diff --git a/00-Introduction.ipynb b/00-Introduction.ipynb index 7bc3bd8..ee31aed 100644 --- a/00-Introduction.ipynb +++ b/00-Introduction.ipynb @@ -9,13 +9,36 @@ } }, "source": [ - "# Data Science in Practice\n", + "# Introduction\n", "\n", - "Welcome to the hands on materials for the Data Science in Practice class.\n", + "Welcome to the hands on materials for Data Science in Practice.\n", "\n", "This notebook will guide through getting the tools you will need for working with these tutorials and assignments." ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Alerts" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Throughout these tutorials, you will see colored 'alert' text:\n", + "\n", + "
\n", + "Green alerts provide key information and definitions.\n", + "
\n", + "\n", + "
\n", + "Blue alerts provide links out to further \n", + "resources. \n", + "
" + ] + }, { "cell_type": "markdown", "metadata": { @@ -28,9 +51,11 @@ "\n", "### Software\n", "\n", - "- Working install of python3.6, with the anaconda distribution ([datahub](http://datahub.ucsd.edu) satisfies this requirement)\n", - "- Jupyter Notebooks ([datahub](http://datahub.ucsd.edu) satisfies this requirement)\n", - "- git/GitHub" + "- Working install of Python (>= 3.6), with the anaconda distribution\n", + " - If you are in the official class, [datahub](http://datahub.ucsd.edu) satisfies this requirement\n", + "- Jupyter Notebooks\n", + " - Also satisfied by [datahub](http://datahub.ucsd.edu)\n", + "- git and a GitHub account" ] }, { @@ -39,12 +64,17 @@ "source": [ "### Prerequisites\n", "\n", - "This class, and this series of tutorials, presumes that you already have some basic knowledge of programming.\n", + "These tutorials presume that you do already have some basic knowledge of programming. \n", "\n", - "In particular it assumes some knowledge Python, covering the standard library. \n", - "\n", - "If you are somewhat unfamiliar with Python, you can follow the links in the Python notebook to catch up. \n", + "In particular, it assumes knowledge of the Python programming language and standard library. \n", "\n", + "If you are somewhat unfamiliar with Python, you can follow the links in the Python notebook to catch up." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "### Computational Resources\n", "\n", "The examples throughout these tutorials, and in the assignments are not computationally heavy. \n", @@ -52,6 +82,19 @@ "You should be able to run all these materials on any computer you have access to, assuming it will run the aforementioned tools. " ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Installing Python\n", + "\n", + "- If you are running code locally, we recommend you install a new version of Python with Anaconda, as described below\n", + " - If you are in the official course, you can use [datahub](http://datahub.ucsd.edu) for everything you need\n", + "- If you are on Mac, you have a native installation of python. This native installation of Python may be older, will not include the extra packages that you will need for this class, and is best left untouched. \n", + " - Downloading Anaconda will install a separate, independent install of Python, leaving your native install untouched. \n", + "- Windows does not require Python natively and so it is not typically pre-installed." + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -65,61 +108,61 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "" + "" ] }, { "cell_type": "markdown", - "metadata": { - "nbpresent": { - "id": "0f4dd046-4020-465c-85f6-3d92ac9fe145" - } - }, + "metadata": {}, "source": [ "
\n", - "Jupyter notebooks are a way to intermix code, outputs and plain text. \n", - "They run in a web browser, and connect to a kernel to be able to execute code. \n", + "Anaconda is an open-source distribution of Python, designed for scientific computing, data science and machine learning. \n", "
\n", "\n", "
\n", - "The official Jupyter website is available \n", - "here.\n", - "
\n", - "\n", - "
" + "The anaconda website is \n", + "here,\n", + "with the download page\n", + "here.\n", + "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Note that you do not need to download Jupyter separately, as it comes packaged with anaconda, described below. " + "Anaconda itself is a distribution, meaning that is a version of Python with a collection of packages that are curated and maintained together. \n", + "\n", + "Using a pre-built distribution is useful, as it comes with the packages that you need for data science.\n", + "\n", + "Anaconda also comes with `conda`, which is a package manager, allowing you to download, install, and manage other packages. \n", + "\n", + "The anaconda distribution includes all packages that are needed for these tutorials." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "" + "" ] }, { "cell_type": "markdown", "metadata": { "nbpresent": { - "id": "a0fd64ab-0202-4900-8e6d-155c29c2e750" + "id": "0f4dd046-4020-465c-85f6-3d92ac9fe145" } }, "source": [ "
\n", - "Anaconda is an open-source distribution of Python, designed for scientific computing, data science and machine learning. \n", + "Jupyter notebooks are a way to intermix code, outputs and plain text. \n", + "They run in a web browser, and connect to a kernel to be able to execute code. \n", "
\n", "\n", "
\n", - "The anaconda website is \n", - "here,\n", - "with the download page\n", - "here.\n", + "The official Jupyter website is available \n", + "here.\n", "
" ] }, @@ -127,28 +170,25 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Anaconda itself is a distribution, that is, a collection of packages that are curated and maintained together, and serve as powerful. \n", - "\n", - "Anaconda also comes with conda, which is a package manager, allowing you to download, install, and manage other packages. \n", - "\n", - "The anaconda distribution includes all packages that are required for these tutorials." + "Note that you do not need to download Jupyter separately, as it comes packaged with the Anaconda distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Notes\n", - "-----\n", - "- If you are on Mac, you have a native installation of python. This native installation of Python may be older, will not include the extra packages that you will need for this class, and is best left untouched. \n", - " - Downloading anaconda will install a separate, independent install of Python, leaving your native install untouched. \n", - "- Windows does not require Python natively and so it is not typically pre-installed. \n", - "- If you want a local copy (which is a good idea going forward!), follow this tutorial step-by-step. Alternatively, you can use [datahub](http://datahub.ucsd.edu) for everything in this course." + "#### Checking Your Python Version\n", + "\n", + "You can check which installation of Python you are using, and which version it is.\n", + "\n", + "Once you have installed anaconda, you should see you are using Python in an anaconda folder. \n", + "\n", + "The version number that is printed should also be 3.6 or greater. " ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -161,10 +201,8 @@ } ], "source": [ - "# You can check which python you are using, and what version it is.\n", - "# Once you have installed anaconda, you should see you are using Python in your anaconda folder\n", - "# Make sure that the version you have is 3.6 (or at least 3.X)\n", - "# Note: these are command-line functions that may not work on windows\n", + "# Check the installed version of Python\n", + "# Note: these are command-line functions that may not work on windows\n", "!which python\n", "!python --version" ] @@ -185,7 +223,7 @@ }, "source": [ "
\n", - "Git is a tool, a software package, for version control. Github is an online hosting service that can be used with git, and offers online tools to use git. \n", + "Git is a tool, a software package, for version control. \n", "
\n", "\n", "
\n", @@ -206,6 +244,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "
\n", + "Github is an online hosting service that can be used with git, and offers online tools to use git. \n", + "
\n", + "\n", "
\n", "Create an account on \n", "Github.\n", @@ -293,17 +335,20 @@ "You do not need to use environments, however you may find it useful if you want or need to maintain multiple different versions of Python. \n", "\n", "If you want to use an environment, and already have conda, you can run this command from command line:
\n", - "$ conda create --name *envname* python=3.6 anaconda
\n", + "\n", + "``$ conda create --name *envname* python=3.7 anaconda``
\n", + "\n", "^ Replace '*envname*' with a name to call this environment.
\n", - "This will install a new environment, with Python 3.6 and the anaconda distribution.\n", + "\n", + "This will install a new environment, with Python 3.7 and the anaconda distribution.\n", "\n", "You will then need to activate this environment (everytime) you want to use it. \n", "\n", "To activate your environment:
\n", - "$ source activate *envname*\n", + "``$ conda activate *envname*``\n", "\n", "To deactivate your environment:
\n", - "$ source deactivate *envname*" + "``$ conda deactivate``" ] } ], diff --git a/01-JupyterNotebooks.ipynb b/01-JupyterNotebooks.ipynb index eabcf90..a786ac4 100644 --- a/01-JupyterNotebooks.ipynb +++ b/01-JupyterNotebooks.ipynb @@ -227,12 +227,16 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Code Cells" + "### Code Cells\n", + "\n", + "Code cells are cells that contain code, that can be executed. \n", + "\n", + "Comments can also be written in code cells, indicated by '#'. " ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -243,7 +247,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 2, "metadata": {}, "outputs": [ { @@ -261,7 +265,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 3, "metadata": { "slideshow": { "slide_type": "slide" @@ -269,12 +273,13 @@ }, "outputs": [], "source": [ + "# Define a variable in code\n", "my_string = 'hello world'" ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 4, "metadata": { "slideshow": { "slide_type": "fragment" @@ -290,12 +295,13 @@ } ], "source": [ + "# Print out a variable\n", "print(my_string)" ] }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 8, "metadata": { "slideshow": { "slide_type": "slide" @@ -308,19 +314,19 @@ "'HELLO WORLD'" ] }, - "execution_count": 21, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# tab completion, print(my_string.upper())\n", + "# Operations that return objects get printed out as output\n", "my_string.upper()" ] }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 9, "metadata": { "slideshow": { "slide_type": "slide" @@ -328,12 +334,13 @@ }, "outputs": [], "source": [ + "# Define a list variable\n", "my_list = ['a','b','c']" ] }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 7, "metadata": { "slideshow": { "slide_type": "fragment" @@ -349,6 +356,7 @@ } ], "source": [ + "# Print out our list variable\n", "print(my_list)" ] }, @@ -370,7 +378,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 10, "metadata": {}, "outputs": [], "source": [ @@ -380,7 +388,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -400,7 +408,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 12, "metadata": { "slideshow": { "slide_type": "fragment" @@ -408,7 +416,7 @@ }, "outputs": [], "source": [ - "# get information about variables you've created\n", + "# Get information about a variable you've created\n", "my_string?" ] }, @@ -510,7 +518,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 25, "metadata": { "slideshow": { "slide_type": "slide" @@ -518,13 +526,13 @@ }, "outputs": [], "source": [ - "# access quick reference sheet\n", + "# Access quick reference sheet for interactive Python (this opens a reference guide)\n", "%quickref" ] }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 26, "metadata": {}, "outputs": [ { @@ -562,6 +570,7 @@ "line": { "alias": "OSMagics", "alias_magic": "BasicMagics", + "autoawait": "AsyncMagics", "autocall": "AutoMagics", "automagic": "AutoMagics", "autosave": "KernelMagics", @@ -570,6 +579,7 @@ "cd": "OSMagics", "clear": "KernelMagics", "colors": "BasicMagics", + "conda": "PackagingMagics", "config": "ConfigMagics", "connect_info": "KernelMagics", "cp": "Other", @@ -616,11 +626,10 @@ "pfile": "NamespaceMagics", "pinfo": "NamespaceMagics", "pinfo2": "NamespaceMagics", - "pip": "BasicMagics", + "pip": "PackagingMagics", "popd": "OSMagics", "pprint": "BasicMagics", "precision": "BasicMagics", - "profile": "BasicMagics", "prun": "ExecutionMagics", "psearch": "NamespaceMagics", "psource": "NamespaceMagics", @@ -660,7 +669,7 @@ }, "text/plain": [ "Available line magics:\n", - "%alias %alias_magic %autocall %automagic %autosave %bookmark %cat %cd %clear %colors %config %connect_info %cp %debug %dhist %dirs %doctest_mode %ed %edit %env %gui %hist %history %killbgscripts %ldir %less %lf %lk %ll %load %load_ext %loadpy %logoff %logon %logstart %logstate %logstop %ls %lsmagic %lx %macro %magic %man %matplotlib %mkdir %more %mv %notebook %page %pastebin %pdb %pdef %pdoc %pfile %pinfo %pinfo2 %popd %pprint %precision %profile %prun %psearch %psource %pushd %pwd %pycat %pylab %qtconsole %quickref %recall %rehashx %reload_ext %rep %rerun %reset %reset_selective %rm %rmdir %run %save %sc %set_env %store %sx %system %tb %time %timeit %unalias %unload_ext %who %who_ls %whos %xdel %xmode\n", + "%alias %alias_magic %autoawait %autocall %automagic %autosave %bookmark %cat %cd %clear %colors %conda %config %connect_info %cp %debug %dhist %dirs %doctest_mode %ed %edit %env %gui %hist %history %killbgscripts %ldir %less %lf %lk %ll %load %load_ext %loadpy %logoff %logon %logstart %logstate %logstop %ls %lsmagic %lx %macro %magic %man %matplotlib %mkdir %more %mv %notebook %page %pastebin %pdb %pdef %pdoc %pfile %pinfo %pinfo2 %pip %popd %pprint %precision %prun %psearch %psource %pushd %pwd %pycat %pylab %qtconsole %quickref %recall %rehashx %reload_ext %rep %rerun %reset %reset_selective %rm %rmdir %run %save %sc %set_env %store %sx %system %tb %time %timeit %unalias %unload_ext %who %who_ls %whos %xdel %xmode\n", "\n", "Available cell magics:\n", "%%! %%HTML %%SVG %%bash %%capture %%debug %%file %%html %%javascript %%js %%latex %%markdown %%perl %%prun %%pypy %%python %%python2 %%python3 %%ruby %%script %%sh %%svg %%sx %%system %%time %%timeit %%writefile\n", @@ -668,19 +677,19 @@ "Automagic is ON, % prefix IS NOT needed for line magics." ] }, - "execution_count": 30, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# You can check a list of available magic commands\n", + "# Check a list of available magic commands\n", "%lsmagic" ] }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 15, "metadata": { "slideshow": { "slide_type": "slide" @@ -690,22 +699,22 @@ { "data": { "text/plain": [ - "'/Users/shannonellis/Desktop/Teaching/COGS108/Tutorials'" + "'/Users/tom/Documents/EdCode/108Org/Tutorials'" ] }, - "execution_count": 31, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# see current working directory\n", + "# Check the current working directory\n", "%pwd" ] }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 16, "metadata": { "slideshow": { "slide_type": "fragment" @@ -721,13 +730,13 @@ } ], "source": [ - "# all variables\n", + "# Check all currently defined variables\n", "%who" ] }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 17, "metadata": { "slideshow": { "slide_type": "fragment" @@ -744,18 +753,18 @@ "b int 2\n", "my_list list n=3\n", "my_string str hello world\n", - "np module kages/numpy/__init__.py'>\n" + "np module kages/numpy/__init__.py'>\n" ] } ], "source": [ - "# all variables; more info\n", + "# Chcek all variables, with more information about them\n", "%whos" ] }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 18, "metadata": { "slideshow": { "slide_type": "slide" @@ -766,15 +775,6 @@ "name": "stdout", "output_type": "stream", "text": [ - "### Markdown cells\n", - "# history\n", - "%hist\n", - "# specify you're writing HTML\n", - "%%HTML\n", - "

This is a paragraph

\n", - "%%bash\n", - "# Equivalently, (for bash) use the %%bash cell magic to run a cell as bash (command-line)\n", - "pwd\n", "# In a code cell, comments can be typed\n", "a = 1\n", "b = 2\n", @@ -786,41 +786,20 @@ "my_string.upper()\n", "my_list = ['a','b','c']\n", "print(my_list)\n", - "# Import numpy for examples\n", - "import numpy as np\n", - "# Check the docs for a numpy array\n", - "np.array?\n", - "# Check the full source code for numpy append function\n", - "np.append??\n", - "# get information about variables you've created\n", - "my_string?\n", - "# Move your cursor just after the period, press tab, and a drop menu will appear showing all possible completions\n", - "np.\n", - "# In a code cell, comments can be typed\n", - "a = 1\n", - "b = 2\n", - "# Cells can also have output, that gets printed out below the cell.\n", - "print(a + b)\n", - "my_string = 'hello world'\n", - "print(my_string)\n", - "# tab completion, print(my_string.upper())\n", + "# Operations that return objects get printed out as output\n", "my_string.upper()\n", + "# Define a list variable\n", "my_list = ['a','b','c']\n", - "print(my_list)\n", "# Import numpy for examples\n", "import numpy as np\n", "# Check the docs for a numpy array\n", "np.array?\n", - "# Check the full source code for numpy append function\n", - "np.append??\n", "# get information about variables you've created\n", "my_string?\n", - "# Move your cursor just after the period, press tab, and a drop menu will appear showing all possible completions\n", - "np.\n", "# access quick reference sheet\n", "%quickref\n", - "# You can check a list of available magic commands\n", - "%lsmagic\n", + "# access quick reference sheet (this opens a reference guide)\n", + "%quickref\n", "# see current working directory\n", "%pwd\n", "# all variables\n", @@ -828,32 +807,12 @@ "# all variables; more info\n", "%whos\n", "# history\n", - "%hist\n", - "# For example, we can time how long it takes to create a large list\n", - "%timeit list(range(100000))\n", - "%%timeit\n", - "# For example, we could time a whole cell\n", - "a = list(range(100000))\n", - "b = [n + 1 for n in a]\n", - "# You can run a terminal command by adding '!' to the start of the line\n", - "!pwd\n", - "\n", - "# Note that in this case, '!pwd' is equivalent to line magic '%pwd'. \n", - "# The '!' syntax is more general though, allowing you to run anything you want through command-line\n", - "%%bash\n", - "# Equivalently, (for bash) use the %%bash cell magic to run a cell as bash (command-line)\n", - "pwd\n", - "# list files in directory\n", - "!ls\n", - "# change current directory\n", - "!cd .\n", - "# history\n", "%hist\n" ] } ], "source": [ - "# history\n", + "# Check code history\n", "%hist" ] }, @@ -869,14 +828,14 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1.6 ms ± 26.8 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" + "1.63 ms ± 23 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n" ] } ], @@ -896,14 +855,14 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "6.59 ms ± 97.6 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" + "7.92 ms ± 1.65 ms per loop (mean ± std. dev. of 7 runs, 100 loops each)\n" ] } ], @@ -925,14 +884,14 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "/Users/shannonellis/Desktop/Teaching/COGS108/Tutorials\r\n" + "/Users/tom/Documents/EdCode/108Org/Tutorials\r\n" ] } ], @@ -946,14 +905,14 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "/Users/shannonellis/Desktop/Teaching/COGS108/Tutorials\n" + "/Users/tom/Documents/EdCode/108Org/Tutorials\n" ] } ], @@ -965,7 +924,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 23, "metadata": { "slideshow": { "slide_type": "fragment" @@ -976,29 +935,31 @@ "name": "stdout", "output_type": "stream", "text": [ - "00-Introduction.ipynb 13-OrdinaryLeastSquares.ipynb\r\n", - "01-JupyterNotebooks.ipynb 14-LinearModels.ipynb\r\n", - "02-DataAnalysis.ipynb 15-Clustering.ipynb\r\n", - "03-Python.ipynb 16-DimensionalityReduction.ipynb\r\n", - "04-DataSciencePython.ipynb 17-Classification.ipynb\r\n", - "05-DataGathering.ipynb 18-NaturalLanguageProcessing.ipynb\r\n", + "00-Introduction.ipynb 14-LinearModels.ipynb\r\n", + "01-JupyterNotebooks.ipynb 15-Clustering.ipynb\r\n", + "02-DataAnalysis.ipynb 16-DimensionalityReduction.ipynb\r\n", + "03-Python.ipynb 17-Classification.ipynb\r\n", + "04-DataSciencePython.ipynb 18-NaturalLanguageProcessing.ipynb\r\n", + "05-DataGathering.ipynb \u001b[34m19-Geospatial\u001b[m\u001b[m\r\n", "06-DataWrangling.ipynb A1-PythonPackages.ipynb\r\n", "07-DataCleaning.ipynb A2-Git.ipynb\r\n", - "08-DataPrivacy&Anonymization.ipynb LICENSE\r\n", + "08-DataPrivacy&Anonymization.ipynb LICENSE.txt\r\n", "09-DataVisualization.ipynb README.md\r\n", - "10-Distributions.ipynb \u001b[34mfiles\u001b[m\u001b[m\r\n", - "11-TestingDistributions.ipynb \u001b[34mimg\u001b[m\u001b[m\r\n" + "10-Distributions.ipynb X2-ShellScripting.ipynb\r\n", + "11-TestingDistributions.ipynb XX-GeoSpatialAnalysis.ipynb\r\n", + "12-StatisticalComparisons.ipynb \u001b[34mfiles\u001b[m\u001b[m\r\n", + "13-OrdinaryLeastSquares.ipynb \u001b[34mimg\u001b[m\u001b[m\r\n" ] } ], "source": [ - "# list files in directory\n", + "# List files in directory\n", "!ls" ] }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 24, "metadata": { "slideshow": { "slide_type": "fragment" @@ -1006,7 +967,7 @@ }, "outputs": [], "source": [ - "# change current directory\n", + "# Change current directory\n", "!cd ." ] }, @@ -1016,8 +977,7 @@ "source": [ "
\n", "For more useful information, check out Jupyter Notebooks \n", - "tips & tricks\n", - ", and more information on how \n", + "tips & tricks, and more information on how \n", "notebooks work.\n", "
" ] @@ -1039,7 +999,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.8" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/02-DataAnalysis.ipynb b/02-DataAnalysis.ipynb index ea22def..b87d6e8 100644 --- a/02-DataAnalysis.ipynb +++ b/02-DataAnalysis.ipynb @@ -16,37 +16,35 @@ "This notebook goes through some minimal examples of the kinds of things we might want to do using data science approaches. \n", "\n", "In particular, it briefly introduces analyzing data for the purposes of:\n", - "- Predictions: to analyze available data in order to be able to make predictions about future data\n", - "- Classification: to group data in meaningful ways\n", - "- Knowledge Discovery: to seek to discover new knowledge about the data and the phenomena they represent\n", + "- `Prediction`: to analyze available data in order to be able to make predictions about future data\n", + "- `Classification`: to group and label data in useful and meaningful ways\n", + "- `Knowledge Discovery`: to seek to discover new knowledge about the data and the phenomena they represent\n", "\n", - "These examples will already start using packages in the python data-science toolkit, and some simple algorithms to demostrate example cases. \n", + "These are not the only tasks we might have in data science, but these examples do capture some of the key tasks when doing data science. \n", "\n", - "The goal here is see, in code, the outline of the kinds of things data science is interested in doing. \n", + "These examples will already start using packages in the Python data-science toolkit, and some simple algorithms to demonstrate example cases. \n", "\n", - "These tools and algorithms will be more fully described and properly introduced in future notebooks." + "The goal here is show, in code, the outline of the kinds of things data science is interested in doing. You don't yet need to be able to follow how the code works for these examples. These tools and algorithms will be more fully described and properly introduced in future notebooks." ] }, { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", - "# Import matplotlib and numpy for some quick examples\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np" + "# Import numpy and matplotlib for some quick examples\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# Prediction" + "## Prediction" ] }, { @@ -66,17 +64,17 @@ "source": [ "### Example Problem\n", "\n", - "Let's say we wanted to predict dogs weight, from their length. \n", + "Let's say we wanted to predict the weight of dogs, given that we know their length. \n", "\n", - "Maybe, for example, it's easier to use a tape measure than to get a dog onto a scale, so if we could infer their weight from their length, we could save a lot of time. " + "We could imagine, for example, in the case of a veterinary clinic, in some cases it might be easier to measure a dog with a tape measure, rather than to get it dog onto a scale, if we can then estimate the information we need.\n", + "\n", + "So how do we go about making such predictions?" ] }, { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# We start with some data\n", @@ -91,29 +89,29 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# Plot the data: Always visualize your data!\n", - "f, ax = plt.subplots()\n", - "ax.plot(lengths, weights , '.')\n", - "plt.xlabel('Length (cm)'); plt.xlim([30, 125]);\n", - "plt.ylabel('Weight (kg)'); plt.ylim([5, 25]);" + "fig, ax = plt.subplots()\n", + "ax.plot(lengths, weights, '.', ms=15)\n", + "ax.set(xlabel='Length (cm)', ylabel='Weight (kg)',\n", + " xlim=[30, 125], ylim=[5, 25]);" ] }, { "cell_type": "code", "execution_count": 4, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Polyfit (degree=1) will fit a linear fit to the data, of the form y = ax + b\n", @@ -130,7 +128,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Predicted weight for a new data point, weight is 13.3460674157\n" + "Predicted weight for a new data point, weight is 13.35.\n" ] } ], @@ -138,7 +136,7 @@ "# So now we can predict the weight of a new observation (a new dog)\n", "new_length = 62\n", "pred_weight = a * new_length + b \n", - "print('Predicted weight for a new data point, weight is', pred_weight)" + "print('Predicted weight for a new data point, weight is {:1.2f}.'.format(pred_weight))" ] }, { @@ -148,9 +146,9 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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3s9LUEhDv51cyBUB+/4NZ77344od7Dp1t3QpLl/ZvPWa2jVoC4k5JPwf2knQu8Bgws9iyrC4cdBAMqfIVHDIkG29mpdlhQETEVWT3QNwNTAT+OiJ+VnRhVgcuvBB23TU9btdd4YIL+rceM9tGV0+Uu0jSxyUNi4iWiPjLiLg0Ilr6s0DbiR17LFx6KYwc+eGexJAh2fCll2bjzaw0Xd1JvT9wDXCwpGeAfwXmAv8v76jPrPd+8AM45ZTshPTSpXDggdmehcPBrHQ7fKJc/lzoJuATZM+FOA54IyIOKb687vET5czMuqerJ8rVcpJ6N2BP4A/y10pgfg0rvUnSakmLK9p+LOl5Sc9Imi1pryrzLpO0SNJCSf7FNzMrQVfnIGZImgvcQbbX8K/AlyKiKSKm1rDsm4HJndpagEMj4jDgRT68+S7lhIg4vFqymZlZsbragxgPjAB+D7wKrKAbz3+IiDnA653aHo2IzfngPLLzHGZmNgB11VnfZODjwFV50yXAU5IelfSDPlj314CHq60eeFTSAknTulqIpGmSWiW1rlmzpg/KMjMz2MHzIPI7qBdLegN4M3+dBhwN9Lg3NUnfAzYDt1aZpDkiVkoaC7RIej7fI0nVOAOYAdlJ6p7WZGZm2+rqHMQFkm6X9AowhywYXgDOBPbu6QolTcmXdU5UuYQq7++JiFgNzCYLJDMz60dd7UFMILuD+tsRsaovViZpMlnPsP85IjZUmWYUMCQi3so/nwxc2RfrNzOz2lUNiIi4uDcLlnQbMAkYI2kF2SGpy8lOfLdIApgXEedJ2he4ISJOBfYBZufjhwG/jIhHelOLmZl13w6fSd1TEXF2ovnGKtOuBE7NP78MfKyouszMrDY1PVHOzMzqjwPCzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsyQFhZmZJDggzM0tyQJiZWZIDwszMkhwQZmaW5IAwM7MkB4SZmSU5IMzMLMkBYWZmSQ4IMzNLckCYmVlSYU+Us/K1LV/HrLnttK99h8Yxo5ja3MiR40eXXZaZDRKF7kFIuknSakmLK9r2ltQiaWn+nvzFkjQln2appClF1rkzurrlBc6ZOZ8HnlnF4lfX8+Azqzhn5nyubnmh7NLMbJAo+hDTzcDkTm2XAY9HxIHA4/nwNiTtDUwHjgGOBqZXCxLbXtvydcyc087GTVuIyNq2BmzctIWZc9ppW76u3ALNbFAoNCAiYg7weqfmM4Bb8s+3AJ9LzPpZoCUiXo+IdUAL2weNVTFrbjvvbt6SHPfe5i3MmtvezxWZ2WBUxknqfSJiFUD+PjYxzX7AKxXDK/K27UiaJqlVUuuaNWv6vNjBqH3tOx/sOXS2NWDZ2g39W5CZDUoD9SomJdqSP3kRMSMimiKiqaGhoeCyBofGMaMYktqCwBDBhDEj+7cgMxuUygiI1ySNA8jfVyemWQEcUDG8P7CyH2rbKUxtbmTEsKHJcSOGDWVqc2M/V2Rmg1EZAXEf0HFV0hTg3sQ0vwJOljQ6Pzl9ct5mNThy/GjOPb6R3YYP/WBPYohgt+FDOfd4X+pqZrUp9D4ISbcBk4AxklaQXZn0I+BOSV8HlgNfyqdtAs6LiG9ExOuSfgg8lS/qyojofLLbunDxSROZNHEss+a2s2ztBiaMGen7IMysWxTVzmYOQk1NTdHa2lp2GWZmg4akBRHRlBo3UE9Sm5lZyRwQZmaW5IAwM7MkB4SZmSU5IMzMLMkBYWZmSQ4IMzNLckCYmVmSA8LMzJIcEGZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZkgPCzMySHBBmZpbU7wEhaaKkhRWv9ZIu6jTNJElvVkzz1/1dp5lZvRvW3yuMiBeAwwEkDQVeBWYnJv2XiDitP2szM7MPlX2I6dPAv0XE70quw8zMOik7IM4Cbqsy7jhJT0t6WNIf92dRZmZWYkBI2gU4HfiHxOg24I8i4mPAz4B/7GI50yS1Smpds2ZNMcWamdWhMvcgTgHaIuK1ziMiYn1EvJ1/fggYLmlMaiERMSMimiKiqaGhodiKzczqSJkBcTZVDi9J+g+SlH8+mqzOf+/H2szM6l6/X8UEIGkkcBLwzYq28wAi4nrgi8B/k7QZ2AicFRFRRq1mZvWqlICIiA3AH3Zqu77i87XAtf1dl5mZfajsq5jMzGyAckCYmVmSA8LMzJIcEGZmluSAMDOzJAeEmZklOSDMzCzJAWFmZkkOCDMzS3JAmJlZkgPCzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsyQFhZmZJDggzM0tyQJiZWZIDwszMkkoLCEnLJC2StFBSa2K8JP0vSS9JekbSkWXUaWZWr4aVvP4TImJtlXGnAAfmr2OA6/J3MzPrBwP5ENMZwC8iMw/YS9K4sosyM6sXZe5BBPCopAB+HhEzOo3fD3ilYnhF3raqciJJ04Bp+eDbkl4oqN7uGgNU2zuqZ94u1XnbpHm7VNcX2+aPqo0oMyCaI2KlpLFAi6TnI2JOxXgl5ontGrJg6RwupZPUGhFNZdcx0Hi7VOdtk+btUl3R26a0Q0wRsTJ/Xw3MBo7uNMkK4ICK4f2Blf1TnZmZlRIQkkZJ2qPjM3AysLjTZPcBX82vZjoWeDMiVmFmZv2irENM+wCzJXXU8MuIeETSeQARcT3wEHAq8BKwAZhaUq09NeAOew0Q3i7VedukebtUV+i2UcR2h/XNzMwG9GWuZmZWIgeEmZklOSD6iKShkn4r6YF8uFHSfElLJd0haZeyayyDpL0k3SXpeUlLJB0naW9JLfm2aZE0uuw6+5ukb0t6VtJiSbdJ2rVevzOSbpK0WtLiirbkd6SeuuCpsl1+nP9bekbSbEl7VYy7PN8uL0j6bF/U4IDoOxcCSyqG/xb4u4g4EFgHfL2Uqsp3DfBIRBwMfIxsG10GPJ5vm8fz4bohaT/gAqApIg4FhgJnUb/fmZuByZ3aqn1HKrvgmUbWBc/O6ma23y4twKERcRjwInA5gKRDyL5Df5zP838kDe1tAQ6IPiBpf+C/ADfkwwJOBO7KJ7kF+Fw51ZVH0p7A8cCNABHxfkS8QdaNyi35ZHW5bciu3ttN0jBgJFkPAXX5nclvkH29U3O170jddMGT2i4R8WhEbM4H55HdHwbZdrk9It6LiHayqz8731vWbQ6IvvFT4H8AW/PhPwTeqPgP2dFNSL35CLAGmJUffrshv+9ln457WvL3sWUW2d8i4lXgKmA5WTC8CSzA35lK1b4j1brgqUdfAx7OPxeyXRwQvSTpNGB1RCyobE5MWo/XEw8DjgSui4gjgHeos8NJKfnx9DOARmBfYBTZoZPO6vE7syP+twVI+h6wGbi1oykxWa+3iwOi95qB0yUtA24nO0zwU7Jd344bEeu1m5AVwIqImJ8P30UWGK91HBbI31eXVF9ZPgO0R8SaiNgE3AN8An9nKlX7jtR9FzySpgCnAefEhzeyFbJdHBC9FBGXR8T+ETGB7CTRP0XEOcATwBfzyaYA95ZUYmki4vfAK5Im5k2fBp4j60ZlSt5Wj9tmOXCspJH5+aqO7VL335kK1b4jdd0Fj6TJwHeA0yNiQ8Wo+4CzJI2Q1Eh2Ev83vV6f76TuO5ImAZdGxGmSPkK2R7E38Fvgv0bEe2XWVwZJh5OdvN8FeJmsy5QhwJ3AeLIfyy9FROeTlDs1ST8Avkx2mOC3wDfIjhnX3XdG0m3AJLKuq18DpgP/SOI7kgfqtWRX6mwApkbEdk+k3BlU2S6XAyOAf88nmxcR5+XTf4/svMRm4KKIeLjzMrtdgwPCzMxSfIjJzMySHBBmZpbkgDAzsyQHhJmZJTkgzMwsyQFhdUfS2wUv/88l7VsxvEzSmBrmO0LSDX2w/j+RdHNvl2PmgDDre39O1oVGd30X+FlvVx4Ri4D9JY3v7bKsvjkgzABJDZLulvRU/mrO26/I++X/Z0kvS7qgYp7v533zt+TPdLhU0heBJuBWSQsl7ZZP/t8ltUlaJOngxPr3AA6LiKfz4d0lzcqnf0bSF/L2tyX9raQFkh6TdHRFbadXLPJ+sjv7zXrMAWGWuYbsWQwfB75A3nV77mDgs2TdJ0+XNFxSUz7dEcCZZKFARNwFtJL1k3N4RGzMl7E2Io4ke37BpYn1NwGLK4a/T9aNxJ/kff//U94+CvjniDgKeAv4G+Ak4PPAlRXztwKf6v5mMPvQsB1PYlYXPgMckvXkAMCe+f/VAzyYd3nxnqTVwD7AJ4F7OwJA0v07WP49+fsCskDpbBxZ1+iV9XywBxAR6/KP7wOP5J8XAe9FxCZJi4AJFfOvpmeHucw+4IAwywwBjqv4P34A8sCo7A9pC9m/m1T3yl3pWEbH/J1tBHatXDXp7po3VfTgubVjuRGxtaInWPJlbew8s1l3+BCTWeZR4PyOgbyTwa48CfypsmdJ7072RMEObwF7pGeragnwn7qop7vP7T6IbQ9ZmXWbA8Lq0UhJKypeF5M/Izo/IfwccF5XC4iIp8i6WH6a7PBRK9mT4SB7lvD1nU5Sdykingf+oOKw1t8AoyUtlvQ0cEI3/8YTgAe7OY/ZNtybq1kPSdo9It6WNBKYA0yLiLZeLO/bwFsR0at7ISSNAH4NfLLiEaZm3eY9CLOemyFpIdAG3N2bcMhdx7bnO3pqPHCZw8F6y3sQZmaW5D0IMzNLckCYmVmSA8LMzJIcEGZmluSAMDOzpP8P6drns0nZ1t4AAAAASUVORK5CYII=\n", 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" ] }, "execution_count": 6, @@ -160,8 +158,8 @@ ], "source": [ "# We can check how our prediction fits in with the data we observed\n", - "ax.plot(new_length, pred_weight, '.r')\n", - "f" + "ax.plot(new_length, pred_weight, '.r', ms=15)\n", + "fig" ] }, { @@ -173,7 +171,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The (absolute) error of our prediction is 1.35393258427 kg's.\n" + "The (absolute) error of our prediction is 1.35 kilograms.\n" ] } ], @@ -182,7 +180,7 @@ "actual_weight = 14.7\n", "error = actual_weight - pred_weight\n", "\n", - "print('The (absolute) error of our prediction is', str(error), 'kg\\'s.')" + "print('The (absolute) error of our prediction is {:1.2f} kilograms.'.format(error))" ] }, { @@ -199,7 +197,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Classification" + "## Classification" ] }, { @@ -216,24 +214,27 @@ "metadata": {}, "source": [ "### Problem\n", - "Our local zoologist is investigating a group of squirrels. \n", "\n", - "She would like to know how many different species there are present in the population, but only has basic data to work with. \n", + "Let's now imagine our local zoologist is investigating a group of squirrels. \n", + "\n", + "She would like to know how many different species there are present in the population. However, she only has a limited set of basic data to work with.\n", "\n", - "We can try and cluster the data we have, and look for (what look like) meaningful groupings. " + "We can try and cluster the data we have, and look for (what look like) meaningful groupings.\n", + "\n", + "In this case, let's imagine we were able to weigh and measure a selection of squirrels that otherwise look about the same. \n", + "\n", + "Our task is then to analyze the data to see if there appear to be any meaningful groupings." ] }, { "cell_type": "code", "execution_count": 8, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# We observe a bunch of squirrels with [height (cm), weight (grams)] pairs\n", - "dat = np.array([[10., 600.], [16., 1200], [6., 800], [12., 700.], [17., 1400.],\n", - " [8., 500.], [20., 1500.], [21., 1300.], [11., 800.], [18., 1100.]])" + "data = np.array([[10., 600.], [16., 1200], [6., 800], [12., 700.], [17., 1400.],\n", + " [8., 500.], [20., 1500.], [21., 1300.], [11., 800.], [18., 1100.]])" ] }, { @@ -243,49 +244,58 @@ "outputs": [ { "data": { - "image/png": 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# Visualize our data!\n", - "f, ax = plt.subplots()\n", - "ax.plot(dat[:, 0], dat[:, 1], '.')\n", - "plt.xlabel('Height (cm)'); plt.xlim([0, 25]);\n", - "plt.ylabel('Weight (kg)'); plt.ylim([300, 1700]);" + "fig, ax = plt.subplots()\n", + "ax.plot(data[:, 0], data[:, 1], '.', ms=12)\n", + "ax.set(xlabel='Height (cm)', ylabel='Weight (kg)',\n", + " xlim=[0, 25], ylim=[300, 1700]);" ] }, { "cell_type": "code", "execution_count": 10, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "# Lets try a classification algorithm\n", - "# If you're unfamiliar with KMeans, we'll come back to how it works later\n", - "from sklearn.cluster import KMeans\n", - "kmeans = KMeans(2).fit(dat)" + "# Use scikit-learn to import a classification algorithm\n", + "from sklearn.cluster import KMeans" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, + "outputs": [], + "source": [ + "# Apply K-means clustering\n", + "# We'll come back to how this algorithm works later\n", + "kmeans = KMeans(2).fit(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "array([0, 1, 0, 0, 1, 0, 1, 1, 0, 1], dtype=int32)" + "array([1, 0, 1, 1, 0, 1, 0, 0, 1, 0], dtype=int32)" ] }, - "execution_count": 11, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -297,54 +307,58 @@ }, { "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": true - }, + "execution_count": 13, + "metadata": {}, "outputs": [], "source": [ "# We can use these to split our dataset up into putative groupings\n", - "cl_1 = dat[kmeans.labels_ == 0]\n", - "cl_2 = dat[kmeans.labels_ == 1]" + "cl_1 = data[kmeans.labels_ == 0]\n", + "cl_2 = data[kmeans.labels_ == 1]" ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# And visualize the classification\n", - "f, ax = plt.subplots()\n", - "ax.plot(cl_1[:, 0], cl_1[:, 1], '.b')\n", - "ax.plot(cl_2[:, 0], cl_2[:, 1], '.r')\n", - "plt.xlabel('Height (cm)'); plt.xlim([0, 25]);\n", - "plt.ylabel('Weight (kg)'); plt.ylim([300, 1700]);" + "fig, ax = plt.subplots()\n", + "ax.plot(cl_1[:, 0], cl_1[:, 1], '.b', ms=12)\n", + "ax.plot(cl_2[:, 0], cl_2[:, 1], '.r', ms=12)\n", + "ax.set(xlabel='Height (cm)', ylabel='Weight (kg)',\n", + " xlim=[0, 25], ylim=[300, 1700]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Evaluating classification, especially in unsupervised cases such as this (when we don't know the answer) is very much non-trivial. It's hard to know if there really are two groups here - or perhaps more, or fewer. We'll come back to how these analyses actually work and how to evaluate what you get out of them. " + "In the above example, we tried to see if partition the data into two groups worked well and, visually, it looks quite reasonable!\n", + "\n", + "Note, however, that properly evaluating classification is difficult. That is especially true in this case, since we don't know the answer. That means this example is unsupervised - we don't know the answer, or have any labels to learn these patterns in the data.\n", + "\n", + "So, in this case, the answer looks plausible, but it's hard to know if there really are two groups here. There could be more, or fewer. We'll come back to how these analyses actually work and how to evaluate what you get out of them. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# Knowledge Discovery" + "## Knowledge Discovery" ] }, { @@ -360,14 +374,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Knowledge discovery is not necessarily methodoligically distinct from prediction and classification, in that seeking new knowledge will likely include analysis focused on classification and prediction. " + "Knowledge discovery is not necessarily methodologically distinct from prediction and classification. Seeking new knowledge will likely include analysis focused on classification and prediction, and other related analyses.\n", + "\n", + "However, we can consider that the data science problems can have different contexts and approaches. Asking how predict one known variable from another (such as a dog's weight from it's length), or to classify data into a previously known categorization scheme (such as labeling different kinds of species) are tasks that use data science to answer previously known questions. \n", + "\n", + "Sometimes, in data analyses, we also want to explore and discover new findings and ideas from a dataset without having pre-defined questions. We might try to ask about the structure of the data, or look for new patterns we didn't know before. This is sometimes also called 'exploratory data analysis', as opposed to 'hypothesis driven' work. " ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -381,7 +399,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/03-Python.ipynb b/03-Python.ipynb index 4567849..932a66e 100644 --- a/03-Python.ipynb +++ b/03-Python.ipynb @@ -1,12 +1,19 @@ { "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Python" + ] + }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ - "![title](img/python.png)" + "" ] }, { @@ -17,17 +24,17 @@ "source": [ "
\n", "Python is an \n", - "open-source, \n", - "high-level , \n", - "general purpose, \n", - "interpreted, \n", - "programming language, \n", + "open-source, \n", + "high-level , \n", + "general purpose, \n", + "interpreted, \n", + "programming language, \n", "one of the most popular for data science applications. \n", "
\n", "\n", "
\n", "The official Python\n", - "website.\n", + "website.\n", "
" ] }, @@ -43,27 +50,54 @@ "- Python is explicitly and by design, user-friendly.\n", "- Python also has a massive user community, who contribute to a large number of high-quality, well maintained open-source tools.\n", " - The best language for your project is one which has the things you need.\n", - "- In part for the reasons listed above, Python is heavily used in industry." + "- In part for the reasons listed above, Python is heavily used in industry\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "The Python programming language is developed and maintained by the\n", + "Python Software Foundation.\n", + "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Tutorials for Learning Python\n", + "## Python Versions\n", "\n", - "- [Codecademy](https://www.codecademy.com/tracks/python) is great for beginner levels.\n", - "- There is also the [Official Beginners Guide](https://wiki.python.org/moin/BeginnersGuide).\n", - "- [Learn Python the Hard Way](https://learnpythonthehardway.org/book/) is a great tutorial for a more in-depth overview.\n", - " - It isn't actually particularly hard, although note that the currently available version is in Python2. \n", - "- [Whirlwind Tour of Python](https://github.com/jakevdp/WhirlwindTourOfPython) is a free collection of Jupyter notebooks that takes you through Python. \n", - " - This book is especially good (and specifically designed for) if you have some experience with programming in some other language, and want to quickly run through the specifics of Python.\n", - " \n", + "This class uses Python3, the currently developed version of Python, and more specifically Python version 3.6 or above. \n", "\n", - "## Python Practice\n", + "Python2 has reached \"End of Life\" meaning it is no longer supported or maintained by the Python Organization. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Python Resources\n", + "\n", + "These materials presume prior knowledge of the Python programming language. \n", "\n", - "- [Python Challenge](http://www.pythonchallenge.com/) is a good place for (sometimes infuriating) programming challenges.\n", - "- [Leet Code](https://leetcode.com/) is a place for more intense technical coding questions and challenges (geared towards industry interviews)." + "If you are note yet familiar, here are some entry level materials for learning Python:\n", + "\n", + "- [Codecademy](https://www.codecademy.com/tracks/python) is good for a beginner's introduction to the language.\n", + "- [The Official Beginners Guide](https://wiki.python.org/moin/BeginnersGuide) is supported by the Python organization.\n", + "- [Whirlwind Tour of Python](https://github.com/jakevdp/WhirlwindTourOfPython) is a free collection of Jupyter notebooks that takes you through Python. \n", + " - This book is especially good (and specifically designed for) if you have some experience with programming in some other language, and want to quickly run through the specifics of Python." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "A much broader list of resources and guides for learning Python is available \n", + "here.\n", + "
" ] }, { @@ -83,26 +117,36 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Python2 vs. Python3\n", - "\n", - "This class will use Python3 - it is the currently developed version of Python. Specifically 3.6 is the most recent version, released in 2016. \n", - "\n", - "Python3 was a break from Python2, because there were some larger changes that broke [backwards compatibility](https://en.wikipedia.org/wiki/Backward_compatibility). \n", - "\n", - "Python2 is still popular, and often used, partly because it takes a while with major new releases for everything to be available, and to get things updated. Now though, Python3 has pretty much everything available, and is the future of Python. \n", - "\n", - "In practice, Python 2 & 3 are very similar - learning one will be mostly relevant for knowing the other, and code can usually be made compatible between both with minimal changes." + "## Standard Library" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "
\n", - "The official Python documentation includes a discussion of Py2 vs. Py3, including guidance on which to use. \n", + "
\n", + "The Standard Library refers to everything in Python that is part of standard version and install of Python.\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "
\n", + "The Python \n", + "Standard Library\n", + "comes with a lot of basic functionality. \n", "
" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Part of what makes Python a powerful language is the standard library itself, which is a rich set of tools for programming. However, the standard library itself does not include data science tools, and a lot of the power of Python stems for a rich ecosystem of packages that can be added and used with Python. " + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -115,21 +159,34 @@ "metadata": {}, "source": [ "
\n", - "Packages are basically just collections of code. The anaconda distribution comes with all the core packages you will need for this class. \n", + "Packages are collections of code. Packages from outside the standard library can be installed and added to Python.\n", "
\n", "\n", "
\n", - "For getting other packes, anaconda comes with\n", + "For managing and installing packages, Anaconda comes with the \n", "conda\n", - "a package manager, with support for downloading and installing other packages.\n", + "package manager.\n", "
" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Scientific Python\n", + "\n", + "When we say that Python is good for data science, and scientific computing, what we really mean is that there is a rich ecosystem of available open-source external packages, that greatly expand the capacities of the language beyond the standard library. \n", + "\n", + "This set of packages, which we will introduce as we go through these materials, is sometimes referred to as 'Scientific Python', or the 'Scipy' ecosystem. \n", + "\n", + "For the purposes of these materials, the Anaconda distribution that we are using contains all the packages you need. " + ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -143,7 +200,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/04-DataSciencePython.ipynb b/04-DataSciencePython.ipynb index 3aa2629..5010181 100644 --- a/04-DataSciencePython.ipynb +++ b/04-DataSciencePython.ipynb @@ -4,11 +4,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Data Science in Python\n", + "# Scientific Python\n", "\n", "Python has a large number of tools available for doing data science. \n", "\n", - "The core of Data Science in Python revolves around some a set of core modules, typically comprising {scipy, numpy, pandas, matplotlib and scikit-learn}. \n", + "The core of Data Science in Python revolves around some a set of core modules, typically comprising {`scipy`, `numpy`, `pandas`, `matplotlib` and `scikit-learn`}. \n", "\n", "Here we will explore the basics of these modules and what they do. " ] @@ -100,7 +100,7 @@ ], "source": [ "# Let's flip a bunch of coins!\n", - "coin_flips = [sts.bernoulli.rvs(0.5) for i in range(100)]\n", + "coin_flips = [sts.bernoulli.rvs(0.5) for ind in range(100)]\n", "print('The first ten coin flips are: ', coin_flips[:10])\n", "print('The percent of heads from this sample is: ', sum(coin_flips) / len(coin_flips) * 100, '%')" ] diff --git a/05-DataGathering.ipynb b/05-DataGathering.ipynb index 1536f13..a8916f8 100644 --- a/05-DataGathering.ipynb +++ b/05-DataGathering.ipynb @@ -12,7 +12,7 @@ "metadata": {}, "source": [ "
\n", - "Data Gathering is simply the process of collecting your data together.\n", + "Data Gathering is the process of accessing data collecting it data together.\n", "
" ] }, @@ -20,13 +20,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This notebook covers strategies you can use to gather data for an analysis. \n", + "This notebook covers strategies for finding and gathering data.\n", "\n", - "If you want to move on to first working on data analyses (with provided data) you can move onto the next tutorials, and come back to this one later.\n", + "If you want to start by working on data analyses (with provided data) you can move onto the next tutorials, and come back to this one later.\n", "\n", - "Data gathering can encompass anything from launching a data collection project, web scraping, pulling from a database, downloading data in bulk. \n", - "\n", - "It might even include simply calling someone to ask if you can use some of their data. " + "Data gathering can encompass many different strategies, including data collection, web scraping, accessing data from databases, and downloading data in bulk. Sometimes it even includes things like calling someone to ask if you can use some of their data, and asking them to send it over. " ] }, { @@ -35,32 +33,49 @@ "source": [ "## Where to get Data\n", "\n", - "### The Web \n", + "There are lots of way to get data, and lots of places to get it from. Typically, most of this data will be accessed through the internet, in one way or another, especially when pursuing indepent research projects. \n", + "\n", + "### Institutional Access\n", "\n", - "The web is absolutely full of data or ways to get data, either by hosting **data repositories** from which you can download data, by offering **APIs** through which you can request specific data from particular applications, or as data itself, such that you can use **web scraping** to extract data directly from websites. \n", + "If you are working with data as part of an institution, such as a company of research lab, the institution will typically have data it needs analyzing, that it collects in various ways. Keep in mind that even people working inside institutions, with access to local data, will data still seek to find and incorporate external datasets. \n", "\n", - "### Other than the Web\n", + "### Data Repositories\n", "\n", - "Not all data is indexed or accessible on the web, at least not publicly. \n", + "**Data repositories** are databases from which you can download data. Some data repositories allow you to explore available datasets and download datasets in bulk. Others may also offer **APIs**, through which you can request specific data from particular databases.\n", "\n", - "Sometimes finding data means chasing down data wherever it might be. \n", + "### Web Scraping\n", "\n", - "If there is some particular data you need, you can try to figure out who might have it, and get in touch to see if it might be available.\n", + "The web itself is full of unstructured data. **Web scraping** can be done to directly extract and collect data directly from websites.\n", "\n", + "### Asking People for Data\n", + "\n", + "Not all data is indexed or accessible on the web, at least not publicly. Sometimes finding data means figuring out if any data is available, figuring out where it might be, and then reaching out and asking people directly about data access. If there is some particular data you need, you can try to figure out who might have it, and get in touch to see if it might be available." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "### Data Gathering Skills\n", + "\n", "Depending on your gathering method, you will likely have to do some combination of the following:\n", - "- Download data files from repositories\n", - "- Read data files into python\n", - "- Use APIs \n", - "- Query databases\n", - "- Call someone and ask them to send you a harddrive" + "\n", + "- Direct download data files from repositories\n", + "- Query databases & use APIs to extract and collect data of interest\n", + "- Ask people for data, and going to pick up data with a harddrive\n", + "\n", + "Ultimately, the goal is collect and curate data files, hopefully structured, that you can read into Python." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Data Repositories" + "## Definitions: Databases & Query Languages\n", + "\n", + "Here, we will introduce some useful definitions you will likely encounter when exploring how to gather data. \n", + "\n", + "Other than these definitions, we will not cover databases & query languages more in these tutorials. " ] }, { @@ -68,12 +83,7 @@ "metadata": {}, "source": [ "
\n", - "A Data Repository is basically just a place that data is stored. For our purposes, it is a place you can download data from. \n", - "
\n", - "\n", - "
\n", - "There is a curated list of good data source included in the \n", - "project materials.\n", + "A database is an organized collection of data. More formally, 'database' refers to a set of related data, and the way it is organized. \n", "
" ] }, @@ -81,7 +91,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Databases" + "
\n", + "A query language is a language for operating with databases, such as retrieving, and sometimes modifying, information from databases.\n", + "
" ] }, { @@ -89,7 +101,16 @@ "metadata": {}, "source": [ "
\n", - "A database is an organized collection of data. More formally, 'database' refers to a set of related data, and the way it is organized. \n", + "SQL (pronounced 'sequel') is a common query language used to interact with databases, and request data.\n", + "
\n", + "\n", + "
\n", + "If you are interested, there is a useful introduction and tutorial to SQL\n", + "here\n", + "as well as some useful 'cheat sheets' \n", + "here\n", + "and\n", + "here.\n", "
" ] }, @@ -97,7 +118,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Structured Query Language - SQL" + "## Data Repositories" ] }, { @@ -105,16 +126,12 @@ "metadata": {}, "source": [ "
\n", - "SQL (pronounced 'sequel') is a language used to 'communicate' with databases, making queries to request particular data from them.\n", + "A Data Repository is basically just a place that data is stored. For our purposes, it is a place you can download data from. \n", "
\n", "\n", "
\n", - "There is a useful introduction and tutorial to SQL\n", - "here\n", - "as well as some useful 'cheat sheets' \n", - "here\n", - "and\n", - "here.\n", + "There is a curated list of good data source included in the \n", + "project materials.\n", "
" ] }, @@ -122,11 +139,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "SQL is the standard, and most popular, way to interface with relational databases.\n", - "\n", - "Note: None of the rest of the tutorials presume or require any knowledge of SQL. \n", - "\n", - "You can look into it if you want, or if it is relevant to accessing some data you want to analyze, but it is not required for this set of tutorials. " + "For our purposes, data repositories are places you can download data directly from, for example [data.gov](https://www.data.gov/)." ] }, { @@ -149,6 +162,12 @@ "here\n", "or for a much broader, more technical, overview try\n", "here.\n", + "
\n", + "\n", + "
\n", + "This\n", + "list\n", + "includes a collection of commonly used and available APIs. \n", "
" ] }, @@ -156,45 +175,48 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "APIs offer a lot of functionality - you can send requests to the application to do all kinds of actions. In fact, any application interface that is designed to be used programatically is an API, including, for example, interfaces for using packages of code. \n", + "APIs offer a lot of functionality - you can send requests to the application to do all kinds of actions. In fact, any application interface that is designed to be used programmatically is an API, including, for example, interfaces for using packages of code. \n", + "\n", + "One of the many things that APIs do, and offer, is a way to query and access data from particular applications / databases. For example, there is a an API for Google maps that allows for programmatically querying the latitude & longitude positions of given addresses. \n", "\n", - "One of the many things that APIs do, and offer, is a way to query and access data from particular applications / databases. The benefit of using APIs for data gathering purposes is that they typically return data in nicely structured formats, that are relatively easy to analyze." + "The benefit of using APIs for data gathering purposes is that they typically return data in nicely structured formats, that are relatively easy to analyze." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Launching URL Requests from Python" + "### Launching URL Requests from Python\n", + "\n", + "In order to use APIs, and for other approaches to collecting data, it may be useful to launch URL requests from Python.\n", + "\n", + "Note that by `URL`, we just mean a file or application that can be reached by a web address. Python can be used to organize and launch URL requests, triggering actions and collecting any returned data. \n", + "\n", + "In practice, APIs are usually special URLs that return raw data, such as `json` or `XML` files. This is compared to URLs we are typically more used to that return web pages as `html`, which can be rendered for human viewers (html). The key difference is that APIs return structured data files, where as `html` files are typically unstructured (more on that later, with web scraping). \n", + "\n", + "If you with to use an API, try and find the documentation for to see how you send requests to access whatever data you want. \n", + "\n", + "#### API Example\n", + "\n", + "For our example here, we will use the Github API. Note that the URL we use is `api.github.com`. This URL accesses the API, and will return structured data files, instead of the html that would be returned by the standard URL (github.com)." ] }, { "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# Imports\n", - "# requests lets you make http requests from python\n", - "import requests\n", - "import pandas as pd" - ] - }, - { - "cell_type": "markdown", + "execution_count": 10, "metadata": {}, + "outputs": [], "source": [ - "In practice, APIs are usually special URLs that return raw data (json or XML) as opposed to a web page to be rendered for human viewers (html). Find the documentation for a particular API to see how you send requests to access whatever data you want. For example, let's try the Github API. " + "import pandas as pd\n", + "\n", + "# We will use the `requests` library to launch URL requests from Python\n", + "import requests" ] }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, + "execution_count": 11, + "metadata": {}, "outputs": [], "source": [ "# Request data from the Github API on a particular user\n", @@ -203,16 +225,16 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "b'{\"login\":\"TomDonoghue\",\"id\":7727566,\"avatar_url\":\"https://avatars0.githubusercontent.com/u/7727566?v=4\",\"gravatar_id\":\"\",\"url\":\"https://api.github.com/users/TomDonoghue\",\"html_url\":\"https://github.com/TomDonoghue\",\"followers_url\":\"https://api.github.com/users/TomDonoghue/followers\",\"following_url\":\"https://api.github.com/users/TomDonoghue/following{/other_user}\",\"gists_url\":\"https://api.github.com/users/TomDonoghue/gists{/gist_id}\",\"starred_url\":\"https://api.github.com/users/TomDonoghue/starred{/owner}{/repo}\",\"subscriptions_url\":\"https://api.github.com/users/TomDonoghue/subscriptions\",\"organizations_url\":\"https://api.github.com/users/TomDonoghue/orgs\",\"repos_url\":\"https://api.github.com/users/TomDonoghue/repos\",\"events_url\":\"https://api.github.com/users/TomDonoghue/events{/privacy}\",\"received_events_url\":\"https://api.github.com/users/TomDonoghue/received_events\",\"type\":\"User\",\"site_admin\":false,\"name\":\"Tom\",\"company\":\"UC San Diego\",\"blog\":\"tomdonoghue.github.io\",\"location\":\"San Diego\",\"email\":null,\"hireable\":null,\"bio\":\"Cognitive Science Grad Student @ UCSD. \\\\r\\\\nOn Twitter @TomDonoghue\",\"public_repos\":13,\"public_gists\":0,\"followers\":13,\"following\":35,\"created_at\":\"2014-05-28T20:20:48Z\",\"updated_at\":\"2018-01-09T04:15:59Z\"}'" + "b'{\"login\":\"TomDonoghue\",\"id\":7727566,\"node_id\":\"MDQ6VXNlcjc3Mjc1NjY=\",\"avatar_url\":\"https://avatars0.githubusercontent.com/u/7727566?v=4\",\"gravatar_id\":\"\",\"url\":\"https://api.github.com/users/TomDonoghue\",\"html_url\":\"https://github.com/TomDonoghue\",\"followers_url\":\"https://api.github.com/users/TomDonoghue/followers\",\"following_url\":\"https://api.github.com/users/TomDonoghue/following{/other_user}\",\"gists_url\":\"https://api.github.com/users/TomDonoghue/gists{/gist_id}\",\"starred_url\":\"https://api.github.com/users/TomDonoghue/starred{/owner}{/repo}\",\"subscriptions_url\":\"https://api.github.com/users/TomDonoghue/subscriptions\",\"organizations_url\":\"https://api.github.com/users/TomDonoghue/orgs\",\"repos_url\":\"https://api.github.com/users/TomDonoghue/repos\",\"events_url\":\"https://api.github.com/users/TomDonoghue/events{/privacy}\",\"received_events_url\":\"https://api.github.com/users/TomDonoghue/received_events\",\"type\":\"User\",\"site_admin\":false,\"name\":\"Tom\",\"company\":\"UC San Diego\",\"blog\":\"https://tomdonoghue.github.io\",\"location\":\"San Diego\",\"email\":null,\"hireable\":null,\"bio\":\"Cognitive Science Grad Student @ UC San Diego working on analyzing electrical brain activity. Also teaching Python & Data Science. \\\\r\\\\n\\\\r\\\\n\",\"twitter_username\":null,\"public_repos\":13,\"public_gists\":0,\"followers\":97,\"following\":83,\"created_at\":\"2014-05-28T20:20:48Z\",\"updated_at\":\"2020-06-19T21:35:12Z\"}'" ] }, - "execution_count": 3, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -224,46 +246,48 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ + "login TomDonoghue\n", + "id 7727566\n", + "node_id MDQ6VXNlcjc3Mjc1NjY=\n", "avatar_url https://avatars0.githubusercontent.com/u/77275...\n", - "bio Cognitive Science Grad Student @ UCSD. \\r\\nOn ...\n", - "blog tomdonoghue.github.io\n", - "company UC San Diego\n", - "created_at 2014-05-28T20:20:48Z\n", - "email None\n", - "events_url https://api.github.com/users/TomDonoghue/event...\n", - "followers 13\n", + "gravatar_id \n", + "url https://api.github.com/users/TomDonoghue\n", + "html_url https://github.com/TomDonoghue\n", "followers_url https://api.github.com/users/TomDonoghue/follo...\n", - "following 35\n", "following_url https://api.github.com/users/TomDonoghue/follo...\n", "gists_url https://api.github.com/users/TomDonoghue/gists...\n", - "gravatar_id \n", - "hireable None\n", - "html_url https://github.com/TomDonoghue\n", - "id 7727566\n", - "location San Diego\n", - "login TomDonoghue\n", - "name Tom\n", - "organizations_url https://api.github.com/users/TomDonoghue/orgs\n", - "public_gists 0\n", - "public_repos 13\n", - "received_events_url https://api.github.com/users/TomDonoghue/recei...\n", - "repos_url https://api.github.com/users/TomDonoghue/repos\n", - "site_admin False\n", "starred_url https://api.github.com/users/TomDonoghue/starr...\n", "subscriptions_url https://api.github.com/users/TomDonoghue/subsc...\n", + "organizations_url https://api.github.com/users/TomDonoghue/orgs\n", + "repos_url https://api.github.com/users/TomDonoghue/repos\n", + "events_url https://api.github.com/users/TomDonoghue/event...\n", + "received_events_url https://api.github.com/users/TomDonoghue/recei...\n", "type User\n", - "updated_at 2018-01-09T04:15:59Z\n", - "url https://api.github.com/users/TomDonoghue\n", + "site_admin False\n", + "name Tom\n", + "company UC San Diego\n", + "blog https://tomdonoghue.github.io\n", + "location San Diego\n", + "email None\n", + "hireable None\n", + "bio Cognitive Science Grad Student @ UC San Diego ...\n", + "twitter_username None\n", + "public_repos 13\n", + "public_gists 0\n", + "followers 97\n", + "following 83\n", + "created_at 2014-05-28T20:20:48Z\n", + "updated_at 2020-06-19T21:35:12Z\n", "dtype: object" ] }, - "execution_count": 4, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -277,11 +301,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "
\n", - "This\n", - "list\n", - "includes a collection of commonly used and available APIs. \n", - "
" + "As we can see above, in a couple lines of code, we can collect a lot of structured data about a particular user.\n", + "\n", + "If we wanted to do analyses of Github profiles and activity, we could use the Github API to collect information about a group of users, and then analyze and compare the collected data. " ] }, { @@ -311,6 +333,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "By web scraping, we typically mean something distinct from using the internet to access an API. Rather, web scraping refers to using code to systematically navigate the internet, and extract information of internet, from html or other available files. Note that in this case one is not interacting directly with a database, but simply exploring and collecting whatever is available on web pages.\n", + "\n", "Note that the following section uses the 'BeautifulSoup' module, which is not part of the standard anaconda distribution. \n", "\n", "If you do not have BeautifulSoup, and want to get it to run this section, you can uncomment the cell below, and run it, to install BeautifulSoup in your current Python environment. You only have to do this once." @@ -434,7 +458,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "From the soup object, you can explore that the page is much more organized, and in such a way that you can extract particular components of interest. \n", + "From the soup object, you can explore the page in a more organized way, and start to extract particular components of interest.\n", "\n", "Note that it is still 'messy' in other ways, in that there might or might not be a systematic structure to how the page is laid out, and it still might take a lot of work to extract the particular information you want from it." ] @@ -448,18 +472,18 @@ "Web scraping is distinct from using an API, even though many APIs may be accessed over the internet. Web scraping is different in that you are (programmatically) navigating through the internet, and extracting data of interest. \n", "\n", "Note:\n", - "Be aware that scraping data from websites (without using APIs) can often be an involved project itself - scraping sites can take a considerable amount of tuning to get the data you want. \n", + "Be aware that scraping data from websites (without using APIs) can often be an involved project itself. Web scraping itself can take a considerable amount of time and work to get the data you want. \n", "\n", - "Be aware that data presented on websites may not be well structured, or in an organzed format that lends itself to easy analysis.\n", + "Be aware that data presented on websites may not be well structured, and may not be in an organized format that lends itself to easy collection and analysis.\n", "\n", - "If you try scraping websites, also make sure you are allowed to scrape the data, and follow the websites terms of service. " + "If you try scraping websites, you should also check to make sure you are allowed to scrape the data, and follow the websites terms of service. " ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -473,7 +497,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/06-DataWrangling.ipynb b/06-DataWrangling.ipynb index 5a45532..838fb52 100644 --- a/06-DataWrangling.ipynb +++ b/06-DataWrangling.ipynb @@ -22,34 +22,34 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Note: Throughout this notebook, we will be using '!' to run the shell command 'cat' to print out the contents of example data files." + "In this notebook, we will focus on loading different types of data files. Other aspects of 'wrangling' such as combining different datasets will be covered in future tutorials, and are explored in the assignments.\n", + "\n", + "Note: Throughout this notebook, we will be using `!` to run the shell command `cat` to print out the contents of example data files." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Python I/O" + "## Python I/O\n", + "\n", + "Let's start with basic Python utilities for reading and loading data files. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "
\n", - "Python has some basic tools for I/O (input / output). \n", - "
\n", - "\n", "
\n", "Official Python \n", "documentation \n", - "on I/O.\n", + "on input / output.\n", "
" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -63,12 +63,12 @@ ], "source": [ "# Check out an example data file\n", - "!cat files/dat.txt" + "!cat files/data.txt" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -82,20 +82,29 @@ ], "source": [ "# First, explicitly open the file object for reading\n", - "f_obj = open('files/dat.txt', 'r')\n", + "file_obj = open('files/data.txt', 'r')\n", "\n", "# You can then loop through the file object, grabbing each line of data\n", - "for line in f_obj:\n", - " # Note that I'm removing the new line marker at the end of each line (the '\\n')\n", + "for line in file_obj:\n", + " # Here we explicitly remove the new line marker at the end of each line (the '\\n')\n", " print(line.strip('\\n'))\n", "\n", "# File objects then have to closed when you are finished with them\n", - "f_obj.close()" + "file_obj.close()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since opening and closing files basically always goes together, there is a shortcut to do both of them together, which is the `with` keyword. \n", + "\n", + "By using `with`, file objects will be opened, and then automatically closed at the end of the code block. " ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -108,10 +117,9 @@ } ], "source": [ - "# Since opening and closing files basically always goes together, there is a shortcut to do both of them\n", - "# Use 'with' keyword to open files, and the file object will automatically be closed at the end of the code block\n", - "with open('files/dat.txt', 'r') as f_obj:\n", - " for line in f_obj:\n", + "# Use 'with' keyword to open, read, and then close a file\n", + "with open('files/data.txt', 'r') as file_obj:\n", + " for line in file_obj:\n", " print(line.strip('\\n'))" ] }, @@ -119,9 +127,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Using Python's I/O is a pretty 'low level' way to read data files, and often takes a lot of work sorting out the details of reading files - for example, in the above example, dealing with the new line character explicitly. \n", + "Using input / output functionality from standard library Python is a pretty 'low level' way to read data files. This strategy often takes a lot of work to organize and define the details of how files are organized and how to read them. For example, in the above simple example, we had to deal with the new line character explicitly. \n", "\n", - "As long as you have reasonably well structured data files, using standardized file types, you can use higher-level functions that will take care of a lot of these details - loading data straight into pandas data objects, for example." + "As long as you have reasonably well structured data files, using standardized file types, you can use higher-level functions that will take care of a lot of these details - loading data straight into `pandas` data objects, for example." ] }, { @@ -142,16 +150,14 @@ "
\n", "Official Pandas\n", "documentation \n", - "on I/O. \n", + "on input / output. \n", "
" ] }, { "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": true - }, + "execution_count": 16, + "metadata": {}, "outputs": [], "source": [ "import pandas as pd" @@ -160,9 +166,7 @@ { "cell_type": "code", "execution_count": null, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Tab complete to check out all the read functions available\n", @@ -173,18 +177,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## File types" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "collapsed": true - }, - "source": [ - "
\n", - "There are many different standardized (and un-standardized) file types in which data may be stored. Here, we will start by examing CSV and JSON files. \n", - "
" + "## File types\n", + "\n", + "There are many different file types in which data may be stored. \n", + "\n", + "Here, we will start by examining CSV and JSON files. " ] }, { @@ -210,7 +207,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -225,7 +222,7 @@ ], "source": [ "# Let's have a look at a csv file (printed out in plain text)\n", - "!cat files/dat.csv" + "!cat files/data.csv" ] }, { @@ -237,10 +234,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": true - }, + "execution_count": 18, + "metadata": {}, "outputs": [], "source": [ "# Python has a module devoted to working with csv's\n", @@ -249,7 +244,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -264,8 +259,8 @@ ], "source": [ "# We can read through our file with the csv module\n", - "with open('files/dat.csv') as csvfile:\n", - " csv_reader = csv.reader(csvfile, delimiter=',')\n", + "with open('files/data.csv') as csv_file:\n", + " csv_reader = csv.reader(csv_file, delimiter=',')\n", " for row in csv_reader:\n", " print(', '.join(row))" ] @@ -279,10 +274,8 @@ }, { "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": true - }, + "execution_count": 20, + "metadata": {}, "outputs": [], "source": [ "# Pandas also has functions to directly load csv data\n", @@ -291,13 +284,26 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", + "\n", "\n", " \n", " \n", @@ -310,21 +316,21 @@ " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", @@ -341,14 +347,21 @@ "2 9 10 11 12" ] }, - "execution_count": 11, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's read in our csv file\n", - "pd.read_csv(open('files/dat.csv'), header=None)" + "pd.read_csv(open('files/data.csv'), header=None)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see, using `Pandas` save us from having to do more work (write more code) to use load the file. " ] }, { @@ -374,7 +387,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -390,12 +403,12 @@ ], "source": [ "# Let's have a look at a json file (printed out in plain text)\n", - "!cat files/dat.json" + "!cat files/data.json" ] }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 23, "metadata": {}, "outputs": [ { @@ -421,10 +434,8 @@ }, { "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": true - }, + "execution_count": 24, + "metadata": {}, "outputs": [], "source": [ "# Python also has a module for dealing with json\n", @@ -433,20 +444,18 @@ }, { "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": true - }, + "execution_count": 25, + "metadata": {}, "outputs": [], "source": [ "# Load a json file\n", - "with open('files/dat.json') as dat_file: \n", + "with open('files/data.json') as dat_file: \n", " dat = json.load(dat_file)" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 26, "metadata": {}, "outputs": [ { @@ -471,10 +480,8 @@ }, { "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": true - }, + "execution_count": 27, + "metadata": {}, "outputs": [], "source": [ "# Pandas also has support for reading in json files\n", @@ -483,7 +490,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -494,7 +501,7 @@ "dtype: object" ] }, - "execution_count": 18, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -507,32 +514,41 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "age 53\n", "firstName John\n", + "age 53\n", "dtype: object" ] }, - "execution_count": 19, + "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Read in our json file with pandas\n", - "pd.read_json(open('files/dat.json'), typ='series')" + "pd.read_json(open('files/data.json'), typ='series')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion\n", + "\n", + "As a general guideline, for loading and wrangling data files, using standardized data files, and loading them with 'higher-level' tools such as `Pandas` makes it easier to work with data files. " ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -546,7 +562,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/07-DataCleaning.ipynb b/07-DataCleaning.ipynb index 6af16c9..e2bc6d3 100644 --- a/07-DataCleaning.ipynb +++ b/07-DataCleaning.ipynb @@ -14,16 +14,16 @@ "metadata": {}, "source": [ "
\n", - "'Data Cleaning' is the process of finding and either removing or fixing 'bad data', where 'bad data' typically refers to corrupt and/or inaccurate data points. \n", + "'Data Cleaning' is the process of finding and either removing or fixing 'bad data'. \n", + " \n", + "By 'bad data' we mean missing, corrupt and/or inaccurate data points. \n", "
" ] }, { "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, + "execution_count": 6, + "metadata": {}, "outputs": [], "source": [ "# Imports\n", @@ -69,19 +69,17 @@ }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, + "execution_count": 7, + "metadata": {}, "outputs": [], "source": [ "# Python has the special value 'None', which can encode a missing, or null value\n", - "dat_none = None" + "data_none = None" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -99,7 +97,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -109,19 +107,19 @@ "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAssertionError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Note that 'None' acts like a null type (as if the variable doesn't exist)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32massert\u001b[0m \u001b[0mdat_none\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Note that 'None' acts like a null type (as if the variable doesn't exist)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0;32massert\u001b[0m \u001b[0mdata_none\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mAssertionError\u001b[0m: " ] } ], "source": [ "# Note that 'None' acts like a null type (as if the variable doesn't exist)\n", - "assert dat_none" + "assert data_none" ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -131,15 +129,15 @@ "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Since None is a null type, basic operations will fail when None is in the data\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mdat_lst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdat_lst\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdat_lst\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Since None is a null type, basic operations will fail when None is in the data\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0mdata_lst\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata_lst\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata_lst\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for +: 'int' and 'NoneType'" ] } ], "source": [ "# Since None is a null type, basic operations will fail when None is in the data\n", - "dat_lst = [1, 2, 3, None]\n", - "sum(dat_lst) / len(dat_lst)" + "data_lst = [1, 2, 3, None]\n", + "sum(data_lst) / len(data_lst)" ] }, { @@ -151,19 +149,17 @@ }, { "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": true - }, + "execution_count": 14, + "metadata": {}, "outputs": [], "source": [ "# Numpy also has a special value for 'not a number' - NaN\n", - "dat_nan = np.nan" + "data_nan = np.nan" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -172,31 +168,29 @@ "float" ] }, - "execution_count": 7, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# It's actually a special float value\n", - "type(dat_nan)" + "type(data_nan)" ] }, { "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": true - }, + "execution_count": 16, + "metadata": {}, "outputs": [], "source": [ "# It doesn't evaluate as null (unlike None)\n", - "assert dat_nan" + "assert data_nan" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 18, "metadata": {}, "outputs": [ { @@ -205,19 +199,19 @@ "True" ] }, - "execution_count": 9, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# Numpy actually has multiple versions of NaN - but they are all actually the same.\n", + "# Numpy has multiple ways to write NaN - but they are all actually the same.\n", "np.nan is np.NaN is np.NAN" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -236,7 +230,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -245,7 +239,7 @@ "2.0" ] }, - "execution_count": 11, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -259,7 +253,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## The 'Art' of Data Cleaning\n", + "### The 'Art' of Data Cleaning\n", "\n", "Dealing with missing data is a decision point: what do you do?\n", "- Do you drop the observation?\n", @@ -274,13 +268,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Impossible Values\n", - "\n", - "Data cleaning includes checking for and dealing with impossible values. Impossible values can occur due to encoding or data entry errors. \n", + "### Impossible Values\n", "\n", "Be wary that datasets may also encode missing data as a special value - for example using '-999' for missing age. \n", "\n", - "These have to be dealt with, or they will skew your results." + "These have to be dealt with, or they will skew your results.\n", + "\n", + "Data cleaning includes checking for and dealing with impossible values. Impossible values can also occur due to encoding or data entry errors. " ] }, { @@ -291,23 +285,21 @@ "\n", "Example problem: we have two separate files that collectively have id number, age, weight, and height for a group of people. \n", "\n", - "Let's say that ultimately, we are interested in how age relates to height (is it really true that older people shrink!?)\n", + "Let's say that ultimately, we are interested in how age relates to height. We might want to ask, for example, if older people have a lower average height than younger people (is it really true that older people shrink!?)\n", "\n", "Data Files:\n", - "- messy_dat.json, has id & height information\n", - "- messy_dat.csv, has id, age, & weight information" + "- messy_data.json, has id & height information\n", + "- messy_data.csv, has id, age, & weight information" ] }, { "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": true - }, + "execution_count": 21, + "metadata": {}, "outputs": [], "source": [ "# Load in the json file\n", - "df1 = pd.read_json('files/messy_dat.json')\n", + "df1 = pd.read_json('files/messy_data.json')\n", "\n", "# Since JSON files read in columns alphabetically, re-arrange columns\n", "df1 = df1[['id', 'height']]" @@ -315,25 +307,25 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", - "\n", "
001234
115678
2291011
\n", " \n", @@ -345,22 +337,22 @@ " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", @@ -376,7 +368,7 @@ "3 4 173.0" ] }, - "execution_count": 13, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -388,10 +380,8 @@ }, { "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": true - }, + "execution_count": 23, + "metadata": {}, "outputs": [], "source": [ "# Let's use pandas to drop the NaN value(s)\n", @@ -402,25 +392,25 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", - "\n", "
001168.0
112155.0
223NaN
334173.0
\n", " \n", @@ -432,17 +422,17 @@ " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", @@ -457,7 +447,7 @@ "3 4 173.0" ] }, - "execution_count": 15, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } @@ -469,37 +459,35 @@ }, { "cell_type": "code", - "execution_count": 16, - "metadata": { - "collapsed": true - }, + "execution_count": 25, + "metadata": {}, "outputs": [], "source": [ "# Read in the CSV data file\n", - "df2 = pd.read_csv('files/messy_dat.csv')" + "df2 = pd.read_csv('files/messy_data.csv')" ] }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", - "\n", "
001168.0
112155.0
334173.0
\n", " \n", @@ -512,25 +500,25 @@ " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", @@ -547,7 +535,7 @@ "3 4 -999 12.0" ] }, - "execution_count": 17, + "execution_count": 26, "metadata": {}, "output_type": "execute_result" } @@ -566,10 +554,8 @@ }, { "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": true - }, + "execution_count": 27, + "metadata": {}, "outputs": [], "source": [ "# So, since we don't need it, lets drop the weight column instead\n", @@ -578,7 +564,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -587,7 +573,7 @@ "0" ] }, - "execution_count": 19, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -608,10 +594,8 @@ }, { "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": true - }, + "execution_count": 29, + "metadata": {}, "outputs": [], "source": [ "# Now lets merge our data together\n", @@ -622,25 +606,25 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", - "\n", "
0012011.0
11227NaN
2232514.0
334-99912.0
\n", " \n", @@ -653,19 +637,19 @@ " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", @@ -681,7 +665,7 @@ "2 4 173.0 -999" ] }, - "execution_count": 21, + "execution_count": 30, "metadata": {}, "output_type": "execute_result" } @@ -693,25 +677,25 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", - "\n", "
001168.020
112155.027
224173.0-999
\n", " \n", @@ -724,49 +708,49 @@ " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", @@ -787,7 +771,7 @@ "max 4.000000 173.000000 27.000000" ] }, - "execution_count": 22, + "execution_count": 31, "metadata": {}, "output_type": "execute_result" } @@ -801,17 +785,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "So, it looks like our average age is ~ -300.... \n", + "So, it looks like our average age is about -300. That... doesn't seem right. \n", "\n", - "That doesn't seem right. At some point in data collection, missing age values seem to have been encoded as -999. We need to deal with these data. " + "At some point in data collection, missing age values seem to have been encoded as -999. We need to deal with these data. " ] }, { "cell_type": "code", - "execution_count": 23, - "metadata": { - "collapsed": true - }, + "execution_count": 32, + "metadata": {}, "outputs": [], "source": [ "# Drop all rows with an impossible age\n", @@ -820,7 +802,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 33, "metadata": {}, "outputs": [ { @@ -829,7 +811,7 @@ "23.5" ] }, - "execution_count": 24, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" } @@ -841,25 +823,25 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", - "\n", "
countcount3.0000003.0000003.000000
meanmean2.333333165.333333-317.333333
stdstd1.5275259.291573590.351026
minmin1.000000155.000000-999.000000
25%25%1.500000161.500000-489.500000
50%50%2.000000168.00000020.000000
75%75%3.000000170.50000023.500000
maxmax4.000000173.00000027.000000
\n", " \n", @@ -872,13 +854,13 @@ " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", " \n", " \n", - " \n", + " \n", " \n", " \n", " \n", @@ -893,7 +875,7 @@ "1 2 155.0 27" ] }, - "execution_count": 25, + "execution_count": 34, "metadata": {}, "output_type": "execute_result" } @@ -903,20 +885,29 @@ "df" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that in this example the problematic or missing values were relatively easy to locate - since we could see all our data. In real datasets, we may have hundreds to thousands of rows and potentially dozens of columns. In those cases, searching manually for missing or problematic values will not work very well. Strategies and programmatic approaches for identifying and dealing any bad values are necessary for any data analysis project. " + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data Cleaning Notes\n", "\n", - "This is really just the start of data cleaning - getting data into a fit shape for analysis can include any \n", - "Tips:\n", + "This is really just the start of data cleaning - getting data into a fit shape for analysis can include a considerable amount of exploration and work to ensure high quality data goes into the analysis. \n", + "\n", + "Tips for data cleaning:\n", "- Read any documentation for the dataset you have\n", " - Things like missing values might be arbitrarily encoded, but should (hopefully) be documented somewhere\n", "- Check that data types are as expected. If you are reading in mixed type data, make sure you end up with the correct encodings\n", - "- Visualize your data! Have a look that the distribution seems reasonable\n", - "- Check basic statistics. df.describe() can give you a sense if the something is being really skewed\n", - "- Keep in mind how your data were collected. \n", + " - Having numbers read in as strings, for example, is a common way data wrangling can go wrong, and this can cause analysis errors\n", + "- Visualize your data! Have a look that the distribution seems reasonable (more on this later)\n", + "- Check basic statistics. df.describe() can give you a sense if the data is really skewed\n", + "- Keep in mind how your data were collected\n", " - If anything comes from humans entering information into forms, this might take a lot of cleaning\n", " - Fixing data entry errors (typos)\n", " - Dealing with inputs using different units / formats / conventions\n", @@ -941,7 +932,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -955,7 +946,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/08-DataPrivacy&Anonymization.ipynb b/08-DataPrivacy&Anonymization.ipynb index bafa82d..429fc7d 100644 --- a/08-DataPrivacy&Anonymization.ipynb +++ b/08-DataPrivacy&Anonymization.ipynb @@ -10,7 +10,7 @@ "\n", "A lot of data, perhaps the vast majority of data typically used in data science, is, directly or indirectly, about people. \n", "\n", - "Individuals have certain privacy rights regarding who can know or share information about specifically identified individuals. This is true in particular about certain classes of sensitive information (for example, health-related information has special protections), but also applies to all other data as well. " + "Individuals have privacy rights regarding who can know or share information about specifically identified individuals. This is true in particular about certain classes of sensitive information. For example, health-related information has special protections. Regardless of the data type, data privacy and security should also be a key concern when analyzing human data." ] }, { @@ -29,7 +29,7 @@ "\n", "\n", "
\n", - "Wikipedia\n", + "Wikipedia\n", "has an overview of information privacy.\n", "
" ] @@ -46,7 +46,7 @@ "metadata": {}, "source": [ "
\n", - "Data Anonymization is a type of information sanitization - that is the removal of sensitive information - for the purpose of privacy protection. It is a procedure to modify a data set such that the individuals it reflect are anonymous. Most, typically this means the removal or personally identifiable information of data sets such that the identify of individuals contained in the data set are anonymous.\n", + "Data Anonymization is a type of information sanitization - that is the removal of sensitive information - for the purpose of privacy protection. It is a procedure to modify a data set such that the individuals it reflect are anonymous. Typically this means the removal or personally identifiable information from data sets such that the identify of individuals contained in the data set are anonymous.\n", "
\n", "\n", "
\n", @@ -59,13 +59,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Data protection and anonymization are interdisciplinary components of data science and data practice, including everything from the considerations of ethics & legalities of data use, to the practical and technical challenges of protecting and anonymizing data. \n", + "Data protection and anonymization are interdisciplinary components of data science and data practice. Data protection includes everything from considerations of the ethics & legalities of data use, to the practical and technical challenges of protecting and anonymizing data. \n", "\n", "Anonymizing data typically comes down to removing any personally identifiable data from a dataset, or, if this information must be kept, separating the identifiable data from sensitive information. \n", "\n", - "Part of the difficulty of data anonymization is that while we can provably demonstrate that a given dataset is anonymized, this rests on particular assumptions - most notably that the dataset is only provable anonymized under the assumption that no extra external information is used to attempt to de-identify it. \n", - "\n", - "In practice, de-anonymizing data can often be done by combining multiple datasets - using information from one or several available information sources to decode the individuals included in some other dataset. " + "Part of the difficulty of data anonymization is that while we can provably demonstrate that a given dataset is anonymized, this rests on particular assumptions. Most notably, datasets are only provably anonymized under the assumption that no extra external information is available to be used to attempt to de-identify it. In practice, this means that de-anonymization of data can often be done by combining multiple datasets. By using information from multiple information sources, one can often use processes of elimination to decode the individuals included in a particular dataset." ] }, { @@ -80,7 +78,7 @@ "- What the data is / contains, and who it is about, \n", " - Certain data types, and/or populations may have special protections, for example health-related information.\n", "- Who owns the data and in what capacity they are acting (company, university, etc.)\n", - " - Regulations for scientific research are different than those for companies\n", + " - For example, regulations for scientific research are different than those for companies\n", "- User agreements / consent procedures that were in place when the data were collected. \n", " - Individuals have a right to self-determination in terms of what their data is used for. Data should only be used for things that are covered by it's terms of use / terms of collection / consent procedures.\n", "- What the data is to be used for.\n", @@ -88,7 +86,7 @@ "- Where the data was collected and where it is stored, and who it is about.\n", " - Different regions (countries, etc) often have different regulations.\n", "\n", - "Much of these regulations apply more directly to the collection, storage, and release of datasets, but aspects also apply to the use of datasets, including publicly available datasets. Available datasets often have a user agreement for using the data, and, in particular, attempting to identify individuals from datasets may at a minimum break user agreements, and/or (depending on the nature of the data) be illegal based on consumer and research subject protection laws. " + "Much of these regulations apply more directly to the collection, storage, and release of datasets (rather than analysis), but aspects also apply to the use of datasets, including publicly available datasets. Available datasets often have a user agreement for using the data, and, in particular, attempting to identify individuals from datasets may at a minimum break user agreements, and/or (depending on the nature of the data) be illegal based on consumer and research subject protection laws. " ] }, { @@ -146,7 +144,7 @@ "metadata": {}, "source": [ "
\n", - "Safe Harbor is an official agreement regarding how to deal with datasets that have personal data, in particular, specific guidelines on what information to remove from datasets in order to anonymize them. It is a single set of data protection requirements shared across many contexts and countries. \n", + "Safe Harbor is an official agreement regarding how to deal with datasets that have personal data. It describes specific guidelines on what information to remove from datasets in order to anonymize them. It is a single set of data protection requirements shared across many contexts and countries.\n", "
\n", "\n", "
\n", @@ -160,7 +158,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The Safe Harbor method requires that the following identifiers of the individual or of relatives, employers, or household members of the individual, are removed:\n", + "The Safe Harbor method requires that the following identifiers of the individuals be removed:\n", "- Names\n", "- Geographic Subdivisions smaller than a state**\n", "- Dates (such as birth dates, etc), and all ages above 90\n", @@ -180,7 +178,6 @@ "- Certificate/license numbers\n", "- Any other unique identifying number, characteristic, or code\n", "\n", - "\n", "** The first three numbers of the zip code can be kept, provided that more than 20,000 people live in the region covered by all the zip codes that share the same initial three digits (the same geographic subdivision). " ] }, @@ -190,21 +187,21 @@ "source": [ "### Unique Identifiers\n", "\n", - "The logic Safe Harbor (and/or Data Anonymization in general) is to remove any unique information that could be used to identify you. \n", + "The goal of Safe Harbor, and Data Anonymization in general, is to remove any unique information that could be used to identify you. \n", "\n", - "This is perhaps most obvious for things like names, but some of the seemingly less obvious specifications of Safe Harbour also relate to the idea that leaving the specified information in a dataset is a risk for identification of individuals contained in the dataset. \n", + "This is perhaps most obvious for things like names. Other, perhaps less obvious specifications of Safe Harbour, are also based on the that this information being in a dataset creates a risk for identification of individuals contained in the dataset. \n", "\n", "For example, while it may be innocuous to talk about a 37 year old male who lives in Los Angeles (as there are many candidates, such that the specific individual is not revealed), it might actually be quite obvious who the person is when talking about a 37 year old male who lives in Potrero, California, a town of about 700 people. This is the same reason ages above 90 have to be removed - even in a fairly large area, say San Diego, it may be fairly obvious who the 98 year old female participant is. \n", "\n", - "Basically - any information that makes you stand out is liable to identify you, and so anonymization attempts to remove these idiosyncracies from data, such that individuals do not stand out in a way that lets someone figure out who they are.\n", + "Basically - any information that makes you stand out is liable to identify you. Anonymization attempts to remove these kinds of indications from the data, such that individuals do not stand out in a way that lets someone figure out who they are.\n", "\n", - "This also underlies the difficulty in protecting data in the face of multiple data sources, since collecting observations together makes it much easier to start to pick out people more uniquely - so it may still be relatively easy to identify the 37 year old male from LA if you also happen to know (or figure out) that he has a poodle, is 5'6\", works at UCLA, and was at Griffith Park on Saturday, April 15th, all of which may be relatively easy to figure out by combining publicly available, or easily obtainable, data." + "This also underlies the difficulty in protecting data in the face of multiple data sources, since collecting observations together makes it much easier to start to pick out people more uniquely. It may still be relatively easy to identify the 37 year old male from LA if you also happen to know (or figure out) that he has a poodle, is 5'6\", works at UCLA, and was at Griffith Park on Saturday, April 15th. All of this extra information may be relatively easy to figure out by combining publicly available, or easily obtainable, data." ] } ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -218,7 +215,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/09-DataVisualization.ipynb b/09-DataVisualization.ipynb index 17b175c..6bc1814 100644 --- a/09-DataVisualization.ipynb +++ b/09-DataVisualization.ipynb @@ -4,15 +4,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Data Visualization with Python\n", + "# Data Visualization\n", "\n", - "Data Visualization might mean a of different things. \n", + "Data Visualization can refer to a lot of different things. Here, we will start with making static 2D visualizations of data.\n", "\n", - "Here we are only going to deal with basic 2D plotting, using Matplotlib, which is a library for plotting with Python.\n", - "\n", - "Matplotlib is very well supported with examples that you can use to figure out how it works. \n", - "\n", - "Here, we will run through a quick intro of using matplotlib, with examples adapted from the official materials. " + "To do so, we will use the `matplotlib` package. Matplotlib is a large and well supported package that forms the basis of a lot of plotting in Python." ] }, { @@ -24,46 +20,19 @@ "
\n", "\n", "
\n", - "Check out matplotlibs official\n", - "website\n", + "Check out the matplotlib\n", + "website,\n", "including their introductory \n", "tutorial,\n", - "and list of \n", - "examples.\n", - "
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Pyplot vs Pylab\n", - "\n", - "Note that matplotlib is an and old, and quite massive, module, and actually has a couple different ways to use it. \n", - "\n", - "Short version: import 'matplotlib.pyplot', like we do here is perhaps most common, and will work!\n", - "\n", - "Long version: follow the following link to learn a bit about the different ways in which matplotlib can be used (pyplot, pylab, etc.). \n", - "\n", - "Ultimately, it all calls the same underlying code, there is just different syntax for accessing everything. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "
\n", - "A description of the different ways to interact with matplotlib is availabe\n", - "here.\n", + "and gallery of \n", + "examples.\n", "
" ] }, { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Import matplotlib - the main python plotting package\n", @@ -83,7 +52,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Line graph" + "## Line graph\n", + "\n", + "First, we will create a simple line graph." ] }, { @@ -94,7 +65,7 @@ { "data": { "text/plain": [ - "[]" + "[]" ] }, "execution_count": 2, @@ -103,16 +74,17 @@ }, { "data": { - "image/png": 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AoijaWvok2GeAN0IIE4BNwNmUbE35DPBk1X8LkiSpqv1z+iq+9/RMSjs8XZrV\n5fFRR9OqYXa8waQqFtetNURRtAoYCNwHHE7JlfmhlFypPy6Kon/sc/6/gBMoeQDU+cC3gQLgZuCi\nKIqiKgsvSZJi8dSUldyyR4k/vEU9JlxniVfNFOcVeUof+PTt0h8Hcv47wOmVGkqSJCWl8e8v56f/\nmp0Y92hVn8euOYpm9WrFmEqKT6xFXpIk6UCMeXspd74wNzHu07YB40ceReO6WTGmkuJlkZckSUnt\ngf99xK9emp8Y92vfiHEjh9CwdmaMqaT4WeQlSVLSuve/i7j7PwsT40EdG/PIVYOpn22JlyzykiQp\n6URRxD3/WcifX1ucmDuqcxPGXDmYurWsLxJY5CVJUpKJoohfT5zPA//79IHtX+rajNEjBlE7Kz3G\nZFJyschLkqSkEUURP39hHmPeWZqYG9q9OfdfNpDsTEu8tCeLvCRJSgrFxRG3PTeH8e8vT8yd3Ksl\n911yJLUyLPHSvizykiQpdsXFET9+dhYTpqxMzJ3etxV/uuhIMtNje36llNQs8pIkKVZFxRHff2Ym\n/5z+cWLu7H5t+MMF/ciwxEvlsshLkqTYFBQVc/NTM3l+5urE3PkD2vHb4UeQnhZiTCYlP4u8JEmK\nRX5hMd+ZMIOXZq9NzF08pD2/OLcvaZZ4ab8s8pIkqcrtKizihr9P59V56xNzI47pyO1n9bbESwfI\nIi9JkqpUXkER142fxv8WfpKYu/pLnbn1jJ6EYImXDpRFXpIkVZnc/EJGjZvKO4s3JuauH3oYPzi1\nuyVeOkgWeUmSVCW27ypk5NgpTF66KTH3nZMO56avHm6Jlw6BRV6SJFW6rXkFXDlmMtNXbEnMff/U\n7tzwla4xppJSm0VekiRVqpzcAkaMmcTMVTmJuR+f3oNrjz8sxlRS6rPIS5KkSrNpRz6XPzyJOau3\nJuZuO6sXVx3XOcZUUvVgkZckSZViw/ZdXPbQJOav3ZaY+8V5fbj0qI4xppKqD4u8JEmqcOu35nHJ\nQ5NYvH47ACHAb84/ggsGtY85mVR9WOQlSVKFWpOzk0tGT2Lphh0ApAW4+4J+nHdku5iTSdWLRV6S\nJFWYVZtzuWT0JFZsygUgPS3wxwv7c1a/NjEnk6ofi7wkSaoQyzfu4JLRk/h4y04AMtMD9148gGF9\nWsWcTKqeLPKSJOkL++iT7Vw6ehJrt+YBkJWext8uG8BJPVvGnEyqvizykiTpC1m0bhuXPDSJT7bt\nAqBWRhpXybKaAAAgAElEQVQPjhjECd2ax5xMqt4s8pIk6ZDNW7OVyx6axMYd+QDUzkzn4SsGcWzX\nZjEnk6o/i7wkSToksz/O4bKHJ7EltwCAulnpPHLVEIZ0bhJzMqlmsMhLkqSD9sHKLYx4eBJb8woB\nqF8rg7EjhzCwY+OYk0k1h0VekiQdlKnLNnHlI1PYvqukxDesncn4q4dwRLtGMSeTahaLvCRJOmDv\nL9nIyLFTyM0vAqBxnUweu+YoerdpGHMyqeaxyEuSpAPy9qINXDNuCnkFxQA0q5fF3685mu6t6sec\nTKqZLPKSJGm/Xl+wnuvGTyO/sKTEt6hfi8dHHU3XFvViTibVXBZ5SZL0uf4zdx03/H06+UUlJb51\nw2weH3U0nZvVjTmZVLNZ5CVJUrlemrWGbz8xg8LiCIC2jWoz4dqjad+kTszJJFnkJUlSmR59dxl3\nPD+H0g5Px6Z1eHzU0bRtVDveYJIAi7wkSdpHYVExd74wl3HvLU/MdWlel8evOZpWDbNjTCZpTxZ5\nSZKUsDWvgBv+Pp23Fm1IzPVr34iHRgyief1aMSaTtC+LvCRJAmDFxlyufnQKi9ZvT8ydcURr7v56\nP7Iz02NMJqksFnlJksTUZZu4dvw0Nu3IT8zdeGJXbvpqN9LSQozJJJXHIi9JUg337IxV/PCZWYnt\nJbPS0/jt8CM498i2MSeT9Hks8pIk1VDFxRF/+M9C7nt9cWKuad0sHhwxkIEdm8SYTNKBsMhLklQD\n7cwv4ntPz+Tfs9Yk5g5vUY8xVw52j3gpRVjkJUmqYdZvzWPUuKnMXJWTmDuhW3PuveRIGmRnxphM\n0sGwyEuSVIPMXb2Vax6dwuqcvMTclcd24tYzepKRnhZjMkkHyyIvSVIN8ercddw4YQa5+UUApKcF\nbjurFyOO6RRvMEmHxCIvSVI1F0URD721lF++NI8oKpmrXyuD+y4dwAndmscbTtIhs8hLklSNFRQV\n87P/N5snJq9MzLVrXJsxVw6mW8v6MSaT9EVZ5CVJqqZycgu4/u/TePejjYm5gR0b8+DlA2lar1aM\nySRVBIu8JEnV0NINO7h67BSWbNiRmDvvyLb86mt9yc5MjzGZpIpikZckqZp576ONfOOxaeTsLEjM\nfe+Ubtzwla6EEGJMJqkiWeQlSapGnpqykh8/O4vC4pJVrbUy0vjDBf0544jWMSeTVNEs8pIkVQPF\nxRG/mTifB95ckphrVq8WD10xiP7tG8WYTFJlschLkpTicvMLuWnCB7wyd11irker+jx85WDaNqod\nYzJJlckiL0lSCluTs5NrHp3KnNVbE3Nf7dmCP150JPVq+du8VJ35K1ySpBQ1a1UO14ybwrqtuxJz\no77cmR+d1pP0NBe1StWdRV6SpBQ0cfYabnryA/IKigHISAv8/Nw+XDykQ8zJJFUVi7wkSSkkiiL+\n+sZH/O7lBYm5BtkZ3H/ZQI7t2izGZJKqmkVekqQUsauwiB//czb/mL4qMdepaR0evnIwhzWvF2My\nSXGwyEuSlAI27cjnG+OnMXnZpsTcUZ2bcP9lA2lcNyvGZJLiYpGXJCnJLV6/nasfncLyjbmJuQsG\nteOuc/uSlZEWYzJJcbLIS5KUxN5etIHr/z6NbXmFAIQAPxrWg2uP70II7kwj1WQWeUmSktRj7y/n\ntufmUFQcAVA7M50/XtSfU3u3ijmZpGRgkZckKckUFUf84t/zGPPO0sRcqwbZPHTFIPq0bRhjMknJ\nxCIvSVIS2b6rkBufmMFr89cn5vq2bchDVwyiZYPsGJNJSjZJs0ImhHBZCCEq/XFNOeccG0J4MYSw\nKYSwM4TwYQjhphBCelXnlSSpoq3anMvwv727V4kf1rsVT113jCVe0mckxRX5EEJ74D5gO1DmRrgh\nhHOAfwB5wJPAJuAs4B7gOODrVRJWkqRKMH3FZq4dN5UN2/MTc98cehjfO6U7aWkuapX0WbFfkQ8l\nS+4fATYC95dzTgNgNFAEDI2i6Oooir4P9AfeA4aHEC6qosiSJFWo52au5qIH30+U+Mz0wO+/3o8f\nDOthiZdUrtiLPHAjcCJwFbCjnHOGA82BCVEUTd09GUVRHnBr6fD6ygwpSVJFi6KIP766kBufmEF+\nYTEAjetk8tjVRzF8YLuY00lKdrHeWhNC6An8GvhTFEVvhhBOLOfU3fMTyzj2JpALHBtCqBVF0a5K\niCpJUoXKKyjiB898yHMzVyfmDmtelzFXDqZj07oxJpOUKmIr8iGEDGA8sAL48X5O7176unDfA1EU\nFYYQlgK9gS7AvIrMKUlSRftk2y6uGz+V6Su2JOa+1LUZf7l0AA1rZ8aYTFIqifOK/M+AI4EvRVG0\ncz/n7t40N6ec47vnG+3vi4YQppVzqMf+3itJ0he1YO02Ro6dwsdbPv2t75KjOnDH2b3JTE+GO14l\npYpYinwI4ShKrsLfHUXRe3FkkCSpqr0+fz3ffmIG23cVApAW4NYzenHVcZ0o2ftBkg5clRf50ltq\nxlFym8xPD/Btu6+4l/c4u93zW8o5nhBF0cByck0DBhxgHkmSDlgURYx9dxk/f2EuxVHJXN2sdO69\n5EhO7NEy3nCSUlYcf4dXD+gG9ATy9ngIVATcVnrO6NK5P5aOF5S+dtv3w0r/YNAZKASWVG50SZIO\nTmFRMT/7f3O44/lPS3zbRrX5xzePtcRL+kLiuLVmF/BwOccGUHLf/NuUlPfdt928BlwKDAOe2Oc9\nxwN1gDfdsUaSlExydhbwrcen89aiDYm5/u0bMXrEIJrXrxVjMknVQZUX+dKFrdeUdSyEcDslRf7R\nKIoe2uPQM8BvgItCCPfu3ks+hJAN3FV6zt8qLbQkSQdpxcZcRj46hcXrtyfmzurXht8NP4LszPQY\nk0mqLmLdR/5ARVG0NYQwipJC/0YIYQKwCTibkq0pnwGejDGiJEkJU5Zt4rrx09i0Iz8x952TDuem\nrx7uolZJFSYlijxAFEX/CiGcAPwEOB/IBhYDNwN/jqIoijOfJEkA/5i2iv/75yzyi0qe1JqVkcbv\nhh/BOf3bxpxMUnWTVEU+iqLbgds/5/g7wOlVlUeSpANVXBzxh/8s5L7XFyfmmtXL4oHLBzGwY+MY\nk0mqrpKqyEuSlIp25hdxy9Mf8OKstYm57i3r89AVg2jfpE6MySRVZxZ5SZK+gPVb87hm3FQ+XPXp\nw8eHdm/OvRcfSf3szBiTSaruLPKSJB2iOatzuObRqazJyUvMXXlsJ249oycZ6XE8qkVSTWKRlyTp\nEPxn7jq+M2EGuflFAKSnBW4/uzeXH90x5mSSagqLvCRJByGKIka/tYRfvTSf3ful1a+VwV8uHcDx\n3ZrHG05SjWKRlyTpAOUXFvOz/zebCVNWJubaN6nNmCsGc3jL+jEmk1QTWeQlSToAa3J28p0JHzB5\n6abE3OBOjbn/soE0rVcrxmSSaiqLvCRJ+/HSrDX86J+zyNlZkJj72oC2/OprfamVkR5jMkk1mUVe\nkqRy5OYXcufzc/e6lSYtwC2ndOebQw8jhBBjOkk1nUVekqQyfLhqCzdN+IAlG3Yk5to2qs09F/Zn\nSOcmMSaTpBIWeUmS9lBcHPHAm0u4+5UFFBZHifmz+rXhrnP70LC2D3mSlBws8pIklVqTs5Obn5zJ\ne0s2JubqZqVz5zl9+NqAtt5KIympWOQlSaLsBa392zfiTxf1p2PTujEmk6SyWeQlSTVaeQtab/hK\nV2486XAy09NiTCdJ5bPIS5JqLBe0SkplFnlJUo3jglZJ1YFFXpJUo7igVVJ1YZGXJNUYE2ev4Yf/\ncEGrpOrBIi9JqvZc0CqpOrLIS5KqNRe0SqquLPKSpGqpvAWtZx7Rml+c19cFrZJSnkVeklTtuKBV\nUk1gkZckVSsuaJVUU1jkJUnVggtaJdU0FnlJUsqbtSqH70yY4YJWSTWKRV6SlLKKiyMefKtkQWtB\nkQtaJdUsFnlJUkoqb0HrHef04XwXtEqqASzykqSU44JWSbLIS5JSSFkLWkOAG4Z25TtfdUGrpJrF\nIi9JSgnlLWj9wwX9OKpL0xiTSVI8LPKSpKTmglZJKptFXpKUtFzQKknls8hLkpJSWQta+7VvxJ8u\n7E+nZi5olSSLvCQpqbigVZIOjEVekpQ0ylrQ2qZhNvdc2N8FrZK0D4u8JCl25S1oPeOI1vzy3L40\nrOOCVknal0VekhSrNTk7ueWpmbz7kQtaJelgWOQlSbFxQaskHTqLvCSpyrmgVZK+OIu8JKlKuaBV\nkiqGRV6SVCVc0CpJFcsiL0mqdC5olaSKZ5GXJFUqF7RKUuWwyEuSKoULWiWpclnkJUkVzgWtklT5\nLPKSpArjglZJqjoWeUlShShrQWudrHTuOLs3wwe2c0GrJFUwi7wk6QtzQaskVT2LvCTpkLmgVZLi\nY5GXJB2SmSu38N0nP3BBqyTFxCIvSTooG7bv4ncTF/DUtJVEn65ndUGrJFUxi7wk6YAUFBUz7r3l\n/PHVhWzLK0zMu6BVkuJhkZck7ddbiz7hjufnsnj99r3mT+zRgtvO6kXHpi5olaSqZpGXJJVrxcZc\n7vr3XF6Zu26v+c7N6vLTM3tyYo+WMSWTJFnkJUmfkZtfyF9f/4gH31pCfmFxYr5uVjo3nnQ4Vx3X\nmawMd6SRpDhZ5CVJCVEU8dzM1fzqxfms3Zq317HzB7Tjh8O606JBdkzpJEl7sshLkgCY/XEOdzw/\nhynLNu81f0S7htx+dm8GdGgcUzJJUlks8pJUw23akc/vX1nAE5NX7LWdZLN6WfxgWA+GD2hHWpq7\n0UhSsrHIS1INVVhUzN8nreDuVxawdY/tJDPSAlce24kbv3o4DbLdE16SkpVFXpJqoHcXb+CO5+ey\nYN22veaP79acn53Zi64t6sWUTJJ0oCzyklSDrNqcyy9fnMeLs9buNd+hSR1+dmYvTurZwoc6SVKK\nsMhLUg2wM7+I+//3Eff/7yN27bGdZJ2sdG74Sleu/lJnsjPTY0woSTpYFnlJqsaiKOLFWWv55Yvz\n+HjLzr2Ondu/DT86rSetGrqdpCSlIou8JFVT89du5fbn5vD+kk17zfdp24Dbz+rNoE5NYkomSaoI\nsRT5EEJT4DzgDKAv0BbIB2YBjwCPRFFUXMb7jgVuBY4GagOLgDHAvVEUFVVNeklKblty8/nDfxby\n2PvLKd5jO8kmdbP4/qnduWBQe9LdTlKSUl5cV+S/DvwNWAO8DqwAWgJfAx4CTgshfD2KPt3ROIRw\nDvAPIA94EtgEnAXcAxxX+pmSVGMVFUc8PrlkO8ktuQWJ+fS0wIhjOnLTSd1oWMftJCWpuoiryC8E\nzgb+veeV9xDCj4HJwPmUlPp/lM43AEYDRcDQKIqmls7/FHgNGB5CuCiKoglV+l1IUpKYtGQjtz8/\nl3lrtu41f1zXptx2Vm+6tawfUzJJUmWJpchHUfRaOfNrQwj3A78AhlJa5IHhQHNg3O4SX3p+Xgjh\nVuC/wPWARV5SjbJ6y05++eI8XvhwzV7z7RrX5tYzenFq75ZuJylJ1VQyLnbd/ffBhXvMnVj6OrGM\n898EcoFjQwi1oijaVZnhJCkZ5BUU8eCbS/jrG4vJK/h0SVF2Zho3DO3KqOO7uJ2kJFVzSVXkQwgZ\nwIjS4Z6lvXvp68J93xNFUWEIYSnQG+gCzKvUkJIUoyiKeHnOOu7691xWbd57O8mz+rXh/07rQZtG\ntWNKJ0mqSklV5IFfA32AF6MoenmP+YalrznlvG/3fKP9fYEQwrRyDvU4oISSFJOF67Zxx/NzeGfx\nxr3me7ZuwO1n9eKoLk1jSiZJikPSFPkQwo3ALcB84PKY40hS0sjZWcAfX13IuPeWU7THfpKN6mTy\nvVO6c/GQDm4nKUk1UFIU+RDCt4A/AXOBk6Io2rTPKbuvuDekbLvnt+zva0VRNLCcDNOAAftPK0lV\no6g44qmpK/ndywvYtCM/MZ8W4LKjO3Lzyd1oVCcrxoSSpDjFXuRDCDdRshf8bEpK/PoyTlsADAK6\nAXvdGlN6X31nShbHLqnctJJUNaYu28Rtz81hzuq9t5M8uksTbjurNz1bN4gpmSQpWcRa5EMIP6Tk\nvvgPgJOjKNpQzqmvAZcCw4An9jl2PFAHeNMdaySlurU5efz6pXn864PVe823bVSbn5zRk9P6tHI7\nSUkSEGORL32Y052UXGE/pYzbafb0DPAb4KIQwr17PBAqG7ir9Jy/VWZeSapMeQVFPPz2Uv7y+mJy\n84sS87Uy0vjGCYfxjRMOo3aW20lKkj4VS5EPIVxBSYkvAt4CbizjCtOyKIrGAkRRtDWEMIqSQv9G\nCGECsImSp8N2L51/smrSS1LFiaKIV+et565/z2X5xty9jp3etxU/Pr0n7RrXiSmdJCmZxXVFvnPp\nazpwUznn/A8Yu3sQRdG/QggnAD8BzgeygcXAzcCfoyiKyvoQSUpWi9dv584X5vLmwk/2mu/esj63\nnd2LYw9rFlMySVIqiKXIR1F0O3D7IbzvHeD0is4jSVVpa14Bf351EWPfXUbhHttJNqydyc0nd+PS\nozqQkZ4WY0JJUiqIfdcaSaopiosjnpm2it++PJ8N2z/dTjIEuGRIB245pTtN6rqdpCTpwFjkJakK\nTF+xmTuem8PMVXs/oHpIpybcdnYvercp7zEZkiSVzSIvSZVo/dY8fj1xPv+c/vFe860aZPPjM3py\n1hGt3U5SknRILPKSVAl2FRbxyDvLuPe/i9ixx3aSWRlpXHd8F64fehh1svxfsCTp0Pm7iCRVsNfn\nr+fOF+aydMOOveZP7d2Sn5zeiw5N3U5SkvTFWeQlqYIs3bCDn78wl9fmr99rvmuLetx2Vi++fHjz\nmJJJkqoji7wkfUHLNuzgobeX8OSUlRQUfbqdZP3sDL771W5cfkxHMt1OUpJUwSzyknSIpi3fzOg3\nl/Dy3LXs+Ui6EODCQe353qndaVavVnwBJUnVmkVekg5CcXHEf+atY/SbS5i6fPNnjg/s2Jjbz+pN\n33ZuJylJqlwWeUk6AHkFRfxj+ioeemvpZxaxAgzt3pxrv9yFYw5r6naSkqQqYZGXpM+xaUc+499b\nzrj3lrFxR/5exzLTA+f0b8uoL3ehe6v68QSUJNVYFnlJKsOyDTt4+O2lPD1tJXkFxXsdq5+dwaVH\ndeSq4zrRskF2TAklSTWdRV6S9lDeAlaAto1qM/JLnblwcHvq1fJ/n5KkePk7kaQab38LWHu3acC1\nx3fh9L6t3UZSkpQ0LPKSaiwXsEqSUplFXlKN4wJWSVJ1YJGXVGMcyALWK4/tRKuGLmCVJCU/i7yk\nam/6is08+L+yF7C2aZjNyC915qIhHVzAKklKKf6uJalaKi6OeHXeOh4sZwFrr9YNuO4EF7BKklKX\nRV5StbJ7AevDby1lSRkLWE/o1pzrjncBqyQp9VnkJVULLmCVJNU0FnlJKc0FrJKkmsoiLyklTV9R\n8gTWiXNcwCpJqpn8HU5Syti9gHX0W0uYsswFrJKkms0iLynp5RUU8c/pH/PQW0vKXcB67fFdONYF\nrJKkGsQiLylpbdqRz2PvL+fRd8tewHp2v7aMOr4zPVo1iCmhJEnxschLSjqfu4C1VgaXHN2Bq47t\n7AJWSVKNZpGXlDQOZAHrhYPbUz87M56AkiQlEYu8pFi5gFWSpENjkZcUCxewSpL0xVjkJVUpF7BK\nklQxLPKSqsTyjSULWJ+a6gJWSZIqgkVeUqWasWIzD7qAVZKkCmeRl1ThCouKeW3+ehewSpJUiSzy\nkirErsIi3l28kZdmr+E/c9exObfgM+e4gFWSpIpjkZd0yPIKinhjwSdMnL2G/85bz7ZdhZ85xwWs\nkiRVDou8pIOyfVchr89fz8TZa3l9wXpy84vKPK9Vg2zOObKNC1glSaokFnlJ+5WTW8Cr89bx0uy1\nvLnoE/ILi8s8r13j2pzWpxWn9W1N/3aNSEvz9hlJkiqLRV5SmTZu38Urc0vK+7uLN1BYHJV5Xpfm\ndUvKe5/W9G7TwHvfJUmqIhZ5SQnrtubx8py1vDRrLZOWbqSc7k6PVvU5rU9rTuvbisNb1LO8S5IU\nA4u8VMOt2pzLxNlreWn2Wqav2PyZvd53O6JdQ4aVXnnv3Kxu1YaUJEmfYZGXaqClG3bw0uw1TJy9\nlg9X5ZR5TggwsENjhvVpxbA+rWjXuE4Vp5QkSZ/HIi/VAFEUsXDd9kR5n792W5nnpQU4qnNTTu/b\nilN7t6JFA3ebkSQpWVnkpWoqiiLmrN7KS7PX8NKstSzZsKPM8zLTA8ce1ozT+rTi5F4taVqvVhUn\nlSRJh8IiL1UjxcURM1ZuYeLsNbw0ey2rNu8s87ysjDRO6Nac0/q04qSeLWlYO7OKk0qSpC/KIi+l\nuKLiiMlLNzFx9hpenrOOtVvzyjyvTlY6X+negmF9WvGVHi2oV8tf/pIkpTJ/J5dSUEFRMe99tJGX\nZq/llTlr2bgjv8zz6mdn8NWeLRnWpxU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MfKTO2tQeETGN4k75pcBpFFMqtlDMj/9KZq6q\nsTy9BeN4D/5RZp4w4jErgM8AZwMzKZYdvYXi3O+dmEoPnkFekiRJaiDnyEuSJEkNZJCXJEmSGsgg\nL0mSJDWQQV6SJElqIIO8JEmS1EAGeUmSJKmBDPKSJElSAxnkJUmSpAYyyEuSJEkNZJCXJEmSGsgg\nL0mSJDWQQV6SJElqIIO8JEmS1EAGeUmSJKmBDPKSJElSAxnkJUmSpAYyyEuSJEkN9P89nPOVA6wB\njAAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ - "" + "
" ] }, "metadata": { "image/png": { - "height": 250, - "width": 377 - } + "height": 248, + "width": 375 + }, + "needs_background": "light" }, "output_type": "display_data" } @@ -122,9 +94,6 @@ "x = np.arange(0, 11)\n", "y = x**2\n", "\n", - "# In matplotlib, we can make a figure and then plot to it\n", - "# Make a figure\n", - "f = plt.figure()\n", "# To plot, simply pass the x and y data to the plot function\n", "plt.plot(x, y)" ] @@ -135,7 +104,7 @@ "source": [ "Without any other information, matplotlib will add a number of plotting attributes by default.\n", "\n", - "For example, by default we get lines around the plot, tick marks as well as axis number labels. \n", + "For example, by default we get lines around the plot, tick marks, and axis number labels. \n", "\n", "We can customize all of these things, and add more stuff to the plot as well." ] @@ -146,16 +115,15 @@ "source": [ "## Scatter Plot\n", "\n", - "Lets try creating a Scatter plot\n", - "Let's image two groups of data, that we want to plot together on a scatter plot to compare. " + "Next, lets try creating a scatter plot. \n", + "\n", + "To do so, we can simulate two groups of data, that we want to plot together on a scatter plot to compare." ] }, { "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": true - }, + "execution_count": 3, + "metadata": {}, "outputs": [], "source": [ "# Create some Data\n", @@ -170,119 +138,169 @@ "metadata": {}, "source": [ "### Creating a Scatter Plot\n", + "\n", "The 'scatter' command works about the same as the plot command, but makes a scatter plot instead of a line. \n", "\n", - "Here, we're adding another argument, 'c' which specifies the colour to make the points\n", + "Here, we're adding another argument, `color` which specifies the color to make the points. \n", "\n", - "There are lots of optional arguments we can add to 'plot' and 'scatter'" + "Note there are lots of optional arguments we can add to 'plot' and 'scatter', that we will explore more later. " ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 14, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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3WhNa5yaLHr0u+WqfFqzE1qYUwjb9LVUgbQi1iGXZUarl6hXL+wBTca0IK6Y+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\nbklfkLQo6eNmdm6V+2mKNEUuQ3SH6h5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\n", 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" ] }, "metadata": { "image/png": { - "height": 250, - "width": 373 - } + "height": 248, + "width": 372 + }, + "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the first set of data\n", - "plt.scatter(x, y1, c='blue')\n", - "# We now want to plot the second set of data on the same plot. \n", - "# The 'hold' command tells Python to hold onto the current figure and add the next data to it. \n", - "plt.hold\n", - "# Plot the second set of data\n", - "plt.scatter(x, y2, c='red')" + "plt.scatter(x, y1, color='blue')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 248, + "width": 372 + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Now, plot both sets of data together\n", + "# We can do this by calling the plot call on each set of data\n", + "# Subsequent plot calls, like this one, will by default plot onto the same figure\n", + "plt.scatter(x, y1, color='blue')\n", + "plt.scatter(x, y2, color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We now have a scatter plot!\n", + "We now have a scatter plot!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Customizing Plots\n", + "\n", + "The plot above shows the data, but aesthetically there is more we could do to make it look nicer. \n", + "\n", + "Next up, we will replot the data, and add some customization to the plot. \n", "\n", - "However, it doesn't look very nice. Let's see if we can improve it. Let's experiment with adding lots of the customization functions to make a nicer graph." + "In the next cell, we will add lots of customization. It's a large set of code, but to explore how it all works, work through bit by bit, and try passing in different values, and see what it does to the resultant plot." ] }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 5, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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nnuOss86iV69eVFVV8eEPf5gXX3wxo3NyxhlnMGLEiFbHEREREckHBRIC+O5M\ny5fD5s0wdqzvxpR4P2rml48d69dbvtxvVwj33XcfjY2NfOxjH2PUqFEp1y8rC258u+aaa/jGN77B\n6NGjueaaa1oEJJdddhmzZ89my5YtfOYzn+Fzn/scW7du5YorruCyyy7L2Wt5/vnnmTp1KhUVFVx5\n5ZWcffbZLFq0iEmTJvHUU0/l7DgiIiIiuaSuTUIk4sdEbNwII0b4rkzJlJf79dav99tNnw4l7RyS\nPvPMMwCceeaZbdrPSy+9xIoVKxg6dGiL5Q8++CALFizg5JNPZtmyZVRWVgJw8803M2XKFBYsWMA5\n55zDJZdc0qbjA/zpT39i/vz5XHXVVYeXLVy4kPPPP5/LL7+c1atXU9LeJ1hEREQkBQUSwiuv+IHV\nkQj07p3eNr17+zEUGzb47ceMyW8ZE73zzjsADBgwoNVztbW13H///S2W9e7dmy984Qut1r3uuuta\nBREA9957LwC33nrr4SACoEePHtx2222cddZZ/PSnP81JIDF8+HCuuOKKFsvOO+88pkyZwtKlS3nq\nqaeYMmVKm48jIiIikksKJITaWp+dqU+f1t2Zwpj5gdg7d/pgor0DiWRqa2u58cYbWywbPHhwYCAx\nYcKEwH289NJLlJSUtBgzETNlyhRKS0tZsWJFTso7adKkwBaHqVOnsnTpUlasWKFAQkRERIqO+ksI\n9fW+dSFkGEGosjK/3cGD+SlXMscccwwAb7/9dqvnpk6dinMO5xyHDh1Kaz+Jdu3aRU1NDeUB/bzK\nysro06dPzjJBHX300UnL1hUyTomIiEjHo0BCqKjw80Q0Nma2XWOj36579/yUK5nYoOhFbRztHZbh\nqFevXuzYsSMwEGlsbGTbtm307Nnz8LJYi0JjyEmsq6sLLcOWLVsCl8e6b/Xq1St0WxEREZFCUSAh\nDBniszFt3QrpzoXnnF8/Nklde5s5cyZlZWU8/PDD/POf/8z5/k8++WQikQjLli1r9dyyZctoamri\nlFNOObysuroagDfffLPV+rt37+b1118PPdbTTz/dKp0s+PSwsbKIiIiIFJtOH0iY2cfMbL6ZPWVm\nu83MmVlWU/2a2UAzu9fM3jazejOrNbM7zKw61+VuT6NH+2CgtBSSVJy3UFfn1x882G/f3o477ji+\n/vWv09DQwNlnn82zzz4buF6yloBkLr/8cgC+8pWvsH///sPL9+/fz/XXXw/ArFmzDi+vqqrihBNO\n4JlnnuExEJFOAAAgAElEQVTVV189vLypqYlrr72WAwcOhB5rzZo1/OhHP2qxbOHChSxdupThw4cz\nadKkrF6DiIiISD51hcHWXwfGAHuBt4ATstmJmR0HPAv0AxYCrwETgGuA6WY20Tm3PSclbmclJTB5\nsp+xes0aP09EshSwDQ1+vWHD/HaFykx6ww034JzjW9/6FhMnTmTcuHFMmDCBmpoa6urqqK2t5Ykn\nngBg8uTJGe37kksuYeHChfzmN79h1KhRnH/++ZgZjz76KOvXr+eiiy7i0ksvbbHNl7/8ZWbNmsXE\niRO58MIL6d69O4sXL+bQoUOMGTOGVatWBR5r+vTpzJkzh8cee4wxY8awdu1aHnnkEbp37869996b\ndurXRx99lEcffRRo7hb13HPPHZ4kr0+fPnznO9/J6DyIiIiIhOkKgcQX8QHEWmAKsDjL/fwIH0T8\np3NufmyhmX03eoxbgM+3raiFM20arFwJBw74vyNG+BSv8UMInPMtEWvWQP/+fqbradMKV+bYrNAX\nX3wxd999N4sXL2bBggXs27ePqqoqjjvuOGbPns1ll13WohtSuh588EGmTJnCvffeyz333APAiSee\nyJw5c5g9e3ar9S+//HKcc3z3u9/lgQceoLq6mvPOO4958+ZxwQUXhB7ntNNO44YbbuAb3/gGd955\nJ845zjzzTG655RZOPfXUtMu7cuVKHnjggRbL1q1bx7p16wCfuUqBhIiIiOSKuXQ7xXcCZjYVH0j8\nyjn3iQy2Ow4fiNQCxznnInHPVQGbAQP6Oef2ZVGuFm9Cod6TPXtg/nw/Y/XGjT4jU9++PjtTY6Mf\nE1FaCoMG+SDiqqugqqogRe0UlixZwhlnnME3v/lN5s6dW+jiiIiISNeSZtL/cF2hRSIXzoj+fTw+\niABwzu0xs2eADwHvB9qWRqiAqqpgzhxYtMjPWL1hg58noqHBBxAjR/oxEZMn+5aIiopCl1hERERE\nCkWBRHpGRv+Gpd5Zgw8kjidFIGFmy3NYrpyrqIAZM2D69OYZrw8e9CleYwOrCzUmQjqwSMR/oGpr\n/cQlFRU+XZg+UCIiIh2WAon0xBL5h80MFlveux3K0i5KSvxs1cU0Y7V0QPX1rZu4mpp8E1csd7Ca\nuERERDokBRLtzDk3LnFZ4hgJ6RpiM3B3WmGDbsrL/aCb1ath7Vo/en/lSrj6ag26ERER6UAUSKQn\n1uIQNsVwbHl2kxaIdDb19T6IePpp2Lw5OA3Y4MHNacBi82zMmaOWCRERkQ5CnZPTszr69/iQ50dE\n/4ZPXyzSlSxa5FsiNm/2E5NUV7cMIsD/v7raP795s19/UYfNVSAiItLlKJBIT2zuiQ+ZWYtzFk3/\nOhHYD/y1vQsmUnQiET8mYuNG3xKRbHZD8M+PGOHXX7bMby8iIiJFT12b4phZN+A44JBz7o3Ycufc\nG2b2OD4z05XA/LjNbgR6APdkM4eESKcTS/cVifjuTOno3duPodiwwW+vUf4i0l6UVU4ka50+kDCz\n84Hzo/89Jvr3dDO7P/rvbc65L0X/PQD4J7ABGJKwqyuAZ4EfmNm06Hqn4eeYeB34Wj7KL9Lh1Nb6\n7Ex9+rTuzhTGzA/E3rnTBxMKJEQk35RVTqTNOn0gAYwFPpWwbFj0AT5o+BIpRFslxgM3AdOBGfgZ\nrb8P3Oic25mzEot0ZPX1/mKcqktTorIyP/vhwYP5KZeISIyyyonkRKcPJJxzc4G5aa5bS5Lpwp1z\nbwKfzkW5RDqtigpfo9fYmNl2jY1+u+7d81MuERFQVjmRHFLnPxHJrSFDfLeArVsh3XkynPPrx7oT\niIjki7LKieRMp2+REJF2Nnq0DwbWrvU1etXVqbepq/OtEYMH++1FRGOA8yHbrHLr1/vtpk/XyReJ\no0BCRHKrpMQPUFyzxj/Gjk1+sW5o8OsNG+a300VaujiNAc4jZZUTySkFEhKsA1WFvf7669x9990s\nWbKE2tpa9uzZQ1VVFSNGjGDSpElcfPHFjBs3rtDFzKvt27fzu9/9jj/84Q+88sorbNq0ifLyckaP\nHs2nP/1pPv3pT1PSnu/btGl+gOKBA/5vUB9k55r7IPfvD+PH++1EujCNAc4zZZUTySkFEtJSB6oK\nc85x0003cdNNNxGJRDjllFO46KKLqKmpYc+ePbz88svMnz+f22+/nTvvvJMrr7yyoOXNp4ceeojZ\ns2fTv39/zjjjDAYNGsSWLVt45JFH+MxnPsNjjz3GQw89hKV74Wyrigp/hwP+jmj9+uY7orIyf0e0\ndav/XA0b5oOIq64q+GdKpJA0BrgdKKucSE4pkJBmHawq7KabbmLu3Lkce+yxPPjgg0ycOLHVOu++\n+y533HEHu3btKkAJ28/xxx/P73//e84555wWLQ/z5s1jwoQJ/Pa3v+WRRx7hggsuaL9CVVX5O5zE\nwLShwQcQI0cWVWAqUmiJY4CD7nXjxwCvXNk8BnjGjPYvb4ekrHIiOVVcfVSkcOKrwtatg6FDfS3x\nkCEwcKD/O368X75unV9v/ny/XQGsW7eOm2++mfLych577LHAIAKgX79+zJs3j+uuu67F8pkzZ2Jm\nrFu3jvnz53PSSSdxxBFHMHXq1MPrRCIR7r77bk499VQqKyvp0aMHp556KnfddReRSKTF/mprazEz\nZs6cGViOqVOntmoNWLJkCWbG3Llzee655zjrrLPo1asXVVVVfPjDH+bFF19M+3yceeaZnHvuua26\nLx1zzDF8/vOfP3y8dldR4e9w5s2D66+HK66Az37W/73+er98xgwFEdLlZTsGeONGv13CT5KEUVY5\nkZxSi4R4Hawq7L777qOxsZFLLrmEUaNGpVy/rCz4o37NNdfw1FNPcc455zBjxgxKS0sPP3fZZZex\nYMECjj32WD7zmc9gZvzud7/jiiuu4Omnn+ZXv/pVTl7L888/z7e//W3OOussrrzyStauXcsjjzzC\nsmXLePzxx5k0aVKb9t+tWzcg/By0i5IS369YfYtFAr3yCmysjXDc3leYVFdLtx31NJZWsL1qCJtq\nRuOsdb2fxgBnQVnlRHJKgYR0yHR4zzzzDOBr4tvipZdeYsWKFQwdOrTF8gcffJAFCxZw8skns2zZ\nMiorKwG4+eabmTJlCgsWLOCcc87hkksuadPxAf70pz8xf/58rrrqqsPLFi5cyPnnn8/ll1/O6tWr\nsx4o3djYyM9//nMApk+f3uayikge1Nez/+FFnPfCMvod2EC/vTsx14SzUvZVVLOjcjBr+k/mtQHT\naCxtbr3TGOAsKKucSE4pkJAOmQ7vnXfeAWDAgAGtnqutreX+++9vsax379584QtfaLXudddd1yqI\nALj33nsBuPXWWw8HEQA9evTgtttu46yzzuKnP/1pTgKJ4cOHc8UVV7RYdt555zFlyhSWLl3KU089\nxZQpU7La9/XXX8/f//53ZsyYwYc//OE2l1VEciw6Nm3g48up2baRUmuivqovjSXllEYaObpuNf12\nraXfrjUcu30lT466mvry5rFpGgOcBWWVE8kZBRLS6dLh1dbWcuONN7ZYNnjw4MBAYsKECYH7eOml\nlygpKWkxZiJmypQplJaWsmLFipyUd9KkSYEtDlOnTmXp0qWsWLEiq0DiBz/4AbfffjsnnHACv/jF\nL3JRVBHJpbixaVVbN7PuyBHsLetNVVXz7/D2ysEc0VDH0bvX0K3Jp2n6y0lzDrdMaAxwFpRVTiRn\n1EYnzenwMu1DX1bmtytAVdgxxxwDwNtvv93qualTp+KcwznHoUOH0tpPol27dlFTU0N5QJN3WVkZ\nffr0yVkmqKOPPjpp2bI5zp133sk111zDe9/7XhYvXkxNTU2byigieRA3Ni0yeiyHKqs5eDChMseM\nAxXVvFkzll77NzNo63JO2LQI0BjgNolllZs1y7c0jBzpK8gaGvzfkSP98lmz4NprNVmHSAi1SEiH\nTIc3ceJEFi9ezKJFi7j88suz3k/YvAq9evVix44dHDp06PBg5ZjGxka2bdtGz549Dy+LtSg0hpzD\nurq60DJs2bIlcHms+1avXr3CX0CAO+64gy9+8Yu8733vY9GiRfTr1y+j7UWkHSSMTavuXU7VBti9\nC+oboCKhDqOptJx3e46gz571jNi8jH8cO52ddSUaA9wWsaxy06c3d/E9eNBf02InVWMiRJLSN0Q6\nZDq8mTNnUlZWxsMPP8w///nPnO//5JNPJhKJsGzZslbPLVu2jKamJk455ZTDy6qjmT/efPPNVuvv\n3r2b119/PfRYTz/9dKt0stCcrvXkk09Ou9y33XYbX/ziFxk7diyLFy9WECFSrBLGppn5rviVlbBr\nV3A61/3lvTHXRM3eDfR95xVeftk3DJvB//4vrFqlNLBZiWWV+7d/g49/3P8dM0ZBhEga9C2R5nR4\npaV+cFk6CpwO77jjjuPrX/86DQ0NnH322Tz77LOB6yVrCUgm1srxla98hf379x9evn//fq6//noA\nZs2adXh5VVUVJ5xwAs888wyvvvrq4eVNTU1ce+21HIhNQRtgzZo1/OhHP2qxbOHChSxdupThw4en\nnf71W9/6Ftdffz3jxo1j0aJF9OnTJ63tRKQAAsamDRjgu+kfeSRs2+5bJlowY09FX9z2nWxYtoHd\nu2H7dnjhBbjrLrj1VvjqV+GPfyzYFD8i0sWoa5N02HR4N9xwA845vvWtbzFx4kTGjRvHhAkTqKmp\noa6ujtraWp544gkAJk+enNG+L7nkEhYuXMhvfvMbRo0axfnnn4+Z8eijj7J+/XouuugiLr300hbb\nfPnLX2bWrFlMnDiRCy+8kO7du7N48WIOHTrEmDFjWLVqVeCxpk+fzpw5c3jssccYM2bM4Xkkunfv\nzr333ptW6tcHHniAG264gdLSUiZNmsQPfvCDVusMGTIkdMI8EWlnsbFpcb+1paUw6n3+31u3wp7d\nsNtB9yOgxPzqDdvLKG1qoLTcj0079ljfE6exEVav9tMjrFnjkxFdfbW69otIfimQEK8DpsOLzQp9\n8cUXc/fdd7N48WIWLFjAvn37qKqq4rjjjmP27NlcdtllLbohpevBBx9kypQp3Hvvvdxzzz0AnHji\nicyZM4fZs2e3Wv/yyy/HOcd3v/tdHnjgAaqrqznvvPOYN28eF1xwQehxTjvtNG644Qa+8Y1vcOed\nd+Kc48wzz+SWW27h1FNPTaus69evB3wLyB133BG4zpQpUxRIiBSLkLFp5d3gpJNg0yY/P+ievdAQ\njTn27oVK10ikpJSjB3fn7NNb5sgYPLj5JzrWCDpnjpINiUj+mEu3T7zkjZm1eBMK9p5E85mzfLkf\nABiWDm/QoOZ0eKruytqSJUs444wz+OY3v8ncuXMLXRwRaU+rVvm+SKtX+9/TgMQPzsGOHT6Y2LIF\nNm9yjNj9Inv6j+Qv467nraOC0243NPj6oGHDfNKhGTPy/WJEpINKM+d/OLVISLNYOrxFi3w2kQ0b\nfB/ehgYfQIwc6au8Jk/2LRG5rOaKRPzgw9pa3+RfUeEHgStrhoh0RrGxaWvX+maEaMKGeGZw1FFQ\nUwNb3oEeh+qoOLKUN3sNZlNN+Ni08nLfqLx+vf8pnz5dP6Mikh8KJKSl9k6HV1/fOnBpavKBSywj\nVD4CFxGRQspgbNqOHbB/dwPH1q9h99HDWNN/Ms6S/w737u1/Sjds8D/lRTRnqIh0IgokJFgsHV4+\nrz5hXanKyzVyMIEabEQ6oTTHph3cXMex29awo0d/NvUdz2sDUo9NM/M/pzt3+mBCgYSI5IMCCSmM\n+nofRDz9tB9RGHQB7eQjB2MzcCejBhuRTqyiwleQgK9QWb8+cGxa912lrOs+jDeqx/PSqKtoLE3v\ny15W5numHjyYx9cgIl2aAgkpjEWL/IVz8+bwJn0zf7c8dqyvrVu+3G/XRUYOqsFGpAtIY2zajobB\nPF47mRU10xhQnn6NQWOj30X37nksv4h0aQokpP1FIv6CuXGjb4lINmcFdMmRg2qwEelCUoxN2x8Z\nzdr/KuHt1fCeoYEJnlpxzifai+XIEBHJBwUS0v5iF8pIxN8dp6OLjRxUg41IFxQyNm10JGWCp1bq\n6nxrRCxHhohIPnTual0pTrW1vum+T5/0qtag9cjBTizbBpuNG/12kUj7lFNE2kcswdOgQb4FsqEh\n+foNDX69QYP8dp28AVdECkg/L9L+6qPTtJZl2CBWVua36+QjB3PRYCMincu0aTBuHPTv71sgd+70\n3ZfiOeeXr1zp1xs/3m8nIpIv6tok7a+iwre5NzZmtl0XGTmYiwabTt7zS6TLSTPBE6Wlfkbr8ePh\nqqs0ZkpE8kuBhLS/IUN8J9/Vq30HXo0cbCHWYJOqS1MipXoU6dzSSPCklNAi0q4USEj7Gz1aIweT\nUINNcdPkgFJIKRI86XMoIu1KgYS0v9jIwTVr/CMsLVFMbOTgsGFdYuSgGmyKkyYHlGISkuBJRKRd\nKZCQwpg2zY8IPHDA/w2aKMG55okSutDIQTXYFB9NDigiItKaAgkpDI0cDKUGm+KiyQFFRESCmUvM\nHyftzsxavAld6j1Rf5FA9fVw++3Jb14TG2wmTYJrr+1Sp6ld/PGP8LOfwbp16QV1K1f6oG7WLE0O\nKCIiRS3N3JBJdtClblqLVJcOJGJiI1g1cvCwsO40iQ02gwY1N9ioO01uRSLw1a/6WHfo0PS6me3c\n6RvYpk2DefO67Mc39zTKXUQk19ocSKhrkxQHjRxsRakeCy8XkwPqI91GarUUESlaCiREiphSPRaW\nJgcsMI1yFxEpagokRDoANdgUhiYHLCCNchcRKXqqyxQRCaHJAQto0SLfErF5sx/lXl3dulnIzC8f\nO9avt3y5305ERNqFAgkRkRCxyQG3bvVZstIRmxww1n1fshCJ+DERGzf6lohUTULl5X69jRv9dpFI\n+5RTRKSLU9cmkXQoY0yXpMkBC0Sj3EVEOgQFEiLJKGNMl6bJAQtEo9xFRDoEBRIiYZQxRvAx4sqV\nfizvypXpTQ44frzfTrKkUe4iIh2CAgmRIMoYI1EVFT5GBB9Trl8fPjngsGHNkwPqY9AGGuUuItIh\nqOFdJIgyxkic2OSAs2b5loaRI/3b39Dg/44c6ZfPmgXXXquGqTbTKHcRkQ5BLRIiibLNGLN+vd9u\n+nR1ju+ENDlgO9IodxGRDkGBhEgiZYyRJDQ5YDvQKHcRkQ5Bv7YiiXKRMUZE2mbaNBg3zo9eX7nS\nf7cSuzk555evXKlR7iIiBaAWCZFEyhgjUnga5S4iUvQUSIgkUsYYkeIQG+WeOJdLQ4P/ro0cqblc\nREQKSIGESKJYxpjVq/1NSjrdm2IZY2I3NiKSGxrlLiJStBRIiCRSxhiR4qNR7iIiRUfVOCKJYhlj\nBg3ymWAaGpKvH8sYM2iQMsaIiIhIl6E7HpEgyhgjIiIikpS6NokEUcYYERERkaTMJdaySrszsxZv\ngt6TIlJf3zpjTFOTDyCqq5UxRkRERDqqNCfLSrID3bQWngKJDiASUcYYERER6UwUSHQGCiRERERE\npJ21OZDoElWpZjbQzO41s7fNrN7Mas3sDjNLI69ni/2cY2aPm9lbZnbAzNaZ2UNmdnq+yi4iIiIi\nUow6fYuEmR0HPAv0AxYCrwETgDOA1cBE59z2NPZzG3AdsB14FNgGDAf+DT9o/ZPOuV9mWUa1SIiI\niIhIe1LXplTM7M/Ah4D/dM7Nj1v+XeCLwD3Ouc+n2McxwCZgK3CSc+7duOfOAJ4E1jvnhmVZRgUS\nIiIiItKeFEgkE22NWAvUAsc55yJxz1UBm/EnsZ9zbl+S/ZwG/BX4vXPuvIDnd+PPZVWW5VQgISIi\nIiLtqc2BRFbzSJjZ5LYeOBnn3LIc7eqM6N/H44OI6DH2mNkz+NaK9wOLkuxnDdAATDCzPs65bbEn\noueiCt/dKSUzW55B+UVEREREilK2E9ItAfJVbe7I3UR5I6N/Xw95fg0+kDieJIGEc26Hmf0/4LvA\nq2b2KH6sxHH4MRJ/Af4jR2UWERERESl6bb1hb3OTSJ71iv7dFfJ8bHnvVDtyzt1hZrXAvcBn455a\nC9wfP24ixX7GJS5L7NokIiIiIlLs2pr+1eX4UbTM7DrgYeB+fEtED2AcsA74lZn9V+FKJyIiIiLS\nvjr7PBKxFodeIc/Hltcl24mZTQVuww+2vtY5t845t9859xLwEXxGpzlmllXWJhERERGRjqYtgYTl\n4ZFrq6N/jw95fkT0b9gYiph/jf5dnPiEc24/8AL+XJ6caQFFRERERDqibMdIfDqnpcif2I3/h8ys\nJCD960RgPz61azIV0b99Q56PLW/ItqCSWiQCr7wCtbVQXw8VFTBkCIweDSWdvW0NdAJERESkqHTq\neSQgswnpzKwbfvzDIefcG3Hrfhz4NbAFGOec2xT33NnAH4B6YGA6s2QHlFHzSCRRXw+LFsGyZbBh\nA+zcCU1NUFoK1dUweDBMngzTpvl7606ny58AERERyQNNSJdKdFK6Z4F+wELgn8Bp+DkmXgc+ELv5\nN7MhwHpgg3NuSNw+SoA/A2cBe4DfAe8AJ+K7PRnwBefc97MsowKJEHv2wPz5sHw5bNzo75/79oWy\nMmhshK1b/f30oEEwbhxcfTVUZTUtYJHq8idARERE8qQwE9J1JM65N8xsPHATMB2YgZ/R+vvAjc65\nnWnsI2JmM4ArgX/HD7A+EtgB/BH4gXPu8Ty9hC6rvt7fQz/9NGzeDCNGQO/eYHEf+8GDoa4O1qyB\nAwf8sjlzOknFfI5PgHpGiYiISC61S4uEmQ3CtwIcjZ+zocQ5d1PeD9xBqEUi2B//CD/7GaxbB2PH\nQnl5+LoNDbByJQwbBrNmwYwZ7VfOvMnRCVDPKBEREQlQvC0S0e5AnwS+DJwQ8PzNwEW0nNztXufc\nL/NVJuk4IhF/47txo6+IT3YPDf75ESNg/Xq/3fTpHbyWPUcnIKxnVHm57xm1ejWsXesbNFauVM8o\nERERSV9eAgkz64cfnDyZ4GgnVuX+EjA17v+9AAUSwiuv+NrzSMT35klH797+RnnDBr/9mDH5LWNe\n5eAE1J8wpmt3DRMREZG8ynmdbTSt6pO0DCICZ692zq0GXoltCow1s6G5LpN0PLW1vgtOnz4tb3yT\nMfO17Tt3+nvpDi0HJ2DRIt8SsXmz7xlVXd16V2Z++dixfr3ly303KBEREZFU8tH5427gvdF/xwcP\nYXdDTyQ8d1YeyiQdTH29r1wvy7DNrKzMb3fwYH7K1W7aeAIi+w9m1TNq40bfMyoSSb6+iIiISE67\nNpnZSfisRvEtD6mqU2OTwcW2mQj8JJflko6nosIPBm5szGy7xka/Xffu+SlXu2njCVj/TndWroQd\nO6BnT9i1y499qKkJb+DoVF3DRDo7pWETkSKQ6zESl+ADB0dzAPEY8AtgQcg2/4z7txEwMFu6niFD\nfJeb1at9P/50evc456dVGDnSb9OhZXkCIu9u5Z2eI/nh/w5m1atw6JDfhZm/z6ishP79YcAAH6fE\nS+wapkBCpAgpDZuIFJFcBxJnRv/GgonfOuc+DmBmYYHE5oT/d/RbQMmB0aP99XDtWj8YuLo69TZ1\ndf5aOniw375Dy+IENGyrY9vWUp7fP5jfHxrNvn3+PqKkxFde1tX5loldu2D7dhg1qnWXp7Iyn0m2\nw3cNE+mMlIZNRIpMrgOJQbRsjZiXxjZ7E/7fM6clkg6ppMRXqq1Z4x/pTKOwZo2fRmHy5E7Qsp94\nAsaMgb17/Y1ErPYxrq9S04EGdvx1Desiw3iycTJH9y/hYINvZejRw++ystKfp927/S4ATjqpZctE\np+kalkjdQKSj6/IzdIpIMcp1IJFYbbomjW16Jfy/NHAt6XKmTfOVagcO+L9B103nmq+b/fvD+PF+\nu05h2jR48UXffeGxx/zNgHP+Ed9XqaqKvZt2sykygBUl4zk4cRr998OWLf7cVFb63cU2qanxYye2\nboVNm2DQIP98p+oaFqNuINJZJKZhC6pZiU/DtnJlcxq2TjFDp4gUo1wHEnvxM1fH9APWp9hmYML/\nd+W0RNJhVVT4lnnw18P165tb8svKfO351q3+nnDYMB9EXHVVJ7ofbGjwL/jAAf/vPXv8C4+9wF27\nYPNmXHk5B0rfw/LyCfzttKs44ogKarr7AGLXLr9p/D1HaakfgL1nj78nOfZYf//RqbqGgbqBSOfR\n5WfoFJFiletAYhstA4mzgR+l2Oa8hP9vyWmJpEOrqvIt84mVyg0N/qY3Vnve6SqVY90Y/vY36NYN\n3vc+3ydp3z7/nHOHB0A07qtnX+RImiihsqacJnxg0L9/85iIo45qeR9RXu53sXevb52oqupkXcPU\nDUQ6ky4/Q6eIFKtcBxIvASNoHifxTTN72jn3ctDKZjYEmB23vgP+luMySQdXUeFb5qdPb76eHjzo\n+/HHas87/I1vovhuDCef3Hznv2OHv/tvbPStE5WVvL2jEvfiKkY3raLx7UX8fZDvxjBggB9U3dTk\n//bq1VyRaebPX309vPMOvPFGJ+sapm4gkmMFHWaTixk6FUiISB7kOpBYDFwU/bcD+gJ/NbP/C1j3\nduCT+HEV8fNOPJnjMkknUVLir4Wd/noY1o3BzDctHHVUi9Ub6+CtI0bwnoPrGbF5Gf84djrOSigt\n9Q0Z4LuA7d7tY5EjjvC7qq/3AVl5ub+X7jRdw9QNRBK0JQgoimE2sQkqU32WEykNm4jkWa4DiQXA\nbTRnXnJAd+CC6P8t7u9/0twKEbMdeCjHZRLpWDLsxlBaCvu79cYONFGzdwMDdrzCW0f5aKtbN5+Z\nadMmXzm/d6+/J4lEfFBRWemDiFmzOlHXMHUDkaiMgoBuraONfX2H8P0nR7N8RUlhh9l0+Rk6RaRY\n5TSQcM7tNbNbgP+iOUCITwcbLz6IiP37RudcQy7LJNLhZNiNoaoKyrsb23b3pap+JzV7NhwOJMDf\nR7+fh/YAACAASURBVAwa5AdVx3pGHTrkDzNiBHz96773VKehbiBC+mPt179Wz55fL+L8o5ZRsbk5\n2miyUmrfqWb4vsFsZjIVY6dReVRFYYbZdPkZOkWkWOW6RQLn3HfMbBJwLsmDCZfw/0edcz/MdXlE\nOpwMuzHU1EBVJRzaWkakoYFuTcHdGOJ7Ru3c6bs6jR3bCe+Z1Q2ky0t3rP3BrXs49fn5DIgsZ3vp\nRo7p10RJPx9t7NjcSPeNqxnVsJZhfdfw1psrebLn1dSXNzc5tNswmy4/Q6eIFKt8dQS+APgpPniI\n/XS7hAdxz/8U+HieyiLSsWTYjSGWoalHRSN7DpRywCXvxhCbvG/QoE6SoSmRuoF0eYlj7aurW1fi\nd4vU89FN85lc8jRH7V7Heoby1tHjYcgQ3ICBrIsMYVXZeHYdNZR++9Zx3DtPc+Y/5lPWVN/qeLFh\nNhs3+m5UkUiOX1BsgspBg/yXtyFFw32n/5KLSLHIy6+Lc67ROfc54HTgYfzcEJbw2B197nTn3Oec\nc035KItIhxPrxrB1q++ekIYB73H0L9vKoR7VPLtpMDt3tt7UOd8SsXJlJ8vQlCiL83e4G0is47x0\nWOmOtT9h0yIGbV1O9cHNbD56LFsaqtn8jh1OjrZnLzgzGiurebNmLL32b2bQ1uWcsGlR4P4Sh9nk\n3LRpMG6c//KuXEnX/pKLSLHIedemeM6554GPm1kJMAifxQlgK7DROZfrehuRji+Lbgyle+roe0wp\n66oG03TUaDZ0tcn74qkbSJeWzlh7cxFGbF5Gzd6NbOk5grKKctweHzzs2OHHVzTUNzdONZWW827P\nEfTZ0zIzWot95nuYTVecobOgOXdFJB15DSRiogFDbfQhIsnEujGsWeMfYfMgxES7MZQOG8apn5zM\n5d1KutbkfYmyPH+dZza+ri2dsfYDdrxCzd4NmItwoNxHG92P8MHDnr3+/jzioDTuo7C/vDfmWmdG\ni5f3YTZdZYbOosi5K+1BsWLH1y6BhIhkaNo03z3hwAH/N2i0qHPNKWOi3Ri6TZ/GjIouNnlfkCzP\nn7qBdHzpjLU/ak8tPep3srd7c7RRYtAUgaboUJkS88HEYWbs7d6XHgGZ0WLaZZhNZ5+hM910W3nP\nuSv5pFix88hrIGFmNcAngMnAe4HYTFrbgVeBZcAvnXM78lkOkQ6njd0YuszkfWG6YjcQAdIba1/W\nVI+5JhpLmqONiPPBQ2mZz4JWXgG76vy/Y5pKyiiLBGdGa/dsq53xS55uuq12ybkr+aJYsXPJSyBh\nZt2AG4Fr8BPSQcv0r32BkcBHgG+b2R3AXOfcoXyUR6StCtL82lW6MeSLzl+XlM6UC42lFTgrpTTS\nHG0cPAC9evvAIZZSefcuqG+Aimi8URppxFkph0pbNzlomE0OJKbbCmpWarecu5IPihU7n5wHEmbW\nE/gzMIGWwUNi+pTYc0cA1wNnmtmHnHN7cl0mkWwVvPm1s3djyDedvy4nnbH226uGsK+imqPrVrO9\ncjD1hwyz5iAillJ51y7/6HMUlJij8uBWtvQeyY6qlk0OGmaTA+mm24qJ5dxdv95vN316Xk+8+vLn\nhmLFzicfLRIPA6dF/50s92KL3qf4wONh4MN5KJNIxoqq+bWkhMjoMbzCGH8hOwgVtTAEXcjS0hm7\ngUigdMbab6oZzY7KwfTbtZbuB+t4d281Pat88BCrGR0wALZvh8Ym2LYd3nNEHRErZUflYDbV+CYH\nDbPJoXTSbSVKzLmbh+93wSuTOpEijxVblFNBY/pyGkiY2YXAWSQPIILEZr4+y8wucM79NpflEslU\nMTW/6kImkplUY+2dlfD6MZOp3raGnu+uoWfNWPr2LWfAgOZ9lJbCqPf5f+/Y0sBRW9ewrnwYT5dM\n5s1NJRpmk2vppNtKlOecu0VVmdQJFGmseJiutdnJdYvEJ+P+bTQHCACH8IOswQ+67hb9d2LQMRNQ\nICEFVSzNr7qQiWQunbH2K7dMo5SVvL/nAU6KrKRm4AhKS3oT3yO3vMxx0rF17N2+hs39+7O1cjyr\n+kzTMJt8SCfdVpA85dwtpsqkzqIIY8XDdK3NXq4DiVNo3WXpj8C3geedc40AZlYGvB/4CnB2dJtY\n0DEux2USyUixNL/qQiaSvVRj7YedWMGWY66mcgf03bWc0jfXQ23rzF6lpaX0GjuMqnHjOTT1Kj67\nrULDbPIhnXRbQfKUc7dYKpM6kyKLFVuUS9fa7OU6kIild421RvyPc+7SxJWiAcXTwDlmtgD4d5oD\nkDSmoRXJn2JpftWFTKRtUo+1r6LkUHqZvUqmTWN0RQVKyJQn6aTbSpSnnLvFUpnU2RRZrHiYrrVt\nk+tA4l0grpcpt6Sxzc34QCJme9iKIu2hGJpfdSETyZ2kY+2V2as4pJNuK1Gecu4WS2VSZ1NEseJh\nuta2Xa4DiRXAwLj/r0tjm/h1HPByTkskkqFiaH7VhUyknSmzV2Glk24rXh5z7hZDZVJWijzdUBHF\niofpWtt2uQ4kfgGcG/f/Y4E1KbYZmPD//8lpiUQyVAzNrx32QiYikq1U6bagXXLuFkNlUkY6SLqh\nIooVD9O1tu1yGkg45x42s78AH4wuuga4KsVmX4j+NeAFfDAiUjDF0Pza4S5kIiJtlU66rXbIuVsM\nlUlp62DphookVjxM19q2y8eEdP+Oz9R0GjA7mqHpFufcm/ErmdlA4GvA5/BdmtYAH3XOZToHhUhO\nFUPza4e6kImI5EqqdFvtkHO3GCqT0tIB0w0VSazYojy61rZNVoGEmT2ZYpVYA5QBnwU+a2YbgLej\ny98DDI5bxwENwC/NzDnnNDeoFEwxNL92mAuZiEiuFXgAfDFUJqWlg6YbKoJY8TBda9su2xaJqaQ3\ne3X8hHRDaBk8JK4ziuagQqSgCt382mEuZCIi+VKgAfDFUJmUUgdPN1QsydJ0rW27tnZtShW7JQYG\nsfWDlokUjUI3v3aIC5mISCdV6MqklDpJuqFCJ0vTtbbt2hpIZNp6ELS+WiCkKBW6+bXoL2QiIp1U\noSuTUlK6oZzRtbZt8jHYWqTTKGTza9FfyEREOrFCVyYl1ZZ0Q/X18Npr/u64COebaG+61raNZZMk\nycxqyWNLgnNuaL72XYzMrMW5VOIqiZezFOFFPlmRiEixiv18Fs3E5wsXwl13+WBgyJD0tmlqgpde\n8lXrAwfCkUcW5XwThdJBpuPItTYPL8gqkJDcUiAh6cj6QtZFfx1FRDqtVavg1lt9uqHx41N3b2po\ngL//3ffNKSmBo4+GQYNaV7kPGgTjxhV8volCKrqgMb8USHQGCiQkb8ImK9LFQ0Sk44pE4Ktf9ZVE\nQ4cmTzfU1AQvvwxvvgm7dvnf+0mTWt4VJw4C+Jd/Keh8E9Ju2hxIaIyESGfVAScrEhGRNGSSbmjT\nJtiyxQcRffv6wCOxar0I55uQjqHzNdKIiJc4WVF1devm7/iLx+bNzRcPEREpbtOm+Zbk/v39zf/O\nnb5lIV4k4kcPb90KvXr5Lk0DBoTvMzbfxMaNvjtsJJLf1yAdnlokRDqjDj5ZkYiIpJBOuqENG+Dd\nd/1v/MCB8L73+e6syRThfBNSvPJ2p2BmR5vZN8xskZm9ZWb7zKwpjUdjvsok0mXkYrIiEREpbrEc\ntbNm+RaKkSN9S3NDQ/O8Eb17+7ylY8ZAt26p95k434RIEnlpkTCz2cDtQKyjtWavFmlPmqxIRKRr\nSDbh0WuvweOP+3VStUTEKyvzwcjBg/krt3QKOQ8kzGwm8MOExemmIVLAIZILbZmsSBePzGh+DpGk\n9BVpJyUlvgIovhLIOXjySd/NKRONjT7w6N49t2WUTiengYSZVQLfi/43KHiwhOWWZF3pQnShybFY\n7ZMuHvmj+TlEktJXpAgMGeJP9urV/oSn00LtnB+cHZu6WySJXLdIXAj0IjhYSPy/iz4sYB3pInSh\nyRNdPPIrbH6O8nIfjK1eDWvX+rSMK1dqfg7pcuK/Im9uiDB07yu8/4haKqyeelfBP2uH8OSa0axZ\nU6KvSD6NHu1/z9eu9am+k803EVNX5y/CsVnYRJLIdSAxLe7fBjQB/wucH13mgF8ARwEfAKqjy5qA\nh4CGHJdHipjuxfJIF4/80fwcIknFviJ/XVrP4LWLuKzbMt5zaAM99u3EXBPOStlXXs3bewfz/9m7\n9/i4zvre959nRpqRbcm62LLj2JZ8iePQxIlTG0qaxBC0yXbDKb1CX6ebUvoy9FBIgJJD201bSuhu\noLsNhXq3FNq0cPZuXy09tAROsyHUsGuSkE2jIscNxJYvkhxHsWXdZUkz0sxz/nhmotF4RprLmtua\n7/v10musuaxZ0shrrd/ze57f71jfIZ6Z6QHC+i9SCvn0mwA3tbW/3y3OPnRIUwJkVV4HErexlGWw\nwB9aa/+zMeaVQsTW2ncAGGOagIeADwFBoBv4CWvtqMf7JFVI12IlppNH6aT358j0e1VzJ6ljx47B\n889M88aTR7mjsZeNU0MYG2OmqZPFQIhgfJHNk6fYZM6wbW0/3znZxzPhBzh2rEX/RUqhp8cdh+bm\n3G2mE256Z+uDB93rRFbhdSCxOe37f8j2RGvtPPDrxphW4JeBO4C/Bd7o8T5JFdK1WBno5OE99ecQ\nWVE8Dk99M8KP/ttR7rBPsvHqMJfW72EutPzYM9rczZroBJun+rmzcY7Av8FT33yQw4fD+i/itVz6\nTYyMuIz0rl3uPHD//Rq1k5x4HUisT/v+bA6veQQXSBjgDcaYn7fW/o3H+yVVRNdiZaKTh/e86M+h\nsrriYydPwvp/PcZNV3vZGBzmQsd+YsHMI0Vz4XYudOxn+1gfN831MvOvxzh58j79FymFZL+J9EWJ\n0ag7ByTXxmlRouTJ60AifUXndOI2CoTANaqz1l5Kec5LidvkAu23AQokfEzXYmWkk4e31J9DZEUD\n5+LsuHCcbfEhLrXvyRxEpIgFQ1xev4dto+e5cuE4g+cPc9ttGikqiZX6TSTXxmmUTvLkdSAxB6Qu\nh03+RV4lEUjgpjB9OeU5P5TybwPc4vE+SZXJdi1mbJytYyfZMD1AQyzCYjDMaMsOLnbsAxPQtVih\ndPLwjvpziKyoqf8kLbODBIm76Uw5mA210UaMztlBFk6fxC23lJLJ1G9CpEBeBxJXWB5IrAUiwMtA\nGy5Q+Lgx5oS19rwxZjNLfSeSNnm8T1Jl0q/FGmIRbrp4jD3Dx+mYGWRdJKWyR7idseZu+rcc4mXT\nw2wsrGuxQunkUTz15xBZUdvEAMHFcSYa88vaTTR2sn5xnNjkIAokRGqH14HEBWBXyvdbgHHgFPAq\n3PSlvcAZY8wVXBnY9CZ1Mx7vE8aYbcDHgMOJ9xzGZUUestaO57mtHuB+XGalHRgFTgKfttY+7uV+\n+1XqtVg4Os0bnj9K10gvHTMZKntMnGLT5Bk2TfbT3NDHV7ofoKlJNWBXpQ5/paH+HCIr2twWYboh\nxsRsflm7uWgDbWujtLRqpEiklngdSDwHvC7l+xuA7wPHWeolAS546Ez5PrVk7Akvd8gYsxt4Gpfp\neAx4AXgN8H7gsDHmzlxLzhpj/iuuXO2LwFdwGZhO4ADwekCBRA6S12LnfhDhnrGj7L70JK2zq1f2\n2LMwx8+tgR1bHgQ0lz8jdfgrLfXnEFlR154w/WuDNMwuMhOFcA7xRCQKzSwSWhuk60Zl7URqideB\nRG/iNplhuBt3wf0l4PcT72czvC7VX3u8T3+KCyLeZ609mrzTGPNJ4FeB3wPevdpGjDHvwgURXwB+\n2VobTXu80cud9rPktdimZ49x/VwvrfOrV/Y407Kf6y/10Rrp5eZLxwDVgL2GOvyVnvpziKwosGsH\nLdvbaRg7xcWJbjZuNCv+2cfjMDlh2RUYYc32vQR2KmsnUku8PqslAwmT+HodgLX2AvAnXFvVKd0z\nuAt1TySyEfcCA4n3T/U7uEXgv2CMWbfKdsK4gGOIDEEEgLV2wYt9rgeBABy6K87rA8dpHhvi5eaV\nK3vE4zA2HWK0fQ/b40MEnjzu7pQlqR3+zp2DnTtdOdcdO2DbNnd78KC7/9w597yjR93rJD89PXDg\ngOu70dfnsj42bXzEWnd/X5/6c0h92bePTa/pZs26IJ2hCa6MuoxDJpEoXBmFTaEJ1jQH2fQaZe1E\nao3XGYnv49YOJKWuSPwQsBFX3jWT/wW8xVob83B/7kncPmGtXXblaa2dNsY8hQs0XgscW2E7b8RN\nYfoUEDfGvAlXXWoe+K619jse7nNd+A+bT9IfHiTUGOcH0220BjOnwCNRmJyEtWth7eY21i+qBmxG\n6vBXPurPIZJdIEDDPYfoPNVP4Nl+FtftZ3IqxJSFpjUQMBC3MD+XOCSti3LjQj8bfngXDfcoaydS\nazwNJKy1FvjfWR6LAW83xnwG+Bnc+okwLlvw1RItVN6buD2d5fF+XCBxIysHEq9O3M4D3yOtRK0x\n5jjws9bakdV2yBjTu9pz6kHopQFu3DTOhbmNrF80TE+R9USzvsVdo918iyFwUTVgr6EOf+Wn/hwi\n2fX00NjXR2d0joP9fQxu2MPlhTaiUUMs7o7xra2WTY0TdC/00/yqLQTvUNZOpBZ5nZFYVWL0vlwj\n+K2J28ksjyfvX63YdbIk7YdwWZe7gT5gJ/CHuGDk73ELriUXkQiNJkb3DSEacAPp0zMQjbB0ommD\nlmY3M2TrVnd9pnr8GajDX2WoP4dIZomsXRBoXdfLvsHzzF2NMbO+k0UaaGCR5vkR1jQHMV3K2onU\nsrIHEjUqeTWwCLzZWjuQ+P6kMeancOVtX2eMuWO1aU7W2gPp9xljVluA7j+JGrDB+CJdO2D7dhgb\nc8FEbBGCDS6I6OhIq7CpevzXUrflylJ/DpFrpWTtzPHjrB0cZO34OMQSWbt2Ze0ElSr3gYoHEsaY\nAK6MapK11m7waPPJjENrlseT90+ssp3k499LCSIAsNbOGmO+DhzBlZXVeolcpNXjN8awYQNsWOmT\nVz3+zNRtWUSqkbJ2ko1KlftGxQMJXCWnNpb3kvDKqcTtjVke35O4zbaGIn072QKOZFO7NTnul6ge\nv3fUbdk/NDonfqSsnaRSqXJfqYZAopS+lbi91xgTSK3cZIxpAe4EZnFlZ1dyDBfg/FD6dhKSi6/P\ne7DP9cHDevx1f+2lbsu1T6NzIlIPUkuVDw+7wh9tyxvR0t3tBg77+2Fuzt334IM69lUpXwcS1tqz\nxpgncIuh3wscTXn4IWAd8Flr7VV4pancbmDBWns2ZTuDxpivAm/GdcT+o+Rjxph7gf+Iy1Z8rbQ/\nkc/09LjRhrk5d5vpgGLt0gElrR6/rr0SlN2pqKIDWY3OiUi9UKly3/F1IJHwHuBp4I+NMT3AD4Af\nwfWYOA38ZspztyYeHwR2pG3nvcDtwCcTfSS+h6va9JNADHintTZbdSjJpIh6/Lr2SqFuyxXhSSCr\n0TkRqRcqVe5Lvg8kElmJg8DHgMPAfcAw8GngIWvt+EqvT9nOi8aYA8BHcJmJQ8AU8FXg49ba75Zi\n/32vgHr8uvbKoMjsjuTHs0BWo3MiUi9UqtyXfB9IAFhrLwC/lMPzBnALvrM9PgI8kPgSr+RZ2UPX\nXhmo23LZeBbIanROROqJSpX7Ul0EElIjcqjsoWuvFajbcll4FshqdE5E6olKlfuSAgmpKbr2WoXq\ntpeUZ4FsPA7f+pabA5X842xpydCBMY1G56Ta1H3ZPMmZSpX7kgIJqSnKjOZIddtLothA9t97I9w6\nksgYffvb7k5jXFv3cBiam936la1b3YkzE43OSTVQ2TzJl0qV+1LBgYQx5u0e7YOGLCRnyoxKJRUT\nyM6PTNP4x0dhNrFCe2zMPWjM0kL4yUn3NToKN9+c+Q9do3NSaSqbJ4VQqXJfKiYj8Xm87UItsipl\nRqWSCg1km0yEHx84Stvok0BihXZXF5w44U6ULS0uGxGNwtSUexOAW29dnpnQ6FxhNP3GOyqbJ4VS\nqXJf8mJqU47jciLFU2ZUKqnQQHbf5WPcON3LGjsMhxInT2td8DA56U6YoZB7g44Ol60YGYGLF13A\nkaTRufxo+o33VDZPiqFS5b7jRSDhRVZCwYjkRJlRqaRCAlnicXZfPM6WhSHYnbJC2xh3kkxOZ9qw\nwY24BYOwfr2bPjI8DNu3u+dqdC4/mn7jvXoum6esljdUqtx3qmWxtaZISU6UGZVKKiSQXT94kusX\nBgmH4rR2p63Q3rrVrYeIxdxta6v7g05mLGZm3P3BoEbn8qHpN6VRj2XzlNXynkqV+0qxgYQyCVJ2\nyoxKpRQSyC6eGWBT4zjh6zdiAmmHzGAQbrnF/XtkxK2PsBbWrHH3TUy4P/KODo3O5UPTb0qj3srm\n1VlWq6xJF5Uq941iAokveLYXInlQZlQqKd9A9q2tEdoCMTo2Z4k4GhvdouqLF92F78yMO4snN3Td\ndXD33Rqdy1U9T78ptXoqm1dHWa2KJl1UqrzmFRxIWGt/ycsdEcmHMqNSKfkGsnvWhtk2HCQYX2GF\ndjDoFlVv3+4WWs/MuIuXYBDe+lb3hrq4zU09Tr8pl3oqm1cnWa06S7pICVTLGgmRvCkzKpWSTyD7\nHzp30PjJHFdoG+MWXXd0wOXLbkOvf73+kPNRb9NvyqleyubVSVarjpIuUkIKJKTmKTMqlZBzIBtX\nqbGyKnD6jQ02MDMW5YVvz3N+XkV5MqqXsnl1ktWqk6SLlJgCCRGRIqwayKrUWHnlOf0mFnPLU+Zf\nWGRuPsg/RZt4qk9FeTKql7/lOshq1UnSRcpAfwYiIqXW0wMHDrgSYn197mLDplW9ttbd39enUmPF\nSE6/GRm59necJroAzz0HL/zAEr80wvB8O5eaul+pvnvqlBt9ffRReOQRN5+87tXD33Iyq9WQ51hr\nQ4N7XQ0sKvci6SICykiIiJSeSo2VT47Tb2IxeP7fYfhlCE5N0NAUxHZ1Y2/Zx7bEILTmh2dQqr/l\namr4VgeLyusg6SJlokBCRKQcVGqsPHKcfnPxorvejc5EuT3Yz+j6XZzZcghrli5aNT88Cy//lqux\n4VsdLCqvp0q+UloKJEREykWlxspjlWYf1sLwSxYzMcGt9DPVvIXBzoO8sDXz9BvND8+gyL/leBye\nf2aa4J8epaW/l+bRIcKNMdZs78RUuvZoHSwqLzbpEgrBiRPVkUCSylIgISJSbio1VlqrTL+ZHluk\n88IIzdEgE5t2Mdh5kG/dfD+Lwewj3jVYlKc88vxbTiYgnvpmhH1PHGXX8JM0zg9zbt0eFta10XLZ\nsGULbN0OwUrNLauDReWFJl0uX4b16+ErX3EfSTUkkKSyFEiIiIj/rDD9Zm4+yGB4L5dbu7l80yFe\n2NqzYhABmh/uhdTmZ9ueO0bnSC8d8WHOt+4nakLMT8LUFExOwugo3HyLIVSpuWX5trCvsUXlhSRd\nrlxxs7dmZ+HqVZdVUvM6USAhIiL+lGX6Tf+zTfzt8W4uduxj6/bcR481P7xwqc3PXn4pzi8Ej7O7\ncYiRlj2EwyHCQEszRKIukFiMudfdeisEKzG3zOcFEvJNuszNwTPPuOBhcdH9yGpeJ6BAQkRE/C5t\n+s1oGAafAxvLbzM1VJSn6qQ2P/vx7pNc//wgxsaZCy2vPRoOwcYNcGXUXadfvAhdXVRmbpnPCyTk\nk3Tp7XVBRCAAd94Ja9Zcuz0VJ6hPCiRERKSu1EFRnqqS3vzsuskB1kXGmWnKXHs0EIDWVpiegnPn\nXPwQjxtabCdNQ+M0nx8kUK65ZT4ukJBP0qWhwX29+tWZg4hUKk5QXxRIiIhIXamDojxVJb35WcNY\nBGNjLAYyz6WxFhaiMDMDc/MwMekuYjdFGlgTjPLcX83THipzEsCnBRJySbqsWQNnz7r1K52duW1X\nxQnqhwIJERGpK3VQlKeqpDc/WwyGsSZIMH5t7dF4HMbGYX7OXYguxqAp7KY8Bewi07NB/u37TQw8\nqgW9Xlkt6XLuHHz2s+57Na+TdAokRESk7vi8KE9VSW9+Ntqyg6vhdjZPnGK0uXtZf4+xcZibddNq\nGhrcQ+EwrFtr6Zwd4VLnXgI7uzl3Tgt6vZYt6XLqlJrXSXYlCySMMSHg54DXA3uBdmCVmXUAWGvt\n7lLtl4iIiM+L8lSV9OZnFzv2MdbczabJM6yJTjAXdnPLrl51mYjFRfeaZOWmQADWRiewJshYSzfT\nO/axf6sW9JZLsc3rVJzA30oSSBhj/g/gc8Dm1LtzfLn1fo9ERESW83lRnqqRvrgdE6B/yyE2Tfaz\neaqfCx37iQVDzM7CwiI0hsAEIBaBUBjCwSibpvq50rKL/i2HsCagBb1lpOIEshLPAwljzJuAfwSC\nGR5eLUjINdgQEREpmo+L8lSNTIvbX9jaw/bRPhpjc2wf6+NC0x4WFtrAGoIBiMcALB1mgj0z/Uyu\n3cJg50Fe2Lo0t0wLestDxQlkJZ4GEonpTJ/DBRHKLIiISE3waVGeqpBpcTuhMN+82c0t6xrpZePY\nedbPxxg1ndiFBmx0kU1mhEYb5ErLLgY7D/Ktm+9f1oHcqwW98bgLRAYG3HqOcNiNwiuIdFScQFbi\ndUbiJ4AtLA8iMmUZVntcREREfCLz4vYWvnHrg9x08RidPzhOU3SQ9fFxAtEopiHIxbV7iW/r5sz1\nh3hha8+yICKpmAW9kci109piMTeS3t6uaW2pVJxAsvE6kPixlH8n/7z6gP2Jf1vg28AG4FVAIHFf\nDHgaZTFERER8J/vi9jADDfcx3HaYppGTbDeDdLbOE25tovnmbi5t2oc12Ye0C13QOz0NR4+6fRka\nWlpoHwq5bZ465aby9PfXUZnZFVIz4XBAxQkkI2Otd9fuxphe4PbEtxb4C2vt/2WMiSfvs9YGE8+9\nHvgk8NbEc78EvN1aW3eFwowxyz4ELz8TERGRapEtC3D1Kly86DILt98O27a5i9KVWAvPPusWYs7w\nCwAAIABJREFU9P7Gb+Q+tSkSgUcegSefhOHh3EbX77rLx2Vm80jNRAgri+MvRc8K8jqQuARsxO2Y\nBQ5Za5/KFEikvOZLwE8lnv931tqf92yHaoQCCRERqSfJwe/k4vZQCL7yFXjuOTeincuC3vFxNzLe\n0wMPP5z7XPzHH4dHH3WN1nKZ79/X5/bpyBEflpnNlppJTzN0dcGBA6+kZtI/PxUnqFlFBxJeT21K\nT/ydzuE1D+ECCQP8nDHmb6y1/5/H+yUiIiJVItPi9lAIJidLu6A3Hnej6UNDLhOxWpM1X5eZjURc\nELFSaqa7eyk1k9IBMBAOqziBAG6Ngpca076fTNwuJO8wxmxMe86ZxG1yGP4dHu+TiIiIVLmeHjfo\nvWWLywKMj7spRqmsdff39RW2oDc5ih6Pu2vmXKSXmfWNY8dcJmJ42EVu7e3XNokwxt2/f797XrID\noEiC1xmJOWBdhvuvAsn/svuBf055bGfKvw1wwON9EhERKY5qhJZcObqNDwy4QGTjxtwaq4F3ZWar\nilIz4hGvA4lRlgcSa4AocAVoTdz3u8aY71prp4wxYeDhtG1sRkSKo4seEW/UeY3Qch9KSt1tPBJx\nH99q183piikzW5W8SM34IqKSYnkdSFwEUpuhb8ZNbzoF3ICbvvQa4IIx5gVgF9DB8rKvEY/3SaR+\n1PlFj4in6rhGaCUPJaXsNh4Ou59hcTG/1xVaZrZqKTUjHvE6kDgJ/GjK97twC66fBt6UuM/gFmW/\nOuV5lqVKT9/3eJ9E6kMdX/SIeK6Ihai1HqRXy6GkFN3Gd+xwgdCpU+7jy+Ua2lo3pSqZDfEFpWbE\nI14HEr2J22SG4S7ga7geEf8l7TFD5gZ0/6/H+yTif3V80SM50nS3/KQvRM10wZW6ELWvb2khag3X\nCPX7oWTfPrf/Z864nyGXMrMTEy4bkcyG+IJSM+KRUgUSyUPOIQBr7WljzF8Db2MpeMgURJwC/szj\nfRLxvzq96JEcaLpb/up4IarfDyWBgPtz7+8vbZnZqqfUjHikFFOb/s+U71PXO7wb6CIRXCQkpzSB\nCyLeZK2d83ifRPytji96ZBXVMkel1tTpQtR6OZT09Lg/97k5d5tLZ+t8y8xWPaVmxCOeBhLW2kXg\n77I8NmuMuQcXaPw0bvF1GBgAvgo8aq3VQmuRfNXpRY+swu9zVEqpThei1suhpBxlZqueUjPiEa8z\nEiuy1lrgbxJfIuKFOr3okVX4fY5KKdXpQtR6OpSUusxsTVBqRjxQ1kBCREqgTi96ZAUZ5qhYC2Nj\nbrZTcolESwt0dICp1TkqpVKnC1Hr7VBSyjKzNUGpGfGAp4GEMSaW8q0FQtba+CqvMcBDqfdZaz/i\n5X6J+FqdXvTIClLmqMRa2rg45BIT0zMQjUDcQsBAKAwtzW6gcev1bQRrbY5KqVRwIWoli2vV66Gk\nFGVma4ZSM1IkrzMSOSZDlwkAv8XyKk4KJERypeobki4xR2WhbSP/ftIwMgIzM+5jb1oDwYALJiYn\nYGoSJidhdNRwS3snjbU2R6UUKrAQtRqKa+lQUqfqPjUjxSjF1KbUSkz5ytZbQkSyUfUNSReJEFuI\nMfhiiOE5mJ2F1lYIp01ZaWmGSNQFEosxaJlsYOe2KMFam6PitTIvRK2W4lo6lNS5uk7NSKGqYY1E\nNeyDSO1S9Q1JFw4zNhFkemKR2Rhs3JD9Yw6H3ONXRmF6fpGx5iCdtTpHxUtlWohaTcW1dCgRkXxV\nw0X8jkrvgEjNU/UNSRHv2sHF2XbWTJ+i9bpuAoGVk8SBALSut6x5eYSLs3vZsL2bur8mLNNC1Gor\nrqVDiYjko+BAwhjTxepBwCFjzEqLrTcCD6TdF8v0RBFZgapvSIqT7GPQdHODOUMbE8yx+hyVdiaI\nmSCDphvDPjS5gZIvRK3GBnA6lIhIPorJSPwSmRdFm5TbYzluK3VdxGQR+yRSv1R9QxIGhgI8u+YQ\nG5r76Zrq50LHfmLB7FepwViUTVP9DDXv4tk1hzAXAtx2exl3uJqVcCFqtTaA06FERHJV7NSm1RZV\n57roOrlA2wIvFLVHIvVM1TcEN+++t62HG2b6aJ2bY/tYH5fX72E2dO0clbXRCTZN9TO5dgtn1hyk\nt62HfXW+1jqjEixEreYGcDqUiEguvFgjkZpNSD8UFlKB6Z+K2BcRAVXfqHPhMMQbw/zjtgdonYau\nkV42Tp/H2BgzTZ3EAg0E44s0z49gTZArLbsY7DzIl1vuJ94Yrtl+ALWmFhrA6VAiIiuphsXWqQaB\nP630Tojko5INpEQyWeoH0MITtz/Iq146xp7h43TMDLIuMk5DPIo1QS617WWsuZv+LYf4wfU9DH0v\nrH4AZVSvDeBExD+8CCRWSsjmOrVpEfgK8AFr7VTxuyRSetXQQEokk9R+AFemw/x71308v/0wW8dO\n0jE9SGNsnoVgE2Mt3Vzs2Ic1AcbH1Q+g3NQATkRqXTGBxJeBgZTvDfCXLF/v8E4gW9UmC8wCl4AT\nCiCkllRLAymRTDL3Awjw4obbeHHDtXNU1A+gMtQATkRqXcGBhLX2BHAi9T5jzF+mPe0L1tqVyr+W\nhTFmG/Ax4DCwARjGBUIPWWvHC9zm24D/nvj2Xdbav/BiX6X6VVMDKZFs1A+g+qkBnIjUulKskch1\nOlNZGGN2A08Dm4DHcFWhXgO8HzhsjLnTWjua5za3A/8NmAGavd1jqXbV1kBKJBP1A6gNCvhEpJZ5\nHUjsTP2mGrIRuMXbm4D3WWuPJu80xnwS+FXg94B357oxY4wB/goYBf4B+L893VupatXYQEokG/UD\nqH4K+ESklhlrC6nQWhsS2YgzuLUcu1MDG2NMC26KkwE2WWuv5rjN9wN/BLweeAPwOxQ5tckYs+xD\n8PNnUutOnIBPfAJOn4YDB3JfHPnss+6i7Td+Q2UUpTKS1cXUD6A6qXiDiFRA0bOIqq38q9fuSdw+\nkZ4dsdZOG2OeAu4FXksOXbiNMa8CPgF82lp73Bjzhnx3yBjTm+9rpHpUcwMpkZWoH0B1UwM4EalF\nJQskjDGbgV/GjdzvBdqBXKpeW2utV/u1N3F7Osvj/bhA4kZWCSSMMQ24xdVDwIc92j+pMbXQQEpE\napcCPimUehpJJZQkkDDG/ArwCJBMwFZqAXZr4nYyy+PJ+9ty2NZHgNuBu6y1c4XukLX2QPp96VOb\npHqpgZSIiFQTTYuTSvI8kDDGvAP4k7S7c71QrqqKT0nGmB/BZSEesdZ+p9L741e1MJqiBlIiIlIt\n1NNIKs3TQMIY04xbiAyZgweTdr9Z4bleSGYcWrM8nrx/ItsGElOa/h/c9Kjf9m7XJKmWRlPUQEpq\nIuIVkarl1SFEPY2kGnidkXgL7uI8U7CQ/r1lqQt2qTIRpxK3N2Z5fE/iNtsaCnB9IpKvnzeZh6D/\n3Bjz57hF2B/Iey/rWK2NpqiBVB2rpYhXRKqO14cQ9TSSauB1IJHaIscAMeCrwE8m7rO4BcsbgB/F\nLcC2ief9PRD1eH++lbi91xgTyFD+9U5gFnhmhW1EgEezPPbDuHUTT+KCFk17ykOtjqaogVQdqrWI\nV0SqiteHEPU0kmrhdSBxG0tZBgv8obX2PxtjXrmAt9a+A8AY0wQ8BHwICALdwE/k22V6Jdbas8aY\nJ3CVmd4LHE15+CFgHfDZZA8JY0wjsBtYsNaeTWxjDnhnpu0bYz6KCyS+UEwfiXpVq6MpaiBVZ2o1\n4hWRqlCKQ0iyRHA87raVi7Y2d64aHHSvV2Uw8YLX8ejmtO//IdsTrbXz1tpfBz6HCzzuAP7W4/0B\neA9wGfhjY8yXjTEfN8Z8E9fV+jTwmynP3Qr8gBx6SkhxCh1NGRpyr4tXuGd6smPwkSMu07B3rzsp\nRKPudu9ed/+RI/DBD2pwuqalR7zt7deusk+NeIeHlyJeEal7pTiEeNHTSMQLXmck1qd9fzaH1zyC\n6zdhgDcYY37eWvs3Xu1QIitxEPgYcBi4D9fR+tPAQ9baca/eS3Lnh9EUNZCqA5o/ICJFKNUhpOI9\njVR0QhK8DiTS4+LpxG0UCIFrVGetvZTynJcSt8kF2m8DPAskAKy1F4BfyuF5A+Sx8Nta+1Hgo4Xu\nVz3zU4doNZDyMT9EvCJSMaU6hFSsp5GKTkgar8PG9EZtye1fTbnvjrTn/FDKvw1wi8f7JFUoOZrS\nkGco29DgXqcO0VIWmj8gIkUo1SEk2dNoZMQV98hFsqdR8no/b9PT8Mgj8OijLpg4dcptNBRyt6dO\nufsffdQ9b3p69W1KzfM6I3EFSJ0NvhZX9ehlXPdoA3zcGHPCWnveGLOZpb4TSZs83iepQuoQLTWh\n4vMHRKSWleoQUvaeRio6IVl4nZG4wPKpQVsSt6dYquS0FzhjjLkEXMRlKFLj6RmP90mqUEVGU0Ty\npYhXRIpQqkNIsqdRV5e7bo+uUjw/2dOoq6vAnkYqOiFZeB1IPJf2/Q2J2+Np9xugM/H+JuU+C5zw\neJ+kCiVHU4JBN4CRC3WIlrJTxCsiRch0CDE2zrbRE9w28BgHzn6R2wYeY9voCUyi1VWuh5CeHjhw\nwPUq6utzU6HSD1PWuvv7+oroaVTrZRalpLye2tSbuE3+Kd8NfAX4EvD7ifdb7Wz81x7vk1QhX3WI\nVvUK/yr7/AER8ZPUQ8jMaIQ7Zo+xZ/g4HTODrIuMY2wMa4JcDbcz1txN/5ZDfGdtD8FgeNVDSNl6\nGqnohKygVIFEMsvwOnBVk4wxfwJ8gJUDiWeAL3i8T1Klar5DtKpX+J+vIl4RKbfkIeTC96d57XeO\nckdjLxtnhzA2xkxTJ4uBEMH4IpsnTrFp8gwbx/thoQ9z8AEOHWpZ9RCS7GmUfiqKRt2paO9eD05F\nfiqzKJ7zOpD4PsurMqXOCvwQsBFX3jWT/wW8xVob83ifpErVdIfo6Wm38Ky316VvkzseCrkdP3XK\nDUH197so6YEH1JWuVtV8xCsildRzV4S1nzrKuoUnWTcxzEsb9rC4bvkxZLS5m4arE7SP9PPadXPs\ni8Addz0IrH7CK3lPIxWdkBV4GkhYay3wv7M8FgPeboz5DPAzuPUTYWAA+Kq19nEv90VqQ1lGU7ym\n6hX1paYjXhGptPCTx7izqZfRxmGe79zP5GwIOwdNayBgIG5hfs5gTDtznfu5eaGPDeFeGp885iKE\nHJWsp5GKTsgKvM5IrMpa+x3gO+V+X6leNdchOr16RaZRmtTqFX19S9Ur8jgpSBWpyYhXRCousVC5\ncXiIzh/dw56rIYaHYXoGohGIxV0w0doGLc2wZUuIzrV7CA6t0tq6nJIrxk+dcse5XKY3JVeMJ4+N\n4ltlDyREsqmJDtGFVq84X0UnBSlMzUW8IlJxKQuVgx1tdG2A7dthbMwFE7FFCDa4IKKjI3GNbtvg\nfBUtVFbRCVlBSQMJY8xG3LqINmACGLHWjpbyPUVKStUrpCYiXhGpChkWKhsDGza4r4yqbaGyik7I\nCjz/dI0xh4wxjxpjLgCXgOeBpxK3l40xQ4nHX+f1e4uUnBfVK0REpD4kFyo35Dlu29DgXlctC5XL\n1rRCao1nGQljzA7gz4A3Ju/K8tRtwDuAdxhjvgH8irX2vFf7IVJSql4hIiK58stCZRWdkCw8CSSM\nMa8FvozrVp0MIFbqF5F8zr3AM8aYn7DWPuPFvoiUVOKkYBcWGRt1VWCTrSNaWlLmuKartpOCiIiU\nnp8WKqvohGRQdCBhjNkPfANYl7grNYDI9D/GpjzH4IKPbxhj7rTWPlfs/oh4IVuz6r3X7WBsrh37\nwil+0NxNNGqIW1d1IxROVt2ArVvdcRWo3pOCiIiUlt8WKqvohKQpKpAwxoSBv8MFEanBQfLfq2Ul\nko+vA75ojLnNWhspZp9EirFSs+rmZrhyeR9HznXzwzNniEcmsC3tBAOuDvjkBExNwuQkjI7CzbdA\nqJHqPimIiEjp+HWhsopOSEKxGYn3AXtYHjCkBhTZpGYlkvYktvcHRe6TSEFWalYdjcLTT8PVqwG+\nsniI6xr62Rvs58U1+4kF3UmhpRkiURdILCb6s996U5RgLZwURESkNHp63ALkuTl3m6mJqbVLTUy1\nUFlqSMGBhDHGAO/n2oDAAC/gFl7/CzAETAGtwA7g9cC7cZ2tUzMXBviAMeYPEx2yRcpmtWbVQ0Mu\nozs3B98O9XDQ9rE2Nse20T5GWvcwG3JPDodg4wa4csUye3GCmdF+WvfqpCA+km3en6Y0iGSmhcri\nY6bQa3ZjzF3AcZZnIGLAR4BPrBQMGGMCwEeB30y9O7Gte6y1xwvaqRpljFn2u1IcVX6PPw6PPgrn\nzl2bebYWvvtduHjRrTVrbITIlWneGz/KHaFetsWHMDbGTFMnsUADwfgia66OMBcNEt/Wxc2/eJDA\nA/e7F4vUqpXm/bW3a5GlyGr0f0iqT4517LMrZmrT3Wk7YoGPWms/vtoLrbVx4CMuqcFvsTyrkQxQ\nRMpitWbVY2MwM+MCilDIZSmCbS18avJBBtcd403rj7NhZpB1kXEa4lGsCXKlYy/Pz3Rz+bpD2Df2\ncGuLTgpSw1aa97e46CrSnDnjpmX09bnRVwXOdUEJqjxoobL4UDGBxC1p35+11v5entv4KPDzwM4V\ntitSUqs1q56edifIpqalqU6hEEwS5muB+7i0+zC3mpN0TA/SGJtnIdjEWEs3T025k8KrhuHW8v5I\nIt5Zbd4fuIug5PzuuTl334MPalTVxzS4XgQtVBYfKSaQSF78J7MRn8t3A9bauDHmc8AnWMpKqD6m\nlNVqzapjMZeNSB8oWrPGnUynrwZ4sfs2Xtyw/KQQnFMPOvGBY8dcJmJ4OHvFGWPc1eP+/S4j0dvr\nXnfffeXfXyk5JahEJKmYQKKTpUXSUPh0pH9J+bcBNhWxTyJ5W61ZdTDorpPi8eX3J+/L1rBUPeik\n5q027y9dKOSed/68e93hw5qq4TOeJag0J0rEF4oJJNIngQwUuJ1zad/n0K1FxDuJZtVZA4KWFvec\niQnXSyJ5wrTW/bshw/8i9aATX1ht3l8mbW0uMh8cdK/X9A1fKTpBpTlRIr5STNi/Nu378QK3M7HK\ndkVKascOd/4aGXEBQLqOjqUAIhpdun9uzp3nmpuvfY160IkvrDbvLxNj3DyX8XF3oSi+UWiCamjI\nvS4+OQ2PPOJK5B075uZAJatYWOu+P3bMPf7II24OlYhUtWIyEo1p38cK3E7ahJGim+SJ5GXfPnfB\nf+aMCwDa03Jixrj+QJOTMDXlAotYzN3f3Oy+T1UrjUlFVrXavL9sGhq0QMiHiklQXTwX4dJvHWXL\nWS3aF/GTYi7aG1hetvWQMSY9KMhFcJXvRUoqEHAX/P397itTun7rVhgddSfE5G1bmwswUqc6qTGp\n+Mpq8/6y0QIhXyomQbXj7DHshV6Y16J9ET/xavTfAMc82pZI2fX0uPPW3Jy7TR8sCwbhh37IPT41\n5YKGaBQWFuDFF9WYVPJTM+tMk/P+Tp1yo8W5XD1qgZBvFZqgagzGuXn0OE3BITigRftSgJo5aNYf\nL6cRFd0dT2RFJTyQhMOuRCG4QbDz55dKGjY0LAUKoRDcfLO7r7PTNaqLRl0Akbxu0jpByabm1pmu\nNu8vEy0Q8q1CE1TbJ05yXWSQwFot2pc81dxBs/54GUhkWKaaMwUhkl2ZDiQtLW46bvpbZQoU7rkH\nTp9WY1LJXU3W3s9l3l8qLRDytUITVE0vD9DOOIHNRSzaVyBRf1IOmnZwiLmrMaabOomZEEG7SMvg\nKdb0n8FU1UGz/ngRSBQTQHi5DfGjMl99hcNuOu7hw0sLC7MFClkbkyoFK2lqujn0avP+QAuE6kSh\nCaoNJsLacIyWdi3alxwlDpqx408y0z/MQOMeRhbaiM4Y4hYCBkKhbjrtBDv6+mm+OucW2FbFQbO+\neBFIKJsgpVHBq69AYIVAYaX9VQpWMqjp5tC5zvvTAiHfKzRB9cObwrRFgxgt2pdcHTvGwjO9jD43\nzPON+5mcCrns1hoIBiBuYXLSMGXaubJ2Pzc/18eGUC+NVXHQrC/FBBLHUSZBSqmWrr5qct6KlIMv\nmkPnM+9PgbKvFZKg6rxhBx0vt8MZLdqXHMTjLH7rOCO9Q/TbPYxfDdHaCuG0Y2dLM0SiMD4Z4nTj\nHm7oPc+mbx2noSoOmvWj4EDCWvt6D/dDZLlauvqq6XkrUmq+aQ6dz7w/8a1CElRvfc8+gh/vhvNa\ntC85OHmSy98dZO5qnJFgGxs3Zj+0hEOwcQNcvtLG1liMy98d5PqqOWjWBzV/k+pUS1dftZQ5kbLz\nojl0VZ0TC5r3J36Sf4JKi/Yld/FzA0xfGGcsvpHWDWbVjz8QgNY2w+WRTjoujBM/P0hAx6eyUSAh\n1alWrr5qKXMiFaHm0OJHeSeotGhfcjTUHyE6G2PRhK6ZzpRNOASLNBCdjTJ0ep4dJd1DSaVAQqpT\nrVx91VLmRCpCzaHFz3JOUGnRvuTo0kSY4GKQNY2LzObxujWhRSKLQWYnmxRIlJECCalOtXL1VSuZ\nE6kYNYcWSaizRfuqBF6YibYdNDa00zV3ilmb+0GzbWGEoTV7WWjVQbOcFEhIdaqVq69ayZxIxag5\ntEiKOli0r0rgxZnfs4+Jtd1snTvDmugEc+HVD5proxPECDKytps1N+qgWU4KJKQ61crVV61kTqRi\n1BxaJAOfLtpXJfDi7dgV4GvbD7FxrJ89U/1c6NhPLJj9oBmMRdk01U+/2cXA9kMc3qmDZjkpkJDq\nVCtXX7WSOZGK0jpTEf/zqhJ4vU+J2rcPvvjqHl4420d7bI7tY31cXr+H2dC1B8210Qk2TfVzpXEL\nLzQdZOrVPcrilpkCCaletXD1VSuZE6korTMV8b9iK4FrSpQTCMCdbwjz16cfIP4s3LGul43T5zE2\nxkxTJ7FAA8H4Is3zI1gT5PK6XXxn4SDP/PD9/Kc3hOsi2KomCiSketXC1VeGzIltDDE25lLcyZNA\nSwt0dIBZ0LyVelVn60xF6kqxlcDvvBP+5E80JSrJjSO28I3Ig5w+c4yeDce5fmGQddFxGuJRrAly\nqXUvLzV2c2zhEIM39XDHHWFlcSvAWGsrvQ91zxiz7EPQZ5Km2odpIhF45BFix59kpn+YwcY9XF5o\nIxo1xC0EDIRClk2NE3Qv9NO8ZwvB190NH/ygrhahLvP4yR/Zh+tMRerSiRPwiU/A6dNw4EDus1yf\nfRZuuAE2b4azZ7NPiUpPvt9117VTovwmdb3JhcE4O2dOctOaQZrMPPO2iRfmujnfvI/t3YFXxhH9\nHFyVSI7lJlfYgC5aK0+BRI6q+Opr+qVpet9xlPDzvbRODGFsjKtrO4kHGgjEF1k3O0LcBJlq62L+\nloMc/Kv7abm+zo941R4giojk6LHH4DOfcRf8O3bk/rqBAbhyxWUe5udzWw7Y1+eS2keOuClRfqbT\nRMlVLpAwxtxurf1esTsgCiSKVokR7ZT3XJiJ8OX/Gebb566Hly/xhtCTr6RgjY1hTZCrofalFOwN\nPbz2dWHfjyatKFtpk/Qpa11dbnjP73l8EalpX/wi/PmfuyBg27bcX3fhAnz/++5wd+BAbsvsxsfd\nlKieHnj44YqPo5VFFY8j1rqiA4li1kg8Y4z5OPBfrLV51r4U8UAlhioyvOfEpRg3vBSkJdpObFs3\n57fexffX/Ayts8M0xuZZCDYx1tLNxY59RBYCXOiDxpQFdnXHq9ImIiJVotBK4OPj7pC4dq07DOai\nrc2d6gYH3cV1RSrolnkAz6fVgn2hmECiEfht4CeMMe+w1p7waJ9EVleJYt0Z3tNu7OTKVIj5uUVu\nDJ4i8PIZtsz0M9R5gG/e/ACR0PL3TF9gd/hwHY6mFFvaRESkyhRaCfzyZffvzZtzew2453V2uiBk\ncLDMF9eaayRpvKjadBvwXWPMw7jsRMyDbYpkV4kR7SzvOTZmuGhgMgwLG7pZE51g81Q/jTH3nt+4\n9UEWg8vfsypGkyql2NImdRl5iUi1K7QSOLjTUq7ZiKSGBrdeYn4+/30tmLrtSQZenJEtLjvxEeBf\njTG3erBNkezSR7Tb268dykkd0R4eXhrR9vg9p6chGkk0qDaGuXA7Fzr20zo7TNdILzddvPY900eT\n6kpykms8XngeX0SkyiQrgXd1uevoaHTl5yd7qG7aBBs2uENcPhYXXRKgqanwfc5L6mDauXOwc6cr\nub5jh1sUsmOH+37nTvf4k0+650ciZdpBqRSvhvYsbsHGflww8RFjTNCjbYssKXREe2jIvS4e9/Q9\nYzFeKfH6yn3BEJfX76FjZog9w8cx9tr3bGhwry3raFI1GBhwEdTGjYXn8UVEqlBPj1swvWWLG5Af\nH3fTl1JZ6+7v63PPe/WrYfduV18i1zor1rrnJ2cSlUUlBvCkJng5RyD5X6AR+B3cdCe17RVvVWJE\ne4X3DAZdEBFPOwHMhtowNkbHzCBbx659z7KPJlWLSMR9Fg15zqqs28hLRGpFsofqXXe58qznz7s+\nEQMD8OKL7vbZZ939u3bB3XfD7/6u+3cwuDTVaTUTE+75yapFJVeJATypGcUEEr8CTLO8dJRlKTtx\nOy478dvKTohnKjGivcJ7trRAKAzzc9e+50xTJ+si43RML3/PiowmVYsMpU2shdFR92s+e9bdjo6m\njc7VbeQlIrUk2cH+yBGXodi71502olF3u3evu//IEdeTtLW1sClRXV3udWVZMqYpqbKCghdbW2s/\na4z5KvAZ4MdZykjAUjARAj4K/GSispP+mqQ4yRHt1UZE0hWzMm2F9+zogJZmmJqESBTCKU+JBRpo\niEdpjC1/z7KPJlWTlNImsW3dXHzJMDwM0zNurckrncDD7ve6ZQtsvd4SHBlxZ+C6i7xEpNaEw67A\n3OHDufU+6OlxU53m5txtLp2tDx50rysLLwbw6qqqSH0pqmqTtfYlXPnXnwM+DWxiKaByJ8w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LtctsnnsRhcvOiORTMz7nnWuh8+HHb/Xr/eBRheK+Mv3pdjN+UucVYGdRPYS0EUSIhAdS14FBG/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\n", 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\n", 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" ] }, "metadata": { "image/png": { "height": 287, - "width": 393 - } + "width": 391 + }, + "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Create a new figure\n", + "# In this case we are explicitly creating the figure that we will plot to \n", "fig = plt.figure()\n", "# Add an axes to our figure\n", + "# Figures can have multiple axes. This adds a single new axes to our figure\n", "ax = plt.axes()\n", "\n", "# Plot the data again\n", - "ax.scatter(x, y1, c='blue', alpha=0.6, label='Group 1', s=50)\n", - "plt.hold\n", - "ax.scatter(x, y2, c='red', alpha=0.6, label='Group 2', s=50)\n", - "# Here we've added some more optional arguments. \n", - "# alpha - sets the transparency of the data points\n", - "# label - makes a label for the data we've plotted, which can be used in the legend\n", - "# s - size. Changes the size of the dots we plot\n", + "ax.scatter(x, y1, color='blue', alpha=0.6, label='Group 1', s=50)\n", + "ax.scatter(x, y2, color='red', alpha=0.6, label='Group 2', s=50)\n", + "# Here we've added some more optional arguments:\n", + "# alpha - sets the transparency of the data points\n", + "# label - makes a label for the data we've plotted, which can be used in the legend\n", + "# s (size) - changes the size of the dots we plot\n", "\n", "# Add a title to our graph\n", "plt.title('My Awesome Scatter Plot', fontsize=18, fontweight='bold')\n", "\n", "# Add data labels\n", - "plt.xlabel('X Data Label', fontsize=16, fontweight='bold')\n", - "plt.ylabel('Y Data Label', fontsize=16, fontweight='bold')\n", + "ax.set_xlabel('X Data Label', fontsize=16, fontweight='bold')\n", + "ax.set_ylabel('Y Data Label', fontsize=16, fontweight='bold')\n", "\n", "# Set the ranges to plot of the x and y variables\n", - "plt.xlim([-0.1, 1.1])\n", - "plt.ylim([-0.1, 1.1])\n", + "ax.set_xlim([-0.1, 1.1])\n", + "ax.set_ylim([-0.1, 1.1])\n", "\n", "# Set the tick labels\n", "ax.set_xticks(np.array([0.0, 0.2, 0.4, 0.6, 0.8, 1.0]))\n", @@ -301,10 +319,12 @@ "ax.spines['bottom'].set_linewidth(2)\n", "\n", "# Add a legend. This will use the labels you defined when you set the data.\n", - "plt.legend(loc='upper left', scatterpoints=1, frameon=False)\n", - "# Legend doesn't require any arguments. \n", - "# Here we optionally specify where to put the legend ('loc'), how many points to use \n", - "# in the legend ('scatterpoints'), and wether to have a box around the legend ('frameon')" + "ax.legend(loc='upper left', scatterpoints=1, frameon=False)\n", + "# Note that legend doesn't require any arguments\n", + "# Here we optionally specifing:\n", + "# 'loc' - where to put the legend\n", + "# 'scatterpoints' - how many points to show in the legend \n", + "# 'frameon' - whether to have a box around the legend" ] }, { @@ -312,21 +332,27 @@ "metadata": {}, "source": [ "### Figures and Axes\n", - "Note above that sometimes we are calling these functions on 'ax' and sometimes we are calling with 'plt'\n", "\n", - "We also created a thing called fig. What's all this?\n", + "Note that in the above example, we defined a figure object, `fig`, and an axes object, `ax`. \n", + "\n", + "You might also notice that sometimes we used called function from `plt`, and sometimes called methods directly on the `ax` object. \n", "\n", - "- 'plt' is just our nickname for the matplotlib module\n", - " - Here, whenver we are using 'plt' we are implicitly calling a function from matplotlib on the current figure\n", - "- 'fig' is just an arbitrary variable name we have been using to assign to a figure object. \n", - " - We can use 'fig' (or whatever we call our figure) to update it after we have created it\n", - "- 'ax' is also just an arbitrary variable name for the current axis.\n", - " - We can us 'ax (or whatever we call our axes) to update a particular axis after we have created it" + "So, what are these different things?\n", + "\n", + "- `plt` is then name we have given the imported matplotlib module\n", + " - Here, whenever we are using 'plt' we are calling a function from matplotlib \n", + " - By default, this gets applied to the current figure (the most recent one created)\n", + "- `fig` is a variable name we have given to the figure object\n", + " - A figure object is the whole figure that we are creating\n", + " - We can use 'fig' (or whatever we call our figure) to access or update our figure after we have created it\n", + "- `ax` is also a variable name, for the current axis\n", + " - A figure can have multiple axes (though our figure above only has one)\n", + " - To update a value on an axes object, you can call a `set_` method on the axes object, like we do above" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -342,7 +368,7 @@ { "data": { "text/plain": [ - "" + "
" ] }, "metadata": {}, @@ -359,7 +385,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -367,7 +393,7 @@ "output_type": "stream", "text": [ "\n", - "Axes(0.125,0.125;0.775x0.755)\n" + "AxesSubplot(0.125,0.125;0.775x0.755)\n" ] } ], @@ -375,43 +401,38 @@ "# 'ax' is a name for the current axes. A figure can have many axes (figures can have subplots)\n", "print(type(ax)) # Axes is a class of variable in matplotlib\n", "print(ax) # This is the axes handle 'ax' that we made before\n", - "#print(plt.gca(), '\\n') # gca grabs the current axes. \n", "\n", - "# In this case, current axis is 'ax'. Turned off as it plots an axis. \n", - "# Note that here gca is drawing an empty axis" + "# Note that if you need to grab the current axes, you can do so with `plt.gca()`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Keeping track of figures and axes, and knowing what to call on what can be a bit confusing at first. \n", + "Keeping track of figures and axes, can be a bit confusing at first. Note that typically a lot of managing matplotlib objects objects can happen automatically. In many cases, many figures in different cells, for example, matplotlib will make new figures and axes when it needs to, without you having to explicitly specify this. \n", "\n", - "Note that a lot of it gets managed behind the scenes - you don't have a to explicitly create new figures or axes. Matplotlib will make new figures and axes when it needs to, without explicitly being told to.\n", - "\n", - "If you're wondering why we would bother using fig and ax then:\n", - " - We often don't need to, but it can be very useful to have a label to grab our figure (and manipulate it) when we need to. \n", + "Defining or accessing figure and axes objects can be useful when customizing plots, replotting things later, or for more custom or complex plotting tasks. That is, it can be useful to have a label to grab our figure, and manipulate it, if and when we need to. \n", " \n", - "For example, we can get our figure back just by calling it's name. " + "For example, we can get our figure back just by calling the figure object name. " ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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nnuOss86iV69eVFVV8eEPf5gXX3wxo3NyxhlnMGLEiFbHEREREckHBRIC+O5M\ny5fD5s0wdqzvxpR4P2rml48d69dbvtxvVwj33XcfjY2NfOxjH2PUqFEp1y8rC258u+aaa/jGN77B\n6NGjueaaa1oEJJdddhmzZ89my5YtfOYzn+Fzn/scW7du5YorruCyyy7L2Wt5/vnnmTp1KhUVFVx5\n5ZWcffbZLFq0iEmTJvHUU0/l7DgiIiIiuaSuTUIk4sdEbNwII0b4rkzJlJf79dav99tNnw4l7RyS\nPvPMMwCceeaZbdrPSy+9xIoVKxg6dGiL5Q8++CALFizg5JNPZtmyZVRWVgJw8803M2XKFBYsWMA5\n55zDJZdc0qbjA/zpT39i/vz5XHXVVYeXLVy4kPPPP5/LL7+c1atXU9LeJ1hEREQkBQUSwiuv+IHV\nkQj07p3eNr17+zEUGzb47ceMyW8ZE73zzjsADBgwoNVztbW13H///S2W9e7dmy984Qut1r3uuuta\nBREA9957LwC33nrr4SACoEePHtx2222cddZZ/PSnP81JIDF8+HCuuOKKFsvOO+88pkyZwtKlS3nq\nqaeYMmVKm48jIiIikksKJITaWp+dqU+f1t2Zwpj5gdg7d/pgor0DiWRqa2u58cYbWywbPHhwYCAx\nYcKEwH289NJLlJSUtBgzETNlyhRKS0tZsWJFTso7adKkwBaHqVOnsnTpUlasWKFAQkRERIqO+ksI\n9fW+dSFkGEGosjK/3cGD+SlXMscccwwAb7/9dqvnpk6dinMO5xyHDh1Kaz+Jdu3aRU1NDeUB/bzK\nysro06dPzjJBHX300UnL1hUyTomIiEjHo0BCqKjw80Q0Nma2XWOj36579/yUK5nYoOhFbRztHZbh\nqFevXuzYsSMwEGlsbGTbtm307Nnz8LJYi0JjyEmsq6sLLcOWLVsCl8e6b/Xq1St0WxEREZFCUSAh\nDBniszFt3QrpzoXnnF8/Nklde5s5cyZlZWU8/PDD/POf/8z5/k8++WQikQjLli1r9dyyZctoamri\nlFNOObysuroagDfffLPV+rt37+b1118PPdbTTz/dKp0s+PSwsbKIiIiIFJtOH0iY2cfMbL6ZPWVm\nu83MmVlWU/2a2UAzu9fM3jazejOrNbM7zKw61+VuT6NH+2CgtBSSVJy3UFfn1x882G/f3o477ji+\n/vWv09DQwNlnn82zzz4buF6yloBkLr/8cgC+8pWvsH///sPL9+/fz/XXXw/ArFmzDi+vqqrihBNO\n4JlnnuExEJFOAAAgAElEQVTVV189vLypqYlrr72WAwcOhB5rzZo1/OhHP2qxbOHChSxdupThw4cz\nadKkrF6DiIiISD51hcHWXwfGAHuBt4ATstmJmR0HPAv0AxYCrwETgGuA6WY20Tm3PSclbmclJTB5\nsp+xes0aP09EshSwDQ1+vWHD/HaFykx6ww034JzjW9/6FhMnTmTcuHFMmDCBmpoa6urqqK2t5Ykn\nngBg8uTJGe37kksuYeHChfzmN79h1KhRnH/++ZgZjz76KOvXr+eiiy7i0ksvbbHNl7/8ZWbNmsXE\niRO58MIL6d69O4sXL+bQoUOMGTOGVatWBR5r+vTpzJkzh8cee4wxY8awdu1aHnnkEbp37869996b\ndurXRx99lEcffRRo7hb13HPPHZ4kr0+fPnznO9/J6DyIiIiIhOkKgcQX8QHEWmAKsDjL/fwIH0T8\np3NufmyhmX03eoxbgM+3raiFM20arFwJBw74vyNG+BSv8UMInPMtEWvWQP/+fqbradMKV+bYrNAX\nX3wxd999N4sXL2bBggXs27ePqqoqjjvuOGbPns1ll13WohtSuh588EGmTJnCvffeyz333APAiSee\nyJw5c5g9e3ar9S+//HKcc3z3u9/lgQceoLq6mvPOO4958+ZxwQUXhB7ntNNO44YbbuAb3/gGd955\nJ845zjzzTG655RZOPfXUtMu7cuVKHnjggRbL1q1bx7p16wCfuUqBhIiIiOSKuXQ7xXcCZjYVH0j8\nyjn3iQy2Ow4fiNQCxznnInHPVQGbAQP6Oef2ZVGuFm9Cod6TPXtg/nw/Y/XGjT4jU9++PjtTY6Mf\nE1FaCoMG+SDiqqugqqogRe0UlixZwhlnnME3v/lN5s6dW+jiiIiISNeSZtL/cF2hRSIXzoj+fTw+\niABwzu0xs2eADwHvB9qWRqiAqqpgzhxYtMjPWL1hg58noqHBBxAjR/oxEZMn+5aIiopCl1hERERE\nCkWBRHpGRv+Gpd5Zgw8kjidFIGFmy3NYrpyrqIAZM2D69OYZrw8e9CleYwOrCzUmQjqwSMR/oGpr\n/cQlFRU+XZg+UCIiIh2WAon0xBL5h80MFlveux3K0i5KSvxs1cU0Y7V0QPX1rZu4mpp8E1csd7Ca\nuERERDokBRLtzDk3LnFZ4hgJ6RpiM3B3WmGDbsrL/aCb1ath7Vo/en/lSrj6ag26ERER6UAUSKQn\n1uIQNsVwbHl2kxaIdDb19T6IePpp2Lw5OA3Y4MHNacBi82zMmaOWCRERkQ5CnZPTszr69/iQ50dE\n/4ZPXyzSlSxa5FsiNm/2E5NUV7cMIsD/v7raP795s19/UYfNVSAiItLlKJBIT2zuiQ+ZWYtzFk3/\nOhHYD/y1vQsmUnQiET8mYuNG3xKRbHZD8M+PGOHXX7bMby8iIiJFT12b4phZN+A44JBz7o3Ycufc\nG2b2OD4z05XA/LjNbgR6APdkM4eESKcTS/cVifjuTOno3duPodiwwW+vUf4i0l6UVU4ka50+kDCz\n84Hzo/89Jvr3dDO7P/rvbc65L0X/PQD4J7ABGJKwqyuAZ4EfmNm06Hqn4eeYeB34Wj7KL9Lh1Nb6\n7Ex9+rTuzhTGzA/E3rnTBxMKJEQk35RVTqTNOn0gAYwFPpWwbFj0AT5o+BIpRFslxgM3AdOBGfgZ\nrb8P3Oic25mzEot0ZPX1/mKcqktTorIyP/vhwYP5KZeISIyyyonkRKcPJJxzc4G5aa5bS5Lpwp1z\nbwKfzkW5RDqtigpfo9fYmNl2jY1+u+7d81MuERFQVjmRHFLnPxHJrSFDfLeArVsh3XkynPPrx7oT\niIjki7LKieRMp2+REJF2Nnq0DwbWrvU1etXVqbepq/OtEYMH++1FRGOA8yHbrHLr1/vtpk/XyReJ\no0BCRHKrpMQPUFyzxj/Gjk1+sW5o8OsNG+a300VaujiNAc4jZZUTySkFEhKsA1WFvf7669x9990s\nWbKE2tpa9uzZQ1VVFSNGjGDSpElcfPHFjBs3rtDFzKvt27fzu9/9jj/84Q+88sorbNq0ifLyckaP\nHs2nP/1pPv3pT1PSnu/btGl+gOKBA/5vUB9k55r7IPfvD+PH++1EujCNAc4zZZUTySkFEtJSB6oK\nc85x0003cdNNNxGJRDjllFO46KKLqKmpYc+ePbz88svMnz+f22+/nTvvvJMrr7yyoOXNp4ceeojZ\ns2fTv39/zjjjDAYNGsSWLVt45JFH+MxnPsNjjz3GQw89hKV74Wyrigp/hwP+jmj9+uY7orIyf0e0\ndav/XA0b5oOIq64q+GdKpJA0BrgdKKucSE4pkJBmHawq7KabbmLu3Lkce+yxPPjgg0ycOLHVOu++\n+y533HEHu3btKkAJ28/xxx/P73//e84555wWLQ/z5s1jwoQJ/Pa3v+WRRx7hggsuaL9CVVX5O5zE\nwLShwQcQI0cWVWAqUmiJY4CD7nXjxwCvXNk8BnjGjPYvb4ekrHIiOVVcfVSkcOKrwtatg6FDfS3x\nkCEwcKD/O368X75unV9v/ny/XQGsW7eOm2++mfLych577LHAIAKgX79+zJs3j+uuu67F8pkzZ2Jm\nrFu3jvnz53PSSSdxxBFHMHXq1MPrRCIR7r77bk499VQqKyvp0aMHp556KnfddReRSKTF/mprazEz\nZs6cGViOqVOntmoNWLJkCWbG3Llzee655zjrrLPo1asXVVVVfPjDH+bFF19M+3yceeaZnHvuua26\nLx1zzDF8/vOfP3y8dldR4e9w5s2D66+HK66Az37W/73+er98xgwFEdLlZTsGeONGv13CT5KEUVY5\nkZxSi4R4Hawq7L777qOxsZFLLrmEUaNGpVy/rCz4o37NNdfw1FNPcc455zBjxgxKS0sPP3fZZZex\nYMECjj32WD7zmc9gZvzud7/jiiuu4Omnn+ZXv/pVTl7L888/z7e//W3OOussrrzyStauXcsjjzzC\nsmXLePzxx5k0aVKb9t+tWzcg/By0i5IS369YfYtFAr3yCmysjXDc3leYVFdLtx31NJZWsL1qCJtq\nRuOsdb2fxgBnQVnlRHJKgYR0yHR4zzzzDOBr4tvipZdeYsWKFQwdOrTF8gcffJAFCxZw8skns2zZ\nMiorKwG4+eabmTJlCgsWLOCcc87hkksuadPxAf70pz8xf/58rrrqqsPLFi5cyPnnn8/ll1/O6tWr\nsx4o3djYyM9//nMApk+f3uayikge1Nez/+FFnPfCMvod2EC/vTsx14SzUvZVVLOjcjBr+k/mtQHT\naCxtbr3TGOAsKKucSE4pkJAOmQ7vnXfeAWDAgAGtnqutreX+++9vsax379584QtfaLXudddd1yqI\nALj33nsBuPXWWw8HEQA9evTgtttu46yzzuKnP/1pTgKJ4cOHc8UVV7RYdt555zFlyhSWLl3KU089\nxZQpU7La9/XXX8/f//53ZsyYwYc//OE2l1VEciw6Nm3g48up2baRUmuivqovjSXllEYaObpuNf12\nraXfrjUcu30lT466mvry5rFpGgOcBWWVE8kZBRLS6dLh1dbWcuONN7ZYNnjw4MBAYsKECYH7eOml\nlygpKWkxZiJmypQplJaWsmLFipyUd9KkSYEtDlOnTmXp0qWsWLEiq0DiBz/4AbfffjsnnHACv/jF\nL3JRVBHJpbixaVVbN7PuyBHsLetNVVXz7/D2ysEc0VDH0bvX0K3Jp2n6y0lzDrdMaAxwFpRVTiRn\n1EYnzenwMu1DX1bmtytAVdgxxxwDwNtvv93qualTp+KcwznHoUOH0tpPol27dlFTU0N5QJN3WVkZ\nffr0yVkmqKOPPjpp2bI5zp133sk111zDe9/7XhYvXkxNTU2byigieRA3Ni0yeiyHKqs5eDChMseM\nAxXVvFkzll77NzNo63JO2LQI0BjgNolllZs1y7c0jBzpK8gaGvzfkSP98lmz4NprNVmHSAi1SEiH\nTIc3ceJEFi9ezKJFi7j88suz3k/YvAq9evVix44dHDp06PBg5ZjGxka2bdtGz549Dy+LtSg0hpzD\nurq60DJs2bIlcHms+1avXr3CX0CAO+64gy9+8Yu8733vY9GiRfTr1y+j7UWkHSSMTavuXU7VBti9\nC+oboCKhDqOptJx3e46gz571jNi8jH8cO52ddSUaA9wWsaxy06c3d/E9eNBf02InVWMiRJLSN0Q6\nZDq8mTNnUlZWxsMPP8w///nPnO//5JNPJhKJsGzZslbPLVu2jKamJk455ZTDy6qjmT/efPPNVuvv\n3r2b119/PfRYTz/9dKt0stCcrvXkk09Ou9y33XYbX/ziFxk7diyLFy9WECFSrBLGppn5rviVlbBr\nV3A61/3lvTHXRM3eDfR95xVeftk3DJvB//4vrFqlNLBZiWWV+7d/g49/3P8dM0ZBhEga9C2R5nR4\npaV+cFk6CpwO77jjjuPrX/86DQ0NnH322Tz77LOB6yVrCUgm1srxla98hf379x9evn//fq6//noA\nZs2adXh5VVUVJ5xwAs888wyvvvrq4eVNTU1ce+21HIhNQRtgzZo1/OhHP2qxbOHChSxdupThw4en\nnf71W9/6Ftdffz3jxo1j0aJF9OnTJ63tRKQAAsamDRjgu+kfeSRs2+5bJlowY09FX9z2nWxYtoHd\nu2H7dnjhBbjrLrj1VvjqV+GPfyzYFD8i0sWoa5N02HR4N9xwA845vvWtbzFx4kTGjRvHhAkTqKmp\noa6ujtraWp544gkAJk+enNG+L7nkEhYuXMhvfvMbRo0axfnnn4+Z8eijj7J+/XouuugiLr300hbb\nfPnLX2bWrFlMnDiRCy+8kO7du7N48WIOHTrEmDFjWLVqVeCxpk+fzpw5c3jssccYM2bM4Xkkunfv\nzr333ptW6tcHHniAG264gdLSUiZNmsQPfvCDVusMGTIkdMI8EWlnsbFpcb+1paUw6n3+31u3wp7d\nsNtB9yOgxPzqDdvLKG1qoLTcj0079ljfE6exEVav9tMjrFnjkxFdfbW69otIfimQEK8DpsOLzQp9\n8cUXc/fdd7N48WIWLFjAvn37qKqq4rjjjmP27NlcdtllLbohpevBBx9kypQp3Hvvvdxzzz0AnHji\nicyZM4fZs2e3Wv/yyy/HOcd3v/tdHnjgAaqrqznvvPOYN28eF1xwQehxTjvtNG644Qa+8Y1vcOed\nd+Kc48wzz+SWW27h1FNPTaus69evB3wLyB133BG4zpQpUxRIiBSLkLFp5d3gpJNg0yY/P+ievdAQ\njTn27oVK10ikpJSjB3fn7NNb5sgYPLj5JzrWCDpnjpINiUj+mEu3T7zkjZm1eBMK9p5E85mzfLkf\nABiWDm/QoOZ0eKruytqSJUs444wz+OY3v8ncuXMLXRwRaU+rVvm+SKtX+9/TgMQPzsGOHT6Y2LIF\nNm9yjNj9Inv6j+Qv467nraOC0243NPj6oGHDfNKhGTPy/WJEpINKM+d/OLVISLNYOrxFi3w2kQ0b\nfB/ehgYfQIwc6au8Jk/2LRG5rOaKRPzgw9pa3+RfUeEHgStrhoh0RrGxaWvX+maEaMKGeGZw1FFQ\nUwNb3oEeh+qoOLKUN3sNZlNN+Ni08nLfqLx+vf8pnz5dP6Mikh8KJKSl9k6HV1/fOnBpavKBSywj\nVD4CFxGRQspgbNqOHbB/dwPH1q9h99HDWNN/Ms6S/w737u1/Sjds8D/lRTRnqIh0IgokJFgsHV4+\nrz5hXanKyzVyMIEabEQ6oTTHph3cXMex29awo0d/NvUdz2sDUo9NM/M/pzt3+mBCgYSI5IMCCSmM\n+nofRDz9tB9RGHQB7eQjB2MzcCejBhuRTqyiwleQgK9QWb8+cGxa912lrOs+jDeqx/PSqKtoLE3v\ny15W5numHjyYx9cgIl2aAgkpjEWL/IVz8+bwJn0zf7c8dqyvrVu+3G/XRUYOqsFGpAtIY2zajobB\nPF47mRU10xhQnn6NQWOj30X37nksv4h0aQokpP1FIv6CuXGjb4lINmcFdMmRg2qwEelCUoxN2x8Z\nzdr/KuHt1fCeoYEJnlpxzifai+XIEBHJBwUS0v5iF8pIxN8dp6OLjRxUg41IFxQyNm10JGWCp1bq\n6nxrRCxHhohIPnTual0pTrW1vum+T5/0qtag9cjBTizbBpuNG/12kUj7lFNE2kcswdOgQb4FsqEh\n+foNDX69QYP8dp28AVdECkg/L9L+6qPTtJZl2CBWVua36+QjB3PRYCMincu0aTBuHPTv71sgd+70\n3ZfiOeeXr1zp1xs/3m8nIpIv6tok7a+iwre5NzZmtl0XGTmYiwabTt7zS6TLSTPBE6Wlfkbr8ePh\nqqs0ZkpE8kuBhLS/IUN8J9/Vq30HXo0cbCHWYJOqS1MipXoU6dzSSPCklNAi0q4USEj7Gz1aIweT\nUINNcdPkgFJIKRI86XMoIu1KgYS0v9jIwTVr/CMsLVFMbOTgsGFdYuSgGmyKkyYHlGISkuBJRKRd\nKZCQwpg2zY8IPHDA/w2aKMG55okSutDIQTXYFB9NDigiItKaAgkpDI0cDKUGm+KiyQFFRESCmUvM\nHyftzsxavAld6j1Rf5FA9fVw++3Jb14TG2wmTYJrr+1Sp6ld/PGP8LOfwbp16QV1K1f6oG7WLE0O\nKCIiRS3N3JBJdtClblqLVJcOJGJiI1g1cvCwsO40iQ02gwY1N9ioO01uRSLw1a/6WHfo0PS6me3c\n6RvYpk2DefO67Mc39zTKXUQk19ocSKhrkxQHjRxsRakeCy8XkwPqI91GarUUESlaCiREiphSPRaW\nJgcsMI1yFxEpagokRDoANdgUhiYHLCCNchcRKXqqyxQRCaHJAQto0SLfErF5sx/lXl3dulnIzC8f\nO9avt3y5305ERNqFAgkRkRCxyQG3bvVZstIRmxww1n1fshCJ+DERGzf6lohUTULl5X69jRv9dpFI\n+5RTRKSLU9cmkXQoY0yXpMkBC0Sj3EVEOgQFEiLJKGNMl6bJAQtEo9xFRDoEBRIiYZQxRvAx4sqV\nfizvypXpTQ44frzfTrKkUe4iIh2CAgmRIMoYI1EVFT5GBB9Trl8fPjngsGHNkwPqY9AGGuUuItIh\nqOFdJIgyxkic2OSAs2b5loaRI/3b39Dg/44c6ZfPmgXXXquGqTbTKHcRkQ5BLRIiibLNGLN+vd9u\n+nR1ju+ENDlgO9IodxGRDkGBhEgiZYyRJDQ5YDvQKHcRkQ5Bv7YiiXKRMUZE2mbaNBg3zo9eX7nS\nf7cSuzk555evXKlR7iIiBaAWCZFEyhgjUnga5S4iUvQUSIgkUsYYkeIQG+WeOJdLQ4P/ro0cqblc\nREQKSIGESKJYxpjVq/1NSjrdm2IZY2I3NiKSGxrlLiJStBRIiCRSxhiR4qNR7iIiRUfVOCKJYhlj\nBg3ymWAaGpKvH8sYM2iQMsaIiIhIl6E7HpEgyhgjIiIikpS6NokEUcYYERERkaTMJdaySrszsxZv\ngt6TIlJf3zpjTFOTDyCqq5UxRkRERDqqNCfLSrID3bQWngKJDiASUcYYERER6UwUSHQGCiRERERE\npJ21OZDoElWpZjbQzO41s7fNrN7Mas3sDjNLI69ni/2cY2aPm9lbZnbAzNaZ2UNmdnq+yi4iIiIi\nUow6fYuEmR0HPAv0AxYCrwETgDOA1cBE59z2NPZzG3AdsB14FNgGDAf+DT9o/ZPOuV9mWUa1SIiI\niIhIe1LXplTM7M/Ah4D/dM7Nj1v+XeCLwD3Ouc+n2McxwCZgK3CSc+7duOfOAJ4E1jvnhmVZRgUS\nIiIiItKeFEgkE22NWAvUAsc55yJxz1UBm/EnsZ9zbl+S/ZwG/BX4vXPuvIDnd+PPZVWW5VQgISIi\nIiLtqc2BRFbzSJjZ5LYeOBnn3LIc7eqM6N/H44OI6DH2mNkz+NaK9wOLkuxnDdAATDCzPs65bbEn\noueiCt/dKSUzW55B+UVEREREilK2E9ItAfJVbe7I3UR5I6N/Xw95fg0+kDieJIGEc26Hmf0/4LvA\nq2b2KH6sxHH4MRJ/Af4jR2UWERERESl6bb1hb3OTSJ71iv7dFfJ8bHnvVDtyzt1hZrXAvcBn455a\nC9wfP24ixX7GJS5L7NokIiIiIlLs2pr+1eX4UbTM7DrgYeB+fEtED2AcsA74lZn9V+FKJyIiIiLS\nvjr7PBKxFodeIc/Hltcl24mZTQVuww+2vtY5t845t9859xLwEXxGpzlmllXWJhERERGRjqYtgYTl\n4ZFrq6N/jw95fkT0b9gYiph/jf5dnPiEc24/8AL+XJ6caQFFRERERDqibMdIfDqnpcif2I3/h8ys\nJCD960RgPz61azIV0b99Q56PLW/ItqCSWiQCr7wCtbVQXw8VFTBkCIweDSWdvW0NdAJERESkqHTq\neSQgswnpzKwbfvzDIefcG3Hrfhz4NbAFGOec2xT33NnAH4B6YGA6s2QHlFHzSCRRXw+LFsGyZbBh\nA+zcCU1NUFoK1dUweDBMngzTpvl7606ny58AERERyQNNSJdKdFK6Z4F+wELgn8Bp+DkmXgc+ELv5\nN7MhwHpgg3NuSNw+SoA/A2cBe4DfAe8AJ+K7PRnwBefc97MsowKJEHv2wPz5sHw5bNzo75/79oWy\nMmhshK1b/f30oEEwbhxcfTVUZTUtYJHq8idARERE8qQwE9J1JM65N8xsPHATMB2YgZ/R+vvAjc65\nnWnsI2JmM4ArgX/HD7A+EtgB/BH4gXPu8Ty9hC6rvt7fQz/9NGzeDCNGQO/eYHEf+8GDoa4O1qyB\nAwf8sjlzOknFfI5PgHpGiYiISC61S4uEmQ3CtwIcjZ+zocQ5d1PeD9xBqEUi2B//CD/7GaxbB2PH\nQnl5+LoNDbByJQwbBrNmwYwZ7VfOvMnRCVDPKBEREQlQvC0S0e5AnwS+DJwQ8PzNwEW0nNztXufc\nL/NVJuk4IhF/47txo6+IT3YPDf75ESNg/Xq/3fTpHbyWPUcnIKxnVHm57xm1ejWsXesbNFauVM8o\nERERSV9eAgkz64cfnDyZ4GgnVuX+EjA17v+9AAUSwiuv+NrzSMT35klH797+RnnDBr/9mDH5LWNe\n5eAE1J8wpmt3DRMREZG8ynmdbTSt6pO0DCICZ692zq0GXoltCow1s6G5LpN0PLW1vgtOnz4tb3yT\nMfO17Tt3+nvpDi0HJ2DRIt8SsXmz7xlVXd16V2Z++dixfr3ly303KBEREZFU8tH5427gvdF/xwcP\nYXdDTyQ8d1YeyiQdTH29r1wvy7DNrKzMb3fwYH7K1W7aeAIi+w9m1TNq40bfMyoSSb6+iIiISE67\nNpnZSfisRvEtD6mqU2OTwcW2mQj8JJflko6nosIPBm5szGy7xka/Xffu+SlXu2njCVj/TndWroQd\nO6BnT9i1y499qKkJb+DoVF3DRDo7pWETkSKQ6zESl+ADB0dzAPEY8AtgQcg2/4z7txEwMFu6niFD\nfJeb1at9P/50evc456dVGDnSb9OhZXkCIu9u5Z2eI/nh/w5m1atw6JDfhZm/z6ishP79YcAAH6fE\nS+wapkBCpAgpDZuIFJFcBxJnRv/GgonfOuc+DmBmYYHE5oT/d/RbQMmB0aP99XDtWj8YuLo69TZ1\ndf5aOniw375Dy+IENGyrY9vWUp7fP5jfHxrNvn3+PqKkxFde1tX5loldu2D7dhg1qnWXp7Iyn0m2\nw3cNE+mMlIZNRIpMrgOJQbRsjZiXxjZ7E/7fM6clkg6ppMRXqq1Z4x/pTKOwZo2fRmHy5E7Qsp94\nAsaMgb17/Y1ErPYxrq9S04EGdvx1Desiw3iycTJH9y/hYINvZejRw++ystKfp927/S4ATjqpZctE\np+kalkjdQKSj6/IzdIpIMcp1IJFYbbomjW16Jfy/NHAt6XKmTfOVagcO+L9B103nmq+b/fvD+PF+\nu05h2jR48UXffeGxx/zNgHP+Ed9XqaqKvZt2sykygBUl4zk4cRr998OWLf7cVFb63cU2qanxYye2\nboVNm2DQIP98p+oaFqNuINJZJKZhC6pZiU/DtnJlcxq2TjFDp4gUo1wHEnvxM1fH9APWp9hmYML/\nd+W0RNJhVVT4lnnw18P165tb8svKfO351q3+nnDYMB9EXHVVJ7ofbGjwL/jAAf/vPXv8C4+9wF27\nYPNmXHk5B0rfw/LyCfzttKs44ogKarr7AGLXLr9p/D1HaakfgL1nj78nOfZYf//RqbqGgbqBSOfR\n5WfoFJFiletAYhstA4mzgR+l2Oa8hP9vyWmJpEOrqvIt84mVyg0N/qY3Vnve6SqVY90Y/vY36NYN\n3vc+3ydp3z7/nHOHB0A07qtnX+RImiihsqacJnxg0L9/85iIo45qeR9RXu53sXevb52oqupkXcPU\nDUQ6ky4/Q6eIFKtcBxIvASNoHifxTTN72jn3ctDKZjYEmB23vgP+luMySQdXUeFb5qdPb76eHjzo\n+/HHas87/I1vovhuDCef3Hznv2OHv/tvbPStE5WVvL2jEvfiKkY3raLx7UX8fZDvxjBggB9U3dTk\n//bq1VyRaebPX309vPMOvPFGJ+sapm4gkmMFHWaTixk6FUiISB7kOpBYDFwU/bcD+gJ/NbP/C1j3\nduCT+HEV8fNOPJnjMkknUVLir4Wd/noY1o3BzDctHHVUi9Ub6+CtI0bwnoPrGbF5Gf84djrOSigt\n9Q0Z4LuA7d7tY5EjjvC7qq/3AVl5ub+X7jRdw9QNRBK0JQgoimE2sQkqU32WEykNm4jkWa4DiQXA\nbTRnXnJAd+CC6P8t7u9/0twKEbMdeCjHZRLpWDLsxlBaCvu79cYONFGzdwMDdrzCW0f5aKtbN5+Z\nadMmXzm/d6+/J4lEfFBRWemDiFmzOlHXMHUDkaiMgoBuraONfX2H8P0nR7N8RUlhh9l0+Rk6RaRY\n5TSQcM7tNbNbgP+iOUCITwcbLz6IiP37RudcQy7LJNLhZNiNoaoKyrsb23b3pap+JzV7NhwOJMDf\nR7+fh/YAACAASURBVAwa5AdVx3pGHTrkDzNiBHz96773VKehbiBC+mPt179Wz55fL+L8o5ZRsbk5\n2miyUmrfqWb4vsFsZjIVY6dReVRFYYbZdPkZOkWkWOW6RQLn3HfMbBJwLsmDCZfw/0edcz/MdXlE\nOpwMuzHU1EBVJRzaWkakoYFuTcHdGOJ7Ru3c6bs6jR3bCe+Z1Q2ky0t3rP3BrXs49fn5DIgsZ3vp\nRo7p10RJPx9t7NjcSPeNqxnVsJZhfdfw1psrebLn1dSXNzc5tNswmy4/Q6eIFKt8dQS+APgpPniI\n/XS7hAdxz/8U+HieyiLSsWTYjSGWoalHRSN7DpRywCXvxhCbvG/QoE6SoSmRuoF0eYlj7aurW1fi\nd4vU89FN85lc8jRH7V7Heoby1tHjYcgQ3ICBrIsMYVXZeHYdNZR++9Zx3DtPc+Y/5lPWVN/qeLFh\nNhs3+m5UkUiOX1BsgspBg/yXtyFFw32n/5KLSLHIy6+Lc67ROfc54HTgYfzcEJbw2B197nTn3Oec\nc035KItIhxPrxrB1q++ekIYB73H0L9vKoR7VPLtpMDt3tt7UOd8SsXJlJ8vQlCiL83e4G0is47x0\nWOmOtT9h0yIGbV1O9cHNbD56LFsaqtn8jh1OjrZnLzgzGiurebNmLL32b2bQ1uWcsGlR4P4Sh9nk\n3LRpMG6c//KuXEnX/pKLSLHIedemeM6554GPm1kJMAifxQlgK7DROZfrehuRji+Lbgyle+roe0wp\n66oG03TUaDZ0tcn74qkbSJeWzlh7cxFGbF5Gzd6NbOk5grKKctweHzzs2OHHVzTUNzdONZWW827P\nEfTZ0zIzWot95nuYTVecobOgOXdFJB15DSRiogFDbfQhIsnEujGsWeMfYfMgxES7MZQOG8apn5zM\n5d1KutbkfYmyPH+dZza+ri2dsfYDdrxCzd4NmItwoNxHG92P8MHDnr3+/jzioDTuo7C/vDfmWmdG\ni5f3YTZdZYbOosi5K+1BsWLH1y6BhIhkaNo03z3hwAH/N2i0qHPNKWOi3Ri6TZ/GjIouNnlfkCzP\nn7qBdHzpjLU/ak8tPep3srd7c7RRYtAUgaboUJkS88HEYWbs7d6XHgGZ0WLaZZhNZ5+hM910W3nP\nuSv5pFix88hrIGFmNcAngMnAe4HYTFrbgVeBZcAvnXM78lkOkQ6njd0YuszkfWG6YjcQAdIba1/W\nVI+5JhpLmqONiPPBQ2mZz4JWXgG76vy/Y5pKyiiLBGdGa/dsq53xS55uuq12ybkr+aJYsXPJSyBh\nZt2AG4Fr8BPSQcv0r32BkcBHgG+b2R3AXOfcoXyUR6StCtL82lW6MeSLzl+XlM6UC42lFTgrpTTS\nHG0cPAC9evvAIZZSefcuqG+Aimi8URppxFkph0pbNzlomE0OJKbbCmpWarecu5IPihU7n5wHEmbW\nE/gzMIGWwUNi+pTYc0cA1wNnmtmHnHN7cl0mkWwVvPm1s3djyDedvy4nnbH226uGsK+imqPrVrO9\ncjD1hwyz5iAillJ51y7/6HMUlJij8uBWtvQeyY6qlk0OGmaTA+mm24qJ5dxdv95vN316Xk+8+vLn\nhmLFzicfLRIPA6dF/50s92KL3qf4wONh4MN5KJNIxoqq+bWkhMjoMbzCGH8hOwgVtTAEXcjS0hm7\ngUigdMbab6oZzY7KwfTbtZbuB+t4d281Pat88BCrGR0wALZvh8Ym2LYd3nNEHRErZUflYDbV+CYH\nDbPJoXTSbSVKzLmbh+93wSuTOpEijxVblFNBY/pyGkiY2YXAWSQPIILEZr4+y8wucM79NpflEslU\nMTW/6kImkplUY+2dlfD6MZOp3raGnu+uoWfNWPr2LWfAgOZ9lJbCqPf5f+/Y0sBRW9ewrnwYT5dM\n5s1NJRpmk2vppNtKlOecu0VVmdQJFGmseJiutdnJdYvEJ+P+bTQHCACH8IOswQ+67hb9d2LQMRNQ\nICEFVSzNr7qQiWQunbH2K7dMo5SVvL/nAU6KrKRm4AhKS3oT3yO3vMxx0rF17N2+hs39+7O1cjyr\n+kzTMJt8SCfdVpA85dwtpsqkzqIIY8XDdK3NXq4DiVNo3WXpj8C3geedc40AZlYGvB/4CnB2dJtY\n0DEux2USyUixNL/qQiaSvVRj7YedWMGWY66mcgf03bWc0jfXQ23rzF6lpaX0GjuMqnHjOTT1Kj67\nrULDbPIhnXRbQfKUc7dYKpM6kyKLFVuUS9fa7OU6kIild421RvyPc+7SxJWiAcXTwDlmtgD4d5oD\nkDSmoRXJn2JpftWFTKRtUo+1r6LkUHqZvUqmTWN0RQVKyJQn6aTbSpSnnLvFUpnU2RRZrHiYrrVt\nk+tA4l0grpcpt6Sxzc34QCJme9iKIu2hGJpfdSETyZ2kY+2V2as4pJNuK1Gecu4WS2VSZ1NEseJh\nuta2Xa4DiRXAwLj/r0tjm/h1HPByTkskkqFiaH7VhUyknSmzV2Glk24rXh5z7hZDZVJWijzdUBHF\niofpWtt2uQ4kfgGcG/f/Y4E1KbYZmPD//8lpiUQyVAzNrx32QiYikq1U6bagXXLuFkNlUkY6SLqh\nIooVD9O1tu1yGkg45x42s78AH4wuuga4KsVmX4j+NeAFfDAiUjDF0Pza4S5kIiJtlU66rXbIuVsM\nlUlp62DphookVjxM19q2y8eEdP+Oz9R0GjA7mqHpFufcm/ErmdlA4GvA5/BdmtYAH3XOZToHhUhO\nFUPza4e6kImI5EqqdFvtkHO3GCqT0tIB0w0VSazYojy61rZNVoGEmT2ZYpVYA5QBnwU+a2YbgLej\ny98DDI5bxwENwC/NzDnnNDeoFEwxNL92mAuZiEiuFXgAfDFUJqWlg6YbKoJY8TBda9su2xaJqaQ3\ne3X8hHRDaBk8JK4ziuagQqSgCt382mEuZCIi+VKgAfDFUJmUUgdPN1QsydJ0rW27tnZtShW7JQYG\nsfWDlokUjUI3v3aIC5mISCdV6MqklDpJuqFCJ0vTtbbt2hpIZNp6ELS+WiCkKBW6+bXoL2QiIp1U\noSuTUlK6oZzRtbZt8jHYWqTTKGTza9FfyEREOrFCVyYl1ZZ0Q/X18Npr/u64COebaG+61raNZZMk\nycxqyWNLgnNuaL72XYzMrMW5VOIqiZezFOFFPlmRiEixiv18Fs3E5wsXwl13+WBgyJD0tmlqgpde\n8lXrAwfCkUcW5XwThdJBpuPItTYPL8gqkJDcUiAh6cj6QtZFfx1FRDqtVavg1lt9uqHx41N3b2po\ngL//3ffNKSmBo4+GQYNaV7kPGgTjxhV8volCKrqgMb8USHQGCiQkb8ImK9LFQ0Sk44pE4Ktf9ZVE\nQ4cmTzfU1AQvvwxvvgm7dvnf+0mTWt4VJw4C+Jd/Keh8E9Ju2hxIaIyESGfVAScrEhGRNGSSbmjT\nJtiyxQcRffv6wCOxar0I55uQjqHzNdKIiJc4WVF1devm7/iLx+bNzRcPEREpbtOm+Zbk/v39zf/O\nnb5lIV4k4kcPb90KvXr5Lk0DBoTvMzbfxMaNvjtsJJLf1yAdnlokRDqjDj5ZkYiIpJBOuqENG+Dd\nd/1v/MCB8L73+e6syRThfBNSvPJ2p2BmR5vZN8xskZm9ZWb7zKwpjUdjvsok0mXkYrIiEREpbrEc\ntbNm+RaKkSN9S3NDQ/O8Eb17+7ylY8ZAt26p95k434RIEnlpkTCz2cDtQKyjtWavFmlPmqxIRKRr\nSDbh0WuvweOP+3VStUTEKyvzwcjBg/krt3QKOQ8kzGwm8MOExemmIVLAIZILbZmsSBePzGh+DpGk\n9BVpJyUlvgIovhLIOXjySd/NKRONjT7w6N49t2WUTiengYSZVQLfi/43KHiwhOWWZF3pQnShybFY\n7ZMuHvmj+TlEktJXpAgMGeJP9urV/oSn00LtnB+cHZu6WySJXLdIXAj0IjhYSPy/iz4sYB3pInSh\nyRNdPPIrbH6O8nIfjK1eDWvX+rSMK1dqfg7pcuK/Im9uiDB07yu8/4haKqyeelfBP2uH8OSa0axZ\nU6KvSD6NHu1/z9eu9am+k803EVNX5y/CsVnYRJLIdSAxLe7fBjQB/wucH13mgF8ARwEfAKqjy5qA\nh4CGHJdHipjuxfJIF4/80fwcIknFviJ/XVrP4LWLuKzbMt5zaAM99u3EXBPOStlXXs3bewfz/9m7\n9/i4zvre959nRpqRbcm62LLj2JZ8iePQxIlTG0qaxBC0yXbDKb1CX6ebUvoy9FBIgJJD201bSuhu\noLsNhXq3FNq0cPZuXy09tAROsyHUsGuSkE2jIscNxJYvkhxHsWXdZUkz0sxz/nhmotF4RprLmtua\n7/v10musuaxZ0shrrd/ze57f71jfIZ6Z6QHC+i9SCvn0mwA3tbW/3y3OPnRIUwJkVV4HErexlGWw\nwB9aa/+zMeaVQsTW2ncAGGOagIeADwFBoBv4CWvtqMf7JFVI12IlppNH6aT358j0e1VzJ6ljx47B\n889M88aTR7mjsZeNU0MYG2OmqZPFQIhgfJHNk6fYZM6wbW0/3znZxzPhBzh2rEX/RUqhp8cdh+bm\n3G2mE256Z+uDB93rRFbhdSCxOe37f8j2RGvtPPDrxphW4JeBO4C/Bd7o8T5JFdK1WBno5OE99ecQ\nWVE8Dk99M8KP/ttR7rBPsvHqMJfW72EutPzYM9rczZroBJun+rmzcY7Av8FT33yQw4fD+i/itVz6\nTYyMuIz0rl3uPHD//Rq1k5x4HUisT/v+bA6veQQXSBjgDcaYn7fW/o3H+yVVRNdiZaKTh/e86M+h\nsrriYydPwvp/PcZNV3vZGBzmQsd+YsHMI0Vz4XYudOxn+1gfN831MvOvxzh58j79FymFZL+J9EWJ\n0ag7ByTXxmlRouTJ60AifUXndOI2CoTANaqz1l5Kec5LidvkAu23AQokfEzXYmWkk4e31J9DZEUD\n5+LsuHCcbfEhLrXvyRxEpIgFQ1xev4dto+e5cuE4g+cPc9ttGikqiZX6TSTXxmmUTvLkdSAxB6Qu\nh03+RV4lEUjgpjB9OeU5P5TybwPc4vE+SZXJdi1mbJytYyfZMD1AQyzCYjDMaMsOLnbsAxPQtVih\ndPLwjvpziKyoqf8kLbODBIm76Uw5mA210UaMztlBFk6fxC23lJLJ1G9CpEBeBxJXWB5IrAUiwMtA\nGy5Q+Lgx5oS19rwxZjNLfSeSNnm8T1Jl0q/FGmIRbrp4jD3Dx+mYGWRdJKWyR7idseZu+rcc4mXT\nw2wsrGuxQunkUTz15xBZUdvEAMHFcSYa88vaTTR2sn5xnNjkIAokRGqH14HEBWBXyvdbgHHgFPAq\n3PSlvcAZY8wVXBnY9CZ1Mx7vE8aYbcDHgMOJ9xzGZUUestaO57mtHuB+XGalHRgFTgKfttY+7uV+\n+1XqtVg4Os0bnj9K10gvHTMZKntMnGLT5Bk2TfbT3NDHV7ofoKlJNWBXpQ5/paH+HCIr2twWYboh\nxsRsflm7uWgDbWujtLRqpEiklngdSDwHvC7l+xuA7wPHWeolAS546Ez5PrVk7Akvd8gYsxt4Gpfp\neAx4AXgN8H7gsDHmzlxLzhpj/iuuXO2LwFdwGZhO4ADwekCBRA6S12LnfhDhnrGj7L70JK2zq1f2\n2LMwx8+tgR1bHgQ0lz8jdfgrLfXnEFlR154w/WuDNMwuMhOFcA7xRCQKzSwSWhuk60Zl7URqideB\nRG/iNplhuBt3wf0l4PcT72czvC7VX3u8T3+KCyLeZ609mrzTGPNJ4FeB3wPevdpGjDHvwgURXwB+\n2VobTXu80cud9rPktdimZ49x/VwvrfOrV/Y407Kf6y/10Rrp5eZLxwDVgL2GOvyVnvpziKwosGsH\nLdvbaRg7xcWJbjZuNCv+2cfjMDlh2RUYYc32vQR2KmsnUku8PqslAwmT+HodgLX2AvAnXFvVKd0z\nuAt1TySyEfcCA4n3T/U7uEXgv2CMWbfKdsK4gGOIDEEEgLV2wYt9rgeBABy6K87rA8dpHhvi5eaV\nK3vE4zA2HWK0fQ/b40MEnjzu7pQlqR3+zp2DnTtdOdcdO2DbNnd78KC7/9w597yjR93rJD89PXDg\ngOu70dfnsj42bXzEWnd/X5/6c0h92bePTa/pZs26IJ2hCa6MuoxDJpEoXBmFTaEJ1jQH2fQaZe1E\nao3XGYnv49YOJKWuSPwQsBFX3jWT/wW8xVob83B/7kncPmGtXXblaa2dNsY8hQs0XgscW2E7b8RN\nYfoUEDfGvAlXXWoe+K619jse7nNd+A+bT9IfHiTUGOcH0220BjOnwCNRmJyEtWth7eY21i+qBmxG\n6vBXPurPIZJdIEDDPYfoPNVP4Nl+FtftZ3IqxJSFpjUQMBC3MD+XOCSti3LjQj8bfngXDfcoaydS\nazwNJKy1FvjfWR6LAW83xnwG+Bnc+okwLlvw1RItVN6buD2d5fF+XCBxIysHEq9O3M4D3yOtRK0x\n5jjws9bakdV2yBjTu9pz6kHopQFu3DTOhbmNrF80TE+R9USzvsVdo918iyFwUTVgr6EOf+Wn/hwi\n2fX00NjXR2d0joP9fQxu2MPlhTaiUUMs7o7xra2WTY0TdC/00/yqLQTvUNZOpBZ5nZFYVWL0vlwj\n+K2J28ksjyfvX63YdbIk7YdwWZe7gT5gJ/CHuGDk73ELriUXkQiNJkb3DSEacAPp0zMQjbB0ommD\nlmY3M2TrVnd9pnr8GajDX2WoP4dIZomsXRBoXdfLvsHzzF2NMbO+k0UaaGCR5vkR1jQHMV3K2onU\nsrIHEjUqeTWwCLzZWjuQ+P6kMeancOVtX2eMuWO1aU7W2gPp9xljVluA7j+JGrDB+CJdO2D7dhgb\nc8FEbBGCDS6I6OhIq7CpevzXUrflylJ/DpFrpWTtzPHjrB0cZO34OMQSWbt2Ze0ElSr3gYoHEsaY\nAK6MapK11m7waPPJjENrlseT90+ssp3k499LCSIAsNbOGmO+DhzBlZXVeolcpNXjN8awYQNsWOmT\nVz3+zNRtWUSqkbJ2ko1KlftGxQMJXCWnNpb3kvDKqcTtjVke35O4zbaGIn072QKOZFO7NTnul6ge\nv3fUbdk/NDonfqSsnaRSqXJfqYZAopS+lbi91xgTSK3cZIxpAe4EZnFlZ1dyDBfg/FD6dhKSi6/P\ne7DP9cHDevx1f+2lbsu1T6NzIlIPUkuVDw+7wh9tyxvR0t3tBg77+2Fuzt334IM69lUpXwcS1tqz\nxpgncIuh3wscTXn4IWAd8Flr7VV4pancbmDBWns2ZTuDxpivAm/GdcT+o+Rjxph7gf+Iy1Z8rbQ/\nkc/09LjRhrk5d5vpgGLt0gElrR6/rr0SlN2pqKIDWY3OiUi9UKly3/F1IJHwHuBp4I+NMT3AD4Af\nwfWYOA38ZspztyYeHwR2pG3nvcDtwCcTfSS+h6va9JNADHintTZbdSjJpIh6/Lr2SqFuyxXhSSCr\n0TkRqRcqVe5Lvg8kElmJg8DHgMPAfcAw8GngIWvt+EqvT9nOi8aYA8BHcJmJQ8AU8FXg49ba75Zi\n/32vgHr8uvbKoMjsjuTHs0BWo3MiUi9UqtyXfB9IAFhrLwC/lMPzBnALvrM9PgI8kPgSr+RZ2UPX\nXhmo23LZeBbIanROROqJSpX7Ul0EElIjcqjsoWuvFajbcll4FshqdE5E6olKlfuSAgmpKbr2WoXq\ntpeUZ4FsPA7f+pabA5X842xpydCBMY1G56Ta1H3ZPMmZSpX7kgIJqSnKjOZIddtLothA9t97I9w6\nksgYffvb7k5jXFv3cBiam936la1b3YkzE43OSTVQ2TzJl0qV+1LBgYQx5u0e7YOGLCRnyoxKJRUT\nyM6PTNP4x0dhNrFCe2zMPWjM0kL4yUn3NToKN9+c+Q9do3NSaSqbJ4VQqXJfKiYj8Xm87UItsipl\nRqWSCg1km0yEHx84Stvok0BihXZXF5w44U6ULS0uGxGNwtSUexOAW29dnpnQ6FxhNP3GOyqbJ4VS\nqXJf8mJqU47jciLFU2ZUKqnQQHbf5WPcON3LGjsMhxInT2td8DA56U6YoZB7g44Ol60YGYGLF13A\nkaTRufxo+o33VDZPiqFS5b7jRSDhRVZCwYjkRJlRqaRCAlnicXZfPM6WhSHYnbJC2xh3kkxOZ9qw\nwY24BYOwfr2bPjI8DNu3u+dqdC4/mn7jvXoum6esljdUqtx3qmWxtaZISU6UGZVKKiSQXT94kusX\nBgmH4rR2p63Q3rrVrYeIxdxta6v7g05mLGZm3P3BoEbn8qHpN6VRj2XzlNXynkqV+0qxgYQyCVJ2\nyoxKpRQSyC6eGWBT4zjh6zdiAmmHzGAQbrnF/XtkxK2PsBbWrHH3TUy4P/KODo3O5UPTb0qj3srm\n1VlWq6xJF5Uq941iAokveLYXInlQZlQqKd9A9q2tEdoCMTo2Z4k4GhvdouqLF92F78yMO4snN3Td\ndXD33Rqdy1U9T78ptXoqm1dHWa2KJl1UqrzmFRxIWGt/ycsdEcmHMqNSKfkGsnvWhtk2HCQYX2GF\ndjDoFlVv3+4WWs/MuIuXYBDe+lb3hrq4zU09Tr8pl3oqm1cnWa06S7pICVTLGgmRvCkzKpWSTyD7\nHzp30PjJHFdoG+MWXXd0wOXLbkOvf73+kPNRb9NvyqleyubVSVarjpIuUkIKJKTmKTMqlZBzIBtX\nqbGyKnD6jQ02MDMW5YVvz3N+XkV5MqqXsnl1ktWqk6SLlJgCCRGRIqwayKrUWHnlOf0mFnPLU+Zf\nWGRuPsg/RZt4qk9FeTKql7/lOshq1UnSRcpAfwYiIqXW0wMHDrgSYn197mLDplW9ttbd39enUmPF\nSE6/GRm59necJroAzz0HL/zAEr80wvB8O5eaul+pvnvqlBt9ffRReOQRN5+87tXD33Iyq9WQ51hr\nQ4N7XQ0sKvci6SICykiIiJSeSo2VT47Tb2IxeP7fYfhlCE5N0NAUxHZ1Y2/Zx7bEILTmh2dQqr/l\namr4VgeLyusg6SJlokBCRKQcVGqsPHKcfnPxorvejc5EuT3Yz+j6XZzZcghrli5aNT88Cy//lqux\n4VsdLCqvp0q+UloKJEREykWlxspjlWYf1sLwSxYzMcGt9DPVvIXBzoO8sDXz9BvND8+gyL/leBye\nf2aa4J8epaW/l+bRIcKNMdZs78RUuvZoHSwqLzbpEgrBiRPVkUCSylIgISJSbio1VlqrTL+ZHluk\n88IIzdEgE5t2Mdh5kG/dfD+Lwewj3jVYlKc88vxbTiYgnvpmhH1PHGXX8JM0zg9zbt0eFta10XLZ\nsGULbN0OwUrNLauDReWFJl0uX4b16+ErX3EfSTUkkKSyFEiIiIj/rDD9Zm4+yGB4L5dbu7l80yFe\n2NqzYhABmh/uhdTmZ9ueO0bnSC8d8WHOt+4nakLMT8LUFExOwugo3HyLIVSpuWX5trCvsUXlhSRd\nrlxxs7dmZ+HqVZdVUvM6USAhIiL+lGX6Tf+zTfzt8W4uduxj6/bcR481P7xwqc3PXn4pzi8Ej7O7\ncYiRlj2EwyHCQEszRKIukFiMudfdeisEKzG3zOcFEvJNuszNwTPPuOBhcdH9yGpeJ6BAQkRE/C5t\n+s1oGAafAxvLbzM1VJSn6qQ2P/vx7pNc//wgxsaZCy2vPRoOwcYNcGXUXadfvAhdXVRmbpnPCyTk\nk3Tp7XVBRCAAd94Ja9Zcuz0VJ6hPCiRERKSu1EFRnqqS3vzsuskB1kXGmWnKXHs0EIDWVpiegnPn\nXPwQjxtabCdNQ+M0nx8kUK65ZT4ukJBP0qWhwX29+tWZg4hUKk5QXxRIiIhIXamDojxVJb35WcNY\nBGNjLAYyz6WxFhaiMDMDc/MwMekuYjdFGlgTjPLcX83THipzEsCnBRJySbqsWQNnz7r1K52duW1X\nxQnqhwIJERGpK3VQlKeqpDc/WwyGsSZIMH5t7dF4HMbGYX7OXYguxqAp7KY8Bewi07NB/u37TQw8\nqgW9Xlkt6XLuHHz2s+57Na+TdAokRESk7vi8KE9VSW9+Ntqyg6vhdjZPnGK0uXtZf4+xcZibddNq\nGhrcQ+EwrFtr6Zwd4VLnXgI7uzl3Tgt6vZYt6XLqlJrXSXYlCySMMSHg54DXA3uBdmCVmXUAWGvt\n7lLtl4iIiM+L8lSV9OZnFzv2MdbczabJM6yJTjAXdnPLrl51mYjFRfeaZOWmQADWRiewJshYSzfT\nO/axf6sW9JZLsc3rVJzA30oSSBhj/g/gc8Dm1LtzfLn1fo9ERESW83lRnqqRvrgdE6B/yyE2Tfaz\neaqfCx37iQVDzM7CwiI0hsAEIBaBUBjCwSibpvq50rKL/i2HsCagBb1lpOIEshLPAwljzJuAfwSC\nGR5eLUjINdgQEREpmo+L8lSNTIvbX9jaw/bRPhpjc2wf6+NC0x4WFtrAGoIBiMcALB1mgj0z/Uyu\n3cJg50Fe2Lo0t0wLestDxQlkJZ4GEonpTJ/DBRHKLIiISE3waVGeqpBpcTuhMN+82c0t6xrpZePY\nedbPxxg1ndiFBmx0kU1mhEYb5ErLLgY7D/Ktm+9f1oHcqwW98bgLRAYG3HqOcNiNwiuIdFScQFbi\ndUbiJ4AtLA8iMmUZVntcREREfCLz4vYWvnHrg9x08RidPzhOU3SQ9fFxAtEopiHIxbV7iW/r5sz1\nh3hha8+yICKpmAW9kci109piMTeS3t6uaW2pVJxAsvE6kPixlH8n/7z6gP2Jf1vg28AG4FVAIHFf\nDHgaZTFERER8J/vi9jADDfcx3HaYppGTbDeDdLbOE25tovnmbi5t2oc12Ye0C13QOz0NR4+6fRka\nWlpoHwq5bZ465aby9PfXUZnZFVIz4XBAxQkkI2Otd9fuxphe4PbEtxb4C2vt/2WMiSfvs9YGE8+9\nHvgk8NbEc78EvN1aW3eFwowxyz4ELz8TERGRapEtC3D1Kly86DILt98O27a5i9KVWAvPPusWYs7w\nCwAAIABJREFU9P7Gb+Q+tSkSgUcegSefhOHh3EbX77rLx2Vm80jNRAgri+MvRc8K8jqQuARsxO2Y\nBQ5Za5/KFEikvOZLwE8lnv931tqf92yHaoQCCRERqSfJwe/k4vZQCL7yFXjuOTeincuC3vFxNzLe\n0wMPP5z7XPzHH4dHH3WN1nKZ79/X5/bpyBEflpnNlppJTzN0dcGBA6+kZtI/PxUnqFlFBxJeT21K\nT/ydzuE1D+ECCQP8nDHmb6y1/5/H+yUiIiJVItPi9lAIJidLu6A3Hnej6UNDLhOxWpM1X5eZjURc\nELFSaqa7eyk1k9IBMBAOqziBAG6Ngpca076fTNwuJO8wxmxMe86ZxG1yGP4dHu+TiIiIVLmeHjfo\nvWWLywKMj7spRqmsdff39RW2oDc5ih6Pu2vmXKSXmfWNY8dcJmJ42EVu7e3XNokwxt2/f797XrID\noEiC1xmJOWBdhvuvAsn/svuBf055bGfKvw1wwON9EhERKY5qhJZcObqNDwy4QGTjxtwaq4F3ZWar\nilIz4hGvA4lRlgcSa4AocAVoTdz3u8aY71prp4wxYeDhtG1sRkSKo4seEW/UeY3Qch9KSt1tPBJx\nH99q183piikzW5W8SM34IqKSYnkdSFwEUpuhb8ZNbzoF3ICbvvQa4IIx5gVgF9DB8rKvEY/3SaR+\n1PlFj4in6rhGaCUPJaXsNh4Ou59hcTG/1xVaZrZqKTUjHvE6kDgJ/GjK97twC66fBt6UuM/gFmW/\nOuV5lqVKT9/3eJ9E6kMdX/SIeK6Ihai1HqRXy6GkFN3Gd+xwgdCpU+7jy+Ua2lo3pSqZDfEFpWbE\nI14HEr2J22SG4S7ga7geEf8l7TFD5gZ0/6/H+yTif3V80SM50nS3/KQvRM10wZW6ELWvb2khag3X\nCPX7oWTfPrf/Z864nyGXMrMTEy4bkcyG+IJSM+KRUgUSyUPOIQBr7WljzF8Db2MpeMgURJwC/szj\nfRLxvzq96JEcaLpb/up4IarfDyWBgPtz7+8vbZnZqqfUjHikFFOb/s+U71PXO7wb6CIRXCQkpzSB\nCyLeZK2d83ifRPytji96ZBXVMkel1tTpQtR6OZT09Lg/97k5d5tLZ+t8y8xWPaVmxCOeBhLW2kXg\n77I8NmuMuQcXaPw0bvF1GBgAvgo8aq3VQmuRfNXpRY+swu9zVEqpThei1suhpBxlZqueUjPiEa8z\nEiuy1lrgbxJfIuKFOr3okVX4fY5KKdXpQtR6OpSUusxsTVBqRjxQ1kBCREqgTi96ZAUZ5qhYC2Nj\nbrZTcolESwt0dICp1TkqpVKnC1Hr7VBSyjKzNUGpGfGAp4GEMSaW8q0FQtba+CqvMcBDqfdZaz/i\n5X6J+FqdXvTIClLmqMRa2rg45BIT0zMQjUDcQsBAKAwtzW6gcev1bQRrbY5KqVRwIWoli2vV66Gk\nFGVma4ZSM1IkrzMSOSZDlwkAv8XyKk4KJERypeobki4xR2WhbSP/ftIwMgIzM+5jb1oDwYALJiYn\nYGoSJidhdNRwS3snjbU2R6UUKrAQtRqKa+lQUqfqPjUjxSjF1KbUSkz5ytZbQkSyUfUNSReJEFuI\nMfhiiOE5mJ2F1lYIp01ZaWmGSNQFEosxaJlsYOe2KMFam6PitTIvRK2W4lo6lNS5uk7NSKGqYY1E\nNeyDSO1S9Q1JFw4zNhFkemKR2Rhs3JD9Yw6H3ONXRmF6fpGx5iCdtTpHxUtlWohaTcW1dCgRkXxV\nw0X8jkrvgEjNU/UNSRHv2sHF2XbWTJ+i9bpuAoGVk8SBALSut6x5eYSLs3vZsL2bur8mLNNC1Gor\nrqVDiYjko+BAwhjTxepBwCFjzEqLrTcCD6TdF8v0RBFZgapvSIqT7GPQdHODOUMbE8yx+hyVdiaI\nmSCDphvDPjS5gZIvRK3GBnA6lIhIPorJSPwSmRdFm5TbYzluK3VdxGQR+yRSv1R9QxIGhgI8u+YQ\nG5r76Zrq50LHfmLB7FepwViUTVP9DDXv4tk1hzAXAtx2exl3uJqVcCFqtTaA06FERHJV7NSm1RZV\n57roOrlA2wIvFLVHIvVM1TcEN+++t62HG2b6aJ2bY/tYH5fX72E2dO0clbXRCTZN9TO5dgtn1hyk\nt62HfXW+1jqjEixEreYGcDqUiEguvFgjkZpNSD8UFlKB6Z+K2BcRAVXfqHPhMMQbw/zjtgdonYau\nkV42Tp/H2BgzTZ3EAg0E44s0z49gTZArLbsY7DzIl1vuJ94Yrtl+ALWmFhrA6VAiIiuphsXWqQaB\nP630Tojko5INpEQyWeoH0MITtz/Iq146xp7h43TMDLIuMk5DPIo1QS617WWsuZv+LYf4wfU9DH0v\nrH4AZVSvDeBExD+8CCRWSsjmOrVpEfgK8AFr7VTxuyRSetXQQEokk9R+AFemw/x71308v/0wW8dO\n0jE9SGNsnoVgE2Mt3Vzs2Ic1AcbH1Q+g3NQATkRqXTGBxJeBgZTvDfCXLF/v8E4gW9UmC8wCl4AT\nCiCkllRLAymRTDL3Awjw4obbeHHDtXNU1A+gMtQATkRqXcGBhLX2BHAi9T5jzF+mPe0L1tqVyr+W\nhTFmG/Ax4DCwARjGBUIPWWvHC9zm24D/nvj2Xdbav/BiX6X6VVMDKZFs1A+g+qkBnIjUulKskch1\nOlNZGGN2A08Dm4DHcFWhXgO8HzhsjLnTWjua5za3A/8NmAGavd1jqXbV1kBKJBP1A6gNCvhEpJZ5\nHUjsTP2mGrIRuMXbm4D3WWuPJu80xnwS+FXg94B357oxY4wB/goYBf4B+L893VupatXYQEokG/UD\nqH4K+ESklhlrC6nQWhsS2YgzuLUcu1MDG2NMC26KkwE2WWuv5rjN9wN/BLweeAPwOxQ5tckYs+xD\n8PNnUutOnIBPfAJOn4YDB3JfHPnss+6i7Td+Q2UUpTKS1cXUD6A6qXiDiFRA0bOIqq38q9fuSdw+\nkZ4dsdZOG2OeAu4FXksOXbiNMa8CPgF82lp73Bjzhnx3yBjTm+9rpHpUcwMpkZWoH0B1UwM4EalF\nJQskjDGbgV/GjdzvBdqBXKpeW2utV/u1N3F7Osvj/bhA4kZWCSSMMQ24xdVDwIc92j+pMbXQQEpE\napcCPimUehpJJZQkkDDG/ArwCJBMwFZqAXZr4nYyy+PJ+9ty2NZHgNuBu6y1c4XukLX2QPp96VOb\npHqpgZSIiFQTTYuTSvI8kDDGvAP4k7S7c71QrqqKT0nGmB/BZSEesdZ+p9L741e1MJqiBlIiIlIt\n1NNIKs3TQMIY04xbiAyZgweTdr9Z4bleSGYcWrM8nrx/ItsGElOa/h/c9Kjf9m7XJKmWRlPUQEpq\nIuIVkarl1SFEPY2kGnidkXgL7uI8U7CQ/r1lqQt2qTIRpxK3N2Z5fE/iNtsaCnB9IpKvnzeZh6D/\n3Bjz57hF2B/Iey/rWK2NpqiBVB2rpYhXRKqO14cQ9TSSauB1IJHaIscAMeCrwE8m7rO4BcsbgB/F\nLcC2ief9PRD1eH++lbi91xgTyFD+9U5gFnhmhW1EgEezPPbDuHUTT+KCFk17ykOtjqaogVQdqrWI\nV0SqiteHEPU0kmrhdSBxG0tZBgv8obX2PxtjXrmAt9a+A8AY0wQ8BHwICALdwE/k22V6Jdbas8aY\nJ3CVmd4LHE15+CFgHfDZZA8JY0wjsBtYsNaeTWxjDnhnpu0bYz6KCyS+UEwfiXpVq6MpaiBVZ2o1\n4hWRqlCKQ0iyRHA87raVi7Y2d64aHHSvV2Uw8YLX8ejmtO//IdsTrbXz1tpfBz6HCzzuAP7W4/0B\neA9wGfhjY8yXjTEfN8Z8E9fV+jTwmynP3Qr8gBx6SkhxCh1NGRpyr4tXuGd6smPwkSMu07B3rzsp\nRKPudu9ed/+RI/DBD2pwuqalR7zt7deusk+NeIeHlyJeEal7pTiEeNHTSMQLXmck1qd9fzaH1zyC\n6zdhgDcYY37eWvs3Xu1QIitxEPgYcBi4D9fR+tPAQ9baca/eS3Lnh9EUNZCqA5o/ICJFKNUhpOI9\njVR0QhK8DiTS4+LpxG0UCIFrVGetvZTynJcSt8kF2m8DPAskAKy1F4BfyuF5A+Sx8Nta+1Hgo4Xu\nVz3zU4doNZDyMT9EvCJSMaU6hFSsp5GKTkgar8PG9EZtye1fTbnvjrTn/FDKvw1wi8f7JFUoOZrS\nkGco29DgXqcO0VIWmj8gIkUo1SEk2dNoZMQV98hFsqdR8no/b9PT8Mgj8OijLpg4dcptNBRyt6dO\nufsffdQ9b3p69W1KzfM6I3EFSJ0NvhZX9ehlXPdoA3zcGHPCWnveGLOZpb4TSZs83iepQuoQLTWh\n4vMHRKSWleoQUvaeRio6IVl4nZG4wPKpQVsSt6dYquS0FzhjjLkEXMRlKFLj6RmP90mqUEVGU0Ty\npYhXRIpQqkNIsqdRV5e7bo+uUjw/2dOoq6vAnkYqOiFZeB1IPJf2/Q2J2+Np9xugM/H+JuU+C5zw\neJ+kCiVHU4JBN4CRC3WIlrJTxCsiRch0CDE2zrbRE9w28BgHzn6R2wYeY9voCUyi1VWuh5CeHjhw\nwPUq6utzU6HSD1PWuvv7+oroaVTrZRalpLye2tSbuE3+Kd8NfAX4EvD7ifdb7Wz81x7vk1QhX3WI\nVvUK/yr7/AER8ZPUQ8jMaIQ7Zo+xZ/g4HTODrIuMY2wMa4JcDbcz1txN/5ZDfGdtD8FgeNVDSNl6\nGqnohKygVIFEMsvwOnBVk4wxfwJ8gJUDiWeAL3i8T1Klar5DtKpX+J+vIl4RKbfkIeTC96d57XeO\nckdjLxtnhzA2xkxTJ4uBEMH4IpsnTrFp8gwbx/thoQ9z8AEOHWpZ9RCS7GmUfiqKRt2paO9eD05F\nfiqzKJ7zOpD4PsurMqXOCvwQsBFX3jWT/wW8xVob83ifpErVdIfo6Wm38Ky316VvkzseCrkdP3XK\nDUH197so6YEH1JWuVtV8xCsildRzV4S1nzrKuoUnWTcxzEsb9rC4bvkxZLS5m4arE7SP9PPadXPs\ni8Addz0IrH7CK3lPIxWdkBV4GkhYay3wv7M8FgPeboz5DPAzuPUTYWAA+Kq19nEv90VqQ1lGU7ym\n6hX1paYjXhGptPCTx7izqZfRxmGe79zP5GwIOwdNayBgIG5hfs5gTDtznfu5eaGPDeFeGp885iKE\nHJWsp5GKTsgKvM5IrMpa+x3gO+V+X6leNdchOr16RaZRmtTqFX19S9Ur8jgpSBWpyYhXRCousVC5\ncXiIzh/dw56rIYaHYXoGohGIxV0w0doGLc2wZUuIzrV7CA6t0tq6nJIrxk+dcse5XKY3JVeMJ4+N\n4ltlDyREsqmJDtGFVq84X0UnBSlMzUW8IlJxKQuVgx1tdG2A7dthbMwFE7FFCDa4IKKjI3GNbtvg\nfBUtVFbRCVlBSQMJY8xG3LqINmACGLHWjpbyPUVKStUrpCYiXhGpChkWKhsDGza4r4yqbaGyik7I\nCjz/dI0xh4wxjxpjLgCXgOeBpxK3l40xQ4nHX+f1e4uUnBfVK0REpD4kFyo35Dlu29DgXlctC5XL\n1rRCao1nGQljzA7gz4A3Ju/K8tRtwDuAdxhjvgH8irX2vFf7IVJSql4hIiK58stCZRWdkCw8CSSM\nMa8FvozrVp0MIFbqF5F8zr3AM8aYn7DWPuPFvoiUVOKkYBcWGRt1VWCTrSNaWlLmuKartpOCiIiU\nnp8WKqvohGRQdCBhjNkPfANYl7grNYDI9D/GpjzH4IKPbxhj7rTWPlfs/oh4IVuz6r3X7WBsrh37\nwil+0NxNNGqIW1d1IxROVt2ArVvdcRWo3pOCiIiUlt8WKqvohKQpKpAwxoSBv8MFEanBQfLfq2Ul\nko+vA75ojLnNWhspZp9EirFSs+rmZrhyeR9HznXzwzNniEcmsC3tBAOuDvjkBExNwuQkjI7CzbdA\nqJHqPimIiEjp+HWhsopOSEKxGYn3AXtYHjCkBhTZpGYlkvYktvcHRe6TSEFWalYdjcLTT8PVqwG+\nsniI6xr62Rvs58U1+4kF3UmhpRkiURdILCb6s996U5RgLZwURESkNHp63ALkuTl3m6mJqbVLTUy1\nUFlqSMGBhDHGAO/n2oDAAC/gFl7/CzAETAGtwA7g9cC7cZ2tUzMXBviAMeYPEx2yRcpmtWbVQ0Mu\nozs3B98O9XDQ9rE2Nse20T5GWvcwG3JPDodg4wa4csUye3GCmdF+WvfqpCA+km3en6Y0iGSmhcri\nY6bQa3ZjzF3AcZZnIGLAR4BPrBQMGGMCwEeB30y9O7Gte6y1xwvaqRpljFn2u1IcVX6PPw6PPgrn\nzl2bebYWvvtduHjRrTVrbITIlWneGz/KHaFetsWHMDbGTFMnsUADwfgia66OMBcNEt/Wxc2/eJDA\nA/e7F4vUqpXm/bW3a5GlyGr0f0iqT4517LMrZmrT3Wk7YoGPWms/vtoLrbVx4CMuqcFvsTyrkQxQ\nRMpitWbVY2MwM+MCilDIZSmCbS18avJBBtcd403rj7NhZpB1kXEa4lGsCXKlYy/Pz3Rz+bpD2Df2\ncGuLTgpSw1aa97e46CrSnDnjpmX09bnRVwXOdUEJqjxoobL4UDGBxC1p35+11v5entv4KPDzwM4V\ntitSUqs1q56edifIpqalqU6hEEwS5muB+7i0+zC3mpN0TA/SGJtnIdjEWEs3T025k8KrhuHW8v5I\nIt5Zbd4fuIug5PzuuTl334MPalTVxzS4XgQtVBYfKSaQSF78J7MRn8t3A9bauDHmc8AnWMpKqD6m\nlNVqzapjMZeNSB8oWrPGnUynrwZ4sfs2Xtyw/KQQnFMPOvGBY8dcJmJ4OHvFGWPc1eP+/S4j0dvr\nXnfffeXfXyk5JahEJKmYQKKTpUXSUPh0pH9J+bcBNhWxTyJ5W61ZdTDorpPi8eX3J+/L1rBUPeik\n5q027y9dKOSed/68e93hw5qq4TOeJag0J0rEF4oJJNIngQwUuJ1zad/n0K1FxDuJZtVZA4KWFvec\niQnXSyJ5wrTW/bshw/8i9aATX1ht3l8mbW0uMh8cdK/X9A1fKTpBpTlRIr5STNi/Nu378QK3M7HK\ndkVKascOd/4aGXEBQLqOjqUAIhpdun9uzp3nmpuvfY160IkvrDbvLxNj3DyX8XF3oSi+UWiCamjI\nvS4+OQ2PPOJK5B075uZAJatYWOu+P3bMPf7II24OlYhUtWIyEo1p38cK3E7ahJGim+SJ5GXfPnfB\nf+aMCwDa03Jixrj+QJOTMDXlAotYzN3f3Oy+T1UrjUlFVrXavL9sGhq0QMiHiklQXTwX4dJvHWXL\nWS3aF/GTYi7aG1hetvWQMSY9KMhFcJXvRUoqEHAX/P397itTun7rVhgddSfE5G1bmwswUqc6qTGp\n+Mpq8/6y0QIhXyomQbXj7DHshV6Y16J9ET/xavTfAMc82pZI2fX0uPPW3Jy7TR8sCwbhh37IPT41\n5YKGaBQWFuDFF9WYVPJTM+tMk/P+Tp1yo8W5XD1qgZBvFZqgagzGuXn0OE3BITigRftSgJo5aNYf\nL6cRFd0dT2RFJTyQhMOuRCG4QbDz55dKGjY0LAUKoRDcfLO7r7PTNaqLRl0Akbxu0jpByabm1pmu\nNu8vEy0Q8q1CE1TbJ05yXWSQwFot2pc81dxBs/54GUhkWKaaMwUhkl2ZDiQtLW46bvpbZQoU7rkH\nTp9WY1LJXU3W3s9l3l8qLRDytUITVE0vD9DOOIHNRSzaVyBRf1IOmnZwiLmrMaabOomZEEG7SMvg\nKdb0n8FU1UGz/ngRSBQTQHi5DfGjMl99hcNuOu7hw0sLC7MFClkbkyoFK2lqujn0avP+QAuE6kSh\nCaoNJsLacIyWdi3alxwlDpqx408y0z/MQOMeRhbaiM4Y4hYCBkKhbjrtBDv6+mm+OucW2FbFQbO+\neBFIKJsgpVHBq69AYIVAYaX9VQpWMqjp5tC5zvvTAiHfKzRB9cObwrRFgxgt2pdcHTvGwjO9jD43\nzPON+5mcCrns1hoIBiBuYXLSMGXaubJ2Pzc/18eGUC+NVXHQrC/FBBLHUSZBSqmWrr5qct6KlIMv\nmkPnM+9PgbKvFZKg6rxhBx0vt8MZLdqXHMTjLH7rOCO9Q/TbPYxfDdHaCuG0Y2dLM0SiMD4Z4nTj\nHm7oPc+mbx2noSoOmvWj4EDCWvt6D/dDZLlauvqq6XkrUmq+aQ6dz7w/8a1CElRvfc8+gh/vhvNa\ntC85OHmSy98dZO5qnJFgGxs3Zj+0hEOwcQNcvtLG1liMy98d5PqqOWjWBzV/k+pUS1dftZQ5kbLz\nojl0VZ0TC5r3J36Sf4JKi/Yld/FzA0xfGGcsvpHWDWbVjz8QgNY2w+WRTjoujBM/P0hAx6eyUSAh\n1alWrr5qKXMiFaHm0OJHeSeotGhfcjTUHyE6G2PRhK6ZzpRNOASLNBCdjTJ0ep4dJd1DSaVAQqpT\nrVx91VLmRCpCzaHFz3JOUGnRvuTo0kSY4GKQNY2LzObxujWhRSKLQWYnmxRIlJECCalOtXL1VSuZ\nE6kYNYcWSaizRfuqBF6YibYdNDa00zV3ilmb+0GzbWGEoTV7WWjVQbOcFEhIdaqVq69ayZxIxag5\ntEiKOli0r0rgxZnfs4+Jtd1snTvDmugEc+HVD5proxPECDKytps1N+qgWU4KJKQ61crVV61kTqRi\n1BxaJAOfLtpXJfDi7dgV4GvbD7FxrJ89U/1c6NhPLJj9oBmMRdk01U+/2cXA9kMc3qmDZjkpkJDq\nVCtXX7WSOZGK0jpTEf/zqhJ4vU+J2rcPvvjqHl4420d7bI7tY31cXr+H2dC1B8210Qk2TfVzpXEL\nLzQdZOrVPcrilpkCCaletXD1VSuZE6korTMV8b9iK4FrSpQTCMCdbwjz16cfIP4s3LGul43T5zE2\nxkxTJ7FAA8H4Is3zI1gT5PK6XXxn4SDP/PD9/Kc3hOsi2KomCiSketXC1VeGzIltDDE25lLcyZNA\nSwt0dIBZ0LyVelVn60xF6kqxlcDvvBP+5E80JSrJjSO28I3Ig5w+c4yeDce5fmGQddFxGuJRrAly\nqXUvLzV2c2zhEIM39XDHHWFlcSvAWGsrvQ91zxiz7EPQZ5Km2odpIhF45BFix59kpn+YwcY9XF5o\nIxo1xC0EDIRClk2NE3Qv9NO8ZwvB190NH/ygrhahLvP4yR/Zh+tMRerSiRPwiU/A6dNw4EDus1yf\nfRZuuAE2b4azZ7NPiUpPvt9117VTovwmdb3JhcE4O2dOctOaQZrMPPO2iRfmujnfvI/t3YFXxhH9\nHFyVSI7lJlfYgC5aK0+BRI6q+Opr+qVpet9xlPDzvbRODGFsjKtrO4kHGgjEF1k3O0LcBJlq62L+\nloMc/Kv7abm+zo941R4giojk6LHH4DOfcRf8O3bk/rqBAbhyxWUe5udzWw7Y1+eS2keOuClRfqbT\nRMlVLpAwxtxurf1esTsgCiSKVokR7ZT3XJiJ8OX/Gebb566Hly/xhtCTr6RgjY1hTZCrofalFOwN\nPbz2dWHfjyatKFtpk/Qpa11dbnjP73l8EalpX/wi/PmfuyBg27bcX3fhAnz/++5wd+BAbsvsxsfd\nlKieHnj44YqPo5VFFY8j1rqiA4li1kg8Y4z5OPBfrLV51r4U8UAlhioyvOfEpRg3vBSkJdpObFs3\n57fexffX/Ayts8M0xuZZCDYx1tLNxY59RBYCXOiDxpQFdnXHq9ImIiJVotBK4OPj7pC4dq07DOai\nrc2d6gYH3cV1RSrolnkAz6fVgn2hmECiEfht4CeMMe+w1p7waJ9EVleJYt0Z3tNu7OTKVIj5uUVu\nDJ4i8PIZtsz0M9R5gG/e/ACR0PL3TF9gd/hwHY6mFFvaRESkyhRaCfzyZffvzZtzew2453V2uiBk\ncLDMF9eaayRpvKjadBvwXWPMw7jsRMyDbYpkV4kR7SzvOTZmuGhgMgwLG7pZE51g81Q/jTH3nt+4\n9UEWg8vfsypGkyql2NImdRl5iUi1K7QSOLjTUq7ZiKSGBrdeYn4+/30tmLrtSQZenJEtLjvxEeBf\njTG3erBNkezSR7Tb268dykkd0R4eXhrR9vg9p6chGkk0qDaGuXA7Fzr20zo7TNdILzddvPY900eT\n6kpykms8XngeX0SkyiQrgXd1uevoaHTl5yd7qG7aBBs2uENcPhYXXRKgqanwfc5L6mDauXOwc6cr\nub5jh1sUsmOH+37nTvf4k0+650ciZdpBqRSvhvYsbsHGflww8RFjTNCjbYssKXREe2jIvS4e9/Q9\nYzFeKfH6yn3BEJfX76FjZog9w8cx9tr3bGhwry3raFI1GBhwEdTGjYXn8UVEqlBPj1swvWWLG5Af\nH3fTl1JZ6+7v63PPe/WrYfduV18i1zor1rrnJ2cSlUUlBvCkJng5RyD5X6AR+B3cdCe17RVvVWJE\ne4X3DAZdEBFPOwHMhtowNkbHzCBbx659z7KPJlWLSMR9Fg15zqqs28hLRGpFsofqXXe58qznz7s+\nEQMD8OKL7vbZZ939u3bB3XfD7/6u+3cwuDTVaTUTE+75yapFJVeJATypGcUEEr8CTLO8dJRlKTtx\nOy478dvKTohnKjGivcJ7trRAKAzzc9e+50xTJ+si43RML3/PiowmVYsMpU2shdFR92s+e9bdjo6m\njc7VbeQlIrUk2cH+yBGXodi71502olF3u3evu//IEdeTtLW1sClRXV3udWVZMqYpqbKCghdbW2s/\na4z5KvAZ4MdZykjAUjARAj4K/GSispP+mqQ4yRHt1UZE0hWzMm2F9+zogJZmmJqESBTCKU+JBRpo\niEdpjC1/z7KPJlWTlNImsW3dXHzJMDwM0zNurckrncDD7ve6ZQtsvd4SHBlxZ+C6i7xEpNaEw67A\n3OHDufU+6OlxU53m5txtLp2tDx50rysLLwbw6qqqSH0pqmqTtfYlXPnXnwM+DWxiKaByJ8w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LtctsnnsRhcvOiORTMz7nnWuh8+HHb/Xr/eBRheK+Mv3pdjN+UucVYGdRPYS0EUSIhAdS14FBG/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\n", 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\n", 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" ] }, - "execution_count": 15, + "execution_count": 9, "metadata": { "image/png": { "height": 287, - "width": 393 + "width": 391 } }, "output_type": "execute_result" @@ -426,16 +447,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "
\n", - "As well as the official documentation, another useful tutorial is available\n", - "here.\n", - "
" + "### Conclusion\n", + "\n", + "This is only a brief introduction to the main concepts of matplotlib, that we will use throughout the rest of these materials. For much more in depth explanations and examples, visit the official documentation. " ] } ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -449,7 +469,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/10-Distributions.ipynb b/10-Distributions.ipynb index d4ec1eb..692f1c7 100644 --- a/10-Distributions.ipynb +++ b/10-Distributions.ipynb @@ -26,9 +26,7 @@ { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", @@ -41,7 +39,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Probability Distributions\n", + "## Probability Distributions\n", "\n", "Typically, given a data source, we want to think about and check what kind of probability distribution our data sample appears to follow. More specifically, we are trying to infer the probability distribution that the data generator follows, asking the question: what function could it be replaced by?\n", "\n", @@ -49,7 +47,7 @@ "\n", "Informally, we can start by visualizing our data, and seeing what 'shape' it takes, and which distribution it appears to follow. More formally, we can statistically test whether a sample of data follows a particular distribution.\n", "\n", - "Here we will start be visualizing some of the most common distributions. Scipy (scipy.stats) has a series of code and functions for working with, and generating different distributions - all with a consistent API. We will generate synthetic data from different underlying distributions, and do a quick survey of how they look, plotting histograms of the generated data. \n", + "Here we will start be visualizing some of the most common distributions. `Scipy` (scipy.stats) has code for working with, and generating different distributions. We will generate synthetic data from different underlying distributions, and do a quick survey of how they look, plotting histograms of the generated data. \n", "\n", "You can use this notebook to explore different parameters to get a feel for these distributions. For further exploration, explore plotting the probability density functions of each distribution. " ] @@ -58,7 +56,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Uniform Distribution" + "### Uniform Distribution" ] }, { @@ -78,9 +76,7 @@ { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from scipy.stats import uniform" @@ -89,12 +85,10 @@ { "cell_type": "code", "execution_count": 3, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "dat = uniform.rvs(size=10000)" + "data = uniform.rvs(size=10000)" ] }, { @@ -104,24 +98,26 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "plt.hist(dat);" + "plt.hist(data);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Normal Distribution" + "### Normal Distribution" ] }, { @@ -141,9 +137,7 @@ { "cell_type": "code", "execution_count": 5, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from scipy.stats import norm" @@ -152,12 +146,10 @@ { "cell_type": "code", "execution_count": 6, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "dat = norm.rvs(size=10000)" + "data = norm.rvs(size=10000)" ] }, { @@ -167,24 +159,26 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "plt.hist(dat, bins=20);" + "plt.hist(data, bins=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Bernouilli Distribution" + "### Bernouilli Distribution" ] }, { @@ -192,7 +186,7 @@ "metadata": {}, "source": [ "
\n", - "A Bernouilli Distribution is a binary distribution - it takes only two values (0 or 1), with some probably 'p'. \n", + "The Bernouilli Distribution is a binary distribution - it takes only two values (0 or 1), with some probably 'p'. \n", "
\n", "\n", "
\n", @@ -204,9 +198,7 @@ { "cell_type": "code", "execution_count": 8, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from scipy.stats import bernoulli" @@ -215,12 +207,10 @@ { "cell_type": "code", "execution_count": 9, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "r = bernoulli.rvs(0.5, size=1000)" + "data = bernoulli.rvs(0.5, size=1000)" ] }, { @@ -230,24 +220,26 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "plt.hist(r);" + "plt.hist(data);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Gamma Distribution" + "### Gamma Distribution" ] }, { @@ -271,9 +263,7 @@ { "cell_type": "code", "execution_count": 11, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from scipy.stats import gamma" @@ -282,12 +272,10 @@ { "cell_type": "code", "execution_count": 12, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "dat = gamma.rvs(a=1, size=100000)" + "data = gamma.rvs(a=1, size=100000)" ] }, { @@ -297,24 +285,26 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "plt.hist(dat, 50);" + "plt.hist(data, 50);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Beta Distribution " + "### Beta Distribution " ] }, { @@ -334,9 +324,7 @@ { "cell_type": "code", "execution_count": 14, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from scipy.stats import beta" @@ -345,12 +333,10 @@ { "cell_type": "code", "execution_count": 15, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "dat = beta.rvs(1, 1, size=1000)" + "data = beta.rvs(1, 1, size=1000)" ] }, { @@ -360,24 +346,26 @@ "outputs": [ { "data": { - "image/png": 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "plt.hist(dat, 50);" + "plt.hist(data, 50);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Poisson Distribution" + "### Poisson Distribution" ] }, { @@ -397,9 +385,7 @@ { "cell_type": "code", "execution_count": 17, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from scipy.stats import poisson" @@ -408,12 +394,10 @@ { "cell_type": "code", "execution_count": 18, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "dat = poisson.rvs(mu=1, size=100000)" + "data = poisson.rvs(mu=1, size=100000)" ] }, { @@ -423,23 +407,25 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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"text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "plt.hist(dat);" + "plt.hist(data);" ] } ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -453,7 +439,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/11-TestingDistributions.ipynb b/11-TestingDistributions.ipynb index 4d07f81..bacb9f7 100644 --- a/11-TestingDistributions.ipynb +++ b/11-TestingDistributions.ipynb @@ -4,7 +4,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Testing Distributions " + "# Testing Distributions \n", + "\n", + "Knowing what distribution your data follow is important for knowing which statistical tests to apply to it. If you are using statistical tests that assume data to have a particular distribution, you need to test whether this is indeed the case.\n", + "\n", + "As we saw previously, different statistical distributions have different 'shapes'. But just looking at the shape isn't enough for saying definitively what distribution the data follows. Here, we will explore some statistical tests for checking the distribution of data. " ] }, { @@ -12,23 +16,14 @@ "metadata": {}, "source": [ "
\n", - "Sometimes it may be useful (or necessary) to formally test whether some data you observe follows a particular distribution.\n", + "By 'testing distributions' we mean statistical tests that evaluate whether observed data follow a particular distribution.\n", "
" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Perhaps most commonly, if you are using statistical tests that assume data to have a particular distribution, you need to test whether this is indeed the case. " - ] - }, { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Imports\n", @@ -44,9 +39,7 @@ { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Set up a helper function for checking p-values against an alpha level, and printing result\n", @@ -58,6 +51,13 @@ " print('We do not have evidence to reject the null hypothesis.')" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Evaluating a Normal Distribution" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -68,9 +68,7 @@ { "cell_type": "code", "execution_count": 3, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Create a dataset of normally distributed data\n", @@ -84,12 +82,14 @@ "outputs": [ { "data": { - "image/png": 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0B/oBT4pI27oL3zQ2s9eHl1jmEs9yFyOJT2W6blrSNxWI5k6/H5ClqptUtRiY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\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -99,32 +99,33 @@ "xs = np.arange(d1.min(), d1.max(), 0.1)\n", "fit = stats.norm.pdf(xs, np.mean(d1), np.std(d1))\n", "plt.plot(xs, fit, label='Normal Dist.', lw=3)\n", - "plt.hist(d1, 50, normed=True, label='Actual Data');\n", + "plt.hist(d1, 50, density=True, label='Actual Data');\n", "plt.legend();" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot above shows a histogram (in orange) of 'observed' data, and the expected distribution of the data, under the assumption of it being normally distributed. There seems to be a pretty good alignment! Now, let's asses this statistically. \n", + "\n", + "To do so, we will use the `normaltest` function, from scipy, which tests whether a sample of data differs from a what would be expected under a normal distribution. The null hypothesis is that the data come from a normal distribution. We can use `normaltest` to check this null, and to decide whether we should reject the null (to claim the data are not normal), or accept it. To assess this, the `normaltest` function compares the skew and kurtosis of the observed data to what would be expected if it's normally distributed. " + ] + }, { "cell_type": "code", "execution_count": 5, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "# In scipy, the 'normaltest' function tests whether a sample differs from a normal distribution\n", - "# The null hypothesis is that the data are normally distributed.\n", - "# We can use normaltest to check this null - do we have to reject the null (to claim the data are not normal).\n", - "# It does using a combined statistics comparing the skew and kurtosis of the observed\n", - "# data, as compared to as expected under a normal distribution. \n", + "# Check the documentation for normaltest\n", "normaltest?" ] }, { "cell_type": "code", "execution_count": 6, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Run normal test on the data\n", @@ -141,7 +142,7 @@ "output_type": "stream", "text": [ "\n", - "Normaltest p value is: 1.34e-01 \n", + "Normaltest p-value is: 0.49 \n", "\n", "We do not have evidence to reject the null hypothesis.\n" ] @@ -149,7 +150,7 @@ ], "source": [ "# Check the p-value of the normaltest\n", - "print('\\nNormaltest p value is: {:1.2e} \\n'.format(p_val))\n", + "print('\\nNormaltest p-value is: {:1.2f} \\n'.format(p_val))\n", "\n", "# With alpha value of 0.05, how should we proceed\n", "check_p_val(p_val, alpha=0.05)" @@ -159,23 +160,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Different Distributions\n", + "In this case, we do not reject the null, meaning we do not reject that this data is normally distributed. \n", "\n", - "Visually inspecting datasets can give you a quick sense about whether they are normally distributed or not. \n", + "This statistical test is therefore consistent with the data being normally distributed. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Testing a non-Normal distribution\n", + "\n", + "Let's test another dataset for normality.\n", "\n", - "However, visual inspection is not enough, and can be misleading, since non-normally data can 'look normal'.\n", + "For this example, we will explore case when visual inspection can be misleading, to emphasize the point that although visually inspecting datasets can give you a quick sense about whether they are normally distributed or not, this is not enough. Visual inspection can be somewhat misleading, since non-normally data can 'look normal'.\n", "\n", - "As well as visualling checking data when it looks pretty normal, it is important to perform other checks.\n", + "This is why, as well as visually checking data when it looks pretty normal, it is important to perform other checks.\n", "\n", - "For example, under some paramters, the Beta distributed data can look like it is normally distibruted. " + "For example, under some parameters, the Beta distributed data can look like it is normally distributed. " ] }, { "cell_type": "code", "execution_count": 8, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Generate some data from a beta distribution\n", @@ -189,18 +197,20 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# Plot a histogram of the observed data\n", - "plt.hist(d2, 50, normed=True, label='Actual Data');\n", + "plt.hist(d2, 50, density=True, color='C1', label='Actual Data');\n", "plt.legend();" ] }, @@ -220,12 +230,14 @@ "outputs": [ { "data": { - "image/png": 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YX2etZGz8KzbHdG7SGjp2GfN9td5v69SIV+/qWNFR2U5L/oaHiyn5W+KwjIgkisgyEVkt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\n3JVSKgr9P54WV+HHwqonAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -235,19 +247,25 @@ "xs = np.arange(d2.min(), d2.max(), 0.01)\n", "fit = stats.norm.pdf(xs, np.mean(d2), np.std(d2))\n", "plt.plot(xs, fit, label='Normal Dist.', lw=3)\n", - "plt.hist(d2, 50, normed=True, label='Actual Data');\n", - "plt.legend();\n", + "plt.hist(d2, 50, density=True, label='Actual Data');\n", + "plt.legend();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the above plot, we can see _some_ difference from the expected normal distribution. \n", + "\n", + "Overall, though, we might think it looks pretty normal, especially if examined without adding the probability density function. \n", "\n", - "# Note that we can see *some* differences, when plotting the PDF\n", - "# However, if you turn off the PDF plot, we might guess these data look pretty normal" + "Let's check this statistically. " ] }, { "cell_type": "code", "execution_count": 11, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Run normal test on the data\n", @@ -264,7 +282,7 @@ "output_type": "stream", "text": [ "\n", - "Normaltest p value is: 2.17e-184 \n", + "Normaltest p-value is: 1.05e-170 \n", "\n", "We have evidence to reject the null hypothesis.\n" ] @@ -272,7 +290,7 @@ ], "source": [ "# Check the p-value of the normaltest\n", - "print('\\nNormaltest p value is: {:1.2e} \\n'.format(p_val))\n", + "print('\\nNormaltest p-value is: {:1.2e} \\n'.format(p_val))\n", "\n", "# With alpha value of 0.05, how should we proceed\n", "check_p_val(p_val, alpha=0.05)" @@ -282,11 +300,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Non-Normal Data\n", - "\n", "In this example, the plot is ambiguous, but 'normaltest' suggests these data are actually very unlikely to come from a normal distribution. \n", "\n", - "In this case, we happen to know that this is indeed true, as the 'ground truth' of the data is that they were generated from a beta distribution.\n", + "We happen to know that this is indeed true, as the 'ground truth' of the data is that they were generated from a beta distribution.\n", "\n", "Therefore, using this data in statistical tests that expect normally distributed inputs is invalid, since we have violated the assumptions upon which these tests are based. We will have to use different methods to perform statistical comparisons with these data." ] @@ -295,19 +311,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Testing other distributions\n", + "## Evaluating Different Distributions\n", + "\n", + "So far we have examined checking whether a dataset is normally distributed.\n", "\n", - "More generally, you can use the Kolmogorov-Smirnov test to check if a set of data has some other distribution (that you specificy). \n", + "More generally, you can use the Kolmogorov-Smirnov test to check if a set of data has some other distribution (that you specify). \n", "\n", - "This test is implemented in scipy, and you can explore using it. " + "This test is implemented in `scipy`, and you can explore using it. " ] }, { "cell_type": "code", "execution_count": 13, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "from scipy.stats import kstest" @@ -316,9 +332,7 @@ { "cell_type": "code", "execution_count": 14, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Check out the documentation for kstest\n", @@ -329,11 +343,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The kstest has a similar form to the normaltest, in this case we are comparing a sample of data, to a specified distribution. \n", + "The `kstest` has a similar form to the `normaltest`, in that we can compare a sample of data to a specified distribution. \n", "\n", "The null hypothesis is that the data comes from the specified distribution. \n", "\n", - "If we reject the null, with some preset alpha value, we can conclude that the data do not conform to the tested distribution." + "If we reject the null, we can conclude that the data do not conform to the tested distribution." ] }, { @@ -370,7 +384,7 @@ "output_type": "stream", "text": [ "Statistic: \t0.00 \n", - "P-Value: \t1.69e-01\n", + "P-Value: \t6.00e-01\n", "\n", "We do not have evidence to reject the null hypothesis.\n" ] @@ -378,16 +392,24 @@ ], "source": [ "# Now compare the data to the beta distribution.\n", - "# Note that in this case, we have to specify some parameters for the beta distribution we are testing against\n", + "# Note that in this case, we have to specify some parameters for the beta \n", + "# distribution we are testing against, so we will use the simulation parameters\n", "stat, p_val = kstest(d2, 'beta', [7, 10])\n", "print('Statistic: \\t{:1.2f} \\nP-Value: \\t{:1.2e}\\n'.format(stat, p_val))\n", "check_p_val(p_val, alpha=0.05)" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this case, the data sample is consistent with being from a beta distribution!" + ] } ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -401,7 +423,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/13-OrdinaryLeastSquares.ipynb b/13-OrdinaryLeastSquares.ipynb index 32c3877..5b4e6bd 100644 --- a/13-OrdinaryLeastSquares.ipynb +++ b/13-OrdinaryLeastSquares.ipynb @@ -4,7 +4,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Ordinary Least Squares" + "# Ordinary Least Squares\n", + "\n", + "If you recall, in an early notebook, we introduced the notion of fitting a line, or a linear model, to some data. We can then use the definition of that line to predict new data points. However, what we didn't dig into at that point was how we learn and evaluate our linear model, and how to learn the best model.\n", + "\n", + "To do so, we need a way to measure how good our model is, or an error measurement, that we can use to evaluate our model. Together with a procedure to update models, we can try and learn models that minimize error - that is to say, models that best fit the data. \n", + "\n", + "Ordinary least squares is on such approach for learning and evaluating models. OLS seeks to minimize the sum squared errors. Squared errors are calculated as the square of the difference between the model prediction of a data point, and the data point itself. One way to think about this is as an error function - OLS defines how we will calculate the error of a model, given the data. The model with the lowest error, defined in terms of OLS, is the best model. When we talk about fitting a model with OLS, we mean finding the solution that has the lowest OLS error - the lowest value for the sum of squared errors." ] }, { @@ -30,37 +36,34 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Ordinary Least Squares\n", - "\n", - "Ordinary least squares can be thought of as an error function - a formalization of how we will calculate the error of a model, given the data. \n", - "\n", - "Typically, we want to minimize this error term. So the OLS solution to, for example, a linear model, is the model which has the lowest value for the sum of squared errors, calculated as the square of the difference between the model prediction of a data point, and the data point itself.\n", + "For this example, we will create a minimal dataset, and explore fitting a simple linear model fit to it, using OLS.\n", "\n", - "Here, we'll create a minimal dataset, and explore fitting a simple linear model fit to it, using OLS." + "In this case, we will be using `numpy` for measuring least squares. Note that for real datasets, this is unlikely to be how you apply models, since it will usually be more practical to use `scikit-learn` or `statsmodels` to manage all the components of model fitting full datasets, but the underlying math is all the same. " ] }, { "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, + "execution_count": 62, + "metadata": {}, "outputs": [], "source": [ - "# Imports\n", "%matplotlib inline\n", "\n", - "import random\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Simulate Data" + ] + }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, + "execution_count": 49, + "metadata": {}, "outputs": [], "source": [ "# Create some data\n", @@ -73,52 +76,62 @@ "y = true_rel * x\n", "\n", "# Add some noise to the y dimension\n", - "noise = np.random.normal(0, 0.5, len(x))\n", + "noise = np.random.normal(0, 1, len(x))\n", "y = y + noise" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 50, "metadata": {}, "outputs": [ { "data": { - "image/png": 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"text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# Plot the data\n", - "f = plt.figure()\n", - "plt.plot(x, y, '.');" + "plt.plot(x, y, '.', ms=12);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Observing the data above, we can see that there is some relation between the x and y dimension, but we want a way to measure what that relation is. OLS is a procedure to do so: find the model (in this case, line) that minimizes the squared distances between each observed data point and the model prediction. " + "Observing the data above, we can see that there is some relation between the x and y dimension. \n", + "\n", + "We would like to measure what that relation is. That's where OLS comes in. \n", + "\n", + "OLS is a procedure to find the model (in this case, line) that minimizes the squared distances between each observed data point and the model prediction. " ] }, { "cell_type": "code", - "execution_count": 4, - "metadata": { - "collapsed": true - }, + "execution_count": 51, + "metadata": {}, "outputs": [], "source": [ - "# Reshape data to play nice with numpy\n", + "# Reshape that data to play nice with numpy\n", "x = np.reshape(x, [len(x), 1])\n", "y = np.reshape(y, [len(y), 1])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Fit an OLS Model" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -127,20 +140,22 @@ "\n", "$$y = \\theta x $$\n", "\n", - "Note that we are not fitting an intercept here (no 'b' value, if you think of 'y = ax + b'). In this simple model, we are therefore implicitly assuming an intercept value of zero. You can fit intercepts (and linear models with more parameters) with OLS, you just need to add them in. " + "Note that we are not fitting an intercept here (no 'b' value, if you think of 'y = ax + b'). \n", + "\n", + "In this simple model, we are therefore implicitly assuming an intercept value of zero. \n", + "\n", + "You can fit intercepts (and linear models with more parameters) with OLS, you just need to add them in. " ] }, { "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": true - }, + "execution_count": 77, + "metadata": {}, "outputs": [], "source": [ "# Fit the (Ordinary) Least Squares best fit line using numpy\n", - "# This gives us a fit value (theta), and residuals (how much error we have in this fit)\n", - "theta, residuals, _, _ = np.linalg.lstsq(x, y)\n", + "# This gives us a fit value (theta), and residuals (how much error we have in this fit)\n", + "theta, residuals, _, _ = np.linalg.lstsq(x, y, rcond=None)\n", "\n", "# Pull out theta value from array\n", "theta = theta[0][0]" @@ -148,76 +163,82 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 78, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "1.98695402961\n" + "Estimated theta value is: 2.1194\n" ] } ], "source": [ "# Check what the OLS derived solution for theta is:\n", - "print(theta)" + "print('Estimated theta value is: {:1.4f}'.format(theta))" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 79, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The true relationship between y & x is: \t 2\n", - "OLS calculated relationship between y & x is: \t 1.98695402961\n" + "The true relationship between y & x is: \t2.0000\n", + "OLS calculated relationship between y & x is: \t2.1194\n" ] } ], "source": [ "# Check how good our OLS solution is\n", - "print('The true relationship between y & x is: \\t', true_rel)\n", - "print('OLS calculated relationship between y & x is: \\t', theta)" + "print('The true relationship between y & x is: \\t{:1.4f}'.format(true_rel))\n", + "print('OLS calculated relationship between y & x is: \\t{:1.4f}'.format(theta))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks good! The absolute error between the true value, and our estimate is quite small!" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 80, "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "1.3701226131131277" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" + "name": "stdout", + "output_type": "stream", + "text": [ + "The residuals for the model fit are: \t3.2984\n" + ] } ], "source": [ - "# Check what the residuals are\n", - "residuals[0]" + "# Check what the residuals are. Residuals are the error of the model fit\n", + "print('The residuals for the model fit are: \\t{:1.4f}'.format(residuals[0]))" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 81, "metadata": {}, "outputs": [ { "data": { - "image/png": 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OWWv30icyRKEuco4U6F4u/aiTPXPf4pL9T+JjCjl25dP4X3F3jfb1PH3OvE9k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\nLiLiIRToIiIe4v8BgwXYOv/rlLgAAAAASUVORK5CYII=\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -225,21 +246,28 @@ "# Plot the raw data, with the true underlying relationship, and the OLS fit\n", "fig, ax = plt.subplots(1)\n", "ax.plot(x, y, 'x', markersize=10, label='Data')\n", - "ax.plot(x, 2*x, '--b', alpha=0.4, label='OLS Fit')\n", - "ax.plot(x, theta*x, label='True Fit')\n", + "ax.plot(x, 2*x, '--b', alpha=0.4, label='OLS Model Fit')\n", + "ax.plot(x, theta*x, label='True Relationship')\n", "ax.legend();" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Predict New Data" + ] + }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 82, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The prediction for a new x of 2.5 is 4.967\n" + "The prediction for a new x of 2.5 is 5.299\n" ] } ], @@ -252,17 +280,17 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 83, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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" ] }, - "execution_count": 11, + "execution_count": 83, "metadata": {}, "output_type": "execute_result" } @@ -272,49 +300,62 @@ "fig" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Recalculate Model Error\n", + "\n", + "We can use the same procedure as we just used to predict new point to predict the models predictions of the data point we know, and compare these \n", + "\n", + "Note that this is the same as what the fitting procedure does, and, as well see, this should lead to calculating the same error as the model returned to us. " + ] + }, { "cell_type": "code", - "execution_count": 12, - "metadata": { - "collapsed": true - }, + "execution_count": 94, + "metadata": {}, "outputs": [], "source": [ - "# We can also see what the model would predict for all the points we did observe\n", + "# Calculate model predictions for our observed data points\n", "preds = theta * x" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The residuals, as returned by the OLS fit, are the just the sum of squares between the model fit and the observed data points. " + ] + }, { "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": true - }, + "execution_count": 95, + "metadata": {}, "outputs": [], "source": [ - "# Residuals are the just the sum of squares between the model fit and the observed data points\n", "# Re-calculate the residuals 'by hand'\n", "error = np.sum(np.subtract(preds, y) ** 2)" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 96, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Error from : 1.37012261311\n", - "Error from : 1.37012261311\n" + "Error, returned by the model \t\t: 3.2984\n", + "Error, as recalculated residuals \t: 3.2984\n" ] } ], "source": [ "# Check that our residuals calculation matches the scipy implementation\n", - "print('Error from :', residuals[0])\n", - "print('Error from :', error)" + "print('Error, returned by the model \\t\\t: {:1.4f}'.format(residuals[0]))\n", + "print('Error, as recalculated residuals \\t: {:1.4f}'.format(error))" ] }, { @@ -333,7 +374,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -347,7 +388,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/14-LinearModels.ipynb b/14-LinearModels.ipynb index 688ee99..05ed224 100644 --- a/14-LinearModels.ipynb +++ b/14-LinearModels.ipynb @@ -12,7 +12,7 @@ "metadata": {}, "source": [ "
\n", - "Linear (regression) modelling is a method of predicting the value of an output value as a linear combination of weight input values.\n", + "Linear (regression) modelling is a method of predicting the value of an output value as a linear combination of weighted input values.\n", "
" ] }, @@ -20,17 +20,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Linear Models - Overview\n", + "## Linear Models - Overview\n", "\n", - "In the simplest case, we are trying to fit a line, so our model is of the form:\n", + "In the simplest case, we are trying to fit a line. In this case, our model is of the form:\n", "\n", "$$ y = ax + b $$\n", "\n", - "In this equation above, we are trying to predict some data variable $y$, from some other data variable $x$, where $a$ and $b$ are parameters we need to figure out, by fitting the model, and reflect the slope, and y-intercept, of the model (line) respectively. \n", + "In this equation above, we are trying to predict some data variable $y$, from some other data variable $x$, where $a$ and $b$ are parameters we need to figure out (learn), by fitting the model, and reflect the slope, and y-intercept, of the model (line) respectively.\n", "\n", "We need some procedure to go about finding $a$ and $b$. We will use OLS to do so - the values of $a$ and $b$ we want are those that fulfill the OLS solution - meaning the values that lead to the smallest distance between the predictions of the model, and our data. \n", "\n", - "Note that you need data in which you know both $x$ and $y$ already to do so - to train your model).\n", + "Note that to train this kind of model, you need data in which you know both $x$ and $y$ already, to train your model. This kind of model only applies to predicting values you have at least some information about. \n", + "\n", + "Having training data makes it a 'supervised' model, meaning that learning the prediction model is 'supervised' or guided by knowing some 'answers' to our prediction problem already, and the goal is to use this data to learn a model that can generalize to new data. \n", "\n", "This approach can also be generalized, including, for example, more features used to predict our output of interest. \n", "\n", @@ -40,15 +42,17 @@ "\n", "In the equation above $a_0$ is the intercept (the same as $b$ from above), and $a_1$ to $a_n$ are $n$ parameters that we are trying to learn, as weights for data features $x_1$ to $x_n$. Our output variable (what we are trying to predict) is still $y$, and we've introduced $\\epsilon$, which is the error, which basically captures unexplained variance.\n", "\n", - "### Linear Models Pratice\n", + "### Linear Models Practice\n", "\n", - "In the following, we will generate some data, with two features 'D1' and 'D2', that are correlated. \n", + "In the following, we will generate some data, with two features, that we'll call `d1` and `d2`. \n", "\n", - "Given the correlation, we can try and predict values of 'D2' from 'D1', and we will create a linear model to do so. \n", + "We will generate this data such that `d1` and `d2` are correlated. This means that they share some information, and so we can use this to property to try and predict values of `d2` from `d1`, using a linear model to do so. \n", "\n", "This model, using the second notation from above, will be of the form:\n", "\n", - "$$ D2 = a_0 + a_1 * D1 $$" + "$$ d2 = a_0 + a_1 * d1 $$\n", + "\n", + "Where `a_0` and `a_1` are parameters of the model that we are trying to learn, reflecting the intercept and slope, respectively. " ] }, { @@ -69,13 +73,21 @@ "import statsmodels.api as sm" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First, lets generate some example data to use." + ] + }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ - "# Generate some correlated data\n", + "# Set random seed, for consistency simulating data\n", + "np.random.seed(21)\n", "\n", "# Settings\n", "corr = 0.75\n", @@ -83,7 +95,7 @@ "means = [0, 0]\n", "\n", "# Generate the data\n", - "dat = np.random.multivariate_normal(means, covs, 1000)" + "data = np.random.multivariate_normal(means, covs, 1000)" ] }, { @@ -93,7 +105,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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4NlXh8ESZtufw0GSFU3Mt4kxiITg85vPxB8cZK3u8ebnJx4/qFM5yJ+T0YpdmEGMJa5C+6B87k5JOlOFYAs+xcGxBN9/ln17UqpBMKoSwmKw4TNU8hBC8dGppg9pkcyrnM8cnB3ruOJM8fXR0ELAnKj7NIEYgNgRxU5i8s5hAbrij3Cn3u/0jRd682GCsvL6A9At471zZmPfe3KjyKz9+hOPTdX7rq2/zytlVKr4zaHn/wbk1jk1VBnn/Zi8BATOLHSq+w2TV59F9dRCC6ZrHfCuiFSacXuyyt5YyVfNphylJlvHahYaW6NkWCMHz3zrHZ45P8tKpJepFl1LBIcsUqdK78UwqbEvQDBJmGz2maz4XmgEImKx6+K5NO0+79BerrWoUL51aGqQ1nntxhmaQbHjvvC2Mskxh8s5iArnhjnKn3O+efXyKr5+YpxWm1PIp71EqGS06XF4LODBaYrruc365w1dfv8yTB0c4PFGmGST87gvvUnQsvnt2hV6cUfEcRksOnUjSCmKuNAMmKh7TI0Uur/UAQZBkfHNmiZ88Nsl4xcNC8frFxsBIqxkkXGkEfP4TB/ne2TVOXtE79oJtUXQtfvShCQqOvSH14jkWkWtjZZIozah4LgXHwhaCIJbMtyKkgv11n7LnECYZNd/dsHu+keXBVgvtRMUbNB0Z69m7AxPIDXecO+V+N1F1+cH5BkoqakWHx/fVmG/FPLx3Pe8938obVdoRRycrxGnGe/NtOolWi5QLNu0wYa2XYAsQAhKpuLwWMN8MyBSUXIuq7xLEGa9fbHBsTwWJ4MmDIwNr21rR5dieChdWAiwh8rQLKBR58puq73BxpQtK0YkyokxSKlis9TKkAs+1KBVsRsse0zWPty41sIXgSiOk4MQUCzb7R7QVbpIpnntxhneuNDk+XdvwvgwH+i0X2p/SskVjPXv3YAK54QPHqbkmv/f1Ga40Ig6PFWkECb044/xKj70jRQ6NlwePbYUJVc8euA2eXuqSSIlAS/7aYUoi9WNTBeSzrxSQ5t/vxRLbyih7+s9tZqHDgbEihyfKHJ2sDDo031vssNSJ+LEHxzk2VSVMMnzXJkyyQQdnkqnBXUQ30kqXTIEAVjoxsuTy9JExpFKEmaRWdFhohWRSECUpb19uUXAsPv7AKM0g4fJaQMm1r+vRcq2F1gTuuwcTyA0fOF44scByJ6KadzyOlj3CfIctlQ5k/R15zXdpBgm1/OtOmBJnCltAkkmSTF7zPIpc3yu0j/ioI6j5DvWSy6PTWrYXp3qX7jkWri3IpOLv59s8OFnm7LLOTRdswWonptVL+JH9NeZbEQutkCsNHcT75wpTyUIr4j/NLJFm+i7jZ35k3/pCMd/GdTJ+4uEJJiq6UPnwVIV35zuMVTyTJrmHMYHccE+xUxvUU3NNXjy5wOW1LhXPZbxSoFRwtOdHmDJZ9QbFvarvsLfmcaURcGxPhcV2wEpHp0KE0N2UNxo+KwFLwVTN42c/cmCg0Onnns8udfBsnTqJM8WB0SJJpljpJjwwUeKty01aQUq16HBotMiPHBihtNjm795dGtwJbD7fcjvEtW2KBZuldshk1Wey6tMOEhRqEMRB2+v2kmyDR4tJk9x7mEBuuKvZ7XmVz3/rHK4tBl7cVxoh+0b8vLnG4rF9usDXP+eRiQr/6LEpvnt6hf98eoVa0SGTGSvdlOSGYVwj0UH/m+8ustZL+PGHxgFtpPXP/vhtgjghypSWEFq6KNkJE5o9l6rvUvEcHtlb5d0FbVW70k3ylIvc8goSCcemyiRSbZgkVHCu7v9rhymP5k06hnsXE8gNdy3D0rh2EPPXp5eJUsWJ2SZPHR7l2F5dpBvWfW+1Y+8/5m9OzlOwLaqezflU0YsThIKZKMHNv//eQusqmSFo75JPPbKHetHlpVMLdKIWcaZTMTfCErDQirAsQdW3+f65NV6/0ODXPv0gTx6s8/LZVSYrzsAjPEl1yiZxJRMVj4f2lAe76HfnOyRS4jvWNZcR17Z44mCdV8+vsdqJBy3vY+UClhCcX+4w1wwHQyl+7VMP7uwXZbjjmEBuuGvpS+MWmgEvn10lyRSuBe0o4TtnVgB4aKo6UFhspYn+va/PIJXi8HgZFPSilHPLXUZLLgJdOFSpYqJsI4TN3893BoXA4d3+cAdqEKeDoAv6j2irGTsi/79jCcqehW1ZOJZFuWwNukiPjpcQQBBnLLbDwS67XLD5mR+ZxhJicLx+GqQZpHSja0/1Kbk2ExWfR/ZWOb3U5aVTCwgETx6sc2i8yJ++Pkcq1WAoxeYGIcO9h/FaMdy19OdVvjXbpGBr72phCQSCgm3x1mxzg8JiK9+W5U7EajemXnSpFl2auU3qajcmztMZo0UHJSzGKwWqvsPZpR5JlnF2qcP/+Mdv8dyLM3i2oB2mLHdCmkFKnGlDQQuQQu+6h7EF+K6F7+oiZjfOBl2kQuiiZ5JJzq/2eGhPmZVuTJhIiq7NZFnbul5c2TjTs58G+Z1/8igjpQJFR7DptDhWPgkoSGiFKXtrPh8/Os6nj+/BdWz+9I05jk1VNgyluB3eNoZbi9mRG+5a+u373Sij5FpYlk0zSHEsgWtDO9iosNjaRzxDIFhqh/SilNWunqBj5cVKcr+TVpBwIF8QltohzSChYAtQekzbuwttrqwFrPYSMinJFNhArejQi7XixXcs2lGGQqdc4lQyWS2QZBDk49XWr0t3kXaijPlWxIHR4sAqIEwypoTg3YUOo+Wr1STHp+scGC3SChLa+cJkW3rB6EQJnTjjlXMr2EIwUSlwaq7FYjskSiWNXkwrSAZdpnDt9nozX/PewQRyw23lZoJDX9nhOxZJJrEt3eXo2hbdWFItOhsKnVv5tniOTS9O1yV+FkSpLkC6FhQLjm7ASVPOr3RJMkWU67cVUCrYLLYC5hsh7ShFobCEIJUKlcfletElySSeY9FLMhwLHMtCCEGSwZ6Kw9mVlDcurmlJohCUCjYfOTjCh/ZU+M+nVxgpOiilBh2mTx0ZZakdX1NN8ti+OiXXHph+eY7FUjsiSiU/+sA4hyfK/Nkbs1xY6TKWLxgAWaZohQmvX2zw0UMjTFZ9Lix3mW9H/PqfvLWhrnCn7IUNN48J5IbbxvW8x4EtA/wXPnmUME75T+8tU3IF+0d8MqXNoX7zpx/eYCL1zpUml9e0p/Wh8fKgnfzMUoxt6WBnWRaQYQtACO0FrhQopfPTUgfTJJM6YGeSv3t3CdcWOLZFreiSZookzegmGQXHYqTo0ggSglSyr14kzfSOPVOKNJOcW+lRsCy6GSgFGYowzfj7+TY//5S+mzhxpUU7Sqn5Lo/vr+HaNo/tK15TTbLVZPtWmPLRg/VBc0+UZMSZ1Iofx6LsORQL9iC3f3qxQydMeeOSDurDv5Oia123dd9wd7ErgVwI8W+BfwwsKqUe341jGu4/Nvt69PPQ/82/fx3PtgcOgZsD/LG9NVa7MeeWu5xbCVBKMVp0+e5pXfDsm0gdn66RpBnfPr2Cd36NA2MlfvmZQ/zZm1do9hJm1wKiNMOy+p2XOkculcCxBQdGiyy0QqJMkkqFbSmqvsNyJyZKJWMli7FygSuNEMex8KQO/pejkAMjReI0w7UFK90U37EGjUC610hiCb0bJ0/rVH2HmYUuP/rQOK9dbAwWldnVHvOtmIPjRf75V99mtRtzfrU3KFh+/pnDgG79/+7FtXwBcPBdi6VOzJ+/eZlulLHSiUHoxUNK7Y3iuzZjJZea77DQjkAIPnpohCMTOvj3fzevnFvhM8c3epYbh8O7l93akf/fwP8O/LtdOp7hPmQ4h73cCXntQoNCXkT0KvYGh0CAr7x8gSCR1IsuD+wpc7kRYCUZ03WfYsHh5bOrfOfMCk/sr1Mvuiy1QxbaMZNVD1voHem/fGGGmu8wUSkQppJywSHOJFIpBILRcoHVrh5APFUr8jcn5wHypiABCFxbkGQqT7U47BvxWWxF2LZFsWDz1KFRjk5WePnsCheWuxRdG8+1KLo2a0tdJJClULDAdQRS6dSLbQlOzjW5uLq+s77SCGkFCR89PMJEpcA3Z5b0kImaN3jN7y12AFjrxSy2Q6SCTpggpWK1GyHQXi0SBpYBmQLXFtjAgbEyx6drPJOnbbbygxeIDR2uYBwO72Z2JZArpb4lhDiyG8cy3L8M57D7ftl9+g6E/QaWqu/w0qkVPn50nHrR5XtnW6SZwndseolkrOIghODsUodXL6xxeqlLI4ipFBwyKTnbCCgXHFxbIFBcXO2RSUXNd7BT7UboWIK1bkyYZHzt7XmqRYeiYxEm2SAPvtaLcS1B0RX0opTzyx3iTKEUHJuqUCu6HJ7Q3iwPTZZ5d76FhWKxFZNKNmi9YwlkevBDlEiS1R7zzZDJqofn2EgFEsVY2SVIJGeXelu+5jOLHTKllTKpVLnJlsIRgiBRWGhbW4t+MxKAoujq93hvzRsUTl84sbClH/yTB+sbOlw3t+6bQujdxW2THwohviCEeFUI8erS0tLtOq3hLuLZx6doBkn+Xwx5cW9vzc9nSVoDc6p2mCLQ6QfQ5lWZ1K5Ua72EM0sdrjQCgiSjG+uJ7EGcMd8KuLgaYAtB0bVBQSNIcIQiTiXL3Zh2mOZpDn0e37FxbehFGVeaIZ0oI5USx9Ie32Eqmap6FFyHONOKl6mqR9V32VP1BqPRJqs+kxWPbixJJYNzDBNnilTqACvQi8N8M+TyWoBAEcQZ7Sjl0mqXM0sdGkFMkKR082Kl51i0I20REKYSW2idukAvAv3gLQTYli7oeq6FUgLbspisehyZqAyKlsO/k741bTNI+Pwzh68ad9d/Tr/WcTMj7gy3lttW7FRKPQ88D/DUU09tr7fZcF8xbIlqCSvPz9YRAl670CBKJTVfa6AvrHSxBfzVD+eYqHi5r4nuUHRtrSNf68UDHXWUag32cjshkf0gnWh/biBIFY6ti5eWpdMbrVAHx8mqR7Fgs9qN6cUpjpXnlRUUbAshYLYZ8SP7a9i2PZgGVC7YCNiwc41TiVJ6J96/NksASgdY0Dtk17Y4OlHm3HKHVCptRxskFAs27dyNsea72Ja+M0iyhLNL+rGpVAilUEoh8oYhkefC+39YtmWRZhLXFlQKNokDj+6rsa/uM9sIBrrxG/nBb7XLvpGH+TBm5357MKoVw22lb4n67ONT/N7XZ3jnSosozVASokxyYFQXDS0hODpRZmaho3eJvYhmkJDlQTqIUzIp8V2byXIh12ArEqkDaCoVSZTRjTPKBQtL6MBcKjhkSu/OFVD1LIIkY7ziUSo4hHFGJ045PFamE6fEqQ6GSTfh/ErAgdEiFc+m2Ys5s9jBtQWffmQPcZrx/bNNrjSDQcROc3tZW4DKgzno66h5WkXi2hbdXNYYJ4qxcoHFZohlCcIkJU0lsdS3zqvdeKChD1OJKyCSCiXyRWNoe9R/fTLVBlz76tpPxnVsxirOVXLCzTNGhyckbQ6+252zej2Vkgnmu4vp7DTcMaRS9OKU5XbMYicCFP/0yX1MVn0OjpU4Olnho4dHsC1BJ8qwBNR8re/uxRmlgnYndF2bTzwwzsGxMiXXoh8zLUsH0W4ssS3BWLlA2dPWtROVAr5j4TnrcjwAIXTn6EjJ5eBoiQcnK+yp+ji2lir6rk2QZCx3YrI8P+06NgutiIurXSwhcFxBYegvK1UM7Gb717bYTfnhbJMk03cSAh2NC46FZevCpOvY+PmuX6F33BXPYaLsUfZsHMfGFoJM6kQN1vqdQP//At1haluCimdv6HrdqqNzO2mT/SPFQTqpz1aF0K06bU0X6a1ht+SH/wH4SWBCCHEZ+G2l1Jd349iGm2cnt7O361b4hRMLVD0H27LYP1rEc9b9Rw6OFXkkN8SarPqUvS4PTJSZbYbsHykOhi1kUueUC7aVT46PcByLkhAUbEEsFWmmyFLJaKlA1XdZakeA3rHXfZvVIEUAZxbbpHk+3LZgsRWyJ8/dR6mkXLBJMkWY5LI+QEpJL4bvn1tlvtGjEaQ4NqSZVqUUhCLO1rfJVc8mSjPyRlB6cYZr6TuMatHlU8cmef18A4HAEnqgsiUgTCSOpRU2B0ZLhElGN0poBK406mAAACAASURBVCm+axEkuljcClPKBUGQaA18rnTEtW0c22auGQ5khgBRmvLiydUNv+vtpE22O2d1uzt3w87ZLdXKf7kbxzHsnJ3czt7OW+HrTbFvBtpnpD+YeKkdMVZymc4DK+hhC2tRxqHxEvvqPnPNkPGKR5RI6kWHtSAhi1KU0vnn5U5EkGREicSxdbBLM0nZ1bn6RpBiW4KnDtVxHZvXLzRIJewb8RkpOiy1I1xbsNTR11TMOz89x0KgaEdZXsDUxcdU6ruAQi5d3FsrYFkWy52MoSzL4LUXHYvlTsxcK2RPxaOXSMJE0okSBJBkOu0CkEnJfCvmwcnyYAEEXScoOBZRXg/od5xKBWNll5VuPHj/lzshr5xdo+o7G37XnSgZLKJ9hoNvf6FvhwmzjYB60eHR6fqWHuZbddoaCeOtweTI7zNuphB1s8/dzd369abYbx5MvKjgSiPkk8cmGC0XOL3YZbkTMV7x+I1nH95gYfvFP3qLTMFo0aUVJKRSB9sgTgmTeOCDAlrXjRCUPIc9VR8h4NxqMJjW04kSljoCJRU/sq/KfEs32IRxRpxKbFurQNZ6cX+sJlEGjqVTLplcrz4udRKKrkWS5TlzwLIERybKLLRClroxY4E2uSoWbOpSsdqL6UYCiaTsaSsBpRTzzQjHEjy2r8abl5oD6aZjaxmiZUGS6oUqzhRjJZdGL2G5E/HNdxc5Pl3l1FwbATy2rzZIe4BeYK+lHx9e6I9P1wY78Wt9Dra7czfsHBPI7zN2cjvbf+5yJ+T0YjefV6lHk+32bv1aU+yPjJeYa0UbBhPvrfu6M7MRUiu6eXoj4koj4J/+/ncYq3j88jOH+OSxPTwwWeI7Z1YGNq+2EHTDFMn66DXPEUSpIpbg5emZbqgbgKSCKPf6lgoKlkWKYt9oiZLn8NblJmEqCZOM/XWfUsHm4mqKlAobXeeUEtI8ghddi6pjsRZoCaFkXb1S922uNEKUUri2xUonIsskcaaboA6MFCm7FrPNiI8cHKEXZ6x0Y2IpeeboGJNVn4rfJcoNuaq+i5KKRqAIZEYqoegI4lSBo/jRB8a40oz47plVLKH4xAPjg+ar/uek5jtcWOlqd8h8hz9WLvAbzz58zYX+Ky9fYLLqX7XA30gRY9g9TCC/z9jJ7ez+kSLnlzu8u6CNmKqezru2gpQ/fPnCTe/0N0/3UcBSJ6IZ6OD9wGSJk1daJJneiR8ZL2FZFjXfGQwm7rPQCvjWzBLnV3pEaUqYKByhOyVbvYR/9eJ7/PEPLuVeKuuDj1OUlhPmX0t0mqJPmEj2FF1WuykgsC2Bk4u/XdtipRczVnJ58eSC3vUKndYJE5hthqz1YqSCiu9gW1oXnuQ7cUvAwdFSfhfRys+hKRUsglhSsHWBdV/Np+xpNYltCTxXyxxLnstPfKjKsb01ZhsBzzw4wVI7pODolMxDk2Vev6ilm5MVj+m6z1uXm5TSjDhTBIlkT7XA00dHAVjtpbh2SpBIerk2HXSq5cRsS+v7EXi2hcgLtn1P9K02CWGS8t0zq3zqkT1bLvDXGtxs2F1MIL/P2Mnt7LOPT/HF/0e3qA8PTjg2VeGNS00+fXzPhsf3d/rXmsrT38G7Nrx8dlWnI3LHwVYv4dhUhQf3VJmqeSy2I+ZaEfWiXjwuLHc3BPJelBGlium6z5nFttZm59ppYYGSirPLAfWSq+1pcwSweT7y8FSfRCo8W5BmIJBYCNqRljnWfIcwTrkSp4SpQqDIcn25Tq3rnX0mdVHTtgT76z5rgW44ilLJSMnN30+Hiqe9XVZ7CXGqm4aSTLKn6vHEAa2nf/X8GlGi+NQjY4Pf3WeOTzKzsO5N/mMPjfPSKd1UN17xOLanwsxCh3pJj4U7OlHm8HiZqu/w1z+cRwhY68acXe7hORZjJZf5luSNSw2aQcxKN+bMorYScG2B79jgO/zY0XEmKjo4v3BiYctNwqm5NqMlY651pzHyw/uM/u3sVh1523nugdEijgVnl7vMNgI93ca3B804w7TDFM8WW8rVhnfwZ5d6VH2HJMsGCoylTsiLpxZ47cIa3zu7glLw6HSNR/bWmK55vHGpwbmlzqDbcGahQ6lgU/Md7QUu+kFad4fGeTt8N0zoRsngGhUb2+Q341iw3EvwHT3HM5V6cah6NkpBlCo6scwbcdYXAf04RSIVEq2CUUqx0I6xLXRKqugOFsNOlJLkZlyOpXf7Fvp4jSDh7cta3jdd9+klKX/x1hVOzrV4ZG+Zl04tbXh/Xzq1xGeOTw5+x0cnKzz3ix/m//qvnmai6nN4vDyQ/I1VCgghePNyc1BYjjPF9EiRByfLnLjS5sJKD6kUvmMRp5JMSpq9hLcu6WvqL9hbdYGu9RIe3Vfd8J4aZcrtx+zI7wO22hG/32G6U1WPs0td9o8UB7vyV86u8chUZUvvjWvZnX7/3OpgB9/PtadSkUnJ5bUevTjLBx4LLq8GulW/7mEJdyCRm2tFFFyb/SNFDo4XmWsEXFjpopTWZluir89eD9VbTZa/Hq4lSFKtNynYglrRoRNlNEOd9x7KwmxYENTQuYa78C0BJVcvNh+aLDPf0s6JUZKh1Hpnqu/aA7vbkmuz2A755rtam/6xI2McnihzYbnL8986T6mg9d99LblrC77jWvyvP/fEVa9nc/pjouxyZrFDM4hRUlErugihC6WnFzuMlgo0gphiwca1LVIpiTJJ1XOYb4XAempuq5z3P3xoHDdP8/QxypTbjwnk9zi7XYQcbi3vI4CRcoFfeubwVYWrL3/7POOVjR+jqu8MdvD1okvN1wVKxxKE2tN1kIsWCKw8mJ5e7A6GDB8aL+M6Nr/38x8G4J9/9W1OzraIMkW5YNGJ5YYg+37oy/ocWwdgx7Jo9BIcy0LmzT6Z0ifpe5hc6ziuI5BS0Y0y4izk6cOjLHYSwjQly5TOy/fb6JWilefCS47AdSx6sUSgqBUdjk5WWGqHzCx2SDJJEOd3QwL21316Ucpfvj3HUifi0bxLtq8qurja02qgSoGJssvZ5Z7OwyNY7sY0goR/kA+UeOXcKuNlHcj7q1TRtWmHKWl+69HfgfdTc1t1gRplyp3HBPJ7nJ3IDbcizhRPHx3l7HJv4ClyfLpKnKktC1f9vGmSZQOlS8G2ODpWGuzgH5gs8crZNVzbRsqETClsy0IoPa1GoWiGCYvtcKCY6csLT801OT5dR6E11yXPphtlhGk4KGhuFzfvfOy3+btOvpAInSppBgmWgERKnfoQOocOsEH8vQmZP8C2BImURKnie+dWKRUsiq7DWi/Bc/QOPlVaoghgKUWt5DFZ8fBc7bGi8pN8/9wqV5oBUSJpK6j6NkXHZrEdkUhFwbZo9pLBwv2Z45O8dGqJ6ZpHMx/ndmaxQ8HWna37RnzaYYpUcGq+w1jZw7Ut9tZ8giTj0mqAEDrPXy7YZFJrz+tF97pKE6NMuTswgfweZ7e75/qB+ZkHxgE9v/KdKy2STPHcizNXaYaffXyK3/7zd5hZ6ACKgmMhEDR7MVM1n9mGoF50eGSqwsW1gNVeTBLryTWxBWXXxrYsenHGciviO+8tIyxBK0iJkoxf/cPXOVD3+eFcK+9StKh4DiOlAnGS0ol1w0v/LmI41uq5nOS6agaSwn7ePEoUCkXBFhRdi2a4Hq+l7Ifn9eddCyt/XJxXVS20BLETSdphfM0cfSJ1Tn+tG6OULpoWHJuvvX2Fc8td3aZvC8JU0Ql1I1GUKnzXZu+IRzta13v/wcsXeXS6Rr3oUvEdTi92mV3rEaWwr15ktFyg6qesdmPaYcJ8O+LXPvUgL51a4mg+TakTpkRpxnS9yMGxEr/+U8e2XVsxgfvOYgL5Pc5ud88Nq17CJOUH5/ScyY8/MEozSPjdF95lX90nyhT7R4ocmyqz2AqxLYHIm2CCOKVU8FHoAuaFlS7NKNHj09AFxkSCkNCNdYDyXAvLEqz2ElzbYqzsUnAszi12mV0LBna2/QEPUzWfhWaIncSD4DxMv3jZDlOSvEZrK9112fcT7z8nzVMiGzbdeTFVbRGF+0ZYad8EC21i1f9Z/ylbPXczzTDDt0EhkFIPab640s0XD33n4jva56UT6dFyB0Z9bMuinHeFVn2HhVbIx4+OATBR8Zmo+CilODXXHihnyp6WSB4YLXJorMTnntjPA5MVXjixQC/JaIXpoFNzO81extnw7sEE8nuc3e6eG75VfuXcChXf4fH9NSYqPjPzLd642OBNAR/aUyFOMr7+zjyphAcnywghuLzWAwRhmtGJMupFXWxbaOvCmS0ExYJDGqakALkCRfunaA/w/kT5S2s9HVBzz+1M6Z3yYjvE6VpkUuqfAemm1xGmikxlG4JpomA4sd7fxcvcYrbf0HO9HfggV56f17IYqFk2B/jtEmbgOzBeLRAlklaYYudujdWCjSWgGUikEjwwUSaVkErJ4/t1K307TJmq+RtsDWq+S6lgU8hb+PtNV80gwbMt3omagzus91MYN86GdxdGfniPsxO54fWO+cXPHuOxfXU+eWySiYrPUjvk++fXcHKTpyiVzCx29IixfEAEkA+IEISJDrLfOLXA5UaguwsBhNZO94OonStPVroJ3TijGWa5m5+2Yk0yiZSK5a7WO7fClF6sOysrnh5Jplt59E7ftfoTcfTufas0ej/g+o7Qryf/vuLqQRD9x/fpH09KqBVdasUCx/dW8RyLgiOuWRC93jFB1ybiVFL2dOCuFd2BU6NCUCo4jJQcpvM7rYenKoyVvUEx8tOPTPD6xQbNIKFSsGkGCWeWuvzsR/YCsNKNSTPdtp9KxYcP1Hc0EMI4G95dmB35fcCtylFuGM221EXm0+ZTqZhtBAML1WLB2WBm1Yv1TMxulNKLtbugEFrzLfKiYD/gbaU8Obfc5ehEmTjJrisnnKx6lDyH88s9Roo2xYJLJhWdMKGbbEx1CPTEnP74NYV2HAwTvSgMd3u6/dQP19ahS6DRSxivFHBsi4OjRZY6EXG6+d5g6zrp5q+l0lpzqdYHVHiuzb66TzvK6EYpv/nTD/O5J/ZfldLoj2wbtjWoFV2O7alQ9T2e+4UP88KJBV48ucB4xeOxfbUNrfnvpzBunA3vLkwgN1yT4bRNO0hI04xunv5QShfmwlTvjPvDg23LQqpMd/v56y3n0Jf7SYS4/o1gkiou5trya2EJWOsl7B8pMrsWEKYK29aT6oeD5PDknOHDDeJ2vjBZuRe4VCqf1ymv20gEOph3o4TLa1pV4jsWHbF+bIt8ERHg9O8S8mvof90fPtFX04Rxxo8+NE4v1kMxFju6aPxrn3qQzz2xH9h64f7yt89fZWsglV5w+4/vB19rqPP1/QZf42x4d2EC+Qec6xWshvPlYapb5PtjyiR6B+k5FgfGisy3IxbaEdMjRT7/iYP8+ZvzRJmkmHdjNoKUJMvIlB4+fD2kUnnAv/Zj+h2dUSo5OFZkrhnpol8joDeUpL6e2iRMJH5Be4QrtK49zdQg966UDrhb5bz7QTpMFPtHHMJ8HqhrQ9G2iBK9ENQ8h26eZvrQZIWa73B6qZtbyuqByVLqAq5tQb3k8uGDozddOCzYgm/NLJFkiorv8NBkmYJjDwJrX2P+xsU1JioeD+0pM1Hx33fwNc6GdxcmkH+A2U7Bqr+bW2qH/H/tuVxxosgyPS+y7jtcXA351CN7+PhR7Q/y9/Ndnjyofb2TLOO7p1ewUQSpyqV9UHLEhoA7jIS8eejaO/JEQpxkRKnksek6D++RfPfsCkF+TLe/A950CiffsduWoOI7FGxBM7CoeRbdWBKmarATt9k69WMLGCm5ucOiIJUw34ywhE4boRSOrbtiW1HKZ49P8d9/5kMcn67ztbdn+Z//8qROMwko2CCFwLUtnj4yOgjiX3n5Am9c0kMmnjxY5/PPHL6uOdlCK6Id6iHUUZzyytlVDo2X+I1nHx78nvdWPVq59vzV82s8sreKZVnvK/ga/fjdhQnkH2BuppkozhSHxosstSNsBYWixWjJ5Uoj5FDVv+oYcZppTw6p8+VZnt4oFxySNKNadOi1E7bCtgTFgh6pdj2iTDJVLWDbFr/6XzzI97+8xnjZJVN68PLwxn+4iGlbglLBxnP0vEzHWh/E7Oae3gAZeRFV5Pa0av1YjZ4+fq1oD9Inbn9QcqoYKdqM5O3+fkH/mZ2aa/LSqSVqxQLdKKMTZ8Sp7uYcLReYb0X8/FSZ333hXS6u9Kh4+tgvn11lvhVdU9f9wokFDo6V2Fv3Bk1ZFd9hX93n+HSd516cGfyeK/kdwWonZq4V8Tv/5NH3HXyNfvzuwQTyDzA3U7DaP1IkTjKyfFBDfzJNphTHpzeaJkVpyluXWuwb8Tk518IWgrLvsKfmMVb2eG++RSPIBkXFYVwLDo+VkErRGJposxVK6cHCv/kzxzk+XSfJFBZ6XJtjWWRK3zmAnnUphFbC6Kk+sNZN9ABnx8K1oRmkWxYlJeuyQ8F6IbRgCzpROihSZlINFo9EKkSmC6pSSn77L06y1Arz3HdK1XeYrHp0Ip1uKhd0x+rv/91ZVjoRtaIzWACEEFxc7fLbf3GSQ2Olq1Jg67lvd2BxIJVirhle9XuerPpMVv3Bz00gvj8w8sMPMNsdogs6J2rbFnurBZbaEafm2iy1I56YruG76/uB9xZa/PUPF5hrBsw1AtpBQitI6EUpBVt/3GzbQkqJu+nT5wg4MFriY0fHmKj6FAvX32dYwuLiao+zSx0ADo0W6eYDMR1bULAtXEE+F1NweKzERNklSCTtKMO2YE/VQ6JTG9dKp0ulg6nvDDX7ACgduLPcMTFT6zr0dpSx2o1pdGNeOrXAidkml9d6NEM9sKEXZTSClIlqgarv0IsltaKLVJI4lSy2I84utTmz1GF2rceVRsBKJ9pyIPKNfo8383s23JuYQP4BZitb0gsrXZbbIb/+J2/x3Iszg2BxfLrOZ45PMt+KKRW0/8qPPTiO69pcWu3RDBIWWgHfPbuKlIrRosNsMyTOJEopwjTjvYUOb1xcZbUb6y7GPLa4ltaApwqCJOWNiw3mGj3iLLtKbz2MhS6K/k9/eoJf/cqr1IvaYTHO3QalkhRcm6cOjzJadnVBLsrYW/MoFywyqVjqxHnX5NWyQVhPyUipiDc9JFG5Hzo6teI71mCMG+g0TZhInXuPMyxLm1dJpYc4C2CpFdGN0sHYtXqxgBAQxBm9OKNgC7qxlkcWXXtLzfZWv8f+CLbt/Nxw7yPUdvqId5mnnnpKvfrqq7f9vIarGVatFGzBQivi4FhpgxKhP9jgxZMLuLbYoENuBglxmjFZ9fmbk/PMN0P2jfg0esmg+aQTpoPWepFr7foZldGS7kAM4oxmL0FYOnWTZHqQAwiiLSqOfdVI0YFU6n76UsGhYCnauX/4SNHlqcOjTNWLJGnGe0tdrjR6BLFujEmkJM3WVTSZXA/C/aahvmMh6B13/7x9bXpe28QvWHogs4LVnh6YXHQtekO5I88R+dxNkEoyUtK58j01j48fHWOqVmS5E/KXb8/Ri1Jsy6JWdGj0Egq2YG/NZ6zqazMzz6ZWdPk3v/z0Vb/HrdrlTTv9/YEQ4jWl1FObv29y5Pc515res9Uf9XMvzlBw7A2Fy7VuxJe+cYZPPDiOVBKUxesXG3w0t0Kt+g5zzZQvfvYYJ+eaNHoxVxohYaon1HuOTVMODXpQG28Dw0SnXNphonPQKje2Ugry3WepYHN5LdioIBH6sdpJUKEk9OKUHrroWHS1v7ZrW1xa1YMTVjsxYZxpc6hMDUy1VH5OK2+Lty2tmlH59XqungSE1BN+gqHg3M+hp5mip/TsTCdfABCC/j8lOodeL7t0ohQlBdP1Io/vqzFR9QdOkRMVn/FyAVsIgiRDKhgpuviuxWI3puy7VDxbj+AL04E75I0Kj6YweX9jAvl9xrV22P3c6u99fQapFIfHy1dJDrcqfs41Q7pxyqm5FsudGFsIRkq603Oyuq5DPjXX5NJKoCfQ5GN22lGKm2RkCtzcEzuVCscWyFzmFyWK2M0G49gsofXdCrCFTgPoRp31nwvWFSQDjxNL7/ajVHt/+0rRkIqZxQ5Hx0tM1UsstbUPicwXE6k2eqT4BZtSQV9/J0yxbYunDte5tBYwu6atEePcXqC/K+9rzUsFh8lKgaWOLtBWPYeS50BuX2Dl55JSD3TeM+LzwGSFzz9zGGCDJrvquwgEzz6gBywvtUP+6ofzFCxrwwi+h6cqZqSaAdilHLkQ4lkhxLtCiNNCiN/cjWMabp6+Xrg/FuydKy3OLXdJsmyQW13uRKx24y09MrYqis01A3pxSphkTNU84lQy3wxZaocbcq0vnFjg2FQFz7GZqOgctJTQSyRVT1vVplLh2rrxxu0nnwU0e+tT7ofTG5nSssdGd90KVuZFxeHW+X5gj3INuSVACT0k4dieCudXe3lBMSWTucnV0GtU+blsoZiuFxkrF3hkusZ03eP8co9GL8G2dNDe/Fxt+GUxUSngOjZTNQ/PsciU7mL1nLzAa2mrXNsS+AWbp4+MbhhQPOyX8/i+GofGSxQcG5l30Pquxd6atq71XZt/cHiEQ+Nl0xJvAHZhRy6EsIHfBz4LXAZ+IIT4C6XUyZ0e+17nduclN+vCk0xR8ewNk3eiNENsKiH2JYe/8uNHrurW68V67Jfv2oDN/lHBpdUe882QV86t8OTBEUBL3A5PlAc6ZduymKopLqz2GK8UhgYOK+J8N66DubqqaWcYAQPflGthbeq+zBSITKGk5JsziySZ4o9fvUSjl+DZWzciKaAZSuYaAWEqefJgEYXiyloHBOyt+az2Yrrx+rW4tqDkWuytFxkpFfjEA+NIpfjB+VXmGwGNIMWxLQ6MFhHAh/ZWmax42lc8U7xwYoGzSx1mFrqDz8iv/PiRwbSf4c/Opx/ZgzuU9gJdnzDKEwPsTmrlY8BppdRZACHEHwE/C3ygA/mdsPncnBqp+A5RnNIK13PU3qb5inD9mYwPTZb1+LBLqyTZumvfeNnlwwfqvHOlxX/9ldep+w5xknF0ssJaN+byWo92Lks5PF7m+LTNN/5+cVD0BFAoXNvCthSlgp6kA5s8vbfxuvuFx+HH9ifUR5miVLBZ7UR6WLMlrju2baUbU/EcXr3QIJUZaZ4OudQINzzOsUCgu1vbYYqV32FcWO4ilQ7azUDbxz62rz6oTfQ/E2MVh/PLHb76+mWePDjC4YnyVZ8RM1LNsF12I5DvBy4NfX0Z+PguHPeeZrdHsG2HzUZGD02WeeXsKhXfQeaDfycqHu0w4ZvvLhKl2SAV8gs/pT2pNweQX51v8ealNd24o3S3I8BSJ+E/vjaL5wjGSi5RavHK+VVeObfMcjcZRFXfsfjeuVWmqh6HRkvMN0PCVLsa9n21ATKp0xfDuXJHQHz9zTgw1FW5yba2nT85DdJBMw9SXXdx6Bc9k0wOrmUrMgmWJejFuhnowGiRc0sd3rikC8GH8qk7/dTT5g5LgPlWRNlzmG9HHJ2sXPczcita4o2S5f5hNwL5VlLfq/5WhBBfAL4AcOjQoV047d3NrbL5vN4f32Yjo06YkklJK0z4xqlFnjxY52NHR/gP379EM0ixhWC07CJV4ZrHf2+hrQuL6uop8koppIKFdkzNz/Bdh/lmMlB+gJ6ckym4sBpQKtiEuRJjM8PZEwuoFOzca0VtOcYNtJ+KVoOAZWsVihhabPrIoedfywRrcEwLgkTqwQ75xKOtUOjJQn1/9UtrAeeWuzgWfOfMCt85s8Lems+Dk+VBYN78mWiFCVXPpjNUl7jeZ2Qr5cn7DcZmMMT9xW4UOy8DB4e+PgBc2fwgpdTzSqmnlFJPTU5O7sJp725uRTfd5mLm5g6/4aLZqbkWM4sdPnxwhH/8xD4+dnSM9xY7/B/fPMdqN8F3LcbKBWzLouo5vHBiYcvjzzbDDR7ewyj05HlQrHZ1q3qmtBGUY1mDyTl9evHWQfwqcnWIElApWBTsq/cKjgArL5z2n+S51lVBfNNhb3h+YenJQxKdA78eff+VR/dW+IljE3TjjKV2jJTaJXJ2LeDNSw1OXqMDs+a7tKOMir++n9r8GTk1pyf5bG7Q6v/sep+H62EGQ9xf7EYg/wHwISHEUSFEAfhF4C924bj3NLeim+5m/viuNEI8x6LsOVhCkGQZMwsdelGClIq1bsKltR5BnDLfCpltBBuOv9qNeO38KkEuBeznoYeRqj/FR6tECrlCI8kYSORutt1MoHfj9WJhMF+zWLAputbgwyrQ57KEACGoeFqe2IvXh0lseWyxvjvva8iHsdCvR0pdKEapax6rT8WzsB2Hs8s9lNJpm1aY0Ms7ObtRRjOvFWz+TOyteXSjlL1Vb8vPyI0C9U6C8WxjfQ5qHzMY4t5lx6kVpVQqhPjvgK+jnT//rVLqnR1f2T3Orchp3ihdM3y7vLl554eXm/TilESCSjM9W1LC5bWAtV7CQ3sqnJxr0uwlLHUi1rpxPtHn+oXHKFODIcXNIMF3IExvPoBDf1ybIFOKbpwOPL2jNMN3LITQzTieLQhTmevHBZmEWj7Eoi9N3Irh3Xh/JqYFA2lh3xzLsQV1zyGWkKmE+Drb/EOjJTphSpikJP3FS+nmn3aY4joWtTxgbv5MHJmo8I8em9qgWhn+jNyozrKT9J0ZDHF/sSsNQUqpvwL+ajeOdT+x2910N/rjG/7DrxcLhEmG5wh+ONvkwmqPTCosdE45ZT2YRWnG6cUOi+0Q33WIEt0Qc72gCDqFEmf6MZXcuySTG/UjW405uxb9Fv5erAO4BUxWHDqxpJPLIPfVfd2ckx81lYo0A9eR25pa36efk3cFuI5Fkkpcy6JcsLEswWceneKdKy1mGwGrnfgqlUu/Y3OxHYOAKMly5YpCKZF3dSrSLGO2EQwGHW/1mfjcNa7xRoH6b64+1QAAIABJREFU/QTjfk79nStNLq8FPDxV2VCYvZYKxhRG726MadY9xI3SNcO3yw/tKROl2rBqrhlS+P/be/Mgu87zTu/5znLPuXvvC5bGSkAAN3MTBVujaCSSgkeOXKOKZjwVO66MM4pTM5oJE0UTl6qScqWcctmaKBVNqmIlTuJISrxU7LJLGpEi6XEYOSAlCiRILASItYFGd6O3u9+zf/njO/fidqNXdAPdDZynikV0973nfnd7z3ve731/P11Jt5q6QIvf9TDelOzLWbhBhBnvUM7VXYIlgrgm1GWXKk0r8+K0IdjblyNlGui6+l0q7nLUNXX71dLZnmjogrITkU0Z7O3NcHAghx9JenIW3RmznUlLlMiUrglVO1/F47QCsS/BjR18simdCNUzLoTSfEnpGnnbwDYEtqGhCWJbODUI5AQh3WkDKSVhJIkiyFnK9k1l/GJJo+Pl6t+w8j7LWst3rSu2K1M1Kk2fuhvw44sz/PTKzLKm3eupxSfcH5JAfg9Z6Yu6VhZOAC788nV+8ftyNs/s6UIIgR9GDBaVUbFt6u0gBpCK5VvLTQ9D03h6pGvZtjuArqzJ0eECO7psCrZJhODirSquH6isXEJXJhVn6Uv3bC9GqxbfCv5BGDFb97gx1+TaTJ2aG9KbNTk4kOfwUAEjLnRHUtCVMShmTKxYH1cXS9fLWycLDVWyKKRTCCHospVb/SunJ/lwogqok6KuCUxdkLd0utMmhqazszvNpx7poydnY6cMcpZBzjbQdY2mH5JO6RwYyDNYSN9Rv15NcFwpUK/0eVjIK6cnCcOIC7dquEHEcNGmP29RagbLZtjJxujWJ9FauUe0vqhRFDFednh3dI5Xz0zMM9G9G5Yr1yxsPzR1nf39OR7dUSBl6OzpafL2lTk0IYiQpHTlxJO3DCYrLqm8Tn/extAF3hLtHYYGTT/k6nSNmqfq1LahxKtadxHAdNXDMgS6Fm8irjKapw2BH6qTQRiq7g8hwPMjJn0PXSjD451dGXpzFtmUTsML0IQgbxmMlV1aip6aWNyqrYUQYOnKhEFD9YRLGfHOVRdDE1imTtbSqXsRz+3pphHItrHDmZtljgwX0ITgEVSwf+fqHGEEv/j4ED/8YAJdgyd3336vOssiq5kzWM0+y1rKd2OlJhMVtQmuJnXV3sJM3Vt2vuFetdImbBxJIL9HvHJ6kiiKOD9ZwzI0erMpKk7At964xP7+3IbWFzvrl2lTww9CxstB+4sPaqJwoJDmpUdNXv1ggrITkLUMhos2uqaRs4y2PZvWcZ22sMZt6hpSSuq+2uTUmB/E6bh9M5CYsc74ctOUnQSRMp4I4o1DpYSo/qYJ5coThJJrMw1AtmVhQxkxFnfqGLpGqREQRMvX6COpavzplKA3qwweJsoOfhAhdYGhC+YaProQ6AKO7CjyjS89CcA3X7swrz7dl7P52FCe8YrLeNmhJ5ciYwg+ulXn3dEyOdtgKG+1Xe5XGxw3cp9lZ1ea90ZL9GRv19TdIKI3m1o2KCcbo1ufpLRyjxgrNRkv385+hBAUbGV8sJGXpAsv0VOGTsOP+I1P7uXlFw/dIcrkhzDUleHFowMcHMwTSZV5fvKRXh4ZylNMm1iGroKmBpmUplr/hMq8i5kUeTsVj6jP97LspPUrP+4lX+0+pB9Jgo7aTuf9Igl+ILFMJSZ1aUoZWvgR8aSoJIgkhXSKnz/Yg20u7frTQglzRdimzkDexjZ1UvH9/DAipQskSjOms599sbKHpmn89heO8o0vPcmvHxvh0nSDStMnm9KoNH3evV7i0GAW2BzXnuOPDWJogooTKLOP2Lx6uGgv+7iJMcXWJwnk94idXWlm6l5b/Q5U9tOTNTf0knS19csjw0VefvEQ3/jSk7x4dJChYoZj+3t58eggx/b30oj7ncdKTQ4M5Dk8kEHXNdwgDqwSQCAkOH7YVgFcS0fKRhAAfhC26+CRjDdf4387fkQYRTyzp5dPH+rD0ET77wtpheUglO33KW1q7WlOdT5R7Y2Gps2rt69Un74wWefpkS6KaZOaF1JMmzw90sWFyTqwOcHxyHCRr3z2AED7s3l4MIemacs+7lpr8Qn3n6S0co84/tggr56ZoOIo4SQ3iHCDiD1xjXWjuJv65cJa+rXpelsjxNShXPe4XnIp2DpOPM/uBRHdGRMnfh5C3LY526gg3ULXBDKSS05huiH02gZNz1NZt1SKilpcT79VdQEYLGbY3ZNWG7oSLt6qtcs7LUs2HSXe5QYqK8/bJtM1j7SpE0pJ01cSwMf2d9/hVLRc2WOs1GSkN8vevlz7d5GU7fflXswZrIbPP7GT/f25NbcSJsYUW5sH2upts3tff/D+GN964xJBJOnJmgwVbKpuwI6ijRvKDVnTwlot0P755RcPLXm/ztdmdLbBcMHCDyPevjJHFE80NrwQQxMMFW2Qklt1D01CLdb1Xssnp1WVWGzzMaULwlASojLnjKUzlLe4NN1Y8jEMTdXTW4i47bA12HNoIIcTRMqtPpei6UecvDbblhuA21m6ocOOYlq51ktoegFlN6ArbTBYSHNwIEvNCRivuIu62C/G3b4vCQnLsZTV2wNbWtkKva+ff2In3/yVJ/n8E8OM9Cqtbk0ITEPfsDUtdYl+aDC7aOtjqyXyD398FYDf+OReRnoyZCydt6/MAcqQoTVhmbM0xkpNZho+GuAE4bxguBy6gLylY2pKE6XtgIbqFmkRRZJixqRgqdfll39uB88f6G0LbwlumyC3CKMFH94OoS4NFTR//kAPB/qyXJqqM1Sw2N2djk0tlDiWaYjYNFnHCSJMTbCrJ80nH+njqd1dfPrwIB/f10PNCTg5WmIob636fUvqygn3kwc2I9+KGdG9WtNCe7dS3eP0eJXujMnRHXksw2ibKP/5yZtM19x5ErZDBYvTNyuMzjZImzp+GNHwApp+RCRV9tudSbU3yYhVD5fa6GxhxFOTIGm2ulwE7OiyKaZTjM7WqTlK5Dyb0inYBiEwmLc5uiPPqdE5zk6omnKn6THctnfrzMpb/puWIcjaJp97dJC+nM2VqRoTVZepqsN01cUPlaitHmuT7+3P8syennnvw8Irls6Ok6Xet4VXgIcGs/PG75NpyIT18tCZL2/F3td7taZW/bJ1FTJWduhOq7f23dEy+/syjJUcvv7hJGEoMWPBqSiKuDxVo5g2qTgBulBlhYavxEVaI/xSQs3x4/5zQAiyhraimmEoQcYyti00oXxAx0tOu15t6YKmF9L0Q1K6oOEEXJqqMZC3GMynKDU9/FCtJ6Vr8wKx0pSJ5WxlPASkCaIw4mfXSjyzR5k2pEydkZ4Mpg6vnb2FlBLb1OnOmITRne9DZ034q392asX3bTFZ2NfPTSWbggn3hQc2kG/F3teV1rTemn6rg6Vl8SaECpBvX5ljZ5dNwwvVxmAkSZtKgEpGEaXYF7LqBASRGhTK2wZVN0DEZslKhVAja2jU3CgeljGZrXtkUjpzDX9RmdvOIN7SUonPE+2N0mZLIFyqFkJNhKQMQcbUeXxnkZOjJQCGChaXpupt6YEgPou0pkGtuFQShBJfSG6Vm7x6xmVn13y3+gP9ORw/xDaVPnrG1OeZSC/MqkdnG6r/OpfiYH92nun0wtf+fhqJJCS0eGBr5FuxRrncmloZ3dXpGqMzdb7//k1e/pNT/OD9sVUfv6W1omtwcbLK+zdKXJ6uU3V8mn5IJGWshSKouQFRFBFEKEEq2yBrqdq4cqNXwTJrae2BHCEldS8iiKLY6FiiC0nNCZTI1UqarzBPSXCpZF4AXiC5UWqSsw3Sps50zeXDiWrbxb7V+tipzCiEIGeZpHTlNN8MIsJQre9m2SGTErx1eYabpQbXZxvcqji4fsRQ3qLc9MmkBC//8Sl+8P44ozN13hud5Xd/eJ6MqaFrUGn6nLxW4spU7Y7PUqfOzXTN4a3LM7x1eZrXzk4mmiQJ95wHNpBvxd7X5dbUOQnamrYD+NYbl+7YqFxOZGl0ps501aHqhUhU1uqFksvTdaJI+U+GcQBv1bkFquYbhFH79n4YUbQNDE1vDwRVvQg/jBjpTtOdNig1fEzDaAcwKZcP5qsJ9KCyeKUvHvKzayVsU2Mwb6HrGhoCXb9tH60Rl1w00IRgf3+OdCrerI0kaUvn+f095C2Dv3h3nEMDOYaLabKWQcUJMDSYqLqMlxp8+82ruEFIT9bEDSJO36yqcpMf8ezebnW1E0VMVN07PkutAZ/pmsPPrpWU8qSuYeoiEZhKuOc8sKUV2Jq9r0utaeEkKCgdjNm63x7uWcqa6/JUjT86McroTJ1yU3lf5i2Dph8CSrrW0ARCE/hBRCCY10GSMgR1NySM1GBMJCVuIBGEpAzVS65pgpwuSFsGEWoC09A1LEPjs0cG+OBGmetzTRpegLeEwMmq3IE68EJJ0wuIDB0vkviBSuf9UJJJaWRS6uM71/BUicYPKTU8IqkMlyWCTx/qpz9vc/HWNH4Ysa8/1960PHV9jg/GKnQFEU0vxPHVpGXWMshayufUC5VVXl/Opi9nE8Vqkgvfw1Zv/uWpWnsC1A0lT48USRl6UmJJuKc80IF8K7FS/XtnV5p3R+famTjMnwRdqgb7rTc+4oOxClnLYHd3mqrj03AjSKngnU2pMoMXSFIGpEwN149IG0L1bUvaXSgIyNs6YQRzDR83lGhaxCMDWcZKDpGMqDkelaY6E0gpkVJycrTE/r4MNTeg6alN0+XEqtbCzVITQ9dIG7cnLqVUwbzi+Er2tkOsa7zcREql13JsXzf9ebVJOVv357220zWH92+UCaWkN5vio3ot1lOPmG14ZC0D29SoeyG7e1beZ2ldbf1nf3oKJOTTBo/uKNCft+cNAiUk3Ase2NLKVmK1kqWmrt2hgzFUUDoYS1lz/eTqHFnLUCP6mkZXJoVpaEQQd3WgRJ80ECgp1oylsaM7y8GBPCM9GSIEEqUhrgkNIQS2qSmt8ZRB1jIxdUHdCWkGoGnq2EF4u5Y+Xff5+YO9FDMmpq61dcE7JXOXYim9coFqL/TDCNNQU5dBrFfuh2qas5Xla0DO1pFSMFiweWp3F4PFdHsvwtDEvM6Ti7fqBJEkmzIQQpBJ6fHmp8rOpZTYho6UapN1NfssR4aLvHR0iOf393Jsf2/7JLLZm+wJDz5JIL8PrEYP5chwka985gBIlT1ahsahgRy6rnQwlhJZ8sOIfMd0TXcmhWUIvCDCCyOVxQrIWiYHB3Ls6MqwpzfH47uKPLe3h198fJh9vVkMoYJ+xfHjTVCJHyrDhrrrE8TSsgIlXNWyYZNSMlf3qDZ9ak5ANmUQSWVebOjKyGJhcr4wuGdtY94H0dDANpRBRVufXBNoQtXHU/rt+2tC3T6f1jkyXGR/XwbT0Pja8cPtvQgvCNnfn+Hd62V++ME4r5+d4OzNCn4YtYeIujPKiNrQlGHETN3DMnX+6d/dz96+3Kr3WbbiJnvCg09SWrkPrLZ/fCUdjE59lJY1167uDFU3pJhWESlrGfRkUqSMAKfD+UbJ1SoJ2OGiPU/nYyCvhnNCqUbl5+JasS5UeWZ0ttl2xfGCWKhKF5hxq1/TD3GCkPMTNR7fWaTmqOCl2gzlPAnbVgBuBXdTExwZLvDe9RJuEMX64wJd04ikulYwDQ0vjEgZGmnTIKVDFB9JE2oytOFHXJqqoQnIpm5/rEsNZUoxVLAwNbg6owaM0qZGd8ak3AywTZfuTKp9QnxsZ5Gjw8W7GuDZLA2VhIebJJDfB9bS077UZuhSAeLyVI3f/eF5QI3DV92QUMI/+Tv7eOPDacZLTUIpaXgh/QWTPT0Z9sV66K0hov/kuyexDJ2aG9wxvCOEiIdyfJq+RsaMTYrjKUpdh5Shc2x/LylDxwtC/EguqYyoC6VP3ho2KsaDSwLVeRKhjIuFoTRYvFDGzvYBedtAQ+L4MNKbxvECRmebBFIJZlm6wI3A1EJ+75Xz7OnNUmn6uH7IydESpi7aA0BBFJEydHoNnbobIqWPbRr8F8cPr8v4Y7n3MCHhXpEE8vvAQrXBlYxul2KxANH6+Y9OjDJZcchZBnt60nzv7RukY4/JrGXi+CFzdZeJskPeNvjB+2NcmKzzV6fGGCup0fyFXSV+pEotTT+gL2eRTWlEUpkKu4Eqv6RTOgf7s3ihJJIB710vo6G8KluhvFUeEYBlakj/tlFyFElm6y4pQwMp0DRlTSeAhh9hG2BqOn4UUW54GIaGbWj0ZU2uugESJXYuhLp9b8YkFw8qPbGri5qrrhZMXaPhBXEJRRL6ylEondKZrLp8/onhNWXgmy3IlpDQyQOrtbJa1vuFXO3978cXv7WpevZmmbmGhx9KIikpWAZzDZ+sZfCZI/3UnZC3r87SZZtcna3Ht1v6uAIYLlg8ubuLi1M15ho+oEyK9/dl2+18f3P+FqA6R0oNDy+8LXjV0myxDQ031v8u2galZoBhaBwdyjE606TmhXRnTRpuSKXpkU6pNsBWx0o6pfPsnm6m6z4zNZfJikMUSUIp4w3NNIYuEAheenSIE5dn+GiyStrUmGv4FGwTkOiaRjFj8vy+3jVr3XSO43eemDd7TiHhweeh01pZDYvpY7R6s1fzhVzL/e/l5XbrJPHa2UnCKOLGXINsSk1EukHEdN2jP5ei4Ue8dWmWiYqDH0pqjgrIrTLHUkig1PSpOj660OhKp9qyvLqucWgwy99enOHirRrZlI4XRmgINHG7NbBo6zQDiRtK9vVmeXZfN305m+maw0+vzHHhVp28ZbA7m2Koy+ajySp1T8PQBIauE8buP5mUTsYyGbFMDvRn+OEHE7hRy/JNMlFxGC7aZFKq3n2wP8ulWzUaXkQ2pV4PBPTbGildu6sro2QcP2Gr8UAF8rVmvev9Qm6FL/S58TLfePUC0zWXq9O1uFMFwsgjbyvbtnJTcrPsYGiCqhOoYAZocUF8pZ5vgWoBfO9GmZ3FNHMNl5m6y62qyz/6+C5ePzdFMW2yty/DZNml4alBpN5sCi+IaPohDV8NF9mGzkuPDaEJoXq5r5cZL6te8ef392CbSqkxZ5lUnRARm0UYuiCIVK2/tbfwygfjhJE6Weiaeh6BH1F3Q3Z1Zyg3fXpzFo/tyPPu9TLplEkhbeAFSmLg4zsK/OqxPWt+r86Olyk3fKpuQME2OTiQpSdrJb3iCZvGutoPhRBfEkKcEUJEQog70v37yd3ojy/Vm73aL+R6778RfPfENa5M11XvM2oEH5SmScVRAzoqm1X6JZ1+mGEEOctc1cSlH0HDDSk1fQSirUL4/VMT7ZPZk7u66Mtb7IgNnR0/pOEFpE2dvJ2iL5tCIrg2XW+Pst+qqvp4Std473oZL1C2aA0vIGfpuLFcgB8oCzdNExx/bJDjjw0yEd83Z+mqFTKCrKVjm7fbDz+cqNAMJEeG8gx3pdnRlebvPb6DP/i1p/mdLz6x5iB+brzM9ZkmFScgbxk4vpIRGJ2pJ73iCZvGejPy08AXgT/YgLWsi7vJjterkLiW+9+rGvm718vkLJ3putfWEg+jePoxkJSDYJ6wVOeWiAQsQ2t3hyxF5/39IMROGYSRpB7Xhj/9sQGmaw6Xpuo4vhrRtww1UWoZejzyrqNrGnv7slyYrGGZrceN0ISgP2+ha4KLU3We39eDZeocGshxaarORMUhCCW6ENiGxiunJzn+2CDdGYOmp7p0ujMptZEpwIvPTNNVh/MTNbozJkeG8zTckAuTtXnPba3vwSunJzk0mOPCrVr8/NTzPD9Z4zc/fWBNx0pI2CjWlZFLKc9JKc9v1GLWw91kx+sd3ljt/e+lW5FExmqBynNSaYyooJs2NUTcuN3qIekM1wKYbXiAmq7MLHFa12NtFlNTGitCQCQj3DCi4YV8761r/MXJMa5O18lZBoW0yVAhzZO7uzi6o0AxY9KTtXhmTxeP7+pid28aL4xizRSdnqxJ1jKwDI3pqsObF6ZwvJDzkzUO9Gd58egAPdkUXZkUn9jf2379jgwVyFkmO7vSdKVNpqoul6cb+EHE771yntM3K3TF7Y1vXZrh/bEyCCg3/Lt+D8ZKTfb0ZXl6pAvL1Km5IQXbYFd3OqmPJ2wa961GLoT4MvBlgJGRkQ0//t1k12sZ3lgqo17N/e9lLf2p3V28fXkWTdBWL1TWapAyddwwwhBq1L1tFBHfV8RGDSM9GaZrLlM1D0PM1xEXQE821ZYM8EOJ6wdU3ZAork+XYi3yMHJpuAF9eYvHdxaZqLoc3VG8wxHp6LAauFFDQ2FbLbDhBczWfUDwiQM91B01ZOSFIXnbbGuXTFUdLk/VqDo+UaQmS0tNn5Su0ZM10YVgdKZBKCMG8jZCCCb8CIlkIG9RdYO7fg9an7P+vN0ewV/4uUtIuN+sGMiFEK8DQ4v86etSyr9c7QNJKb8NfBtU++GqV7hK7rZXezXdJCt1p6x0/9VOdnaeLKx4tN1bYNK88ITyCwd7GS87jM01mYxLEGlTMNyVQQiBlNBwfdXHLUB0BPKCZXD88WH68zZvnJtktu5hGqorpdz08IIIU1dTla2yja5B3VPlkFBKzFjpL4rr8Ag1nLOnL0vDDyk3/SXfk9Zr+tRIkbM3q0xWXQbzFh/f10NfzoY89OQs3r4yw6cO9aMJwVTV4eRoCUsXpAyNw4N5fnxxhkLaYGdXhoMDWU6OlsiZGtN1dfKxTZ0wFvhygyhuQby7/YyNmglISNhIVgzkUsoX7sdC1su9HI1eLqNu/X+52vdqnIG+c+IaP744Q3fGZEfR4uRkHQE8t6+7feJ44Uh/u0Ok007s33tmJxcm65y5WebseAVdCIoZ5WbzwViZczd9UgaYut4WnTI0GCym21mlmrI0qbohXhgH8ECZSBRNE9vUqbgBvVmLsuNj6RpzkY9tCJp+PMkpldb5zbLD6EydR3eoMfdXTk+qTo9mQME22jXuL39qH989cY1T1ytIJL2ZFM/uvd2WePFWnXLTY7zs8KMzE+iaRqnpkUsZYGgU0yn29uU4c7NKT9bkE/t7ASjYJk0vaNevgViRUeAGEY/tLNzxHizHwpPnC0f653lxJiP4CZvNA9V+eK96tZfKqM/cLDM621ixj3y5LK6V7V+eqmEZgomyw4fjFXK2QW/W4vJ0g2NxgPqjE6McHS7ccUK5MFlvD7T84P0xvvXXl5ipuSAlvRkTy9TjfmxBNiXIpAyMOKNtkbMNmp6JRLCzK81U1Y2FstT0Zl/eZqQnzWzdp+HHY/ihpBaXV1pZfiRVq+LJ0RIvPXr7pDY622BnV4a8bcw7MTX8iI/v6yFvG7x5YYq3L8/xsSGfy9MNLEMjDCOiSDI212RHl03TC2k4Qbwmi9fOTtLwApzgtqDYwYEsJy7NkreV+fTZm1UQgpytc3gwR0/Wau9nrJRJJ16cCduBdQVyIcTfB74F9AM/EEK8J6X83IasbAvQysTO3qzw0WS1XaMFlc1VnIBd3ZkVa9+LXS08t7erPcRj6oLpqkPTV5kwAupuSN2tc7PcRADdGYOzN8t8OF7GDyWWobO7J82jOwrU3KC93tfPTXFoIMdExWG27lPRBP/wuZ38fxfnCCLZHuSpe2F7g9bxA+bqLpNVl/5ciiCMqDo+lqnz/L5uHhlUGez5iTLXrpcp2CZV129n4Z1EHS5Bf3RitC0CttgVzcIT06M7Crx9eZZ3rs0xVIh1xBsBw0WVNde8AF0T+JGk6avyTtrSaLiC2YbP1ekaI71ZTF1nX1+WwYKFF0o+fXigvQG91BXbUnsgW2FWICFhJdYVyKWUfwH8xQatZUvRmYk9ubvA25fnePvyLM/t624PrRTTxqo7ZTqvFjqPrVzgNWYbarMunRLoQuD4EaahIuJs3eX9GyV8P0LTlbZ40wu4Ol1nru7zqUN9wPwSUGtsvtz0ydsm3/yVJ+8IVAD/w+sf8beXZtA1wXDRQhOCqhuytzfLvo7x+6mqw1tX5uJx+4i6G8zrgNEgNpuATMpgqGAxU3P59ptXqDo+R4YLd7xOkxWHnozBa2cr1NygrRMzPe7ih5J82qCYNujKqOCp64Kndnfx6plJ/PB265+dMni6N8N4xcU0dBWkP3doSfGx5d7rhVdWq93fSEjYTB6o0spGMj8TMzl2QHB6rMKpG2VeOjrEP3xuF6+cnryrPvTOYxfTqiPE0FRPdRBriEcoidgwCrlZauIHahhGCOVNKTTlOF9zg7Y0bGfQ6awxa0KN0S/GlZkGO7rSFGwDN4hwg4if25VTpRY/ik8EBmduVmh4PkKqkwzcbmlsbaRKVEDP2wZeKOnLWRTTyuGo6gR3vE6mgB9fnME2dDKmjutHvD9WYShv8fx+pYFy4vIM5YZHqeETSsmlqTqmLkgZenuy8rGdBXqyFuNlh2986cl1vtfzs+71zhokJNwPEmOJJVjYl96Xs/nUoX4e3VHk5RdVtne3feidxz44kKXc9AkjqfRP3AA/biHUNKUHHsS921IoL05N3DZr6MoYuHGv4FIGwEEY8bs/PM/V6dq8jPO7J67hhxEF24hdgXQsQ2Oi4uCFcp5RdKWpgjixkUNnXVxyW9ZWCvVvN4g4OJAlb6useuHrdG2mzkxdScw2/ZAgkso8AjWT37p9T0Zlv00vZCCfotz0aXghhwfzvHR0iE/s76UvZ68ruC43g5AYRSRsB5KMfBHOjatNzHdH5+jLWRwcyC4aLO62U2ZhlicAU9cIwpC0aRCEPqauYZnKEGK24TFTc9smDqoOLdA1QcMLOXOzzDdfu8ChwSyvn5vi8lSNMAyZqHs4QYhA1a7/5sIUWWsO29DI2yZVx6cvZ7Vb9EBNes7WfY4dSM8rB/2DPzjBrapDJFVPeicaIGORLNNQTkPP7OmiL2e3+8Zb3StjpSYpXbn9BJGkkFaZf8VRHS27emzqXtR+XX9yRYlgWYabnpvYAAAZ9klEQVSS2S2kDQbzKSYqLnvjq4X1tgAul3UnRhEJ24EkkC+gVS8dyltU4gnAd67O8bGhPJqm3REs7qZTprOL5aPJmgrYXWn292WYqft8MFYiiCQ7sikyKR0vMJiKHEIJDS9qbyZKCWkzxZO7iu1uiheO9PP7o7PM1n1sU6Mvm+L6XJNIyng6U8PxQnRNMF3zGOnJUIkt5CxDeYYasZ5JJ8W0EQdTOa8+3tIYL9hK0lXXBGHEsp0hF6fqDBcsCmkD14/ozhhqBF8XRLHnZut1bZWLtNaIKhBJybnxCn4Q8sa5WSSSp3Z3rek9WOr9WOzEkBhFJGx1kkC+gM56ac42uDhVZ7bmMV5x+e0vHN2wL3Ta1Hj7ygw3Sw67u22e2NVFf97mEZQP5njZoTubouIo/07D0BCxvngYqXJGShPkbYPBwu2rhAuTdQYKaWxTGTJfn2tg6ALHl+hCBd0glFSaAYMFi4mKy+FB5Uk5U/cwdY2vfPbAHc/z6HARP4j4YKyizIpN1WcuhODgQI60qWrWg3mLMzcr/G9/ewUvjLB0jZ9cmSGlazy+s8ievizvjZYoNzz29WZ4f6wCgKlDzQnRhVDepTFLZcsDeWte62LVCdYkQdxJknUnbHeSQL6Azg3D1hh2FAfWjfhid3ZIvHBkkDcvTFF1AjoSTjIpnXLTp+oEGLpARhIhBbu7bWXEoKkaskAyVfOYrjn05WwcP+DtKzOUGz5uEBJGEZ4fYRs6TU8ZIt+qum2ThoMDGdIpk719OUxD59iBviXFvI4/NsjobINPHuzlJ1dnqbsh6ZRB1tTQhMDxQ6JQcm6iqjZf4yK6G0TcqjikDI13roZcnq5TanpIqcpJnzzYy6kbZWZrHrou2Nmd5sJknf3j5fY+xGLZcsbUNrQtMMm6E7YzSSBfwM6uNFena0xUXCqOcpQZKljs7cttyPEXdki0eqdPj1X41CGL0Zk658YrpE1NjegHqtXPih1uTF3D0NVwjxdIbEPn4q06UsJPr8yRiwWcpmous3WfIFKB3DY1mn6EjJQZsq4JTl2v8KlDfatyx+nMWht+yPWZJocGc2QsnXPjVUrx1GbBNqg0lfaKGt9XQT6IImYaHoGUDOYtxkoOV2fqPLazwDMj3bx7vcTTI12M9GbvGKxaLFv+wx9fpSe3uRLCCQlbhSSQL+DQYJY/P3mDrGWQt1RmfLPU5KVH19+lcG68zI/OToCEfNrkYH+W/rzNc/u6OXWjzHjZYbziUkynSKf09gbk1ek6jh9SdwOKGVMZKcQpfMHWKTc9ztxUeuSt8fOKE9Cf1zE0VVefqbuYGhi6hpSSrGXgh5Jrs2sPfMV0iv49FgJwOwZu/vDHVzkzViaIJJEU6ELS6o0MQjB0temas00G8pJS0+PUjTJ52+Tpka72yXI1EghJW2BCwm2SQL6AC5N1ntrdxUTVpeYEFNImhwZyXJis8/l1HLdVUknpGg3X59q0x/mJCru7M+zvy/LS0SFefvEQX/2zU1Sbqi7eoi+fYnSmQcpQlsZNP8LQNT6+s0DVDfFD1br4/H6lUwKqa+SjyRqTVZdPHuhlsuKgCyV6a+jqJDGYN5ire3zztQur8hztHJpZzKdyZ1eajyarGFps8wYQl1BasrV1Vw0yZVI6nz0ygB+q4y82dHM27h6KoojxssO7o3O8emaCr3zmQCJelZDQQRLIF9DSm25tdNacgAkpabQizhroHPsenW0wXLDY2WXz44v1tn3ahxMVLkxWOTyUByAVa6B0tgQamsZwMU0q7ioZKioNEcsw2sH0ldOTXJ2u8caNSSYqDgC9mRSfPNDL73zxCT6aqlNZkMHeqjq4QXSHTvpiG4arGVU//tgg798oMVPzEChLuTACYvlcDaWSWG76OEHIeMnhyd3dwJ1SsCowB2RMnfOTNSxDozebouIEfOuNS3zzV55MNigTEmKSQL6AnV1prkzVuHBLBY+cpVOJdVXOxRtwq2FhBtvq1EgZGt0Zk1tVFz+MiKTqYBmba3J1ukbNDTF1wVzdB6my2pobsq8vy1c/p2rZreA1kDfbwevyVI3vvHWVmhPEE5eSUsNjqu4ggc9+rI/vvnUdgLylU3VDZmoeT+0urmrDcDWj6keGi3zt+GG+c+Ia/8+FKSYrjnK0F6Ah8ULa5hdNXwlrfenZXezvzy2aXRdsg/Gyg2Vo7ZNawTaYrfu8cnqyPZiVkPCws60D+b2wTzv+2CAv//EECObJoB4ezK2pI2JhBtuTS1Fp+oyXHVK6RsE22mJXeduk6YdMVFyGCha3KhGRlIyVHQq2wbH9vfNMghdbw/dPjVOp+wQdv9MBpODMzQpNP+JXP7GbNz6cZrLiMFiwKdoGT8QZcYulNgxXW5M+Mlzkv/3iE3zztQvt2//o7ATlhk/dDQilxI+UM5AmVCnr80/sXDS7fuX0JN9//ya92VT7+G4Q0ZM1k03NhIQOtm0gX8ns4W45Mlxkd296nkt6S8tjrNRc9cljYQZ7sD/LyWultn6KqQmCSG1WhpEkbercqjqUGh5hBL/05I52ZtoZxBd7fIA3L04TCRW8Wy5AEVBzffxQxobGkj/9j4+119QZbFsstWG41pp05/Mv2CYTZYdMSsePJAf6c0o+wNDaAXmp9r9Xz0y0pz5bWjB7ejLJpmZCQgfbVmulM+PVhGj/u9XpsB6ODhc5uqN4h5aHpYtVe29auuDNC1P86OwEb12eQQg4NJijJ2tSdwPKToAmYmf7SJKPA5UXRjT9gNfPTXJuvEIURe3n9IP3x3j5T07x/fdvMjpT5+p0jW+/eYXvnLhGEEYIbkvIttrSw0hpjS+Waa9FR6TVBtjSXimmzWVPmi3dF1B6MpoQNP2IlK61beOGi/aKVnxf+cwBkDBbVxvAhwZy6LqWaJ0kJHSwbTPyeykvulT2mV7lEMq58TI3yw41JyBn6TS9gBOXZunLpdjXl2OkJ8P7N8q4gRKM6rNU/TcMI2aaPoNFm7xl4PghH05Uafgh58bLfOPVC1SdAInyqbwwWSUfqxQamlCqiR1iVqD+3Zc1lyyDfPlT+/jOiWu8fm4GgeCp3UtfzaxlaKbzNezJWjy+I8/J62U0TZWs9vZm0LSVA/Lnn9jZ1jTfyBJaQsKDxLYN5Peyj3i5IZTeVQyhvHJ6kj29WYaLdrvzJW8bNLywbUa8szvNxVt1xkoNIgkjvRmqbkBPVqcnawFqY1B1lQR898Q1pmoeGVNDIqi4AWEY4fqhMkqWys6s0zgZVJnlzQvTHN1R4Ld/+dFFn2/Tj3h+X++6R91hfulHjfGHjJcDnhzp4UvP7Z5nkbbagJxMXSYkLM+2DeT3uo94seCx2pPHbaEns8MTU/JXp2625VL7cjZ9OZtI9rR1tP+jP/opN2ab7fqxGyhRlYJtcOLyDFEUUXbCtiuPBNxAKQjW3QA/vK0P3orlKR28MOL6bH3R57mRDjir6TVfTy9+QkLC4mzbGvlaa7br4dy4kok9c7PMW5dnuDpdW7am3FkfblF1AgYL9qK/b50IHt1R5NBgDsvUqbkhlqlzaDDHYN5iuuZhtORfQ4kXqjJKq0c7bxvEHXpKUEsX9OdS9OdtujImji8X3T9YTot7rdzLfYuEhISl2bYZOdyfS+7OLPPIcEENqEyoickozpZbgapzMGaxq4VfPzbC6+em7vh96ypC3a/B0eHCvL9LYLBgMVXzSAtJEEZEbQVESMcRvDenM1v3iaKIlKHdNleWyiZtPW2FqyGxRUtI2By2bUZ+v1iYZe7rz3F4KMdk2cH1Q27MNfib87f4xqsX2t0rS10ttPqll7qKWOp+Xih5Zk83aUPDCaN5m5kRgprr4/ghecukmFZuP34YISU0vZCy4+P6EaOzjTs6bDbSAWepK5GkVTAh4d6yrTPy+8FiWealWzWmah6FtEnBNnGDiCvTdb574hq/88UngKWvFla6imj9rbVh+MrpSVK6oOYEWIZG3jJx9JBaMyACRKxPrgmJF0Y8M9LNydESpaZH1fHxQtXR0pM1GS5Yd2xkbqQW96HBLN964xJBJOnJmgwVbHT9TjOOlbgXg14JCQ8ySSBfhHPjZb5z4hrvXi8xVXXpzaR4dt9tQaqxskMmdXts3DZVi+GrZydxw1OrDj5LDfcsHHSarLhculXFThkMFAyuzTQQaUExrTphVLDWyKZ0Botpju6ISJsaP7k6h65p7OpO8+TuYtt6beFG5kaUqM6Nl3n93BSHh26bVFScgK985k6TipWOcy8GvRISHmSSQL6Ac+Nlfu+V84zONMhZOt1pg7Fyk/r5gL9zqA/LMAilpM++XVNueAG3qi4Csergs1TAWtQwoSfD5ekaBdugGo+592ZNmr4aINrdnQEpqXohxbTJ144f5shwkX/yf/y0PaF68ZbqWmlNqG40nSWolhxtuemvWTVyI7toEhIeFtYVyIUQvw/8u4AHXAL+QyllaSMWtlm8cnqS2bpHzjawTR07ZYAQVJoBp65XePHoIL+wv5cLk7V2m+CtijIl3t2TbndrtI61VPBpBSwvCHn7SoWaE2Dqgqrj8/kndsy7bd42SJtGuwf9rz+c5PpsE10TZFPKJ7PqhHzyQG/bJOLceJnrM00QakPW8UN+dq3E4cHcmk0yVlPq2KiNzmTDNCFh7ax3s/M14DEp5RPABeC31r+kzWWs1MQLonl64N2ZFN1Zk6M7Crz84iH++QuPMNKbAdRmnhtIejImT+66HdxWCj5jpSaOH3BytITrh+QsHaRkuuYxOjO/57vqBDy1u3h7UzJqeXdKujPqpNHZOw7qRHFoUAVst+P5nJ+srWkjs3XlsJIswUZsdJ6L9cf/zQfjvHV5humac1fHSUh42FhXIJdS/khK2fr2vgVse1X/nV3pth54CxUI9XYwacm1fvrwAI/uLHJoKN82T26xUvDZ2ZXm5LUSs3WXsVKTG6UmTT9isGBxfrJ2RxfJrx7b0+5oqXkhu7vT7OpOIxFYps5z+7rxOkY6W7rqT490tfvSC7EN3FpKFKvtDV9v90vrhDGUtzA1jXLT552rc1ydrt11F01CwsPCRtbI/zHwJ0v9UQjxZeDLACMjIxv4sBtLyxxhdKZxhx54ZzDp3CDszFpXO2V6aDDL//z/NrENDdvUcP2ImuPwCwd68CNVG16si6T1/4W93wt/bvWHtwykW7fxgnCeI9ChweyyY/OrLXWst/ul84TRMvWYrXmMV1x++wtHk/p4QsIyrBjIhRCvA0OL/OnrUsq/jG/zdSAAvrfUcaSU3wa+DfDss8/KpW632XSaI7x7vYRAcGx/zzwp2cXus9YgdmGyzu7uNKWGhxdKbFOjL5fiZtnl04cHljVEXo08wWK3uTZTRxOClKEzXLS5Ol3jz0/e4KndXezpu9P0GNY2MLSe7pfOE0br5BNJyXjZSYJ4QsIKrBjIpZQvLPd3IcSvA78EfFZKuWUD9FpomSOs9T5rCThjpSZPjXTx3vUylqEpbRU/ZK6xeBlh4YbjC0f652XSC08ci51cdhRtTENvB+WJikvWMpiouuzrzy1p33Y/vDETM+WEhLtnvV0rx4F/Cfw7UsrGxizp4aAVuJ4e6eLiVJ3pqkPdDUmntDtG/hdrVXz93NSKvdULTy5f/bNT9HSoN1Ycn7ylU+vYpFzMvu1+eGMmZsoJCXfPemvk/xqwgNeEEABvSSl/c92reghoBa5i2uRAf4bpqkvOMnhuX/cdJY6N6q1emPUWbFN5Y67Cvu1elzfu1wkjIeFBZF2BXEp5cKMW8rDRGbheOztL3jZ4dEdhXudLK1Av3HCcqjpcvKWEu4BVj7AvzHqHChY3S00ODeSIpNz0LDjRHU9IuDuSyc77xLnxMt89cY13r5eRSJ7a3cWvHdvDyy8e6tAvF+3bd5Y4OjPpqarDyVE1czWYt9Y0wr4w693bl+OlRweXrbUnJCRsfZJAfh9o2bRdma6Ts3QEgrcvzzJedvja8cMrbvQdf2yQb7x6gXdrLjfmGggEedvgkT1dayqzLDWhmZg9JCRsbxIZ2zXQMpj46p+d4puvXVjUdHkxXjk9yXTNVaP2KQM7ZZCzDWbrHq+cnlzVME0UNwQFkUQT86c4VzPCvtoJzYSEhO3HtgrkdxtIN+qx7zYQjpWauEE4b+zfMjS8IGKs1FzR7ajlAfrpwwMcHiow3JWmmDbbQliradNL3HsSEh5ctk1pZbPlTdfTObKzK81Hk1XcIGpL37qBcvHpHPtf6jidm50H+7OcHC1h6YJy02tn7yttUCZiVAkJDy7bJiPf7IxyPd6Wxx8bpC9nUXUCml6A4wXUnICebGpVGiKdglT9eZunR7pACDShrdqrNHHvSUh4cNk2gXwjTYLvhvUEwiPDRb76uUMc299DEIEXSZ7f39PWDV+JhTX0lKGzvz/Hv/oHT/Dyi4fu6hjrsXRLSEjYWojNmKp/9tln5TvvvLOm+3zztQtLCkUtp0uyUbRKO2EYMVFxmK37GJrgK589wOef2LnmY63Vymwj7M8SC7WEhO2NEOJnUspn7/j9dgnknTXyzhHu+2kB9oP3x/jWX1/CDyN6synV+61pa1rDVngeCQkJ25OlAvm22ezcCiPcFybrfGJ/7x1XBWsZld9KVmZJhp6Q8GCwbQI5bP4I90Z0fmyV7pHN7gJKSEjYOLbNZudWoHPDc7rm8NblGf7NB+OMzjZW3dO+VbpHNrsLKCEhYeN4aAP53QwXtTo/rk7XeOfqHOWmj6lpDOWtVQ8HbZXukc3uAkpISNg4HspAfrdTmq06/XjFJYygkDZ5ek9X25RhNdnsSlOc94utcmWQkJCwfrZVjXyjWO+GY9XxMXUx73dryWY3u9YPiZFDQsKDxEMTyDs7NM7erPDk7gJwu/tkLcJTKV1DSonrh5wcLfH0SBcpQ99W2exW6AJKSEjYGB6KQL6wQ+OjySpvX57j2AFBX051kKxFeOqxnQV+dq2EZQgsXXDmZoX9/bltl81uhSuDhISE9fNQ1MgXdmg8uqOAAE6PVda04djaIOzL2Tyzpwvb1HHDCD+UvHCkn1dOT26KMmNCQsLDzUMRyBd2aPTnbZ7b140XRmvacOzcIOzL2Xxify+f2N/HU7uLvH5uKtH6TkhI2BQeitLKYg48tmnw0tGhNem0LLVBmDa1LTOtmZCQ8PDxUGTkG9W7vVTroBfKpCc7ISFh03goMvKN7NBYbINwJc/NhISEhHvJQxHI4d52aCQ92QkJCZvJukorQoj/RgjxvhDiPSHEj4QQOzZqYduJrTKtmZCQ8HCyLj1yIURBSlmJ//3PgaNSyt9c6X53o0eekJCQ8LCzlB75ujLyVhCPyQL336UiISEh4SFn3TVyIcTvAP8BUAb+7jK3+zLwZYCRkZH1PmxCQkJCQsyKpRUhxOvA0CJ/+rqU8i87bvdbgC2l/K9XetCktJKQkJCwdu7a6k1K+cIqH+P/BH4ArBjIExISEhI2jvV2rTzS8eMXgA/Xt5yEhISEhLWy3hr57wohDgMRcA1YsWMlISEhIWFjWVf74V0/qBBTqMC/VvqA6Q1ezr0kWe+9ZbutF7bfmpP13lvWut49Usr+hb/clEB+twgh3lms0L9VSdZ7b9lu64Xtt+ZkvfeWjVrvQyGalZCQkPAgkwTyhISEhG3Odgvk397sBayRZL33lu22Xth+a07We2/ZkPVuqxp5QkJCQsKdbLeMPCEhISFhAUkgT0hISNjmbLtAvt000IUQvy+E+DBe818IIbo2e03LIYT4khDijBAiEkJs2TYuIcRxIcR5IcRFIcR/udnrWQkhxP8qhLglhDi92WtZCSHEbiHEvxVCnIs/C/9is9e0HEIIWwjxEyHEqXi9v73Za1oNQghdCPGuEOL76z3WtgvkwO9LKZ+QUv4c8H3gv9rsBa3Aa8BjUsongAvAb23yelbiNPBF4M3NXshSCCF04H8EfhE4CvwjIcTRzV3VivzvwPHNXsQqCYD/XEp5BPgE8E+3+OvrAp+RUj4J/BxwXAjxiU1e02r4F8C5jTjQtgvk200DXUr5IyllEP/4FrCl/d+klOeklOc3ex0r8HHgopTyspTSA/4Y+OVNXtOySCnfBGY3ex2rQUo5LqU8Gf+7igo2Ozd3VUsjFbX4RzP+b0vHBSHELuDzwP+yEcfbdoEclAa6EOI68O+z9TPyTv4x8MPNXsQDwE7gesfPN9jCgWY7I4TYCzwFvL25K1meuEzxHnALeE1KuaXXC/z3wNdQOlXrZksGciHE60KI04v898sAUsqvSyl3A98D/tnmrnbl9ca3+TrqkvV7m7fS9lpWXO8WRyzyuy2dgW1HhBA54P8G/tMFV8JbDillGJdbdwEfF0I8ttlrWgohxC8Bt6SUP9uoY67bIehesN000FdarxDi14FfAj4rt0Dj/hpe363KDWB3x8+7gJubtJYHEiGEiQri35NS/vlmr2e1SClLQoi/Qe1HbNWN5V8AviCE+HuADRSEEN+VUv7q3R5wS2bky7HdNNCFEMeBfwl8QUrZ2Oz1PCD8FHhECLFPCJECfgX4q01e0wODEEIAfwick1L+d5u9npUQQvS3usGEEGngBbZwXJBS/paUcpeUci/qs/vX6wnisA0DOUoD/bQQ4n3gJdTO71bmXwN54LW4ZfJ/2uwFLYcQ4u8LIW4Ax4AfCCFe3ew1LSTePP5nwKuojbg/lVKe2dxVLY8Q4v8CTgCHhRA3hBC/sdlrWoZfAH4N+Ez8mX0vzh63KsPAv41jwk9RNfJ1t/RtJ5IR/YSEhIRtznbMyBMSEhISOkgCeUJCQsI2JwnkCQkJCducJJAnJCQkbHOSQJ6QkJCwzUkCeUJCQsI2JwnkCQkJCduc/x/Vz9e6rEBHywAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] @@ -106,8 +118,7 @@ ], "source": [ "# Check out the data we generated\n", - "plt.scatter(dat[:, 0], dat[:, 1], alpha=0.5);\n", - "#plt.scatter(dat[:, 0], dat[:, 1], alpha=0.5);" + "plt.scatter(data[:, 0], data[:, 1], alpha=0.5);" ] }, { @@ -116,8 +127,8 @@ "metadata": {}, "outputs": [], "source": [ - "# Put data into a DataFrame\n", - "df = pd.DataFrame(dat, columns=['D1', 'D2'])" + "# Put the data into a DataFrame\n", + "df = pd.DataFrame(data, columns=['d1', 'd2'])" ] }, { @@ -146,47 +157,47 @@ "
\n", " \n", " \n", - " \n", - " \n", + " \n", + " \n", " \n", " \n", " \n", " \n", - " \n", - " \n", - " \n", + " \n", + " \n", + " \n", " \n", " \n", - " \n", - " \n", - " \n", + " \n", + " \n", + " \n", " \n", " \n", - " \n", - " \n", - " \n", + " \n", + " \n", + " \n", " \n", " \n", - " \n", - " \n", - " \n", + " \n", + " \n", + " \n", " \n", " \n", - " \n", - " \n", - " \n", + " \n", + " \n", + " \n", " \n", " \n", "
001168.020
112155.027
D1D2d1d2
0-1.1482160.33201200.0879220.009294
10.6887431.7641931-0.530187-1.418836
2-0.886799-0.3328162-0.092297-1.302195
3-0.241192-0.40966330.2755020.109635
4-0.6624260.9498134-1.050818-1.059746
\n", "
" ], "text/plain": [ - " D1 D2\n", - "0 -1.148216 0.332012\n", - "1 0.688743 1.764193\n", - "2 -0.886799 -0.332816\n", - "3 -0.241192 -0.409663\n", - "4 -0.662426 0.949813" + " d1 d2\n", + "0 0.087922 0.009294\n", + "1 -0.530187 -1.418836\n", + "2 -0.092297 -1.302195\n", + "3 0.275502 0.109635\n", + "4 -1.050818 -1.059746" ] }, "execution_count": 5, @@ -195,7 +206,7 @@ } ], "source": [ - "# Eye ball the data\n", + "# Have a quick look at the simualed data\n", "df.head()" ] }, @@ -225,19 +236,19 @@ " \n", " \n", " \n", - " D1\n", - " D2\n", + " d1\n", + " d2\n", " \n", " \n", " \n", " \n", - " D1\n", + " d1\n", " 1.000000\n", - " 0.758206\n", + " 0.773245\n", " \n", " \n", - " D2\n", - " 0.758206\n", + " d2\n", + " 0.773245\n", " 1.000000\n", " \n", " \n", @@ -245,9 +256,9 @@ "
" ], "text/plain": [ - " D1 D2\n", - "D1 1.000000 0.758206\n", - "D2 0.758206 1.000000" + " d1 d2\n", + "d1 1.000000 0.773245\n", + "d2 0.773245 1.000000" ] }, "execution_count": 6, @@ -256,7 +267,7 @@ } ], "source": [ - "# Check the correlation between D1 & D2 (that it matches what was synthesized)\n", + "# Check the correlation between d1 & d2 (that it matches what was synthesized)\n", "df.corr()" ] }, @@ -272,7 +283,7 @@ "metadata": {}, "source": [ "
\n", - "Statsmodels is a module for statistical analyses in Python. Patsy is a useful package to work with and describe statistical models.\n", + "Statsmodels is a module for statistical analyses in Python. Patsy is a useful package for describing and applying statistical models.\n", "
\n", "\n", "
\n", @@ -283,15 +294,26 @@ "
" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Patsy gives us an easy way to construct 'design matrices'. \n", + "\n", + "For our purpose, 'design matrices' are just organized matrices of our predictor and output variables. \n", + "\n", + "'Predictors' refers to the features we want to predict from, and 'outputs' refers to the variables we want to predict. " + ] + }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ - "# Patsy gives us an easy way to construct design matrices\n", - "# For our purpose, 'design matrices' are just organized matrices of our predictor and output variables\n", - "outcome, predictors = patsy.dmatrices('D2 ~ D1', df)" + "# Use patsy to organize our data into predictor and outputs\n", + "# The string `d2 ~ d1` indicates to predict d2 as a function of d1\n", + "outcome, predictors = patsy.dmatrices('d2 ~ d1', df)" ] }, { @@ -300,9 +322,11 @@ "source": [ "If you check the type of 'outcome' and 'predictors', you will find they are custom patsy objects, of type 'DesignMatrix'.\n", "\n", - "If you print them out, you will see that they reseble pandas Series or DataFrames. \n", + "If you print them out, you will see that they resemble pandas Series or DataFrames. \n", + "\n", + "You can think of them as customized dataframe-like objects for the specific purpose of being organized into matrices to be used for modeling.\n", "\n", - "You can think of them as customized dataframe-like objects for the specific purpose of being organized into matrices to be used for modelling." + "Next, we can use `statsmodels` to initialize an OLS model object. " ] }, { @@ -311,18 +335,19 @@ "metadata": {}, "outputs": [], "source": [ - "# Now use statsmodels to intialize an OLS linear model\n", - "# This step initializes the model, and provides the data (but does not actually compute the model)\n", - "mod = sm.OLS(outcome, predictors)" + "# Initialize an OLS model object\n", + "# Note: This initializes the model, and provides the data \n", + "# but does not actually compute the model yet\n", + "model = sm.OLS(outcome, predictors)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Note that statsmodels, just like scikit-learn that we will encounter a bit later, uses an object-oriented approach. \n", + "Note that `statsmodels`, just like `sklearn` that we will encounter a bit later, uses an object-oriented approach. \n", "\n", - "In this approach you initialize complex objects that store the data and methods together, giving you an organized way to store and check data and parameters, to fit models, and then even to use them to make predictions and so on." + "In this approach you initialize objects that store the data and methods together. This allows for an organized approach to storing and check data and parameters, and applying computations to them, such as fitting models. Outputs parameters of the model are also stored in the object, which can then also be used to make predictions." ] }, { @@ -343,8 +368,8 @@ ], "source": [ "# Check the type of the model object we just created.\n", - "# You can also explore, with tab-complete, what is availabe from this object\n", - "type(mod)" + "# You can also explore, with tab-complete, what is available from this object\n", + "type(model)" ] }, { @@ -354,7 +379,7 @@ "outputs": [], "source": [ "# Finally, fit the model\n", - "res = mod.fit()" + "results = model.fit()" ] }, { @@ -368,25 +393,25 @@ "text": [ " OLS Regression Results \n", "==============================================================================\n", - "Dep. Variable: D2 R-squared: 0.575\n", - "Model: OLS Adj. R-squared: 0.574\n", - "Method: Least Squares F-statistic: 1350.\n", - "Date: Fri, 28 Feb 2020 Prob (F-statistic): 1.42e-187\n", - "Time: 13:29:56 Log-Likelihood: -1006.3\n", - "No. Observations: 1000 AIC: 2017.\n", - "Df Residuals: 998 BIC: 2026.\n", + "Dep. Variable: d2 R-squared: 0.598\n", + "Model: OLS Adj. R-squared: 0.598\n", + "Method: Least Squares F-statistic: 1484.\n", + "Date: Sun, 21 Jun 2020 Prob (F-statistic): 1.18e-199\n", + "Time: 16:14:06 Log-Likelihood: -953.74\n", + "No. Observations: 1000 AIC: 1911.\n", + "Df Residuals: 998 BIC: 1921.\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", - "Intercept -0.0029 0.021 -0.140 0.889 -0.044 0.038\n", - "D1 0.7817 0.021 36.736 0.000 0.740 0.823\n", + "Intercept -0.0116 0.020 -0.582 0.561 -0.051 0.027\n", + "d1 0.7396 0.019 38.523 0.000 0.702 0.777\n", "==============================================================================\n", - "Omnibus: 6.935 Durbin-Watson: 1.959\n", - "Prob(Omnibus): 0.031 Jarque-Bera (JB): 9.140\n", - "Skew: 0.037 Prob(JB): 0.0104\n", - "Kurtosis: 3.462 Cond. No. 1.03\n", + "Omnibus: 0.715 Durbin-Watson: 2.008\n", + "Prob(Omnibus): 0.699 Jarque-Bera (JB): 0.787\n", + "Skew: -0.014 Prob(JB): 0.675\n", + "Kurtosis: 2.866 Cond. No. 1.04\n", "==============================================================================\n", "\n", "Warnings:\n", @@ -396,7 +421,7 @@ ], "source": [ "# Check out the results\n", - "print(res.summary())" + "print(results.summary())" ] }, { @@ -405,17 +430,17 @@ "source": [ "### Interpreting Outputs\n", "\n", - "Statsmodels gives us a lot of information!\n", + "`statsmodels` gives us a lot of information!\n", "\n", "The top section is largely meta-data: it includes things like the model type, and time and date of us running it. \n", "\n", - "It also includes the R-squared, which is an overall summary of the amount of variance the model is able to capture. This value ranges from 0-1, and ~0.5, that we see here, is quite a high value, suggesting a good model fit. \n", + "It also includes the `R-squared`, which is an overall summary of the amount of variance the model is able to capture. R-squared values are bound between 0-1. An r-squared of ~0.5, that we have here, is quite a high value, suggesting a good model fit. \n", "\n", - "The middle column is the actual model results. \n", + "The middle section is the actual model results. \n", "\n", "Each row reflects a parameter, and gives us it's value (`coef`), the error (`std err`), the results of a statistical test regarding whether this parameter is a significant predictor of the output variable (`t`, which associated p-value as `P>|t|`), and the confidence interval of the parameters value (`[0.025` - `0.975]`).\n", "\n", - "The last model includes some other tests that are run on the data, that can help you check some descriptors of the input data, and also that they meet the required criteria of such a model fit. " + "The last section includes some other tests that are run on the data. These can be used to check some properties of the input data, and to check assumptions of the model are met. " ] }, { @@ -424,18 +449,27 @@ "source": [ "### Checking our Model\n", "\n", - "In terms of the model itself, the most useful components are in the second row, in which the summary gives the parameter values, and p-values of our predictors, which in this case are 'Intercept', and 'D2'. \n", + "In terms of the model itself, the most useful components are in the second row, in which the summary gives the parameter values, and p-values of our predictors, which in this case are 'Intercept', and 'd2'. \n", "\n", "From the results above, we can grab the values of the parameters, and obtain the following model:\n", "\n", - "$$ D2 = -0.0029 + 0.7817 * D1 $$\n", + "$$ d2 = -0.0116 + 0.7396 * d1 $$\n", "\n", - "However, we should also keep in mind the statistical test that is reported, a test of whether the parameter value is significant (significantly different from zero). Using an alpha value of 0.05, in this case, the 'D2' parameter value is significant, but the 'Intercept' value is not. Since the parameter value for 'Intercept' is not significantly different from zero, we can decide not to include it in our final model. \n", + "However, we should also keep in mind whether each parameter is significant. To check use, let's look at the statistical test that is reported that checks whether the parameter value is significant (as in, significantly different from zero). Using an alpha value of 0.05, in this case, the 'd2' parameter value is significant, but the 'Intercept' value is not. Since the parameter value for 'Intercept' is not significantly different from zero, we can decide not to include it in our final model. \n", "\n", "We therefore finish with the model:\n", - "$$ D2 = 0.7817 * D1 $$\n", + "$$ d2 = 0.7396 * d1 $$\n", + "\n", + "With this model, it is promising that are value of $a_1$, of 0.7396, is very close to the correlation value of the data points, which we set at 0.75! This suggest our model is working well!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Visualizing our Model\n", "\n", - "With this model, it is promising that are value of $a_1$, of 0.7817, is very close to the correlation value of the data points, which we set at 0.75! " + "Next, we can visualize our model, with our data." ] }, { @@ -445,7 +479,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -457,18 +491,16 @@ } ], "source": [ - "## Plot the model fit line\n", - "\n", "# Plot the orginal data (as before)\n", - "plt.scatter(df['D1'], df['D2'], alpha=0.3, label='Data');\n", + "plt.scatter(df['d1'], df['d2'], alpha=0.3, label='Data');\n", "\n", "# Generate and plot the model fit line\n", - "xs = np.arange(df['D1'].min(), df['D1'].max())\n", - "ys = 0.7817 * xs\n", + "xs = np.arange(df['d1'].min(), df['d1'].max())\n", + "ys = 0.7185 * xs\n", "plt.plot(xs, ys, '--k', linewidth=4, label='Model')\n", "\n", "plt.xlabel('D1')\n", - "plt.xlabel('D2')\n", + "plt.ylabel('D2')\n", "plt.legend();" ] }, @@ -478,11 +510,15 @@ "source": [ "### Using multiple predictors\n", "\n", - "The model above used only one predictor, fitting a simple straight line, and as such actually mimics previous approaches we've taken to fitting lines. \n", + "The model above used only one predictor, fitting a straight line to the data. This is similar to previous examples we've seen of and tried for fitting lines.\n", + "\n", + "We can also fit more than 1 predictor variable, and that is where the power and benefits of using `patsy` and `statsmodels` really comes through. We can use these tools to specify any models we want, including multiple predictors with different kinds of interactions between predictors, and these functions take care of fitting these models. \n", "\n", - "We can also fit more than 1 predictor variable, and that is where the power of patsy and statsmodels really comes through, as these functions will fit more complex models, including as many parameters as we want, also dealing with some aspects of correlated features, and so on. \n", + "To briefly explore this, let's now add a new variable to our dataframe, and fit an OLS model with two predictors. \n", "\n", - "Here, we will add a new variable to our dataframe, and fit an OLS model with two predictors. " + "In this case, we will fit a model of the form:\n", + "\n", + "$$ d1 = a_0 + a_1 * d2 + a_1 * d3 $$" ] }, { @@ -511,53 +547,53 @@ " \n", " \n", " \n", - " D1\n", - " D2\n", - " D3\n", + " d1\n", + " d2\n", + " d3\n", " \n", " \n", " \n", " \n", - " 0\n", - " -1.148216\n", - " 0.332012\n", - " -0.117398\n", + " 0\n", + " 0.087922\n", + " 0.009294\n", + " -1.611758\n", " \n", " \n", - " 1\n", - " 0.688743\n", - " 1.764193\n", - " -1.140705\n", + " 1\n", + " -0.530187\n", + " -1.418836\n", + " 1.933703\n", " \n", " \n", - " 2\n", - " -0.886799\n", - " -0.332816\n", - " -1.894862\n", + " 2\n", + " -0.092297\n", + " -1.302195\n", + " 0.334072\n", " \n", " \n", - " 3\n", - " -0.241192\n", - " -0.409663\n", - " -0.413454\n", + " 3\n", + " 0.275502\n", + " 0.109635\n", + " -0.124464\n", " \n", " \n", - " 4\n", - " -0.662426\n", - " 0.949813\n", - " -0.864684\n", + " 4\n", + " -1.050818\n", + " -1.059746\n", + " 0.278050\n", " \n", " \n", "\n", "
" ], "text/plain": [ - " D1 D2 D3\n", - "0 -1.148216 0.332012 -0.117398\n", - "1 0.688743 1.764193 -1.140705\n", - "2 -0.886799 -0.332816 -1.894862\n", - "3 -0.241192 -0.409663 -0.413454\n", - "4 -0.662426 0.949813 -0.864684" + " d1 d2 d3\n", + "0 0.087922 0.009294 -1.611758\n", + "1 -0.530187 -1.418836 1.933703\n", + "2 -0.092297 -1.302195 0.334072\n", + "3 0.275502 0.109635 -0.124464\n", + "4 -1.050818 -1.059746 0.278050" ] }, "execution_count": 13, @@ -567,7 +603,7 @@ ], "source": [ "# Add a new column of data to df\n", - "df['D3'] = pd.Series(np.random.randn(1000), index=df.index)\n", + "df['d3'] = pd.Series(np.random.randn(1000), index=df.index)\n", "df.head()" ] }, @@ -577,10 +613,10 @@ "metadata": {}, "outputs": [], "source": [ - "# Predict D1 from D2 and D3\n", - "outcome, predictors = patsy.dmatrices('D1 ~ D2 + D3', df)\n", - "mod = sm.OLS(outcome, predictors)\n", - "res = mod.fit()" + "# Predict d1 from d2 and d3\n", + "outcome, predictors = patsy.dmatrices('d1 ~ d2 + d3', df)\n", + "model = sm.OLS(outcome, predictors)\n", + "results = model.fit()" ] }, { @@ -594,26 +630,26 @@ "text": [ " OLS Regression Results \n", "==============================================================================\n", - "Dep. Variable: D1 R-squared: 0.575\n", - "Model: OLS Adj. R-squared: 0.574\n", - "Method: Least Squares F-statistic: 674.3\n", - "Date: Fri, 28 Feb 2020 Prob (F-statistic): 6.05e-186\n", - "Time: 13:31:04 Log-Likelihood: -975.65\n", - "No. Observations: 1000 AIC: 1957.\n", - "Df Residuals: 997 BIC: 1972.\n", + "Dep. Variable: d1 R-squared: 0.599\n", + "Model: OLS Adj. R-squared: 0.598\n", + "Method: Least Squares F-statistic: 745.1\n", + "Date: Sun, 21 Jun 2020 Prob (F-statistic): 1.21e-198\n", + "Time: 16:14:06 Log-Likelihood: -996.62\n", + "No. Observations: 1000 AIC: 1999.\n", + "Df Residuals: 997 BIC: 2014.\n", "Df Model: 2 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", - "Intercept 0.0104 0.020 0.510 0.610 -0.030 0.050\n", - "D2 0.7354 0.020 36.722 0.000 0.696 0.775\n", - "D3 -0.0080 0.021 -0.389 0.697 -0.049 0.033\n", + "Intercept 0.0179 0.021 0.861 0.389 -0.023 0.059\n", + "d2 0.8070 0.021 38.471 0.000 0.766 0.848\n", + "d3 -0.0368 0.021 -1.763 0.078 -0.078 0.004\n", "==============================================================================\n", - "Omnibus: 0.506 Durbin-Watson: 1.994\n", - "Prob(Omnibus): 0.776 Jarque-Bera (JB): 0.389\n", - "Skew: -0.024 Prob(JB): 0.823\n", - "Kurtosis: 3.084 Cond. No. 1.05\n", + "Omnibus: 0.703 Durbin-Watson: 1.985\n", + "Prob(Omnibus): 0.704 Jarque-Bera (JB): 0.574\n", + "Skew: 0.015 Prob(JB): 0.751\n", + "Kurtosis: 3.113 Cond. No. 1.06\n", "==============================================================================\n", "\n", "Warnings:\n", @@ -623,16 +659,24 @@ ], "source": [ "# Check the model fit summary\n", - "print(res.summary())" + "print(results.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Note that statsmodels, as used above, is a powerful, general OLS model approach. \n", + "Note that in this case, we simulated the `d3` column with no relation to the `d1` values we were trying to predict, so the `d3` predictor isn't significant, and overall this bigger model doesn't explain anymore variance of the data (the r-squared is no better). \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conclusion\n", "\n", - "You can further investigate how to include other features, such as interactions between input variables, and so on. " + "`statsmodels` offers a powerful and general approach to fitting statistical models to data, investigating properties of these model fits, and comparing between models. You can further investigate how to include other features, such as interactions between input variables, and so on. " ] }, { @@ -641,9 +685,11 @@ "source": [ "## Linear Regression with sklearn\n", "\n", - "Scikit-learn also has implementations of Linear Regression models. \n", + "As we've already seen with the `OLS` tutorial, there are multiple ways to apply the same underlying computations. \n", "\n", - "Here we will quickly demonstrate running the same linear OLS model fits as above, using sklearn instead of statsmodels. " + "Another popular module that can be used for fitting models to data is `sklearn`. \n", + "\n", + "Here, for a quick demonstration and comparison, we will fit the `sklearn` implementation of Linear Regression models to our same data. The underlying computations are approximately the same, but as we can see, the API for using `sklearn` and the exact results are different." ] }, { @@ -672,10 +718,10 @@ "metadata": {}, "outputs": [], "source": [ - "# Convert data into shape for easier use with sklearn\n", - "d1 = np.reshape(df.D1.values, [len(df.D1), 1])\n", - "d2 = np.reshape(df.D2.values, [len(df.D2), 1])\n", - "d3 = np.reshape(df.D3.values, [len(df.D3), 1])" + "# Convert data into arrays for easier use with sklearn\n", + "d1 = np.reshape(df.d1.values, [len(df.d1), 1])\n", + "d2 = np.reshape(df.d2.values, [len(df.d2), 1])\n", + "d3 = np.reshape(df.d3.values, [len(df.d3), 1])" ] }, { @@ -696,7 +742,7 @@ { "data": { "text/plain": [ - "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)" + "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)" ] }, "execution_count": 19, @@ -706,7 +752,7 @@ ], "source": [ "# Fit the linear regression model\n", - "reg.fit(d2, d1) #d1 = a0 + a1*d2" + "reg.fit(d2, d1) # d1 = a0 + a1*d2" ] }, { @@ -718,16 +764,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "0.010669383005965798\n", - "0.7353817173669228\n" + "The intercept value is: \t0.0164\n", + "The coefficient value is: \t0.8084\n" ] } ], "source": [ "# Check the results of this\n", "# If you compare these to what we got with statsmodels above, they are indeed the same\n", - "print(reg.intercept_[0])\n", - "print(reg.coef_[0][0])" + "print('The intercept value is: \\t{:1.4f}'.format(reg.intercept_[0]))\n", + "print('The coefficient value is: \\t{:1.4f}'.format(reg.coef_[0][0]))" ] }, { @@ -745,7 +791,7 @@ { "data": { "text/plain": [ - "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)" + "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)" ] }, "execution_count": 21, @@ -755,7 +801,7 @@ ], "source": [ "# Initialize and fit linear model\n", - "# d1 = a1*d2 + a2*d3 + a0\n", + "# d1 = a0 + a1*d2 + a2*d3\n", "reg = linear_model.LinearRegression()\n", "reg.fit(np.hstack([d2, d3]), d1)" ] @@ -764,43 +810,32 @@ "cell_type": "code", "execution_count": 22, "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(1000, 2)" - ] - }, - "execution_count": 22, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.hstack([d2, d3]).shape" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Intercept: \t 0.010374409482633963\n", - "Theta D2 :\t 0.7354300664652448\n", - "Theta D3 :\t -0.008040442777931771\n" + "Intercept: \t +0.0179\n", + "d2 value:\t +0.8070\n", + "d2 value:\t -0.0368\n" ] } ], "source": [ "# Check the results of this\n", "# If you compare these to what we got with statsmodels above, they are indeed the same\n", - "print('Intercept: \\t', reg.intercept_[0])\n", - "print('Theta D2 :\\t', reg.coef_[0][0])\n", - "print('Theta D3 :\\t', reg.coef_[0][1])" + "print('Intercept: \\t {:+1.4f}'.format(reg.intercept_[0]))\n", + "print('d2 value:\\t {:+1.4f}'.format(reg.coef_[0][0]))\n", + "print('d2 value:\\t {:+1.4f}'.format(reg.coef_[0][1]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "The pattern of results with `sklearn` is about the same as before, though we can see there is some small differences in estimation. In general, if you have data organized into Dataframes, then `statsmodels` does offer a more direct way to apply statistical models, but `sklearn` does also offer a lot of useful functionality for model fitting & analysis. " ] } ], @@ -820,7 +855,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.0" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/15-Clustering.ipynb b/15-Clustering.ipynb index 02b8151..f24ad36 100644 --- a/15-Clustering.ipynb +++ b/15-Clustering.ipynb @@ -4,7 +4,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Clustering" + "# Clustering\n", + "\n", + "A common task or goal within data analysis is to learn some kind of structure from data. One way to do so is to apply clustering analysis to data. This typically means trying to learn 'groups' or clusters in the data. \n", + "\n", + "This example is a minimal example of clustering adapted from the `sklearn` tutorials, to introduce the key points and show an introductory example of a clustering analysis. \n", + "\n", + "As with many of the other topics in data analysis, there are many resources and tutorials available on the clustering analyses. A good place to start is the extensive coverage in the `sklearn` documentation. If you are interested in clustering analyses, once you have explored the basic concepts here, we recommend you go and explore some of these other resources. " ] }, { @@ -16,17 +22,18 @@ "\n", "\n", "
\n", - "Clustering\n", - "article from wikipedia. \n", + "Clustering\n", + "article from wikipedia. The sklearn \n", + "user guide \n", + "has a detailed introduction to and tutorial on\n", + "clustering. \n", "
" ] }, { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Imports\n", @@ -34,7 +41,7 @@ "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", - "from sklearn import datasets\n", + "from sklearn import cluster, datasets\n", "from sklearn.cluster import KMeans\n", "from scipy.cluster.vq import whiten" ] @@ -43,21 +50,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Scikit-learn has a bunch of example datasets. Here, we'll use the iris dataset: which contains data about different species of plants. " + "## Load an Example Dataset\n", + "\n", + "Scikit-learn has example datasets that can be loaded and used for example.\n", + "\n", + "Here, we'll use the iris dataset. This dataset contains data about different species of plants. It includes information for several features across several species. Our task will be to attempt to cluster the data, to see if we can learn a meaningful groupings from the data." ] }, { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Load the iris data\n", "iris = datasets.load_iris()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that `iris`, as loaded by `sklearn` is an object. The data is stored in `iris.data`. " + ] + }, { "cell_type": "code", "execution_count": 3, @@ -67,16 +83,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "sepal length (cm)\n", - "sepal width (cm)\n", - "petal length (cm)\n", - "petal width (cm)\n" + "There are 150 samples of data, with 4 features and 3 labels.\n" ] } ], "source": [ - "# Check out the available features\n", - "print('\\n'.join(iris.feature_names))" + "# Let's check how much data there is\n", + "[n_samples, n_features] = np.shape(iris.data)\n", + "n_labels = len(set(iris.target))\n", + "print(\"There are {} samples of data, with {} features and {} labels.\".format(\\\n", + " n_samples, n_features, n_labels))" ] }, { @@ -88,15 +104,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "setosa\n", - "versicolor\n", - "virginica\n" + "sepal length (cm)\n", + "sepal width (cm)\n", + "petal length (cm)\n", + "petal width (cm)\n" ] } ], "source": [ - "# Check out the species ('clusters')\n", - "print('\\n'.join(iris.target_names))" + "# Check out the available features\n", + "print('\\n'.join(iris.feature_names))" ] }, { @@ -108,23 +125,21 @@ "name": "stdout", "output_type": "stream", "text": [ - "There are 150 samples of data, each with 4 features.\n" + "setosa\n", + "versicolor\n", + "virginica\n" ] } ], "source": [ - "# The actual data is stored in iris.data\n", - "# Let's check how much data there is\n", - "[n_samples, n_features] = np.shape(iris.data) \n", - "print(\"There are \", n_samples , \" samples of data, each with \" , n_features, \" features.\")" + "# Check out the species ('clusters')\n", + "print('\\n'.join(iris.target_names))" ] }, { "cell_type": "code", "execution_count": 6, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Let's set up some indexes, so we know what data we're using\n", @@ -141,25 +156,38 @@ "outputs": [ { "data": { - "image/png": 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J6fOrgL+uPTyzfL0wlj83JyJnTodui9usHmUbiYeB7dPn9wFvSZ/vB3iQtTVN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\n8WSSAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "# Let's start looking at some data. \n", - "# Let's start with a scatter plot of petal length vs. petal width\n", - "fig = plt.figure(1)\n", + "# Let's start looking at some data - plotting petal length vs. petal width\n", "plt.scatter(iris.data[:, pl_ind], iris.data[:, pw_ind])\n", "\n", "# Add title and labels\n", "plt.title('Iris Data: Petal Length vs. Width', fontsize=16, fontweight='bold')\n", - "plt.xlabel('Petal Length', fontsize=14);\n", - "plt.ylabel('Petal Width', fontsize=14);" + "plt.xlabel('Petal Length (cm)', fontsize=14);\n", + "plt.ylabel('Petal Width (cm)', fontsize=14);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just from plotting the data, we can see that there seems to be some kind of structure in the data. \n", + "\n", + "In this case, we do know that there are different species in our dataset, which will be useful information for comparing to our clustering analysis. \n", + "\n", + "Note that we are not going to use these labels in the clustering analysis itself. Clustering, as we will apply it here, is an unsupervised method, meaning we are not going to use any labels to try and learn the structure of the data. \n", + "\n", + "To see the structure that is present in the data, let's replot the data, color coding by species." ] }, { @@ -169,53 +197,76 @@ "outputs": [ { "data": { - "image/png": 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Lt0ohxJgrRflYDmNMtILu5/dTUtK68chlLkBYhRBj1PKuu8kYU7iSuW8//lbZ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\nSUVORK5CYII=\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "# Plot the data colour coded by species\n", - "fig = plt.figure(1)\n", - "plt.scatter(iris.data[:, pl_ind][iris.target==0], iris.data[:, pw_ind][iris.target==0],\n", - " c='green', label=iris.target_names[0])\n", - "plt.scatter(iris.data[:, pl_ind][iris.target==1], iris.data[:, pw_ind][iris.target==1],\n", - " c='red', label=iris.target_names[1])\n", - "plt.scatter(iris.data[:, pl_ind][iris.target==2], iris.data[:, pw_ind][iris.target==2],\n", - " c='blue', label=iris.target_names[2])\n", + "# Plot the data color coded by species\n", + "for ind in range(n_labels):\n", + " plt.scatter(iris.data[:, pl_ind][iris.target==ind],\n", + " iris.data[:, pw_ind][iris.target==ind],\n", + " label=iris.target_names[ind])\n", "\n", "# Add title, labels and legend\n", "plt.title('Iris Data: Petal Length vs. Width', fontsize=16, fontweight='bold')\n", - "plt.xlabel('Petal Length', fontsize=14);\n", - "plt.ylabel('Petal Width', fontsize=14);\n", + "plt.xlabel('Petal Length (cm)', fontsize=14);\n", + "plt.ylabel('Petal Width (cm)', fontsize=14);\n", "plt.legend(scatterpoints=1, loc='upper left');\n", "\n", - "# Note that splitting up the plotting per group is basically a hack to make the legend work, \n", - "# The following command plots the data perfectly well, colour coded by target:\n", - "# plt.scatter(iris.data[:, petal_length_ind], iris.data[:, petal_width_ind], c=iris.target)\n", - "# However, it's a pain to get a labelled legend when plotted this way" + "# Note that the data, colored by label, can also be plotted like this:\n", + "# plt.scatter(iris.data[:, pl_ind], iris.data[:, pw_ind], c=iris.target)\n", + "# It is, however, more difficult to add labelled legend when plotted this way" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Task:\n", - "If we didn't already know the Species labels, we might notice that there seem to be distinct groups of datapoints. Clustering is the approach of trying to find these groups algorithmically. \n", + "In this data, we know we have 3 different 'groups' of data, which are the different species. \n", "\n", - "Here, we will do so with the KMeans algorithm. For information on KMeans and how it works, see the lecture. " + "As we can see in the plots above, these different species seem to be fairly distinct in terms of their feature values.\n", + "\n", + "The question then is whether we can learn a clustering approach, based on the feature data and without using the labels, that can learn a meaningful grouping of this data. \n", + "\n", + "If this approach works, then we might be able to try to use it on other data, for which we have feature data, but might not be sure about the groupings present in the data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Apply K-Means Clustering\n", + "\n", + "Clustering is the process of trying to learn groups algorithmically. \n", + "\n", + "For this example, we are going to use the K-means clustering algorithm. \n", + "\n", + "K-means attempts to group the data into `k` clusters, and does so by labeling each data point to be in the cluster with the nearest mean. To learn the center means, after a random initialization, an iterative procedure assigns each point to a cluster, then updates the cluster centers, and repeats, until a final solution is reached. \n", + "\n", + "
\n", + "K-means is a clustering algorithm that attempts to learn k clusters by grouping datapoints to the nearest cluster center mean. \n", + "
\n", + "\n", + "
\n", + "For more information on K-means, see the article on \n", + "wikipedia\n", + "or on the sklearn\n", + "user guide. \n", + "
" ] }, { "cell_type": "code", "execution_count": 9, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Pull out the data of interest - Petal Length & Petal Width\n", @@ -227,20 +278,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#### Whitening Data:\n", - "If your different dimensions use different units (or have wildy different variances), then these differences can greatly impact the clustering. \n", + "### Whitening Data\n", + "\n", + "In this example, we are using two features (or two dimensions) of data. \n", + "\n", + "One thing to keep in mind for clustering analyses, is that if different dimensions use different units (or have very different variances), then these differences can greatly impact the clustering. \n", "\n", - "This is because KMeans is isotropic: it treats different in each direction as equally important. So, if the units or variance are very different, this is equivalent to weighting certain features / dimensions as more or less important. \n", + "This is because K-means is isotropic, which means that it treats different in each direction as equally important. Because of this, if the units or variance of different features are very different, this is equivalent to weighting certain features / dimensions as more or less important.\n", "\n", - "To correct for this it is common, and sometimes necessary to 'whiten' data: to normalize each dimension by it's respective standard deviation. " + "To correct for this it is common, and sometimes necessary to 'whiten' the data. 'Whitening' data means normalizing each dimension by it's respective standard deviation. By transforming the data to be on the same scale (have the same variance), we can ensure that the clustering algorithm treats each dimension with the same importance. " ] }, { "cell_type": "code", "execution_count": 10, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Check out the whiten function\n", @@ -250,9 +302,7 @@ { "cell_type": "code", "execution_count": 11, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Whiten Data\n", @@ -263,24 +313,20 @@ { "cell_type": "code", "execution_count": 12, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "# Combine data into shape for skl\n", + "# Combine data into an array to use with sklearn\n", "data = np.vstack([d1w, d2w]).T" ] }, { "cell_type": "code", "execution_count": 13, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "# Initialize KMeans object, set to fit 3 clusters\n", + "# Initialize K-means object, and set it to fit 3 clusters\n", "km = KMeans(n_clusters=3, random_state=13)" ] }, @@ -293,8 +339,8 @@ "data": { "text/plain": [ "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n", - " n_clusters=3, n_init=10, n_jobs=1, precompute_distances='auto',\n", - " random_state=13, tol=0.0001, verbose=0)" + " n_clusters=3, n_init=10, n_jobs=None, precompute_distances='auto',\n", + " random_state=13, tol=0.0001, verbose=0)" ] }, "execution_count": 14, @@ -303,7 +349,7 @@ } ], "source": [ - "# Fit the data with KMeans\n", + "# Fit the data with K-means\n", "km.fit(data)" ] }, @@ -314,38 +360,83 @@ "outputs": [ { "data": { - "image/png": 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KZWR7fZw0aAj7dWi9K8NlSjAUivv5nDx4SL0S49dbNvPy0m8Iq3LMfgMZGe12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\n29bRy+nwsyfStlM+Hl91nw9/to82HXK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IMvGggfzQFui/AzKfIcqcFJ/L7oGBNZBeSjTj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\nkicJ55xzJXmScM45V9L/A+vEfQKr5KfkAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# Let's check out the clusters that KMeans found\n", "plt.scatter(d1, d2, c=km.labels_);\n", - "plt.xlabel('Year');\n", - "plt.ylabel('Age');\n", "\n", "# Add title, labels and legend\n", "plt.title('Iris Data: PL vs. PW Clustered', fontsize=16, fontweight='bold')\n", - "plt.xlabel('Petal Length', fontsize=14);\n", - "plt.ylabel('Petal Width', fontsize=14);" + "plt.xlabel('Petal Length (cm)', fontsize=14);\n", + "plt.ylabel('Petal Width (cm)', fontsize=14);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the plot above, each data point is labeled with it's cluster assignment, that we learned from the data. \n", + "\n", + "In this case, since we do already know the species label of the data, we can see that it seems like this clustering analysis is doing pretty well! There are some discrepancies, but overall a K-means clustering approach is able to reconstruct a grouping of the datapoints, using only information from a couple of the features. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "It looks like it's doing pretty well! Other than some discrepancies between the versicolor and virginica boundary, KMeans is able to reconstruct the species labels algorithmically, given only information on a couple features. " + "## Other Clustering Approaches\n", + "\n", + "Clustering is a general task, and there are many different algorithms that can be used to attempt to solve it. \n", + "\n", + "For example, below are printed some of the different clustering algorithms and approaches that are available in sklearn." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Clustering approaches in sklearn:\n", + " AffinityPropagation\n", + " AgglomerativeClustering\n", + " Birch\n", + " DBSCAN\n", + " FeatureAgglomeration\n", + " KMeans\n", + " MeanShift\n", + " MiniBatchKMeans\n", + " OPTICS\n", + " SpectralBiclustering\n", + " SpectralClustering\n", + " SpectralCoclustering\n" + ] + } + ], + "source": [ + "print('Clustering approaches in sklearn:')\n", + "for name in dir(cluster):\n", + " if name[0].isupper():\n", + " print(' ', name)" ] } ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -359,7 +450,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/16-DimensionalityReduction.ipynb b/16-DimensionalityReduction.ipynb index ed267ce..73c989c 100644 --- a/16-DimensionalityReduction.ipynb +++ b/16-DimensionalityReduction.ipynb @@ -4,7 +4,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Dimensionality Reduction" + "# Dimensionality Reduction\n", + "\n", + "Datasets are sometimes very large, containing potentially millions of data points across a large numbers of features. \n", + "\n", + "Each feature can also be thought of as a 'dimension'. In some cases, for high-dimensional data, we may want or need to try to reduce the number of dimensions. Reducing the number of dimensions (or reducing the number of features in a dataset) is called 'dimensionality reduction'. \n", + "\n", + "The simplest way to do so could simply be to drop some dimensions, and we could even choose to drop the dimensions that seem likely to be the least useful. This would be a simple method of dimensionality reduction. However, this approach is likely to throw away a lot of information, and we wouldn't necessarily know which features to keep. Typically we want to try to reduce the number of dimensions while still preserving the most information we can from the dataset. \n", + "\n", + "As we saw before, one way we could try and do something like this is by doing clustering. When we run a clustering analysis on high dimensional data, we can try and re-code data to store each point by it's cluster label, potentially maintaining more information in a smaller number of dimensions.\n", + "\n", + "Here we will introduce and explore a different approach to dimensionality reduction. Instead of dropping or clustering our features, we are going to try and learn a new representation of our data, choosing a set of feature dimensions that capture the most variance of our data. This allows us to drop low information dimensions, meaning we can reduce the dimensionality of our data, while preserving the most information. " ] }, { @@ -16,8 +26,11 @@ "\n", "\n", "
\n", - "For an explainer on dimensionality reduction, with examples in real data, go\n", - "here.\n", + "For more information on dimensionality reduction, see the scikit-learn \n", + "user manual,\n", + "and / or \n", + "blog post\n", + "with an explainer and examples in real data.\n", "
" ] }, @@ -25,15 +38,11 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Overview of Dimensionality Reduction\n", - "\n", - "Datasets can be very large, containing not only potentially millions of data points, but also potentially very large numbers of features about each data point. We can consider each feature of our dataset to be a 'dimension'. For large-dimensional data, we may want to, or need to, try to reduce this number of dimensions. \n", - "\n", - "The simplest way to do so could simply be to drop some dimensions, and we could even choose to drop the dimensions that seem likely to be the least useful. This would be a simple method of dimensionality reduction. \n", + "## Principal Component Analysis\n", "\n", - "Typically though, we want to reduce the number of the dimensions in a way that preserves the most information. One way to do so could be clustering - if we run a clustering analysis on high dimensional data, we could re-code the data to store each point by it's cluster label, potentially maintaining more information in a smaller number of dimensions. \n", + "The method we will for dimensionality reduction is Principal Component Analysis (PCA).\n", "\n", - "Here we will explore another common method for dimensionality reduction - Principal Component Analysis (PCA). " + "PCA can be used to learn a new representation of the data, 're-organizing' our features into a set of new dimensions that are ranked by the variance of the dataset that they account for. With this, we can do dimensionality reduction by dropping dimensions with a small amount of explained variance. " ] }, { @@ -56,27 +65,21 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Principle Component Analysis\n", + "### PCA Overview\n", "\n", - "To use PCA for Dimensionality Reduction, we can choose to preserve _n_ components, where _n_ is a number lower than the original dimensionality of our data set. \n", + "To use PCA for Dimensionality Reduction, we can apply PCA to a dataset, learning our new components that represent the data. From this, we can choose to preserve _n_ components, where _n_ is a number lower than the original dimensionality of our data set. By transforming our data with PCA, and choosing the keep the top _n_ components, we are able to keep the most variance of the original data in our lower dimensional space.\n", "\n", - "By transforming our data with PCA, and keeping _n_ components, we are able to keep the most variance of the original data in our lower dimensional space.\n", + "Broadly, PCA seeks to take advantage of the correlational structure of the variables, and uses this structure to re-encode the data. For example, if feature $x_1$ and $x_2$ of our data are correlated, PCA looks for how it could re-organize the data into some new dimension $x_pc$ which captures most of the shared variance (correlated structure) between the two. \n", "\n", - "Most broadly, PCA seeks to take advantage of the correlational structure of the variables, and uses this structure to encode the data. \n", + "In practice, PCA is most useful to go from _m_D -> _n_D data, where D is the dimensionality of the data, _m_ is a large number and we want to choose a new dimensionality _n_, where _n_ < _m_. \n", "\n", - "For example, if feature $x_1$ and $x_2$ of our data are correlated, PCA looks for how it could re-organize the data into some new dimension $x_pc$ which captures most of the shared variance (correlated structure) between the two. \n", - "\n", - "In this notebook, we will work through a simple PCA example, with a simple example of using PCA to perform PCA to go from 2D -> 1D data. \n", - "\n", - "In practice, PCA is most useful to go from _m_D -> _n_D data, where _m_ is very large, and _n_ < _m_. " + "For this this notebook, we will work through a simplified example, illustrating the point in dimensionalities that we can plot, by going from 2D to 1D data." ] }, { "cell_type": "code", "execution_count": 1, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Imports\n", @@ -88,23 +91,26 @@ "from sklearn.decomposition import PCA" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For this examples, we will create some example data, with 2 dimensions, in which the two dimensions are correlated (share some variance). " + ] + }, { "cell_type": "code", "execution_count": 2, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "## Create some random, correlated, data\n", - "\n", "# Settings\n", "means = [50, 50]\n", "covs = [[1, .75], [.75, 1]]\n", "n = 1000\n", "\n", "# Generate data\n", - "dat = np.random.multivariate_normal(means, covs, n)" + "data = np.random.multivariate_normal(means, covs, n)" ] }, { @@ -114,20 +120,22 @@ "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# Plot our two random variables\n", - "f, ax = plt.subplots(1, 2)\n", - "ax[0].hist(dat[:, 0]);\n", - "ax[1].hist(dat[:, 1]);" + "_, ax = plt.subplots(1, 2)\n", + "ax[0].hist(data[:, 0]); ax[0].set_title('D1');\n", + "ax[1].hist(data[:, 1]); ax[1].set_title('D2');" ] }, { @@ -137,51 +145,61 @@ "outputs": [ { "data": { + "image/png": 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\n", 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" ] }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] + "metadata": { + "needs_background": "light" }, - "metadata": {}, "output_type": "display_data" } ], "source": [ "# Check out how the data relates to each other\n", - "plt.scatter(dat[:, 0], dat[:, 1])" + "plt.scatter(data[:, 0], data[:, 1]);\n", + "\n", + "# Add title and labels\n", + "plt.title('Simulated Data', fontsize=16, fontweight='bold')\n", + "plt.xlabel('D1', fontsize=14);\n", + "plt.ylabel('D2', fontsize=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Task:\n", + "As we can see, there are features are indeed correlated. \n", + "\n", + "\n", + "Note that one way to think about PCA is as a 'rotation' of the data to a new basis. If we want to choose a single dimension to represent this data, we can see that choosing one or the other of the original dimensions (the X or Y dimension in the plot) would not be ideal. What we want to do with PCA is chose a new set of dimension - like drawing new axes into our plot - to best represent our data.\n", "\n", - "Let's say that we want or need a lower dimensional representation of our data for some further analysis. \n", "\n", - "Instead of simply choosing a subset of dimensions though, dimensionality reduction is the process of trying to capture the most information from the original space, in a smaller number of dimensions.\n", "\n", - "Note: here we are going from 2D -> 1D for simplicity, and convenience. In practice is most useful when you have an intractably large number of dimensions, say 20,000, and want to transform the data into a lower dimensional space (that captures the most information you can), but is much more manageable, containing, perhaps closer to 20 dimensions. \n", "\n", - "Here we will use Principal Components Analysis (PCA) for dimensionality reduction." + "In this case, we have 2-dimensions of data. What we want to do, with PCA, is chose a lower dimensional (in this case, 1D) representation of this data that preserves the most information from the data that we can, given the new dimensionality.\n", + "\n", + "Note that in this example, we are only going from 2D -> 1D, for simplicity and convenience. In practice is most useful when there is a very large number of dimensions, say 20,000, and want to transform the data into a lower dimensional space, maybe something like 20 dimensions, that is more manageable and usable for further analyses." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Applying PCA\n", + "\n", + "Now, we want to apply PCA to our data, to reduce it's dimensionality, while capturing the most information we can from the original space.\n", + "\n", + "To do so, we will use the PCA implementation from `sklearn`.\n", + "\n", + "We will use the `PCA` object to initialize a `PCA` model specifying any settings we want, that we can then apply to the data. " ] }, { "cell_type": "code", "execution_count": 5, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Initialize the PCA model, here specifying 1 component\n", @@ -191,45 +209,139 @@ { "cell_type": "code", "execution_count": 6, - "metadata": { - "collapsed": true - }, + "metadata": {}, + "outputs": [], + "source": [ + "# Fit PCA to the data\n", + "pca = pca.fit(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `pca` object has now learned the principal component representation of our data. \n", + "\n", + "We can now apply this to our original data with `transform`." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, "outputs": [], "source": [ - "# Fit the PCA model, and apply it to transform the data\n", - "out = pca.fit_transform(dat)" + "# Transform the data, using our learned PCA representation\n", + "out = pca.transform(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The returned variable is a new array, with our data, after dimensionality reduction. \n", + "\n", + "Recall that are original data was 2 dimnensional. Our transformed data is now 1 dimensional." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 28, "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - }, + "name": "stdout", + "output_type": "stream", + "text": [ + "Original data dimensions: \t (1000, 2)\n", + "Transformed data dimensions: \t (1000, 1)\n" + ] + } + ], + "source": [ + "# Check out the dimensions of the data\n", + "print(\"Original data dimensions: \\t\", data.shape)\n", + "print(\"Transformed data dimensions: \\t\", out.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By reducing the dimensionality, we off course lose at least some information.\n", + "\n", + "Using PCA, we are nevertheless trying to preserve as much variance as we can. \n", + "\n", + "Next, let's check how much variance we have kept. \n", + "\n", + "We can do so, our the sklearn PCA object computes and stores how much explained variance each component captures. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The proportion of variance explained by the first principcal component is 0.8861.\n" + ] + } + ], + "source": [ + "# Check how much variance is captured by the first component\n", + "print(\"The proportion of variance explained by the first \" +\n", + " \"principcal component is {:1.4f}.\".format(pca.explained_variance_ratio_[0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, let's plot the transformed data. \n", + "\n", + "Note that in the plot below, the data is 1 dimensional, so the x-axis here is just index number. " + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ { "data": { - "image/png": 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lUTKXOoxV8ca6vrtyrD6bwSRIdHkIDMh1YbEJLpubOsAvu2A5Bi9Yjn1Hp1Nj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\nOM/3I8Kj1zjuiAgX9Nq+CBkVE9EBiFEaERHN6LV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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# Check out the transformed data, in the new space\n", - "# Note: since the new data is 1D, the x-axis here is just index number\n", - "plt.plot(out, '.')" + "plt.plot(out, '.');\n", + "\n", + "# Add title and labels\n", + "plt.title('Simulated Data', fontsize=16, fontweight='bold')\n", + "plt.xlabel('Samples', fontsize=14);\n", + "plt.ylabel('PC-1', fontsize=14);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion\n", + "\n", + "Dimensionality reduction, and PCA in particular, are common data transformations, especially for large data. \n", + "\n", + "As for our other topics related to machine learning and data analysis, here we have merely introduced the basic ideas behind dimensionality reduction, and one of the most common algorithms to do so, PCA. For further information on these topics, look into more technical courses or resources. " ] }, { @@ -247,7 +359,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -261,7 +373,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/17-Classification.ipynb b/17-Classification.ipynb index 9bfab78..6ef08fe 100644 --- a/17-Classification.ipynb +++ b/17-Classification.ipynb @@ -4,7 +4,17 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Classification" + "# Classification\n", + "\n", + "Another general task in data analysis and machine learning is classification. \n", + "\n", + "Classification, in general, is the process of predicting the 'class' of datapoints, meaning to assign a label to the data point, or assign them to a grouping or cluster. \n", + "\n", + "Classification is a type of supervised learning, meaning we typically have some data for which we know the classes, and we want to learn a procedure that can use this information (the data with known labels), to learn a mapping from data to labels that we can apply to new data. \n", + "\n", + "Note that if we have data that we are trying to categorize, but don't already know any labels, we typically call this clustering. \n", + "\n", + "Classification can also be thought of as the categorical version of prediction. Prediction, as we've talked about it, is process of predicting a continuous output from a set of features. Classification is the same idea, except in case we are predicting a discrete category (or label). " ] }, { @@ -12,7 +22,7 @@ "metadata": {}, "source": [ "
\n", - "Classification is process of categorizing data - of assigning data points to predefined groups (or clusters). \n", + "Classification is process of categorizing data - of assigning data points to predefined groups (clusters) or labels. \n", "
\n", "\n", "
\n", @@ -27,7 +37,15 @@ "collapsed": true }, "source": [ - "## Support Vector Machines" + "## Support Vector Machines\n", + "\n", + "There are many algorithms for doing classification.\n", + "\n", + "For this example, we are going to use Support Vector Machines (SVMs) as an example algorithm. \n", + "\n", + "SVM is one of the most common algorithms for classification. SVMs are an algorithm that seeks to learn a boundary - or dividing line - between groups of data of interest. Once we learn this boundary, we can label datapoints based on where they sit relative to this boundary - basically which side of the line they are on. \n", + "\n", + "To separate the data, we want the dividing line, or 'decision boundary' that separates the data. There might be many different lines that do this. To try and find the best solution, SVMs try to learn the learn that has the greatest separation between the classes. To do so, SVMs use 'support vectors', which are datapoints nearby the boundary, that are used to calculate the line of greatest separation. " ] }, { @@ -40,34 +58,23 @@ "\n", "
\n", "This \n", - "article\n", + "article\n", "provides a nice overview of the SVM algorithm. This is also a code-based explainer from\n", - "scikit-learn.\n", + "scikit-learn.\n", "
" ] }, { "cell_type": "code", - "execution_count": 1, - "metadata": { - "collapsed": true - }, + "execution_count": 23, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ + "import matplotlib.pyplot as plt\n", + "\n", "# Imports - from scikit-learn\n", "from sklearn.svm import SVC\n", "from sklearn.metrics import classification_report" @@ -77,62 +84,96 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Overview\n", + "### Data Generation\n", "\n", - "In this example, we will generate some 2 dimensional data that comes from two different (known) groups, and apply an SVM classification model to this data. " + "In this example, we will generate some 2 dimensional data that comes from two different groups. \n", + "\n", + "This training data has labels, meaning for each data point we also know which group it comes from. \n", + "\n", + "We will then use a SVM classification model, to try and learn the decision boundary between the groups of data. If we are successful at learning a decision boundary, we can use this to predict the label of new datapoints." ] }, { "cell_type": "code", - "execution_count": 3, - "metadata": { - "collapsed": true - }, + "execution_count": 26, + "metadata": {}, "outputs": [], "source": [ "# Setting for generating some random data\n", - "n_points = 50\n", - "label_prop = 0.5\n", + "n_points = 50 # Total number of data points\n", + "label_prop = 0.5 # Proportion of points in class 1\n", "\n", "# Initialize data matrix (as zeros)\n", - "dat = np.zeros(shape=[n_points, 2])\n", + "data = np.zeros(shape=[n_points, 2])\n", "\n", "# Set up the number of data points in each class\n", - "n_dat_1 = int(n_points * label_prop)\n", - "n_dat_2 = n_points - n_dat_1\n", + "n_data_1 = int(n_points * label_prop)\n", + "n_data_2 = n_points - n_data_1\n", "\n", "# Generate the data\n", - "dat[0:n_dat_1, 0] = np.abs(np.random.randn(n_dat_1))\n", - "dat[0:n_dat_1, 1] = np.abs(np.random.randn(n_dat_1))\n", - "dat[n_dat_2:, 0] = np.abs(np.random.randn(n_dat_1)) + 2\n", - "dat[n_dat_2:, 1] = np.abs(np.random.randn(n_dat_1)) + 2\n", + "data[0:n_data_1, 0] = np.abs(np.random.randn(n_data_1))\n", + "data[0:n_data_1, 1] = np.abs(np.random.randn(n_data_1))\n", + "data[n_data_2:, 0] = np.abs(np.random.randn(n_data_1)) + 2\n", + "data[n_data_2:, 1] = np.abs(np.random.randn(n_data_1)) + 2\n", "\n", "# Create the labels vector\n", - "labels = np.array([0] * n_dat_1 + [1] * n_dat_2)" + "labels = np.array([0] * n_data_1 + [1] * n_data_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Data Visualization\n", + "\n", + "Now that we have some data, let's start by plotting it." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 27, "metadata": {}, "outputs": [ { "data": { - "image/png": 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4/AMAyKZWLrsslvTqpNuj9bbp/sHMdpvZU2Z2UaMHMrNBMxs2s+FDhw6dRbnJ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\n", "text/plain": [ - "" + "" ] }, + "execution_count": 27, "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ "# Plot out labelled data\n", "fig = plt.figure(figsize=[9, 7])\n", - "plt.plot(dat[0:n_dat_1, 0], dat[0:n_dat_1, 1], 'b.', ms=12, label=\"Label=0\")\n", - "plt.plot(dat[n_dat_2:, 0], dat[n_dat_2:, 1], 'g.', ms=12, label=\"Label=1\")\n", - "plt.legend();" + "plt.plot(data[0:n_data_1, 0], data[0:n_data_1, 1],\n", + " 'b.', ms=12, label=\"Label=0\")\n", + "plt.plot(data[n_data_2:, 0], data[n_data_2:, 1],\n", + " 'g.', ms=12, label=\"Label=1\")\n", + "plt.legend(fontsize=15)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see above, we have two fairly distinct groups of data. \n", + "\n", + "Now we want to learn a mathematical procedure that can learn the labels of these datapoints." ] }, { @@ -141,21 +182,22 @@ "source": [ "### Scikit-Learn Objects\n", "\n", - "As we can see above, we have two fairly distinct groups of data. Now we want to learn a mathematical procedure that can label these data into two groups, and we want it to learn a general procedure, that we can apply to new datapoints.\n", + "The SVM implementation we are using is from `sklearn`.\n", + "\n", + "Scikit-learn, as we have seen before, is object oriented. \n", "\n", - "Here we will use the typical scikit-learn approach:\n", - "- Initialize an sklearn object for the model object we are using, setting the desired parameters\n", - "- Train the model on our labelled training data\n", - "- Check our performance on our labelled data (typically both the train set, and a separate, labelled, test set)\n", + "Here, we will again use the typical scikit-learn approach, which is to:\n", + "\n", + "- Initialize a sklearn object for the model we want to use, setting the desired parameters\n", + "- Train the model on our labeled training data\n", + "- Check performance of our model (in real applications, using a separate, labeled, test set)\n", "- Apply the model to make predictions about new datapoints" ] }, { "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": true - }, + "execution_count": 35, + "metadata": {}, "outputs": [], "source": [ "# Initialize an SVM classifer object\n", @@ -164,55 +206,55 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n", - " decision_function_shape='ovr', degree=3, gamma='auto', kernel='linear',\n", - " max_iter=-1, probability=False, random_state=None, shrinking=True,\n", - " tol=0.001, verbose=False)" + " decision_function_shape='ovr', degree=3, gamma='auto_deprecated',\n", + " kernel='linear', max_iter=-1, probability=False, random_state=None,\n", + " shrinking=True, tol=0.001, verbose=False)" ] }, - "execution_count": 6, + "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Fit our classification model to our training data\n", - "classifier.fit(dat, labels)" + "classifier.fit(data, labels)" ] }, { "cell_type": "code", - "execution_count": 7, - "metadata": { - "collapsed": true - }, + "execution_count": 37, + "metadata": {}, "outputs": [], "source": [ "# Calculate predictions of the model on the training data\n", - "train_predictions = classifier.predict(dat)" + "train_predictions = classifier.predict(data)" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - " precision recall f1-score support\n", + " precision recall f1-score support\n", "\n", - " 0 1.00 1.00 1.00 25\n", - " 1 1.00 1.00 1.00 25\n", + " 0 1.00 1.00 1.00 25\n", + " 1 1.00 1.00 1.00 25\n", "\n", - "avg / total 1.00 1.00 1.00 50\n", + " accuracy 1.00 50\n", + " macro avg 1.00 1.00 1.00 50\n", + "weighted avg 1.00 1.00 1.00 50\n", "\n" ] } @@ -226,74 +268,74 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Predicting New Data Points\n", + "Now we have a trained classifier!\n", + "\n", + "We have trained our classifier on our data, and also checked it's performance. \n", "\n", - "Once we have a trained model, we can predict labels for new data points - data for which we do not know the answer." + "For this example, we have set up a simple example that is easy to predict, so our predictions are very accurate. \n", + "\n", + "Note that above all we doing is checking if our classifier can predict the labels of the training data - the data that is has already seen. This is _not_ a valid way to properly measure performance of machine learning algorithms. If you wish to continue to explore and use classification and other machine learning algorithms, you will need to look into how to properly test for accuracy, which is outside of the scope of these materials. " ] }, { - "cell_type": "code", - "execution_count": 9, - "metadata": { - "collapsed": true - }, - "outputs": [], + "cell_type": "markdown", + "metadata": {}, "source": [ - "# Set a new point - to predict a label for\n", - "new_point = np.array([[3, 3]])" + "### Predicting New Data Points\n", + "\n", + "Now that we have a trained model, we can use it to predict labels for new data points, including for data points for which we do not know already know the correct label." ] }, { "cell_type": "code", - "execution_count": 10, - "metadata": { - "collapsed": true - }, + "execution_count": 39, + "metadata": {}, "outputs": [], "source": [ - "# Add our new point to figure (in red)\n", - "fig.gca().plot(new_point[0][0], new_point[0][1], '.r', ms=12);" + "# Define a new data point, that we will predict a label for\n", + "new_point = np.array([[3, 3]])" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 40, "metadata": {}, "outputs": [ { "data": { - "image/png": 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mNbKVrcenC315MBADhA8AXcHKk/YQ0pBFhA8AXRHFypOw55gEgZCGLCJ8AOiKsFeeJPXy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\nAABCRfgAAACh+v8vNhyVZOE8EQAAAABJRU5ErkJggg==\n", 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\n", 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" ] }, - "execution_count": 11, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# Redraw figure\n", + "# Add our new point to figure, in red, and redraw the figure\n", + "fig.gca().plot(new_point[0][0], new_point[0][1], '.r', ms=12);\n", "fig" ] }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Predicted class of new data point is: 1\n" + "Predicted class of new data point is: 1\n" ] } ], "source": [ "# Predict the class of the new data point\n", "prediction = classifier.predict(new_point)\n", - "print('Predicted class of new data point is: ', prediction[0])" + "print('Predicted class of new data point is: {}'.format(prediction[0]))" ] }, { @@ -302,52 +344,50 @@ "source": [ "### Support Vectors\n", "\n", - "One of the key features of SVMs are that they use 'support vectors', meaning they prioritise using information from data points close to the decision boundary, and use them to try to find the widest margin - the distance between the two groups. Here we can briefly explore the support vectors for our trained model." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# Add the support vectors to plot\n", - "# Support vectors will be indicated by being highlighted with black circles\n", - "for row in classifier.support_vectors_:\n", - " fig.gca().plot(row[0], row[1], 'ok', ms=14, mfc='none')" + "As we mentioned befor, SVMs use 'support vectors', which are the points closest to the decision boundary, to try and learn the decision boundary with the highest margin (or separation) between the classes. \n", + "\n", + "Now that we have a trained model, we can have a look at the support vectors, and the decision boundary learned from them. " ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 42, "metadata": {}, "outputs": [ { "data": { - "image/png": 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dAOQn/vUCQnTo0CGVlJTozjvvnGpLpaREQioqSt+mUm/1TyaTOu+883T48OHA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\nZpEKH2a2QlKbpPdJukLSh83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\n", 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" ] }, - "execution_count": 14, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# Redraw the figure\n", + "# Add the support vectors to plot, and redraw the figure\n", + "# Support vectors will be indicated by being highlighted with black circles\n", + "for row in classifier.support_vectors_:\n", + " fig.gca().plot(row[0], row[1], 'ok', ms=14, mfc='none')\n", "fig" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see, the support vectors, which are identified with some meta-data that is stored in the model object, are some datapoints at the end of the classes - those closest to the boundary. " + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Drawing the decision boundary\n", "\n", - "Let's now draw the decision boundary - the boundary at which our learned model thinks the labels switch between groups." + "We can also draw the decision boundary - the boundary at which our model thinks the labels switch between groups." ] }, { @@ -362,10 +402,8 @@ }, { "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": true - }, + "execution_count": 43, + "metadata": {}, "outputs": [], "source": [ "# Grab the current plot, and find axis sizes\n", @@ -387,17 +425,17 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 44, "metadata": {}, "outputs": [ { "data": { - "image/png": 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d9StJlfbXqo3lrPr9q6uB/U0lHpZl9QXOGWOMZVlJ1K8l8YoFF1FRUcydO5fk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\nCDGkpPkQQgghxJCS5kMIIYQQQ+r/A6rS91r46T9GAAAAAElFTkSuQmCC\n", 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\n", 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" ] }, - "execution_count": 16, + "execution_count": 44, "metadata": {}, "output_type": "execute_result" } @@ -411,17 +449,41 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### Explorations\n", + "In the above plot, the solid line is the decision boundary that the model has learned. \n", + "\n", + "The dashed lines are the margins - the separation between the classes that the algorithm is trying to maximize. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### SVMs in more dimensions\n", + "\n", + "Note that, for simplicity, in this example we have used SVMs to learn a decision boundary in two dimensional data. \n", + "\n", + "In this case, with 2D data, the decision boundary is a line. \n", + "\n", + "SVMs also generalize to higher dimensions, and can be applied to data of any dimensionality. In higher dimensional data, the algorithm works the same, and the solution learned is a hyperplane that attempts the separate the data into categories in whatever dimensionality if lives. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conclusions\n", + "\n", + "The example above is a simplified example of an SVM application. With the code above, your are also encouraged to explore SVMs - investigate what happens as you change the data, change some settings, and predict different data points. \n", "\n", - "With the code above, your are encouraged to explore SVMs. \n", + "This example is meant as a brief example for using classification models with scikit-learn. Much more information can be found in the `scikit-learn` documentation. \n", "\n", - "Investigate what happens as you change the data, change the kernel, and predict different data points. " + "Classification is a vast area of machine learning, with many tools, algorithms, and approaches that can be applied to data within the realm of data science. This example seeks merely to introduce the basic idea. If you are interested in classification algorithms, then you are recommended to look into resources and classes that focus on machine learning. " ] } ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -435,7 +497,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/18-NaturalLanguageProcessing.ipynb b/18-NaturalLanguageProcessing.ipynb index 5a3373f..73990de 100644 --- a/18-NaturalLanguageProcessing.ipynb +++ b/18-NaturalLanguageProcessing.ipynb @@ -4,7 +4,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Natural Language Processing" + "# Natural Language Processing\n", + "\n", + "Most of the data we have encountered so far has been numerical (or at least, numerically encoded).\n", + "\n", + "However, one of the most powerful aspects of data science is acknowledging and considering that there are vasts amounts of data available in many other modalities, with potentially valuable information, if the data can be leveraged and analyzed. \n", + "\n", + "Here, we will introduce natural language processing (NLP), or the computational analysis of text." ] }, { @@ -25,7 +31,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## NTLK: Natural Language Tool Kit" + "## NTLK: Natural Language Tool Kit\n", + "\n", + "There are many tools for analyzing text data in Python. Here, we will use one of biggest and most prominent ones: NLTK.\n", + "\n", + "NLTK provides interfaces to over 50 corpora and lexical resources, as well as a suite of text processing libraries for classification, tokenization, stemming, tagging, parsing, and semantic reasoning.\n", + "\n", + "In this notebook, we will walk through some basic text-analysis using the `NLTK` package." ] }, { @@ -33,7 +45,7 @@ "metadata": {}, "source": [ "
\n", - "NLTK is the main Python module for text-analysis. \n", + "The Natural Language Tool Kit, or NLTK, is a Python module for text-analysis. \n", "
\n", "\n", "
\n", @@ -41,52 +53,56 @@ "here\n", "and they have a whole book of tutorials \n", "here.\n", - "
\n", - "\n", - "#### NLTK\n", - "\n", - "NLTK provides easy-to-use interfaces to over 50 corpora and lexical resources such as WordNet, along with a suite of text processing libraries for classification, tokenization, stemming, tagging, parsing, and semantic reasoning, wrappers for industrial-strength NLP libraries, and an active discussion forum. " + "
" ] }, { "cell_type": "code", - "execution_count": 2, - "metadata": { - "collapsed": true - }, + "execution_count": 1, + "metadata": {}, "outputs": [], "source": [ "# Import NLTK\n", "import nltk" ] }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Set an example sentence of 'data' to play with\n", + "sentence = \"UC San Diego is a great place to study cognitive science.\"" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "In this notebook, we will walk through some basic text-analysis using some useful functions from the NLTK package.\n", + "### Downloading Corpora\n", + "\n", + "To work with text-data, you often need corpora - text datasets to compare to. \n", "\n", - "To work with text-data, you often need corpora - text datasets to compare to. NLTK has many such datasets available, but doesn't install them by default (as the full set of them would be quite large). Below we will download some of these datasets. " + "NLTK has many such datasets available, but doesn't install them by default (as the full set of them would be quite large). Below we will download some of these datasets. " ] }, { "cell_type": "code", "execution_count": 3, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# If you hit an error downloading things in the cell below, come back to this cell, uncomment it, and run this code.\n", "# This code gives python permission to write to your disk (if it doesn't already have persmission to do so).\n", - "import ssl\n", + "# import ssl\n", "\n", - "try:\n", - " _create_unverified_https_context = ssl._create_unverified_context\n", - "except AttributeError:\n", - " pass\n", - "else:\n", - " ssl._create_default_https_context = _create_unverified_https_context" + "# try:\n", + "# _create_unverified_https_context = ssl._create_unverified_context\n", + "# except AttributeError:\n", + "# pass\n", + "# else:\n", + "# ssl._create_default_https_context = _create_unverified_https_context" ] }, { @@ -95,7 +111,7 @@ "metadata": {}, "outputs": [ { - "name": "stdout", + "name": "stderr", "output_type": "stream", "text": [ "[nltk_data] Downloading package punkt to /Users/tom/nltk_data...\n", @@ -136,18 +152,6 @@ "nltk.download('treebank')" ] }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "# Set some test sentences of data to play with\n", - "sentence = \"UC San Diego is a great place to study cognitive science.\"" - ] - }, { "cell_type": "markdown", "metadata": {}, @@ -173,10 +177,8 @@ }, { "cell_type": "code", - "execution_count": 6, - "metadata": { - "collapsed": true - }, + "execution_count": 5, + "metadata": {}, "outputs": [], "source": [ "# Tokenize our sentence, at the word level\n", @@ -185,7 +187,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -224,10 +226,8 @@ }, { "cell_type": "code", - "execution_count": 8, - "metadata": { - "collapsed": true - }, + "execution_count": 7, + "metadata": {}, "outputs": [], "source": [ "# Apply part-of-speech tagging to our sentence\n", @@ -236,7 +236,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -254,157 +254,34 @@ }, { "cell_type": "code", - "execution_count": 10, - "metadata": {}, + "execution_count": 40, + "metadata": { + "scrolled": false + }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "$: dollar\n", - " $ -$ --$ A$ C$ HK$ M$ NZ$ S$ U.S.$ US$\n", - "'': closing quotation mark\n", - " ' ''\n", - "(: opening parenthesis\n", - " ( [ {\n", - "): closing parenthesis\n", - " ) ] }\n", - ",: comma\n", - " ,\n", - "--: dash\n", - " --\n", - ".: sentence terminator\n", - " . ! ?\n", - ":: colon or ellipsis\n", - " : ; ...\n", - "CC: conjunction, coordinating\n", - " & 'n and both but either et for less minus neither nor or plus so\n", - " therefore times v. versus vs. whether yet\n", - "CD: numeral, cardinal\n", - " mid-1890 nine-thirty forty-two one-tenth ten million 0.5 one forty-\n", - " seven 1987 twenty '79 zero two 78-degrees eighty-four IX '60s .025\n", - " fifteen 271,124 dozen quintillion DM2,000 ...\n", + "NNP: noun, proper, singular\n", + " Motown Venneboerger Czestochwa Ranzer Conchita Trumplane Christos\n", + " Oceanside Escobar Kreisler Sawyer Cougar Yvette Ervin ODI Darryl CTCA\n", + " Shannon A.K.C. Meltex Liverpool ...\n", "DT: determiner\n", " all an another any both del each either every half la many much nary\n", " neither no some such that the them these this those\n", - "EX: existential there\n", - " there\n", - "FW: foreign word\n", - " gemeinschaft hund ich jeux habeas Haementeria Herr K'ang-si vous\n", - " lutihaw alai je jour objets salutaris fille quibusdam pas trop Monte\n", - " terram fiche oui corporis ...\n", - "IN: preposition or conjunction, subordinating\n", - " astride among uppon whether out inside pro despite on by throughout\n", - " below within for towards near behind atop around if like until below\n", - " next into if beside ...\n", "JJ: adjective or numeral, ordinal\n", " third ill-mannered pre-war regrettable oiled calamitous first separable\n", " ectoplasmic battery-powered participatory fourth still-to-be-named\n", - " multilingual multi-disciplinary ...\n", - "JJR: adjective, comparative\n", - " bleaker braver breezier briefer brighter brisker broader bumper busier\n", - " calmer cheaper choosier cleaner clearer closer colder commoner costlier\n", - " cozier creamier crunchier cuter ...\n", - "JJS: adjective, superlative\n", - " calmest cheapest choicest classiest cleanest clearest closest commonest\n", - " corniest costliest crassest creepiest crudest cutest darkest deadliest\n", - " dearest deepest densest dinkiest ...\n", - "LS: list item marker\n", - " A A. B B. C C. D E F First G H I J K One SP-44001 SP-44002 SP-44005\n", - " SP-44007 Second Third Three Two * a b c d first five four one six three\n", - " two\n", - "MD: modal auxiliary\n", - " can cannot could couldn't dare may might must need ought shall should\n", - " shouldn't will would\n", - "NN: noun, common, singular or mass\n", - " common-carrier cabbage knuckle-duster Casino afghan shed thermostat\n", - " investment slide humour falloff slick wind hyena override subhumanity\n", - " machinist ...\n", - "NNP: noun, proper, singular\n", - " Motown Venneboerger Czestochwa Ranzer Conchita Trumplane Christos\n", - " Oceanside Escobar Kreisler Sawyer Cougar Yvette Ervin ODI Darryl CTCA\n", - " Shannon A.K.C. Meltex Liverpool ...\n", - "NNPS: noun, proper, plural\n", - " Americans Americas Amharas Amityvilles Amusements Anarcho-Syndicalists\n", - " Andalusians Andes Andruses Angels Animals Anthony Antilles Antiques\n", - " Apache Apaches Apocrypha ...\n", - "NNS: noun, common, plural\n", - " undergraduates scotches bric-a-brac products bodyguards facets coasts\n", - " divestitures storehouses designs clubs fragrances averages\n", - " subjectivists apprehensions muses factory-jobs ...\n", - "PDT: pre-determiner\n", - " all both half many quite such sure this\n", - "POS: genitive marker\n", - " ' 's\n", - "PRP: pronoun, personal\n", - " hers herself him himself hisself it itself me myself one oneself ours\n", - " ourselves ownself self she thee theirs them themselves they thou thy us\n", - "PRP$: pronoun, possessive\n", - " her his mine my our ours their thy your\n", - "RB: adverb\n", - " occasionally unabatingly maddeningly adventurously professedly\n", - " stirringly prominently technologically magisterially predominately\n", - " swiftly fiscally pitilessly ...\n", - "RBR: adverb, comparative\n", - " further gloomier grander graver greater grimmer harder harsher\n", - " healthier heavier higher however larger later leaner lengthier less-\n", - " perfectly lesser lonelier longer louder lower more ...\n", - "RBS: adverb, superlative\n", - " best biggest bluntest earliest farthest first furthest hardest\n", - " heartiest highest largest least less most nearest second tightest worst\n", - "RP: particle\n", - " aboard about across along apart around aside at away back before behind\n", - " by crop down ever fast for forth from go high i.e. in into just later\n", - " low more off on open out over per pie raising start teeth that through\n", - " under unto up up-pp upon whole with you\n", - "SYM: symbol\n", - " % & ' '' ''. ) ). * + ,. < = > @ A[fj] U.S U.S.S.R * ** ***\n", - "TO: \"to\" as preposition or infinitive marker\n", - " to\n", - "UH: interjection\n", - " Goodbye Goody Gosh Wow Jeepers Jee-sus Hubba Hey Kee-reist Oops amen\n", - " huh howdy uh dammit whammo shucks heck anyways whodunnit honey golly\n", - " man baby diddle hush sonuvabitch ...\n", - "VB: verb, base form\n", - " ask assemble assess assign assume atone attention avoid bake balkanize\n", - " bank begin behold believe bend benefit bevel beware bless boil bomb\n", - " boost brace break bring broil brush build ...\n", - "VBD: verb, past tense\n", - " dipped pleaded swiped regummed soaked tidied convened halted registered\n", - " cushioned exacted snubbed strode aimed adopted belied figgered\n", - " speculated wore appreciated contemplated ...\n", - "VBG: verb, present participle or gerund\n", - " telegraphing stirring focusing angering judging stalling lactating\n", - " hankerin' alleging veering capping approaching traveling besieging\n", - " encrypting interrupting erasing wincing ...\n", - "VBN: verb, past participle\n", - " multihulled dilapidated aerosolized chaired languished panelized used\n", - " experimented flourished imitated reunifed factored condensed sheared\n", - " unsettled primed dubbed desired ...\n", - "VBP: verb, present tense, not 3rd person singular\n", - " predominate wrap resort sue twist spill cure lengthen brush terminate\n", - " appear tend stray glisten obtain comprise detest tease attract\n", - " emphasize mold postpone sever return wag ...\n", - "VBZ: verb, present tense, 3rd person singular\n", - " bases reconstructs marks mixes displeases seals carps weaves snatches\n", - " slumps stretches authorizes smolders pictures emerges stockpiles\n", - " seduces fizzes uses bolsters slaps speaks pleads ...\n", - "WDT: WH-determiner\n", - " that what whatever which whichever\n", - "WP: WH-pronoun\n", - " that what whatever whatsoever which who whom whosoever\n", - "WP$: WH-pronoun, possessive\n", - " whose\n", - "WRB: Wh-adverb\n", - " how however whence whenever where whereby whereever wherein whereof why\n", - "``: opening quotation mark\n", - " ` ``\n" + " multilingual multi-disciplinary ...\n" ] } ], "source": [ - "# Check the documentation that describes what all of the abbreviations mean\n", - "nltk.help.upenn_tagset()" + "# Check out the documentation for describing the abbreviations\n", + "nltk.help.upenn_tagset(tagpattern='NNP')\n", + "nltk.help.upenn_tagset(tagpattern='DT')\n", + "nltk.help.upenn_tagset(tagpattern='JJ')" ] }, { @@ -430,10 +307,8 @@ }, { "cell_type": "code", - "execution_count": 11, - "metadata": { - "collapsed": true - }, + "execution_count": 10, + "metadata": {}, "outputs": [], "source": [ "# Apply named entity recognition to our POS tags\n", @@ -442,7 +317,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -492,7 +367,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": { "scrolled": true }, @@ -514,25 +389,27 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Text Encoding\n", + "## Text Encoding\n", + "\n", + "In order to analyze text _as_ data, we often need to encode it in some way. \n", "\n", - "One of the key components of NLP, is deciding how to encode the text data. \n", + "By encoding here, we just mean choosing a representation of the data, and for text data the goal is to choose a representation that is more amenable for computational analysis. There are many possibilities, and which approach works best depends largely on the context of the data and the analyses to be performed. Choosing how to encode text data is a key topic in NLP. \n", "\n", - "Common encodings are:\n", + "Here, we will explore a couple simple encoding approaches, which in this case are basically ways to count the words and measure occurrences in text data. By measuring how often certain words occur, we can characterize the text as numerical data, and open up access to numerical analysis of the data. \n", + "\n", + "Some common encodings for text data are:\n", "- Bag of Words (BoW)\n", " - Text is encoded as a collection of words & frequencies\n", "- Term Frequency / Inverse Document Frequency (TF/IDF)\n", " - TF/IDF is a weighting that stores words with relation to their commonality across a corpus.\n", "\n", - "We will walk through an example of encoding text as BoW and TF-IDF." + "Next we will walk through an example of encoding text as BoW and TF-IDF." ] }, { "cell_type": "code", - "execution_count": 14, - "metadata": { - "collapsed": true - }, + "execution_count": 13, + "metadata": {}, "outputs": [], "source": [ "# Imports\n", @@ -555,27 +432,29 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "### Load some Data\n", + "\n", "The data we will be looking at is a small subset of the BookCorpus dataset. The original dataset can be found here: http://yknzhu.wixsite.com/mbweb.\n", "\n", - "The original dataset was collected from more than 11,000 books, and has already been tokenised at both the sentence and word level. The small subset provided and used here contains the first 10,000 sentences." + "The original dataset was collected from more than 11,000 books, and has already been tokenised at both the sentence and word level. \n", + "\n", + "The small subset provided and used here contains the first 10,000 sentences." ] }, { "cell_type": "code", - "execution_count": 15, - "metadata": { - "collapsed": true - }, + "execution_count": 14, + "metadata": {}, "outputs": [], "source": [ "# Load the data\n", - "with open('files/book10k.txt', 'r') as f:\n", - " sents = f.readlines()" + "with open('files/book10k.txt', 'r') as file:\n", + " sents = file.readlines()" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -595,15 +474,22 @@ "print(sents[-1])" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Pre-Processing\n", + "\n", + "First, let's do some standard text pre-processing." + ] + }, { "cell_type": "code", - "execution_count": 17, - "metadata": { - "collapsed": true - }, + "execution_count": 16, + "metadata": {}, "outputs": [], "source": [ - "# Preprocessing: Strip all extra whitespace from the sentences\n", + "# Preprocessing: strip all extra whitespace from the sentences\n", "sents = [sent.strip() for sent in sents]" ] }, @@ -611,15 +497,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We first take a look at the word frequency in the document, and print out top 10 most frequently appeared words with their frequencies." + "Let's first take a look at the word frequencies in this data.\n", + "\n", + "To do so, we can tokenize the text, count occurences, and then we can have a look at the most frequent words in the dataset. " ] }, { "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": true - }, + "execution_count": 17, + "metadata": {}, "outputs": [], "source": [ "# Tokenize all the sentences into words\n", @@ -631,14 +517,14 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Number of words in the data: \t 140060\n", + "Number of words in the data: \t 140094\n", "Number of unique words: \t 8221\n" ] } @@ -649,31 +535,92 @@ "print('Number of unique words: \\t', len(set(tokens)))" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Bag-of-Words\n", + "\n", + "Next, let's try a 'bag-of-words' representation of the data. \n", + "\n", + "After tokenization, a 'bag-of-words' can be computed by counting how often each token occurs, which we can do with the `Counter` object. \n", + "\n", + "
\n", + "A 'bag of words' model, of representation, is way to represent text data by counting occurences of tokens.\n", + "
\n", + "\n", + "
\n", + "Bag of words on \n", + "wikipedia.\n", + "
" + ] + }, { "cell_type": "code", - "execution_count": 20, - "metadata": { - "collapsed": true - }, + "execution_count": 19, + "metadata": {}, "outputs": [], "source": [ "# Use the 'counter' object to count how many times each word appears\n", "counts = Counter(tokens)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we can explore the counter object, which is basically a 'bag-of-words' representation of the data. \n", + "\n", + "Note that in this encoding we have lost word order and grammar. All we have is a collection of words. \n", + "\n", + "This representation is quite different from how humans interact with language, but can be useful for some analyses. \n", + "\n", + "What we do have is a list of all the words present, and how often they appear. Basically, we have turned the text into a _distribution_ and we can try and analyze this distribution to try and programmatically analyze the text. " + ] + }, { "cell_type": "code", - "execution_count": 30, - "metadata": { - "collapsed": true - }, - "outputs": [], + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[('.', 8601),\n", + " (',', 6675),\n", + " ('the', 6062),\n", + " ('and', 3382),\n", + " ('to', 3328),\n", + " ('``', 2852),\n", + " ('i', 2747),\n", + " ('a', 2480),\n", + " ('of', 2122),\n", + " ('was', 1752),\n", + " ('he', 1678),\n", + " ('in', 1616),\n", + " ('you', 1483),\n", + " ('her', 1353),\n", + " ('his', 1349),\n", + " ('?', 1153),\n", + " ('she', 1153),\n", + " ('that', 1134),\n", + " ('it', 1050),\n", + " (\"'s\", 1023),\n", + " ('had', 898),\n", + " ('with', 894),\n", + " ('alejo', 890),\n", + " ('wara', 875),\n", + " ('at', 818)]" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "# Check out the counts object\n", - "# This is basically a 'bag-of-words' representation of this corpus\n", - "# We have lost word order and grammar - it's just a collection of words\n", - "# What we do have is a list of all the words present, and how often they appear\n", - "counts" + "# Check out the counts object, printing out some of the most common tokens\n", + "counts.most_common(25)" ] }, { @@ -704,9 +651,7 @@ { "cell_type": "code", "execution_count": 22, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Drop all punction markers from the counts object\n", @@ -718,9 +663,7 @@ { "cell_type": "code", "execution_count": 23, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Get the top 10 most frequent words\n", @@ -730,9 +673,7 @@ { "cell_type": "code", "execution_count": 24, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Extract the top words, and counts\n", @@ -747,12 +688,14 @@ "outputs": [ { "data": { - "image/png": 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\n", "text/plain": [ - "" + "
" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -769,15 +712,17 @@ "source": [ "As we can see, 'the', 'was', 'a', etc. appear a lot in the document. \n", "\n", - "These frequently appearing words aren't really that useful to figure out what these documents are about, or as a way to use and understand this text data. " + "However, these frequently appearing words aren't particularly useful for figuring out what these documents are about.\n", + "\n", + "They do not really help us to understand this text data. \n", + "\n", + "These words are all 'stop words', so let's drop them from the dataset. " ] }, { "cell_type": "code", "execution_count": 26, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Drop all stop words\n", @@ -789,9 +734,7 @@ { "cell_type": "code", "execution_count": 27, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Get the top 20 most frequent words, of the stopword-removed data\n", @@ -805,12 +748,14 @@ "outputs": [ { "data": { - "image/png": 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -825,54 +770,98 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "This looks potentially more relevant / useful. We could continue exploring this BoW model, but let's instead pivot now, and explore using TFIDF." + "This looks potentially more relevant / useful! \n", + "\n", + "As a distribution of meaningful word, bag-of-word representations can be used to analyze text data in various ways.\n", + "\n", + "If you are interested in further analysis of this data, look through the `nltk` tutorials for further analyses." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Term Frequency - Inverse Document Frequency (TF-IDF)\n", + "\n", + "Finally, let's look at another approach for encoding text data - term frequency / inverse document frequency.\n", + "\n", + "Note that TF-IDF is a similar kind of word counting to bag-of-words. \n", + "\n", + "First, let's consider a difficulty with bag-of-words encodings, which is it's difficult to interpret the word counts. For example, knowing a word occurs 10 times isn't itself really enough information to understand something about the document the word come from. If that document is 100 words long, that word seems like it must be quite important. But if the document is 10,000 words long, then this word seems less important. \n", + "\n", + "TF-IDF tries to address this, and does so by scaling the counts of words by the typical occurrence. \n", + "\n", + "- The term-frequency is the count of the term in the document, which is the same as in the bag-of-words. \n", + "\n", + "- The inverse-document-frequency is a measurement of how commonly the term occurs across a corpus. \n", + " - Since it's calculated as an inverse, a higher IDF score is a rarer word. \n", + "\n", + "The TF-IDF score is calculated by multiplying the TF by the IDF. One way to think of this is that it normalizes, or scales, term occurrences in a document by a population measure of the occurrence of the term. \n", + "\n", + "This allows for a representation of the text data which indicates if terms in the document of interest occur more or less frequently than expected (given a corpus). A high TF-IDF score could occur, for example, due to a relatively large number of occurrences of a typically rare term. This may be an interesting and useful feature to describe the text.\n", + "\n", + "Here, we will briefly examine applying TF/IDF to text data. Note that in this case, we are using an object from `sklearn` that can be used to compute the TF/IDF. \n", + "\n", + "
\n", + "Term Frequency - Inverse Document Frequency is representation of text data that scales term occurrences by corpus statistics.\n", + "
\n", + "\n", + "
\n", + "TF-IDF on \n", + "wikipedia.\n", + "
" ] }, { "cell_type": "code", "execution_count": 29, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "# Initialize a TFIDF object\n", + "# Initialize a TFIDF object, applying some settings\n", "tfidf = TfidfVectorizer(analyzer='word',\n", " sublinear_tf=True,\n", " max_features=5000,\n", " tokenizer=nltk.word_tokenize)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The TfidfVectorizer will calculate the inverse document frequency (IDF) for each word across our corpus of words. \n", + "\n", + "The TFIDF for each term, for a particular document, can then be calculated as TF * IDF. " + ] + }, { "cell_type": "code", "execution_count": 30, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ - "# Apply the TFIDF transformation to our data\n", - "# Note that this takes the sentences, and tokenizes them, then applies TFIDF\n", - "tfidf_books = tfidf.fit_transform(sents).toarray()" + "# Learn the TFIDF representation of our data\n", + "# Note that this takes the raw sentences, tokenizes them, and learns the TF/IDF representation\n", + "tdidf = tfidf.fit(sents)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The TfidfVectorizer will calculate the inverse document frequency (IDF) for each word. \n", + "Before we apply this representation to our data, let's explore what the data object and calculated scores. \n", "\n", - "The TFIDF is then calculated as the TF * IDF, working to down-weight frequently appearing words. This TFIDF is stored in 'tfidf_books' variable, which is a n_documents x n_words matrix that encodes the documents in a TFIDF representation. \n", + "If you explore the tfidf object you'll see it includes attributes:\n", + "- `vocabulary_`, which maps the terms to their indices\n", + "- `idf_`, which has the IDF values for each term. \n", "\n", - "Let's first plot out the IDF for each of the top 10 most frequently appeared words (from the first analysis). " + "Let's now plot out the IDF for each of the top 10 most frequently appeared words (from the first analysis). " ] }, { "cell_type": "code", "execution_count": 31, - "metadata": { - "collapsed": true - }, + "metadata": {}, "outputs": [], "source": [ "# Get the IDF weights for the top 10 most common words\n", @@ -886,12 +875,14 @@ "outputs": [ { "data": { - "image/png": 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+ "image/png": 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -911,13 +902,11 @@ }, { "cell_type": "code", - "execution_count": 34, - "metadata": { - "collapsed": true - }, + "execution_count": 33, + "metadata": {}, "outputs": [], "source": [ - "# Get the words with the highest IDF score\n", + "# Get the terms with the highest IDF score\n", "inds = np.argsort(tfidf.idf_)[::-1][:10]\n", "top_IDF_tokens = [list(tfidf.vocabulary_)[ind] for ind in inds]\n", "top_IDF_scores = tfidf.idf_[inds]" @@ -925,22 +914,24 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 34, "metadata": {}, "outputs": [ { "data": { - "image/png": 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S9oXAEZ3BJGnXMv8q4M1l3k5U97Cgusf0Mkmblgc9Dmxp6yLgA51fJE3rpv5X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\n0f4/mjqpWFNYm2IAAAAASUVORK5CYII=\n", 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\n", 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" ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], "source": [ - "# Get the words with the highest IDF score\n", + "# Plot the terms with the highest IDF score\n", "plt.barh(top_IDF_tokens, top_IDF_scores)\n", "plt.title('Inverse Document Frequency');\n", "plt.xlabel('IDF Score');" @@ -950,15 +941,81 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "As we can see, the frequently appearing words in the document get very low IDF scores, as compared to much rarer words. \n", + "As we can see, comparing across the two plots, the frequently appearing words have much lower values for their IDF scores, as compared to much rarer words. This is basically by definition, for the IDF score. \n", + "\n", + "What this means for TF-IDF is that the weighting helps account for which words in a document are specific to that document. Because the TF and IDF values are multiplied, rare terms get a higher TF-IDF score, per occurrence, than common words, which helps to compare across terms and documents. Ultimately, this allows us to represent a document by distribution of terms that are most unique to the particular document, as compared to the average across the corpus. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Applying TF-IDF\n", + "\n", + "Now that we have learned the frequencies, we can apply this representation to our data. \n", + "\n", + "In the next line, we will apply the TF-IDF representation to our data, and convert this to an array. \n", + "\n", + "This array is an `n_documents` x `n_terms` matrix that encodes the documents in a TFIDF representation.\n", + "\n", + "Note that in our TFIDF object above we set the number of features to use as 5000, which is the number of terms. " + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [], + "source": [ + "# Apply TF/IDF representation to our data\n", + "tfidf_books = tdidf.transform(sents).toarray()" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of documents: \t\t 10000\n", + "Number of terms: \t\t 5000\n", + "TFIDF representation shape: \t (10000, 5000)\n" + ] + } + ], + "source": [ + "print(\"Number of documents: \\t\\t\", len(sents))\n", + "print(\"Number of terms: \\t\\t\", len(tfidf.vocabulary_))\n", + "print(\"TFIDF representation shape: \\t\", tfidf_books.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the TFIDF array, each row stores a representation of the document based on the TF-IDF score of our 5000 terms. \n", + "\n", + "This is a new representation of our text data, a numerical one, that we could now use for analysis and comparison of text data. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion\n", + "\n", + "Text analysis and NLP is itself a huge field, and an area in which one can take whole classes or research programs. \n", "\n", - "After TF-IDF, we successfully down-weight the frequently appearing words in the document. This allows us to represent a document by the words that are most unique to it, which can be a more useful way to represent text data. " + "Here, we have introduced some of the core idea related to NLP. For more information on these topics, look into NLP focused resources and classes." ] } ], "metadata": { "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -972,7 +1029,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/A1-PythonPackages.ipynb b/A1-PythonPackages.ipynb index ee420eb..547fb37 100644 --- a/A1-PythonPackages.ipynb +++ b/A1-PythonPackages.ipynb @@ -7,7 +7,7 @@ "# Useful Python Packages for Data Science\n", "\n", "
\n", - "The following is general overview of packages availabe in Python that may be useful for data science.\n", + "The following is general overview of packages available in Python that may be useful for data science.\n", "
\n", "\n", "
\n", @@ -20,9 +20,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Data-Science Modules\n", + "## Data-Science Modules\n", "\n", - "These packages are all included in the anaconda distribution.\n", + "These are all external (non-standard library) packages. Many of them are available in the Ananconda distribution. \n", "\n", "### Core Packages\n", "\n", @@ -43,15 +43,17 @@ "\n", "### Web Scraping\n", "\n", - "- [requests](http://docs.python-requests.org/en/master/) - HTTP requests.\n", + "- [requests](https://requests.readthedocs.io/) - HTTP requests.\n", "- [scrapy](https://scrapy.org) - web scraping.\n", " \n", "### Plotting / Vizualization Libraries\n", + "\n", "- [matplotlib](https://matplotlib.org) - 2D plotting library.\n", "- [seaborn](https://seaborn.pydata.org/) - visualization (based on matplotlib).\n", "- [bokeh](http://bokeh.pydata.org/en/latest/) - interactive visualizations.\n", " \n", "### Graph Theory / Networks\n", + "\n", "- [networkx](https://networkx.github.io/) - network analysis.\n", "- [graph-tool](https://graph-tool.skewed.de/) - manipulation and analysis of graphs.\n", " \n", @@ -66,40 +68,44 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Useful parts of the standard library\n", - "\n", - "\n", - "The full list of packages in the standard library is available [here](https://docs.python.org/3.6/library/index.html).\n", + "## Useful parts of the standard library\n", "\n", + "The full list of packages in the standard library is available [here](https://docs.python.org/3/library/index.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "### Basic Utilities\n", "\n", - "- [os](https://docs.python.org/3.6/library/os.html) - miscellaneous operating system operations.\n", - "- [sys](https://docs.python.org/3.6/library/sys.html) - system operations.\n", - "- [datetime](https://docs.python.org/3.6/library/datetime.html) - manipulating dates & times.\n", - "- [glob](https://docs.python.org/3.6/library/glob.html) - searching path names.\n", + "- [os](https://docs.python.org/3/library/os.html) - miscellaneous operating system operations.\n", + "- [sys](https://docs.python.org/3/library/sys.html) - system operations.\n", + "- [datetime](https://docs.python.org/3/library/datetime.html) - manipulating dates & times.\n", + "- [glob](https://docs.python.org/3/library/glob.html) - searching path names.\n", "\n", "### Useful Functions\n", "\n", - "- [math](https://docs.python.org/3.6/library/math.html) - mathematical functions.\n", - "- [random](https://docs.python.org/3.6/library/random.html) - (pseudo) random number generators.\n", - "- [re](https://docs.python.org/3.6/library/re.html) - regular expressions.\n", + "- [math](https://docs.python.org/3/library/math.html) - mathematical functions.\n", + "- [random](https://docs.python.org/3/library/random.html) - (pseudo) random number generators.\n", + "- [re](https://docs.python.org/3/library/re.html) - regular expressions.\n", "\n", "### File Formats\n", "\n", - "- [json](https://docs.python.org/3.6/library/json.html) - support for working with JSON files.\n", - "- [csv](https://docs.python.org/3.6/library/csv.html) - support for working with CSV files.\n", + "- [json](https://docs.python.org/3/library/json.html) - support for working with JSON files.\n", + "- [csv](https://docs.python.org/3/library/csv.html) - support for working with CSV files.\n", "\n", "### Data Objects\n", "\n", - "- [collections](https://docs.python.org/3.6/library/collections.html) - container data types.\n", - "- [pickle](https://docs.python.org/3.6/library/pickle.html) - serializing & de-serializing (saving and loading complex objects)." + "- [collections](https://docs.python.org/3/library/collections.html) - container data types.\n", + "- [pickle](https://docs.python.org/3/library/pickle.html) - serializing & de-serializing (saving and loading complex objects)." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python [default]", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -113,7 +119,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.3" + "version": "3.7.4" } }, "nbformat": 4, diff --git a/A2-Git.ipynb b/A2-Git.ipynb index abc64e9..b789d5f 100644 --- a/A2-Git.ipynb +++ b/A2-Git.ipynb @@ -4,7 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Version Control with git/Github" + "# Version Control\n", + "\n", + "This notebook explores version control, and using git & Github." ] }, { @@ -37,11 +39,12 @@ "
\n", "Git is a version control system: a tool to track changes in files, across multiple locations. \n", "
\n", - "
\n", "\n", - "Click through to \n", - "git.\n", - "Git is an open-source software project. \n", + "
\n", + "Information for using git is available in the \n", + "official documentation, \n", + "as well as in many external resources, collected in \n", + "this list.\n", "
\n", "
" ] @@ -58,12 +61,13 @@ "metadata": {}, "source": [ "
\n", - "Github is a web based version of Git, and version control repository or internet hosting service. It's a place to put code that is tracked with git. \n", + "Github is company that offers version control services, using git.\n", + " \n", + "Github is a hosting service, with git built in, or basically, a place on the internet to put code that is tracked with git. \n", "
\n", "
\n", "Click through to \n", "Github.\n", - "Note that Github is a company. \n", "
\n", "
" ] @@ -72,7 +76,31 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Git Graphical User Interfaces (GUIs)" + "## Using Git" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are several ways to use git, including:\n", + "- from the command line, typing in commands directly\n", + "- using a graphical program to launch git commands\n", + " - This kind of program is referred to as a 'graphical user interface' (GUI).\n", + " - It basically just means you can click buttons to do things, rather than writing out commands\n", + " \n", + "Either way the underlying commands, and code that gets executed, are the same. Behind the scenes, it all reduces to the same thing. \n", + "\n", + "You should use whichever approach you are most comfortable with. If you already know some command line programming, using git from command line can be useful, as generally slightly more functionality is available to you, with more specific control. Using a GUI is much more straight forward if you are not very familiar with the command line." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Git Graphical User Interfaces (GUIs)\n", + "\n", + "If you plan to use a GUI, one option is SourceTree." ] }, { @@ -86,17 +114,10 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "There are several ways to use git, including:\n", - "- from the command line, typing in commands\n", - "- using a graphical program to launch git commands\n", - " - This kind of program is referred to as a 'graphical user interface' (GUI).\n", - " - It basically just means you can click buttons to do things, rather than writing out commands\n", "\n", - "Either way the underlying commands, and code that gets executed, are the same. Behind the scenes, it all reduces to the same thing. \n", "\n", - "You should use whichever approach you are most comfortable with. If you already know some command line programming, using git from command line can be useful, as generally slightly more functionality is available to you, with more specific control. Using a GUI is much more straight forward if you are not very familiar with the command line.\n", "\n", - "If you plan to use a GUI, we recommend SourceTree." + "\n" ] }, { @@ -104,8 +125,8 @@ "metadata": {}, "source": [ "
\n", - "Source Tree tutorial documentation is available \n", - "here.\n", + "See the Source Tree\n", + "documentation.\n", "
" ] }, @@ -113,19 +134,27 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Local vs. Remote\n", - "\n", - "What git is mainly doing is keeping two (or more) versions of the same repository consistent.\n", + "## Git repositories\n", "\n", "A repository is simply a collection of files, like a folder on a computer. \n", "\n", - "We will refer to these copies as:\n", + "What git is mainly doing is keeping two (or more) versions of the same repository consistent." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Local vs. Remote\n", + "\n", + "Given a repository with multiple copies (or versions), we can refer to these copies:\n", + "\n", "- the 'local' copy, which is a copy of the repository on your computer (the one 'local' to you)\n", "- the 'remote' copy, which is a copy of the repository somewhere else, such as on Github\n", "\n", "There is often a particular copy of the code that is referred to as the 'master', which just means it is the master version of the repository in question. Most typically, this is the copy of the code on Github - so there is one 'master' copy of the code on Github, and one or more people also have local copies of the code, with local updates. When local updates want to be shared, they can be sent to master, to update the main version of the code, for everyone.\n", "\n", - "Here we will consider the case, descriped above, of having two copies of the repository. What is described here can all be extended to multiple copies of the code, including multiple different remote copies of the repository.\n", + "Here we will consider the case of having two copies of the repository. What is described here can all be extended to multiple copies of the code, including multiple different remote copies of the repository.\n", "\n", "The main function of git, as a version control system, is to automatically check all of the files in each copy of the repository, tracking any changes that happen. It then provides tools to synchronize between different copies when there are changes." ] @@ -136,58 +165,78 @@ "source": [ "## Getting Code from Github\n", "\n", - "Most typically, there is code available on Github, and you want to get a local copy, to use the code, and potentially update it, and then send your updates back to Github. \n", + "As a starting point, it if often the case that there is code available on Github, and you want to get a local copy. This allows you to access the code, to use, and potentially update it. Then, if you want, you can contribute your code updates back to the main version of the code up on Github. \n", "\n", - "First you need to get a local copy of the code. Git calls making a copy of a repository 'cloning'.\n", + "First, you need to get a local copy of the code. Git calls making a copy of a repository 'cloning'.\n", "\n", "From command line, to clone a Github repository to your computer, use the clone command with the URL to the repository.\n", - "- $ git clone 'repo_url'" + "- $ ``git clone 'repo_url'``\n", + " - For example, you can clone these materials with:\n", + " - ``git clone https://github.com/COGS108/Tutorials``" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# Tracking & Propagating Changes\n", + "## Tracking & Propagating Changes\n", "\n", "Once you have a local copy, connected to a remote repository, changes can go in two directions:\n", + "\n", "- sending changes you make locally to the remote\n", - "- updating your local copy with changes from the remote" + " - this is called a `push`\n", + "- updating your local copy with changes from the remote\n", + " - this is called a `pull`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Tracking and Sending Changes from local -> remote\n", + "### Tracking and Sending Changes from local -> remote\n", "\n", - "When working on local files, git has multiple 'levels'. These multiple levels are useful to organize groups of changes into well organized actions. \n", + "When working on local files, git has hierarchical 'levels' of how it is tracking files (or, of what it is paying attention to). These multiple levels are useful to organize groups of changes into well organized actions.\n", + "\n", + "The repository can have many files in it, within which there are:\n", + "- tracked files\n", + " - these are files that git is tracking\n", + " - any files that are not tracked by git are untracked, and won't be version controlled\n", + "- staged files\n", + " - these are tracked files that have been indicated to be added to an update of the code\n", + " - staging allows for specifying which files to save updates to, and how to group files\n", "\n", "The typical workflow is:\n", - "- add: select which changes, on which files, you would like git to \n", + "- ``add``: select which changes, on which files, you would like git to add to staging area\n", " - You can add multiple files together, each with their own changes\n", - "- commit: make a checkpoint, saving all files that have been added together\n", + " - If a file is untracked, this adds it to tracking\n", + "- ``commit``: make a checkpoint, saving all files that have been added together\n", " - These changes will be 'saved' together with a message (a commit log) about what the changes are\n", - "- push: send the changes to the remote\n", + "- ``push``: send the changes to the remote\n", + " - These changes will now be available in the remote copy of the repository" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Example Workflow\n", "\n", "First, in a local git repository, you make some changes to a file, or perhaps many files. \n", "\n", - "You can now add files. This needs to be done for each file you changed, that we want to log:\n", - "- $ git add 'f_name'\n", + "You can now add files. This needs to be done for each file you changed, that we want to add to staging:\n", + "- $ ``git add 'f_name'``\n", "\n", "After you've added one or more files, you use a commit to save the status of these files:\n", - "- $ git commit -m 'Commit message'\n", + "- $ ``git commit -m 'Commit message'``\n", "\n", "The '-m' flag is an option to write your commit message directly with the command. If you don't add it, git will send you into a text editor for you to write a commit message there. You should always add an informative message about what you have changed / added.\n", "\n", - "Making small, incremental changes and commiting often, with detailed messages means that your Github log can serve as a history for your project, keeping track of what you've done. \n", - "\n", - "This also allows you to step back to an older version of the code if everything suddenly breaks.\n", + "Making small, incremental changes and commiting often, with detailed messages means that your Github log can serve as a history for your project. This is useful as a way to use version control to keep track of a projects history. This also allows you to step back to an older version of the code if everything suddenly breaks.\n", "\n", "A committed change is still only stored in your local copy. To update the remote repostory, you have to push:\n", - "- $ git push\n", + "- $ ``git push``\n", "\n", - "You do not have to push after each commit, git push can push many commits at once. \n", + "You do not have to push after each commit, you can push many commits at once. \n", "\n", "Once you have pushed, you should see your updates have been added to the remote repository, on Github." ] @@ -196,13 +245,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Getting Changes from remote -> local\n", + "### Getting Changes from remote -> local\n", "\n", "Git refers to updating a local copy with changes from a remote copy as 'pulling'\n", "\n", "On command line, if there are changes on the remote branch, use the 'git pull' to copy those changes to your local: copy.\n", "\n", - "- $ git pull" + "- $ ``git pull``" ] }, { @@ -213,20 +262,22 @@ "\n", "The most common git functions are:\n", "\n", - "- git status\n", + "- ``git status``\n", " - Check the status of a git repository\n", - "- git add 'file'\n", + "- ``git add 'file'``\n", " - Add a file to staging area\n", - "- git commit -m 'message'\n", + "- ``git commit -m 'message'``\n", " - Log a 'save point' of all changes in the staging area.\n", - "- git push\n", + "- ``git push``\n", " - Copy commits to remote\n", - "- git diff 'file'\n", + "- ``git diff 'file'``\n", " - Check what has changed in file since last commit\n", - "- git clone 'repo'\n", + "- ``git clone 'repo'``\n", " - Create a local copy of a git repository\n", - "- git pull\n", - " - Update your local copy of a git repository from the remote" + "- ``git pull``\n", + " - Update your local copy of a git repository from the remote\n", + "- ``git log``\n", + " - Check the log of git commits" ] }, { @@ -252,14 +303,14 @@ "
\n", "There are many tutorials for working with Github, including an \n", "interactive tutorial, \n", - "and a \n", + "and\n", "Hello World,\n", - "both made by Github\n", - "
\n", - "There are also several other useful guides and tutorials, including these ones available on\n", + "made by Github, and many other guides and tutorials, for example those available from\n", "LifeHacker, \n", "Atlassian, and\n", - "neuroplausible.\n", + "Neuroplausible.\n", + "For a list of many resources, see\n", + "this list.\n", "
" ] }