{ "cells": [ { "cell_type": "raw", "metadata": {}, "source": [ "---\n", "title: \"Photometry\"\n", "teaching: 3000\n", "exercises: 0\n", "questions:\n", "\n", "- \"How do we use Matplotlib to define a polygon and select points that fall inside it?\"\n", "\n", "objectives:\n", "\n", "- \"Use isochrone data to specify a polygon and determine which points fall inside it.\"\n", "\n", "- \"Use Matplotlib features to customize the appearance of figures.\"\n", "\n", "keypoints:\n", "\n", "- \"Matplotlib provides operations for working with points, polygons, and other geometric entities, so it's not just for making figures.\"\n", "\n", "- \"Use Matplotlib options to control the size and aspect ratio of figures to make them easier to interpret.\"\n", "\n", "- \"Record every element of the data analysis pipeline that would be needed to replicate the results.\"\n", "\n", "---\n", "\n", "{% include links.md %}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 6. Photometry\n", "\n", "This is the sixth in a series of notebooks related to astronomy data.\n", "\n", "As a continuing example, we will replicate part of the analysis in a recent paper, \"[Off the beaten path: Gaia reveals GD-1 stars outside of the main stream](https://arxiv.org/abs/1805.00425)\" by Adrian M. Price-Whelan and Ana Bonaca.\n", "\n", "In the previous lesson we downloaded photometry data from Pan-STARRS, which is available from the same server we've been using to get Gaia data. \n", "\n", "The next step in the analysis is to select candidate stars based on the photometry data. \n", "The following figure from the paper is a color-magnitude diagram showing the stars we previously selected based on proper motion:\n", "\n", "\n", "\n", "In red is a theoretical isochrone, showing where we expect the stars in GD-1 to fall based on the metallicity and age of their original globular cluster. \n", "\n", "By selecting stars in the shaded area, we can further distinguish the main sequence of GD-1 from mostly younger background stars." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Outline\n", "\n", "Here are the steps in this notebook:\n", "\n", "1. We'll reload the data from the previous notebook and make a color-magnitude diagram.\n", "\n", "2. We'll use an isochrone computed by MIST to specify a polygonal region in the color-magnitude diagram and select the stars inside it.\n", "\n", "After completing this lesson, you should be able to\n", "\n", "* Use Matplotlib to specify a `Polygon` and determine which points fall inside it.\n", "\n", "* Use Pandas to merge data from multiple `DataFrames`, much like a database `JOIN` operation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Reload the data\n", "\n", "You can [download the data from the previous lesson](https://github.com/AllenDowney/AstronomicalData/raw/main/data/gd1_data.hdf) or run the following cell, which downloads it if necessary." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "from os.path import basename, exists\n", "\n", "def download(url):\n", " filename = basename(url)\n", " if not exists(filename):\n", " from urllib.request import urlretrieve\n", " local, _ = urlretrieve(url, filename)\n", " print('Downloaded ' + local)\n", "\n", "download('https://github.com/AllenDowney/AstronomicalData/raw/main/' +\n", " 'data/gd1_data.hdf')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can reload `candidate_df`." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "\n", "filename = 'gd1_data.hdf'\n", "candidate_df = pd.read_hdf(filename, 'candidate_df')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting photometry data\n", "\n", "Now that we have photometry data from Pan-STARRS, we can replicate the [color-magnitude diagram](https://en.wikipedia.org/wiki/Galaxy_color%E2%80%93magnitude_diagram) from the original paper:\n", "\n", "\n", "\n", "The y-axis shows the apparent magnitude of each source with the [g filter](https://en.wikipedia.org/wiki/Photometric_system).\n", "\n", "The x-axis shows the difference in apparent magnitude between the g and i filters, which indicates color.\n", "\n", "Stars with lower values of (g-i) are brighter in g-band than in i-band, compared to other stars, which means they are bluer.\n", "\n", "Stars in the lower-left quadrant of this diagram are less bright than the others, and have lower metallicity, which means they are [likely to be older](http://spiff.rit.edu/classes/ladder/lectures/ordinary_stars/ordinary.html).\n", "\n", "Since we expect the stars in GD-1 to be older than the background stars, the stars in the lower-left are more likely to be in GD-1." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following function takes a table containing photometry data and draws a color-magnitude diagram.\n", "The input can be an Astropy `Table` or Pandas `DataFrame`, as long as it has columns named `g_mean_psf_mag` and `i_mean_psf_mag`.\n", "\n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def plot_cmd(table):\n", " \"\"\"Plot a color magnitude diagram.\n", " \n", " table: Table or DataFrame with photometry data\n", " \"\"\"\n", " y = table['g_mean_psf_mag']\n", " x = table['g_mean_psf_mag'] - table['i_mean_psf_mag']\n", "\n", " plt.plot(x, y, 'ko', markersize=0.3, alpha=0.3)\n", "\n", " plt.xlim([0, 1.5])\n", " plt.ylim([14, 22])\n", " plt.gca().invert_yaxis()\n", "\n", " plt.ylabel('$Magnitude (g)$')\n", " plt.xlabel('$Color (g-i)$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`plot_cmd` uses a new function, `invert_yaxis`, to invert the `y` axis, which is conventional when plotting magnitudes, since lower magnitude indicates higher brightness.\n", "\n", "`invert_yaxis` is a little different from the other functions we've used. You can't call it like this:\n", "\n", "```\n", "plt.invert_yaxis() # doesn't work\n", "```\n", "\n", "You have to call it like this:\n", "\n", "```\n", "plt.gca().invert_yaxis() # works\n", "```\n", "\n", "`gca` stands for \"get current axis\". It returns an object that represents the axes of the current figure, and that object provides `invert_yaxis`.\n", "\n", "**In case anyone asks:** The most likely reason for this inconsistency in the interface is that `invert_yaxis` is a lesser-used function, so it's not made available at the top level of the interface." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the results look like." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cmd(candidate_df)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our figure does not look exactly like the one in the paper because we are working with a smaller region of the sky, so we don't have as many stars. But we can see an overdense region in the lower left that contains stars with the photometry we expect for GD-1.\n", "\n", "In the next section we'll use an isochrone to specify a polygon that contains this overdense regioin." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Isochrone\n", "\n", "Based on our best estimates for the ages of the stars in GD-1 and their metallicity, we can compute a [stellar isochrone](https://en.wikipedia.org/wiki/Stellar_isochrone) that predicts the relationship between their magnitude and color.\n", "\n", "In fact, we can use [MESA Isochrones & Stellar Tracks](http://waps.cfa.harvard.edu/MIST/) (MIST) to compute it for us.\n", "\n", "Using the [MIST Version 1.2 web interface](http://waps.cfa.harvard.edu/MIST/interp_isos.html), we computed an isochrone with the following parameters:\n", " \n", "* Rotation initial v/v_crit = 0.4\n", "\n", "* Single age, linear scale = 12e9\n", "\n", "* Composition [Fe/H] = -1.35\n", "\n", "* Synthetic Photometry, PanStarrs\n", "\n", "* Extinction av = 0\n", "\n", "The following cell downloads the results:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "download('https://github.com/AllenDowney/AstronomicalData/raw/main/' +\n", " 'data/MIST_iso_5fd2532653c27.iso.cmd')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To read this file we'll download a Python module [from this repository](https://github.com/jieunchoi/MIST_codes)." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "download('https://github.com/jieunchoi/MIST_codes/raw/master/scripts/' +\n", " 'read_mist_models.py')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can read the file:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reading in: MIST_iso_5fd2532653c27.iso.cmd\n" ] } ], "source": [ "import read_mist_models\n", "\n", "filename = 'MIST_iso_5fd2532653c27.iso.cmd'\n", "iso = read_mist_models.ISOCMD(filename)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is an `ISOCMD` object." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "read_mist_models.ISOCMD" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(iso)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It contains a list of arrays, one for each isochrone." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "list" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(iso.isocmds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We only got one isochrone." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(iso.isocmds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we can select it like this:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "iso_array = iso.isocmds[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's a NumPy array:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "numpy.ndarray" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(iso_array)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But it's an unusual NumPy array, because it contains names for the columns." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dtype([('EEP', '= 0) & (iso_array['phase'] < 3)\n", "phase_mask.sum()" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "354" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "main_sequence = iso_array[phase_mask]\n", "len(main_sequence)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The other two columns we'll use are `PS_g` and `PS_i`, which contain simulated photometry data for stars with the given age and metallicity, based on a model of the Pan-STARRS sensors.\n", "\n", "We'll use these columns to superimpose the isochrone on the color-magnitude diagram, but first we have to use a [distance modulus](https://en.wikipedia.org/wiki/Distance_modulus) to scale the isochrone based on the estimated distance of GD-1.\n", "\n", "We can use the `Distance` object from Astropy to compute the distance modulus." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "14.4604730134524" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import astropy.coordinates as coord\n", "import astropy.units as u\n", "\n", "distance = 7.8 * u.kpc\n", "distmod = coord.Distance(distance).distmod.value\n", "distmod" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can compute the scaled magnitude and color of the isochrone." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "mag_g = main_sequence['PS_g'] + distmod\n", "color_g_i = main_sequence['PS_g'] - main_sequence['PS_i']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can plot it on the color-magnitude diagram like this." ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cmd(candidate_df)\n", "plt.plot(color_g_i, mag_g);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The theoretical isochrone passes through the overdense region where we expect to find stars in GD-1.\n", "\n", "Let's save this result so we can reload it later without repeating the steps in this section.\n", "\n", "So we can save the data in an HDF5 file, we'll put it in a Pandas `DataFrame` first:" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " mag_g color_g_i\n", "0 28.294743 2.195021\n", "1 28.189718 2.166076\n", "2 28.051761 2.129312\n", "3 27.916194 2.093721\n", "4 27.780024 2.058585" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "iso_df = pd.DataFrame()\n", "iso_df['mag_g'] = mag_g\n", "iso_df['color_g_i'] = color_g_i\n", "\n", "iso_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then save it." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "filename = 'gd1_isochrone.hdf5'\n", "iso_df.to_hdf(filename, 'iso_df')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Making a polygon\n", "\n", "The following cell downloads the isochrone we made in the previous section, if necessary." ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "download('https://github.com/AllenDowney/AstronomicalData/raw/main/data/' +\n", " 'gd1_isochrone.hdf5')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can read it back in." ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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mag_gcolor_g_i
028.2947432.195021
128.1897182.166076
228.0517612.129312
327.9161942.093721
427.7800242.058585
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" ], "text/plain": [ " mag_g color_g_i\n", "0 28.294743 2.195021\n", "1 28.189718 2.166076\n", "2 28.051761 2.129312\n", "3 27.916194 2.093721\n", "4 27.780024 2.058585" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "filename = 'gd1_isochrone.hdf5'\n", "iso_df = pd.read_hdf(filename, 'iso_df')\n", "iso_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the isochrone looks like on the color-magnitude diagram." ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cmd(candidate_df)\n", "plt.plot(iso_df['color_g_i'], iso_df['mag_g']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the bottom half of the figure, the isochrone passes through the overdense region where the stars are likely to belong to GD-1.\n", "\n", "In the top half, the isochrone passes through other regions where the stars have higher magnitude and metallicity than we expect for stars in GD-1.\n", "\n", "So we'll select the part of the isochrone that lies in the overdense region.\n", "\n", "`g_mask` is a Boolean Series that is `True` where `g` is between 18.0 and 21.5." ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "117" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = iso_df['mag_g']\n", "\n", "g_mask = (g > 18.0) & (g < 21.5)\n", "g_mask.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use it to select the corresponding rows in `iso_df`:" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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mag_gcolor_g_i
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9621.2333800.648449
9721.1444270.626924
9821.0545490.605461
\n", "
" ], "text/plain": [ " mag_g color_g_i\n", "94 21.411746 0.692171\n", "95 21.322466 0.670238\n", "96 21.233380 0.648449\n", "97 21.144427 0.626924\n", "98 21.054549 0.605461" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "iso_masked = iso_df[g_mask]\n", "iso_masked.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, to select the stars in the overdense region, we have to define a polygon that includes stars near the isochrone.\n", "\n", "The original paper uses the following formulas to define the left and right boundaries. " ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "g = iso_masked['mag_g']\n", "left_color = iso_masked['color_g_i'] - 0.4 * (g/28)**5\n", "right_color = iso_masked['color_g_i'] + 0.8 * (g/28)**5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The intention is to define a polygon that gets wider as `g` increases, to reflect increasing uncertainty.\n", "\n", "But we can do about as well with a simpler formula:" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "g = iso_masked['mag_g']\n", "left_color = iso_masked['color_g_i'] - 0.06\n", "right_color = iso_masked['color_g_i'] + 0.12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what these boundaries look like:" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "image/png": 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OHboinI/AwRM6O7+N/V9lGjKlqbBpJ5ebynjbJr9AMW1qc3DwA+cjcAiMoBE9KgYqHzojOpdt/QO5XJHbZCt1QsChq8EJAoe8QnfojOhvADLPMm5uTpxyGrZpyGYvhINDV4cTBA6+IEb9+F2VRyL7D52R26yrq1M6jSORCAYPHoy5c+ciGo2GNg7er7P3Ozg4QeDgATlip7q6GlVVVWhubg7ERHWrbCLSmmVKSkowZcoUlJSUZM28ZbOUl3bhhIRDd4ATBA5aqCJ2ysvLUVZWhoaGhrQVvN92RfBoIrEtOfrIxnbvdzxiPyq6nMbg0F3gBIGDFrpcPyUlJRgxYkRqhS7vCzDBdNKZjlGHlW/IJERs+3Zw6IpwgsDBCFOOIO4vMIUgqxi+KRpHdS8bRsxpVGkapr47Q+oLB4ew4ASBg29wpgkA9fX1KCsrs15le8Xg69oJAq6trFixIi1s1aSVmO6HAa82i8kM5UfLc+jcyOfh9Q8zxrYzxtZJ169mjG1kjL3OGLslX/Q4ZAfxbIGSkhJtGXmV7ZfBZsOUuU9j/PjxKR+Eii4vusOC11iKySdhS0sx0ewQHHnbWcwYOwNAFMCjRDQyee0sANcA+BIRxRhjnyCi7V5thbGz2O0OzQ9sdgUH2aEcRr/ZIgy6wmgzV7ClpZhodjCj4DuLiWgJgGbp8g8B3EREsWQZTyEQBtwqRo9sI4Dke6YoHVUZ1V4BLyajivYRHdi5+L35LmlOr4oGFfzuxi4kbGkpJpodgqHQPoKhAE5njK1ijC1mjFXoCjLGrmSMVTPGqrM9xMJFg6jhl2F6lRd9CTqIv0U0GsXs2bM9N47JPgcVDaKmG9Z+AblMW1sbamtrlbui3ULDoTMhr0nnGGODAMwTTEPrALwM4GcAKgDMAnA8eRDlks7lBqZIGVH91/2vKhuNRj1PIRMRjUbTfA4qE4+cDC6IuUkuG+S0NXG+eH/yXweHYkLBTUMabAPwNCXwKoAOAEcWmKZuCc7oTPd4GKa8yUwuyyN0eJjp4MGDjQxWhCwEVKYl+djIbBPD2WgMuv0MogNapNcJAYfOhEILgjkAPgsAjLGhACIAdhaSoO4K2/h+G6bJE8txpt3Q0KA0k9ialsQVuLiHwRY2ZW0Yt2kXskyvMws5FANsn8N8ho8+AWAFgBMZY9sYY1cAeBjA8UkT0UwA3/YyCznkDrbx/V7lxMRyJSUlvjaQecX2A/B1kLxsvw8DpjZ1O6QdHPINP8+hO5jGIS8wmUtEu7rJVs8faNuD5Hl7PB1GGLBt05mHHIoB8nNYrD4Ch24A08pEvhfEVm8qG6YQEPv3alPlO3FwyDdsFyNOEDjkHDb+BwAZzmpdmKiN49nWn2Ab/y/T7AfOVORQ7HCCwKFgECOPvNJReDliVZFNAIz7GPjGM3FTmFcKiCAwCUInHByKAU4QOOQcKgbrtetYF66pY9aiZiHXNTH31tZW1NbWpjQNrzTVQU9Js03K5+BQCDhnsUNekO2mL5t6OmezjTnJprzfzXE2yJdT2TmvHQDnLO7S6AwrSr+bvmTtwaaebt+Bl/NZFgKiuUiEKRRWRacX8ikEnObhYIITBJ0cXfElF8fk92xkUQjw85X9OoRFc5Gufbkd2Ufh1V8+fzevSCsbGrrS8+WQCScIOjmCJtDTMaewENSWDuwfUzwex9y5c40pKkxtlJeXp51DAGQyYJW2IZ9foILOmQ0go32dT8PPxrhs4ZVDySuyqqstNhzS4QRBF0AY4YxhvuxiFtFsIm1KSkowZcqUwPsAZLMPv8YZsE4oqOqp2tblHhKv6xh+kFQZuYCNthB0seHQeeAEQTeEjon5fdl1TIwz8EgkYn3KlYnWMFejIgOWQ1L99mPyVaj6k8sUC3O10RaKgU6H3MFFDTkEQlipFsRIHMCcAjsshmSKOrJJWxFEAysEI/XqN1fjdSheuKghh1DBTR5e5g0vRlRfX48RI0YA0Mf7cyEgnjqWLe0yHV608nIqk5rf/vIBm81xNhqQEwLdA04QoHgiIoqFDhkmE1A25g0xb4+NqSQX2quts1SkV7f7uZigm0/dWBy6N7q9ICiWl7lY6JChS7kcVhoG2U+haycSiXhG8gShwyt6RxUdJNb1SqNdSKiEgOlQIYfui24vCLxWToWmI9fwWglz040qBDOMs3pVZhZTyKVtm7Z0xONx7Z4B3qfpdzGFpur6C4psn0mnBTjo0O0FAeC9cioUHWEhqJ1YNN2IdcTrcqikH0Yjb8ISI1TCMDnZ1ucnqpnaC6Nf2+cqlxvQCi0EikljctgP34KAMXYwY6xHLogpFnSllZNpA1U2jFsXxaOLxlFB7F8Vf29Lk21/OhrEE9Wyhakdm/k2aUOd/ZksVvOng4UgYIwdwBj7BmPsOcbYdgAbADQyxl5njN3KGBuSezLzj87+wnGIO15VL2KQ3bN+4u69Im1Ex6sfISK2LaaR5tFFy5cvT333oi+ojT8IQwuyUc22bjbIB3PuCsKsq8JGI6gEcAKA3wI4moiOIaJPADgdwEoANzHGvunVCGPsYcbY9uT5xPzaLMbY2uRnM2NsbbBhOHDI5hYOMT+/TZgkh2rjGf8r5vrXrcxV5eR0zjphYRI2vG0ewsr9FQBQWlqaElZiriGVw9vk4zBpG7k4C5kj387nMENzveCEQHHCRhB8nohuIKI6IurgF4momYj+Q0QXAZhl0c4jAM4VLxDR14loNBGNBvAfAE/bk+6ggsh4VTZ321h5kbGaoHIai+3wayItqv0HqrBM+bqq7ZKSkpQzm5ctKSlJmXu4/V+nDel8HKYx8U1wuc4VFLYpxdROZ9xY6hAe8rqzmDE2CMA8IhopXWcAtgL4LBFt8mrH7Sy2g87cYlvPpr6prHhNDlkU6631eYaAXL+qqgqMsTRbv4ouLxrFa7pd00HmxgYm01g2v6H4vbq6WusPCdqPQ+dC1juLGWObGGNPM8amMcYuSDL1sHA6gA9MQoAxdiVjrJoxVr1jx44Qu+66yJaB2NQ3lZWvqWLYdXZjG1s6/1tRUZEhBFQ5cmyjw1TRUqp+bfwXNqt5L4e+X+j6Ni36nBDo3vATNfR3AO8DaALwRQDrGGOvMcauZ4z1ypKOSwA8YSpARA8SUTkRlffv3z/L7jo3gpoKgjh2w6LBjxNUZoimvqLRaJrJi5cVndrZ0qTzFdiE3trAxiSl+mvTnnjNz4a8YoaLOgoffgTBN4noR0R0LxFdBeAzAF4G8DGA24MSwBjrCWAy7PwM3R5B7cYqJ614D7CP6vBLg6wFiNfkcrKPIhqNah2ZYrprXp8fRmNLp81YVYfb2M6V7TxxoSX7HsR5WLt2rfVBPdlEHRUzow3bb+KQBBFZfQAsBlAqXVuV/Lvaso1BANZJ184FsNiWDiLCuHHjqDsjFotl/C9eE9HS0pL6v6mpiVatWpVRf9WqValyYnlbGrzK6frUXRPHFIvFaOnSpWnXxf5lenXlTDSbxhKLxWjZsmWe86yr66e83L7qtxG/5wKq3yaMNsNE2O11JwCoJgVP9aMR/ADADMbYQ4yxqxlj9wLgUUSeSw3G2BMAVgA4kTG2jTF2RfLWxfAwCzmkQ7aF60IZ5QNiGhoalJEuPIqnubkZs2fPRnNzszUNNuVUK2fdeQiyj4KbNID9q2s5aoiD11X5BWxCVFWrTHHDWRC7v1+o5oSPke/k9kr7nQ2Cxvrr+jVpokHRFcxbRQeVdNB9APQA8FUANwD4OYAjABwM4Pd+2sn20901AhF+NAK5jGoVrtIasqVN16eK1hkzZihXvJxG3XhtVrLyapuv9PlHV99Gq9DRlE/YrubDpotrKqZnMGwtwyEYoNEIPMNHGWOMPArZlAkTLnzUDrYhjiJsQyNt+laFhcp0yX1Fo1FlyCYP5+SH2GQbAslt/6IDVVVfPDjHK5xVN958wibsNkw6TaG2fuhyyA904aM2gmAREpu9/ktEW4XrESQcxt8GUElEj4RJsAndVRDYvkziJi4bBsadsaIZJB/0+mFKfuL3w6aPMznbvQ1h9J1LhN13mPPikFtks4/gXADtAJ5gjDUyxuoZY28D2IRE2Ocd+RQC3QXySl1n4xb/F23egF06iUgkgtLSUkyYMCFUIcDb9rrvRwjYtBkWfbxPbpMPI1pFDP8M227uB17jDru9YojyKXT/xQ5PQUBE+4joPiI6DcCxAD4HYAwRDSSi7xPR2lwTaYuu8mOrXh6ZacpOzqqqKnAtyW9G0fr6+lQf+UbYoaphQOzTa+ObF50y8+dt2hzzqesnV8jFXAd1PoeJYhFGxQzrFBPJLKO/AbCXiH6SU6o8oDINFYuNVkQ2KrGtfV+MN5c3VtnY6LOlM9s2TCYf3b1cmIn80GVTVmWes5130/VcP+OdwYwThMbOMK58IIzD6/8FYDaAM5INjmSMPRoSfVkj3ysPr9VFtqsQm3GITIev6vl33XzotA25jB8EHasp/FW1KjfVCXu1ZxsuqqJTZ56T59nE7HWhrGE846bxFDuzDPqsFfu4Cg0/GsGrRHQyY2wNEY1JXltNRGNzSqEChXYW267M8rkKEVelnDYOmZHK1+R2vMamWwH7GavchkkjkK9x+lVjDnu+bRyhnB7beoV0rgadq2zGE6RNr3qAY+5BkOTZ4+TrfjSC9xhjxwGgZIMMwIEh0depYLsyy+eDKvbFhQBPt8A3lNmspkyaBP+rSnXgl6mobPByGZ02I4+5UHZo7ptRwa8vwaYurx8UJk3Rq56O5my1waDjCdvm3x38B8kxKnm2H0HwcwDTARzNGPsugJkA1hlrdGEUgul43RMZZTweR3l5OcrKylBXV5diWIMHD045KXVtmsxJ3NGp26VsA86MTONRvegmJpaL38Pm8BnVecdBBK0N5Hnxw7xEk5pN37Lp0DTvXtqjCtnMQ9iCX/e86QRfZ0Vyvvaq7tkcVflFxtiniGgzEqGkPwVwPBK5hy4Lj0wHHbxWZDwpGn9B4vE4Zs+ejXg8njqkhadpaGhowODBgwHsP1TGCzLjtkl1AMCzbV3/4osuC6xcmH5U37nfxSTsIpHMfRfZrvhNkOfFz6rYT6SSjR9Jbtu2HZt6NgjzOVAJFhXt2WoxRQKlL8BmQ9k/AIwGcBQS5xWvBVCb/LueiNpDJNIKhfYRFAKmSBLVgSOqHbr8Ot8py5mdn4yjNlFIANDc3Iy5c+diypQpWoHhtWuXCzn50BlTv34gj0n1PexIKD/1dd+9rtu2bWP3D2OOO6st39Zv1ZkQeGex0MDPAQwB8DqAcUhsJmsmogEh0mmF7igITPDrfFQ5XIP2oxIQ/NrgwYPRr18/LQ02/ZucsWE4iG2Zrt862ThlVcLJK4WDLa1yP6Z2w3TCh8VAOzsjLjTCCB/9LhH9OLm57AokThVbGhqFDoHhxUi5OiuqtKLNX1Z/xb9e/ejstaNHj04TArJtWxUaKtPN2w9im7aFKLxU32WaTGMJgz5uwhEd4dlsPjOFonq16+XLsenfiw6/7eXCNNPJTT2hwI8g+Jgxlgo7IqIaAEPDJ8khG+gYkuws5C+4eF383+Q8U/UhlhEje0QaZOaWTWSN3G82sGHu4jV5LDpmGdQsJDNn7pMJIlRM9UztqhYNfiAL+7CEdtjRYV7+t+4CP4LgCgD3McZmMMZ+whj7O4DWHNHVbZHNw6db/QNAfX19WsQQgBTD5itDYH/oqc55Fo1GlSd2ceheVrktm5WoH5NVNlAJKrl/cQWtQlgrVdv5k/8P6pA1mY2CMHFRs9LtZfHTjg292UA3PtvFSFcRFtaCgIjeADABwHwkHMfrAZyXI7q6JbJVfeXVv/xS9uvXL/XQiy+AHI0iHmbDo3rEMl4hkzbMJxuTgwibEE8OP2Yv1Rj4ClpVN8yVqpepj2eL9dLgTDCtgFWC0bZNmY5C7DHwaltGUNNjLulU9ZXL8taCgDFWBeBBAJ8GUAngMSJq8tWbgxFhrYRVYY+66AfOWMRy5557LjZs2IDFixdj5syZKaHAhYZtyKRq5SrCpJLrNBu5nFeIp1i2urra+sxfE3Q+Ad5PrkFEaat1v6YjL9MXEGzlbaNZBWknLPhl3LYLmlw7r/3SHURA+Yka+hSA0uSnHMCXAOwkooHWvYWE7h41JJp2bMM5eZ3q6mqUlpamMdCqqiqUlZUhEomguroaRISysrJU3Ugk4hk9IvfJH0a+glaFuNo4i/32q0M8Hsfy5csRiSTSbgeJwPHqUxxzLpmDHHZrOwcidM9IV4/sMf12xUBzWPTpymcdNURE7xHR80R0CxF9DQlh8A/b+oyxhxlj2xlj64RroxljKxljaxlj1Yyxk23b664QnbE6hqOzd0ajURBRyt5dV1cHACgrK0vZvvnms0gkgvr6+pQW4LXqVplWRPpUCw6v9mxWXDqBpyrHz1xQnYDmBRvTV1grRC9NStQAbLQxHa0212zaNGkWYSBMR66OyZr8XvmCae6CaFV+4Mc0dKz4nYjWAzjJR1+PILEzWcQtAK4jotEA/pj87mCAbNu3rcPTQgwfPjxVl5sYSkpKUoxe/IiRRUHCF0UTgXgkZJA2vCDazHVMUTVnNlEjfphbtk5R0d5vwxhUwkeuFwaDM82tyh9lI6Bt6LMxYwUZiwyV38uLtrCRL1OTCn6ihmYxxrYxxl5hjN3HGLsdwHDbykS0BECzfBlA3+T/hwJ4zwc9XQ5yuoVde+JY8sYO1Gz5MO266UHRpXXgzH79+vUptZFrAtzUoLPjAxrtI74b2LIc2LTQc2xBH25xPKYVqUynjomrbPteUSOmFzQbRqGiTTTZ2TIG0T8h0xvmCl0XzSTPuY2wFbVUL/pUEVxBGaaKFpXfS1c218h2IREUfnwEg4hoM2NsMIBRAPoBeIGItll3xtggAPOIaGTy+3AALwBgSAilCUS0RVP3SgBXAsCxxx47bssWZbFOi5aWFjz4xDM4cvh41DbuxuotH2Jz0x4AwLknHY0HLsvIHJvxMEejUcyePTsjrYPsGBZt5OI91UPY3Ny8f2NY81YcsGUFer67CnhnFbC9HqAOUL/jwX66JtT5AJA2Hi8/hUi/bKsXx+jHhu9llw3DJ6Dyrdj6UeR2dOk4bNrw8teI/p4g/hGTT8LG56LrNwi8xio/M/lwBns9Z2H5pMJIMZFx9gBj7FQiWmnVAJSC4G4Ai4noP4yxrwG4kog+79VOV3EW72ttx7KGnXhpw3YseWMHtn2YSAzY7+AIygcejtHHHobRAw7DyAGHom+fXml1o9Eo6urq0Nraip49e6KsrAwlJSUZOYbi8ThWrFiB8ePHp4RFbW2tlammeecOLJt1B84Z2I6eWxbjgB3rAQDU62CwY04GBlSg9agyvNbcCyNPOSvUF4Y//OJ4/LyUOsYD6BlKWE7XsBBEcAF6Rm3SaGyc8l7ldPmtbOgwlef9Bk2zYdsvn2++XySfEUEmAepXwJoQWBAkGfRYABcBmATgDZ5ojjFWR0SlPogYhHRB8BGAw4iIkucbfEREfU1tAJ1XEMTjcRzQoyeWvdmEp1dvw4v1H2B3vB0HR3pg/AlHYuLQIzH+hCNxQv+DtTZL3g5/YDl0D240GsXMmTNx8cUXpw5h5xE8gIJpEAHv1qB9zWNof+1pROK7QAf0Ahs4Hm2DzkT806di7fsdKD/5lLQVeFjM1ZYx+UW2L1wY/Qc1ZYThfFaNLciKO5vVaTZz7JWg0Itm237D1gT8aB+68mEuNrIRBJ9G4sD62wFUATgRwC4k7Pn9iegUH0QMQrogWA/gh0S0iDH2OQC3qE7PkdEZBcH2Xbtx57NVqNzWjsaP9qFvn574Uukncc5JR2P8CUegd88eVu3wh6K5uRmRSCT1cgDQPkx8pSY+eABQVVW1XzNo3QvUzQJWPQhsfx3o2QftQ85B6wnnos/I84E+fVNti/VsTQo2qq+OMWX7Iti+3Lla3edayHj17WV+CWKKMvVlaius9m20j7D6DQrT7666l4/nRCcIQERWHwCnCf/3QyID6cE+6j8BoBGJtBTbkEhZ8RkANUiktV4FYJxNW+PGjaPOguZojP4yv55G/OF/NHDqPLrkwRX0XN17tK+1zXdbsViMVq1aRU1NTTR9+nSqrKyklpaWtPu8TCwWU9bl12OxGC1btoxi0V1Ey+4hunUI0bS+RPedRlT1MNHeXca2VG3qaBb/inTq6LIZj6oP05yJ85RPqMaluu91zbYf+ZrX3PktL/8+2bRl044KLS0tNGPGDOVvGmTu/MJPH36f21zTD6CaVPxZdZHSGfi05N8JAA7xKp+PT2cQBG3tHfTw0rdo5LTn6bjfzKOrH19N6xs/yqpNkYG2tLRkvJT8xbNlOvHa/xD9dQTRtL7UPuN8orcWE3V0pJWRBY2JJl05mbalS5cmhJCBSdqMRy6no6GlpcUXQ7SBrfDT9asTcirBFXQOvOj0ot3UT7YCWtWmH+iEQNi/s00f+RA+Jnr8IBtBMD7590kA9QDeADAHwPUApnjVz8Wn2AXBjpZ99LUHltPAqfPom/9YSRvf/zhwWyam4sWAtYjvIXr6qqQGMIH2vP6CpxahWrmL1/mLmdI0DFqEjrEFHY+X9qMrE/QF9mK88nyY6qto5IKLC3tZcOrGExZsBUtYfeZLQIfVhm4Blqv+TPVs+hbvBxYEGRWA3kg4j78N4Da/9cP4FLMgeKd5N51+88t04u/n05NVW6lDWmH7gYr56u7p6mdg38dED51DNK0vbf3nVdTy0YdG04nqxefMadGiRRSLxdJW3PyeFwMMMh4/8JoXG63Epn1VPZGR68p4Ca+WlpbUPJq0v1yhkKtcFfJFT5C5zVYIZGv69NN+1oIAwGcBPATgrwC+m/QR9LatH+anWAXBrj1xOvPWSho17XlavaU5436Qh8vPQyCbEzIesLZWoke/QnTt4dS6ZiYtXbo0xWT8mhVaWlq0jNSG5nyq2LqxmWixbVdXTxQGQWzlXLPS1c/FXBWa+ev6z4fg09ERVCsN2p/qnm7xZAtxQRKGIHgPwIUAvgrgBgD/BdBgWz/MT7EKgqsfX00n/PY5evXtpox7OnOACrxsU1NmO7qVe1NTU4YDLaOfJbclzEE1/6SWlhZqamrSMis/KxXTmLJZzYRRJ4j6HBY92by8pvpB5tqrXBgMx09/uv5tNNNs+vHThp9nJ1eOcbGOPEdeCzW5zrJlywhADWUpCJbYls31pxgFQfXmJho4dR7dvmCjtgxnmDYPDWfsojBQMXverkpwpPXR8gHRn44mmnkptbS00PTp02nhwoW+zBe6MS1btizDHGQaa1BG5ndlGESrKhT8aFQ2UWF+64v9ZmuuUPUnm7dUMGlPXrSEoTVko6X6EXbZ0GijacpRVXx+li5dGooguAHAL5Dce1DITzEKgh/+u5pGX/cC7Y61epa1fRD4il180FVagqrNDA2k8iaiaYcS7WxIta2z5dvSrNMI+EOnevl1L1tYK3fd6klX1ubFD1ub8PqtggYFhM20dNf8MjS+GlU9bzZj8xJetpq2DcISftm2YdO+jUYglw/DNPR0MmLofQDPAfgzgK/a1g/zU2yCYF9rGw29Zj79cc5rgdvgP5Zqta/6X1Vf9VLxlUP738YTPXyetm0v2sSXTcWwxP5jsRgtWrTI6DQW64T1Iss02djn5fn1ayILoqV4aUnyXObTPq6D6vf2Wz+oFuPVn60wyQZ+FirF8HtxyPSEGTV0IBJnEXzHRQ0l8Nq2XTRw6jx6ru69QPX5j9XY2KjdKCOWFf/y/1WMN7Uq/nBHQht4+c/W9KiuxWLpZiDxI/fvxdi9BIDtKliGSZDaoBAageq+LHiz7TMMBO0z1ytkub0g/i7btv2WCyo4w4TYt04Q+ElDzXci7yWiaiJ6hIh+6bd+V8QHH+8DAHzqsAMD1Y9EIhg8eDC2bt2KSZMmaVMB8JS9qtS9vXr1Sp0yJrY7evRolGAPAAIOHeBJiy71Lk+LLB5cA+w/tpEnvuPXeXneptxHJBJJS7esooGnoG5ubs44OESVfldMp+2VYE4HVXndOHR1vFIDe9HEfzc+DzLk+ckXwkr7nG2bJvC5U70H2aZ4NiXtU5Xzk2o7V7BNreHnYJpNjLGnGWPTGGMXJPMGOSCRpw1I5NIOgng8joaGhlR2RVXu9qqqKtTV1aXKiA82Z9Cq3CuRSGQ/gR4U8oeG5/pRQWbco5Nn5lZUVCj750nuONMSXw75DAQu7LiQqK+vR3NzM55++mns3bs3rZycxz8e35/LHwh2aLrYvuqaTZu6cja0yGV05zGL82NDj821XID3k+8cSyZhbgub39tGyPH3IxfnWXjB9pkF4MtH8EsA9wH4CYAHAEQBvIbEDuNetu2E8bE1DeVLHavZ0kwDp86jF+vf911XZ+qR4RV1YRzrvpZE2OiS27TlZXOEjW1dNhHpyi1YsEC550Bl3po+fTo1Njam3dc5nVU+hmxs2PI86MrYtiV+t5lPvxErtiYmcf6CmEmC2PBlM2KuEMR34Od3DNssKNfN98ZAhGAa+iYR/YiI7iWiq5BIGPcygI+RyExaVPAlDbPECf0TK+H1jR/7qifS6JUVk58pLF+X21GidwnQdwDw/jpteVF9VqnSqrYZY4jHE4fCr1ixIs0kI9ZhjKG0tDRNgxH/8v/HjRuH888/H/PmzUtpBkDidDXV/IinkonXxLq6+ZKv25xGZruqVK3gbc5eVpk0/PSjus/PpuamNb9mkqArY5UZUVc3KEwmF5XWGMRM41U2G00nqMnKFhq+ojQL+BEEHzHGUmcPENFaAKcS0W0ATvNLZK6R60kWceiBvTDs6EOwtGGnr3o6hmti0qpyVmMdOB54ewnQ0a4tr2NCphc9EomAMQYiSnvZuDkrGo1i8+bNaf3IAoNfq6urQ0lJCYYMGZKWLttm7rhQ0JlMdIxANX+5eGZs2lSVsTmq04SSkpIMhuzl85BpklMly3VNz5OXEAi6WBNNgapnRfWbeplpZAQRmn6Rq7YNc6s8d8CPILgKwAzG2EOMsasZY/cC6Ejey2+ib0vk0y75hRFH4dW3m7E96Ti2hc7+Kz/cqjzvvpjXiecBe3YCm1+xKy/RZHrRx48fjwkTJqCkpASDBw9OMWJ+uM7FF1+cxkiqq6tTK1SRsRBRqj0AqK6uzigjz4E8F7oXXSzD/8rCtBDOPBP4UZ1csAZlmiaHvK0wEOuE5fzMZrEmMnbdWHQLHb/Pvg1yaYFQaTde8Du31oKAiNYDOBnA8wA+AaABwPmMsYMBzLRtp6ti8tgB6CDgiVff8V1XZnC1tbXal83GnKR8UE78ItDnMKD6Yd/0efXBGY3s9B42bBjmzp2b8SCXlpaioqICwH5TTn19fSrqiI+Laxnc2SxqG/x/LixERm56+LnmIDsy82lKNEHsv6SkJHX+dBCm6UejsoFuVZ2tkPJDt3hfXu3nSpjngvH6gW7xYlNPgexMQ4yxI5A4PL4EwLMA/k5ETUS0m4j+ZNtOV8VxRx6Ms07sj3+u2IzdsTbreqofljFmfLDESBKToEhDrwOBcd8B1j8L7GywHxiQwYRNKzDOKACgX79+mDRpEvr165ey4/PoJ7G8XI+DmzO4psDNPsB+Bk7JiCjdqkkOseR0iFqJTIvXXOQKqnkV58SvEMiFfVu1qvbDBG2YPKfbxvYv0hCWMJcXZlky3lCgEnp+kRyDOsZd5UFWfQAsAfBHJE4ZWwwgDmCDbf0wP8W2oYyDRw/d9eIbvurpImJUh5MsW7YsdTKZalOWMdKhZXsi39Csb1nTxnfnNjU1UWVlZSr6xzaSRI6K8DpQRxW1ZIqk0W3ekTfoqdr0e2CN6WSssJBtFEpYbYUN8Xf1mj+vyLVcblALEr1VLLChGZpcQ358BIcQ0fUAPiCiiQAuATDDt1jqwhh77OE456Sj8MDiN/H+R/a+AtXqfsWKFZg5c2ZqFc5NIKWlpWCMpVbVfIUr225VmgJK+gMTrgbq5wBblgMwr3C5yYabeiKRSCr6x0YNVzka5egnXgZIaAv8LGqd/0Nl9xVX9dxMNGLEiNQGPb6qltv0G9/NTTX5WPnpoJtznUPfVCdf4IEDgN6ZL4I/X0FWvtn+Nqp+8+lrDApZkzJoMepD6lXSQfUBsCL5dxWAA5P/L/ZR/2EA2wGsE66VAViBxH6EZwH0tWmrWDUCIqItO3fT0Gvm0w8erfZVT7di5f/Lq3F5VS7G3PNDV3j9tJVvLEp0+0lE955CLbuaMrIUyvSIqzfP8w6k8Xhd12lCXuVNGoVKk/C7yvNajQaJww+6v8FP32HRa9Ou3/ri81jssfeFRtCxWWoEWSeduwiJQ+v/HxIH0V8NH+cRADgDiZPNREFQBWBi8v/LAdxg01YxCwIiontf3mSVe8iPKt/U1JRhYtElL2tpaclIV5umjm98PrHB7OU/Z+Qt1z1Mfpipzcvqt4womHR02B6ywxmTqe+g6blVvwffWGVrigrb9FEMjNdr7H5MMYUUarlGrgVdYEGAxMlk/aVrlwG4BcBJXvWleoMkQfAxkmmtARwDoN6mnWIXBK1t7fTle16h0de9QB98tFdZxmQHl8vx8wNUh02IELUB0yo0FovRjgcnU8e1hxO9U5123QQbJivSomvD9L98TTUOVVk+R2LqbtM4TDteTULHBN1L7PVbyOWKbcUbBi26Z4ff42P2Kyz9ambZZLrNxW9is2gJEzpBYOMjeBHAa4yx9xhjCxhjtyERbfQEEiGk2WAdgEnJ/7+aFAZKMMauZIxVM8aqd+zYkWW3uUXPHgfg9q+Nxt7Wdvzfk7Vo78g0y9mEhPHrADBw4EDl5hixLA/B5Bu9THHTfb/+AFjfTwH/uQLY93FGOZ0NV6ZTFebKafGKaJLDD5ubm1OhomJZvmtZ9AGo2hoyZIiV3T8SiRh3vNpuPpIjlFT2ZU6v6rdQ2XWB/Ofm8UK2tIhj07U/OplkT5dfSdWe7X4G7gcT/VF+4/JzEV7stf8hryHNKulA6av4nwBYDeA3SJh3vg/gbgCVAN73qi+1NQjpGsEwAAsA1ACYBqDJpp1i1wg4nli1hQZOnUd3LNzoWda0WrIxZejaUK1AUyuuLSuIrj2caOY3iTo61GU07cnmGj/jke/HYjFqbGykZcuW0YIFC2jhwoWp9sWVvrySlyOQvNJ3V1ZWWq0GbVZhfOzy4UFe5jRTX2GbhGyRD+3D5nkwHbxkqmeCLtJL7tf2Nw+CbH5Xv3W92kNQjYCI7kUihQQBuBNAK4CfEdFZRHR0lkJoAxGdTUTjkNAw3symvWLD1yuOwQVln8RdL21C5cbtxrKm1Wkksj+dA4cqMshm92jaqvXYU4HPTwPWzwWW36Muo6BHXr1qs54KdKjq8zEsX74cc+bMwbBhwzBu3Dhs3rw5tZIuKSnB5MmT0dDQgHh8/25lvvFO3H2s00L434aGBs9VpNd9cfU/YsQINDQ0YPDgwQD2Rz3Z7E1QbX4zaR5iuzrYrhyDxslnA90ciJsj+Xz6idn30lbETXlyfd6vKoWG7Ri84DW/Xm2angmVJq6zLHhCJR10HwB9AfwJCSfvKX7qkloj+ETy7wEAHgVwuU07nUUjiMVitGTZSjrnjkU0ctrztOmDcOLP+cp40aJFVisi03fq6CCadRnRtYcRbVpoTYNtLL2oNehWvy0tLbRo0aK0KCedLV3WSHTagdi3WEbVlopW1ThUq0fRpm1rezb1owL3/XitDoOeoJWtRpBNfZPPJAyYfFW5OsBG1Vcu4NsCQNk5i09HYkfx7QD+h4QZZxGA87zqSu08gcRmtFYA2wBcAeBnSBx/+QaAm2B5HnJnEQREiR/inebdNPb6BXTGLS9TUzT7l46bTFSbu+QDq2VGqNwQta+F6L7TiP4ygOiDeisa/DIy3QlqHNzEotr8petfnAt5XF6mA10fupfLz2lqNvDjFLWda1s6wmRMuWKeYcBrA6Dut8zWdFhscyHSk40g6ACwBsCvAQzyKp+PT2cSBBzVm5toyDXz6aL7ltHeeFugNvjKkGsCMrPnD75st5bbUOLDrUS3DknsMfi40UhHLBazis6R6VbtQxBDXZuamrSH3sv9q8Yu3rOxzQfxbZjglwEUg38gDBQzfX53gftZhJju53L3eTbQCQKbqKEfAlgG4EsAVjHG6hljsxhjv2eMfcWivgOAcQP74Y6vjUbN1g/x0yfWoK29w7uSAG4DHz58OHr16gUgcwcmt4cC+yNPuI2RR06o7PkAgMOOAb4xC7SnCfj3FGDfR1o6qqqqsGHDBs/oDpluOW/OiBEjUFtbm3by2t69e1FbW2tsj/sn5LFzW7o4fpW9lJerra21tpfbjFM+TtMLNtEh3I5drCh2+rTPuwZeCey8djyLObFMz0Khd3tnQCUdTB8AAwCcB2AqgH/5rR/GpzNqBBwPL32LBk6dR796ai11CJE6NtDZyUU0NTXR7373u7QNaOI+BK+V5/p5f6OO6/oRPfxFothubTk/q0CTGURsi/s+vFZTus1esdj+yCD+Xd6rIZqfwjLz8Ho2PhtTffl7MZtdiAprFsp1n9mOLQx/jlc7QYAQD6/fRkTziehmIrosXLHU9fHd047DTz87GE9Wb8P18+q5cLWCHEcvZ9AEEiugM888E5FIJO3ekCFDAJhPXIpEIjj+C98Dm/xgIhfRk5cBbTFlvLyfVSCPxzeNi//VnX3MwTWM5ubmVCy5qi1VRIicwVS16rPNO6QC19T81pP7DWtPgW18fFBkkwkzG4jaV1D6veplOzZVBJ/ftvO5j8C3IHDIHr/4wlBcftpxmLFsM256foO1MJDD7cSTp8SHZeLEiYhEImhra0M8njj5a9y4cZ4MGUg+wCMvAr58F9DwIjpmfQu1q6tCOYzEJtxNZ84R74thm/X19WkbhsrLy9P6kl82cQ7kMFYVvF5GUUiKIb629VQQGUU2QkAlKMX7YTCabARnNoKKH5MahH7betmMTdWf+FvoTE9y/3kTtCo1odg/ndk0xNHR0UHXPFNHA6fOoxvnr7c2E6lURTmvEDcr8JBMHq2ji8jRqp+rHiSa1pfaH7uYqDXYtnyxfVWfXuFuXtE9ppxLOhrkKCCvOTE5BpcuXZqW7tpEg26MXuVtoQoM0PWTTaoFLxqChrHqypic+kEd9H7MMqZ8XLaQfwtf76GBNr/1kG3SuWL6dAVBQETU3t5Bv3s6IQxuePZ1ozCwjVIQmRu3tzc1NaVFFIm7Nz2jf1b+PZGg7rGvEcXVeZNMUDF2L0ZkwyBVZzWo2hH7kwWlrg8+dzbMbNGiRbRs2bLUnPrZXyF/z9Ym7Ue45NLGbtu2TTnbZHW2jN32jINYLJb6Xfl7Y9uPqX/dd79+A6+Muzo4QVCk6OjooGn/XUcDp86ja56po/b29FQP/K+8MjKtXsWQyoULF9I999yTEgCLFi2i6dOn05YtW9KEg6ot/v2tJ3+fEAb/nEQUi1qPTX445QfYb1I3Dv5yemVO5Yf4iIzf5oXhdW1fSnHl6HVwjWklF3R167d+LoVAWP3ZamR+kwPqhIDq+eGLAT+h0tkgiEYgP9tedDpBUMTo6Oigv8yvp4FT59FPn1hN8bb2jB9VNP94rf7EvwsXLqQ77riD5s+fn6q7adMm+sMf/pDSFMT6unZbqx5J7D6e/nmiPc2eY7KhMchGKV5PzkmjYvDipjuxnM0LE5Qpq8xDqhc1qBAU2w1SP1vNQ24r2/5sGbOunup3z1bwqK7lW3ja9KnSBpxG0MnR0dGROsfgOw+vot2x1owf1cu0obrX0tJCW7Zsofvvv58WLVqUWt1s2rRJSYfpxYzXzia6/kiiv51K9NF7nqtrmyMJve7rVmuqdnRlVem7g2w0Mt1Thb3y66IwEseU7aYjP4xKfib8tK2772dDoU0bKoHtt+8ggqcYYTu/frQBIicIOg0eW7mFjvvNPLrg3qXKdBReDElUaUVGxE1Dq1at0jo3dW2m9ftmJdGfP0Udt59EtS89ZeWQtGlfdd0mh4/MVFXCUxwr1xJM6S68aFHdV6XQ4P15rTazhQ3z09mUVbR4MVpdvaC0qcoFZehBBUgxwWuBpYPOdCzCCYJOhP+91khDrplPZ95aSVt2qjd16RCLxZRHWsoM05Tu1/NlfHcN0S0nUMeNxxJtXh7oZTW2rygnr6pFeEUO6cw1uvZ1NPByugR3qn7yxXj8CFz5fxszo6lstrTp6ArST9gmv3zDpCWZ6ojvt2kedILA7SMoQpw78mg89r1T8OGeOC68bxlWb/3Quq4cS8+v8fh7noqBp2QG0lNay3sVlHHMnxqN+Lfmgx18JPDoBYi8MU9Liwyr9hX1E8+wOk003xugG4cqBTGfH16ety/SKdMKAK2traipqVGmk6itrc2IFVft2/BKExwkVl2MS5f3avD7YlmZRjmuXXf4Ty4PlJf3YPiFDX1hx+SHtdlLNcfy/Kt+V3GuxM2Svn8nlXQo9k9X1wg4Gra30Ok3v0xDr5nv+/xj+Zq8SuBmoqamprToGiI72/6qVaso9mEj0UPnEE3rS62VN6cdbuOXVps6JjNQU1MTTZ8+PS3Ng1dSOfF/ndNcDhvkKy7V6l9lHvKKH7eJL9fRL1+Xz0X2s4L3oxnkA8W8cpe17GxNfzbtmMx7fsx1cKahzomdLfto8n3LaODUeXT3i28o9xrYvvCcsXGmwYUA/6titqa2iIgovpfanvwu0bS+1Db7e0St+wKP1QbyiyGqwo2NjUaGqjMBqcpyh/KMGTNSp6fJG/e8IoR4uyphIvari4BSjd3EMGSToKktXfu665WVlUWRUdOPCSxX/Ys+Jt1v4deEZiusOYL+FgBqyJmGOh+OKOmNx753Ci4c82n8deEb+NnMtdjX2p5WxitjIkc0GsVf//pXNDc3gzGGSCQCIkJJSUnaOcdy9kTR3JFhaujVBz2mPIS206eix2tPAv/8MhA1n8YmtuMXurxBI0aMwNatWzNUbLnP1tZWZZuiKh2NRlFXV4dIJIJzzz0Xb731Vpopq6SkJNW3bAqKRCIp8xWnSzwZLRqNpuZWdyqXSaU3nRwnprjgJ5rZmAdU5iP5/oYNG1BTU5OXvDfZpPsImjLDto6c2kX3W/g1zZjmXi7D820F/C3U+WxU0qHYP91JI+Dg4aWDfjOPzr/7FXr3wz0ZZXSrYPH/BQsWpEwbKtOHvKIUo248tYV1T1PHDUcR/XU40burlUV0KnXQlZyXGUY830A2gYkQV+n8zAeenkPM5Cr2q3JSq+bI5mQ0L6j2ROjAV/Cqfmy0IV3/+TDXBDWN2d4P0mdQZNuelwYY5DmCcxZ3bjDG8OOzBmP6ZeV4e+dufPmepVjxZlNaGdX5q/JZtxMnTgQA1NTUYMmSJXjyySfx/vvvp1arVVVVWLFiBYDEyjgSiaTOfFVpC2kO2iFfwuun3A4CAx46B1j7eBp9uqyaXgnSTBC1INVKrK2tDTU1NQCA8vJyTJgwIYOmaDSK2bNnp/qvqKjA+PHjEY/H0dbWhg0bNijHoepP1Bqi0WiGBsDL8HbE7zrE44nzmVXajGlexPrxeOJsaPl5sF298t8/1/ATQACkO01V920RdnK3sBL6meiSHcleCRRNcIKgk+HzI47CnB+fhkMP6oVL/7ESf6tsQEfHfm1PfmgSi4DMSIyePXti7NixGDhwIDZu3IgRI0YAAMrKytCrVy80Nzdj5syZWLFiRVqbPEJHlQo7Eolg6MQpYD9YjI4BFcCcHwJzrwbie1K0yVk1RRNJEHVXFCKqSJNRo0al5kCOFhIZ+pQpUxCJRFIH28TjccydOxejRo1KM7nwdvihPDrTQDQaxcyZM1FdXZ2aWxXdqvHK1yKRRHrucePGWTEr0UwUj8fTfp9hw4YpI4R0fRcCtgxZ/u2zyQyaLVS/WRjCxSQQ5RTr3BTqMRdMeVWlJuTiA+AYAJUA1gN4HcDPktf7AVgIYFPy7+FebXVH05CMln2t9OPHamjg1Hn0zX+spA8+VieEM5mJ+FnClZWVafl7xKMjbVRxpblhxXJqe+EPiRxFfzuV4ttqlXVVzlS/UJlcxGM95QNjTDmbxKgf3QE2svlHR7dY3yshnFckismcpnNa8nvcpGTj7NZdDwu2bfktlw2NXr+jDQ3Fsl/EVCYWixGAelLxZ9XFXHwAfBLA2OT/hyBxYP0IALcA+E3y+m8A3OzVlhMECXR0dNBjK7fQ0Gvm07gbFtDLGz6wqicyHNH229i4/6xi2SasY2K666lImE0LqePmE6j9uiOpdcXfM0JM5QRyKlptIdIkjk1lw7exQXPBoMpXpEr9bUObjt7Kysq0qB9VHZU/hAs8k/9A9Tuq/Cm662HmJrKdq3wyVvl39BIMpt8yKA1+aDWV92oLwGoqpCDI6Bj4L4AvANgI4JO0X1hs9KrrBEE6NjR+TGffvpgGTp1H0/67jvbG29Lu6xiheF1kyCID5BqCGC7H78sOTHGFL7ZFH79P7Y9MSmgHj19CFN2RRpcpDUPQOHjbDKA27Yof+XwHm/Z0YxNX6tw5rRuPTI+skQRZGeuYfVgaQTYMM5/l5N+XZ+T1kzolW20iaPpyG9rE+zqNoCA+AsbYIABjAKwCcBQRNQJA8u8nNHWuZIxVM8aqd+zYkTdaOwNOPPoQ/Pcnp+E7EwbhkeWbMenepXj9vcTh86bdoWK4ZENDAyZNmpTahVtRUYFhw4ahrq4OK1euRFtbW+p4SO5EBdJ35IqOUm5zX7t2LeK9D8cBlz0DnPMXoGEhcP8EtK6fn7ZrV+Xo8mNnFW2kXuF1Ns5ZuSx3otfU1KROfuPho6aTrFS+AD5OIkI8HkdNTQ2ISLvjV6xTVVUFAKl55mVVO1FtIO/w9hOaqNrxKt5T0eJ3l7FX/zbjtSnH/QT82e3Xr5/y2VM9k9k4av34x7zCgS0d7XuVN1XSIZcfACUAagBMTn7fJd3/0KsNpxHoUbnhAyr/00Ia/Lvn6N6XN1FrMqW1DqrVJV/V87+VlZXU2NhI06dPT/kNZDOG2B7XJPj3tDKNdYnspdP6Utucq4n27S8XNDWzamUbtr1XNDOJ+ZrE8FSxrG7np2jK4dqWOF+mcdmEkOrMebrfSRdmyv+aVsBeprFsTTu2mmAYbYVBq18N1uv3Cdq2CSiGncUAegF4AcD/CdecaShkNEdj9KN/JxzJF9y7lBq2+0sHzXcacwbH01eLTleT+inbuzMe4PheoheuIZp2KNGdpURvL9WqyH7tyWHYak3mAFFQLlq0iBYuXJgar9deC/GeysQjlpOFrUyb7byYkpB5CSHZh2Q7X0EhM7/OkClUhq0Q4IEMOgGqSicRxlwUXBAgEbb0KIA7peu3It1ZfItXW04QeKOjo4P+u/ZdKrvuBRp6zXx6cPGb1NauTk8hf5dP9po/f35Gvn2VM1lkDOJ97QO8eXlCEEw7lGj+r6mlKd3ZbcsMgmoQur5UdMur+mXLltGCBQvScg/ZvLA6TYPfExkw9xvIwsJ2XrhWp/ot+F/Tij6ohiaOxU/5sDYZyu3aXMsFTHZ/0dekQtjzwFEMguAzSGxvrgOwNvk5D8ARAF5CInz0JQD9vNpygsAeH3y0l654pCqlHWxo/Dh1j69MVMKAX+PJ3MR8OI2NjXTPPfekNAXejriCVZkdlOpwLEo07/8RTetLe28aSvENC3L2EvD2vHZrqkweutW0TnDo+pbHJpqJxKgV8bfR7WCW21aNU3R62o7N1K4NZPOXLWz78lNOt/M7V8JAFLB+ji3NFwouCML8OEHgDx0dHTRnzTYac/0COuG3z9Etz6+nvfG2NPODCiIzER/we+65h+644w7asmVLWnSQatUsmjZ4si7eXtpK9+2l1HHXaKJpfWnHgxdRrPldJT06Or3K2LQj3xf/qlb7/LvtQfcqc4AsSHSaiRdDsc0caiu0VO3YluW/q5fACSKAvDQHlcC2bTsITEImmyR9YWi5KjhB4EBN0Rj9YtYaGjh1Hp1+88u0aON261WsyJy4JkCUecCNismJ5gkxtFTMekpERPE9RC9eTx3XHUF000Cimn8Stben2lIxFbl9kc5sXngV01IxNi9hKkKlRXj1LQrQoIzTz3VVuWwyaYpzJY7BSzPzs9fDlJ45jNV/UKGUTX9+6NYtVFRwgsAhhWUNO+is2ypp4NR59MN/V9N7uzIT2MmQmR9RurORM3nVjlvZfi7uTVA6zD5YT/TQuYl9B//4AsXfWZ1Bg7zykgWADfNUjU/Vvkqg+Xn55H50L7rOUR5UqJk0BRtHcBDtwUSLamOeqbyftoNoHbZtZ5MELygNfp9b3TMpt6MTBCxxr3OhvLyceE4Yh2CItbXjwcVv4d7KBvQ4gOHnnx+C7552HHr10G8t4fHSPM9OdXU19uzZg549e6KtrQ0NDQ34yle+gq1bt6Zio+VU0FVVVSgrK0N9fT0GDx6sT2ZGhLaaR9HjpeuAfR+io/z76PG5a4A+h6ZoUSVvi0ajqVPY+DUv8HHJcfsc/J7qO4+9t00k19zcjH79+mXsVeCJ7/j+Cx7PL/ZjC5ke3TzV1dWhtbUV48ePTxsHzyFFRCgrK0vtVxDvy8n+/NIVJlS/n6lvv3RkQ7f4zsgn5WXbD/+dxFxY/DfhffJniN9njNUQUbnclks6103Ru2cPXP25IVj4i4kYf/wR+Mv8DfjiXa9gWcNObR1x8wuQyOZ5xhlnYMKECTj11FMxfPjw1EYcnpwOSE/yxs9B4Hn4dYi3tmJ1x3DsvnwxOkZfhh5VDwL3VgC1MxGPxTIylwLIyCJqKwTEJHIiVJlS5Q154maiaDSaloRPRnNzM+688068//77AJBWVtyEV11djdra2lSyOj+bxFQbCHnffFMcF5alpaXo2bMnotFoRr3y8vKUwBYT9PEEb83NzcaxBkWQtsTNhKq25A1fNvMpnzMRFLYbxvxsjhPBF/Li7y1u7FTNixIqNaHYP840FD5erH+fTr/55ZS5aJvivAMOG3OCCDnc0qsdsV4qKd22GqIHzyKa1pc+vvNUim+pUqq/KielaRy6TVHyWLxs2jbmFqJExJWYrkPlUORjCJoMTWVy4ietLVy4MM1kxn02TU1Nyj0HKlOOGNJqa7ayMbFkY4bx8g/4seOLaSbCgo0ZzPZ5VT2nXulI+D04H4GDF/bG2+iuF9+gE38/n078/Xy6Y+FG2hNr866YhMlu3tjYSPfff78no5SRlpSuvZ2o5lHquPl46ph2KH3wj0vSootkhmxLs/iXSB8/b8NAbPrj+wNUtPL7CxcupOnTp1uFH+oYgOzPicX2H1Eqgjvt5eMXbZmXn920uuuq/Q4yw/OKuw/TP6DKNRSGr0SGn/mTaTDRpnsXnSBwMEJ8WLZ9uCeV4nrCjS/R3LXvKs9K1rUjv7ScuXGNwO8msQwn6kfbif73W+q4rh/RX44hWn4vtezK3DwVBH4FiVzPRliIh9yrIpH45j0xG6zqRZf3H4j1uTCRU2Do0lTYakA6jShbyA5/2dlvSq/hJSSCwlYjDLMfP3W86FHdc4LAQQvdQ7XyzZ30xTuX0MCp8+ii+5bRmq0fWrcnZyXV5R+SzR9eJoK0e9s3EP1rMtG0vrTn5uH0cdVMWrVyZeAXS/V/0DZ091XCSsVsxQ1JKsEqXpNX8GIOI9Vq35ZpmlaZ2cyDXFalgcjXTcJZft5yhaD7ArKZr6D3dHCCwMEI3UPV1t5BM1/dQuNuWEgDp86jqx9fTVubdvtqT7fabGxsTEv5a5OmQXUvXv8c7b7lJKJpfan9oS8SvbvGOCZVe/nKa+OnD1FIqnI3qdJOiCYNXeI/09x60W4r7Gz704X52mgiNvfD+k2DPiNe9Uz3s0nxoevLCQKHrNCyr5VufX4DDb1mPg25Zj795bl62rUnTkTeqxbVi84f8i1btqS14SUEtE6xPVGiVQ8S3XxcIrPpU1fQmkXPetIWZkIvjmx2lHKo5ku8p6JddOLKTMSLJi8G7ocR+qmnmnu/TFcnNLJh3n6ue5UJIsS8tKCg7QGoIScIHLLFe7v20P/NWkuDfjOPyq57gR6ofIOWLtebY0xqu+p0slgsltpkZvNSyS9M7KMd9O4/r6SOGz5BHdf3J3rh90R7mrXtBHlxTbDJMePVl8zAjAJQUVbUuGxp0mltKsHgdc1mjF73/AgBm2ihIO2FvfqXywYpE0QjE+85jcAhVLz+7kd02UOraODUeXTajS/SM6u3Ubsmu6mKyehWqi0tLTR9+nRqbGy0zlOjzGmz6x2ip69KZDa98ViipXcl0l+T98uSrTruRwiY6DB99+pPjNISy/gZs47heyWx86JZbCsMJ69Xv35X1+LYTClUbGjRlQmqqdj4QmIxfW4qnSBwG8ocAmHEp/ri0ctPxr+vOAWHHhTBz2etxfn3LMXiN3YkVhhI3yTDNyHxU7aqq6szdgHz074mT56c2p0styN/l0/YSuHQAcCF9wNXvQIMKAcW/gG4Zxyw9nFEevbQ7kL1cyqaDqodpKqNQqa+VCdjqdqLx+Ooq6vLOAFtw4YN2LdvX9pGI9OpYaoNdWJ7fDMZgLQNdeLGJd2pXaq2+HXGmLJPG+h2Nqu+6zZ16X6XSCSCwYMHY+7cuWhubjaOSdW3V5mgzxh/t0yIx+NpGyutG+5sH6cRFBfa2zvomdXb6LSbXqKBU+fRxX9fkYow4isT+Rxj0Z7NV173339/mllIXAGpbOb8vlUyszcriR44I5G/6G+nEm2YT2QZEusFv+q6yezl1ZYquZ68qubzK4aPmswdqhWz3IeYWtqPmcXruo0WEZbmpjIXyedsyJD3E+RyxW8DW5OVX42g4Ew9yMcJguLEvtY2mrH0LRp7/QIaOHUeXfnPV+mZF/czDlVSNfGzcOHCjEgXXUQJFx7y7laVWpyq395O9Np/Uumu6R9nE21ZoS5rgMzI/IRUxmLpJ7iJY+VCTfcSi7Z+mWmL8yYzcJtxqTZQBcno6odhquqqBJJp/4CuL5MQEscj7ukw0eUXYQiBMASgXE4nCJxpyCE09O7ZA9857Tgs/vVZuPqs47G0oQn/76Vd+OOzG/Derr1KkwnP5wMABx10UJoJAwAqKirSynPz0eDBg/Hkk0+mTEzcdFFVVYW6urqUWiyapXDAAYgPPR/VJ/8NbefeBny4GXj4HODxrwPvv2al+qty+dio+fLB9KWlpRljlfP7yBDzEdXW1qaZh2bPno3m5uYMeurr61O5hHhZeTzxeBwNDQ1p5iGe9A5ARm4lr7nhv4efvEFizidxbEBmPh1xHlW/mdfvKI5n/PjxKCsr8zwUXqbVCzYmIhNMZjzV86bqh5thrWhQSYdi/ziNoLjBVy3vNbXQtXPX0ZDfJUJOr3/2ddrZsi+jrEpjEK+JIZE87QJfzalSX8vOSzk6KbVKiu0mWvJXohuPSWgIT11OscZ6z/GpQjn9zo/Xd68Vqpy+Wz6JTKS1srIywwHvZXpT0aWLPlKZemzCVcWxyruK5TZNK2FZI1TRrmsjyArbj4M/GxNRtjSp5hLONOSQT4gP37YP99CvnlpLx/1mHo34w//orws20kd742kvp4qRyfd4egaZoauSg8kMwZh6Yk8z0YvXEf3paKJrDyea+1OK7Xhb2564O1g+otM0D7bz5cVAeL/8pDf5o/JHyOcX8/9V/gWxngzxtDoi9dm7MmNX0a/bQGgSgl7mHlP0Er9uelZsoHuOTMzYpk0v2JjkvJ6/WKwIwkcBHAOgEsB6AK8D+Fny+leT3zsAlNu05QRB58SmD1roR/9O5DAqu/YF+u2jlfRhy540h7GKkfG/IkMTGbwuRl5mSLJTOQMfv0/03K+o47ojqP26I6jtuV9TrHlbxspKZmCmBHI2+WB0K1UT+FnSCxcuTLNzewkFuX0VA+fpKVQMXk5XsWzZMuXhQjareF3/JmGgg5cvhD872WQVNWUlDUKz2KbXHg+b58hLYyqKDWUAPglgbPL/QwC8AWAEgOEATgSwyAmC7oHXtu2ib/1jJQ2cOo/G3bCQZix9i5o+/MjIBMSoFZ2jVAWRQXBntEnYEBHFPthE8ae+Tx3XHkZt13+CYv/7Pa2ofF65ahUFjGpFahI82TA+PjYV47dJ1SHTpBO8cnlVniTbPnT3VO155RYSoRuvSsjI+1O8aJShy0rqN7JIrJsrjUAWxiaNIG/OYiJqJKLVyf9bkprBp4loPRFtzBcdDoXH0P4H4sejGJ64ogIn9D8Y1z5bjy8/UI1N7f3BevRUOsLq6+tRVlaG8vLytBOz1q5dm+aYEx1j0Wg07WCVhoYG8JPt+IEdsoMzGo2iatMHWN7/UqwZ/wA6Bp+NyMq7ccrK7yOy8i7EW5oznHg8Fp47O0Vwh6bKaScfciOO1wZ8HuRDc8S4fp3TUndYi9iWSBM/dKe2tjZjDH4crXL/smOZt2eK+5f3lNTX16cd4qM6aIfPzdFHH51xEp24R0JHKwc/eEl2/vNrtgfMiH3b7CcwOZ/FgAPxmvise/1OBbHxAxgEYCuAvsK1RXAaQbcBX710dHTQkje206R7l9LAqfPojFtepqdXv0Nt0i5lLxuoymwhryplm7rKvCP2lervvVqix76ecCjffBztXngTVS1fnFGem0l0JhWblSKny8Z8odIATOVUK0bV/6r64tnUNuVt4KWF6NoxOatttSGxnmn+bBK/mebVC37L2obSipqqCBTaR5DqECgBUANgsnTdKAgAXAmgGkD1scceaz15Dp0DHR0dtPD19+ncZNrrz/11ET1b+y7t3ZuIMvKyk2Ywb9Lbv1XJ2qzyA71TRe2PTEpkOb1lMNHKB4ha9+kFiESfzTUi8mXLllNI+O1LBRVjs9q053HPiz5+joJXXa/UIzZjVaYl0fSVrf0+LMRimdFi8n0vPxiA1VRoQQCgF4AXAPyf4p7TCBxo7959dNfTS+izt1UmNIS//I/mrX2HOjo6jCtEv5u6VG3YIr6pkujhLxJN60sdtw2jt576A8X22B/BycuYNmqpbNG6NmThZrKXm5gIkbe9XffXpg953DJUEUiq9nQCyaT56BYFXvT6sd97LVJMY7KBbpUv3vfSPAuuEQBgAB4FcKfmvhMEDkSUeKDbkmkrJt6SOEf5S3cvoZfWv59xUppu1ZbrFVps3z5a/9z91P7gZxMmoztGEtU8SrE9UWuhxD+mnPx+zBtyPT/J4cT7Koe6WE5kfNxkZBLGJk1NNx5dn3ysJo1A/q6LgNK1b+rbRLdqvlT9ezF0r36yua8TBCxxL/dgjH0GwCsAXkMiVBQAfgegN4B7APQHsAvAWiI6x9RWeXk5cUeIQ9dGW3sHnlnzLu5+eRPead6LsmMOw88/PwRnDu0Pxpgy8Rh3nvlJ7MUdpaLDVL6n/L9XL6DhRaDyz8B7a4DDj0Pbab9AzzGXAj16avsS6dMlT+NO5oqKCkQikVSSPl17I0aMSLuvolvXl5gAUDVW1TwBwPLly8EYQ8+ePTF8+HCUlJRk/BZVVVVgjKG8vNzz99DRzK9Fo1HMnDkTQ4YMwfjx4zPGoqNZNWZ57Co6dHPu1Y74G4vg46murkZ5eXkGXXIb2SQ/VIExVkNE5Rk3VNKh2D9OI+h+iLe10xOrttCEGxOJ7S64dym9uO5dWpk8mtKv6q0zFZhWwcYVYkcH0frniO7/TEJDuGs00ZrHidpaPfs30chVfa/9El4rctV4TNe86JLNWnyzX1DNRm7XpL2IYbM2piF5DuS2dPNhCgc20a4qq6JVvib+xn5/ExPENlBojSBMOI2g+yLe1oHZNdvwt8oGvLtrL8YccyiuPusEHNyyFWPGjLFaQckrbX7Nr0agBBGwcT6w6Ebg/deAficAE38NjJyi1RBU/aiuNTc3o1+/fhn3xZWnqr6sHXn1YwN5pcxXuaWlpcYVtFc/fPWu03BMYzFpVioNjGsqMs1iO6ZVvtcciu2YaBOfuyAagamcPHadRuCSzjl0KkR6HoBvnHIsKn95Jv70lZH44OMYLn90NW6sasWKzR/BdmEj58EX4+cz+pRixj0aBoZ9CbhyCVov+ifQ6yDgmR8AfzsZqJ0JtLcpq5mSjPH7DQ0N1nsRVPdNsEkoJ/4vx/hHIpE0048qyZ1NjL18zoHch+7cBFUsvVhP3jcCIGNfinxfHqfYjum3Avbvu6iqqkrtlZDng9cR50WkxVYIyPsqVGP3bEulJhT7x5mGHDj2tbbRv1duTjMZVW74IMOpLCPXzuSUWWHfXqL6Z4nuP00wGT2mNBnZRstkA1NkjZ9YepNzVT5rwqaeDa0231V/5bKyA91Ejy6EV/fbyG2LZh+ZBps5MEE1Xq8QaxQ6xUSYHycIHGTEWtvpsZX7fQiT7l2qjDLKCy0qJtPRQbR+3n6BcGcZ0ep/EbXFjW3kQmDZRtyIdPg55tHUh659E2P1074fIeR1xKZtHiCVALQRQtkyf5tNgmL5ZcuWEYD15HwEDl0d8bYOPL16G+6tbMC2D/eidMCh+Olnh+Bzwz+R1bGIvunQ2W2JgI3/AxbfBDTWAocNBM74JVB2CdCjl10bIdFnG1kVFh06PwxPc6GyxZvMQLrjMblvwUS3KkpK1bYpakgsy+nnaU1EP4Iuss0r2slr3F6+gerqahBRyhcWj8fRu3fv1UQ0Ti7vBIFDl0RreweeWf0u7q1swNbmPTh5UD/M+sGpeRUGRhABb7yQEAjvrQEOOxa4cjFwUD/vuiEhl4JG1Rdn0pxRiiGhs2fPxpQpUzIcpToaVfe9wkQ5VP3Jbdu0I5ZVOaN14/WqrxurbtxetHGYnMVOEDh0abS2d2DOmnfx0d5WfO/04wtNTiaIgE0LgbcXA+f8uWBkhBGh4lVejIyRndu6WH7biChAHWmkg0kj4G0F2YeiumYSZvJeA1E4cvpUkVJ+tDlxH4fTCBwcHJSwZSx+GJCufJANZkDmilsVPiqaZcRyNoyYCyjZrJMNbFftYuQQNzOJGotKcPoRyLw+APTu3XsDEQ2XyzhB4ODgkBeNQLwG+GO0MsPUrfxV5WTTjM7UIrcbZL+FirEH0SpE5u1HcMqQhSNjTKkRuH0EDg4O1gwmWyHA28hmtW06q0DcDyKfzRCPx5XnH8jleVvyXgHxmmovhHif73kQ75kgz1UkEkntPaioqEBpaamxHZlO/reurk7ee6Fc+TtB4ODgEDpsNo/5bYszcdUmKVV/IpPnUTS1tbUpxmjaEKbqw2ZDmWhmqq2tRXV1dYbwEWk20S72X1tbixUrVigPOOJj4wJKFFZEJAtdZbSEMw05ODjkBGFGJdlEy9iYbYD03by2zmW/dPC2ufbjFaZqSzunX74npkzhQoCf3Cbu0O7du/d6Iko/Rg9OI3BwcMgRwgxNFVf3QfsTTVLcdKMyMelgq+WozExyO/KKXw6BFcuKtOt8FqIQAJAhBIT0G3tVNDtB4ODg0C0h+g9sIJuGTOccA/tX6qJJRzQT6cJhTSYj8X+xLdEsBCBNEElCx/kIHBwcHET41Vr4qtzksBYZckVFBcaPH4+KigoA+1fqOie6rCWo9g/Iph8ebhqPx7Whr17jdD4CBwcHhwCQV/U2+xCy9ZuY9lDIG9BkGuLxOHr37u3SUDs4ODiEBZnJiqt9HbPP1m8iRzFxyGYgAEozEzRRQ+aTMhwcHBwcPKEKNy0kLQCUZiY4H4GDg4ND7lAMQkCEHz9B3gQBY+wYxlglY2w9Y+x1xtjPktdvZYxtYIzVMcaeYYwdli+aHBwcHBzyqxG0Afh/yYRHpwL4MWNsBICFAEYSUSmANwD8No80OTg4OHR75E0QEFEjEa1O/t8CYD2ATxPRAiLiB7muBDAgXzQ5ODg4OBTIWcwYGwRgDIBV0q3LAczS1LkSwJXJrzHG2LqcEZgbHAlgZ6GJ8IHORi/gaM4HOhu9QOejOZf0DlRdzPs+AsZYCYDFAP5MRE8L168BUA5gMnkQxRirVsXCFjM6G82djV7A0ZwPdDZ6gc5HcyHozatGwBjrBeA/AB6ThMC3AZwP4HNeQsDBwcHBIVzkTRCwxGGxDwFYT0S3C9fPBTAVwEQi2pMvehwcHBwcEsinRnAagMsAvMYYW5u89jsAdwPoDWBh8mDxlUR0lUdbD+aKyByis9Hc2egFHM35QGejF+h8NOed3k6Za8jBwcHBITy4ncUODg4O3RxOEDg4ODh0cxS1IGCMncsY28gYa2CM/UZxnzHG7k7er2OMjS0EnQI9XvRemqSzjjG2nDFWVgg6JZqMNAvlKhhj7YyxKfmkT0GHJ72MsTMZY2uTqUwW55tGBT1ez8WhjLFnGWO1SZq/Wwg6BXoeZoxt1+3VKbb3LkmTF83F+O4ZaRbK5f7dI6Ki/ADoAeBNAMcDiACoBTBCKnMegP8hkVr1VACripzeCQAOT/7/xULSa0uzUO5lAPMBTClmegEcBqAewLHJ758o9jlGImji5uT//QE0A4gUkOYzAIwFsE5zv2jeOx80F9W7Z0Oz8Pzk/N0rZo3gZAANRPQWEcUBzARwgVTmAgCPUgIrARzGGPtkvglNwpNeIlpORB8mvxZDOg2bOQaAq5HY/7E9n8QpYEPvNwA8TURbAYCIOgPNBOCQZIh1CRKCoA0FAhEtSdKgQzG9dwC8aS7Cd89mnoE8vXvFLAg+DeAd4fu25DW/ZfIFv7RcgcSqqpDwpJkx9mkAFwJ4II906WAzx0MBHM4YW8QYq2GMfStv1KlhQ/O9AIYDeA/AawB+RkQd+SEvEIrpvQuCYnj3PJHPd6+YD6ZRnaQjx7ralMkXrGlhjJ2FxMP4mZxS5A0bmu8EMJWI2pP7PAoJG3p7AhgH4HMADgSwgjG2kojeyDVxGtjQfA6AtQA+C+AEJPbUvEJEH+eYtqAopvfOF4ro3bPBncjTu1fMgmAbgGOE7wOQWDH5LZMvWNHCGCsF8A8AXySipjzRpoMNzeUAZiYfxCMBnMcYayOiOXmhMB22z8ROItoNYDdjbAmAMiRSnBcCNjR/F8BNlDAKNzDG3gYwDMCr+SHRN4rpvbNGkb17Nsjfu1doh4nBSdITwFsAjsN+J9tJUpkvId1p9WqR03ssgAYAEwo9v7Y0S+UfQWGdxTZzPBzAS8myBwFYh8R5F8VM8/0Ark3+fxSAdwEcWeBnYxD0jteiee980FxU754NzVK5nL57RasREFEbY+wnAF5AwnP+MBG9zhi7Knn/ASQ86ech8QPvQWJlVcz0/hHAEQDuS0r5NipgVkRLmosGNvQS0XrG2PMA6gB0APgHERUsZbnlHN8A4BHG2GtIMNepRFSwtMmMsScAnAngSMbYNgDTAPQCiu+947CguajePcCK5vzRkpQ2Dg4ODg7dFMUcNeTg4ODgkAc4QeDg4ODQzeEEgYODg0M3hxMEDg4ODt0cThA4ODg4dHM4QeDg4ODQzeEEgYODg0M3hxMEDt0GjLGvMsZWJXPSNzDGpnmU/zxj7F8++ziQMbaYMdYjO2oz2p3AGLuOMRZhjC1hjBXtZlCHzgcnCBy6BRhj3wYwFcBFRFQKYDQSu2JNKEMiJYRN+5zxX45EGuz2gKQqQYk0ytMokcr6JQBfD7N9h+4NJwgcujwYY30B3A7ga0S0DQCIKEpEtzLGhiVX2K8zxl5kjB0pVC0DsFZXhjH2FGPsdsZYJYDfJutcCuC/Qt/Dk3XrGGO/Yow1BBzDU4wxnjFzTrIfB4dQ4ASBQ3fAhUicSPWWeJEx1huJQz9+RkQnAVgI4BdCkTIkzgfQlRkFIEpEZxHRnxhjEQDHE9HmZPs9ATyWrFuKxCllQfMejUzSgmQbFQHbcXDIgBMEDt0BJyGR71/GVwAsJaI1ye/1AD4BAIyxXgD6IpEULKMMY6wPgH4ArhfaOxLALuH7ZAC1Ut00U1NSw1in+FwglOkDoBcRfQQASbNTnDF2iP0UODjo4RxODt0Bu5E4pEbGCOxfZQOJFX69cG+9ocxJSGgZ4pGSewH0Eb6XIl0AjQTwvEgAEX3egv6TBLo4egPYZ1HXwcETTiNw6A6YD+CrjLGjgIRJiDH2fSTy/o9IXjsewGUAHk3WKUOCievKjEIi1XUKlDgTt0dyBQ8ATUgcnQnG2GgA34Sl81lCWl+MsSMA7CCi1gBtOThkwAkChy4PIqoCcC2AF5I5/9ciYQL6F4BPJa/NBHA57T+5ikcM6cpkCIIkFmD/MYj/AlDOGKtCIppos+ynsITc11lICDcHh1DgziNwcAgRjLExAP6PiC5jjJUQUTR5/VcADiWi34fQx9MAfktEG7Nty8EBcBqBg0OoSDqGK5P7Cn6RDDldi8SRhDdk234yMmmOEwIOYcJpBA4ODg7dHE4jcHBwcOjmcILAwcHBoZvDCQIHBweHbg4nCBwcHBy6OZwgcHBwcOjmcILAwcHBoZvDCQIHBweHbo7/D1zcxv5VvFZxAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cmd(candidate_df)\n", "\n", "plt.plot(left_color, g, label='left color')\n", "plt.plot(right_color, g, label='right color')\n", "\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Which points are in the polygon?\n", "\n", "Matplotlib provides a `Polygon` object that we can use to check which points fall in the polygon we just constructed.\n", "\n", "To make a `Polygon`, we need to assemble `g`, `left_color`, and `right_color` into a loop, so the points in `left_color` are connected to the points of `right_color` in reverse order.\n", "\n", "We'll use the following function, which takes two arrays and joins them front-to-back:" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "def front_to_back(first, second):\n", " \"\"\"Join two arrays front to back.\"\"\"\n", " return np.append(first, second[::-1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`front_to_back` uses a \"slice index\" to reverse the elements of `second`.\n", "\n", "As explained in the [NumPy documentation](https://numpy.org/doc/stable/reference/arrays.indexing.html), a slice index has three parts separated by colons:\n", "\n", "* `start`: The index of the element where the slice starts.\n", "\n", "* `stop`: The index of the element where the slice ends.\n", "\n", "* `step`: The step size between elements.\n", "\n", "In this example, `start` and `stop` are omitted, which means all elements are selected.\n", "\n", "And `step` is `-1`, which means the elements are in reverse order.\n", "\n", "We can use `front_to_back` to make a loop that includes the elements of `left_color` and `right_color`:" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(234,)" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "color_loop = front_to_back(left_color, right_color)\n", "color_loop.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And a corresponding loop with the elements of `g` in forward and reverse order." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(234,)" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mag_loop = front_to_back(g, g)\n", "mag_loop.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the loop looks like." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cmd(candidate_df)\n", "plt.plot(color_loop, mag_loop);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To make a `Polygon`, it will be convenient to put `color_loop` and `mag_loop` into a `DataFrame`:" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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color_loopmag_loop
00.63217121.411746
10.61023821.322466
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" ], "text/plain": [ " color_loop mag_loop\n", "0 0.632171 21.411746\n", "1 0.610238 21.322466\n", "2 0.588449 21.233380\n", "3 0.566924 21.144427\n", "4 0.545461 21.054549" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "loop_df = pd.DataFrame()\n", "loop_df['color_loop'] = color_loop\n", "loop_df['mag_loop'] = mag_loop\n", "loop_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can pass `loop_df` to `Polygon`:" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from matplotlib.patches import Polygon\n", "\n", "polygon = Polygon(loop_df)\n", "polygon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a `Polygon` object , which provides `contains_points`, which figures out which points are inside the polygon.\n", "\n", "To test it, we'll create a list with two points, one inside the polygon and one outside." ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [], "source": [ "points = [(0.4, 20), \n", " (0.4, 16)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can make sure `contains_points` does what we expect." ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ True, False])" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "inside = polygon.contains_points(points)\n", "inside" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is an array of Boolean values.\n", "\n", "We are almost ready to select stars whose photometry data falls in this polygon. But first we need to do some data cleaning." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Save the polygon\n", "\n", "[Reproducibile research](https://en.wikipedia.org/wiki/Reproducibility#Reproducible_research) is \"the idea that ... the full computational environment used to produce the results in the paper such as the code, data, etc. can be used to reproduce the results and create new work based on the research.\"\n", "\n", "This Jupyter notebook is an example of reproducible research because it contains all of the code needed to reproduce the results, including the database queries that download the data and and analysis.\n", "\n", "In this lesson we used an isochrone to derive a polygon, which we used to select stars based on photometry. \n", "So it is important to record the polygon as part of the data analysis pipeline.\n", "\n", "Here's how we can save it in an HDF file." ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [], "source": [ "filename = 'gd1_data.hdf'\n", "loop_df.to_hdf(filename, 'loop_df')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Selecting based on photometry\n", "\n", "Now let's see how many of the candidate stars are inside the polygon we chose.\n", "We'll put color and magnitude data from `candidate_df` into a new `DataFrame`:" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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colormag
00.380417.8978
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" ], "text/plain": [ " color mag\n", "0 0.3804 17.8978\n", "1 1.6092 19.2873\n", "2 0.4457 16.9238\n", "3 1.5902 19.9242\n", "4 1.4853 16.1516" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "points = pd.DataFrame()\n", "\n", "points['color'] = candidate_df['g_mean_psf_mag'] - candidate_df['i_mean_psf_mag']\n", "points['mag'] = candidate_df['g_mean_psf_mag']\n", "\n", "points.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which we can pass to `contains_points`:" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([False, False, False, ..., False, False, False])" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "inside = polygon.contains_points(points)\n", "inside" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result is a Boolean array. We can use `sum` to see how many stars fall in the polygon." ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "454" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "inside.sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can use `inside` as a mask to select stars that fall inside the polygon." ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [], "source": [ "winner_df = candidate_df[inside]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's make a color-magnitude plot one more time, highlighting the selected stars with green markers." ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cmd(candidate_df)\n", "plt.plot(color_g_i, mag_g)\n", "plt.plot(color_loop, mag_loop)\n", "\n", "x = winner_df['g_mean_psf_mag'] - winner_df['i_mean_psf_mag']\n", "y = winner_df['g_mean_psf_mag']\n", "plt.plot(x, y, 'go', markersize=0.5, alpha=0.5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks like the selected stars are, in fact, inside the polygon, which means they have photometry data consistent with GD-1.\n", "\n", "Finally, we can plot the coordinates of the selected stars:" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,2.5))\n", "\n", "x = winner_df['phi1']\n", "y = winner_df['phi2']\n", "plt.plot(x, y, 'ko', markersize=0.7, alpha=0.9)\n", "\n", "plt.xlabel('ra (degree GD1)')\n", "plt.ylabel('dec (degree GD1)')\n", "\n", "plt.axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example includes two new Matplotlib commands:\n", "\n", "* `figure` creates the figure. In previous examples, we didn't have to use this function; the figure was created automatically. But when we call it explicitly, we can provide arguments like `figsize`, which sets the size of the figure.\n", "\n", "* `axis` with the parameter `equal` sets up the axes so a unit is the same size along the `x` and `y` axes.\n", "\n", "In an example like this, where `x` and `y` represent coordinates in space, equal axes ensures that the distance between points is represented accurately. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Write the data\n", "\n", "Finally, let's write the selected stars to a file." ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [], "source": [ "filename = 'gd1_data.hdf'\n", "winner_df.to_hdf(filename, 'winner_df')" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.6441001892089844" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from os.path import getsize\n", "\n", "MB = 1024 * 1024\n", "getsize(filename) / MB" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Summary\n", "\n", "In this lesson, we used photometry data from Pan-STARRS to draw a color-magnitude diagram.\n", "We used an isochrone to define a polygon and select stars we think are likely to be in GD-1. Plotting the results, we have a clearer picture of GD-1, similar to Figure 1 in the original paper." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Best practices\n", "\n", "* Matplotlib provides operations for working with points, polygons, and other geometric entities, so it's not just for making figures.\n", "\n", "* Use Matplotlib options to control the size and aspect ratio of figures to make them easier to interpret. In this example, we scaled the axes so the size of a degree is equal along both axes.\n", "\n", "* Record every element of the data analysis pipeline that would be needed to replicate the results." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 2 }