1a4b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PyuBoeQM7CyspKq2j5FQjR8sbvvX7zSYTA+LDGD4ojnFZ/UlPjJQxbeFRejxs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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffbbe48edd8>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "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()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TB9FlWei0qML"
   },
   "source": [
    "There are also more complex formatting options for such plots as demonstrated in the upcoming examples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "IVrVI82r0qMM"
   },
   "source": [
    "# [Scipy.Stats](https://docs.scipy.org/doc/scipy/reference/stats.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hX4AWF6u0qMN"
   },
   "source": [
    "Scipy is a scientific computing library with many useful submodules. Many of you coming from R will find the Scipy.Stats module useful as it contains statistical functions that can sample from and calculate the pdfs of common distribution. For example, consider the following [tutorial](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.foldnorm.html#scipy.stats.foldnorm) with the folded normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 348
    },
    "colab_type": "code",
    "id": "fgeU1yGp0qMN",
    "outputId": "0efc5aee-b0bb-43f6-efc4-076d101aa8a3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean:1.9693959800032417\n",
      "var: 0.9239794739470715\n",
      "skew:0.20293492205914787\n",
      "kurt:-0.2951986521710155\n"
     ]
    },
    {
     "data": {
      "image/png": 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iu1zVCgXjnktRqiW0uHc1kQgZS16whcPZ3SgfO96BhNTJCOd0o3z0RbZ47tub\ncetyfOokaHHvYtJ27SRtj32FpdKJk4lkZDqQkTpZ5WMuJuJpsOxhJEzeupfjd1AqAVrcu5JwmIyl\n9qP2QEEvKs7/ogMJqbYQzs6m7MIJtnjOjm1YR444kJFKBlrcuxD3prdwxfljL5l0BaS1dp1P1RmU\njx5HOCu7fjASIePllc4kpLq8hG5iEpEHgTFABLjbGLO5TtslwC+BENEl9m4DLgaeA96PbbbDGPPt\nNsw79fh8ZLy03B7uP5AaGe5AQqotRTIyKRs3MTptcx3ubW/jmjSl1Ytpq9TV7JG7iEwAhhhjxgK3\nEl02r67HgNnGmHFALnDi9rp1xpiJsX9a2E+SZ91qrPI466JO1WkGkkXFqLGEcrrZ4p6XVjiQjerq\nEhmWmQQsBjDG7ALyRaTu9XYjjTEHYl8XAQVtm6KyKsqj84404Dv7XHz9BzqQkWoPkXQPZRddaou7\nd2zH9el+BzJSXVkiwzKFwNY6j4tisXIAY0w5gIicAkwF7gfOAYaLyItAT+ABY0yTp/7z87Nxu1s3\nbuz15raqX5ex6kVwRSDrX9dD+yNQPG0G+XmpuxBHUu77pZeQ/vZGXLHJ4LJiv/Os11fDt//1ATjp\nX/NN0H1PTGsmDrONAYhIb2AJ8C1jzHER+RB4AHgWGAysEZEzjDH+hn1PKClp3Wx4Xm8uRUXJOxeH\n68hhsletti2fd+wLo4j08lJSWuVQZs7Kz8tJ2n0PjBpPwfJFANTUxD5cb95G9ebthAedlvSv+abo\nvtv3vbGCn8iwzCGiR+on9AU+O/EgNkSzArjPGLMKwBhz0Bgz3xgTMcbsAQ4D/RLdCfUvnqUv2gp7\nJDND10VNYpXnXUCwR74tHu+EulKNSaS4rwJmA4jICOCQMabu28fvgAeNMZ9fsyUiN4rID2JfFwJ9\ngINtlnWKSPtwN+6d79vi/klTdV3UZOZ2UzZhsi2ctns3aR/bb2BTKp5mh2WMMRtFZKuIbATCwJ0i\nMhcoA14CbgaGiMhtsS5PAU8DT4nIlYAHuKOpIRkVRyRCxpLF9nBeHoHxE+B4jQNJqY5S+YUR9Niw\nBmrqXyHlWbEcvqgrbKnmJTTmboy5p0Go7qxVDe6b/tyXWpWRAsC9ZROug/YPO74rZkB6OqDFPam5\nXJROmEz+yoX1wmkf74EPPoBe/R1KTHUVeodqZ+T3k7FimS0cHjCA4IgLHEhIOaHqrHMJ94kzN/8L\nL9jOwyjVkBb3TsizbjVWWZkt7pt5ld6wlEpcLvzTrrDH9+4lbdfOjs9HdSla3DsZq6wUz+pXbPHg\n2ecQGnyGAxkpJwXPOZdwX/vT1siqAAAZeElEQVTUAxkrl+nRu2qSFvdOxrNiGfgD9YMuF77pM51J\nSDnLsvBNm24Luw4exP3edgcSUl2FFvdOxHXgU9K3bLbFAxeNJ9K7twMZqc4gNPwsQqeeaot7ViyD\ncNiBjFRXoMW9s4hEyHhxsf2GpewsfJMvcygp1SlYFv7L7GPvriNHcL/ztgMJqa5Ai3sn4X5ve9wV\nlvxTpkGO3rCU6kJyJqHTBtvinlUr9OhdxaXFvTMIBPDEWxfV6yUwTtdFVUSP3i+Pc/RedAx3nKE8\npbS4dwKe19bgOn7cFvd96SpdYUl9LnT6EEJDh9riGS+vhGDQgYxUZ6bF3WFWWSnpr9pnQw6JEBp+\nlgMZqc7MF2fs3SouJv2tNxzIRnVmWtwd5lm+FMvXYNodlwvflVfrDUvKJjzoNPjCF2xxz6svQyAQ\np4dKVVrcHeTa+3H8Sx8vHEe4T2GcHkoBM+33PFhlZaS/vt6BZFRnpcXdKeEwmYuft4Uj2dn4pl7u\nQEKqyxgwgOC59pkhPatfgdpaBxJSnZEWd4ekv/UGrgMHbHH/tCv00kfVLP9ll9uG7ayqKjzr1zqT\nkOp0tLg7oaoKz/KltnC4Xz8CY8c5kJDqasJ9CgmMtM8Qmr52NVQl5/KDqmW0uDsgY8VSrGr7mrG1\ns2aDS38lKjH+qZfbXi9WrQ/Pmlcdykh1JlpJOpjrk32kv2m/bC1wwSjCce5AVKoxkYICAqPH2OKe\nDeuwykodyEh1JgmtxCQiDwJjgAhwtzFmc522S4BfAiHAALcZY8JN9UlZ4TCZzz8bd8Fr/3RduEq1\nnH/KZaRv2QSBOjcxBYJ4XlmF75rrnEtMOa7ZI3cRmQAMMcaMBW4FHmqwyWPAbGPMOCAXmJZAn5SU\nvnFD3KXz/JddQaR7DwcyUl1dpEce/nEX2+Lpb76BFeeuZ5U6EhmWmQQsBjDG7ALyRaR7nfaRxpgT\nl30UAQUJ9Ek5VnkZnhVxTqL27UvgIvsfp1KJ8l86mUhmg6WMw2EyXlruTEKqU0hkWKYQ2FrncVEs\nVg5gjCkHEJFTgKnA/USHaRrtE09+fjZud+vmUfF6c1vVr0MtehqsMGSl14/ffgs5fVp+1F5WGwIg\nPy91L5tMhX1v7LVdL+7NhZnTYcmS+hvt2k6uvxz69WvHDDtel/h7byct2feExtwbsN0TLyK9gSXA\nt4wxx0Wk2T4NlZTYrx5JhNebS1FRRav6dpS0998ja8Obtnhg9Bh8uV5oRf4lpVXk5+VQUpqal72l\nyr4XZdoPeOK+5s8dTc6yl7AaXAYZ/Mcz1N56e3um2KG6wt97e2ls3xsr+IkU90NEj7pP6At8duJB\nbLhlBfAjY8yqRPqkFJ+PzEULbOFITo4unaeate+w/cNuWW0o7htb7oiL6LmqwdH71m0cPuddfKee\n1qLvO6gwpUdRk0IiY+6rgNkAIjICOGSMqfv28TvgQWPMyhb0SRkZK5dhlZTY4r4rZ+mdqKpNVY4c\nTahHni2e/8oKXUw7BTV75G6M2SgiW0VkIxAG7hSRuUAZ8BJwMzBERG6LdXnKGPNYwz7tk37n5tq3\nl/T1r9nioaFDCY6w312o1MmIpKdTMnEqvV54tl4848AnZH24i5qhwx3KTDkhoTF3Y8w9DULv1vm6\nwWn6RvuklkCAzPlP2Y+Y0t3UXvNlnc5XtYuqc86nx8Z1pBcdqRfPf3UlNWecqXdApxD9TbcTz6qV\nuI4etcV9Uy8n0quXAxmplOByUXLpNFs4vegI3bbrYtqpRIt7O3B9uh/P2tW2eHjAAAITL+34hFRK\nqRk6DF//gbZ43tpVWLqgR8rQ4t7WAgEyn/6nfUX6NBe1c27Uj8Wq/VkWJVPsy/GllZeRu+l1BxJS\nTtBK08Y8K5biOnLEFvdPuYxw4SkOZKRSkW/AIKrFvgZvjw1rcMWZkVQlHy3ubSjtow/xrFtri4f7\n9cN/6ZSOT0iltJJJ08Cq/yfu8tXSY4N9yFAln9bcoapi6t5g4qqpoe8TfyFYU3+x60iam88mX0Wg\nKPnvplSdS7BXbyrPv4Bub2+qF+++aSMVF4wl2LPAocxUR9Aj97YQiVCw7HnS4syhXXrJVAK9dbFr\n5YzSCVOIeDz1g+EQ+atXOJOQ6jBa3NtAt3e2kL1zhy3uO/U0yseMdyAjpaJCud0pG2OfdTR75w4y\nDnziQEaqo2hxP0nuY0fpufIFWzziyeDYldfp1THKceUXXkwop5stnr9qqU5LkMS08pwEK+DH+/xT\nca8dPj7jaoL5PR3ISqn6Ip4MSidOtcUzDuwne+d2BzJSHUGLe2tFIhQsW4TniH2yy8rzRlF19nkO\nJKVUfJXnjyLg7WOL57+yQm9sSlJa3Fsp/a03yIlzO3egoBfF03Q9VNXJuFwUT5luC7vLSsh9a4MD\nCan2psW9FVz7PyEj3hztbjdF19xIxBN3LjWlHFV7hlBz+lBbPG/DGlyVKTkjd1LT4t5CVlkpWX99\nHIIhW1vxFbMIFPZ1ICulElMydYbtxibL7yN/9UsOZaTaixb3lggEyJz3BFa5fXWcyvNHUXmeztGu\nOreAtw8VI0fb4t3e3YLn0IE4PVRXpcU9UZEImfOfIm3/fluTv7AfxdOudCAppVqudOIUwplZ9YOR\nCD1XvqiXRiaRhKYfEJEHgTFABLjbGLO5Tlsm8ChwljHmglhsIvAc8H5ssx3GmG+3Yd4dzrNiGe5t\n9hOooZxuHJ1zM5H0dAeyUqrlwtk5lF482bbeasaBT8h57x2qzjnfocxUW2q2uIvIBGCIMWasiAwD\n/gKMrbPJb4B3gIZT0K0zxsxus0wdlL7hNTyvvmyLR9LcFH35ZkLd7etWKtWZVYwaS+7bb5F+rP6C\nMvmvLKdadDm+ZJDIsMwkYDGAMWYXkC8idZdGvxdY1A65dQru7e+QsXhh3LbjM66OuyiCUp1eWhrF\nl9kv2U2rKKfHep01MhkkMixTCGyt87goFisHMMZUiEi86eWGi8iLQE/gAWOM/dC3jvz8bNzutMSy\nbsDrzW1Vv2Zt3w7PPw2ZcX5MM2bgOW88HntLh8rPy3E4A+fovp+kkefD++eRsfO9euHeb79Bj+u/\nBH3sNz11Bu32994FtGTfWzPlbyIrO38IPAA8CwwG1ojIGcYYf2MdSkpat4CA15vL5h0HW9W3KZkf\nGXrP/ztWKGhrqzx/FMcHng+lzk7jm5+XQ4nDOThF971t9r3ioqn03fFeg9d5kMrH51Hz9Ts63ULu\nXm8uRUWpeU1+Y/veWMFPZFjmENEj9RP6AvZ77uswxhw0xsw3xkSMMXuAw0C/BL5Xp5D14QeNFvaa\nocM4Pv3qTveiV6o1gj0LKL9wgi2eZgzu93Tema4skeK+CpgNICIjgEPGmCbfOkXkRhH5QezrQqAP\n0PaH1+0gZ8c2ej/zt7iFvXbgYIquuUFnelRJpeyiiQR75NviGYsXgs/nQEaqLTRbpYwxG4GtIrIR\neAi4U0TmisgsABF5Dngm+qWsFZEbgBeBCSKyHngBuKOpIZnOInfT6/RaPB8iYVubr/9Ajl4/l0i6\n06PsSrWtSLon7slVq7QUz6qVDmSk2kJCY+7GmHsahN6t03ZtI926zuxZoRA9X1pC7pY34jb7+g3g\nyI236JwxKmnVyHBqzhCyPjL14p7X1hIceQHhvl1mVFXFpPz4gqu6mj5P/aXRwl476HSOfOU2IhmZ\nHZyZUh3IsiiediURd4PjvXCYjAXP6p2rXVBKF/fMvXvo++iDZO79KG579dDhHL3+a1rYVUoI9iyg\nbPyltnjaJ/tIfyv+wY/qvFKyuFuBAHmrV9Lnn38mrcI+CRhA5YgvUnTdTTqtgEopZWMnECjw2uKe\npS9glZc5kJFqrZQr7pl7dtP30d/TY8Oa+B81LYviy2ZGL3fUq2JUqnG7o6/9BqyaWjIWPe9AQqq1\nWnMTU5fkOXyIHmtfJnv3zka3CWdmUXTNDdTGWdBAqVThGzSYz4Z+gW7vbqnf8NZmjg4cRs2ZDaeR\naluDCrs3v5FqVnIX90iEzL0fkbtpY5NFHaLXsB+b9WWdBEwpoGTKdLI//ABXdWW9eMGKxRwcNJhI\nwymDVaeTfMU9FCLjwCdk7dlNznvv4i4tbnp7y0XpxMmUjbtEh2GUiglnZ1M87Uv0Wvh0vXhaRTk9\nVy3j+MykmPA1qSVVce+29S3yV6/EVZPYPDW+U0/j+BVXEehd2PzGSqWYqrPOJWf727Zr37u9s5mq\ns76gw5edXNIcqnoOfkrBsoUJFfZQ9x4cu/I6Dn/1G1rYlWqMZXF8+qy4N+/1WrIAy1frQFIqUUlT\n3DMOfdrsNqHuPSi+4ioO3PUfVJ07Uif/UqoZoR75FE++whZPKy+j58vLHMhIJSpphmV8fQfEb7As\nagYPoXLEaKqHDoO01s0Zr1Sqqhw5mpxdO2w3+3V7exPVchY1Q850KDPVlKQp7v5+Azg+/WryNqyG\ncBhf/4HUnD6UmjOEUPceTqenVNdlWRyfcQ19H30Qy19//r+CJQs49M1/I5yd7VByqjFJU9wheoRR\nOXK002kolXSC+T0pmXQ5PVe8UC+eVllBz+WLOHbNDTrM2ckkzZi7Uqp9VVwwltrBQ2zxnJ3bydmx\nzYGMVFO0uCulEmNZHJt5LeE4NzAVLF+Mu6SZe0pUh9LirpRK2Ikrzhqy/D56LXoawvaFbpQztLgr\npVqk6uzzqDrrXFs848B+erz2qgMZqXgSOqEqIg8CY4AIcLcxZnOdtkzgUeAsY8wFifRRSnVtxVfM\nIuPAftxlJfXieetfpXbQ6fgGDXYoM3VCs0fuIjIBGGKMGQvcSnQd1bp+A7zTwj5KqS4snJXFsavn\n2K+QiUTwPv8krsoKZxJTn0tkWGYSsBjAGLMLyBeRunNy3gssamEfpVQX5xswiNLxk2zxtKpKvIvm\n6/i7wxIZlikEttZ5XBSLlQMYYypEpKAlfeLJz8/G7W7d3aP5eTmt6pcMdN9TU6fZ95kzcR35lPS9\ne+qFMw7uxb1tI9WTLmvxU3q9uSfVnsxasu+tuYmpNXcqNNunpCSxmRwb8npzKSmtalXfri4/L0f3\nPQV1tn0vv/wa+j72B1zV9XNyL19KTQ8vtWdIi56vKLPxgzyvN5eiotQc8mls3xsr+IkMyxwietR9\nQl/gs3boo5TqgkLde1B01Zfjj78veoa00pL4HVW7SqS4rwJmA4jICOCQMaa5t87W9FFKdVG1Zwhl\nF11ii7tqqun97N+xAgEHskptzRZ3Y8xGYKuIbCR61cudIjJXRGYBiMhzwDPRL2WtiNwQr0/77YJS\nqjMonTCF2tPs0xN4Dh+iYMmC+AvSq3ZjRTrJD7yoqKJViXi9uWzecbCt0+kSOtvYa0fSfe+c++6q\nrqLvnx8irazU1lZy6TTK4xzdN9TUAtk65h53zD3uOU29Q1Up1WbC2TkcvfYmImn2azXy17xEVjML\n1au2o8VdKdWm/H37c3zG1faGSATvwqdJP3yo45NKQVrclVJtrurckZSPvdgWt/x++jz9V9LK7cM2\nqm1pcVdKtYuSSZdTE+ca97SKcno/PU8X2G5nWtyVUu3D5aLo6usJePvYmjxHPqP3s/+EYNCBxFKD\nFnelVLuJZGZx5PqvEcrpZmvL3PshvRbrHDTtRYu7UqpdhfLyOXrDLUQ8Hltbzs7t0XVZO8kl2clE\ni7tSqt35T+lH0dU3gGUvOblb3yRv9Uot8G1Mi7tSqkPUDB3GsZmz47b1eH2truLUxrS4K6U6TNW5\nIymZMj1uW966l+m+YU0HZ5S8tLgrpTpU+diLKRs3MW5b/uqVeF55qWMTSlJa3JVSHa700mmUj74o\nbptnxXI8L63QMfiTpMVdKdXxLIuSqTOoGDk6brNn1Uo8S1/UAn8StLgrpZxhWRRfMYvK80fFbfas\nXU3G/Kf0OvhW0uKulHKOZXF8xjVUjBwTtzl98yYy//o4+P0dnFjXp8VdKeUsy6L4iqsaHYN373yf\nrD8+jFVR3sGJdW0JLZAtIg8CY4AIcLcxZnOdtsnAL4AQsNwY8zMRmQg8B7wf22yHMebbbZm4UiqJ\nxMbgw5lZ5G5aZ2tO27+f7IcehB9+H9z2qQyUXbPFXUQmAEOMMWNFZBjwF2BsnU0eAi4DDgLrROT5\nWHydMSb+HQtKKdWQZVE2YTK9+3vJWPS87WSqVVwMv/oVabPmEDrrbIeS7DoSGZaZBCwGMMbsAvJF\npDuAiAwGio0xnxpjwsDy2PZKKdUqgXHjqf3KzeBOszfW1pL118ej18LrlTRNSmRYphDYWudxUSxW\nHvu/qE7bUeB0YAcwXEReBHoCDxhjXm7qm+TnZ+OO98tMQH5eTqv6JQPd99SUzPvu9ebClAkwuD/8\n3/9BZWW99qxMN1lrX4aSozB3LmRnO5OoA7ze3IS3TWjMvYG4i7E2aPsQeAB4FhgMrBGRM4wxjZ7y\nLimpbkUq0Z3trIsFt7fOvFBye9N9T959L8qMHeR17411211kPf4nXEXRY8isrHRqagLR9je3ENn9\nMTU3zSV86kCHsu04TSyQHXf7RIZlDhE9Qj+hL/BZI239gEPGmIPGmPnGmIgxZg9wONamlFIJi/Tq\nRfV3/o3gsGFx263iYrIf/j3pq1/W6+EbSKS4rwJmA4jICKLFuwLAGLMP6C4ig0TEDcwAVonIjSLy\ng1ifQqAP0ROuSinVMtnZ1N5yO/5JU+K3h8NkLFtK1h8fwSo+3rG5dWLNFndjzEZgq4hsJHplzJ0i\nMldEZsU2uQN4GlgPzDfG7AZeBCaIyHrgBeCOpoZklFKqSS4X/itmwB13EMnKjLtJ2sd7yP7tr0jf\nuEFPtgJWpJP8EIqKKlqViNeby+YdqfmhINnHXpui+568+z6osHujbV5vLsc+2EfWP/6K69NPG90u\nNPh0aq+dQ6R37/ZI0RFNjLnHPQ+qd6gqpbqUSEEB1Xd9F/8lk8CKf31H2sd7yPntL/EsX5qyUxdo\ncVdKdT1uN/4ZM6m5404i+fnxtwmF8bz6Mjm//gXubVtTbqhGi7tSqssKnT6Equ//kMCYsY1uY5WU\nkPnPv5P18O9xfbynA7NzlhZ3pVTXlpWF79o51HzzTsIFBY1ulvbJPrL/9yEyH/8TrgONj9cni9bc\nxKSUUu1m3+HGZ38sqw01fjI5txDrpm/RY8Maum98DSsUjL/d2+/Ctu0UT5tJxagLPw83dSK3K9Ij\nd6VU0oikeyi95DIOffN71JwhTWwYIX/VMixfbccl18G0uCulkk6woBdHb7iFI1+5jUDvwrjbWKEg\nadWtm/akK9DirpRKWrWDh3Do9rs5duV1BPN61mvz9T+VYF4jV9okAR1zV0olN5eLqnNHUnXWuXR7\n7x0y935EMC+f8tHjG71OPhlocVdKpQa3m8rzLqDyvAuczqRD6LCMUkolIS3uSimVhLS4K6VUEtLi\nrpRSSUiLu1JKJSEt7koplYT0UkillKLpOW3aU3vNaZNQcReRB4ExQAS42xizuU7bZOAXQAhYboz5\nWXN9lFJKta9mh2VEZAIwxBgzFriV6DqqdT0EXAOMA6aKyPAE+iillGpHiYy5TwIWAxhjdgH5ItId\nQEQGA8XGmE+NMWFgeWz7RvsopZRqf4kMyxQCW+s8LorFymP/F9VpOwqcDvRqok9cjS3ymohR5/Rr\nbdeub0Ce0xk4R/c9NaXwvnu9uQlv25qrZZoqwo21Je/sPEop1QklcuR+iOhR9wl9gc8aaesXi/mb\n6KOUUqqdJXLkvgqYDSAiI4BDxpgKAGPMPqC7iAwSETcwI7Z9o32UUkq1PysSiTS7kYj8CrgYCAN3\nAucDZcaYRSJyMfDfsU2fN8b8Nl4fY8y77ZC/UkqpOBIq7koppboWnX5AKaWSkBZ3pZRKQl12bplU\nn95ARM4GXgAeNMY84nQ+HUlEfg2MJ/r6/aUxZqHDKXUIEckG5gF9gEzgZ8aYpY4m1cFEJAt4j+i+\nz3M4nQ4hIhOB54D3Y6EdxphvN9evSxb3utMbiMgw4C/AWIfT6jAikgM8DLzqdC4dTUQuAc6O/e4L\ngG1AShR34EvAFmPMr0VkIPAykFLFHbgPKHY6CQesM8bMbkmHrjosk+rTG/iAK4jeU5BqXgOujX1d\nCuSISJqD+XQYY8x8Y8yvYw8HAAeczKejiciZwHBgmdO5dAVd8sidpqdESHrGmCAQFBGnU+lwxpgQ\nUBV7eCvRmUhDDqbU4URkI9Cf6H0lqeR3wF3AV51OxAHDReRFoCfwgDHm5eY6dNUj94Z0eoMUIyJX\nEi3udzmdS0czxlwIzAT+KSIp8doXkZuBN4wxe53OxQEfAg8AVxJ9Y3tCRDzNdeqqR+5NTYmgkpyI\nXAb8CJhmjClzOp+OIiIjgaOxWVjfid0V7iU6YV+ymw4MFpEZRD+1+ETkgDHmFYfzanfGmIPA/NjD\nPSJymOhUL02+0XXV4r6K6DvZozq9QWoRkR7Ab4DJxphUO7F2MTAQ+K6I9AG6AcecTaljGGO+fOJr\nEfkpsC8VCjuAiNwInGKM+a2IFBK9Wupgc/26ZHE3xmwUka2xsccTUyKkjNgR3O+AQUBARGYDV6dI\nsfsy0Smln61zzuFmY8x+51LqMH8i+pF8PZBFdFqPsMM5qfb3IvBUbCjSA9xhjPE310mnH1BKqSSU\nLCdUlVJK1aHFXSmlkpAWd6WUSkJa3JVSKglpcVdKqSSkxV0ppZKQFnellEpC/x+MR3aMx3QG+wAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffbbbbb6780>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import foldnorm\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "c = 1.95 # Shape parameter\n",
    "\n",
    "# Calculate & print the moments\n",
    "mean, var, skew, kurt = foldnorm.stats(c, moments='mvsk')\n",
    "print(\"mean:{}\\nvar: {}\\nskew:{}\\nkurt:{}\".format(mean, var, skew, kurt))\n",
    "\n",
    "# Plot the probability density function (pdf):\n",
    "x = np.linspace(foldnorm.ppf(0.01, c), foldnorm.ppf(0.99, c), 100)\n",
    "ax.plot(x, foldnorm.pdf(x, c), 'r-', lw=5, alpha=0.6, label='foldnorm pdf')\n",
    "\n",
    "# Generate random numbers and compare the histogram:\n",
    "r = foldnorm.rvs(c, size=1000)\n",
    "ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)\n",
    "ax.legend(loc='best', frameon=False)\n",
    "ax.set_title('Folded Normal Histogram')\n",
    "# Display Plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "p666zH7r0qMO"
   },
   "source": [
    "# [Scikit-Learn](http://scikit-learn.org/stable/documentation.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sGGI4EE70qMO"
   },
   "source": [
    "Scikit-Learn is an open source machine learning library which implements many standard off-the-shelf machine learning algorithms and utility functions. Even if you are not using any of the models from this library, you will find a lot of the built in functionality useful in running your own experiments. For example consider the following [tutorial](http://scikit-learn.org/stable/auto_examples/plot_cv_predict.html#sphx-glr-auto-examples-plot-cv-predict-py) which efficiently plots cross validated predictions from a linear regression against their true values.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 294
    },
    "colab_type": "code",
    "id": "ONPlfZ5n0qMP",
    "outputId": "aeed005a-63c5-496c-eced-5b6270923198"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uZ6Qbc/B53HTUbya34qiYw/x+H02b3iGvaAIulQmPvQlnTwumolnoVY6IwOzv\n74+ZkQwn2ulg5BAaqbDMZPV9pK4rcu8IBMNk4LTcZDKxdesW1jXURLT0sAPU2dNCxeyz4mzizdWr\nyKuYQ8DvQ5c7O1J9abBZxNSiVKrq+tBYYjV6gzmflpo1ikI/HIq5Z08tF192GRu/Xg2DKHIFk4+j\naMpJGHNKSDfmAIObaprkFeRPOw2NLjSjsZRi8rgp08kxZQa1Wi0VFROGvQgrGTH8Q2EkwjKT2ffR\nqA0thL5AkICUlBRef/czNu22x+Vab65eRU7xTLoGRLdAUAAQgAb5M7IKp0WE6sYaO4/dfqFioe0z\nv3Myt/x5ZZzpR6NLpd9pV7She2x1LF58P0899Tg+n1fxHnJKv8GU4xeQmT+Jzt2r0KUYYvZby2az\nc92bmK0VpButpPk7SE9XtvPXduwtthc9IA5XCA43hj26vYO9UG5/+j5URMI1geAgEx1pE51rHUCj\nTcXT7xh0BWhGdhHdzTvA74vEWxuzi2hoqOfs757ARSYTOp0fj0cdyYw5qANZb6Zp+wp06Sb0plx6\nWnfR77RRWFRIXd1WRYFvzqskb+LRTDzqzEiKgnkz8lGru/l841a0hoJIfvnKb56N1+WgPGUH5/3w\ndBYtVU6y5vAbuXvx42RlWdhS58QZMBGw10BGWUzMf5jBhOBwYtjH2kK50Sh2otfrsVrzkmIKFUJf\nMG45EM1vKOcqTePDcfCevh6yCqcnDF/ss7dRNOUENLrUiMmndsNb3PtMF25NDmmBLlSuZkgvoo+g\nMHN115JqrIzT6PudPejNVtzOHvp6O0hNN5NTVkF3TzPpqWZUag0Bvw8AQ1Yh0rwFFEw6Fnt7LV0N\nW8gypobMBBeg1Wq5zGbjgUf/zG6/Bo+ulEDXNmZXGLlm4XX09/ejV32o+Ez67G3sMUxm7ZqvKZp6\nAhmAz5RLe90mjDlK5idlITicGPYDWSiXDEar2EmyEEJfMO44EM1vOOcqTePDuda7GqvQetrR6MoG\nDV9UWgGaZsxHnTWNDF0qjdv3kFdx4l67OaAzVLDjy9fIyq0gPbMwpIn3UzLzFHz9fbTt/prCyfMi\n1zVZy3A7beSUfo29fQ+Tj/0pxdO/FYlJd3Y3cs9V/w9JmhIjjEwmE3ffdqPi4KfVahMmNkvRm9Cm\n6iP3rNGl4vO6h11taqD92qC2M6s0I8Z+fbBs//tiNGzvyUIIfcG4YzDNb/GTf+WcM05JqL0vfnwp\na+p1GMyVZAySgyVMomm8KdXP1JJMqnrcMatg041W+u31OOx2xRWgGdkle3OqKPgCdKl6TDnl9Ltd\n9DVUUTztZDrqN7P8pRtJ1WfSXqG3AAAgAElEQVRSceT34s5J0Zsw509i9nd/TUr6XiOLz+PG3Wcj\nMzMzYR1ZpZz31yxcwJ2LH+eraicZmYU4ba0xZQb1plxcjs5I8e78yrnUbf4f+Xn5eHWWIQnBgc7y\nGTMm4XD4Yo5Jpv38QEhWkrbRQAh9wbgikeb3+YYWPtvwKhZzCkdUWmK0d6/Xy+In/8rnm9vQZxZF\nbOz5lXMH1Rr3NY2P1vbMOaXoPO0UZzTxw5+exsMvfaa4ArS3sx5r+eyE2SAzsovp7+uhz97Bl/+6\nk86GrQDYgaIp8xXPKZg4l6YdX5CWkY3elBsR0oUFhfu0MQ82+7nhiou58nfP0K/VkVMyM+YZBJOX\nzYx8Vqs1FBeV8OBNPxt2xa7wwKPX63E4Ym3Yo1UsfH8Z6SRto4EQ+qPEeNQIxiKJNL/0zCJcve10\nOfz8d/Vu/L7nufHqS4Dg7KCqp5i8yolAbFhl4eR5g2qNiabx0dpeQ0M9/3z3U6rqXDzw6hbs3Q4C\nXZ9RIM2LCH+fx01vVwOBgJ/8iUcP6gvoqN9C666vaKtdH7ev+qvXKZ7+LVSq2DBsn7OVgtAA5nJ0\nRgTyLEvLPt+3wWZOzyx7nSMqLWzsyI4b9Lxup+JAaLHkYLHkJGxvOIx3+/lYRAj9JOP1evn9A0/z\nZVXnmIg8GO8MpXpSOFLlg5Xvc+UlToBBZwcabfDYwbTGoUzj9Xo9b/5vZXBRlSU1JtXwrjVvkDdh\nTkTzrpj9PWo3vAcQ5wuwt9dRtfwFWncpR84ApKQZ6XfaSDWYI9t8Hjd9tlYMqm78hkLQZIGtep/m\nlWB64pq4FMvhZzNYeOmMMgPSN/JYJ38GhiIMGldS7dnj2X4+FhFSJ8ns1aIKxkTkwXhnKNWTICi0\n1IZcZHkbmZmZg84O9KZcHD3NHDshsdaYaBqfyORkzCkhQCDGPGLILqR193rUah07171JekYO9Vs+\npLNhK4GAX7GN7KJp5FbMwddvw9+8nE6NJRJy6XH3Yi45ClWakek5bZxzxvyEM8poc05Hj5vUDAsm\nheNcKhMdHe0xg1545e32Zi9qUzk6XxdTSzKSqsSMZ/v5WCRpQl+SJD3wHJAHpAF3ARuAFwEN0ASc\nL8uyO1l9ONiM1ciD8YzT6eTM78zD8/bHVDW4gtWTOpsIBPZWTwpjMOdz95P/5JvTy0hH+TXr7axj\n/kwr1yy8dL/7lMjkpDflodbGljA0mPPp6+3AmFVM+56vqV71d/w+j+K1M/MnIx33M/SZ+aQZsgGY\naq5nc00Pbo0Gr9tJSpqRgM9LZ9M2PpIbuOKicxK+V9HmnGxjMA2D8mrfvbOf8KAXv/K2lKqe0VFi\nxqP9fCySTE3/DGCNLMsPSJJUBvwPWAE8IcvyPyRJuhe4GHgqiX04qIzVyIPxSKyz0YjH3oGju5EU\nYzF+rxuVJv5V7u1sIG/C8VTZwWv/GEzx8e8+j5vU1LQD0lITmZwGOjyD/aqnvW4z67ctxtvfp3ie\n0VKKteIoJs89B21KWsy+TTV2XJhxtNcGC4BHhW/6PG4uvvY2XlnyoOI9KSkiju4m+gckVFOymQsl\nZvQ40AI7iUia0Jdl+dWojyVAPXAScHlo21vADRzCQn+sRB6M92mx0+nk3gefYHf/JFLCGmYoF0xL\nzRqKpp4Y45SFvXHy4fDIQKqVpi3vozMVxka3TD2RjTXbFOuVDvWZJTI5KTk8ezsbsBRNY8/G9+Ku\nlW6yIh13LkVTTsDeUY/b2YU2pSDmGI/OQqBzOxqtWTFVQp+2iMWPL+WmaxfGXT+siOijCqdYimfS\nXr8JR3cTeRVHYVA7FW3mQolJPgdSYGeoJN2mL0nSSqAY+B7wQZQ5pxUoGPREICtLj1YbH/Y2fjBy\n9NRsVtfHC4NjpmVTVqZcfWik8Hq93PPgX1i7vRu7LwOjppejJmdy668vPahOZKtVacF+POH+f7Wt\ni15vDn29OyJhlgGfF5ejE1DvXSSkVtHVtAO3oxNbxx7M1gr8Xg8d9ZuxtdVgspSRmT8Zl7OLdJMV\ngzkftVqDQ2XC6+3Fas3b72d2962/DPW1g16fEWd3A329PWj9fTTJKzBkF9Nnb8XjcmDILKRwyvHs\nWvcmPS3BoiYp6WYmHfNjSmedhkarA6Cvp5GcsiPj2spQ2ymZmMmWduUoGb0pj/XbazEYNHEDlsEw\nCaP2XRpCyeAGzhIq03dw/6LrFAe68LlK6dwMajszZkw6YKViqO/GocrvH3haMZJqyYuvsug3lyc8\nd6gk/Zcvy/JxkiQdASwjWOgxzKCpP8N0dTmT1q/RYuH558CLr7J6a2dM5MHC8xckPcVwxP5qDjqR\nA8Dqeje33fPUQXMiDye1cqT/WQXBiBhrGR63k+qvXiczdwLpRitqtZr6qk8pmXEKacZcempXoTYU\nMvHI70cEmt6cR5oxh7bd67F11qE355GRVRyJ1bdmGdFqM2hrs+/XMwuHbNrsTrweDw5bM6kBJ7Om\nW7noJ9/nX+9+xpp6yCmZhcvRid/rQaVSMXX++Xz1xn3kVhzJjJMXkmrIjFzT53GT7m+Ja8vncTOr\nNIPLFlzA+Tc8Cgq2eKetlfSMQjZv3qGoeU/K09HcoZxQrbpFRVubHb3eF3cewLQSg3L4ZGkGDocv\nLs5+OIyXtNvJwul0snprBxpLrC6s0aWyemsntbX7Dr8Nk2jwTKYj9yigVZblOlmWv5YkSQvYJUlK\nl2W5DygCGpPV/lhBq9Wy6DeXU1vbMqomlvFufx2s/22162MEejjevvqr1zFbijGVHoOzpxWNLjWu\n9qvP54k5N6zdehs+HlZVqzDRU/G6ujoKp5xAW3czWl0aff3pvPbqyzz31B9Y89UGdG98wMaaany+\nNPpsrRhzSskp/QanXvYXNCnpNFevgkBwYVafvQ2vvZGli3/LU3/9G7tb1Hh0OXFrBI6dkUdVj3IU\nk0HTh8vVp/g9/+h7J7O2frnic9+XmUaETyaP0TKfJVPTPwEoA66VJCkPyADeA35IUOv/YejzYcFo\nRx6Md/urUv99Hrdi6gKNLpWMzEJM1kr8AS/GUOz9ns3/o0g6gRS9CZ/HjdlaoZwC2VgcseEP9sz6\nFJ5ZOAoGYx5pxj7aateTkVVM9Zev0Sh/Hjnukssv57233o608epbH0aEtS4t2FpexRyaqr9Ao0vB\nnDsRlbqdWx95HWcglzRND1J2FzdccTEm015n6w1X/JwLr7qFdr8FvSkv4qewls2mWf6ARUvN6FUf\nxdmECwuLMKh7FZ/7vnxNInwyeYyWD1C970P2m6eBXEmSPgfeAa4EFgEXhrZlA88nsf3DmrHiRE6E\n0+mkpmYXTme8GU+p/4lTFxTRtGMldVs+pmHb57Tt2YileCbdLTto3L4Cp71t0HNdKvNeATbIM3N0\n1vHqGx/g9Xojfd9YY4usgFWp1NRt+YjPX/p1jMAHWP/VCqqqtkYG/huu+DmzLC34Orbg6Kyjc/cq\nmre+j9laTpqvE1X7arRFJ6POnk6GpQRtzgxqPRLPLHs95rparZbnH7+X+dOyCNh3k56RRVqKhtZd\nayiYcToZlhLU2dPZ2JHHI0uWRc4LO57DKaLDDGeVa3TqBMHIMBLfy1BIZvROH3Cuwq74LFSCEWcs\nL18fSqZLvV7PtOJ0tvQEfwAuRye6FANdndsVUxc4eppJM+Xiaa+l8uiz4kw4zdWr0aUZFM8NV59K\nuPDLH2BzZy533Psgt91wVWRWkOrqpXbD+9Ssf5uAX7mIiTGnnMefeY4nHnwAUC6UAUQKkvz6/r/t\nsx5uGK1Wy03XLgytrt3NPUv+Q3b53H2eOxwzTUdHO1u3bmHatOkjmmJBEI+onCU4IMaq/XWo+dHX\nbtxKQ/saMrKLyMgqpqe1hu6m7WQXTUOXulfw+Txu/F4PgYAPo6VEUWBqU9PpbNqOpXhGnEBvrNlA\nSkoKEHxmi5/8K59+3UxGdglOWyvefhcQoLtlB64MK5ff8RcmFWhp3PQhNVu+wONWNpWYrOVMOf58\n/H4/PQGtYkK36EIZFRUTqKnZtV9mOb1eT1paGv1aKylDOHcoZhqXy8Ul195Bt9dMurmQvueXk6nt\n4dmH7yQtLU2hlbHBeDY9HfTKWZIk+UExQgvAK8ty6iD7BGOAsWh/HYqzFECWt9HU0Rep+gRBrT2v\n4qio0n45kXzzoMJkrUA1SFBYutFKIBCguXo12lR9KFa/hZ623VQccRaLn/wrN/3qMrRaLWd+ex6r\nd36OOpRdsqVmDXkV34w4h+s2f8jH/3wZt6NLsS29OQ9p3nkUSsfj93poqVmDR5c/JD/KgZjl9ufc\nRL6mS669A23RyeQNmDVdcu0dvPT0Awnv42Aw1ipsHQgHs3KWjmBo5a3ARuAjgikUvg1MHvHeCJLC\nWFq+3tTUNKgm6wwYuP/RJezp1NDaYccwiNZutlaQlT+ZruYdpJtyMZjzaa/bhMGcP2jmyt7OBtJN\nuXjUNvpddlAXkFMyC1ChVmvYFGP+COB2dJJVMCnGedzTuot17yzG0aUcdJaSZiC7eBpF004lI7OA\n1pp1kRz0ga5tQ/KjHIhZbiRNeh0d7XR7zRGBH0ajS6Xda6ajo33MmXrGWoWtsUpCR64syz5Zlr3A\nSbIs/0uW5R5ZljtDq22PG50uCg4lCgoKYrRRn8eNo7sJn8eNrWEjtR4JdfZ09FkFGMwFccdAMEma\np9+Bz+PCYM6POHg1utRI5spofB43qCCrYBK5FUdRUHks9vbdaHSpkWIgHp2FlpZmAMrKKvA5W/B5\n3DHO43RjDm5Hd9w9GY1GfvnLq/h63UYuXHA+lsKpkVlC4eR5BHzeYQndaxYuiHH0+jq2MMvSMiSz\n3IGcG83WrVtINxcq7ks3F7J165ZhXS/ZRDvWoxk4gxwvBNMw7ExKv4c65zFIkvQLYDngJyjwlUMh\nBIIQSmalsDb6dZuTttr1kRj6tj0bcXv6Izl0DOZ8mnZ8QW9XfeSY8GIqtVpHduEUbG27yZswJ6ZO\nbXQVK70pF3tHHQG/jwJpXqRf0SmVI7lxbNUxycVOPXYmH6xZjUqjQ61WY8wpJSXdxMQ5P0Be+TcA\n1Botl126kOuuu5HsbAswwI9i9+6XH+VAzHIjZdKbNm06fc8vV0zE1tfTyLRpZwz7mslkvIcohxlL\naRgWEAy3vJKguWcLcMGI9EBwyJHItgpBwXjhVbeQV3HygEVWsyL5c3weN93NO5g6/4K4hVjyypfx\neVxUzv0xLbu+IuD343H1RtIxhM939DTj6u1kwlHxAiqcUtnnDc4KojXxXbt2cu3lF6B+5iXW7+ig\nrm535NoVR57B7g3vYS07gjNOO5Hf33xdzHVH0o9yIGa5AzXpWSw5ZGp7FOveZmp7xpxpZzyEKA+F\n0TBRDUnoy7K8XZKk84E8WZabRqRlwSHDQAGX6MW9f9HV9Pf3ozUWK07F1WodDVWfgVqDpXSm4jFZ\nhRKGrEK02hQKJ8+joepz0jIsNFevRqVWk5FdTG9nAy5HF6mGLMU+2zvqcPV2ojdmM9VczzULf05D\nQz1//ON9vPLKSyxZ8ld+edFPqK3djdfr4Z2Pv6SqzoVbZeKEM6/myMmWhNr7vvLvh58XjN1cM88+\nfCeXXHsH7eHonZ7GSPTOWGMshygPldFaRT8koS9J0inAXwA3MEWSpIeAD2VZfvuAeyAYtyhp9FOK\n09hS24vOOviLm3Aq3ttByfRvRXLUKBEuxh1OsxAgGGSWO2EONevextvfhyGrCG+/E0d3g6K22tvd\nhLXsG2jUav7vhKO4665FLF26BLc7qPnf+JsbOOZ7tbhUWZGZymO3n0NHR/t+a+9Kz+voqdksPP+c\nMRldkpaWxktPPxAVp3/GmNPwoxmrIcpDZaylYbgHmAu8EvX57dA/wWGKkkZf1eOmsfFjyqzfiDve\npTLR1NQ06FTc53GTqjeh0aXG2OkHEsyTP4fm6lXkFM/E0++gq0mmoepTJs45M9iWo5PMvIn4/T52\nrnsTo6UEg7kAW/tu+myt5JUfhb1zD3Ub/8vZ/15Eb29srH1XZxsNjc2UzZoF7K0ZO9QptpJ5R+l5\nra530zfGo0sslhzmzz/xYHdjn4zFEOXhMFomqqEK/V5ZllskSQJAluV2SZL6R6QHgnFJoqlomsEc\np11D8MUtKCjA4fApTsUdPc0Ysooi1xlYQxaCA4Ozpxlb2256OxsjTl5dSgbOnlaad36JLlUf4/g1\nWcpw9jTTtH0lU+edT+rk49iz6X/sWPV33M74aBwAQ1YRaRnZMfc1lCn2YP6MyxacPa4T4I0nxlKI\n8nAYLRPVUIV+nyRJJwIqSZKygJ8CrhHpgWBckrBEYGYhjp5mTDl7Iz+iX1yHw644Fdd278KGFZO1\nHCAmEifdmIOjq5F+Vy/F077FrnVvUjnnrEjum5zSmeSUzqS5ejW5FUcBQcevx+1k51f/wpBdxMQ5\nZ1Gz4R3qt35Mv7NH8b6s1lyyKk+h8pgfoVbH1nKInmIPpk0O5s+4/6GncAZyFS344ym6RJBcxlIa\nhisIVrj6JlBNMHTzshHrhWDcEBZ2JpNp0Kloqq+D/HQHO3dUozGXY9C4Ii9uOMlaXl5+yFFaA6jI\nzc3l1/f/DV9rZ0S7V6s1FE6eR7/TRv3WT7B3N5Cmz6ajYStF0nz2bPkgLje+RpcWMztoq11P5dE/\npKN+M1+/9wj29t2Kfdbo0qmcdSKv/OVBbn3kX3ECH4IzFYslhz89+ZyiJt/QUM/6He2k5MVr81+t\nqyMlU4UxJ3EtWsHhzUFPwxDFRFmWvxe9QZKkHwC1I9obwUFhKDZQJbOFx1aH2lARyYPj9/to3PY5\nWp0Wl7oUt6oZT+Mmjpw7jSsv/imPLFnG1joH3S4djrZqfB4n5uIjSQ90kaVux8lkcidMYOfaf2PO\nnRhT1rD8yNPZteYNKmafjkaXSuP2FVQccXpcYrW6LR/jcnRiyCwILdJS8eW/7qSzYavifWm0qVjL\nZzN1/oUQ8NLf359wiv3MstdjNHm/38d/V69g+cYn0BkL6LV78PesIL9ybmTg8Hnc6EyF+LxuRXPV\n5AKtMO0IYjhoaRgkSSoHJgKLJUn6NXurXemAh4F/j3iPBKPGcHKVKJkttMZKvA0f4zOW4FKZ6K5b\nT8G00yJCzZCZj6Mnn4/XVLPl2jtQF5xAW0sdWl0axvxpOG2t1G/9BEvxdHr15Ti6a3Da28mfOBdD\nZnClbU5JMGzT53GTbrJGsm1qtME2HN1NpBmygwuudKmkpBvRpRiAoDPXmF2MRhefHEylUlMoHY90\n3HnUb/sUQ1YBvo4t5OXlDzrFvmzB2Vx913Mxdvnm6lUxxckzLKVx9Xpdjk705gIyLMUx5qrezgb6\n+2z05+fxpyefG5c5YgTjj329YQXAOUA5cEfUdj/BfPmCg8RIRCgMdSFIIqctxhIevOlnNDU1cuuj\n9TEVq1SqoKbb77JTa+vD4FpL/sSjYxZb5ZTMpGnHF/h8/ag1OnweD71dDZisZTGhmfVVn5KqN+P3\neuhsr6K7uRoCAfTmvIhpJ79yLhnZRXj6HaToTaQZsmmv28SU4xfQtntdpN+FU04gu2gqKemZNG5f\nQZrBEucsU4oCGZgBM1FRl/CKX40uFV2Kgf7uPaitZeRVzGHP5g9IN1nJm7C3Rq3IESMYLRIKfVmW\nvwC+kCTpP8AbsiwHACRJ0oZy8ghGmZHKJDichSD7ih+22Wy88u/30RmDuVqatq8k4PPhcraQkVWE\ntWw2vZ31dDfvoGByMGVTOK9NmiEb1BpyimdGKlztWvdWjBmkuXoVxVNPjBksrGVH0FKzBmNOKcac\nUpw9rdRt/gCNLpWA3x9ZkWtv3xPMgSPNx+N2MOX4BWRkFVFf9Sl5FUfi7Gmhs2EzU411XLPw4pjn\nM3BQHRhSl6ioS7rRSlfDFrKMqcyuMOLNyeGjtZ+h1qaQZrTEOLkHe+4CQTIYqpTQAm8C4fXsyyVJ\nWizL8mvJ6ZZgMEZqmfZQFoLk5eXv02mbFrBhMpnY3aGiz9GGITOfPlsb6cacOJt73oQ51G/9BJ+n\nj7SMHDKyCoNauquXntadmHMn4ul3kJaRzc61b2DOrSBVnwUBBtWmXY4uaje8x661b5CZV0m6OY/c\nijk4e1ro69hNIBBg59o3yK2Ygzm3AqetFUd3EyUzTkGt1uC0tZJZIHHOmaeg1Wrxer0sfnwpa7c1\n4k8vwqhzRQbVgSF1idYSGNR27rrmu5SVVaDX6/nj40vJrzwm4aKzA43iGa/x6YLRZahC/9fAd6M+\nfwd4HxBCf4RJ9MMdyWXaiReC9PDqGx+wrdEdmU24unaTaqxUdG7abDb6tVZ83j3YOvaQbrKiTUlX\nLmaiS8VoKcXjstHdvIPUjGzyKuawe+N7eD19GDKLSEk30Wdvp6t5B/gDFErHx/XR5+2ns34LX7/3\nMB5XcGFVR/0WKnIryas4Eo0ule0de6icEyyEXl/1CQECER9BuP8+r5sMjYu8vHy8Xi8XXnUL3f4c\n9KZy3PY2HB4XPkNFZFAdaO/32BrweeILs8yqMDF16vTI97a5theNJfFAsb9RPIdSHnlB8hnqG6GS\nZTkS2CzLsi1UYEUwQgzlhzuSy7QTLQTx2uupsp+MJjsVvd9Hc/Ue1Gorri0fkZ6RiT6zEL3KzqwK\nE9csXEB/fz96lQ195Vx2rX0To6UUvcmq2K7RUgpqNX32VlL0ZtIMWXS37iAQ8GPOm0zA7yErfzLp\nJivN25dTWZhGU3ttJNtjwO+jvuoTtq98hT5724CrB2jbvZbSWaeSmmYiI7Mwcm+F0nyaq1dFZiHh\n4ivWstnMsraj1+u5/9FnYoqGhBO8tdSsYWNvZmRQjbb3WyxnBSN6EsRVR39viRad7e8CHJFHXjAc\nhir010iS9CrwCcEc/P8HrE1Wpw5HhvLD3Zd27nL1DUvbj49S6aHY7KEmNSfGnp5XMSdGO3b0NDO1\nKC3SL61WGxpAvFQc8f9o2vEFfSoUtVmnrRWv2xkT8WKylpNbfhQ7175B/sRjsLXV4HbY0GeVsqfH\nht8TLFnYvudrtq14id6OOsX70aakUzL9W/Q07yQtI4uM7OLIvnDMv8/jpr1uEz6vDwLgafiEK397\nN06nk001dlLzlM1IDl9azKAavepzX0v/B35vMemfjVb06r0D6HAZrSRdgkOHoQr9XwHnAccQLJ/4\nEvD3ZHXqcCA20yJD+uEm0s6bG3axaKkZveqjIU/twwtBbDYbDzz6Z2o71ezosdDraMK/fQXWstlx\n0SkaXSqmnDKqGrbECJTLFpzNA4/+mV1tAXo76zGGQhcH9tPj7kWXmqFcESt3AobM/EjMfUvNGkpm\nnMrGD//MJ89fhcverngfam0KeRPmMPPUK0hJy6Bl1xoM5gK6W3fE5YOPhH+aczGFnvcTS1/h7O+e\ngEebjVL9T70pl4B9d4zpZaCQT7T0f+D3Fr3obIppN7++YuF+C+ZDJY+8YPTYV5x+QSiVcgWwMvQv\nTDmwK3ldOzRRMuMUm1z0YR3SD3egdu62NdDX10/BjNMJ+Lz0ObSsbzYMa2r/zLLXqQvMQJebio69\nseb1VZ+SXThF8Zxwv0pKSqPuJxe3q560jGy87j52rX+LjOxiDOZ8ejvrQaXCnDcJ/D7Fa4arWBky\nC4LpFXq7+OqN+2jf87Xi8Sq1hqKpJzL52J/FmJP0plz8AS/2zgZyFTNsNlIYVVRlY42di0wm9Kr4\nhTA+j5vOpm2cdEQxer1+v+3nSrH/syuM3H3rzXR19Q163r44VPLIC0aPfWn6fwLOBT5U2BcAhAox\nTJTMOLudNjz2KrDs27kXvUy7tnY39yxpI7P0mzRXr4okH+vu2sF/dzRw2YJgZE0iEiZOy8iit6sx\nodNx4P1kWErI9LjZte5NtCl62vdsIn2qBb/fS0HlsQC0121SNv30tJBuzsXncbNtxTJq1r01SK9V\nZBdPp3jqSZTOPDVub29nHYbMfMrKK2nc8BpaUzmGrGJ6O+vp7W5kwlFnxhwfDjuN1sbDaw002lSy\n8idT3ergT08+h9/vZ3NXwbDt54NlgDxQR+uhkEdeMLrsK07/3ND/FaPTnUObwQRsit5EW08LpiE4\n96KFRlpaGv1aK+0D7O5BB+QMFj+5lDtvujbuXJMpKOTCIZl9mGJmGeEY+pT0TNpq15FbPluxXzC4\nWcoUKl6+Z/MHZBZMwpQ3ISJEuxrlmCia8DV72nfHLLZSIm/i0UjzzkOFis7GbYomJJ+jlbtu/CFl\nZeXo9XpaWlq44677aevxMPHI76PRpsRcMzyARWvj9Q11FE89Oeba65tt9LZuJbu8PO5+h2o/T0YG\nyPGeR14QT7BGbuvo596RJGlpov2yLF+caL8glkT2V1PRLMp0MrUdGsUfbtis8HV1B92OAJkGFdPL\nTeg8XYOuCq1u9tHR0Y7ZnBkRCs5ABs7uRlyOHgoK8vDa6nGQQ4alNGYlrUarw+t2cMKRk8gw1iI3\neOL6VVe3J27ACBMuXm7ILowpY9jvtOHz9tNSsyaujm3lN89GrdZgzCklq2AKzTtW4XEFTS5ZhVOx\nVsxm8jE/CT7LXWsolI6npWYNBCAjuzgUkePGXDKbtLS0iDlm2T/fxa2fQO6EjJAT1x3JjaO0Erej\no51f3f1C3DP19DvQGgoUv9uDaT8f73nkBXsZCzVyV4T+PxbIAT4GNMApQM2I9OAwIpH9Va9ycNOv\nFgIo/nAfeup5PlhThy7NEFztaW/jwy93o3bsQl96kuI1+zXZXH7r46TgRFt0MhpLKUbAmBN0lO5c\n9yYTj/w+3TVrgs7gnV9CIIA2LY2UdDOu3k6+2u7hO8dk8dTvL4iZJTidTl594wPsna1kKJilwgXH\nfR43XU0yppxyPP0OfN5+MrKKMFnL6O+z075nI6jUFE2dF3O+Ls1A6YxTad75JVOPP5+8ymNorVkb\nSqIGPq8bXaqevIo5NFNiXkUAACAASURBVFV/gUaXsjdPTyiHDsSa06LvvW7z/yguKlHUiG02Gx6t\nJc6pm2bIpq32a8Vi4WPBfj5e88gL9nLQa+TKsvwsgCRJZ8uyfHp4e6hc4r9GpAeHEUO1v0b/cMO2\n+/9+vp7CmadH7M32zjpS9GbS876No7uBxu2tMdqry9FJb1cjOcVH0NUsR2LPw2h0qWRkBtMm5FfO\npVH+HGdPGxWzT6etdj0AWQUSTlsr/37/c849+zRef/eziAPTY2/E2ecGlUrZxOINbutp2UWfo5N+\nl52MrGJ6uxrx+7x0Ncls/+IVAn4vR//gdsXnVTjlBLKLp6NSqWjasRKDuYA9m/6Hz+sit/xIGuXl\nBPx+CqX5MRktw88y2pwWnfZBo0slPy+fB2/6mWL5v8EGZ40uFZ+jRfF+yyzKzmmBYKiMqRq5QKkk\nSZmyLIfLDBkZghNXkqQHgPmhdu4DvgJeJDhbaALOl2XZPexeJ5lkTpOHan+NjRIxosnIo6VmTSTG\nO9qGb7KW4/O4adr+BSq1Cq0ujbSMHMBPg/wZluKZin3JyC6OCEJdagZGSxpttevj/AM5JTP50aU3\nMfm48/ZqIJYSTB43TTu+oHbD++jSMzDnTqTP3obH3YvJOoG6zR/S5+gM2tF1qQQCfnq76qn6bClu\nR1ekH7s3/IcjCq6J65+rtyMmy+bOtW9QOOk4Zubb2bC9juyiWTTtWEFz9ZcYs4uCawDsjTz252Dh\n7paWZhx+A73bV0Sc3B31m/G4HKSk6mltbVEU+okG51OPm4la08LGGjt9KhP9tgb6bK04CmZxxe+e\nFSthBfvNWKuR+xRQLUlSDcGonQqCdXIHRZKkk4EZsiwfK0mSBVhPMAroCVmW/yFJ0r3AxaFrjwmS\ntZw9unDIwBWdgw0six9fypp6HQZzJRm61EgYZaP8+aBx7uAnp/gIUvTBiB1DZj729j3Y2msUTRL2\n9j1AAF2aAVCRlmGhv69H8dqmvElx52t0qag1OrKKpuLq7aB243vo0oxk5k2EgB9dugm3sweVRktb\n7ddsW/4iPS07467TKC9HmreAdKMlsi16thBuK91kxVbzIT+44Ho+WbOMdHaRUzILp62VzsZtFErH\n0+/Io6MjuMJ22Wv/oXH7OiYd/eMBTm43dVs+4r5nP+QbE75S/H4HH5wvRKvV4nQ6uffBJ9idNo3s\n8rmR88RKWMH+MqZq5Mqy/KQkScuASoI59XdGaf2D8RnwZejvbsAAnARcHtr2FnADY0joj7Q9LTyI\nbK1zYPdmxAwig9lfvV4vi5/8K59vbkOfWRSTNlijS8Xn7ceUo5ziQB8q/G3Oq6Stdn1Eu1Wp1DRU\nfUaBNC/GDNLTuhPpuJ9FNOn6bZ+SXaAcl2+0lEZi6GO3l6DW6sgqmITf2x+30rYjRc/nL16HvWOP\n4nVVai3ZRdNo2r6SdLMVg7kAR08TAb+P/Mq5McearRV01Pdx3aKHKZ4dL8hbataQZ8nEYsnhwqtu\noaPfjDmvUnEQSzdZUZknsbEDxe93KM7Rup5UUiyxIbFiJaxgf4meYQJ7s9DC6NfIDdXFvQUokGV5\ngSRJZ0iStEqW5YHJTyLIsuwDHKGPlwD/AU6LMue0EszXPyhZWXq02viydcnA6XSyZU8vmsx4e9qW\nPb0YDJphP/TfP/B0cBAxp8YMIktefJVFv7l80HOqeorJq5wIBAVav9NG7f9v78zj46rKPv6dJdts\nSSaZTNYmbdOepiulhbLYUhTxRRCU3VcQRa2yKIoovMALqCivyKIIRStUkKIoCLLJIlhRWmlpLZSU\n9tI2aZpm32eSyUxme/+YpTOZO9mapGnmfD8fPiQ3c+/cOU1+95znec7vef8VZiz8JKbcUvq6G+Nm\n7pGqGwBTbil1O1+Nc7iMiOK+rc9QOHsFfd3NONsPkG2fFc0RtNRuw9PXjcvRqlpD39t5CPus5QnH\nnZ0NmKzFDLgc6DMM0ffs7TzEnrc3RO8rEQ355UuoXP45PP0OPP09BHz+0JQiSLQBSSx9Pc3kFM1h\nwNWt7rqpS2dppYnHnnoOfcnpZA/haBm7EWzof18z5eV2IPQ70tTURFFREQ5HL/2a5Etxn68Xm82e\n5LPHY7Opdc5NTVJ9LO648Wucf8V36fCYybQU03HwP+RlOLnj7nvJzExsBjQWRhqzeAR4Czgl/H0G\n8Djw6eFOFEKcR0j0zwT2xvxIo37GYbq6XCO8vSOntraGXr9Z9Y+4L2CmunrvqOJpLpeLLR92oMsr\nSkgibvmwk7q6FlUXzcg5cFjM9WmZWIvnU7vjZbIs+XjdfQl+85E4vN/rwZw3Q1UUTbmltB/cSVqm\niZKq0/B7B+LOL6w8iX3vPqtaQ9/b3UishAUCfpqUTWh0ulDNfNMe3M5O+npa2Lflaep3/R2C6p58\nOYVzWPSJq8i2Hx5Pv9eDsvkPFM5eTm/nIdVkaV9nI8acIjIMuXEdsyJkWWycceoy7nr0DTLsZUM6\nWkaqi2D4f1+1sN+84gyygurpqMygA73eNKJWdzabeUJa4h2LyLGAe9c+BvbTKBjUBvSOn/5mVNGG\noR6eIxV9m6IoDwghPgegKMozQohrhztJCPEp4BbgvxRF6RFC9AohshRF6QdKgMYRvv+EM97xtFAS\n0ZSQRPR53ZitJapJmcGJnFgxb/xoU7Q/7OHdoumkZ2XH+c0P1djDnFeGKa+U1prtpKUb6etqxJhT\nGFfnX3nC+TQpm9CmZWDMtuNytOLp66a06nQOVv+N9KxsLHllNO1/l9nLzo1bTRzatZF//PZqgkls\nFnIK51IwcynG3NI4wYfQ/eeVLaRReRs0Wup3/Z30LAsmawn9znZ8HheZpjycbXVo9Xp0+tK40JdW\nq6O/pwmv1xv10BnK0TI2XzDcv69a2G+304PPuREs6nbTMrQjGS1TrXoHIUQaoSQuQgg7oRj9UK/P\nBn4GnKEoSmf48BvABcCG8P9fHcM9j4jRVuCMZjv7SK5ttxfibNpJYdWnEsIszR++ht1+acI5FouF\noLMWf1i0I2I8uC1frGPk/v+8QOGsE6PXGMns1mgtxu3qwud109fTHPeQ0Gp1lFStirpR9ve0otHq\n6Wn5iLzSRbi6G6ivfhVzgUhYTVhL50MwmPC+WWYb1tJFzD4hZH+gSbLIM1gKMFlL6Gk9wEB/D4GA\nj35nB36fF41OB4EghbNPSBzP8MPR7eoJbcqK8dCJdbSMtVSO5AuGE+mh/hADxmKqsg+xu94td8JK\njpipVr3zIKFyyyIhxAvAiUBijV08lxDa0PUnIUTk2BXAI0KIrwN1hEJE48qRVOAMV0452mtnWQrU\nk4jZ8TPx2OtiKqe9/gNcPc3RUstks3ddWgYF5Utx9TRHY/wjmd0as0Oz2sLKk9i35c+Y8koTHhKh\nc4OkZ1kGJWfLsVUsC4VvBmHItlMkPkbjnn8CkGnKI7ekipzCuSH3zPDGqOEeSgGrl+yCCjKNVg5W\n/40SsQpdWgbt9R+oVy0FoWnfvykuKqa8fGZSR0vn/r9y6vLjURq99Hc3jkikh/pDHNDlcslnVkbt\nLOROWMmRMNWqd/4khNhMaGeuB/h62H1zqHPWAetUfvTJUd/lKDiSCpzhKjZG00h8+/Z30WUl1oAD\npFviwztqu0YHXA7aDu7EYisfcvbucXXhaD+Arfy4qCAWVp5Ek7KJIEGybaEWgRHrAYDezgbss5YT\n9Psw5hQS9PuS2CD3JZSHBoMBOhv3kJ5lSTgHoGDm8XQc3EnF0rMpmLkMt7OD7pYaDJZQRmAkD6WI\n+OvSMihfchZNH7xMlsFIVk6l6niarKWggeNmaTAYDHEP736NhTRvB4tmmrnhtrXRcsuRivRI/hDl\nTljJeDBZ5nkjrd75o6IolwBPj8u7ThDjFRNT+yMeybXT09PjNlS5nW309bREY84RsmKe2kOZsAX6\n26PimEwozcFWgtbSOC8bl6MVjU6Ho7UWi62C3MK5eAf6QuLu9zHQ30N7/U56WmtDNsb6DOp3bSQ9\ny4zJWoKzox6vu5e8GYujNsjBYJDW2u0omzbgaDvA4k9eQ19Pc1yDb7/Xg6unFfuck7HYKggGAvS0\n1TDzuLPobjnsbT9UyGVwvD3o93HmyuNw9fXyb6U5mtiKTYz39zSycqEt2th8uIf3aERaulhKJpPJ\nMM8baXinVghxJSE//YHIQUVRppSf/kTGxEZy7Wdf+ecgm+HDMedICWKsQ2VtbQ1utzvuurGCllN2\nXNSEzWQtobH6FYw5haRnl5AV/mU499Kvc8u6zdH3cvd1RmfJRoudRmUTFlsFptwSWmq34WitJSPL\ngsHXhHXpOaRlGKLnaTV6mmu2UDhrBd2tezGY80M7WAdc7PnXE3Q27Ip+5v3b/kLligvp627CmF2E\ns+MgQb+XmUvPoaXmXdBo8fk8GHNLSDdY4h5asSGXj7Y+g7W4CrO1jLaaLZi13dhyS+nrrI/+wn/t\nsvP55o8ew+8boGH3P6P+Q5HdtSvmWbjkvDMYGBiIC7ON1wxculhKJovYCYvP1zv5LpsxXEIoiRub\ngZtyfvrj3U4wdqY43DLfYrEkXQnotFocrfsx6twsnGEgENBw9R2P4gpayPC343UNEMgtjvPE7zhU\njdfRwLdvvo11v3uG7XsOYilehEHjoNzSyve/9XUsFgsul4sMfwd93WlkGq1xm6faDu5kzokXxMXj\n7TOX4zn4Bhse/mlcCKSvsx5/IEj5krPQanXU7/kHWWYbyuY/0NOyL+Ez93U1oE/LIuDz0t/bjiG7\nEF1aOvu3/QWLrYIsUz69XQ042+rwzT4xvkWgpYDe7kY8rh7mr7qCoN9HX08zKxcWcNO3b02YodfW\n1tBPNtBNYeWJ0c9jtJbQpGzi/dp+blz7rwlrCC5dLCWTjcFgwGazT0gJ63DWyhbgVqCa0A7bnyuK\nor7bZQowXu0EkyVsF8wwUt2lvsx3OBxJVwImaynXfqaCZctO4OHH/hReDUQ2bJXh2v1PXMqmuIRp\nxBP/mzf/H/qS0zFXHI5n13s9/GbDs1y35jIefuxP9LoG0GkG4koYfe4+DNl21cRnRk45AwMDUSHb\nvv1dfv7sANn20IYwV08LvR31fLTpyaRjXSQ+hjG3iNaa7cxcejYtNdvobt4b3eELkYdMqPft3BUX\nRSuO3H2dBLxu7Hm50YTqybPM0fDM4Bm63V5Ihr8dfXpm3Odp3vdO3JjBxNogyNi9ZDow3HRoLaFa\n+l8D5wP/C9w20Td1JAzVTjASVx9OGJIlbBfmNLI4r0V1mT8wMJB0JWDUOlm27ITQdVRWAwWzltNS\ns01VoNu8ZgabLujSMtixt4Pv33YnrfrjyK0IXS8S767Z9jy6tPSkRmtuTXY01GUwGFi27ATML+7E\n4+pm35ZnqNv5KgG/T/Vci20Wc1ZciFafjrOtDp0+dM9eRwM5hXPUN4XlhHbsphssoY5cRis+r5vb\nrr6UzMzMYWfOBoOBcmuAfs3hkYiUsQJxG7WkDYJEMjTDiX6FoiiXAQghXkG9beKUQq2dYKwhFgyd\n2B0qYVt90MXDP/gKkOh5r9frk64yVojcuDDF4NXAQH9PXEI0FkNOaZznTSDgp/GjTRAI4LbNxN2x\nN26Dki4tA6utmKx0LT0xpZyxDC7/8vt99NT+i3c2/wN/ko5VxtwSZp9wPlqdHkd7PSZrKS5nKwZT\nPr6GjVx72Sd58m31h57JWsqBD16jaPaKaCVRRqaZ5197mxuuvXJEoZjvf+vrXPH9hyD8eVzONvod\n7XQcqo7b+FZYeZJsCC6RDIF2mJ9HQzlhL53EnTdTFIPBEG0nqEZEGAYTSdgOdU5kmR/7wPD5fAT8\nfpp3v0bTvndwtNXReeAdFuY2ccv1XwWS5xwyjVZ6uxpU37O/uyFqugShkEbR7BWUzl+NxVZOwcxl\n2Gcuj/O4ycgu4barz2V5ZVa06UiEwVUnBw7UcuKJS9j01quqgp9hyOH4s29g9ZceZMbCT1BadRqV\nJ3yWoN+DMaeIonkrae838Mjz7yX9DL2dhyibtxqtPo38skXYZy4nAFR3FnDH/92PyzW83YbFYuFj\ni4uin8fRUkPZgtMpmLkMc/6MuHGYCg1NJJKpynCiP1jkjxnRh7FtdhjrBolfrNtAdXcxJYvPpaB8\nKbq0dEwF89FqtdGZbCTnMFiIgajfTCx+r4ecNEfc91pdmrrZmD4jen5m0EF5eQW33XAti/Na8Hfs\nCiVqO6opT1O47IL/ora2BpfLRXl5BTNmqKwGjNnMO/ULzD/9K6DREIzx0dGlZaDVp2MrXxqNq9vn\nnU5vV4PqZ+hu3oujo46Az0tLzTaa9v6bYCBAd8te9nTl843bHuHetY/h86mHlCJct+YyFue1MNCy\nA11aepJxSKeqJEOGdiSSJAy3rj5FCBHriVsQ/l4DBBVFSdwtNIUYS431SM4ZXMUxOCSkS8uIhmN2\n1tbHzWSvufJSvvLt22j3ZZOVXUx/TyPZ2m7OPm0J/9j6GlpjAcbsInx9TZy6sJBvfu+HPLT+KXbW\nOulyepL66kRcIzON1oSerw6Hg7sf+DW17UE2vd/O9lsexZBTjEHTy+KZZv7nf27j4os/C0CWwUjF\nsgupWHoOOn1a9LPHlp0CmKxlHPzgdUzW0ug4zVp2Hvu3P48ppxiTtZTezkP0djcy99T/RhMM0tfT\njM/rwu/1UCJWRX3/YWQJ2EjobvfuD7l9/VbV1xgsBVx4zseSXkMiSXWGE30xzM+nPGOpsU52zjVX\nXsq9ax9LqOo578xTh6zhb2pqwhIW64fWP4W+5HTyCdkr5JcfD0B6RgvPPfoT6upqAQ3l5RVxwh3K\nUdRy57rXVe+5t7sR/4Cb044r4ro1X4v72dr1T7G5ug2Pq5uZx306QWz58CCf/vQ5dDo8DJgXUFy1\nOu782JVEROD7nW3klSxAq0+Pvk6vT2fuiosYcDlo2r8Fj7MLo7UIV1cTzrZa+hytZNtmkWW30d2S\nmIsYaQK2vLwCg0Y9vWTQ9FJcXDLk+RJJKjNcj9y6ybqRiWIsNdbJzrl37WOqVT3elzZi0CS32S0q\nKqKvz5+wIoitqd9ZG6rHrapaoHqd9PR0/rrxXdpb6ii0zktYhXh6uygw+bjl+h9Gj/t8Pr536494\n8YXncLQfwD7rBA7ueoMss42iuafEie28pavZXp9GRhIztCyzLZpQjuyaNefPoKV2e0KyON1gIdOY\nS+m8VXha3+fGyxbz07XVFC47L66cc/AKYqQJWLlLViIZO8PF9KcNasnXSBvDZInE2HOigq0SR97d\n4GFeaeawSdORJImTESkjLVp4Nk37t3Bo91s42g7QtO8dane8iN0S5LEH74q+vqZmP5848wyeXH8/\njvYDALTV7Qg5cgaD1Fe/eTgp6tGy9YODZBpy6XfG98Xxez30dTfhaKulZf82mvdtjfbq1aVlMODq\nifvcfq8HR3sdXk9vqC9uVhGZmZlk5JSPKBcx0gRsJL5/OF+xi8V5LXKXrEQyDCnZvXksTpyxNgyD\nvV/cGgsXnHUyL/xt85BhpLEmiQevEErnhayPne0HCfY28vsH/ofS0jIAmpubuPfeu3nyyccTEqMB\nv499256laM4poNHQUvsfersOYc4pxGidTXfLXrpba8grXYhGp4/uEM405aPVp5FhyMbncVG6YPXh\n+zZZad63BV1aJu7eTtINZky5paRlmGj8aBO2XDOgSRr+SpaLGA65S1YiGRspKfpjceK02wvJDHbR\n+NHBhKYotlwzJSWlw4rQWMMSLS3N9Poy0Q/ahJRTNAd9RiZer5eenm5++cuf85vfPEx/f7/qdawl\nCyhfdCb6dAP9zjaMucXYZx5PS+02LLZyLLZycour2L/9L4A2rklKJBxTu+PlaGzf7/UQCPgorFxB\n/a6/U7bg4wmv9zVspKCgINonYPBsv7e7kTxzBotneMc0S5e7ZCWS0TFtRT+Z+I7VidNgMODvbcQ+\n8/SEJh6+ho3Rc4YTodEmln0+H3988U1cjlZMuSrdojoP8NxzLfzqVw/S3a3eq95iq2Dexy7HVnE8\nGo2Glppt+H3eww+QmCRtWoaBtEwTmcY81XCM0VpM64EdBAN+Aj4vGp2e1gM7yDDlJrxeo9PT3jPA\nd+76fbRPQMTiWavV4fd6OKHSwE3fWiNn6RLJJDHtRH+40M1YnTgdDgd95GBVa+JhLh3xtv/RhiV+\nsW4Du3tKKZpzuFG63+uh6aNNDPQ7UTZtYMsL6jP7dEM2VSuvoHT+ajSaUPrG7/Xg87jQ6HRRkY5t\nEg6QYYg3bovFmF1Ib3cTZk0H3UEjlvyZgHo3rOZ971A4P9Q5LNInwO/1UF/9N0pLysIPu2vH1RxN\nIpEMzbRL5EZCN1rrAkx5ZWitC9jZYecX6zYAY4+r3/3Ar9Eb1YUw4mUzUmIFH0iaTE6WPNbq01E2\n/Z5dG3+DbyBR8PXpWRTPW8VpX/wlWl06TR/9Oybp+zJoNNGGKhDqWBW76zfHqGPAob671tFeh9vR\nxuwZxegzMtGgoa+rCWdnfdzrBrd4jKBLy6DQXsh9N32e7179JSn4EskkM63+4kYauhltXN3lcnGg\nQ4Pb1Y4xpzAuiQsh2+aRVJ04HA7uWbueA+1a3BoLXmcTLkcL5qLFmHR9CcnkuroD9GNJSB5rdHpM\nuSW4euIfNFpdGvbZKyiaewqm3GK6mz9Co9VgK19Kv7ONvo5GSuatJBD0EfT7IBxiiW1a4vd6OKGq\nkIGBAfY4E8eIYJAMPTTpFlE053CYq2H3P+Pq+N19nWSZ1S0wfGl5OBwO8vLUO4tJJKmOy+Vi//7W\no+qnf0ww0tDNcHH1waGXlpZm3For3a3vEgwGMVgKDidxy5cyMy8w5D+Mz+fj3rWP8frb71FY9Sn0\n+WFb5bwZWLyeUCJ17qnRZHLk/t7b14Gz242joz4uedzdWkPhnJPpbtnHQH8PWl0aFcedzcyl59DZ\n8CHFc08BQrF8v9cT6oplsFCQrcHdVYPOWEhb3Xv4epvJs6QlNC2JjMMV195Mm9+KwWKn39mK3zdA\n/owluNqVhBl8kTiVmm3PY84vI8tcQGagg4F+b9QgLRbpjSORqBMXnsaCgfHvETGtRH+koZtkcfWI\nOA/OB3ztsvNxNu1k9vHnJiRx92/9Iw89+cCQ9/Xj+x5hR3MOelNx0lr1AZcD70AfOzo7uGftb9nd\nU4pHr6W17nkWrv7q4fh7th2f14NOn87cUy6lp6WGuSdfQpY5NGvWtqZHbYwj188w5eJ1HMK46JyE\n6hpP/Zs8dPuVdHS0J+QXHn/wJ9zz4Hq27a4jy1SCUeemLLOGj8zFCZ9Rq9Vhn7Ucn8/DvNx2br7+\nmnDvALmBSiIZKUfS43ukTCvRH23oZnClTbIBX7v+KbJUyg0BTNk2vN6BhOMRXC4X25QuvJDUNyfL\nnE/z/i3kFgk6nR5efv1terpaaN73bzIMuWg+/vXoa919nejTMsgy27DPWp5wLWN2Ic37t6DPMESr\nZDKNVtK0PtUHjhMba66/nQ2/+lnCTEKv13PTt9ck5CCuvuNR9c/a3cDKhTZuuPY76PV61RXVivlW\n1lweX6kka+0lkvHr8T0c00r0Yez9TIca8G27G0m3VESPBQL+6MYlk30+3/rxExxfmau6BGtpaaY3\nYCbLbKXjUDXm/ESPun5nGyXzVuEd6Ofg27+jLVwSCeDp6+Rg9d+oWHIWELJhdrTV0e9sU71WX08z\nJfNWAUQtDvo79mEpUrd3MFjstDV1cc+D67np22vUXzPo4ZjswbpycQE3feuw74/aiqq8/HALuLFs\nkpNIpisT2eM7lmn3lzXWnZpDDTjGEtL8XUBIZJv3vYN95vIY0StPugSz2wsx63oJppXFNQeP4Pd6\nGHD3UvOfF9i75WkCvsRVg/L2k5TN/3h0U1Yw6MfrHlC9VsA7ED0WCRutXj6HDw4evv9YXGETtC0f\n1LF794dxRm/JSP5g/bLq65PtXZiMpaxEcqww1srC0TLtRD/CaHdqDjXgRp2bqjITu3tCHjHJShHV\nlmAGg4Flc3PYcsgT1xw8y2zD2b6f5v3b6Ti0iwGX+sYqY24xhZUnEQwebmVgK19KzX9eoHbHyxit\nxaHa+c5D9HY1UnniBdHXZZltVKTv5YZrv8M9a39LdXsobxCpPPJ7PfgG+nG2H8RkLeb29VsxaN4c\ndrY9HhYIk7WUlUiOFSbLSHDa1emPlWQNTiIDfsPVX2ZxXgt9h7YkLUVMZpp2y/VfZXFeC8GuPWTn\nzyDHoEXXspHWnc+GNlmpCH6mKY/Fn7yG0674JSXzVlH/wes42upo2beZxvefRavVkGWxEQwEaat7\nj0DAR+WJF0T7AEOoN+/N118DgE6ro/PQ+/i9A7TVvce+rc/SvH8rwYCfmUvPprDyJEx5MxL2NQw3\nZoNN7EbKkZjPSSTTlckwEpy2M/2xoNbgJEffwzXf+2F0dtvR0c63fvwEMPJSxMi5fX19PPfcM6xb\n9wx79nyoeg9pGSYqV1xIxZKzok97l6OVkqrVeAf6yC9fBuXL8NS9jsdUiE6fTsDvoajy5DjBDz2s\nLFFL6OquIgrnVgCHK3f2/+dFTDlFqquWf+1s5GsOBxaLhYlgspayEsmxROwq2ufrnZA6fTnTjyHa\n4KT8eHRp6eSXH4++5HQeWv9U9DV5efkcX5k7rI2yGvff/zOuv/6bqoKv06dhq1jKaVc8wOzln43b\nLBXwe0k3WDCGBVqXlkFG7kxWVGgwanrJtlXQ/OFrdB54h95Bs4OhLKFNOUVkJako0huLuPuBX494\n7EbLcCsrGdqRpDIGg4HZs2dPyN/BhM70hRALgeeB+xVFeVAIUQY8AeiAJuByRVHUu49MMsM1OImN\nMY+1Quizn72ABx64L+6YXq/n8su/xFVXfROv18ufX3mL3fVNuDUW9N4OmpubKVv0yYRruTXZXHLe\nSuz2wnBc/VKAtmJM+AAAEj9JREFUhBh7ff3BpAlqS34ZfkctMCfhZ/3ONg4EdBMaWx/rOA6FLP+U\nSIZmwkRfCGEEfgnE9rX7IfCQoihPCyF+AlwJPDxR9zAaRlMuNdZE5sKFizj//It49tmnATj//Iu4\n8cZb4hLON82ZG72uxWLhuz/9Q1zYJkIkBGIwGGKEvzAheT1UGCULB8WlRhpVqoD8Pg/etBnjViam\nxnh64svyT4lkZEzkX4MH+DRwY8yx1cA3wl+/CNzAFBH9scSY1SqE2tra2LjxDS6++POq17rxxlvo\n7XVy4423smjRYtXXxF53qGx+enq66g7iWKEbqiKguaEGUTKPpndeIc1SisFSgMvRGrU/DnbtmZTY\n+nh44svyT4lkZEyY6CuK4gN8QsT1VjfGhHNaAXXbyjC5uQb0+sRZ7sRg5sQqK1sOHW4Q4u7rJC3d\nyCnzrZSX24c82+FwcN9993HvvffS19fH8uVLyM/Pp6go9BFtNnP4/0t47bVXRnxXd95yFT++7xG2\nKV30BcwYtU5WiFxuuT50XE3o1j3xR27//jcSrvHG1oNoDYX0O9vw+zwULTwbxemjKP8AfuvcUKK4\nbFH0868YweceC5GxGC9cLhe7Dvaiy0ks/9x1sBejUTelQz3jPR7HMnIs4pmI8Tia6171DtwxdHWp\n966dKNZcfgl9Dz/OG5s/QGe0Y8guZKD7IH0FdpqaulTDBG63m8cff5Sf//weOjo6osfPvfAK5n/i\nWgwaBydWWVlz+SVjDjNc/eUvJIRAGho62PJhB7q8+OemLi2DLR92UlfXEid0X7rkc2zeuRZvWnpU\n2IGQ02ZWMQutrexu8OB2+qKx9TWXXxbdPTte2Gzmcb9mbW0NvX6zamiuL2CmunrvlO2uNRHjcawi\nxyKeIxmPoR4Wky36vUKILEVR+oESoHGS339I9Ho9Wp0u2vgDAFs51V2JYQK/38/TTz/F3Xf/hEOH\n6hOu1XpIodLdi6lkAVsOeeg/wjDD4BDIaLdst7Q0M6C3YVJpjpKYFJ46SdCRxPtl+adEMnImW/Tf\nAC4ANoT//+okv/+QjGSXaFZWFq+++ld+8pMfoCh7VK+TnmWhcsVFZNsrE84fDzF1uVy43f1kBnuA\nsoSfZwZ7cLv7495vJMI4lfrNjiYxO1k7GSWS6cBEVu8sA+4FKgCvEOJC4AvAY0KIrwN1wOMT9f5j\nYbjZ8yuvvMQjj/ya7dvfVT3fYDBQMOc05q38Ivr0rITzj7QSZrAQ9jTWUJg9RzVBe/v6bAyav0eF\n8lgTxtEmZiei/FMimY5MZCJ3O6FqncEkFp1PEZLNhntaa9i98WE2PrZX9bz09HS+9KWvsGbN1dz2\n4AtoBwk+QJq3HbfbfUSz/cFCaMgtpknZRFZWOhmWEjyOBvr7ByhaeHa0zDNWKI8VYRyLL894ln9K\nJNMZWcAcg9psuK3uPbb8+Y4kZ2hYuOQEHl23LmmJZSDgp0nZhCErg9vXvzsiQzM11IRQq9VRUrWK\n/oatXHZaLhtebcRasSruvMFCeSwI45FYzE6lEJVEMhWRNgwxuFwuzjvzVKrM9VHDoxyDllxrosGa\nffaJrPrizylb9V2efeWf0eODDZOaPniZwsoV5FasUG3UPlLUDMoCAT+NH22ipz/I4xs76emHxo82\nEQh78UcYbGB2JEZpLpcraSP38UImZiWSiUPO9FFLGnqoKsvkgrNOpqSklNdXlrEm7BVvLZnPvJVf\nxFo8L3p+7Ew6NsxQV1fLXY/2jNiGeSjUhHCwr78p3MIx0jwlwngI5WTueD3W8g8SybGEnOkD9zy0\nnuff3EbAPDs6G9/dU8oLf9uMwWDg3HM/x1lnncOiT3yDky/+cZzgg7oVsMFgIC0tnX7U62VdQRON\njQ2Jx5PMpAcblPm9nqS+/jp9RtzrxkMoI/kErXXBEa1YRspkWMxKJKlISs/0fT4fjz++nofu+wGe\nfifBgJ85Ky4CEmfjDz/8CFff8SgaTeKesmQz6Wde2ojL0Y05P9GG2eVo5ZmXNnLTt+dE7+UX6zbw\nfo0jmmRdMssSN5OOTcR2OT1Jff2zzDa6GnaRa84Yl0Tt0Wh4IhOzEsnEkJKiHwwGefHFv3DXXT9i\n//590eP7332O8sWfIj0r5CEfmzQcbcjB5XKxu8GN3+dRbWvo8/Szu8EQFcz7f/U7qruK0OfHlyje\n/6vf8b1rrwRQCR29iRpGrZMfXXcWBQV2HA4HAwMDRxSCmazenWrIxKxEMr6knOi/9dZG7rzzDt5/\nf0fCz3wDLvZve56qlZcDiTP40ZQ8RoSysLIq2iIxYmjW72gnb8ZC3ASjs9hN1c1YKyrirqFLy2BT\ndTPXqLRgrKpawJJZ76o+hBaWm/jrxnfHLf4uE6sSyfQhZUR/x47t3HnnD/jXv/6h+nOtLo2KpWcz\ne/l5gPoMfjQhh4hQarVlFM89NWrgll+2iPb6DzCYbeDYh91eSF3dAfRGde85vbGIuroDVFXNT/hZ\nsodQwB8cV8dJmViVSKYP01709+79iLvu+hEvvfS86s+1Wi2XXvoFsu2VHOjU4+7vQeeqHzIWHgk5\nRJKuauI/WCh1aRkYc4qiXvVAjGAGcfU0Y7Elxv77epqAYMJxUH8IAVx1+yPo8o68YiiWY2Vjl0Qi\nGZppK/qNjQ387Gd38Yc/bCAQCKi+5jOf+Sw33XQrc+bMBUbedWmk5YsRodx1sBenz4iruxG3q4fi\nouK4SpTy8pn4XS2qsf9AXyvl5TOH/Kyxce/a2poJib/LxKpEMj2YlqLf2+tk1aqTcDh6VH++cuVq\nbr31dpYuXRZ3fKRJw5H6wkSE0mjUUV29F4vFgsPhSBBMg8HAGScv4o1tW9BnGKKxf5/HxRmnLBqV\nuE50/F0mViWSY5tpWadvMpm59NL/Tji+ZMlSnn76ef785xcSBH+kDNVoPBI+GUxEKPPy8pPuhP3O\nVVdw5ooKco06PL3t5Bp1nLmigu9cdcWo7k82HJdIJEMxLWf6ANdddwNPPvkEfX29zJ5dyc0338Y5\n55ynWmc/GiaqfHE8wycy/i6RSJIxbUXfZrNxyy23kZGRyec/P35WAcdC+ETG3yUSSTKmregDfPWr\n3xj+RaPkWCpflPF3iUQymGkZ059opC+MRCI5VpnWM/2JItXDJ6n6uSWS6YAUfcmImUx7ZYlEMjHI\nv9RREJnh5uXl85sNz6ac+I22b61EIpl6TF+FGkcGz3C9zkZc/R6KxKmYVHrRHm0mIvxyNOyVJRLJ\n+CNFfwQkzHDzyrAM6lB1NMVvMlYgR9NeWSKRjB9S9IdhqBlupENVpHRzssVvMlcg0l5ZIpkeyJLN\nYVBrSB7BYCnA3dcZ/X6yxW9wC8PcihUUVq6ged870dcMZQ8xGqS9g0QyPZCiPwxDzXBdjlYyjVZg\n8sVvKA+g2B65oN7DdyzI/QkSybGPDO8Mw1A7cH3ORtxO+1Hxthkqxh5ZgRhzQo1ZxmsFkur7EySS\n6YAU/RGQzMDsl7/+IR0d7UdF/IZbgeSXLQImZgUi7R0kkmMXKfojYKgZrsViOSr3NFVXIKmCXO1I\njlUmXfSFEPcDJxHqAXidoijvTvY9jJWpNsOdiiuQ6Y7clSw51pnU31IhxGnAHEVRThZCVAHrgZMn\n8x6mE1NxBTLdkbuSJcc6k1298wngLwCKouwGcoUQUp2OkMgKRM7qJ5axdE2TSKYak70eLQS2x3zf\nFj6mmpHMzTWg1+sm474mHJvNfLRvYcownmPhcrloamqiqKhowh96+/e30q9JvivZ5+vFZrOP+rry\nd+MwcizimYjxONpByCF7F3Z1TY+Zk81mpq3NebRvY0owXmNxNGLrer0Jg/r8hMygA73eNOrPJn83\nDiPHIp4jGY+hHhaTHd5pJDSzj1AMNE3yPUimAYN3I2utC9jZYecX6zZM2HvKXcmS6cBki/7rwIUA\nQojjgUZFUeSjXTIqjmZsXe5KlhzrTGp4R1GUzUKI7UKIzUAAuGYy318yPTiajp9yV7LkWGfSY/qK\notw02e8pmV5MBcfPqbZnQyIZKdJwTXLMIWPrEsnYkaIvOSaRsXWJZGwc7ZJNiWRMyNi6RDI2pOhL\njmlkbF0iGR0yvCORSCQphBR9iUQiSSGk6EskEkkKIUVfIpFIUggp+jG4XC5qa2ukRa5EIpm2yOod\nZDckiUSSOsiZPkfHsVEikUiOBikv+rIbkkQiSSVSXvQjjo1qRBwbJRKJZLqQ8qI/FRwbJRKJZLJI\nedGXjo0SiSSVSHnRB+nYKJFIUgdZj4h0bJRIJKmDFP0YpGOjRCKZ7sjwjkQikaQQUvQlEokkhZCi\nL5FIJCmEFH2JRCJJITTBYPBo34NEIpFIJgk505dIJJIUQoq+RCKRpBBS9CUSiSSFkKIvkUgkKYQU\nfYlEIkkhpOhLJBJJCiFFXyKRSFIIabg2AQghFgLPA/crivKgEKIMeALQAU3A5YqieIa6xnRBCHE3\nsJLQ79pdwLuk4FgIIQzAY4AdyAR+BLxPCo5FLEKILKCa0Hi8SYqOhxBiNfA0sCt86APgbiZgPORM\nf5wRQhiBXxL6BY7wQ+AhRVFWAvuAK4/GvU02QojTgYWKopwM/Bfwc1J0LIDPANsURTkNuBi4j9Qd\ni1huBTrDX6f6eLylKMrq8H/fZILGQ4r++OMBPg00xhxbDbwQ/vpF4IxJvqejxT+Bi8JfdwNGUnQs\nFEX5o6Iod4e/LQMOkaJjEUEIMQ+YD7wcPrSaFB4PFVYzAeMhwzvjjKIoPsAnhIg9bIxZlrUCRZN+\nY0cBRVH8QF/4268AfwU+lYpjEUEIsRkoBc4B3kjlsQDuBa4Frgh/n5J/JzHMF0K8AFiBHzBB4yFn\n+pOP5mjfwGQjhDiPkOhfO+hHKTcWiqKcApwLbCD+86fUWAghvgj8W1GU2iQvSanxAPYSEvrzCD0E\nHyV+Uj5u4yFFf3LoDSesAEqID/1Ma4QQnwJuAc5SFKWHFB0LIcSycEIfRVHeI/QH7UzFsQhzNnCe\nEOId4KvA/5KivxsAiqI0hEOAQUVR9gPNQO5EjIcU/cnhDeCC8NcXAK8exXuZNIQQ2cDPgHMURYkk\n61JyLIBVwHcBhBB2wETqjgWKolyiKMoJiqKcBDxCqHonZcdDCPEFIcQN4a8LCVV5/ZYJGA9prTzO\nCCGWEYpVVgBeoAH4AqFyvUygDviyoijeo3SLk4YQYg1wB/BRzOErCP2Rp9pYZBFaspcBWYSW8tuA\n35FiYzEYIcQdwAHgNVJ0PIQQZuD3QA6QTuj3YwcTMB5S9CUSiSSFkOEdiUQiSSGk6EskEkkKIUVf\nIpFIUggp+hKJRJJCSNGXSCSSFEKKvmTaIoSoEEIEhRDfGHT8Y+Hjq4/SrQ2JEOLtqXpvkmMfKfqS\n6c5e4MuDjn0ZUI7CvUgkRx1puCaZ7jQCmUKIBYqi7Ar72q8E3gEQQlwMfJOQt0kb8FVFUTqEEFcB\nXwQGADdwiaIo3UKI/wM+TshNtYHQZrPPA2coinJZ+Jr/AO4EfITsBdzAs4S80R8CKgEz8AdFUe4N\n39NTgI3QQypzYodEksrImb4kFXiCw17kFxBy+wwQ2h17CyHB/hjwD+Dm8OuygDPD/vcHgMuEELnA\nNcDJYY/zZwltlx+K5YSaXzwKXAc0KopyOrACuFQIsRi4DOgP9x24EVh4xJ9YIkmCFH1JKvBH4GIh\nhB74EiGHSwjN1ouA18Kz80s5bF/bAfxVCPEWoQYw+YqidBGyCnhLCPFdYLOiKAeHeW8lxnfodOBz\n4fd6k9CMvhJYBLwdfnETsOeIPq1EMgQyvCOZ9iiK0i6E+A8he+ciRVG2hfsdeICtiqKcE/t6IUQp\ncA+wQFGUViHEPTHXujDc/ONsQuJ/ATDYyyQ95uuBmK89wA8VRXlm0Pt9nNDKI4JuLJ9TIhkJUvQl\nqcITwK8JtWyMYAROFEIUKorSLIS4iJBI1wPtYcG3AmcCLwshZgHnKYpyP7An7Ia4BHAQChUhhCgA\nFiS5h7cJtUp8RgihJfRguRP4EDgFeChsvyySnC+RHDFS9CWpwovAOuDJmGONhOLsLwkhXICLUGK2\nDdgrhNgK7AduBx4GXgGWho87gS5CbohB4IawN/xuYHOSe3gIWCCE+Deh2fxLiqJ0CiGeAM4VQvwL\nqAW2jt/HlkjikS6bEolEkkLIRK5EIpGkEFL0JRKJJIWQoi+RSCQphBR9iUQiSSGk6EskEkkKIUVf\nIpFIUggp+hKJRJJC/D8+Kg6BAGkS6QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ffbbbbc1518>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.model_selection import cross_val_predict\n",
    "from sklearn import linear_model\n",
    "\n",
    "lr = linear_model.LinearRegression()\n",
    "boston = datasets.load_boston()\n",
    "y = boston.target\n",
    "\n",
    "# cross_val_predict returns an array of the same size as `y` where each entry\n",
    "# is a prediction obtained by cross validation:\n",
    "predicted = cross_val_predict(lr, boston.data, y, cv=10)\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(y, predicted, edgecolors=(0, 0, 0))\n",
    "ax.plot([y.min(), y.max()], [y.min(), y.max()], 'k--', lw=4)\n",
    "ax.set_xlabel('Measured')\n",
    "ax.set_ylabel('Predicted')\n",
    "ax.set_title('Cross Validated Predictions')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sM9ent5QEC_T"
   },
   "source": [
    "# Uploading Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "CIV_9XXWHK2q"
   },
   "source": [
    "As mentioned in the introduction. The VM's hosting your notebook are ephemeral so when we want to upload data files to them, we must do so in a reproducible fashion (i.e. we will write code in a notebook cell to do so)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "OMS0EmomITSi"
   },
   "source": [
    "## From Your Local Machine\n",
    "\n",
    "One of the simplest ways is to select a data file from your local machine which will be uploaded to the current working directory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 86,
     "resources": {
      "http://localhost:8080/nbextensions/google.colab/files.js": {
       "data": "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",
       "headers": [
        [
         "content-type",
         "application/javascript"
        ]
       ],
       "ok": true,
       "status": 200,
       "status_text": ""
      }
     }
    },
    "colab_type": "code",
    "id": "VRgl9X8PEb2M",
    "outputId": "cb40b66a-5127-4336-827d-4e72c61e79b1"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "     <input type=\"file\" id=\"files-a5660fba-2386-42a4-82f0-0127bf384a47\" name=\"files[]\" multiple disabled />\n",
       "     <output id=\"result-a5660fba-2386-42a4-82f0-0127bf384a47\">\n",
       "      Upload widget is only available when the cell has been executed in the\n",
       "      current browser session. Please rerun this cell to enable.\n",
       "      </output>\n",
       "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving local_test.txt to local_test.txt\n",
      "Your notebook file \"local_test.txt\" has been uploaded to the colab machine instance\n"
     ]
    }
   ],
   "source": [
    "from google.colab import files\n",
    "\n",
    "uploaded = files.upload()\n",
    "\n",
    "for filename in uploaded.keys():\n",
    "  print('Your notebook file \"{name}\" has been uploaded to the colab machine instance'.format(\n",
    "      name=filename))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "1Y4OhCykPiBg",
    "outputId": "24c8080d-5304-40ee-c632-32b4f8d9d0e7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "example.txt  local_test.txt  sample_data\r\n"
     ]
    }
   ],
   "source": [
    "!ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "qQmS0fFnIfb-",
    "outputId": "f6df3417-7b69-40e1-f99a-4358008b7b7c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "testing file uploads from our local machine.\r\n"
     ]
    }
   ],
   "source": [
    "!cat local_test.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "e66DxHJIJu-g"
   },
   "source": [
    "## From Google Drive\n",
    "\n",
    "Here we will take a text file from our Google Drive and copy it to our local working directory. It is important to make sure that there is an unrestricted shareable link to access the file if you want this to work without a hitch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 187
    },
    "colab_type": "code",
    "id": "RL4qnugdJucc",
    "outputId": "204e881b-e520-4389-d643-4e68f37a9a33"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: PyDrive in /usr/local/lib/python3.6/dist-packages (1.3.1)\r\n",
      "Requirement already satisfied: oauth2client>=4.0.0 in /usr/local/lib/python3.6/dist-packages (from PyDrive) (4.1.2)\r\n",
      "Requirement already satisfied: google-api-python-client>=1.2 in /usr/local/lib/python3.6/dist-packages (from PyDrive) (1.6.7)\n",
      "Requirement already satisfied: PyYAML>=3.0 in /usr/local/lib/python3.6/dist-packages (from PyDrive) (3.13)\n",
      "Requirement already satisfied: rsa>=3.1.4 in /usr/local/lib/python3.6/dist-packages (from oauth2client>=4.0.0->PyDrive) (3.4.2)\n",
      "Requirement already satisfied: httplib2>=0.9.1 in /usr/local/lib/python3.6/dist-packages (from oauth2client>=4.0.0->PyDrive) (0.11.3)\n",
      "Requirement already satisfied: six>=1.6.1 in /usr/local/lib/python3.6/dist-packages (from oauth2client>=4.0.0->PyDrive) (1.11.0)\n",
      "Requirement already satisfied: pyasn1>=0.1.7 in /usr/local/lib/python3.6/dist-packages (from oauth2client>=4.0.0->PyDrive) (0.4.4)\n",
      "Requirement already satisfied: pyasn1-modules>=0.0.5 in /usr/local/lib/python3.6/dist-packages (from oauth2client>=4.0.0->PyDrive) (0.2.2)\n",
      "Requirement already satisfied: uritemplate<4dev,>=3.0.0 in /usr/local/lib/python3.6/dist-packages (from google-api-python-client>=1.2->PyDrive) (3.0.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install PyDrive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "lGN-vpmCJHVk"
   },
   "outputs": [],
   "source": [
    "from pydrive.auth import GoogleAuth\n",
    "from pydrive.drive import GoogleDrive\n",
    "from google.colab import auth\n",
    "from oauth2client.client import GoogleCredentials\n",
    "# Authenticate and create the PyDrive client.\n",
    "# This only needs to be done once per notebook.\n",
    "auth.authenticate_user()\n",
    "gauth = GoogleAuth()\n",
    "gauth.credentials = GoogleCredentials.get_application_default()\n",
    "drive = GoogleDrive(gauth)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5nNK4_VCKqfK"
   },
   "outputs": [],
   "source": [
    "file_id = '1PniXUsYJDaeKBR_eM7EmjBQuWdnw3P0p' # URL id. \n",
    "downloaded = drive.CreateFile({'id': file_id})\n",
    "downloaded.GetContentFile('gdrive_test.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "pGzsqfYSLpK4",
    "outputId": "0e8771b7-6001-4315-e9cd-b684b324f3b6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "adc.json  example.txt  gdrive_test.txt\tlocal_test.txt\tsample_data\r\n"
     ]
    }
   ],
   "source": [
    "!ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "vqW34QkGLq9T",
    "outputId": "0f09d2f3-6280-40f7-eb23-57ad75b9a56c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "this is a test.\r\n"
     ]
    }
   ],
   "source": [
    "!cat gdrive_test.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "0QIEyjVD0qMP"
   },
   "source": [
    "# Publishing Completed Notebooks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LdwBS-_n0qMQ"
   },
   "source": [
    "We have created a [notebook](https://github.com/ElliottGordon/AdvML-Fall-19/blob/master/python_tutorial/submit.ipynb) to facilitate the process of converting your ```.ipynb``` files created on Colab Instances to ```.html``` files for submission WITHOUT requiring that you have jupyter notebooks installed on your local machine. This is a CRITICAL step for submitting your homeworks so please follow along for practice. "
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Tutorial.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}