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@orbeckst
Last active August 20, 2020 22:59
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Using `regularized_function`\n",
"\n",
"This notebook shows how to [coarse-grain a time series](https://numkit.readthedocs.io/en/latest/timeseries.html#coarse-graining-time-series) by aggregating the data in non-overlapping bins along time.\n",
"\n",
"It uses [numkit](https://github.com/Becksteinlab/numkit)'s [numkit.timeseries.regularized_function()](https://numkit.readthedocs.io/en/latest/timeseries.html#numkit.timeseries.regularized_function). (If you don't want to install numkit (`pip install numkit`) then you can also just copy the code itself as it is self-contained.) "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import numkit\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"'1.1.2'"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"numkit.__version__"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Make plots pretty:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import seaborn as sns # to make plots prettier\n",
"plt.matplotlib.style.use(\"ggplot\")\n",
"sns.set_style('ticks')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Noisy signal\n",
"\n",
"In this example (originally from [GromacsWrapper's XVG reader](https://gromacswrapper.readthedocs.io/en/latest/gromacs/core/fileformats/xvg.html#examples)) we generate a noisy time series of a sine wave\n",
"\n",
"$$\n",
"y(t) = \\sin\\omega t + R(t)\n",
"$$\n",
"\n",
"where $R$ is uncorrelated white noise with $\\langle R \\rangle = 0$ and $\\langle R(t) R(t') \\rangle = \\delta(t, t')$. We use normally distributed noise with $\\sigma=1$ and scaled with a factor $\\rho$\n",
"\n",
"$$\n",
"R \\sim \\rho \\mathcal{N}(0, 1).\n",
"$$\n",
"\n",
"When plotting the data themselves we see large fluctuations that obscure the overall trends.\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"omega = 1\n",
"rho = 0.1\n",
"times = np.linspace(0, 15, 50000)\n",
"R = rho * np.random.randn(len(times))\n",
"\n",
"y = np.sin(times) + R"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.subplot(111)\n",
"ax.plot(times, y, label=\"data\")\n",
"sns.despine(ax=ax, offset=10)\n",
"ax.set_xlabel(r\"time $t$\")\n",
"ax.set_ylabel(r\"signal $y(t)$\")\n",
"ax.legend(loc=\"best\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Coarse-grain the signal"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"from numkit import timeseries"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We use pre-defined \"regularized functions\" such as [`mean_histogrammed_function()`](https://numkit.readthedocs.io/en/latest/timeseries.html#numkit.timeseries.mean_histogrammed_function). See the documentation for [coarse graining timeseries](https://numkit.readthedocs.io/en/latest/timeseries.html#coarse-graining-time-series) how create your own."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Mean\n",
"Show the mean over intervals"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"y_mean, t_prime = timeseries.mean_histogrammed_function(times, y, bins=150)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.subplot(111)\n",
"ax.plot(times, y, label=\"data\", alpha=0.4)\n",
"ax.plot(t_prime, y_mean, label=\"mean\", lw=3)\n",
"sns.despine(ax=ax, offset=10)\n",
"ax.set_xlabel(r\"time $t$\")\n",
"ax.set_ylabel(r\"signal $y(t)$\")\n",
"ax.legend(loc=\"best\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Median "
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"y_median, t_prime = timeseries.median_histogrammed_function(times, y, bins=150)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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KipaBjCWlyR8AJ2KoVcKCkvAKSf2hViNcugD3hnWQyXlNRhFk5Wyug3tTOPxPBEUB3+/jCRVzXgow+Lw9Tgai2PlQLSE2kt8Xc5H5aasJLcFU9kpWwm0l6Qthrqryo8aiJIbwMoVfXrUl+AljII7GYGRBQODCl0hUF/tX1UQzs5hHeScOAeOxUqV99lkbFzMDTRZ4MtlkmL82m0I1M+WshFnF6T0r6WmS8ZWK8Pu/NsZCg2AgMRZvogz8WRXSWlbpB5fGWZmlgKf7ecAGQ2hHPSxOe7URDf5K/HKLdEAcjcEETh5F4IsjEBuvx3xOq0DhE1W20d1l6VvRdjDUKmJsUKJGBKU5eNZD8nripmISkkfyeSG2t+pec4kU/udG+JD+KxX+lLPMkuHecn9osjnmYXHKS85qMokU4/3f0c7hUkB5L+y0rCm2TheDLBJuVS1ePmzRFvFKzva03zMS4mgMpiOdMdabKcvAr65a4QwmAfTmRExyGKM/9aBqVbuu2QR/nAiZZ+vH8O7cbIgdhYZny3p4d+j/Lf+30Yw2VQKI+j1KJxWcjPmqyea9GLsasbWZnNMYgJ4SiCwDb6l2M/eV+zU6Zunk7vLw52pjqwleVdAiUrHCCIijyRCB08d1nc3mNg7b2sMrjCf7eJPulpcqs4r5UG1Fu0jj45b48iSSxx33OqFrNPKUJoz1RC+voY3Llqqc2OY2Dm1C9Act8MUReLdvMs4IQoijHgYng6KpHCUbtsgAgFtsIqrNinfxSJSm7YQcSH8EJRLiaAwnfNbCnz+jueKVgH9X6ZDdVeZPStq7szCUdlfzVpNFPwMpQ9XChUC8BJCNraZQt8RRVkET3jCCkTYRI6zhg+EtbYlliWRBIGnvXSRwVl/YV93IbHFpIKlz2c4KYFKUNiT/1wSLzHRDHE0WUdfN9OAkfLNX4mZFXeXucj+KGWVX08DT2Eg00AxFjpNYsVk10d9T7k/av1PWzmcOLVZlM25sSzzZeD7fAPemDzt9P4ISzYikXaCwTZX9d3+SmYam4aM7bcfi0oCmrubLDJ7TEUdjNHEWKR+p6mYe6EJ81jp1TvLPpYFlql3NnxotuhXDhK4j8zzExgbda/V+Gl/6wmGT2SnsZrj+A2G7dUl4gEn+g3NrCQ8m+KE87mFxNaA/BXSc08g+4xc/hcinrVxoNzvcKmBokgogFMN2eqFRwsqYq/qcZXJXQxxNlqj3a+tmFncy08w0cmzKP3N/hR92VV3F7gh133h6TITk8R3ZD//xg7rX1GGr6UU8HEn6CtuCO8ENHg7aYgXFKROFff4dAADKHEdiJkgpK2OKKjwbS9Xbu/uz5AwiaJAlKe4uFlCSANTF2Xel+N3n+lZ3yjZAJykgQyVzxNFkiY8i62bYxNsKprJH1Jhp4FDNmYqpZjRAx39bHYwSqulgc0QIxbP144S2EBIje/TlRmRZ+ze/NYkCPbZvNeyL7gVttoDSibHZbr0Ttnm3J2XXwhJt+Ey3xIt03uwUnq3r4f70fQgNV8HXn4dPR0vsuJfBxWDbdQst47aSxI7GOm0uLJNmxrzuWLIU5tETEr7OOJuI/kGhXbdEYWubCZTZ+Loq4mgMROZ5CDp94QUZ+ETlaO5MYkVjnTEflonTNdtmU80oAABlc4TG2D79kzrMX6iK1e9s5zK2sikkJJdTd/ysj0a9aqKZkUDXyr7oXljGTgbFaneelgnTwFT1AjgTaIsFVJIhtFnFPKzBHW29n8FpH6mpSRcdTeR8B3bDf/wghEsXop7zoaqp2YKSQNyQOdurL8AwYMorwfboBQCgi0s1zzGPnQwA4KoHwTr7NlBs7HNXigLuVp0Hfdhsyki9HHE0BiLEKNLc62TRKoYlJ6YkUTfDlJaDYthQmAQATENGAABoSzhkQlttsM6YD9OwUWD7D4z5eoPNEgYE0x19MoVdTv0Pp+T1JLSNkBrq3cysIj6hpl2kg+mAqaiCdfJM3R1OPCw0NGdCsRJCYjlKQudxicAW1fsfL2zGVFTBMmEaHIvv04yzPftoHlNc+P1jikpgX3QPTCNuifm6t6uSAq7xdEZahBBHkwXUPUcWlQYS180kCIVFwhSVwDR0RNznUJSymupgS6zsszhN2gipExk2W5BE2CQV7IvvTep56vDZ5jaTbkKI79CedJlFCLKp1QR/MAlgsFnEyHhJAEl/71NbaJSwMp7u68Fom4AnemYm2YP0eM0wLhHYqdo9LEognmmbvRCU3RH3OR0wVT01j6kEH8BbS3i8dkOp49nj4uASkfShNKFzfOFl0MArE4iDljA5wW7WMjl2XF4PiknuKz3JIaCMldAi0GgWaBx0swltIXQdtfzLXQlT2o2rZ1tQymNBaeYkpsiOxkh0Tlk/awsX6Q2zCBgUp7mRbc4i0EXFoJJY2TiWLIV18iztYIKQSn+zhGEqZdfPdOsqSPFmOlHvZuYU83GVAOyL7wVb1avzN4sRcgOU4l21ovfG1uj3PhMaWIXEKS+DM8GUdhMlY1GCid48KsmMUp2eAslkIGYS4mgMJdrRbNCEzeJ/0GhHUZfuzvTsnfA5ahvW60w2MjmjSRuiDGxVpTXHWlGyfZQMs2R3J51FHT77vJ2L2+qZ0HXUZ2HzinkUMfEzTSlTYmdhqhkFpiI6G5Xr0z91Aw2EOBqDkDxuSG1axdZGnsLhYO0MDbnT8XnKbEkqfstW9lSyVuKwqDSgKeCLbIzk3ft5p2wsdPTaQhx2s7gZbAdQxkiYYNcPVVnGRWeYdQW6qFh3fLg1nOrqkShNSJeQXmQZGk3DhfFC5h3Zg0kEE0xDRsRMBqFLy1Mx0VCIozEIz2efgL94VjO2W/VFHm8XUNHJnjO2+XfAvii5Q99ElLIyZhbH39UQUkevUFPdCmJ+CW+YeGoHlgnTwFT0gHXWbUraewQUBdymmvA2kffeME56GdwIns0VMRImxjsPS9C7KllsM+bDfscDaXmtrkIcTQZRO5qZXRBQpGg6qXMbIDldLHUdz6ctpiihTeHGtZTsIyCqfsIjAttUYbPbDeg51IF59ASYx00BW9kT1qmzQVEU6JIy3ecuVJ3T7HGyuorOhK7zmUrXbFYRH7vnEE2HQ2FU7O84ZbHGrZcJPS9HBHKJo8kQfgmoc4XDIdMTZPiYR41Ly31Nw0bBMmFa3OdMcQioZJUAfYtIR0nS8Be+TIsthczWdhN8wSSQQWYRNRb9tNZkJo9EcNWDko7R9zVLGGUNN8TbmoSiMyE1ZFm7yJgbRwmCqegBy4SpSrZpnMWkbf4dsC28O612GglxNBnigJsN5c8PMIvoa4598upYsrTTcuCRUAwDtldfWGfMh3X2bbrPYSitqu/OiJ7y4s3GtNhSKOidz6iVIO4oC8RMCLRMS14gNV0sTFHRmZAaX/oYXOPDXTQnxTibA5QiTYphY56rdUBRVNK7lQ5NvJj37JE4aairEEdjAHoTjTpsNj2B5IgRMKXlYIpKwPUfpHtdHcrb4+LSFSYuSCJl4a/4aRxRJYHEOwimi0oMsYnt3S9mFuP8Eh40wm2er8dQdCZ0DnW22cyi+CntpkHD0n5/vfO5TJNTBZuSJOHHP/4xTp06BZPJhOeeew4DBgwIXX/uuedw4MAB2O12AMBvf/tbFBV1LQXYCCJDTbIM7FLtEhJpW2WDEVYRxYyEdlEp4DvjY1CTpHQ5QQt/7rTm8Q7VImNakRBTQJUbVGNYTJ02W2Cbsyj02LV+bej/ZayMyQ4Be12KnbucLB6oIAre6cAvAR+rkiwW6CwyLBOmwXdwT0rtHlLBNHwM6JJS+I/UGfL6yZBTjmbjxo0IBAKora3FoUOH8NJLL+F3v/td6Prx48fx6quvorw8d9L29AicPKp5fMrLoFEIZ5yMscWewNMRo48HFWNVy1DAVIcQCp3sdrIaRyN53KBtdkNt667sU515zYqzyGAqqzJhji4ziviQo9nj5KIcjeT1gGIYUCbjlX67E1tVzQ17caK+rqHBB/YUw4DrqyzYs+VscmqPXFdXhzlzlBj1+PHjcezYsdA1SZJw8eJFrFmzBitXrsQ777yTLTPjoteLQp3WOqtIP621w8HYVKKZRsANGBIzv14d0tsTUVPh+ewTclaTBJFq3V4JodopAJiag7tZAJiu6lFz0M1GFW96tn5MOm12AnW75nvK9XUNQ+cxBjucDmeTDXLK0bhcLjgcYV0vhmEgBPtieDwePPzww/j5z3+OV199FX/6059w8uTJqNeora3F0qVLsXTp0ozZrcZ/TFs/EZC0LXtvz6C+kB4URYEpr9S9NsUhhGL1X3gZtEakuvoO7zPcvnyGv3QBvgO7NWOH3WxIcmigWUSVTu1Ux06R4jK3W4jsQdLLFFbzDsgUDrlzKtiRs8iyDL7+HGSe14QjAeBLL4MTXuXvyFIylsRIaafMit4gU2J8pKajtUimySlH43A44Ha7Q48lSQIbrJC2Wq346le/CqvVCofDgenTp+s6mhUrVmDt2rVYu3Zt1DWjkXkewtV6zdhuZ3jr3JOTMDZGxol5/BTFAaSxIjwWpiEjwOkcOhazMkYFw3oyKOx1kskmFfw6Ta72ucKLjKkO/UWGacQtsE6dA6akVPe6EejJ28Tb0RL0Ea5dhv/4IfjqdkZd+0SVBDC3mEdZjLM5imFgnbkAlonTDbOzA9OQEaH+NSEykPmTU45m4sSJ2LZtGwDg0KFDqKmpCV27cOECHnroIYiiCJ7nceDAAYwePTpbpuoitbdGjanDZotLA3r6dwAAtqoXrNPmZqTAimJZmGP0q1BPNrtd2slG9vvg3b8zYataQhj1+czUohhprRQNpiLD5zM6NRrTVOcHu52s7vwjNDUYaVX+EYy4iC03oy6pFxmLE6i0MyWlaZUdyjVy6jdbtGgRduzYgZUrV0KWZbzwwgt47bXXUF1djdtuuw333HMPli9fDo7jcN9992HYsPSnAnYWyeuJ0gVrEyjsUU00iT5sucD0Ih6vNihb+X1OFqIMTVxZbLwO/tJ5pYU0IS5XAzQuBZRMIjMl4xabvqPJFaXdMTYBNlqGR6JwnWdwwU9HqYvLbhdQ2TPGKxA6uB6gQu2aTZSM8XFqZzJOxGI2WZWRrpBTjoamafzkJz/RjA0ZEi5cfPzxx/H4449n2qyk8Gz9OGpsr4uFGFTGG2UV0C+ySJOilG1rDq1kBpslVLESGgUaLonGcQ+DsfaIHQyf+w4z00h+X9TYjnattl2s+olMhsziwdHAFAePz4Lij1vaTBhkif69CIlR72bG2QWYdd57pqqXpjtmpmBKtXJETAYWDjkVOutu7HXGr52hi0rgWLIUjjQJZKaK7dY7YZmi7WFDUcA0dfiMxOqTQyfMtEEVo5/dBW07Y9AP0d6qkkfZ1KpTuJsj2lm5zj6V3NTUGHJT1skzYRk3JVMmhaBtDjiWqJKlMvCeEkdjEJIM7Hclis9nt/yetlhA26K7dyY+FCaTTST8RW2R7gUfHWpyxVEy5sfQt6IsVsNt08M0fIxuzdaMIh52WvlcXuUZfOElLVdTRZCBOnUSSI6mtGcS4mgM4oyPQWsw26yUkTBUT0QxF3RedOKzEx0COEqx7ZyfQUOAOJZERKoBqDXDZhbxcEQ0uQpJAWVph8D26AX7ontgv/1+zbiJBuYWq7TPSOuAlDnuYeCRlPe1Jyehvym3O8oxZRWG34M4GoNQZxtNcQgxs82yDa2zorbSSly5g10kfKaL5PMicDY6xV6StRO0nrYZNzg3Eln0DoIXqmq9NrdxmrYR/uOHMmFWXhOZ0p7r0caudvJN6h6G36FA2av6sE2JsXU2SkAxVfRWNDNVNm8lir66+A7uQeD0CfBXL2nGj3kYNASbXBUzkiZtOJJc6ReiZpw93DaiTaRxOKJ4U2yLTuMvRGRJ0i1pOKr6e8VtcFZAJJ3u1NTUhO3bt+PUqVNob29HcXExhg8fjlmzZqGqKnsaTbmIS1S2zwBAQdbVN7JOnwe6ODccDejoOPy8Yh7/cU2GBApHPAyaeAqVwap2yeuOen5BIirvqz9CMWF7u7ZQj9NZznWkNHNDRxhnX5LYF98L96cfhB4zFDCnmMd7QfmUAy4Wk1Sf4cCXX8ATqEwIAAAgAElEQVQ6aUbG7cw1AiePgr90XjPGS0o3zQ5ipbTnArb5d0D2eTNyr4Q7mrNnz+I73/kO7rrrLnzwwQfgeR6VlZXgeR4ffPAB7r77bnznO9/Bl1+S5lgdHHJzkIIH5sMsIkp1KoKZsgrd6uxsYBoxJmqsnJND4TM5oiGWcKUe7q0fI3Dmi4zZmE+oM/Vmxcg2oxhW6TuURf0ptS2RqOs+onY0pOMqAEBsa4kaO+NjEAhKDvXhxJjt2m2zFxpqWzLQVltGzmeAJHY0Tz/9NB577DH84he/gMkUHUIJBALYtGkTfvjDH6K2ttYQI3MZye0CZdEW3B1QZZtNzoOtM1OsX8dxawmPg25l0tzaZsJXKsNnDbLXg8CXX4Dp0Ttn6kBygSt+bZHmhFwq1IuDbcGd8Gz+KPRYfUZ30svAKwJW1cbXd2Q/2D79wZLiTQ1HVQKqoyPrz6C0Vmf79E/Y2Ky7kdDRvP3226H/S5IEOuLw0GQyYcmSJViyZEn6rctxZFGEZ9unUeN1cWK0pppRYHv2Ndy2VKEdxZBc7ZqxucU8Xr6qhM+Oe1lcD1DoZdKu0GTen0kzc57dqkXGBId+oV4uQkeoE5SwMgZbRJzzMRBB4aiH1aToC1fqIVyp19ZjEHDMHfbGY3TCZqbBw8FV6zcf7M6k9DWYOXOmUXbkJzrpyY08hfqg9ARHyVEfNtOQERnJ8kgVbnBN1FgJK2ti85+3k6SARKjrjqbHENHMF+KFzwiA7HFpH8tKh9IOcvl8JtMk5WhOnjwJnufh9+uvXufPn59Om/Kag6oV7Rhb/qxoY6GuaCfS8VrkCNkZr6T9G+m17OaGDAc3ZLjhtqUDtaMh7300ckCbtn45QIdq5xy0hAGRklMFTFKfnieeeALNzc2QZRlPPfUURowYgREjRmDkyJGQJAlOp9NoO/OGA+7winZinsTnFfQPLdWTzRE3A0mGpiYoU1kruUjkRHPAFe49M8gsoqcp+m9qrsktxfF4jLMJoCBDBoWTXgYeEbAVuFCA0HgdlNkCydkWdU29mxltE3O2di4bJOVotm3bhubmZtx6662YNGkSTp06hQ0bNuDMmTPw+/1YuXKl0XbmBbKsTQToDjn0/U0SylgJLUGRzXM+GkOt4ZWa/+gB0EWlJCEAWtmRabradvl1AFzMyhhskXDWxwTT3FlNJ85CxLdf6TtDWW1R19ThRb3zGQCgS8p0x7s7Se+Hy8vLsW7dOlRXV4fGZFmGz+eD1ZodvaZc43KARqOgbJ3ttIzh1jzs20LTgBR2JBQFjLUJIUXfwx4WQ63albzscQEF5mgkX7SqsToJRC/bkBuQf60VJtp5nPUp25jdTq7gHU0HkWFTSYamUWDUIpOiYF90LyimMLeEKZ0gqJ0MoFQ1F7STkbSORF0/Md4u6PYHz0fGacJn0WuTwOnjmTQn6/CXL8Cz5SPNWKIkEAB5qUU6Q+VYdjt11JwLFUl7/nLGx6AleD5TwkhRi0zLpBkF62SAJBzNG2+8gUAgfv+RQCCAN954I21G5Qv+iAl2l2pFo9cWwDJ+quE2dZqOGURHEmV8hKOJnGwkT2EpBQjXr0aNHegGSSDcgCFRY7fYhZCacwNP45xf+4u51q+FLJFDb3WDw6mO6EUmW9UrwxblFglDZ01NTVi0aBHmzZuHKVOmYNCgQbDb7XC73bhw4QL27t2Lbdu24b777suEvTmF+iDcJVKa1b5exhHbu19G7OoUQRkatk9/UJxJo0Y8wCyhmJHQLipZNRf9NAZayOSiJpkkEKY8t6WazKPGQWxqgOQOp+2ylCJzvyWod7erncMQS0T2qSgAdGGnvqvT2iPP55jyykybk3MkdDRPPfUUHn30Ubz33nt45513cPr0aTidzpDW2bx587B69WqUlRXmIVcHe53hbprDrUJM6Ylche3VF7LbCW7gMFAcp3E0dPCcZrszeE7jZjHQUshdNiOKViOSQCbpnM/kS2GjecxEePds04zNUDsaJ4eHe0Q4mgKPp7UJVKhvDw056nzOMnVONszKKZJKBigvL8djjz2GVatWwWaLzrYoWAR9KX29sFmuQ9E0TMNGxbw+zh52NPtdLO6rKExHIwf8kCPqyS4FaDSpkkBq8jEJJIje6nuqQwANRSHiCy+DFoFCmUq/T2y5qbQlzkDv+Vxkr4uFHFxkjrSJKFH9bcy3TMxJhe5Mk9InY/HixfjjH/8IUczfL1I6EVtuKv/KwB6X+nym+2XmqOVH6twcAgUaOXNv+jBKGl7dsnuCnY+Kz5tHT8iEaYZRwsoYbVO+8zIozXkEAPgO7Ebg5NFsmJYTxFODYHv2ybQ5OUlKjuYPf/gDPv/8c9xxxx348MMPjbIp7zjuYeAMZpxUshKG6XXTzDMiJWn6myT04ZTfyytRGvHAQmdLm7r3kE5aczfQtlLv0vUa4Uk6SsaFQKKW7RRX2GdXHaTkaGpqavCf//mfeOGFF/DGG2/g/vvvx/bt242yLW+ILNTT2ynn28rGPFzbOoCigGmqL1HkqlZsbc6IXbnGtQCNE17lb8FAxrwYbQHyHbWj2efiwEfsaAv1lOaMj0FbcJFZFqtlO6FzHTanTJmC2tpafPOb38Q///M/42tf+xqOHDmSbtvyhgMJOuqxvfrAPGFaJk0yBHU2zR6XdlXr3bU1w9bkBptVu5nJDkETn+9ODDBL6K3a0R4mO1oA2pbtk1Ut22mbHfaF92TJqtwjpU9LU1MTjh8/jhMnTuDEiRM4fvw4GhsbUVpaiu9+97uYOHEifvSjH6G0tHCqxL0i8IUnXIgVmdqaL9lGephqRmuKMcfbBZgoGQFZKU68GqDRx1SghzVBNreGQyO3lXaPBAnrzAUAAO/OzaExigJmFAtYe1P5rO9yctrsKlGALIoFV5QYs2U7y4LiokOMhUpKO5q5c+fiF7/4Berr6zF9+nS8/PLLqKurw7vvvotPP/0U/fr1w7e//W2jbM1JDnvCac2DY3TTzFdMESrDZhqaRl6R4bNC47yPxrmgGoCJkjErD7MN9WBK9LXrNOc07drCXcnZDven72fCvKwhi9pFpLplO6CVHTINyX6L7lwipZli//79MdObOY7D6tWrMXny5LQYli9oRDTt3WOiice0Ij4UNjvgYvFARJqzt24XmNLyKCeV7/gO7wNTWq4Z296uTWnXUzY2DR1ptGkZY5xNgJWW4ZUoXOOZgivclXnt9/uAK9yyvcYiaFK+mSrSeVRNSjuaZGpoCk2Kpk5VER5ZqJfPYbNYqHc0hz0spIgNnHjjWrfUPhOuXoL/xGHN2BHVOcXMGLsZ07Du42g4GpjiiJ991p3xbFmvebw3TrYZQUvaK6xGjYpd9NfdaBEonAsq2zKQMa4AOuoNMEsoY5RVrFOkQ78/oLS2LhREGTiucjRjdfrDc4Oiu5bmE+ax0dEJdY1YITkaKUKtWZaB/erzmTzvpmo0hVnKmyauBMJ/vpE2EVZV6MQ2/44sWGQ8FKVVc1Z3XuzuMXo1Z30MvJISNqliJfTkokNITEV+a1zpVfpPK+JBBZOZj3sYtAmFUfUuNjVoHtf7aTTwYTWIUbbCWWR1hpxyNJIkYc2aNVixYgUeeeQRXLx4UXP9z3/+M5YuXYrly5djy5YtWbIyzECzhMFmESwl46tV2hUPxXbf1d4EVYjwYIG2+D3iDq8qbrELurVT+oN5hI79ZayMkUGJHQmUJnxUSOxT7WYmOniwkX8qKqem1qyT9Kfknnvi54SvW7euy8Zs3LgRgUAAtbW1OHToEF566SX87ne/AwA0NjbizTffxLvvvgu/34+HHnoIs2bNgsmUvcpbByPjv4Y6QQHdpvdMJI4lS+E7vA/C1UuhMXXbgMNuFqLcfX//WKjb9t7STUOmTI/euuMzivhQkeouJ4dFpeGwkSxJ3UrzTBYEyIIARISF1Q52SsTZLG2zd6u/QTpI2tH86Ec/inlNTpN6a11dHebMUZROx48fj2PHjoWuHTlyBBMmTIDJZILJZEJ1dTVOnjyJsWPHpuXenSVqJdMNMdWM1jia/iYJ5ayEZoGGW6Jw1sdECUnKPN8t6giE61dAWe2aMVnWJgLcEqMtAMWZDbXNaCiahmPJUsgBP9ybwpJTM4p5/PcNpeHhXicHQQ5/D9yf/AXW6fPAlFVkw+S0497wQdSYX9K2bVafz1BmCyyTZmbEtnwiaUczdarStOvgwYP4/e9/D4/HA1mWIUkSLl++jK1bt3bZGJfLBYfDEXrMMAwEQQDLsnC5XCgqKgpds9vtcLlcUa9RW1uL2traLtvSZfI9bKKCjuiPTlHKrmZzUDr+kJuNcjTujevyPutO8vngO7gnavxqgEaLSq15kDn6fMYyZZZuLUo+QpnMoKw2yF4PAGCwWUIPTsINXlloHHWzmnBq4Nxp0DY7uP6DQDuKYr1s3nLYzSIgK9/varOIXqbwQtu+4M5smZXTpLy/e/bZZzFhwgS4XC7cc889cDgcWLx4cVqMcTgccLvD3RolSQLLsrrX3G63xvF0sGLFCqxduxZr165Ni02dgRswBBTbvWPXEwuhcFPSP+BV72bG2MKyI2rYyu5bR0FR2sZ++yPOaWSvG/yFL+Gr25lp0zLCPnVaM8k2S4qUHQ1FUXjiiScwdepUDB48GC+//DJ27NiRFmMmTpyIbduUpkuHDh1CTU04PXTs2LGoq6uD3++H0+nE2bNnNddzCbb/wGybYDhTVRPNYTcLl9h9dnBh9EPC6iLdsTphs3xPa9bDGhEOUp9L1BVYQsg+TVpz9zyfSzcpf0LsdiVeXV1djTNnzmDSpEmg03TwtWjRIuzYsQMrV66ELMt44YUX8Nprr6G6uhq33XYbHnnkETz00EOQZRmrV6+G2ZzfMfB8ghtUA/58uOtmFSdjuFXAKa8iwbPHyeK2Uu3qjr96CVyf/pk21VAkWbuijeymyPToDdOQ7udo6KJizePx9nAztNNeBk6RQhGjOGY54Nd7ibwjsnYGABoCFC6qZIfGxTifI2hJ2dGMHTsWTz75JL773e/i7/7u73DhwoVQeKur0DSNn/zkJ5qxIUOGhP6/fPlyLF++PC33IqSGecQYjaMBlGr4U8Hso51OLsrRSG0tQDdzNKe8Kll4NloW3jppRjbMyjgORukketKrdJc86GIxt0R5/yM7kOYbrk/+AtpRrBv+Vu9mxtoFmElyWVKk/Gd65pln8Oijj2LQoEF45plnIEkSfvnLXxphW95C2+yJn9QNUMuu7HFG9yjpjr3kNbIjDv3zmUJBfU53oDuFzyQJUnsrZJ836lLk+6+BpDTHpFNnNOPHjwcAzJ8/H8888wwGDx6cdsPyFfPo8aCYbvSli8MQS7gi3i1RmkNyABCu1EMKZip1F9RtmwvtIJjt3U/zWK3td0CvcDPPMy8lj1vzWJAVIc0OIt9/U83ojNiVj6Q8Ix48eBD/+q//ira2Nk39TDoKNrsDXHXhOF2KUnY17zUrZ2U7nZxm8pEFHp6tH+d9mnMHbQKFL7xKfJ6GHHU+0+2JcBxjbOH+RJcCDG4EKPQwdb9dbAdfeBi4g7JDPTgJ1RFp7dzAodkwKy9I2dGsWbMGS5cuxahRo0Dl+YqF0HWmqxzNPicL6BeT5yVSRJ1WnUs5jwCAkVYRxd2o91BnMNGKKkKHgvkBN4c7TOG2EZI7us4tn9kbIaIZOf2R+TA2KTsalmXxt3/7t0bYQshDxtm1q9rrARq9Irpu5qMsCV9/Dv7jhzRje2J1UywQ9ELCkxwqR+NicUdZ9+gyqseOdpLW3FlS/vYPGzYMp06dMsIWQo5jm7s4qqGTmdZqn+mKLMr51xxLbGnWPJZkYK+qMHW6Tv+RyMZo3Q2mV9+osYkR9TT5nv8R2dysgws+GueDac1mSo46n2EqexhuWz6T8o7m0qVLePDBB9GnTx9NHQs5o+n+0HYHrJNnwbVeq7owxSGEwgr7nCzuLe9+q9ozPgatHWnNjIRhEWnNpprR4AYNy4ZpWWWoRUQRI8Ep0mgW6Kium3LAD9BM3ihlxFIz2NIWFu+dXsRrWoIAANsz2gkTwqT87q9evdoIO/IfmoZl/NRsW5EVphbx+M11RWTxgFsrsggAstcLKs80r8SbNzSPd6t2M1OKdNKaGSbvwoPpgAnq3n3erkzEdW4WAy3hhYZ704egOBMoqxVMVS+YczwzS2y5GTUmy8CWtnDY7NYS7W7GPG5KtytMTjcpO5oOcU0CwFRUQbzZCACwjJ0MtmefLFuUHfqblDTnBp6GR6Jw3MNgnKrjpP+Lw7BOmZ1FC1NHjqgKV6c1T9NJa2aKu4eAZmeYpHI0B1wcHqzQ7mhlPgCZD0Bqb8tpR9PxXY7krI/GpYCyhbHQMqapzucsU2Z1a127dJGyo1mwYIEmu4KiKFitVgwbNgxPP/00evQonFglN7gm5oezkKAoJQvnry1KKHWvk9M4GsiA2N4KCAKY8tzvOhnZkjpRWrNtwZ2gzZaM2ZdrqM9p8rk/UWTdTAfqsNnMIh4W1caVIg3OkiLlv9LChQsxffp0/PrXv8ZvfvMbzJ8/H2PGjMHYsWOxZs0aI2wk5BjmcVOixqaqDsf3RSQEiDdvwLtjM7x7thluWzrgz2mTXfap05pt0WnNheJkmPJKcP0HRY33MyltAwClcPeUl4l6Tj6zy6kOm3W/88dMkLKj2b9/P55//nmMGjUKI0aMwLPPPoszZ87g0UcfxZUrV4ywkZBjcH36g+K0nU0n2HkwQbXjMz4WzXncSz7w5UnN4z2qiWZ6gakBqKFoGuYxE0BFdLWlKGCiPXbbgLxB5yPbzFOhbDOOkjUFyYTkSdnRuN1uTcMxl8sFny9a5bTQoGyOxE/qxjgYYLQtHHKqy7PJRpZl+E8chhShbyVGqDVPjUhrLsQEEFPNmKgxdThRLTyZ76hbIIy2CbCSSFmnSHk2ePDBB7F8+XLccccdkCQJGzZswLJly/Dmm28WrOYZbbN3m26KSaOz+pvi4EN6Z3sjesl3IHlcoHPQKUvNTeAvnoXkateMq9Way3XUmgsRrv9A+I8d0IxNdgigIEMGhRMeBi5RWXzkE5LLGTVWp3Kak0hLgE6Tsn9+4okn8Mwzz8DlcsHv92PNmjV49NFHMWHCBDz//PNG2JjzUAWi1qyGtkenK0+JOKeRdIr3vHu3G2lWp+nQ7YtM7ogU0YxMa2aqehluWz5Qwsqhdt4SKI34ZL4gNlzVPJZl7c6chM06T9I7mu9+97v4t3/7N9xzzz2a8e3blYmjEAs2KU7JstKbdLs7lkkz4D9xGMLVS6GxYRYRpYyEVpFGm0jjjI/BcGvEDkDMry/rHtVEMy0ibMYNqsmbQsR0Y7v1Tni2fKQZm+IQQv2J9qr60+QLkVln9X4aTYKyFrfTYUeqRs53KYQMkfS35PHHHwcA/OhHPzLMmHyDKSmFZcrsvEjZTTcUZ4Jp8HCNo6EpZbLZEEwH3edkox1NHtEiUDgZnDj10prZHoW7m6Et0Zl2Uxw8/rdRGd/v4iDL3rzuFLBfdT4z0cFrUrZpu6PbiYYaSdKhszFjlAPAqVOnonfv3pg6dSo8Hg/27duHkSNHGmZgrsNW9ijIinBAae9rGjlWM6YWm9zpzJ/widTSFDW2z6k+CBbhYMjqNR6jbCJstPI3auBpXArk9/ci3vkMZbFm2py8JuVPwpo1a/DKK6/g7NmzePbZZ3H58mU888wzRthGyAMihSSnOZRe8gDwhZdFI69d0kYWQ+YCorMtKqUZ0NZPFFqTs87ARqQ578mjhYYsaYVfvZL2fCZyN8sNHg4AhZcE1ElSdjTHjh3Dj3/8Y2zYsAEPPPAAXnzxRVI/QwhRzMqYoFr9bW+PmGxy0NH4D+2NGgtI2rYAs4qJo0kG9TnW55HvfQ4iSxJ8xw7Af3ifZrzOxSEgK4ukgWYRfSOanLGVPeBYsjSqnoygT8qORpZl0DSNHTt2YPr06QBA6mgKGLqoOGpsjmpSzofJRo9DbhbeYDfFPiYRA83RrQ7oopJMm5XzzCrmQzvaYx4GTRE7Wl51ppcLiE03IFy6AOG6drGsXiBFLjIKsXaqq6TsaKqrq/H444/j8uXLmDp1Kr73ve9hxIgRRthGyAMohoVl0gzNmPqLedjNoi1CJSBw5kTUFzub6NVPaCaaouhuirY5i0Bx+elEjaSMlTEuuKOVQWFbxEKD//KLbJiVEqIM7FKdz80uIr1nukrKjubFF1/E3XffjTfffBMcx2Hy5MkFWz9DCBKRDFHJyRhtVSYbCZTmrANQJF58B/dkzLxUkWRgh8rm2RErWrZvNeg8a3tgBKZho3TH56vSmj9r04aWJLcLrvVrIbbchHvrxzEbjWUCvv6cbv+Zox4G7cEi3UpWik5rJkKaKZPyX8xms+G+++5Dv379AACrVq2C1UoyMAoZ2mKLGptTkjh8FkstN5Po7WZOehk0B+snShhJI60DACwp0gQAmIbqRzJmq8JnRz0MbvLROc6BMycgez0Q21oMtTEeka26O1C3bJ5ZHF2kW6i1U12BuGZCl6EdRbDNXawZU4cb9rlYeHRyADyfbzDatITIQvSKWj3RzCjioyTv9VoaE8KUszLGxgmfKRdyN1VcvQOfVUSSQNIBcTSEtEDbtfplfc0ShgR1wXiZ0mRwhZAkiG2tAAChqQHePdsyWmkdK2yjVh+eVaxNa3UsWarpx1To2G+/X3d8nircuFPH0YjNHXVLueVwrvhpXFE1ORsfqW9GdjOdgjgagmHMKQ737ohKcw4i+xW1ZN++HRCDwpaZIHDuNNwb10GOUGtuFyic8YWbnEVNNAQNsYqV1Qkhhzws3LmX1a6LWnJool2AKeLXs06elWGLugfE0RAMQ53mvMvJIRCdIYwoGegMHQ4LQQHFyLYAh9zhJmc1VqIG0FmqOBnDLIqTFmQqdusAnoecQ/p3kSKqkVBmcybN6TYQR0MwjEFmCX1NylLWK1Ga3h7Zwrv3c/BX6oGAHwAgXKnXXD/g1q5oCYnhhgzXHZ+pKt7UC58BgO/QXrg//cAQu1LFLwEH3bF7DwEAZSqMbqrpJvvf/CA+nw//+I//iJs3b8Jut+OnP/0pysu18ibf+MY30NraCo7jYDab8eqrr2bJWkIyUJSyq/l/TUoo6vM2DjN0vryZQvJ6IN5s1LQCkNpbNc85oA6dEFn4pDDXjAZTVAJfhMLCzGIerwdFNne7WIgyohIrconDbjakBtDfJKK3SbsFt85aQDLOOknO/NXeeust1NTU4Nvf/jY+/PBD/Pa3v8Wzzz6reU59fT0+/PBDchibRyiORplsdjk5iLJXM9mIjdchtTVnxpgEiQaNPIVLgXDb3jE24miShe3dDyaPC4HTJ0JjwywiKlkJTQINp0jjqIfBeLv+YY1r/VqYx00B16e/4ba61q/VHVcnrEzTyTZjiomuWWfJmdBZXV0d5syZAwCYO3cudu3apbne1NSE9vZ2fOMb38CqVauwZcuWbJhJiAPbtzpqbIRVRAWrrAxbRRonPNq2i3z9OV1By2xwULWbGWMTYM6Zb0d+YBqirauhKGVX08GuBHJE/NlTkGU5K2c2oqxNWJlKdrNpJSs7mrfffhuvv/66ZqyiogJFRUq1td1uh9OpLaTjeR5f//rX8dWvfhVtbW1YtWoVxo4di4qKCs3zamtrUVtba+wvQNDFMnYyXBFnHjQFzCzisa5FOUTd3s7hlhirWuOJv6NRH1iT85n0ML2IxwfNynu/z8Xh7xFfFzHwxWHwF8/Bfvv9hrTfiFRp7mC3k8UNPlykOy7i/ef6D0q7LYVEVhzNsmXLsGzZMs3Yt771LbjdSqW42+1GcbFWrLGyshIrV64Ey7KoqKjAyJEjcf78+ShHs2LFCqxYsQIAMHy4/iElwTissxbAu2OzZmxWscrRODl8o5cv5xpieSXFtg70DoIJiWGqekFsvB56PN4ugKVkCDKF834GjTyFKi62w+cvX1T+I0tId8BFaGqAb98O3WsdzhAA7iwLRKU1Mz17p9WWQiNnggMTJ07EZ599BgDYtm0bJk2apLm+c+dOPPnkkwAUR3TmzBkMHjw443YS4qMXx55gF2ANNsS6GmBwwZ/5j50sCJDjqIxvb+fgC6o1DzCLGGbJk8KPHMdKA7eozrr2x0pzzgBiwzXd8asBGvuCYVMKMu4pD+g+j9B5csbRrFq1CmfOnMGqVatQW1uLb33rWwCAn/3sZzhy5AjmzZuHAQMGYPny5Xjsscfw1FNPRWWlEXITE62tSdgRJ1YveYxpj+vZvhHePdtiXt/YGhZ/XFgSyLkdV77AlFVEjU1xqB1NvCCKsTVLfP053fF1zaZQ7dRUhxCVbQYA5APRNXIm68xqteLf//3fo8Z/8IMfhP7/wx/+MJMmEdLI7GIen7Urk/kOJ4eHe/h1nydcvQSMm5L2+8teT8xrzTylmQAXlhJ9q87CDa4Bf/EsZH949zjFIeD3Dcr/98dJc5ZcToBRkkX8xw7BPPIWUKb0FEjKgn4oVJa1i4x7y/U/l4SukTM7GkL3wTprQdTY9CIBTHDFelKnxbMa98a/dun+Ms/HnFj02NxmghRc0Y61Ceilt6IlJAVFUWB7aM8zBltElAUzD9tFGme8jN6PKgQP64Wr9fCfPJoWm4SmG3Bv0C8KPeen0RRU6i5iJE2HUDW0zZ4WWwoV4mgIaUfvnMbBaHXDYlWKA4DMdy1G7t64LubEoseG1rAti0pj35vt3a9LdhUKckQIjKaAyarw2U5nnHOaNIqqypIE1/q18O3bHvM5asmZyQ5Bd6dlv+0u0DZH9AVC0hBHQ8gYaqHFHfEmmwxy0UfjtE8Jm3GUjHklscNmpIVv55muKoB8v9kEbwZyLeQk+h3tTqBtBiBt4btChjgaQsZQ9/Y46GbhyoHErg2qDpAzingURYhoWmJZRfMAABtTSURBVCZOz7RJ3ZK5xTx6c8ob3i7S+Euz8ZO30NQQ97pLBI6pCoj1UtrNBpwXFiLE0RAMgS6NzgjsYdIq+u5NIdXViD41UsRB8CKdJAC2Z5+037e7o1doyVLA31SFD9prm8yG72rU9Tx61Lm40NncMIuAcjb6M0bOZtIDcTQEQ6AY/QPf2cXJpTn7Du/XPHZ//B48EYWgySA622JqWx3zMGjgwwfBsUInhNQw1YzRHV9cGkBPTjnsbxPpUBFvLIQr9Z1u9SzLMsSmG3Gfs1eVaRgrCYAymXTHCalBHA3BEOgYAoTqc5o9Tg58jAQv4Wo9vBGHuJFKy5HIAX+UU/Fu3xTz+Z+qdjPzi/moanDbnEVx70fQJ5bCMUcDD1WF054/aUk8iXt3dk7TULh0Pv7rSpHaZvqLDJIEkB6IoyEYgqlmtO74YLMUitW7JQqH4vSoSbQiDT3P2Qbf0TpIEbUy3r2xs40CErC1TR02i842o6zWpO5PSJ6FJQGYKSVEdc7P4Jwv8RTkWr8WYmtqCt/+44fiXv+w2Yx2Ubl3L07EKFt0HM+++L6U7kmIDXE0BEOIJYhIUalln0kxZGNkSQoJJPoP7IZw+WJUlpF4M7aj2u3k4A5KzvTiRIzRmWiiun8SuoyN0So6b2pNLjTFX1Sq+mVJgnAjfPbiP3kMns8+SckGXlLOiDpYWenXTWuOFf4lpA5xNATDMI24RfcwdVbEOU28c37Z79Mo7sqyDO+ebXB/8hd4tn3aads2tqlrZ/gohRHKbA5NNJTVBlPNqE7fqxCxzlwAbtAw3Wu3lYR3j5vaTJBSyPPgz56Er25nKKOMP38akscN/spFBM4q7SYklzPeS+DTVlOoSLOMlbCkjGibGQ1xNATDMA0aBtu826PGb7GJKGYU59Ek0Djti71ylNxOTTMtiCLE5iYAiqyMcO0yZF5xXMlmprULFHapdlILdcJmtnl3hP5vn39HVK8VQnyYklLQjiLda1MdAoqC738DT+O4J/HOQXIq53MdyQGyXysV4z9Sh8DpE5B8Xng+3xD7dWTtbmZZhT/qbI6QfsifmJBxGAqals7b42Sf+Q/vA3/+dMzrvkN7Q0oC4g19dd5ItrZzEIIte0dYBVSbozMSSNgkDcQQouRopa6mg41ticNnkrMdwvUrEBuVnYxaS02N//C+uK9zwM2GuqjaaZlom2UI4mgIWUGd5vzXZhNahSTPQ+I8LZnkAVkG1quynfR2M4T0wPaKLdmj/rtvajXBn4S8nNgaTnUOnDqmm7besduNxfs3w+/97WUB2Ml6IiMQR0MwHL2ixykOHpWqFs8vX00uwyuyqZqaZDTSjnkYnPSGJWduiyM5Q+gaFMPAPHqC7rVxNhF9TOHsw20J2jwDiLuzTYaGAKXRWbuP7GYyBnE0BMMxT5gG81htIzszDXy/bzgd+bN2E7a0JZ5sJHfX+tW8ezMcn19YEkCpTjU4IY3ECJ9RFLBEtav5KImamq7y1xZzSAlgop3XDZkSjIE4GoLhUBQFru+AqPFpRQLuLAuvKn93zRqzgDMdXA9Q+Fy1cv5Kpf6KljJbjDOCEOL2sgDooNLzITeHKwZ2Xg1IwIfNYWd2fwUJmWYS4mgIWeWbvbwoC2YgNQq0plo/3ay9qV3RDrZEezXz6PFEESBDVHGyRsjSyF3NtnYOLcECzSpWwswiEjLNJMTRELKKnQGWqXYWf2o0QzQgmtUQoDSKwV+p0N/NMFW9QHG50cKgELhLVcOyrsW49gHvq977e8r1CzQBgO1bTYQ0DYA4GkLWua/cH6qruMoz2JzEWU2qvNpgBR9MaR5uFWKKKBLSSyzdsw5mFPHoE5Qkcoo0PjJgR/ull8Yxj2IHS8ka56aGYjmYR42HdeYC3fovQuchjoaQdWwM8KBqh/G/jZa07mpOeRlNrcbf9/KCJuoyGYHp1Rem4WNgGjlW/zqlPSt7uym97z2g3c3MLeZRzunfgBs2EhTLguI4sqtJM8TREHKCpRUB2GhlAqj3M9jUmp5djSwDv70WTp2eXRTAOLt+fIapqCKJAGmGoiiYBteAqx4c8zlLygIhpYgGnk4q+zBZ6v00PlHtkuKlNHMDhqTtvgQtxNEQcoIiRsYy1a7m9UYLhDSsbHc4ORwJhk0YyHiil35FOQBYp86JKQZK6BoUTYPtF515CAAWGnigPBzO+u11K5r5rm85JRn42RVbKGQ60irgFl3x1KCNMVKxCV2HfKsIOcNXKn3hs5oAk1S/kngIMvBf18M7lHvLA+gfo3aC7UU6aRqNeczEmDubByr8KAsW8LYINJ6/bOtyCO39ZhOOqxYZ3+/riVXWQzAY4mgIOYODAZardjVvNloQ6EJdzQfNJlxW6Vp9rUfs3YxlwvTO34iQFBRFxexTVMLK+GE/D6hgXc0BN4f/bYzfgTMel/00ft8QDpk+VOXXTWcnZAbiaAg5xYMVfpSo4vWdra245KfximqieaSHDyVEBSCnmeQQ8HBVeKHxxg0LDrriZ63pIcrAC5dt8AX7DQ0wi3i4KvYig2A8xNEQMo5jydKY16yMsvrs4I+NlqQEF9UEJOD/XgpPNP1NIh4gulY5AcVxYMorY17/Wg8fxtuVYkoJFJ67bENzsoKrQd68YcEX3nDI7Jl+HtIKIMuQPz8hY1inz4Nl/NSEz7u33I9yNtyvRq1PlghJBn511YozvrBw5pr+ZKLJJazT5sa8xlDAD/t5UBrc1TYLNF68ZEu6Odr2dg5vqEJuX+/pQ41VPwHANm8xbPMWwzprAawzFyT/CxBShnz9CBmDKasA2zu2dHwHFhqaUMcrDVb8S70tYSaSEAyZfNwanmi+0cuLoTEmmtD9Js1IaBMhc1Ryyi6k47xmv5vDnxKc1wQkYK+TxfOXbJCDMkPjbAJWxNCzAwDa5gBtc4ApLgVTUpq+X4AQRc45mg0bNuB73/ue7rU///nPWLp0KZYvX44tW7Zk2DJCJrmrLIAB5rCD2NpuwjfPFekKLzYLFF5rsODh08XYpCrMXFQa0KTNxoLt0Ts9RhPSxpQiQRNCfe2GBR+1mKJS3kUZ+M01C+7+ogT/30UHfMFU5j6ciH+pdseUmiFkltRP2gzkueeew/bt2zFy5Mioa42NjXjzzTfx7rvvwu/346GHHsKsWbNgMhkvL05IP5TVBtnriXndRAMvD3Lht9et2BAsuGvgaTx53oHFpQF4JAp9TSIkUHjjhgVuSTuj3Fvux3d7e2Oms9Kl5ZBam9P2+xBSg2I5yEJ8Ycu/7eHDUTeLIx4WEij8/IoNrzVYsLTCj7vLlQLfFy/bNIsLAHDQEl4c6CbJHzlETjmaiRMnYuHChaitrY26duTIEUyYMAEmkwkmkwnV1dU4efIkxo7Vl7boKrIso7m5GZJEUiIBgKZplJeXp62ozTbvdghX6+E/UhfzOaWsEkKZXxzAv1yyIyBTaBJo/KkpdvV+MSNhZaUfKyv9CWsmrLMWECWALEFZLJBd8R0NQwHP9nfjH84WoVFQdrJNgpK2/IcbFpgpaBYYfTgRY+wiHqr0kV4zOUZWHM3bb7+N119/XTP2wgsv4M4778SePXt0f8blcqGoqCj02G63w+XqWhOseDQ3N8Nut8NiIRMRAPh8PjQ3N6OioiItr9fRoyaeo+lgZrGAFwe48cOL9lBoJJJ+JhFf7+nDrCI+6YN/ppjE5bOH8j5SnCluZ9QqTsYrQ514v9mEv9w0h6T+BZnShNHuKfPjyT5Ewy5XyYqjWbZsGZYtW5bSzzgcDrjd7tBjt9utcTwd1NbW6u6IUkWSJOJkVFgsFjidzqzdf6JDwK8HO7GlzQQLLcNEA+d8DG7yFCY6BHylwp9SZpl5jH6LYUJmYPsNQODkUVhn3wbPlvVxn1vCyvhqD2WXuqnNhHeazDjnZ0LXHyj341u9U3MydFFxZ00ndIKcCp3FY+zYsXj55Zfh9/sRCARw9uxZ1NTURD1vxYoVWLFiBQBg+PDhmTaTYCBDrRKGWtNTeMcUlaTldQidwzRoGLiBQ1MKxZpoRYBzSVkAbhHgZQosBTiY1M9iKFPnVQcIqZNzWWeRvPbaa9i0aROqqqrwyCOP4KGHHsLXvvY1rF69GmZzYXxY/H4/FiyInedfW1sLns/PjoFMFjK+aBIyywm6ct5nZ5QzvM44GULmoWRZ7rbv1PDhw3Hq1KlO/WxjYyOqqqrSbFHn8Pv9WLJkCTZv3qx7fcGCBVi/fr3hjteov4nobIN3+6a0v64elNUG+/w7MnIvQnK41q/N2L1MQ0cg8OVJMBVVsE6dk7H7Fjp5EzrLJvyVixAuX0zra7L9BoDrqy+bDihnUN///vfR3t6O6upqAMDevXvxH//xHwCUw/mf/vSn2L9/PxobG7F69Wr8+te/xpo1a3D9+nW0tLRg7ty5ePLJJ9NqtxFkMoxlnTI7Y/ciJIft1jsh8/6MLDbostjyNwTjyPnQWaHy3nvvoaamBn/84x+xcuVKAMCZM2fw85//HG+88QYWLFiAjz/+GMuWLUNVVRV+9atf4dq1axg/fjz++7//G2+99RbeeuutLP8WuQeJzecetMUCiiPvS3eG7GiSgOsbf/dhBGfOnMGcOcrWfty4cWBZFj179sTzzz8Pm82GhoYGTJw4UfMzpaWlOHr0KHbv3g2Hw4FAIHFVfK5gnToHcsAP36G9ht6H4tLXvZGQPmiLBUxVL4iN17NtCsEAyI4mRxk8eDAOHToEADhx4gQEQcCzzz6LF154AS+99BJ69OiBjuM1iqIgSRLWrl2LoqIi/PKXv8TXv/51+Hw+5MsRHFNRBbZ3P5iGRqtCEAoD6+SZAOlw2i0hO5oc5W/+5m/wT//0T1i1ahUGDx4MjuNw3333Yfny5SguLkZlZSVu3LgBAJg8eTKeeOIJrFmzBk899RTq6upgtVoxYMAA3LhxAz179szyb5M8pmEjITRcgeRsT/9rDx2R9tckpBkDW2AyFVWgWGXKI4oQmYVkncUgl7LOcoVM/U082zca4mjsdzxA+sLnOK5P3wfE+GrbKUPTgCTBfvv9oGga/OULYHv1CzkdgvGQvzShYCBOpgDRCcVx/QZm3o4ChwRECQQCgWAoxNEQcg6KSc9G2zr7ttD/7YvuTctrEvKY7ntKkPMQR0PIOcwTpmseM1W9OvU66kJQEo8nELIHcTSEnIOOUM2mbbZOv1ZnnRShe2CdPCvbJhBAHA0hx7HOvBVs34GaMcuEaUn/vGXCNNhuvTPNVhGMxjZnUad+Tp3Cbho2CkxFFWiLNV1mEToJcTTdmLNnz+KRRx4BAKxevTqvlAIAgLbZwZSUgSnRqi2zvfrqPt86bW7UGMUwUTskQu7CVPQAoIifMhWpp9JrJIaCZzKWaXPx/7d3/zFR1g8cwN/PAxwHdyoei0mZU+mLQM4Uh2VfsdwXRZ0/yrlBV+dA01UuUbQoVGA20jaHLRoStCJOJJbdZj9ctdTpwsZYqUNDO5WdYhTS8R2CHh539/2DL1fngYDy8Hmw9+u/57nnuDfHj/c9vz6f4McSIAUE9PEsUhoPXP9D7NmzR3SEQdElP3PHx7Uzn4S77b+Qx4RB1obC0+VEwNihmf2TxNFOT4Dn5s1+S0ET/Shu/XrWd6UsI/DhSej85bTvam0I5AcfHuqoNAgsmgHYV3sZpdUNuOEcuhvJQoMCsPbfk/BCwoQ+t7FYLDh69CgcDgeuXbuGVatW4fDhw7BarXj99dfhdDpRVlYGWZYxc+ZMbNmyBc3NzdiyZQs8Ho/PzZU9UwnYbDbs2rULbrcbbW1t2LZtG+Lj47FgwQLEx8ejoaEB4eHhKCwsRIDAT4BSP0ORBEaMAyL6Pv+i+VfcUEeiYSAFBELSd8+cG/zoDNyy/oKupsYBPVf7WAIkWUZARCRczU0czkZF+JMYgIray0NaMgBww+lCRe3lfrfr6OhAaWkp1q5di8rKSrz//vvYsWMHDhw4gMLCQpSVlaGyshJ//PEHqqur8fHHH2PJkiUwm81ISkry+3oXLlxAVlYWysrKkJ6eDouley6QK1euICMjA1VVVbDb7airqxvS7/deBU3yn031TjjczMgn6/TQTp8FSaPxrrv990AOMyBw3IO+6/Q9U7zzcma14B7NADyfMEGRPZrn77A30yM2tnuQyVGjRiEqKgqSJGHMmDG4ceMG7HY71q1bB6C7kK5cuQKr1Yrly5cDAOLj4/2mCoiIiEBRURG0Wi06Ojqg1+sBAGPHjkVkZPdsl5GRkejs7Byy73UoBMdMhbPhV9ExSADdf5ag48gheDp9p/HWJT8DSBI6T9X4rJeC/l9MQ3Q/Ft07/iQG4IWECXc8xKWkvoZNkSQJkZGR+OijjxAUFASLxYLY2FhcunQJJ0+eRExMTK97Jfn5+di9ezeioqLw3nvv4erVq3d8HSI1CHlyHtztbXC1XOteIUnew6uamGmAJHsvZQ+a+AggywiaMFlUXLoNi2aECgwMRFpaGkwmE1wuFx566CEsWrQIGRkZ2LRpEw4dOoTx48f7PW/ZsmV45ZVXEB4ejnHjxqG1tVVAeqLBkbUhkLUhcLU0+z8WEgrt9FneZUmWoZn4yHDGo35w9OY+cPRmf6Lfk5655fWLVvS5jbv9OiBJkHX64YpFw+jWpV9x6/wZBE+NR9DDE0XHoQHiHg2NGMGPTgf6uRLurxPBdD8KmvgIJI0GgcM84y3dGxYNjRg85k6SLHOY/xGIlzcTEZGiWDRERKQoFk0fZFmGw+Hof8N/CIfDAZl3WhPRXeA5mj4YDAbY7XZcv35ddBRVkGUZBoNBdAwiGoFYNH2QJAnh4RykkYjoXvFYCBERKYpFQ0REimLREBGRolg0RESkqPt6rDMiIhKPezRERKQoFg0RESmKRUNERIpi0RARkaJYNEREpCgWDRERKYpFQ0REimLREBGRojh6M4ApU6aIjkBENCKdP3++/408dE+effZZ0RH6pfaMas/n8ag/o9rzeTzMOBTUnq8vPHRGRESKYtEQEZGiAvLy8vJEhxjppk6dKjpCv9SeUe35APVnVHs+gBmHgtrz9YajNxMRkaJ46IyIiBTForlLbrcbOTk5SElJgclkgs1mEx3Jh9PpxGuvvQaj0YiVK1fi8OHDoiP16c8//8RTTz2Fixcvio7i54MPPkBKSgpWrFiBzz77THQcP06nE5s3b0ZqaiqMRqPq3sPTp0/DZDIBAGw2G5577jkYjUbk5ubC7XYLTuebr76+HkajESaTCWvWrEFLS4vgdN3+nrHHl19+iZSUFEGJBo9Fc5e+//573Lp1C1VVVdi8eTN27dolOpKPL774AmFhYdi/fz9KS0vx1ltviY7UK6fTiZycHGi1WtFR/NTU1ODkyZOorKyE2WzG77//LjqSn2PHjqGrqwuffvop1q9fj3fffVd0JK/S0lJs27YNnZ2dAICdO3di48aN2L9/Pzwej/APP7fny8/Px/bt22E2mzF//nyUlpYKzQf4ZwS6C/HAgQMYSWc9WDR36aeffkJiYiIAYPr06Thz5ozgRL4WLlyIjIwM73JAQIDANH175513kJqaioiICNFR/Pzwww+Ijo7G+vXr8dJLL+Hpp58WHcnPpEmT4HK54Ha70d7ejsBA9dyDPWHCBBQWFnqXz549i1mzZgEA5s6dixMnToiKBsA/X0FBAWJjYwEALpcLwcHBoqJ53Z6xtbUVu3fvRnZ2tsBUg6ee38oRpr29HXq93rscEBCArq4u1fyh63Q6AN05N2zYgI0bNwpO5M9iscBgMCAxMRElJSWi4/hpbW3Fb7/9huLiYjQ2NuLll1/GN998A0mSREfzCg0NxdWrV7Fo0SK0traiuLhYdCSv5ORkNDY2epc9Ho/3vdPpdLh+/bqoaAD88/V82Pn555+xb98+VFRUiIrm9feMLpcLW7duRXZ2tipKcDC4R3OX9Ho9Ojo6vMtut1s1JdOjqakJq1atwvLly7F06VLRcfx8/vnnOHHiBEwmE+rr65GVlYVr166JjuUVFhaGOXPmQKPRYPLkyQgODobdbhcdy0dZWRnmzJmDb7/9FgcPHsQbb7zhc5hFTWT5r383HR0dGD16tMA0vTt06BByc3NRUlICg8EgOo6Ps2fPwmazIS8vD5mZmbhw4QLy8/NFxxoQdf1nHEHi4+Nx9OhRLF68GKdOnUJ0dLToSD5aWlqwevVq5OTkYPbs2aLj9OrvnxhNJhPy8vLwwAMPCEzka+bMmSgvL0d6ejqam5tx8+ZNhIWFiY7lY/To0QgKCgIAjBkzBl1dXXC5XIJT9S4uLg41NTV4/PHHcfz4cTzxxBOiI/k4ePAgqqqqYDabVfdzBoBp06bh66+/BgA0NjYiMzMTW7duFZxqYFg0d2n+/Pmorq5GamoqPB4P3n77bdGRfBQXF6OtrQ1FRUUoKioC0H1iUY0n3dVq3rx5qK2txcqVK+HxeJCTk6O6c11paWnIzs6G0WiE0+nEpk2bEBoaKjpWr7KysrB9+3YUFBRg8uTJSE5OFh3Jy+VyIT8/H5GRkXj11VcBAAkJCdiwYYPgZPcH3rBJRESK4jkaIiJSFIuGiIgUxaIhIiJFsWiIiEhRLBoiIlIUi4aIiBTFoiEiIkWxaIjuM4mJiaivrxcdg8iLRUM0DFavXg273Y66ujpF7za32+2w2+2IiopS7DWIBosjAxANgylTpuDHH39UdKBGm82GpUuXwul0QqvVQqPRoLq6WnWDvdI/D4uGSGFvvvkmLBYLoqOjsWbNGnz44Yf46quvUFNTg4KCAkRGRqKhoQEhISFYt24dzGYzGhoasGDBAmRnZ+PIkSPYu3evt0CysrIwY8aMXl+roqICtbW1qpoAjYgfdYgUtnPnTlgsFnzyySewWq0+j9XV1SE3NxdxcXF48cUXUVJSgvLycrS3t2Pu3LlISkrCnj17UF5ejrFjx8JqtSI9PR3fffddr4Nnnjt3zjt5F5FasGiIBBo/fjzi4uIAdM+mOGrUKGg0GhgMBuh0Opw7dw7Nzc1IS0vzPkeSJFy+fBkxMTF+X6++vh5JSUnDFZ9oQFg0RAJpNBqf5dvPp0iShNmzZ/scCmtqaup16mu32w2r1dprARGJxKvOiIZBz1Tfg5WQkIDq6mpcvHgRAHDs2DEsW7YMDofDb1uHwwGHwwGediW14R4N0TBYuHAhTCYTTCbToJ4nyzJ27NiBzMxMeDweBAYGYu/evdDpdH7bhoaGIjU1FYsXL4Zer8fx48eHKj7RPeFVZ0REpCgeOiMiIkWxaIiISFEsGiIiUhSLhoiIFMWiISIiRbFoiIhIUSwaIiJSFIuGiIgU9T/bBsBkD7SfoQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.subplot(111)\n",
"ax.plot(times, y, label=\"data\", alpha=0.4)\n",
"ax.plot(t_prime, y_median, label=\"median\", lw=3)\n",
"sns.despine(ax=ax, offset=10)\n",
"ax.set_xlabel(r\"time $t$\")\n",
"ax.set_ylabel(r\"signal $y(t)$\")\n",
"ax.legend(loc=\"best\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Mean and standard deviation "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Calculate the mean and the standard deviation and draw bands around the data."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"nbins = 150\n",
"y_mean, t_prime = timeseries.mean_histogrammed_function(times, y, bins=nbins)\n",
"y_std, t_prime = timeseries.std_histogrammed_function(times, y, bins=nbins)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.subplot(111)\n",
"ax.plot(times, y, label=\"data\", alpha=0.4)\n",
"ax.plot(t_prime, y_mean, label=r\"mean$\\pm$stdev\", lw=1, color=\"blue\")\n",
"# draw +/- stdev band\n",
"ax.fill_between(t_prime, y_mean - y_std, y_mean + y_std, color=\"blue\", alpha=0.5)\n",
"\n",
"sns.despine(ax=ax, offset=10)\n",
"ax.set_xlabel(r\"time $t$\")\n",
"ax.set_ylabel(r\"signal $y(t)$\")\n",
"ax.legend(loc=\"best\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that we can change the number of bins and the result still looks similar:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"nbins = 40\n",
"y_mean, t_prime = timeseries.mean_histogrammed_function(times, y, bins=nbins)\n",
"y_std, t_prime = timeseries.std_histogrammed_function(times, y, bins=nbins)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.subplot(111)\n",
"ax.plot(times, y, label=\"data\", alpha=0.4)\n",
"ax.plot(t_prime, y_mean, label=r\"mean$\\pm$stdev\", lw=1, color=\"blue\")\n",
"# draw +/- stdev band\n",
"ax.fill_between(t_prime, y_mean - y_std, y_mean + y_std, color=\"blue\", alpha=0.5)\n",
"\n",
"sns.despine(ax=ax, offset=10)\n",
"ax.set_xlabel(r\"time $t$\")\n",
"ax.set_ylabel(r\"signal $y(t)$\")\n",
"ax.legend(loc=\"best\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 95th percentile band\n",
"We can also plot a band that contains 95 percent of the data with [`percentile_histogrammed_function()`](https://numkit.readthedocs.io/en/latest/timeseries.html#numkit.timeseries.percentile_histogrammed_function)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"nbins = 150\n",
"percentile = 95\n",
"\n",
"p_upper = 100 - 0.5*(100 - percentile)\n",
"p_lower = 0 + 0.5*(100 - percentile)\n",
"\n",
"y_upper, t_prime = timeseries.percentile_histogrammed_function(times, y, bins=nbins, per=p_upper)\n",
"y_lower, t_prime = timeseries.percentile_histogrammed_function(times, y, bins=nbins, per=p_lower)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.subplot(111)\n",
"ax.plot(times, y, label=\"data\", alpha=0.4)\n",
"ax.fill_between(t_prime, y_lower, y_upper, color=\"blue\", alpha=0.8, label=\"95th percentile\")\n",
"\n",
"sns.despine(ax=ax, offset=10)\n",
"ax.set_xlabel(r\"time $t$\")\n",
"ax.set_ylabel(r\"signal $y(t)$\")\n",
"ax.legend(loc=\"best\");"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.5"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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