{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "**This is a fixed-text formatted version of a Jupyter notebook**\n", "\n", "- Try online[![Binder](https://static.mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.19?urlpath=lab/tree/tutorials/api/fitting.ipynb)\n", "- You may download all the notebooks in the documentation as a\n", "[tar file](../../_downloads/notebooks-0.19.tar).\n", "- **Source files:**\n", "[fitting.ipynb](../../_static/notebooks/fitting.ipynb) |\n", "[fitting.py](../../_static/notebooks/fitting.py)\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Fitting\n", "\n", "\n", "## Prerequisites\n", "\n", "- Knowledge of spectral analysis to produce 1D On-Off datasets, [see the following tutorial](../analysis/1D/spectral_analysis.ipynb)\n", "- Reading of pre-computed datasets [see the MWL tutorial](../analysis/3D/analysis_mwl.ipynb)\n", "- General knowledge on statistics and optimization methods\n", "\n", "## Proposed approach\n", "\n", "This is a hands-on tutorial to `~gammapy.modeling`, showing how to do perform a Fit in gammapy. The emphasis here is on interfacing the `Fit` class and inspecting the errors. To see an analysis example of how datasets and models interact, see the [model management notebook](model_management.ipynb). As an example, in this notebook, we are going to work with HESS data of the Crab Nebula and show in particular how to :\n", "- perform a spectral analysis\n", "- use different fitting backends\n", "- access covariance matrix information and parameter errors\n", "- compute likelihood profile\n", "- compute confidence contours\n", "\n", "See also: [Models gallery tutorial](models.ipynb) and `docs/modeling/index.rst`.\n", "\n", "\n", "## The setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:08.661595Z", "iopub.status.busy": "2021-11-22T21:09:08.660604Z", "iopub.status.idle": "2021-11-22T21:09:09.355080Z", "shell.execute_reply": "2021-11-22T21:09:09.355275Z" } }, "outputs": [], "source": [ "import numpy as np\n", "from astropy import units as u\n", "import matplotlib.pyplot as plt\n", "from matplotlib.ticker import StrMethodFormatter\n", "import scipy.stats as st\n", "from gammapy.modeling import Fit\n", "from gammapy.datasets import Datasets, SpectrumDatasetOnOff\n", "from gammapy.modeling.models import LogParabolaSpectralModel, SkyModel\n", "from gammapy.visualization.utils import plot_contour_line\n", "from itertools import combinations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Model and dataset\n", "\n", "First we define the source model, here we need only a spectral model for which we choose a log-parabola" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.362612Z", "iopub.status.busy": "2021-11-22T21:09:09.362317Z", "iopub.status.idle": "2021-11-22T21:09:09.363532Z", "shell.execute_reply": "2021-11-22T21:09:09.363725Z" } }, "outputs": [], "source": [ "crab_spectrum = LogParabolaSpectralModel(\n", " amplitude=1e-11 / u.cm ** 2 / u.s / u.TeV,\n", " reference=1 * u.TeV,\n", " alpha=2.3,\n", " beta=0.2,\n", ")\n", "\n", "crab_spectrum.alpha.max = 3\n", "crab_spectrum.alpha.min = 1\n", "crab_model = SkyModel(spectral_model=crab_spectrum, name=\"crab\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data and background are read from pre-computed ON/OFF datasets of HESS observations, for simplicity we stack them together.\n", "Then we set the model and fit range to the resulting dataset." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.366152Z", "iopub.status.busy": "2021-11-22T21:09:09.365835Z", "iopub.status.idle": "2021-11-22T21:09:09.452875Z", "shell.execute_reply": "2021-11-22T21:09:09.453053Z" } }, "outputs": [], "source": [ "datasets = []\n", "for obs_id in [23523, 23526]:\n", " dataset = SpectrumDatasetOnOff.read(\n", " f\"$GAMMAPY_DATA/joint-crab/spectra/hess/pha_obs{obs_id}.fits\"\n", " )\n", " datasets.append(dataset)\n", "\n", "dataset_hess = Datasets(datasets).stack_reduce(name=\"HESS\")\n", "\n", "# Set model and fit range\n", "dataset_hess.models = crab_model\n", "e_min = 0.66 * u.TeV\n", "e_max = 30 * u.TeV\n", "dataset_hess.mask_fit = dataset_hess.counts.geom.energy_mask(e_min, e_max)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting options\n", "\n", "\n", "\n", "First let's create a `Fit` instance:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.455137Z", "iopub.status.busy": "2021-11-22T21:09:09.454833Z", "iopub.status.idle": "2021-11-22T21:09:09.456105Z", "shell.execute_reply": "2021-11-22T21:09:09.456270Z" } }, "outputs": [], "source": [ "scipy_opts = {\n", " \"method\": \"L-BFGS-B\",\n", " \"options\": {\"ftol\": 1e-4, \"gtol\": 1e-05},\n", " \"backend\": \"scipy\",\n", "}\n", "fit_scipy = Fit(store_trace=True, optimize_opts=scipy_opts)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default the fit is performed using MINUIT, you can select alternative optimizers and set their option using the `optimize_opts` argument of the `Fit.run()` method. In addition we have specified to store the trace of parameter values of the fit.\n", "\n", "Note that, for now, covaraince matrix and errors are computed only for the fitting with MINUIT. However depending on the problem other optimizers can better perform, so sometimes it can be useful to run a pre-fit with alternative optimization methods.\n", "\n", "For the \"scipy\" backend the available options are described in detail here: \n", "https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.533196Z", "iopub.status.busy": "2021-11-22T21:09:09.462717Z", "iopub.status.idle": "2021-11-22T21:09:09.578563Z", "shell.execute_reply": "2021-11-22T21:09:09.578750Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 116 ms, sys: 3.69 ms, total: 120 ms\n", "Wall time: 119 ms\n" ] } ], "source": [ "%%time\n", "result_scipy = fit_scipy.run([dataset_hess])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the \"sherpa\" backend you can choose the optimization algorithm between method = {\"simplex\", \"levmar\", \"moncar\", \"gridsearch\"}. \n", "Those methods are described and compared in detail on http://cxc.cfa.harvard.edu/sherpa/methods/index.html \n", "The available options of the optimization methods are described on the following page https://cxc.cfa.harvard.edu/sherpa/methods/opt_methods.html" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.581348Z", "iopub.status.busy": "2021-11-22T21:09:09.580986Z", "iopub.status.idle": "2021-11-22T21:09:09.936568Z", "shell.execute_reply": "2021-11-22T21:09:09.936757Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "No covariance estimate - not supported by this backend.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 188 ms, sys: 3.23 ms, total: 191 ms\n", "Wall time: 355 ms\n" ] } ], "source": [ "%%time\n", "sherpa_opts = {\"method\": \"simplex\", \"ftol\": 1e-3, \"maxfev\": int(1e4)}\n", "fit_sherpa = Fit(store_trace=True, backend=\"sherpa\", optimize_opts=sherpa_opts)\n", "results_simplex = fit_sherpa.run([dataset_hess])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the \"minuit\" backend see https://iminuit.readthedocs.io/en/latest/reference.html for a detailed description of the available options. If there is an entry ‘migrad_opts’, those options will be passed to [iminuit.Minuit.migrad](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.migrad). Additionally you can set the fit tolerance using the [tol](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.tol\n", ") option. The minimization will stop when the estimated distance to the minimum is less than 0.001*tol (by default tol=0.1). The [strategy](https://iminuit.readthedocs.io/en/latest/reference.html#iminuit.Minuit.strategy) option change the speed and accuracy of the optimizer: 0 fast, 1 default, 2 slow but accurate. If you want more reliable error estimates, you should run the final fit with strategy 2.\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.983754Z", "iopub.status.busy": "2021-11-22T21:09:09.942622Z", "iopub.status.idle": "2021-11-22T21:09:09.985034Z", "shell.execute_reply": "2021-11-22T21:09:09.985209Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 44.7 ms, sys: 1.78 ms, total: 46.5 ms\n", "Wall time: 45.1 ms\n" ] } ], "source": [ "%%time\n", "fit = Fit(store_trace=True)\n", "minuit_opts = {\"tol\": 0.001, \"strategy\": 1}\n", "fit.backend = \"minuit\"\n", "fit.optimize_opts = minuit_opts\n", "result_minuit = fit.run([dataset_hess])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit quality assessment\n", "\n", "There are various ways to check the convergence and quality of a fit. Among them:\n", "\n", "Refer to the automatically-generated results dictionary:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.986983Z", "iopub.status.busy": "2021-11-22T21:09:09.986702Z", "iopub.status.idle": "2021-11-22T21:09:09.987924Z", "shell.execute_reply": "2021-11-22T21:09:09.988083Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : scipy\n", "\tmethod : L-BFGS-B\n", "\tsuccess : True\n", "\tmessage : CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n", "\tnfev : 60\n", "\ttotal stat : 30.35\n", "\n", "OptimizeResult\n", "\n", "\tbackend : scipy\n", "\tmethod : L-BFGS-B\n", "\tsuccess : True\n", "\tmessage : CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH\n", "\tnfev : 60\n", "\ttotal stat : 30.35\n", "\n", "\n" ] } ], "source": [ "print(result_scipy)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.989724Z", "iopub.status.busy": "2021-11-22T21:09:09.989424Z", "iopub.status.idle": "2021-11-22T21:09:09.990617Z", "shell.execute_reply": "2021-11-22T21:09:09.990775Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : sherpa\n", "\tmethod : simplex\n", "\tsuccess : True\n", "\tmessage : Optimization terminated successfully\n", "\tnfev : 135\n", "\ttotal stat : 30.35\n", "\n", "\n" ] } ], "source": [ "print(results_simplex)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.992560Z", "iopub.status.busy": "2021-11-22T21:09:09.992272Z", "iopub.status.idle": "2021-11-22T21:09:09.993356Z", "shell.execute_reply": "2021-11-22T21:09:09.993525Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OptimizeResult\n", "\n", "\tbackend : minuit\n", "\tmethod : migrad\n", "\tsuccess : True\n", "\tmessage : Optimization terminated successfully.\n", "\tnfev : 37\n", "\ttotal stat : 30.35\n", "\n", "OptimizeResult\n", "\n", "\tbackend : minuit\n", "\tmethod : migrad\n", "\tsuccess : True\n", "\tmessage : Optimization terminated successfully.\n", "\tnfev : 37\n", "\ttotal stat : 30.35\n", "\n", "\n" ] } ], "source": [ "print(result_minuit)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check the trace of the fit e.g. in case the fit did not converge properly" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:09.996766Z", "iopub.status.busy": "2021-11-22T21:09:09.996429Z", "iopub.status.idle": "2021-11-22T21:09:09.998260Z", "shell.execute_reply": "2021-11-22T21:09:09.998434Z" } }, "outputs": [ { "data": { "text/html": [ "
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Table length=4\n", "
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typenamevalueuniterrorminmaxfrozenlink
str8str9float64str14float64float64float64boolstr1
spectralamplitude3.8122e-11cm-2 s-1 TeV-13.546e-12nannanFalse
spectralreference1.0000e+00TeV0.000e+00nannanTrue
spectralalpha2.1958e+002.626e-011.000e+003.000e+00False
spectralbeta2.2649e-011.397e-01nannanFalse
" ], "text/plain": [ "\n", " type name value unit error min max frozen link\n", " str8 str9 float64 str14 float64 float64 float64 bool str1\n", "-------- --------- ---------- -------------- --------- --------- --------- ------ ----\n", "spectral amplitude 3.8122e-11 cm-2 s-1 TeV-1 3.546e-12 nan nan False \n", "spectral reference 1.0000e+00 TeV 0.000e+00 nan nan True \n", "spectral alpha 2.1958e+00 2.626e-01 1.000e+00 3.000e+00 False \n", "spectral beta 2.2649e-01 1.397e-01 nan nan False " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result_minuit.parameters.to_table()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot fit statistic profiles for all fitted parameters, using `~gammapy.modeling.Fit.stat_profile()`. For a good fit and error estimate each profile should be parabolic. The specification for each fit statistic profile can be changed on the `~gammapy.modeling.Parameter` object, which has `.scan_min`, `.scan_max`, `.scan_n_values` and `.scan_n_sigma` attributes." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:10.023266Z", "iopub.status.busy": "2021-11-22T21:09:10.010269Z", "iopub.status.idle": "2021-11-22T21:09:10.176446Z", "shell.execute_reply": "2021-11-22T21:09:10.176639Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "total_stat = result_minuit.total_stat\n", "\n", "fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(14, 4))\n", "\n", "for ax, par in zip(axes, crab_model.parameters.free_parameters):\n", " par.scan_n_values = 17\n", "\n", " profile = fit.stat_profile(datasets=[dataset_hess], parameter=par)\n", " ax.plot(profile[f\"{par.name}_scan\"], profile[\"stat_scan\"] - total_stat)\n", " ax.set_xlabel(f\"{par.unit}\")\n", " ax.set_ylabel(\"Delta TS\")\n", " ax.set_title(f\"{par.name}: {par.value:.1e} +- {par.error:.1e}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inspect model residuals. Those can always be accessed using `~Dataset.residuals()`, that will return an array in case a the fitted `Dataset` is a `SpectrumDataset` and a full cube in case of a `MapDataset`. For more details, we refer here to the dedicated fitting tutorials: [analysis_3d.ipynb](../analysis/3D/analysis_3d.ipynb) (for `MapDataset` fitting) and [spectrum_analysis.ipynb](../analysis/1D/spectral_analysis.ipynb) (for `SpectrumDataset` fitting)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Covariance and parameters errors\n", "\n", "After the fit the covariance matrix is attached to the model. You can get the error on a specific parameter by accessing the `.error` attribute:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:10.178835Z", "iopub.status.busy": "2021-11-22T21:09:10.178486Z", "iopub.status.idle": "2021-11-22T21:09:10.179865Z", "shell.execute_reply": "2021-11-22T21:09:10.180100Z" } }, "outputs": [ { "data": { "text/plain": [ "0.2625817875684573" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "crab_model.spectral_model.alpha.error" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And you can plot the total parameter correlation as well:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:10.196367Z", "iopub.status.busy": "2021-11-22T21:09:10.196042Z", "iopub.status.idle": "2021-11-22T21:09:10.261815Z", "shell.execute_reply": "2021-11-22T21:09:10.262076Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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zafR4Q+LxxAuJhOSYFj9sMnhD4vHECQkSkw+O/gxvSDyeOCGJxBRvSDweTywIEpJ808bj8cSEfLDV4/HEhrxH4vF4YkY6aIKtB8dTxkDW/bcxasNbnPLR81XK9PnbjQz/7CVO+WA2rQccU36+43eHMmzFfIZ/9hKHX//jetFn8eLFjBo1kuzs4UyfPr1SuZkxZcotZGcPZ8yY0SxfvjzqurUlsesRpE24jrSJPyc5a2iVcgkdutD8sltI7Nmn/FxSnxNIO+dnpJ17DUl9hsSsC7hnv2fa/+OSM4/hyokDWfVp5BUnbv/ND/nRuH5cce5x/GXSFZQU7zuJ7/PlSzjjuOa8/vKsmPQp80gibQcaDWZIJH0b/O0s6alg/9hg4enaXmuypF/Wt44A62bO4p0xl1dZnn7GKbQ4sievHn0ay666iX53T3YFCQn0vfNm3h17OYv6jaHL98bSsndsSwKXlpYyefJkHnjgQebPf5E5c55n1apV+8gsXryInJwcFi58hVtvncqkSTdHXbdWSKSceCa7X5xJ4dN3kXh4FmrbMbLcoNMoXb9676lD0kk+aiCFz91H4ay7Sep+FGrdru66BLz3xous/3o1D81ewXU33c1dU6+NKJc9+gL++ewy7nvqfYr2FPLCMw+Vl5WWlvLAHTdy/JBRMeuDREJSQsTtQKPBn8jMNpjZhODwWNz8gUbD1teXULx1e5XlGWeOYN2jzwKw7Z2lJLdpTbPMjrQdlMXOL9aw66t1WHEx65+cS8ZZI2LSZenSpfTo0YPu3buTkpLCmDFjWbBgwT4yCxYsYPz48UhiwIABFBQUkJ+fH1Xd2pDQsSuhgi3Yjm8gVErplx+T1KN3JbmkY06g5KsVWOG3e+u27UjpprVQWgwWonRjDkk9j6lUt7a8veh5Ro79PpLonTWYnTu2sWVT5Xlsg4aejiQkcVSf77A5b1152XP/voeTR4ynbbsIRrGWeI+kApKelfS+pBVlOS8lfStpWnB+gaRBkhZJ+lLSWYHMJZKekzRf0ueSJkW4dk9JyyWl4FaI+56kjyR9r6KnEcj1DPZvDK65ADgqTObw4H7vS3pd0tGxfEA1kdolg8J1ueXHu9fnktolg7TOGexeG3Z+XR5pnTNiuldeXh6dOu1NgpWZmUleXl4Emc4VZHKjqlsb1Lw1tnOvgbWd21HzVhVkWpHUszcln723z/nQN/kkZvaEZmmQmExityNRizZ11qWMzfkb6JjZtfy4Q0YXtuRXPbO+pLiYhXMfZ+BJp7n6eet569XnGDOxfpqh4IbIR9oONKINtl5mZlslpQHvSXoaaAEsMrMbJD0D3IpbnPkY4BHcNGeAQUBf3AzF9yTNDdaF3QczK5J0MzDQzH4GrskSSRlJxwPnAwOCZ/gAeD8ongFcaWarJA0G7gGyI1zjCoL8nX/5xa/pFeUHEUGZyufMIp6PdTGySPUr3iayjKKqWyuiqJtywmiK3n3JfR5h2LZNFC99ndQzLoHiIkJbcyEUikGZsgtHfvaquOu2a+l73Mn0O+5kAKb/6Vf86LqpJCbWk8cgHZDeRySiNSTXShof7HfDJZwtAuYH5z4G9gRLRH4M9Ayr+3LZwtqSZgEnA5UMSS0ZCjxjZruC684O/rYETgT+G/YFahbpAkFauxkAWxa/Y2//vW6Btd3rcknrmknZgr+pXTLZvSEfpSST2i2zXC61awa7N+bX6R5lZGZmsnHjXlc9NzeX9PSMCDIbKskUFRXXWLc22M6CfbwItWiD7dqxj0xCxy40yz7Plac2J6lbL/ZYiNI1n1Ky8gNKVn4AQPLAkdjOgjrpMfuJ6bwwy2Vx69XneDbl7m2mbM5bT7uOkdOYPjb9VrZ/s5nrbrq7/NzKT97nDzdcBMD2bVt4940XSUxM4sTss+qkm2vaNHj0YL9QoyGRNAwYCQwxs12SFgGpQHHYWq4hYA9AsM5r+HUr/kzU5me5hH2bX6k1XCcB2GZmx9biHjGRN+cVev70B2z4z1zaDu5PScEO9uRuomjTVloc0ZO0nl3ZvT6PLueN4YOLfhHTvbKyslizJoe1a9eSkZHB3Llz+Otf/7aPzIgRI3n00ZmMHXsmH330Ea1atSI9PZ127drVWLc2hDatJ6F1e9SyLbZrB4mH9WPPq//dR6bwP38t3085ZTylX6+kdE2QGze1BezeiVq0IannMRTOrk260r2cdf6VnHX+lQC889oLzP7PvQw7/Tw++/hdmrdsQ/sIhuSFWQ+y5K0FTJvxAgkJe79eM+d9Xr7/55suZ/Apo+tsRADvkVSgDfBNYESOBk6o5T1GSWqHSy53NnBZNbI7gPCGdg4wFiBYt+PQ4PxrwMOSbsc9w5nAfWZWIOkrSRPN7L/BIt9ZZra0ljqXM+Cxv9D+1EGkdDiEETmLWXnLXSjZfWxfz3iC/HmLST/9VIZ//jKluwpZevlvAbDSUlZcN4XB8/6JEhNZ+/DTfPvJ6upuVSNJSUlMmjSJSy+9hNLSEBMnTqBXr148/vjjAFx44YUMGzaMRYsWkZ2dTVpaKtOmTau2bp2xEEVvzSH1jB+CEihZ+QG2LZ+ko78DUCkuUpHUkeejZs2xUIg9b82Bolizurog6ntvzOfSM4+hWWpzfnHLXuP0u6vH8X+T7qV9emfunHoNGZ268/OLTwXgpBHj+MFPboz5/pURqq9mUiOnxkXEJTUDnsVlqP4c6AhMBuaYWctAZjLwrZn9OTj+1sxaSroE1wvTAjgCeNzMbqkg0zO4Vt/A4LyIywT1B1yc5TkgHXgP1yw6w8xyJN0IXAysweWv/MTM/izpUNwaH52C6zxhZlOqe8Yti9+xAzH5cyyUJ3/+120NrIkjdcxlbK+X5M+xM/DwZJZ8UVxjFvn+Ge1s3vmRu5G73vnk+zEmf25U1OiRmNke3GI8FWkZJjO5Qp2WYYf5ZcHTSDJmloMLxmJmW4HvVBA9rQq9pgJTI5z/iuoXFvJ49g++aePxeOoDb0jqATN7GLf0oMdz0CEJeUPi8XhiQpBwkARbvSHxeOKGUMKBN4o1Et6QeDzxQvimjcfjiQ3p4BlH4g2JxxNHfK+Nx+OJjYPIIzk4ZhR5PA1AWdMm0hZl/dODVBmrJf06QvkwSduDtBsfBbPnGwTvkXg88SShbr/VkhKBu3GpOdbhUnDMNrNPKoi+bmZjY1MydrxH4vHEi9g8kkHAajP70syKgCeAcXHVNwa8RwK0PXkgI3Z81NBqkJKSAuydMNeQlOlS9P3fNrAmASkptMEY2qseEiDFrIpxeMv1wGE1ysYQI+kCrA07XgcMjiA3RNJSYAPwSzNbUdcbxoI3JB5PvKh+iHwHSeEJvmYEybbKa0eoU3Gq/gdADzP7Nkia/iwu6dh+xxsSoKioqFFN3fe6VKYx6RO1xyigao9kcw1pBNbhshGW0RXndZRjZgVh+/Mk3SOpg5ltjk7B+sPHSDyeuCGXbzHSVjPvAUdKOjRIjH4+e/Mgu6tLmUHyLiQNwr3PW+r5IaLCeyQeT7wQKLFur5iZlUj6GS7RVyLwoJmtkHRlUD4dmABcJakEl4Hw/LD0p/sVb0g8njihGFMtmtk8YF6Fc9PD9v8B/KPON6hHvCHxeOKFVF2M5IDCGxKPJ554Q+LxeGJCAh0c/RnekHg88cR7JB6PJyaaeIxEUjbQJzhcbmavViXrDYnHE08Smp4hkZQJPINblrds9O25kqYC482s0urz3pB4PPGi6XokdwD/NLMHwk9K+jHwd+CCihUOjkiQx9MgyHkkkbbGzfEVjQiAmd1P5QXsAG9IomLx4sWMGjWS7OzhTJ8+vVK5mTFlyi1kZw9nzJjRLF++POq6Xpf60aUx6oNw+UgibY2bwmrKIi7SHJcnknStpE8l/Sse19+flJaWMnnyZB544EHmz3+ROXOeZ9WqVfvILF68iJycHBYufIVbb53KpEk3R13X6xK7Lo1RHwBDWEJixK2RkyOp0oRCSVlATqQKdTYkclRV/6fAaDP7fpTXarSxmqVLl9KjRw+6d+9OSkoKY8aMZcGCBfvILFiwgPHjxyOJAQMGUFBQQH5+flR1vS6x69IY9SmjiRqSnwOjJf1N0l8lnROcbxWUVaJWhkRSz8DTuAeXC+EmSe9JWibplkBmOi7jy2xJ/yephaQHA7kPJY0L5C6R9F9JzwMv1SA3S9J8Sask/TFMn9MlfSBpqaSFwbmI16kreXl5dOq0d9p4ZmYmeXl5EWQ6V5DJjaqu1yV2XRqjPoALtjbNGMkVwBBgKbAM+ImkP5nZm2a2OlKFungCRwGX4pKoTMClhBPOcJxiZldKOh0YbmabJd0GvGJml0lqC7wrqczcDwGyzGxrDXLHAgOAPcDnku7CtdXuB04xs68ktQtkb4x0HTPbGf4Qkq4IPjDuuusuzjhjdMSHjTSZsuIs8MgyiqpubfC6NB19gqtgTbPXZjTQ38zK0tE9LOlj4FdVVaiLIVljZv+T9GfgNODD4HxLXHam1yrInwacJemXwXEq0D3Yf9nMtkYht9DMtgNI+gToARwCvGZmXwFEcZ1Pw5UKslHNACgsLLSqEuZkZmaycePestzcXNLTMyLIbKgkU1RUXGPd2uB1aTr6AO7ntWkOkQ8B7YFNAJLSg3NVUpenLPtlF/AHMzs22I6I1GUUyJ0bJtfdzD6tcK2a5PaEyZXiDKConHqupuvUmqysLNasyWHt2rUUFRUxd+4cRowYsY/MiBEjeeaZZzAzPvzwQ1q1akV6enpUdb0usevSGPVxNNlg6+9xnvxMSY/gkixNra5CLEHOF4HfS/pXkDOyC1BsZvkR5K6RdI2ZmaQBZvZh5ctFLVfG28Ddkg4ta9oEXkltr1MtSUlJTJo0iUsvvYTS0hATJ06gV69ePP744wBceOGFDBs2jEWLFpGdnU1aWirTpk2rtq7XpX51aYz6lNEEjEYlzOwpSa/hwhYA10cazRqOapNQSVJPYI6Z9Q2OrwMuD4q/BX5gZl9IygEGBjGSNNxouBNx3kKOmY2VdEkg87PgWtHKzQH+bGaLJJ0B3IbzrPLNbFRV16nuuapr2uxPGmNe0sagCzQufTp37sSGDRs5/PDDqo2kDDimly1+9K6IZW0Gnv5+DTlbGwxJp0Y6b2aLq6pTK4/EzHKAvmHHd+CG01aU6xm2Xwj8JILMw8DDdZAbG7b/AvBCBfmI1/F4GgJT0/NIgF+E7bfAeSbvAdlVVWi04zc8nqaPsCYYbDWzs8KPJXUH/lBdHW9IPJ54oaYZI6mImX0tqb+khLAu4X3whsTjiRNlQ+SbGlXESK6uyoiANyQeTxwRIR8j8Xg8MdFEmzY+RuLxNCqEHQCZOnyMxONpQAwINUGPJFgG9HLgu7jHeAnoV90qfk3fXHo8jRYXI4m0NXJuxU3cuw/oB3QEplVXwXskHk+cMCDUBMeRAGcCxwXrDxea2W2S3qmuQpN8So+nSaDYPJIg387nklZL+nWEckm6MyhfJum4+tLczErC7pMCNKuugjckHk8cqashkZQI3A2cARwDXCDpmApiZ+BSdxyJy61zbz2pnS/pyGC/NfBmoEuV+KYNkJKSUj4prKH1ALwuEWhM+pTpUhMW2xD5QcBqM/sSQNITwDjgkzCZccDMIAj6P0ltJXUys1hnNp4NlHkkPwFWmdma6ip4QwIklBSRsi23odUgoV0moaTovqT7i13vLmtoFQBI6t+bPSkt+PLr0oZWhcO6w89u/ZYXHqpZtpoYSQdJS8KOZwTJtsroAqwNO14HDK5wjUgyXYBYDUk7cNnjgFXBfo+ywkhGxRsSILQ1l91zH2xoNUgdcxlFbTMbzVR5gLdHXNzAmjiGLJzJ+ow+3DDty4ZWhWk3HBalpAhZlc2YzTWkEYiUoqBi92s0MnXh+WrKhOvJ2QdvSDyeOGFAqO5hyHVAt7DjrsCGOsjUGjPLqm0dH2z1eOKGCJEQcYuC94AjJR0a9JqcD8yuIDMbuDjovTkB2F4P8REkHSG3DMUkSa0lpYU3bSLhDYnHE0fMFHGruZ6VAD/DpQ79FHjSzFZIulLSlYHYPOBLYDVuRYWf1pPaT+NiLy2Af+DyJD9aXQXftPF44kSMTRvMbB7OWISfmx62b8DVdb5B1ew0s78BSFpmZkWSmldXwXskHk/cECFLiLg1cl6VdGkwlqVU0hE1VfAeiccTJwwobZq/1dfgmjX3AUXAv3HNrCrxhsTjiRdGU/A+KmFmrWtbxxsSjyduRBdYbWxISgKycIuGl3E78BvgKz8gzePZjxhN0yMB5gOJwI6wc0fjUjA+DnhD4vHsT0qboEcCtDezAeEnJH1gZmdWVcEbEo8nTljQa9MEeTjCuUeqq9Akn3J/k9j1CNImXEfaxJ+TnDW0SrmEDl1oftktJPbsU34uqc8JpJ3zM9LOvYakPkNi1mXx4sWMGjWS7OzhTJ8+vVK5mTFlyi1kZw9nzJjRLF++POq6tSXr/tsYteEtTvmo6qkZff52I8M/e4lTPphN6wF7Z8F3/O5Qhq2Yz/DPXuLw638csy7gnv2Td27ntafH8sZzE9i+JfLa8Vs2vsNbs7/HG8+ew7LXf0coVFKr+tEr5DySSFsj5yNJp4ZvwEcAko6PVKFRGhJJOZI6xCpTT8qQcuKZ7H5xJoVP30Xi4VmobcfIcoNOo3T96r2nDkkn+aiBFD53H4Wz7iap+1Godbs6q1JaWsrkyZN54IEHmT//RebMeZ5Vq1btI7N48SJycnJYuPAVbr11KpMm3Rx13dqybuYs3hlzeZXl6WecQosje/Lq0aex7Kqb6Hf3ZFeQkEDfO2/m3bGXs6jfGLp8bywtex8eky4Am9e/wa6Crxl6zvP0HXIzn7x9ayUZsxAfv34T/U+dxslnzyKtZSc2rJ4ddf3aUBYjaYLjSH4RYftlUHZRpAqN/okamoSOXQkVbMF2fAOhUkq//JikHr0rySUdcwIlX63ACr/dW7dtR0o3rYXSYrAQpRtzSOpZMTdN9CxdupQePXrQvXt3UlJSGDNmLAsWLNhHZsGCBYwfPx5JDBgwgIKCAvLz86OqW1u2vr6E4q3bqyzPOHME6x59FoBt7ywluU1rmmV2pO2gLHZ+sYZdX63DiotZ/+RcMs4aEZMuAHlfv0rnw89EEm3Tsygu2sHuXZv2kSnes42ExBRatOkJQPvOQ8hdszDq+rXFLPLWmDGzsyJsZwZlP49Up8ENiaRnJb0vaYWkKyqU9ZT0maRHglRyT1UYqnuNpA8kfSzp6KDOIElvSfow+HtUTPo1b43t3Puy2M7tqHmrCjKtSOrZm5LP3tvnfOibfBIze0KzNEhMJrHbkahFmzrrkpeXR6dOexP7ZGZmkpeXF0GmcwWZ3Kjq1jepXTIoXLc3z8vu9bmkdskgrXMGu9eGnV+XR1rnjJjvt2dXPmkt9l4ntUUGe3bl7yOT3OwQQqEStm9eAUBezsvs3pkbdf3aYIhSS4i4NWYkHSLpjuAd+iBI53hIdXUawxNdZmbHAwOBayW1r1B+FC7pSxZQwL4Tkzab2XG4FHNlrtdnwClB1Plm4LaYtIuiOZtywmiK3n2p0k+NbdtE8dLXST3jElJPv5jQ1lwIVbnqYY1EWg1AikZGUdWtdyLdwCzi+WpWOohViQoqif6nTuOzd//E23MuJDG5Bap2yYjYPqSQKeLWyHkI2ASMB84J9qtN2NMYem2ulTQ+2O+Gyz8ZzlozezPYfwy4FvhzcDwr+Ps+7oEB2gCPBDknDUiOdNPA+7kC4N4/TuWiKuyt7SzYx4tQizbYrh37yCR07EKz7PNceWpzkrr1Yo+FKF3zKSUrP6Bk5QcAJA8cie0siHyjKMjMzGTjxr2zxHNzc0lPz4ggs6GSTFFRcY1165vd63JJ65rJN8FxapdMdm/IRynJpHbLLJdL7ZrB7o11++Vf8+kTrFvpvgZtOvShcGceZf/K3TvzaNa8cjzrkPT+DB79MACb17/FrgI3LKJZ8/So6keLGZSGGr3RiMShZnZ22PHvJS2trkKDeiSShgEjgSFm1h/4EEitIFbxpyr8eE/wt5S9RvH3wKtm1heXVr/i9dxFzGaY2UAzG/jjH1xQpY6hTetJaN0etWwLCYkkHtaPkjWf7SNT+J+/lm8lX61gz5tzKF0TRPxTW7hnbdGGpJ7HUPJF3VMXZmVlsWZNDmvXrqWoqIi5c+cwYsS+sYURI0byzDPPYGZ8+OGHtGrVivT09Kjq1jd5c16h60VnA9B2cH9KCnawJ3cT29/7mBZH9CStZ1eUnEyX88aQ9/wrdbpHj97nc9K4Jzlp3JOkdx/Ohi+ex8zYlr+M5JSWpEYwBHsKtwAQKi3iy+UP0e2oCQCkdxsWVf3a0ER7bXYG7yYAkoYDO6ur0NAeSRvgGzPbFcQ4Togg013SEDN7G7gAeCOKa64P9i+JWUMLUfTWHFLP+CEogZKVH2Db8kk6+jsAleIiFUkdeT5q1hwLhdjz1hwo2l1nVZKSkpg0aRKXXnoJpaUhJk6cQK9evXj88ccBuPDCCxk2bBiLFi0iOzubtLRUpk2bVm3dWBjw2F9of+ogUjocwoicxay85S6U7L5SX894gvx5i0k//VSGf/4ypbsKWXr5bwGw0lJWXDeFwfP+iRITWfvw03z7yerqbhUVHbsOZfP6N3ht1lgSE1Ppd/KU8rIlL19N35Mmkdo8na+WP8Kmda9hFqL7UefRvtPgGuvXlcYeWK2CHwMzw3pFt1JFb00Zil/btGYkNQOexSWs/Ry3otdk3ICYgUBLXD6G14ATcYloLwoMTw4w0Mw2SxoI/NnMhkkaghs8swl4JZDvWZ0epRu/Mp+zdV/KcrYubHVswyoS0Nhytt4w7UteeCirWtfiiN4D7c8zI68rNX5Q0vs15GxtcCS1xNmIHTXJNqhHYmZ7cGtzVKQnlD9IyMyurCgQbhzMbAkwLNh/Gwj/qb2p3hT2eGpJEwisVkLSpArHAJjZLVXVaeimjcdzwGJAad076RqScA+kGTAG12KokkZtSMwsB+jb0Hp4PHWhqfbamNlfw48l/Ql4ubo6jdqQeDxNnSYabK1IG/Zd9qIS3pB4PHGkKTZtJC1j70i8BCADqDI+At6QeDxxwwxCTbBpA4wN2y8B8sys2rVSvSHxeOJEUw22mtnXta3jDYnHE0eaoiGpC96QeDxxwgxKq20QHDh4Q+LxxJEDpNemRrwh8XjihBtHUv/XldQO+A9uBHgOcJ6ZfRNBLgc3uKwUKInnkPzGkI/E4zlgCYUs4hYjvwYWmtmRwMLguCqGm9mx8Z7X4z0SIKFdJqljLmtoNUhol0lKUkr5hLmGJCUlBXCT5RoDrfv3pllKGtNuOKyhVeGw7mlRycUxRjKOYG4ZboLqIuCGuNwpSrwhAUqSUtnRqkdDq0GrJJFA4wrzr8/oU7PQfqBZShrNinbSJS/GzO71oUtmb65+dCI8VO30E6Dapk0HSUvCjmeY2YwoVcgws40AZrZRUnoVcga8JMmA+2px/VrjDQmwo9BY8kVxQ6vBwMOTSUssalRpBBrDtH1wU/e75H3K2yMubmhVauWlWdXNmM3VNTckLQAyIxTdGPXN4SQz2xAYmpclfWZmr9WiftR4Q+LxxIlYgq1mNrKqMkl5kjoF3kgnIGKeSjPbEPzNl/QMMAiX26fe8cFWjydOGFBaahG3GJkN/DDY/yHwXEUBSS0ktSrbB04DlleUqy+8IfF44oUZpaHIW4zcDoyStAoYFRwjqbOkeYFMBvBGkLT5XWCumc2P9cZV4Zs2Hk+cMCAUu/dR+bpmW4BKmbuDpszoYP9LoH+937wKvCHxeOKFxbSMUZPCGxKPJ0642b8Hxxh5b0g8nnhh8WnaNEa8IfF44oSZUXqQ5BHwhsTjiSP10NXbJPCGxOOJIw25AN3+xBsSjydOuEl73pB4PJ4YOJhiJH5kaxSYGfdM+39ccuYxXDlxIKs+/TCi3O2/+SE/GtePK849jr9MuoKS4n0nAn6+fAlnHNec11+eVWddFi9ezKhRI8nOHs706dMj6jplyi1kZw9nzJjRLF++POq6dcHM+OSd23nt6bG88dwEtm+JPDt3y8Z3eGv293jj2XNY9vrvCIVKalW/JrLuv41RG97ilI+er1Kmz99uZPhnL3HKB7NpPeCY8vMdvzuUYSvmM/yzlzj8+h/X6f5VESoJRdwONBqdIZHUU1LUcwIkXSKpczx1eu+NF1n/9Woemr2C6266m7umXhtRLnv0Bfzz2WXc99T7FO0p5IVnHiovKy0t5YE7buT4IaPqrEdpaSmTJ0/mgQceZP78F5kz53lWrVq1j8zixYvIyclh4cJXuPXWqUyadHPUdevC5vVvsKvga4ae8zx9h9zMJ2/fWknGLMTHr99E/1OncfLZs0hr2YkNq2dHXT8a1s2cxTtjLq+yPP2MU2hxZE9ePfo0ll11E/3unuwKEhLoe+fNvDv2chb1G0OX742lZe/D66RDRcqaNnGYa9PoaHSGpA5cAsTVkLy96HlGjv0+kuidNZidO7axZVPlqf6Dhp6OJCRxVJ/vsDlvXXnZc/++h5NHjKdtu4511mPp0qX06NGD7t27k5KSwpgxY1mwYME+MgsWLGD8+PFIYsCAARQUFJCfnx9V3bqQ9/WrdD78TCTRNj2L4qId7N61aR+Z4j3bSEhMoUWbngC07zyE3DULo64fDVtfX0Lx1u1VlmecOYJ1jz4LwLZ3lpLcpjXNMjvSdlAWO79Yw66v1mHFxax/ci4ZZ1UafV43gqZNpO1Ao7EakiRJj0haJukpSc0lHS9psaT3Jb0oqZOkCcBA4F+SPpKUJulmSe9JWi5phsqWUo+Bzfkb6JjZtfy4Q0YXtuRvqFK+pLiYhXMfZ+BJp7n6eet569XnGDMxNrc5Ly+PTp32Zk/LzMwkLy8vgkznCjK5UdWtC3t25ZPWIqP8OLVFBnt27TurPbnZIYRCJWzfvMLpmPMyu3fmRl2/PkjtkkHhutzy493rc0ntkkFa5wx2rw07vy6PtM4ZkS5RJ8ws4nag0VgNyVG4jFFZQAFwNXAXMMHMjgceBKaa2VPAEuD7QV7KQuAfZvYdM+sLpLHvqmHlSLpC0hJJSx55sIbEURH+8dXZp7tuu5a+x51Mv+NOBmD6n37Fj66bSmJiYg2PXZMakfSIRkZR1a0/9r2wJPqfOo3P3v0Tb8+5kMTkFiihus8iDopFeliziOfr60U3O3hiJI2112atmb0Z7D8G/Bboi8vyBJAIVJVGbLik64HmQDtgBVApAheknZsBsPXbkFXMkDb7iem8MOtBAHr1OZ5NuXubKZvz1tOuY+S8qo9Nv5Xt32zmupvuLj+38pP3+cMNFwGwfdsW3n3jRRITkzgx+6xqPoLKZGZmsnHj3sfOzc0lPT0jgsyGSjJFRcU11o2WNZ8+wbqVLmDcpkMfCnfmcUhQtntnHs2aV26+HZLen8GjHwZg8/q32FWwBoBmzdOjqh8ru9flktY1k7JU66ldMtm9IR+lJJPabW8istSuGezeWF8eke+1aWgq/iTsAFYEXsexZtbPzE6rWElSKnAPznPpB9wPpNZFgbPOv5J7n3yXe598lxOHn8WCOf/CzPh02Ts0b9mG9hEMyQuzHmTJWwv4ze0zSUjY+9HOnPc5M19YycwXVjJ05Hiu+e0dtTYiAFlZWaxZk8PatWspKipi7tw5jBixb3t+xIiRPPPMM5gZH374Ia1atSI9PT2qutHSo/f5nDTuSU4a9yTp3Yez4YvnMTO25S8jOaUlqREMwZ7CLQCESov4cvlDdDtqAgDp3YZFVT9W8ua8QteLzgag7eD+lBTsYE/uJra/9zEtjuhJWs+uKDmZLueNIe/5V+rlni7YenDESBqrR9Jd0hAzexu4APgf8OOyc5KSgV5mtgJnZFoF9cqMxmZJLYEJwFOxKjNo6Om898Z8Lj3zGJqlNucXt+xtCv3u6nH836R7aZ/emTunXkNGp+78/OJTAThpxDh+8JPapNisnqSkJCZNmsSll15CaWmIiRMn0KtXLx5//HEALrzwQoYNG8aiRYvIzs4mLS2VadOmVVs3Vjp2Hcrm9W/w2qyxJCam0u/kKeVlS16+mr4nTSK1eTpfLX+ETetewyxE96POo32nwTXWrw0DHvsL7U8dREqHQxiRs5iVt9yFkt3X++sZT5A/bzHpp5/K8M9fpnRXIUsv/y0AVlrKiuumMHjeP1FiImsffppvP1kd46dShhE6AI1GJNTYAj+SegLzcLklTwRWARcBvYA7gTY4A/h3M7tf0rnAbUAhMASXHPd83MJBa4E1Zja5untGato0BC75855Glfz5nJ/G3kVcH7jkzysaTfLnt0dczNiSz6sN5rTLzLLvXjwnYtkTf+rxfrzXmtmfNDqPxMxygGMiFH0EnBJB/mng6bBTvws2j6fBORCbMZFodIbE4zlQMLMDsocmEt6QeDzxwtyI4oMBb0g8njhhB1Gw1RsSjydeGIQOkuzP3pB4PHHCeSS+aePxeGIhGCJ/MOANiccTJ1xiI++ReDyeWDAIlRwchqSxzrXxeJo8hvNIIm2xIGmipBWSQpKqHB0r6XRJn0taLenXMd20Brwh8XjihYGFQhG3GFkOnIObRhIRSYnA3cAZuJHiF0iKNGK8XvBNG48nbsSn18bMPoXqc+IAg4DVwWLiSHoCGAd8Uu8K4Q0JAK3SxMDDkxtaDVqliQRSyifMNSQpKSmAmyzXGDisexrNMnszZOHMhlaF1v17RyXnhsg3WIykC27SahnrgMHxupk3JEByotSuZdzShdWSRNLS0hpaiXKyjm7Z0CrspXlr2p8at3ehVowt+bxGmZ3bV7745pxhHaooTpW0JOx4RpBsCwBJC4DMytW40cyei0LFSF/ouE3194bE44kTZnZ6DHVHxnj7dUC3sOOuQNWJhmPEB1s9ngOT94AjJR0qKQWXo2d2vG7mDYnH08SQNF7SOlwir7mSXgzOd5Y0D8DMSoCfAS8CnwJPBhkF46NTY8uQ5vF4mh7eI/F4PDHjDYnH44kZb0g8Hk/MeEPi8XhixhsSj8cTM96QeDyemPGGxOPxxIw3JB6PJ2b+Pxkfpa46dH11AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "crab_model.covariance.plot_correlation()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, this step is needed to produce a butterfly plot showing the envelope of the model taking into account parameter uncertainties." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:10.264241Z", "iopub.status.busy": "2021-11-22T21:09:10.263951Z", "iopub.status.idle": "2021-11-22T21:09:10.530467Z", "shell.execute_reply": "2021-11-22T21:09:10.530719Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "energy_bounds = [1, 10] * u.TeV\n", "crab_spectrum.plot(energy_bounds=energy_bounds, energy_power=2)\n", "ax = crab_spectrum.plot_error(energy_bounds=energy_bounds, energy_power=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Confidence contours\n", "\n", "\n", "In most studies, one wishes to estimate parameters distribution using observed sample data.\n", "A 1-dimensional confidence interval gives an estimated range of values which is likely to include an unknown parameter.\n", "A confidence contour is a 2-dimensional generalization of a confidence interval, often represented as an ellipsoid around the best-fit value.\n", "\n", "Gammapy offers two ways of computing confidence contours, in the dedicated methods `Fit.minos_contour()` and `Fit.stat_profile()`. In the following sections we will describe them." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An important point to keep in mind is: *what does a $N\\sigma$ confidence contour really mean?* The answer is it represents the points of the parameter space for which the model likelihood is $N\\sigma$ above the minimum. But one always has to keep in mind that **1 standard deviation in two dimensions has a smaller coverage probability than 68%**, and similarly for all other levels. In particular, in 2-dimensions the probability enclosed by the $N\\sigma$ confidence contour is $P(N)=1-e^{-N^2/2}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing contours using `Fit.stat_contour()` " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After the fit, MINUIT offers the possibility to compute the confidence confours.\n", "gammapy provides an interface to this functionality through the `Fit` object using the `.stat_contour` method.\n", "Here we defined a function to automate the contour production for the different parameterer and confidence levels (expressed in term of sigma):" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:10.533798Z", "iopub.status.busy": "2021-11-22T21:09:10.533494Z", "iopub.status.idle": "2021-11-22T21:09:10.534567Z", "shell.execute_reply": "2021-11-22T21:09:10.534786Z" } }, "outputs": [], "source": [ "def make_contours(fit, datasets, result, npoints, sigmas):\n", " cts_sigma = []\n", " for sigma in sigmas:\n", " contours = dict()\n", " for par_1, par_2 in combinations([\"alpha\", \"beta\", \"amplitude\"], r=2):\n", " contour = fit.stat_contour(\n", " datasets=datasets,\n", " x=result.parameters[par_1],\n", " y=result.parameters[par_2],\n", " numpoints=npoints,\n", " sigma=sigma,\n", " )\n", " contours[f\"contour_{par_1}_{par_2}\"] = {\n", " par_1: contour[par_1].tolist(),\n", " par_2: contour[par_2].tolist(),\n", " }\n", " cts_sigma.append(contours)\n", " return cts_sigma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can compute few contours." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:10.615692Z", "iopub.status.busy": "2021-11-22T21:09:10.615385Z", "iopub.status.idle": "2021-11-22T21:09:15.046404Z", "shell.execute_reply": "2021-11-22T21:09:15.046594Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 4.49 s, sys: 19.1 ms, total: 4.51 s\n", "Wall time: 4.51 s\n" ] } ], "source": [ "%%time\n", "sigmas = [1, 2]\n", "cts_sigma = make_contours(\n", " fit=fit,\n", " datasets=[dataset_hess],\n", " result=result_minuit,\n", " npoints=10,\n", " sigmas=sigmas,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we prepare some aliases and annotations in order to make the plotting nicer." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:15.049677Z", "iopub.status.busy": "2021-11-22T21:09:15.049373Z", "iopub.status.idle": "2021-11-22T21:09:15.050552Z", "shell.execute_reply": "2021-11-22T21:09:15.050774Z" } }, "outputs": [], "source": [ "pars = {\n", " \"phi\": r\"$\\phi_0 \\,/\\,(10^{-11}\\,{\\rm TeV}^{-1} \\, {\\rm cm}^{-2} {\\rm s}^{-1})$\",\n", " \"alpha\": r\"$\\alpha$\",\n", " \"beta\": r\"$\\beta$\",\n", "}\n", "\n", "panels = [\n", " {\n", " \"x\": \"alpha\",\n", " \"y\": \"phi\",\n", " \"cx\": (lambda ct: ct[\"contour_alpha_amplitude\"][\"alpha\"]),\n", " \"cy\": (\n", " lambda ct: np.array(1e11)\n", " * ct[\"contour_alpha_amplitude\"][\"amplitude\"]\n", " ),\n", " },\n", " {\n", " \"x\": \"beta\",\n", " \"y\": \"phi\",\n", " \"cx\": (lambda ct: ct[\"contour_beta_amplitude\"][\"beta\"]),\n", " \"cy\": (\n", " lambda ct: np.array(1e11)\n", " * ct[\"contour_beta_amplitude\"][\"amplitude\"]\n", " ),\n", " },\n", " {\n", " \"x\": \"alpha\",\n", " \"y\": \"beta\",\n", " \"cx\": (lambda ct: ct[\"contour_alpha_beta\"][\"alpha\"]),\n", " \"cy\": (lambda ct: ct[\"contour_alpha_beta\"][\"beta\"]),\n", " },\n", "]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally we produce the confidence contours figures." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:15.064701Z", "iopub.status.busy": "2021-11-22T21:09:15.064403Z", "iopub.status.idle": "2021-11-22T21:09:15.221256Z", "shell.execute_reply": "2021-11-22T21:09:15.221507Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 3, figsize=(16, 5))\n", "colors = [\"m\", \"b\", \"c\"]\n", "for p, ax in zip(panels, axes):\n", " xlabel = pars[p[\"x\"]]\n", " ylabel = pars[p[\"y\"]]\n", " for ks in range(len(cts_sigma)):\n", " plot_contour_line(\n", " ax,\n", " p[\"cx\"](cts_sigma[ks]),\n", " p[\"cy\"](cts_sigma[ks]),\n", " lw=2.5,\n", " color=colors[ks],\n", " label=f\"{sigmas[ks]}\" + r\"$\\sigma$\",\n", " )\n", " ax.set_xlabel(xlabel)\n", " ax.set_ylabel(ylabel)\n", "plt.legend()\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Computing contours using `Fit.stat_surface()`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This alternative method for the computation of confidence contours, although more time consuming than `Fit.minos_contour()`, is expected to be more stable. It consists of a generalization of `Fit.stat_profile()` to a 2-dimensional parameter space. The algorithm is very simple:\n", "- First, passing two arrays of parameters values, a 2-dimensional discrete parameter space is defined;\n", "- For each node of the parameter space, the two parameters of interest are frozen. This way, a likelihood value ($-2\\mathrm{ln}\\,\\mathcal{L}$, actually) is computed, by either freezing (default) or fitting all nuisance parameters;\n", "- Finally, a 2-dimensional surface of $-2\\mathrm{ln}(\\mathcal{L})$ values is returned.\n", "Using that surface, one can easily compute a surface of $TS = -2\\Delta\\mathrm{ln}(\\mathcal{L})$ and compute confidence contours.\n", "\n", "Let's see it step by step." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First of all, we can notice that this method is \"backend-agnostic\", meaning that it can be run with MINUIT, sherpa or scipy as fitting tools. Here we will stick with MINUIT, which is the default choice:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, we can compute the confidence contour for the `alpha` and `beta` parameters of the `dataset_hess`. Here we define the parameter space:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:15.224056Z", "iopub.status.busy": "2021-11-22T21:09:15.223759Z", "iopub.status.idle": "2021-11-22T21:09:15.225074Z", "shell.execute_reply": "2021-11-22T21:09:15.225324Z" } }, "outputs": [], "source": [ "result = result_minuit\n", "par_alpha = result.parameters[\"alpha\"]\n", "par_beta = result.parameters[\"beta\"]\n", "\n", "par_alpha.scan_values = np.linspace(1.55, 2.7, 20)\n", "par_beta.scan_values = np.linspace(-0.05, 0.55, 20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we run the algorithm, by choosing `reoptimize=False` for the sake of time saving. In real life applications, we strongly recommend to use `reoptimize=True`, so that all free nuisance parameters will be fit at each grid node. This is the correct way, statistically speaking, of computing confidence contours, but is expected to be time consuming." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:15.229870Z", "iopub.status.busy": "2021-11-22T21:09:15.229448Z", "iopub.status.idle": "2021-11-22T21:09:15.664468Z", "shell.execute_reply": "2021-11-22T21:09:15.664639Z" } }, "outputs": [], "source": [ "fit = Fit(backend=\"minuit\", optimize_opts={\"print_level\": 0})\n", "stat_surface = fit.stat_surface(\n", " datasets=[dataset_hess],\n", " x=par_alpha,\n", " y=par_beta,\n", " reoptimize=False,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to easily inspect the results, we can convert the $-2\\mathrm{ln}(\\mathcal{L})$ surface to a surface of statistical significance (in units of Gaussian standard deviations from the surface minimum):" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:15.666513Z", "iopub.status.busy": "2021-11-22T21:09:15.666216Z", "iopub.status.idle": "2021-11-22T21:09:15.667529Z", "shell.execute_reply": "2021-11-22T21:09:15.667706Z" } }, "outputs": [], "source": [ "# Compute TS\n", "TS = stat_surface[\"stat_scan\"] - result.total_stat" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:15.669326Z", "iopub.status.busy": "2021-11-22T21:09:15.669036Z", "iopub.status.idle": "2021-11-22T21:09:15.670065Z", "shell.execute_reply": "2021-11-22T21:09:15.670236Z" } }, "outputs": [], "source": [ "# Compute the corresponding statistical significance surface\n", "stat_surface = np.sqrt(TS.T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that, as explained before, $1\\sigma$ contour obtained this way will not contain 68% of the probability, but rather " ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:15.671800Z", "iopub.status.busy": "2021-11-22T21:09:15.671497Z", "iopub.status.idle": "2021-11-22T21:09:15.672542Z", "shell.execute_reply": "2021-11-22T21:09:15.672774Z" } }, "outputs": [], "source": [ "# Compute the corresponding statistical significance surface\n", "# p_value = 1 - st.chi2(df=1).cdf(TS)\n", "# gaussian_sigmas = st.norm.isf(p_value / 2).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can plot the surface values together with contours:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2021-11-22T21:09:15.690479Z", "iopub.status.busy": "2021-11-22T21:09:15.690187Z", "iopub.status.idle": "2021-11-22T21:09:15.748281Z", "shell.execute_reply": "2021-11-22T21:09:15.748527Z" }, "nbsphinx-thumbnail": { "tooltip": "Learn how the model, dataset and fit Gammapy classes work together in a detailed modeling and fitting use-case." } }, "outputs": [ { "data": 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qnes4H5TcDKtTa0wzxtXNNWiMYdClHe1m0N+EITWgjfu7Mov/fcDm/Z1orffw+f+1v5vWcQAZAbuQXX8d5/aVB1RpVdjqUBzaiyev6VRhDAc2n6FxvwrU717aoZKhEOL/STEG4RRsNs2SsZv5NmMyfvr9e6vDcWjv3/nQv8E01szcRTnP3+k0sTYeEZzvhJAQrkzKEQqn8vfyQzy49YSqrYtYHYrDs9k0E7stZWqflfxWIisDFzUjWqzIVoclhPiIDbcQb47O8SMUweLna2PJuM2kz5aSLL+mszocp7Bi8t8M8JxB2szJGLq8ldQVFkLYhSRgF7Rl0QEe330mo+Bg2L32OF2rTSB+ktgMXtaS2AmiWx2SEGGe1uCnVYg3RycJ2AX5ePuydMJWMuZKww85v7U6HKdxev9lulebQJyEMRiyvCVxv4lpdUhChHlyDVg4nU0L9vLs0UsZBQfT2cNX6VplPDHjRGPIspYkSCqrZglhFf9JWOaVI7Sa40coQuT9Wx+WjN3Mj7+l5+c/M1odjlO5cOw6nSuNJUr0SAxf1ZpkaRNaHZIQwgVJAnZha2fu5MbFe3j2LU/4iFIJKDj+OXWLDuVGAzB0RSvSZpalK4Wwgsn1gC0lCdiF+fnamNBlMQmTxaV8k4JWh+N0bly8R7syI3nz8i0DlzQnU+40VockRJjyYSUsuQYsnNKpff+wc9URKjYrKNczQ+D+zSe0KzOSh7ef0nduY36W9aOFsCO5Biyc3LQ+K7HZNI36lLc6FKf09MFLOpQfzdVzd+g+rb7UXRbCjswuR2glScBhwON7z1kwYj25CmfipwKyRGVIvHrmRZfK4zh94DIdRlajeI1frA5JCOHkJAGHEaumbufW5ft49qsgax6H0Ns37+lRcxL7Np+maZ9yVG76h9UhCeHSZCEO4RJ8ffyY2HUp36SMR9lGplfZclk+733p32Q2W1ccpla7otTvUsLqkIRwaa58DdjphkJaKfwihj5s5WdQLUyD2nHzM6gG7xfaOb7/Cns3nKRyy0JsW3mUx/dfBLqf8vUzJBTt521QO8bEg0F1jm3AiBZz8XruRbkG+YkSJQJjOy7CZmDd4uBQRtSqdbAax45Wn9iowZSbUfWJjYjHCUpwfqiG5KpM/YiglCqslLqolLqslOr0hf1+Ukr5KaVklpDJpvRdjXJT1OtayupQnJrWmondl7Fg5AYKV81Np4l18AjvdJ9nhXB4MgkrBJRS7sB4oAiQAaiilMrwmf0GA5vMikX8v4e3n7Js0t/kK5WVH3Kksjocpzd32Hom91rBr8V/pOfMhkSIFN7qkIQQTsLMEXAO4LLW+qrW2htYBAQ27GoOLAcemhiL+MjSCdt4cPspjfuUw83d8a+TOLpVU7czss18svyajv4LmxIleiSrQxLCJchCHCGXGLj10de3A577l1IqMVAGmPSlhpRSDZVSR5RSR3x83hgeaFjz/p0P0/qtJlWGxBSpmsvqcFzC5sUHGBhQU3jwshbEjCs1hYUwgitPwjIzwsA+fnw6S2UU0FFr/cVZNlrrKVrr7Frr7B4eUYyKL0zbs/4kJ/Zeolb7okSLGdnqcFzC3vUn6VVrMolTxmPw0ubEiBPV6pCEcG6hGP2G9RHwbSDpR18nAe5+sk92YJFS6jpQHpiglCptYkziI5N6riBy1IjUal/M6lBcxrFdF+hRYxLxk8Zh4OLmxIgtSVgIETgzE/BhII1SKqVSKjxQGVjz8Q5a65Ra6xRa6xTAMqCJ1nqViTGJj9y4dJ+1c/ZQpFouUn+f+OvfIILk9IHL9Ko1mW9SxGXA4mZEiyVnGIQICY3Mgg4RrbUv0Az/2c3ngSVa67NKKU+llKdZ/YrgmT9yIy+fvqHZgIq4GXE/qQDg5N5L9K4zhSSp4jNoSQsZCQsRQnIKOoS01uu11mm11qm11v0Dnpuktf6fSVda69pa62VmxiP+1+sXb5nUayXpf0xOyTq/WR2OSzm++yK9avtfEx64RK4JCxFcMgtauLyda45xaNtZarUvSoKksa0Ox6V8SMKJUsRl8FKZHS1EcEkCFi5vXNel2GyaFgMrWh2Kyzmx5xI9akwkQdLYDF7Wgljxo1sdkhDCAUgCFgA8uvucmYP+Iutv6fmjUk6rw3E5p/dfpnv1icT7JhZDlrUgdgJJwkJ8zYe1oGUELFzeurl7OXv4Kg37ViBmPDlVarQzB6/QvdoEYieIweBlLYmTIIbVIQnh8GQWtAgTtNaM6rCIiJHD4zmgktXhuKSzh6/SrdoEYseLxpBFTYmbKKbVIQnhuLRcAxZhyO0rD1kwYj15S2fn50KZrA7HJZ0/co2uVScQI3YUhixqSvzEsawOSQiH5OqzoJ2vfpob+EUM/ecG5WfMoSuDasAaVfNW+XmEuo1lk7fzW+mfaDa0KqePXMPr1buQNWTQMWlvY+oKGxWPEc7vv0iXKuPpv6AJgxc0oWOFMTy8/TRkjRlQY9aoOr7KzaDP9EaVzTUqHHdjfj7a16D64QaE4wT5yeXJCFj8D18fP0a1W0Cs+NGp26Wk1eG4rEsnbtC50jiiRIvIkOUtSZgsjtUhCeFwXHkELAlYBOrSiRusnr6DYjV/5YefU1sdjsu6fPoWnSuNI1KUCAxZ3pJEKeJaHZIQDkNmQYswa86Qddy78ZiWQ6vgEcH5rlY4iytnb9Op4ljCR/RgyLIWJE4Vz+qQhHAYWqsQb45OErD4rPdvvRnTcRFJUiegausiVofzWRnzpKNa59Kk+TGF1aGE2LVzd+hUYQzhPMIxeGlLkqROYHVIQgiTSQIWX3Ri90U2Lz5Ahca/kzKD41VMihozMl3nNKVm1zKM292buedH0HhoNTLn/Q43d+f67339wj06VhiDm7ti8LIWJP1WkrAQch+wCNOm9lnJy2dvaDWsqsMltVo9yhE9TjQ6Fh/MsEZTuXLyBkVq52PIuk4svjqWtpPqk6t4ViJECm91qEFy89J9OlUYC8DgZS1IliahxREJYR0t9wGLsO71cy8mdl9G2szJKFM/n9Xh/CvNjykoXr8AayZv5cSOc2yZv4delUdTIXlT+lQdw6HNJ8lVLCu9FrVkyY1xdF/QnD+q/EK02FGsDv2Lbv5zn47lx6BtmgGLmsnELBGmufI1YJlZI4Jk99rj7C9zihrti3F4+zluXrpvdUhUbF2MNy/eMqffiv88/97Lm71rjrJ3zVHcw7mTKU86cpfIRq7iWclTMjsAt/+5z8WjV/23I1e5cuomPu99rDiMQN2+8oDOlccxZHlLBi5uToeyo3h455nVYQlhZ84xkg0pGQGLIBvbcRFer9/RZVJdIkQM/YIfoXX/+iMiRY3wxX38fP04vuMc49vOpUb6NrTI25uZvZZy48IdsuT9jiZDqzN6ew9W3Z/E2F29KN+iCG5GrHJggJuX7tO18ngiR43IwMXNiZNQ1o4WwpVIAhZB9uzRK4Y2n0PSNAlo1Ke81eGwf/1xwnmE46eCGYO0v9aai0evsmjYX/SpMoaqaVpRNU0relcZw7LRG/F570uDAZUZuLYDcRI5xvKQV87epnv1CcSMG5WBi5tLPWER5rjyKWhJwCJYju++yOKxmylSLTd5S2a1NJYLhy7z/PFLchb9McRtPLn3jH1rjzKz11LaFOzH8MbTSJ89NZMO9AtVu0a6ePwGPWpMIt43MRmwqBnRYzn2NWwhjOLqa0FLAhbBNm/4Bs4evkrzwZVJkNS65RNtNs2hDSf56c/MuIdzN6TNzXN30zRPDx7cekzvJa1oOrwG4R3gdPvZw1fpVXsK36SIS/+FTYkaI5LVIQlhPu0/Ezqkm6OTBCyCzeZnY0iz2Wit6TCupqW3Ju1ff5xosaLwQ+40hrV5+5/7tC7Ql+VjN1Ky0R+M3tGTZOm/Maz9kDq59xJ9608jedqE9J3XhMhRI1odkhCmk/uAhfjEw9tPGdtpMRmyp6JaG+tWyTr29xm833mTs6ixp8N9vH2Z0nkhXcsMJ3aCGIzb3ZuidfMZ2kdIHN1xngGeM/k2Y1L6zPUkYmTnuL9ZCPG/JAGLENu15hibF+2ncos/yZjrW0tiePfmPcd3nCN3cXOuRx/ZcgrPn7txZt8lWo6pQ/f5zYgaM7IpfQXVgc2nGdxsFumzpaTnrEaEl3W6hYvSyCQsIT5rYvdl3L32iA5jaxItljWJae+aoyRMEY9vs6Qwpf1nD1/QtfQwpnZZRM6iPzJxZw9+yGXcKe+Q2PPXCYa3mkumXN/SfVJtPMIbcw1cCMfi2tWQnO6js3ZT+EY0oAC5nzFX6JXNoB+hQfG4GdCOCkbh+ne+mkEt5zFyRUtaDa9OX8+Z/9+Or2+oYwHgK+3sX38cP18/fiuTgyunbn52P+3tHeIQNLBsxFpO7TxL5znNGLyqLQsGr2bB4DXY/Gwhbjc0/l64Fw83aD26Fl3GVKd/oxn4+gT9d/cfBt37rJRBb3oGDQ3cDIpHG/TzMSoemwHNOMr97l/jDJOpQkpGwCLUrpy9w8wh68hdKCNFq+aye/+vnr7hxM7z/Fomu+l9XTp6lSa/9ODvRfuo0aUMQzd0Jr6FM8E3zd/LuC5LyPlnRjqMtXZCnBAieOSvVRhi1YxdHNl5gYbdS5M8rf0LCOxeeZhvUiUgdaZkpvf19vU7hjWayuB6k0mVMSkT9vUlT2nzk//nrJuzh8m9VvBr8R9pN6q604xshAgKuQYsxFdorRnebgFer9/RcXQNwkew772z+/46hp+vH7+W/sluff69eB9Ncvfg7pUHdJ/XnJZj6xDBolnJq6btYObAteQvk50WQyobdypYCAv5388rCViIr3r++DXD2y4kZfpE1OtSwq59v3z6mpO7LvBrGfslYIB71x7SpmA/Fg//i6J18jFud29S/ZDUrjF8sGT8FuaP3EChyrlo0s/6pUKFMIIrT8KSBCwMdXTXBZZP20HJmnn4uVAmu/a9e9VhEqdOQEo7J0BfHz9m9FxKp+KDiRIjMqN39uTP6r/aNYYP5g3fwNIJWyle61ca9ixjSQxCGElWwhIiGGYPXcflM7dpM6qGXSv47Ft7LGA2tH1HwR8c33GOxjm7cWbvRdpOqk+ZpoUsiWPGgDWsmr6DMg3yU7uTfc9ECCGCThKwMJyPtx+DWs4lfEQP2k+oY7eZuS+evOLU7gv8VjaHZRORXjx+RfdyI9i96jCeg6tSs3tZS+KY3HMF6+ftpVKzgpauVCZEaMk1YCGC6c7VR4zvuIjMv6Sjph1HYRtm7yJx6gT8XuUXu/X5KV8fPwbUmsDG2Tup1rEU7SY3IJyH/RfKGNd5CZsXH6B6myJUaPqH3fsXIrQ0IU++koBFmLZ1yQHWzd5FpRaFyV0ks1363LXiEOcPXaZOz3JEjBLBLn0GxuZnY2TTGczuu5yC1fLQb2VbosSw70phWmtGt1/I9lVHqNu5JEWrW/ehRIiQ0qHYHJ0kYGGqyd2WcvH4ddqOrUXiVPHt02fnhcROGJOKrYvapb8vWTB4DUMbTCHjL+kYsaUr8ZLEtmv/NptmeKt5HNx6hqYDKpC3lLU1nIUIFpNvQ1JKzVBKPVRKnfnouV5KqTtKqRMBm2lvJJKAhal8vH3pX28KPt5+dJvZyC73yV44fJXtSw9Qrnlhuye8wGxduJcupYcR95tYjN7ewy6LhXzMz9fGAM+ZnD10lXajapDj9+/t2r8QDmwWUDiQ50dqrbMEbOvN6lwSsDDdozvPGOQ5naRpEtJyeHW79Dmj51IA6vRyjPthT+48T5uC/fHztTF8c1d++tO+t2h5v/OhV+0pXD13hy6T61hWvUqIYDPxHLTWehfw1ISog0QSsLCLE7suMHfwWvKX/YmS9fOb3t+j209ZMW4TBSrmIl32VKb3FxQ3zt+hZf4+3L58n95LWlG01m927d/r9Tu6V5/Ig5tP6TWzIWkz23ckLkRIWDQJq5lS6lTAKepYRh3LpyQBC7tZMmYT+zeepEGvcmT4yfykuHjEOp7ef06jgVVM7yuont5/TrtCAzi67QwthlenTrcydl028uWzN3SpOp6XT9/Qd15jkqWx/7rdQgRHKBfiiKuUOvLR1jAIXU4EUgNZgHvAcLOOTRKwsButNcObz+bBrSd0mdaAWPGim9rfuzfvmdVnBRl+/pa85XKY2ldwvHvznp4VR7Fu1k4qtSpCx8n18Ahvv8qgT+6/oEuV8fh6+9J/YRMSJLX+OrkQJnmstc7+0Tbla9+gtX6gtfbTWtuAqYBpbx5OWA8YfCOHfsSgbMZ89lAGlYJVNqPqE4c+ICPaACCQOrlv3tvo5zmTkatb03laAzpXnYCf71f6C0Z94k9tXXaQkp5/ULdPRfatOoz3O58Qt/WBfv8+1G34AWOaTuf+lfvU61uJOPGj07vyaF49exPqtoPi7sXbdC43kmFr2zNgQVPalR/Ds4cvQ92uo9UDxqB4DFvYxaifjzLgB+Tm+DfqaLD7/bxKqURa63sBX5YBznxp/9CQEbCwu+sX7jGm02Iy5vyWOiYv0mGzaaZ0X0KCpHEo2zywyY7WWjJiHQNrTyDdT6kZua07CVPEs1vfNy7cpWvF0cSMF40BC5oQLaZ971MW4qs0oFXIt69QSi0E9gPplFK3lVL1gCFKqdNKqVNAfqC1WYcnCVhYYvvKo6yZuYtyDfOTu7C5M4JP7b3E3nXHqdS+BLES2G9t6qDasfQAnUsMIWa86Iza3oO0WVPare9Lx6/Tq/p4vkkelz5zGhHJwsVLhAiMmcUYtNZVtNaJtNYeWuskWuvpWusaWuuMWutMWuuSH42GDWdqAlZKFVZKXVRKXVZKdQrk9VIBM81OBFwgz2NmPMKxTO23mgvHb9BmWBUSJY9jal/Tei3DI4IHtXo6xm1Jnzqz9yKtf+/Ley9vhm7qQq5i9lsw49SeiwxoMos0GZPSY3p9PCI43ZUp4cpceCks0xKwUsodGA8UATIAVZRSGT7ZbRuQWWudBagLTDMrHuF4fH38GNh0NjabjS4Tapv6xn/v2iPWTNxMoVq/kcrOC2EE1a1L92iZvzc3zt2mx6IWlGxkv/WbD245w/A2C8jyS1o6ja+Fezg5OSaE2cz8K8sBXNZaX9VaewOLgFIf76C1fq31vycKouAUn1mEkR7efsrwNgv4NmNSGvUwt37t/IGrefX0DZ5DqpnaT2g8f/iS9kUGcnD9CZqOqEnNbvarprR95RHGd1tK7kKZaD2sql1vjxIicFKMIaQSA7c++vp2wHP/oZQqo5S6AKzDfxQswpiDW8+ydNI2itX4hXwmrlX85oUXc/utIHPeDOQqkc20fkLrvZc3faqM9q+m1Lk01buY+8HkY3/N3sOswX/xe7mf8OxjTSlFIf5DTkGHSGAfP/7nR6K1Xqm1Tg+UBvoG2pBSDT/cSO37zj63aQj7mj1kHWcPX6XFoEok/TaBaf2sm/Y3N87focGAyna99za4bDbNqKYz2DRnFzW6lqFa59J263vxuC0snbiNkrV/o2Z76wtaiDDM5GIMVjMzAd8Gkn70dRLg7ud2DliTM7VSKm4gr035cCN1uIhRjI9UWM7P18agprN5/9abHlPrETVGJFP6sfnZmNR+Hom/TUi9AZVN6cMoWmtGNpnO5rm7qNmtrF1PR88YsIYN8/dRpUUhyjUyf+lQIcIiMxPwYSCNUiqlUio8UBlY8/EOSqlvVcCFJqVUViA88MTEmIQDe3z/Bf08Z5IgaWw6jauFm7s5/z2PbTvDirEbKdO0EL+Uym5KH0bRWjOi8XQ2zNpBtc6l7VpcYlyXJexcc4z63UpTuEouu/UrxH/IKejg01r7As2ATcB5YInW+qxSylMp5RmwWzngjFLqBP4zpit9NClLhEFnD11lfLdlZMubnvpdS5rWz/Sui7h45Ar5Kzl+YtFaM7rZTNZN+5vK7UtSv799Ru42m2ZYq3kc/vsczQdV5NfiWezSrxD/pUKxOTZTL4IF1FFc/8lzkz56PBgYbGYMwvlsWnSAFOkTUaZ+Pq5fuMemWdsN78PXx4+upYbx5rlzzCnQWjOm5Sz8fP2o0Koo4TzcmdRhvun9+vr40b/RDPrNb0yHMTV58/Itx3ZdNL1fIf7lwkMyudlPOKSpfVdzbNcFmg2owPc/m1O79tXT19gMWoPbXsa3ncuKcf6nz5sOr2GXW4Xev/OhZ+0p3Lh0j25T6kkZQ2FfcgpaCPuy+dkY2HQ2D24/pfssT+InkYo9H0zuuIClo9ZT0rMgzUfVsksS9nr1ju41J/PiyWv6zG5E4pT2W7NaCFclCVg4rNcv3tK73jTChQ9Hz7lNiWjBOsUeETzIWuAHcpfMZlxFHANM67qIRUPXUKx+AVqOrG6XJPzs4Uu6VpuI1pr+8xsTO4G55SSFMLsYg9UkAQuHdvvKQwY2mEqKDIlpN66O3Vdn8nnvQ6HaeWk5ri717DT5Kahm9lrGvAErKVz9V9qMrWWXDwh3rz+iR63JRIsVhb5zPIkS3ZzbxYT4wMxiDFZz3JUIPkO7gW8kB6oHbNQvWbsb0ozy8wh9I37GHJRbIPWAQ+LYvitM77eahj3LUL1LaeYN3xCyhoIZj5u7GzY/G8OazqTFyJqUbVGY50/fsGTg8pD1/wnb27ehbmN2twX4+dmo1b0c7gqGNpyKLQQ/dxWM+rL/HLpMv9qT6b2gKT2n1qVrxTH4vPf90FCw+w48Hseqv+vmYPEYMcFXO9AZnS9y4ESqlEqC/y22vwLfAG/xrx+8Dtigtf7iH6OMgIVTWDl1O5sXHaBa6yLkKZbF9P6UUv8msgTJ4hIpagRePH5NqoxJHW4FrQWD1zC9xxIKVMpNpxmeuIcz5sPclxzfeZ7hTWeRMXdaOk6q51Cn54WLcdBT0EqpmcAMwBv/u3mqAE2ArUBhYI9S6rcvteFY7yRCfMG4LktInDo+bUdV596Nx1w5c9uUfpRSfLgd/ddS2ShWNx+x4kVn1aQtLB29EV9vX1P6DY0lI9Zh87XRYEBl3MO5MbD2RHx9/Eztc+eqI8SIF43GAyrRdEgVxrZbYGp/QjiY4VrrM4E8fwZYEbAA1RdvGZARsHAaPt6+9GswnZdPX9NzRgNixYtmeB8fkm+EyOGp1LoIldsWI0LE8MwZuJrFIzdgs2mHHe0tG7OBSR3mk6fUT3Sd09QuI/U1U7ezaNQGitb6jeodipvenwh7lA75ZqZPk69SykMp9aNSKn7A695a68tfakMSsHAqzx+/onedqUSLGZluU+sbkmQiRApP/KT+tzlprUmSJiGN+leiYJVfuHftEaNazWbv2mNAwKlpB753eOWEzYxrM4fcJbLRfX5zPCIYMCfgK2b3X82m+Xup1r44xWr8Ynp/IgwJzT3AJv+ZKqUmKaW+D3gcAzgJzAGOK6WqBKUNScDC6Vw9d4dhreaRIXtKmg+qFOr2Gg2oRNeZjYkVPzrZCnxPw/6VyJg7LfvWH2do4+ncOP//NUScYaXUtVO2Mar5TH4ukoVei1oQPqL5SXhM2/kc2HiSJn3LkadoZtP7E2FFKK7/mn8b0q9a67MBj+sAl7TWGYFsQIegNCAJWDilvetPMnf4egpW/JmyDUNXrWfpmE2kyJCYbrMbU7NLaWLGjcaS0RuZ0Ws57728nbIw/YaZOxjeeBpZf/+B3ktaESFSeFP7s/nZGNRwGuePXqfD6BpkymXO6mVCOBDvjx4XBFYBaK3vB7UBScDCaS0ctYndfx2nbtdSZM//XYjacHN34961hwyqP4XvcqQmYpQITOm2mC0L9gL/nZDlbDbP3c1wz2lkyZeB7vObE87D3NnR79/60KvuNO5cf0TPafVJ/X1iU/sTYYSDnoIGniuliiulfgR+ATYCKKXCAUG6QT7ICVgpVUwp1UEp1ePDFqKQhTCI1prhredz7dwdOk+oQ8rvvgl2Gx9uNdq//gRLx2widoIY+Lz3/XfU+yH5OurEq6/ZumAvo5vP4qc/M9Fxuqfpx/H6hRfda0zi9cu39JndiARJZQlREUqOm4Ab4V/xbybQ6qOR7+/43wf8VUFKwEqpSUAloDn+t4BXAJIHN1ohjPb+rTe9607lzau39J3bmPiJYwW7jQ/Jdmbv5bx8+poyjf8gXPj/jhY/TLxK9UNSkn2XmDTZUhE1ZpTQH4AdbJy9k8mdFvBb2Ry0GF3b9P4e339BtxqT8AjvTr85nkSP5Rw/J+GgHDcB/6m1Lqy1zqK1nvVvuFpv0lq3DUoDQR0B59Za1wSeaa17A7mApMEOVwgTPL73nO41JhEhkgd95zYmaszIwfp+rTVu7v5/Ck1+682kzov/f2UnIHxEDzL9ko6Bq9rSY14TJh0dzMgdvRiwvjP5KvrXE3b0EfKKcZuYP3g1Rerko17fiqb3d+vyA3rXm0b8xLHoOb0+EewwEUy4IMdeC7puaBsIagL+sGael1LqG8AHSBnazoUwyo2L9+hTfxqJksel5/QGeEQI3u1JH05Fv/fy5vmjl/95rUKLwvRf0Rp3dzeWjN5I89zd6FZiMGf2XKDttMZ8+2MK//uD3R17SsWcvitYM3krFVsXo2KbYqb3d/bwNQa3mEv6rMnpOK6mw/98hLC3oP5F/KWUigkMBY4B14FFJsUkRIic3n+ZoS3n8sPPqekwpqYho9LCNX+lWscSLB6xnl7VxrF+5k6unLjOiR1nmdNrKRcOXabr/Ja4ufkvXenoI+EJ7eaxbdE+6vWpSLF6oZs9HhT7Np5iUs8V5PozI036ljO9P+F6HHUhDiCTUuplINsrpdTLr3970BPwEK31c631cvyv/aYH+oU0aiHMsvuv40zutYI8xbLQqHfZULf3XfZU3L/xmHUzd+D10v9E0Ie1lt95veflk1ckSp2AzvNaADj0Ih0QMHHNcxoH1h+n2cia5KuQ0/Q+187ew+LxWylW/RcqNytoen/CxTjuNeDTWuvogWzRtNZBqtUZ1AS8/8MDrfV7rfWLj58TwpGsmraD5ZP/pmSdvJRv/Huo2gofKTwvHr/C6/W7f5/z8/VfYzlXiWzkKPIjV05c59dyP1OuVdFQ9WUvfr5+9K85ntN7L9J+SgN++jOT6X3OGvwXW5cfplaHYhSskMP0/oRwBl9MwEqphEqpbECkgDUuswZs+YDgzXQRwo6m91vNztVHqde1FPnLZA9xO0tHbyR1xmRUaF6YFBkSEyNuNNJmT0XLCfXpuawtu5YfYGzzGUzvspAnd58ZeATm8n7nQ6+Ko7h6+hbd5zfn+5zmL5wxusMiju26QMvBlcj6W3rT+xOuwYFPQS8NbQNfm6lSCKgNJAFGfPT8S6BLaDsXwiwf7hGOGS86rYdX5dmjlxzfdCJYbbi5Ka6eucXIFrMoWb8AZZv+iZ+fHzZfP7xevmVqx3nsXX2E+9cecunIFYc//fwpr1fv6FZ2OMM2daH3/KZ0LDOCK6dumdafr48f/T1nMmRJc7pOqk2HCmO5cvaOaf0JYTJ3pVRsrfXTwF5UShUAImut//pcAyooq/wopcoFXP+1XKSESfW31dqEuh2PNwYEA3i8MeZN1+ONMcXrPV6HvgRduDc+BkQC7m+8v75TEKg3776+02dEiRaRoQsbkyBxLNqXHsnVsyErYRg1RiRSZkiMzU8TwV1zdGtgVciCx+/161C3AYAK3ezieEniMHJ3HyJECk+7QgO5fTnIK+n9byiRv74AUOwEMRixrh0eHuFoXWwoD28H8v4VMUKIY/iPSBENaUYbVNTCFtGYClW28KFf1cwWwZiV0bZv7XxUax3y00xfECFZUp24besQf/+1Vm1Ni00pVQr/NZ/f4T85+REQEUgDZMG/LvAArfWjz7UR1L/cvUqp6UqpDQEdZ1BK1QtF7ELYxZtX7+hRfwZvXr2jz7zGxE8SspWZXr94y+n9lzl76Mq/ydcZ14gOzKPbT+hcahhaawasbke8EP6Mgurpgxf0qDaB8BE96LugKVFjBGnVPhEWOXA1JK31aq31L4AncBZwx//s8Dwgh9a69ZeSLwQ9Ac8ENgEf1vq7BLQKSdBC2Nvj+y/oVnc64SOG93/DD+ZCHZ/jrGtEB+bulQd0LTOcyNEiMXB1O2LENb7W8sduXrxHnzqTSZQ8Lj1medqldrFwUg6agD+SRWs9S2s9UGs9Smu9CQhSceygJuC4WuslgA1Aa+0LhP5cpxB2cvPyA/rWnUyiZHHoNdvTLiX6nM3V07foUWEkcRPHpv+KtkSObu7I9PS+fxjeci4Zc6Wh7ZiaLnNGQYQ5nYP43P8IagJ+o5SKQ8BnCqVUTuBFEL9XCIdwev9lhjafw3fZU9J+XC1TFs2IGjMynWY0IkGyOIa3bQ/nDl6mb/VxJM+QmD52KGO4c9URpvddSd7S2anTrbSpfQnn5KizoJVSRZRSY4HESqkxH22zAN+vfDsQ9ATcBlgDpFJK7QXm4F+YQQinsnvtMab0XE6eYj/SqE95w9uPHica2X7PSPf5zZ12lH106xmGNJhChpzf0nVuU9PLGC4bv4W1M3dSoWlBStTNa2pfwgk57inou8AR/CdhHf1oW4P/HURfFdQEfA5YCRwGHgBT8b8OLITTWT1tB8smbKVkvXyUb/KHoW3fvfKAwfUnkypjUpqPrGlo2/a0e+VhxrScTY4/M9Fucn3Tl9ic1HUJ+zacxLNfBXIVzmxqX8LJOGgC1lqfxH/C1R6t9eyPthVa6yAtChDUBDwH/+UnBwBj8Z9mPTckQQvhCGb0W8WOlUeo170Mf1T42dC2j2w5zfxBayhYLQ+lmzjv0osbZ+9iWvcl5CufE88h1Uzty2bTDGkyg0vHb9BxYh3SZUlman/COYTm9LMdFuJAa+0HxFFKhehaTVCnHqbTWn/8sXS7UupkSDoUwhForRnRai7RY0eh1cjqvPV6z951Jwxrf8HgNaT8Pgmeg6ry+rkXWxfsNaxte1o2egMx40ajfMsi3Ll8n9WTtprW1/u3PvSqOZGR69rTc2p9WpUZycPbzrO6mAizbuB/q+4a4N8VJrTWIz7/Lf6COgI+HjDxCgCl1M+Ac76jCBHAx9uXvnWncvHYdTpOqEPWfN8Z1rbWmsH1JnP07zO0Hl+X3MWzGta2vU3vsZS9a4/ScGAVcph8evjFk9f0qD6BcOHd6TOjIZGjGbOQhnBijlsP+IO7wF/459NoH21f9bW1oE8rpU4BPwP7lFLXlVLX8C/E8FuoQhbCAbzzek+P6hO4eek+3Wc05PufUxvWto+3L32rjePS0at0munJj/kyGNa2PWmtGdJgCldO3qDzDE++zZzc1P5uX35Af8+ZJE4Zj67ja+MeTuoIh2kOeg343/C07h3YFpTv/dr/7OJACaAwkBLIC+QLeGx+RW8h7ODNy7d0rTyWR3ee0ntOY77NlNSwtt+9eU/38iO58899eixoTvqfUhnWtj299/KmV6XRvHz6mt5LWhI3sbmrZZ3cf5mxXZaQ9bd0NO4tdYTDMke+BgyglFqrlFrzue1L3/vFBKy1vvGlzdjDEMI6L568pkulsbx++ZZ+C5uRLG1Cw9p+/dyLLqWH8fTBC/oua0PK75MY1rY9PX3wgh4VRhExcgT6Lm1l+unhzUsPsXjCVopVy03Z+vlM7Us4MAcfAQNXgbf43x00FXgNnAGGB2yfJed2hAjw+O5zOlcYg5+PH/0XNSdBUuMW03j28CWdSw7lndd7+q9qR6JU8Q1r255unL9Dv5rjSZouEV3nNMU9nLn3CM8eup7d605Qr0sJcv35g6l9CRFCP2qtK2mt1wZsVYE8WuudWuudX/pGScBCfOTe9Ud0rTyOCBE9GLi0BXESxjCs7Ye3ntCl1DDc3N0YtLq96adxzXJ8+znGtppDtt9/oOnw6qb2pbVmWJsFXDp1iw6jqvPtD8559kCEkIPfhhQgnlLq32tLAY/jBeUbJQEL8YnrF+7Srep4YsSJyoDFzYkeO4phbd+6dI9uZYYTNWZkBm/uToy40Q1r2542zd3NomF/UbROPiq0KmpqX97vfehdfxovnr6h1/T6xE0U09T+hINx/FPQrYAdSqkdSqntwN9Ay6B8o/OVIHEDXyPeD4365Rg01V1pYz4LGfGpTxlV5cegZtxtxtRKVn5Bb+fSxYf0ajCTvjPr03dRczpXn4zXK/+6xKH9+Vz55yG9ak2i38JmDNzUnQ7FBuH18m2I27N5eYUqHgDb2+D3P7PLfBImjU29PhW4988ddi07gJtBBRU+Lczw/M5TelSbwIi1bek9rR7tSo3g7Zv3X2/IzZhT5EYVijCqHSN+ztrk1c0MY79EGlLRgR/wn5xcEsgNPA7KN8oIWIjPOH3wCv2bziFV+m/oPa0uEQxc2/nMgcv0rTaWlD8koc/S1qYXPTCD1pqh9SZyZu8FOsxsQoZcaU3t7+alewxoOI3k6RLRaVJd3Nzl7Us4hO5a65f43/tbEJgETAzKN8r/YCG+4PD28wxts4AM2VLQbWItPMIbN+no8OZTDKk/me9zpbFL0QMz+Lz3oVe54Ty69YRey9uRKGWQLn2F2LGdFxjfZQk5/viBRnJ7UpjgBNeAP5TmLQZM0lqvBoL0iVoSsBBfsWvdSUZ3WUb2vOnpMLKaoSOvncsPMabFLH4unIX2UxuaXvTADC+fvKJrycG4uSn6Lm1NtFjGXTMPzIa5e1g+0b+YRsl6+UztS4gguKOUmgxUBNYrpSIQxNwqCViIINi85BCT+60mT5FMtBxezdDi8Rtm7WRq10XkK5+TZqNqGdauPd29fJ+e5YYRP1kcesxvhkd4c6eXzOi3in0bTtCwdzly/CG3J7k0x5+EVRHYBBTWWj8HYgPtg/KNkoCFCKJVM3Yzd9Qm/qyci4YG1xJeNnoDC4euoVjd/NTrW9HQtu3l7N6LjGg8g4y/pKP1+Dqm9mWzaYY0nc2VM7foNKkuqeX2JNfkBLchaa29AkoQ/hPw9T2t9eagfK+pCVgpVVgpdVEpdVkp1SmQ16sppU4FbPuUUpnNjEeI0FowZgsrJm2jdIP81OhQ3NC2Z/VezpopW6nYuhiV2hrbtr3sWH6QWX1XUKBiLmp0KW1qX+/fetO71mReP/ei12xPQ+/ZFsIeTEvASil3YDxQBMgAVFFKfboa/TUgr9Y6E9AXmGJWPEIYZWqv5WyYt4eqbYpSrskfhrY9oe08/l68j7q9K1C8QQFD27aXRcP+YtPc3VTrWJI/quQ2ta+nD17Qo8YEIkePRK85nkSMHMHU/oQFHP8UdIiZOQLOAVzWWl/VWnsDi4BSH++gtd6ntX4W8OUBQM4jCacwrsNCdq46Qv0eZSnd0LhEqbVmWKNp7P/rGM1H1qJEw98Na9uexrSaw/Gd52g+sqbpa19fP3+XgY2mkzJDEtqOqWHo9XnhACQBh0hi4NZHX98OeO5z6gEbTIxHCMPYbJqhzWaxe+0xGvUpT+kG+Q1r28/Xj/41x7P/r2M0G1GTiq3NXWnKDH6+fgyuN4U3L7zoPNOTiFHMHZke+fsc0/uuJE+xH6napoipfQn7UTj+NeDQMDMBB/YxNNAfiVIqP/4JuONnXm+olDqilDri6/XGwBCFCDk/XxuDG89gz1/HaNS3gqG3xPh4+9K3+ji2Lz1Avb6VqNm9rGFt28vzRy8Z3GAKSdIkpOnQaqb3t3Ly32xetJ/q7YqRp/iPpvcn7ERGwCFyG/i4sGoS4O6nOymlMgHTgFJa6yeBNaS1nqK1zq61zh4usrn3GAoRHH6+NgZ5zmDvuhM07l/R0CTs5+vHkHqT2DBrJ9U6lqLRoKqGtW0vJ3ddYMGQtRSslsf068EA4zou4tzhq7QdU1NmRguHZ2YCPgykUUqlVEqFByoD/ylOrJRKBqwAamitL5kYixCm8U/C09m33j8JF6/zm2Ft22ya0c1nsnLCZso2K0SrsXWcbrGOBYPXcHLXeZoNr0HStIlM7cvH25d+9aby6ukbesxqRMy4UU3tT5jMCW5DCg3TErDW2hdohv8NyueBJVrrs0opT6WUZ8BuPYA4wASl1Aml1BGz4hHCTL4+fgxsNJ19G07SdGBlQ5Ow1ppJHeazYMgaitTJR4dpjUyvw2skm00zuMFU3r31psusxoQ3cE3twDx79JLedSYTPXZUuk0wdvlQYQETT0ErpWYopR4qpc589FxspdQWpdQ/Af/GMvaA/p+p9wFrrddrrdNqrVNrrfsHPDdJaz0p4HF9rXUsrXWWgC27mfEIYSZfHz8GNpzG/o3+SdjoZRJn91nO9B5LyF8xF93mNsUjgrmJzEhP7z9naMOppPw+CZ6DzT+VfuX0LUa0nMv32VPSrK+sGe3UzL0GPAso/MlznYBtWus0wLaAr00hK2EJYSBfHz8GNJjGvg0nDb8mDLBkxDrGt51L7hLZ6L2kFREiO08VpaPbzrB4xDqK1s5LwWp5TO9v99pjLBizhT8r5KB0nV9N7084H631LuDpJ0+XAmYHPJ4NlDarf6erB6zdwMclL+sYdV3PgM9U2rFO2SltzC0sRn3a/NpvyhcY2GoBndzcaNy/Im4RI7Bq5u7/jSeEdYX/mreP976aliOqM2BNR7qXHRaqesIAtrfvQvX9H+j3X67RO6v7ItJmSU7zEdW5fvIal45eDXxHd2P+D84b+hfJ08SnfpcS3Lxwh2M7L4SsIYOuuyt3g/7OfULfjrPMJQjltdy4n1zanKK1/tqCTwm01vfAf1lJpVT8UEXwBTICFsIEvj5+DGw+lz0bTtGoeylK1zV2BLZl0X4Ge04nfbaUDP6rI9FiO8fdATY/GwNqjPVfwWpxK2LEi25qf1prhrWcy42L9+g8oTaJU5n2XirMErpT0I8/3EETsDnUaouSgIUwiZ+vjUEt57F7/UkadStF2Xp5DW1/95pj9K0ziRQZEjN0Q2dixY9haPtmefnkNX0qjiR6nGh0nd/c9All77y86V13Kn6+NnrNbECU6JFM7U8YKDTJN+Qj5wdKqUQAAf8+DHFLXyEJWAgT+fnaGNxqPrvWnSRNJuPvSz205Qzdy48kYfJ4DN/chXhJYhvehxmunLzB6KbTyfxbBuoPqGJ6fw9vP6Vvg2kkTBaXThNqG1rTWZjLgtuQ1gC1Ah7XAlYbcRyBkf+FQpjsQxIe2mZhkPYP7m06J3aco0upocSIG43hm7vyjZOcZt22YA8rx26gbIsi5K9s/iIdZw9dZXzXJWTP9x31upYyvT/h+JRSC4H9QDql1G2lVD1gEFBQKfUPUDDga1NIAhbCDmx+Nmx+tq/uly5rCpoPqUq5xn/gESHocyTPHbxMx2KDiRglAsM2dyX5d19adt1xTO28kJO7ztFqQn1SZUpuen8bF+xn9YydlG2Yn4IVfza9P2EAE09Ba62raK0Taa09tNZJtNbTtdZPtNa/a63TBPz76Sxpw0gCFsKBvH/rjUfEcOQpmZVha9oRPRiTqy6fvEG7QgNAa4Zu7My3WVKYF6hB/Hz9GFB9LK+evqbnklZEi23+LQ5Teq/k2K4LNB9Yie+ypTS9PxE6shKWEMIurp+/y5DGMxnddj5PH7yg/+IWwZo0dPPCXdr+OYC3r98xZF1HMuRMY2K0xnj+8CV9K48idqJYdJ7TzPTbY2x+NgY2mcXDu0/pPq0e8b4xbaEjYQT7T8KyG0nAQjgYm5+N6+fuMH/YOtw93Pk2U7Jgff+9aw9p9+cAnj54wcA17cn+R0aTIjXOxSNXGdtiJtn+yEil9iVN7+/1cy9615lK+AgedJtaL1in+4UdWTML2m4kAQvhYD6MAF8+fU3ilPFJlCJusNt4dOcp7QoP4PY/9+m1pBV/VP3F6DANt3n2TrYv2Ue1rmVJ9UPSr39DKN26/IChLeeSNnMymvWvaHp/QnxKErAQFlDKP8m6uan/uSXGZtNEihKBbPkz8P6dDy+fhqwG9vOHL2lfZCBn9l2k/ZSG1OlV4d9+HdX4VrN5+eQV7SbUwSO8+aPSg1vOsGDURv6snJNiNcxfHlMEjwrl5ugkAQthRx8SoA5YhtJm+//zZNFiRSH1D0nIlj8DLYZXo1q7Ypw9eJl960+EuD+vl2/pWno462Zsp3K74nSb19Sh149+9fQ1oxpPI9UPSanavrhd+pw3fAOHtp2lUe+yMinLEbnwKWi58CGEHWmtUUrRtE8ZYseJQvzEsYkaIzIRI4cnXPhwRIgUHu/3Plw/f4cti/Yze6B/CW03N/WfZB0cfr5+jGkxi1sX7tJgYBWGb+pKz4qjeHLvmZGHZphDG0+wce5uKrYqwoGNJ7l49Jqp/WmtGdpiDqPXtaPblLo0KzKUZw9fmtqnCDpnmM0cUpKAhbCzRMnj8Gf5HLh7uLFqyt88uvsMr1fveHznGc8evcTH25c7Vx7+O0oOTfL92MoJm7lz5QGdZzVmzM6e9Kw4issnroe6XTNM6baEH/NloP2EujTN15f3b71N7e/1i7f0qTeNUWvb0HVyXTpVHIuvj5+pfQohp6CFsLO71x/TovQo3nl5EylqRNbN3MXmBfs4tvM8187d4fblB4Yn3w8ObTpJ6z/64evjy/DNXfilZDbD2jaS16t3jGg2iyRpElK7exm79Hnj4j1GtFnA9z+lomHPsnbpUwSBC5+ClgQshJ25uSmuX7xP6yKDyVM8Kx0m1iVGnMAXoPj0GnHEyBGIHC0iQIgnVF0/e5uW+ftw9fQteixoQaW29rnWGlwnd19g9eRtlPH8g0x50tmlz91/HWfZpG2UqP0rf1TIYZc+xVdIAhZCGMVm07i5KW5euk+T/P1I92Nyus/yJGa8aIHuX7ByLrrPbMSMg32YtLM7veY2IWOuNP+OkkPi+cOXdCg6iO1L9lO3dwXaz2xil1nHwTWjzwpuX35A23G1iRTVmLrQXzNz4FqO775I84GVSJPJ/NuhxBeEYhUsZ7h27Hh/cV+h3cE3mhHXZhys6LwjtaSN+Vxm2B/A15dQDpJwoUhYH3MzoB0/wJ0oPH7+jmYlRjJoQWPipkzI8ze+/+4TK140arcvRp4imTh7+BpTB6wlQkQPkqdNyIClLenXeCYHt50L8adoP2BI8zncuvqImp1K8s23CelTdSwvHr8K+YH5+n59nyDQ3v7XfN95ezOs4WSGb+lGg97lGd18ZrDaUe7B/zu3AYMbTGX0ls50m1KPFn8M4IWXT7DbCTQeN4PGPAbcTubm4Lek/csJEmlIyQhYCIvY/Gy4ubvx8tkbmhQZxuUzt/99zc3djXqdS/Br0cyM676c4e0XsnnJQdbO2cO0AWs4deAyPabUJXeh0K9ytXDkBvrXHE+aH1MyensPkqX/JtRtGun8oSssHbmeonXy8dOfmezS54snr+lXezIx40aj05T6Ur5QmEL+Vwlhoc9VSMr5x/fkL5WVcd2XsX3VUV48eQ34Xz9+5+XNneuPAOg6oRZFDFhAYteKQ7QvPJAIkcMzalt3sv3+Q6jbNNK8ASu5dvYWrcfXJVqsoBeoCI3Lp24ytv0CsvyWnrqdHPM6eVjgyqegJQEL4YDiJIiB9zsfbly8/+9zSvnPiE6QJDYFSmXjwNazbF99jN8r/EzkqBFD3efFo1dpkbc39288ou+KtpRs9Eeo2zSKj7cvQxtMIUbcaDQZVt1u/W5dtJ+1M3ZQrlEB8pb40W79io/IJCwhhD09f/IKrSFG3Kj/To6KFCU832VNwfBlzbl97RGzh61n2oA19K0zGa/X7wzp99Htp7Qp2J9DG07QdHgNmg6v4TCnX6+cusn8QaspUCk3eUpnt1u/U7ot5ezhq7QaWpkU6RPZrV/hz5VHwE43CUuIsGD3upP8lO87Wg+uzKkDl3n13IuU6RORNnMyTu77hyUTt3Hznwf+O3u9NbTvd2/e06fqGOr2qUiFVkX5JnUCBtSawJsXXob2ExKLh68jZ9EfaTG6Nmf2XeK5HVas8vXxo3/jWYxd15YeU+vRovhwXr8w9mcuwibH+GgrhPjXh2pII9ovYvGErbx9857vfkzOlbN3mNBjOb3qT+fc0eumxmCzaaZ1W8yIJtPJkvc7Rv3dnUQp45vaZ1D4+foxtOEUIkWJQKuxde3W77OHL+nvOZO4iWLSYXQN02sWiwChOf0sI2AhRHB9uE/YZtP8NXcvYPyKWEG1ac4u7l17SPd5zRmzoydjW89m14pDdo/jY7cu3mNGj6V4DqlG/go52b70gF36PX/0OpN7raTZgApUbvEnC0Ztsku/YZ4TJNKQkhGwEA7o02Rr0C3MIXJq9wVaFujD/RuP6DqnKd3nNyNW/BjWBYT/utaP7z4jZzH7ToxaN28vW5cfpmrLQmT8ObVd+w6LFK59DVgSsBBOIKirXhWsnIuoMSMb3v/dKw9omb8P03ssIUehzEw5PIAClXIb3k9wnN5zgYx50tu93wndlnH/5hM6jKlBNBN+1uITLnwKWhKwEC4iQbI4NB9ShWGr2xL3m1iGt2/zs7FkxDqa/NKD2//co+P0RvRZ2tqUvoLi1J4LxEkYk8TfJrBrv2/fvGdQs9nEiBOV1sOq2LVv4VokAQvhIh7cfEK3KuOI+00sRvzVjmTpzLll5tbFe7T9sz+TOswnc97vmHJ4AIVq/mZKX19yes9FADJZMAq+fPo2MwauJdefGSlRK/QLoYjPU1qHeHN0koCFcCGn9l6ifanhuIdzZ9iadmT4KZUp/dhsmpUTNuP5czcun7pBmwn1GLimPQmSxzWlv8DcunSPpw+eW3IaGmDV9J0c2naW+l1LkfI7x1q+02W4+CxoScBCuJhr5+7QutgQXjx+xYClLfm5kHnrJ9+79pCORQczttVs0v+UmslHB1OiUcEQl0oMrjN7L9mtVGFgRrRdwKsXXnQeX4sIkcJbFocrk0lYQgin8vDWU9qVHMa183foPrMRxWqZd4pYa81f0/6mUY6unN1/iWajazNkc1e+SWX+tdlTey4QL0kcEqaIZ3pfgXnx9A1DW84jcap4NO1X3pIYXJ6MgIUQzubFk9d0KjeKI9vO0GxIFer3KmfqAhIPbz2ha4nBDG84mVQZkzHxyEDKNC9sap+n9lwArLkO/MHJff+waMwWClbIQcEKOSyLQzgf51uIw12jooe+NqcxVUvB0eoKG0EZVA/Y8RhzitCoPxqjfspfSm/vgT6NZ9Owe2nKNf6DRKkTMKTVfN6/9f5vLAadMtZv37Fl8UGO7bpI85E18Rxag7wVcjGi6UxuXboX9HaCWFf45rk7vHj8iox50rF57q4Qt/M1ytv7i6/PH7KGDNmS07Rfef45do3r5+8EvqNBH0aUEetzG1Wb2GTOcCo5pJzjNyCECDGbTTOp90om9l7Jz79/z5BFTYkVL5qpfT6595xelccwqN5kEn+bkPF7elGpTVHDCztorTm996KlI2Dw/xkPbjyT1y+86DqtviHVqUQAOQUthHB2a2btpk/DGSRNHZ9RK1uRwqTblD62Y9lBGuboxsENJ6jTszyj/+5Gyh+SGtrHqd3nSZgiHvGSxDG03eB6/vgVgzxnkCh5XFqOqGZpLC4jFBOwnGHkLAlYiDDk0N/naF9xHG7ubgxf2pysv5k/g/j5o5f0rzWRfjXHE/ebWEzc25v+K9qQu3hWQ0bEpz9cB/7VutnQH5w5cJnZg9bwW8lslKib1+pwhIOTBCxEGHPl3B1alxnFvVtP6DO9PkWq5LJLv3tWH6Vhjm7M6beSZOm+ocf8Zsw5M5TqnUoRJ1HMELd77cxtXj19bdn9wJ9aNn4rBzefpkGvcqTNktzqcJyfnIIWQriSx/df0L7iOI7uukiLARWo16OMXe7dffXsDQuGrqVWpg70qjyGa2dvU7VjCeacGUr3ec3IWuD7YMehtebMvkuWXwf+QGvNsBazefrgBV2m1jdlbe6wQooxCCFc0ts37+ndcAZr5uyhfJOCdJlanwiRPOzSt83PxoENJ+hefiR1f+zMsrGb+D7ntwxY2ZbpxwZQvlVRoseJGuT2Tu25QOJvExI7YUzzgg6G18+9GNBwGrETxKDdmFp2W5jEJWkd8s3BSQIWIgyz+dmY2HMFk7otJXfRzAxe0ZpY8aLbNYb71x8xs9cyamRox6C6k3ly7zkN+ldm/j+jaT+tESm+T/LVNi4euQpApl8dYxQMcOn4Dab1XsHPf2akbOPfrQ7HackIWAjh0lZP207fOlNIni4RIze0J0V6+69t7OPty47lB2lfdDANs3dm/fTt5C6elcmHBtBzUUvSZk0Z6Pdl+jU9nWc1xtfHl5dPX9s56i9bM30Hu9ceo1ankqT+4esfJETYYmoCVkoVVkpdVEpdVkp1CuT19Eqp/Uqp90qpdmbGIoT4sgObTtGu1Ajc3d0ZvrYt2fJnsCyWG+fvMLH9PGp+14a5/VeSMU96xu7uTf9V7fghd1oAwnm4U7dPRQav78T7tz60LtCXY9vOWBbz54xpv4AXT17Tfnxtwkewzyl+lxGaCVhheQSslHIHxgNFgAxAFaXUp3/RT4EWwDCz4hBCBN2V07doVWQwd689ove8JhSvY/8ygx979ewN8waspOZ3rZnefTHfZknB8C3dGLqxC6O296BS2+JsnLWTpr9059Kxa5bG+jmvn3sxouUckqf7hjodi1kdjtNRtpBvjs7MEXAO4LLW+qrW2htYBJT6eAet9UOt9WEg9GtLCiEM8eT+C9qXHsmhLadpOrAyjfpWMHU956DwevWOJSPWUfO7NkxoN5dEqeITP2lcelUaxejmM3n35r2l8X3N8V0XWD1tO6Xr5iXLL2mtDse5yAg4RBIDtz76+nbAc8GmlGqolDqilDri9/KNIcEJIT7vndd7+tWdwvJJWyndID89ZnsSKUoEq8Pi/VtvVk/cQs30ramUohn7/zpmdUhBNqPfKm5efkDbYVWIGj2S1eE4DZmEFTKBfWQO0Y9Eaz1Fa51da53dPXqUUIYlhAgKm00zrdcKxrRfQPb8GRi2pi0Jklm73OMHNptGO8FtJh/zfufD0FbziBk3mpQuFIC5Cfg28PGir0mAuyb2J4QwwYa5e+hedTzxEsdmzMaOZHGAJR+d1eUzt5k/aiP5SmYlb8kfrQ7H8WnkPuAQOgykUUqlVEqFByoDa0zsTwhhkuO7LtCy8GCePHhBv0XNKdf4D6tDclpLJv3N2SPXaNavAnFDsQRnWOHKp6BNqwestfZVSjUDNuFfNHeG1vqsUsoz4PVJSqmEwBEgOmBTSrUCMmitX36uXXd3GzFieoU6vpfKmGswvsqYGrMoYz4LaQNW3DHq/6026Jgcj+vVFVZB+F3de/iGNhXG03pwJer3LEuarCkZ2Wnpf2oLG7bi0zuDJlXZjJkKa1hdYR93bD4wvMUcxm3uSNuhlelSeXzwT6e7GTBv1UnqATvDZKqQMvU3oLVer7VOq7VOrbXuH/DcJK31pIDH97XWSbTW0bXWMQMefzb5CiGs9c7Lm4HN5zJ90F/kKZqZkcubkchBrgs7k3s3HjO553Ky5ElHqXp5rQ5HWMRJPgIJIRzJsik76FFnGnETxmT0qpZk/VVurQmuzYsOsH/TKep0LklyO9RmdkZSjEEIIQJxbM8lWpQaxaN7z+k7sz4VPPNbHZLTGd1+IW9evaX92Jp4hDftiqDzCs0ErDA+CUsI4eLu33pKm/Lj2LXuJHU7FKPLlHpEjGz9/cLO4sWT14xuv5DU3yehetuiVofjkGQELIQQn/H+rTeDW85nav+15C6ahZHr2vFNynhWh+U0Dm45w4Z5eynf5He+z5Ha6nAcj6yEJYQQX7Zi+k66VRlHrPjRGb2hAz/9/r3VITmNKb1XcP/GE9qNrkHkqBGtDkfYiSRgIYRhTuy+SItCg3lw8wm95nhSuVVhKUYfBO+8vBnacg7xEseiyYAKVofjUOQUtBBCBNHD209pW2o4O1YeoVbHEnSbXt8h1pF2dBeOXmfByI38Xi6HnD34QAM2HfLNwUkCFkIY7v1bH4Y2m83kHsv4uWBGRq1vT+JU8a0Oy+EtGbeZW5cf0LBXWcJ5uFsdjmOQa8BCCBF8q6Zup2vlccSIG43RGzqQ448frA7Jofn6+DG553KSpIpPqXr5rA7HIcgpaCGECKGTey/RotBg7t14RM/ZjajSWq4Lf8nRHec5uOU0VVsVIla8aFaHI0wkCVgIYbqHt5/SrtQIdqw8Qs0OJei7oAkx40py+ZwpvVfiEcGD2p1LWh2K9WQhDiGECJ0P14XHdFhIxpxpGL+1M5l/kSUsA3P32iNWTdvBn5VykjZLcqvDsZScghZCCINsmLuHlkWH8ObVWwYsaU71dsVwc5NT0p9aNHoTTx++pHHfcmH3lH1oJmBJAhZCiP91/fxdWhQawt/LDlGtbVEGLGlB7AQxrA7LoXi9fsfMgWtInzUlBcr9ZHU4LkspdV0pdVopdUIpdcSefUsCFkJY4p3Xe4a3nMvwFnNI92NyJmzrTLb8GawOy6FsW3qIC8euU6dzyTB5L7V/NSQd4i0Y8muts2its5t0KIFyuvIbEdx9SRnzaajbuekWM/TBAM8N+gjjq4wp8q6DUFj96ww63WXYWTODfsgGncbTRh2XmzG/83AGHJebQT8bFYJTyVvXn+bixQd0HlOdfguasmTy38wZsBo/X1voA/I2oHA9oLUBsQD4+QWvX2BS1yWM2tCBSs0KMmvAav8XfH1DHYrycZL7jA360TsiGQELISx368pDWpUdw/qFB6jYqABDlrck3jexrA7LIVw8fp2tSw5QtlEBEqUIe0UuQjkCjquUOvLR1jCQLjSwWSl19DOvm0YSsBDCIXi/92Vs9+UMajmPFOkSMX5zR3L+mdHqsBzCjH6r8PHxo0GvslaHYl+hn4T1WGud/aNtSiC9/KK1zgoUAZoqpX4z9Zg+IglYCOFQdq47SbPCQ7h/6wk9ZzakUe+yYb5Y/bOHL1k0agO5Cmcma97vrA7HpWit7wb8+xBYCeSwV9+SgIUQDufe9ce0LTWS1dN3ULp+foatak2i5HGtDstSq6Zs587VhzTqWx73cGHlrTsUi3AEYRKWUiqKUirah8fAn8AZkw/qX2HltyiEcDI+3r5M6rGcvvWmkih5XMZu7MCvJX60OizL+Hj7MrXncpKlTUSJWr9aHY7dmLwQRwJgj1LqJHAIWKe13mjm8XxMErAQwqHt23iKZoUGc+vyfbpMqkuzgRUJH9HD6rAscXDLaY78fZZqrQoTI3YUq8OxDxNHwFrrq1rrzAHb91rr/nY4on9JAhZCOLyHt5/Srswolk7YSrGavzJybVsSpwp7M4IBpvRcTsTI4anWurDVoZhPg7KFfHN0koCFEE7Bz9fGjP6r6VFjInESxmDc5k6UbpA/zC1jeeuf+2xecpDClXMRR1YPc2qSgIUQTuXw3+doWnAQJ/dcpFGvsgxf3Ybk6RJZHZZdLZmwFTd3RblG+a0OxXxSDUkIIRzHk/sv6FV7CoMazyRR8jiM3diBam2KhJnblR7cesrfK49SpFpuYsSJanU45pJiDEII4Xh2rjlGw7z92b32ONXbFmXMhvak+zG51WHZxeLxWwkfIRxlG+SzOhRT2WktaEtIAhZCOLWXz94wtMUcetSYSJTokRixpg0NepYhQiRj1tp2VHeuPmTX2hMUr5mHqDEiWx2OCAFJwEIIl3D473N45h/Aujl7KNuwABO3dSbLb+mtDstUi8dtIXLUiJSuZ7fVE+1PrgELIYTj83r9jgldl9K+7Cj8/GwMXN6KVqNquOwI8frFe+zdcJKSdX4jcrSIVodjPI1/NaSQbg5OErAQwuWcOXiFpgUHsXj0Rv6olJPJe3uSu1gWq8MyxaJxW4gWIzLFa+axOhTDKUJ+/dcZrgE73ZTBSO7eZI5xO9TthDPoLu0bQVzv7GueKGNWtfEzosasMqhOqFH3Zxp1m6dh9YAN+vkYFk/o2zGipjCAu1F1hQ1oxxuYNWwDuzeepvXQKnSf5cmedSeY0H0Zzx69Cl48PsbUFTaM7f/fvy6fvMnhv89Stn4+Vk/bwfu33kFrw9GO6XOcIJGGlIyAhRAu7cqZ27QsMZyZg9aS4/fvmfx3Z/6oYLeCN3axYNQmYsSJStHqv1gdiggGScBCCJfn52tjyfitNCk0hBuX7tN2RDX6z29M/CSxrQ7NEBeOXefEnouU9yzgeutkyyQsIYRwfneuPqRD+bGM67qU9FlTMHlbJ8o1KoBHBKe7Gvc/FozeROwEMfizUk6rQzGOTMISQgjXobVm3Zw9eP4+iJP7LlO/Wymmbu9C/jLZDbn2bJXT+y9z9tAVKjT5nXAeBs1TcACuPAlLErAQIkx6dPcZvepMoXOV8bx67kWHMTUYs64tWfKktTq0EFs4ZjPxE8fm9/IudI1bTkELIYRrOrHnEi2KDWdI8zlEixmZgQub0m+eJym/+8bq0ILt6I7zXDpxg0pNC+LmLm/vjk5+Q0KIME9rzfZVR2mQrz9T+qwkbeZkjNvYnrYjqhEnoXOV/Fs4ZjOJUsQlb6msVodigFCMfmUELIQQzsPH24+VU3dQN09flk/6m7wlszJtZ1eqtC7iNLOLD245A0CyNAktjsQAGknAQggRlrx+8ZYZA9fSsMAAjmw/T82OJZi6pyd5S2WzOrSv+vBB4c3LtxZHYhCZBS2EEGHP/ZtP6O85kw5lRvLq2Rs6Ta7HsDVtSZvFcUseRo0RCXChBOzCTE3ASqnCSqmLSqnLSqlOgbyulFJjAl4/pZRyhYsWQggXc3r/P7QoNIiRrefxTcp4jN7YkbZjahI7geNdH44Wy39ZW1dJwHIbUggopdyB8UARIANQRSmV4ZPdigBpAraGwESz4hFCiNCw2TSbF+6jfq5eLBm7ibylsjFtX08qtyzsENeHw3m4U7zWrwxY0ASbzcbNyw+sDskYcg04RHIAl7XWV7XW3sAioNQn+5QC5mh/B4CYSqlEJsYkhBCh4vX6HTP7r6bRb305uv08tTqXZMqeHvxZJbclK2oppchbMiuTt3ehaf8K3Lr8gLalR3H9/F27x2I4Ddh0yDcHZ+b/lsTArY++vg38HIR9EgP3TIxLCCFC7d6Nx/SvP5WMudPQoGc5Wo+sTt1upVg3ezd/zdrFs4cvTY/hx1/TUadzSdJkSsq183foXmMiR7afN71f+3GOkWxImZmAA1vT7dOfZFD2QSnVEP9T1MRIFCn0kQkhhEFO7/O/Ppzpl7SUbpCfyq0KU6HZn+xafZRVU//m8qlbX28kmL7NmJQ6nUuQ9bf0PLj1hKEt57Jj5RFsTjDqE//PzAR8G0j60ddJgE/PiQRlH7TWU4ApAGkzRtK/RLkU6uAiuBlTCzO8u68h7bi7GTNn/ol76OsKv3eLYEAkoN2M+e9lRL1b/3YMaQZtWJ1jY64AGXJchtVcNqYZNzdjfjZGtYP319dWPnXsJqcazyZR8riUrJWHPyvk4PcKP3Pm8FVWzdjF/i1nsL0LYq3ez0iUIi612hcjb6lsvHj6msk9V7Bu7h58vEPwPuTnBPfpgIyAQ+gwkEYplRK4A1QGqn6yzxqgmVJqEf6np19oreX0sxDCad278ZjJfVYxd+RG/iyfg5K1f6XbxNo8uP2UNTN2smnRgWDPUI4ZNxpVWxWmSLXc+Pr4smDURpZP/huvV+9MOgoHIgk4+LTWvkqpZsAmwB2YobU+q5TyDHh9ErAeKApcBryAOmbFI4QQ9uT16h2rZu5izezd/Pz795Su+xsNepShetuibFl6kDXTd3Ln2qMvthE5akTKNspP2YYFCB8hHBvm72PB6E12ub7sED5MwnJRpk7Z01qvxz/JfvzcpI8ea6CpmTEIIYSVbDbN/i1n2L/lDKnSJKBUvbwUqZKbkrV/4+DWM6yatoMTe/57Wc0jfDiKVM9N1ZaFiREnKrvWHmfOkL++mrBdjwbtJKfKQ8D5q1ALIYSTuHruDiPbLmDmwLUUrfELxWvmYeCiZly/cJdV03eyY9VRchXKSM32xUiUPC4n9lxk5sC1XDp50+rQhQkkAQshhJ09f/yKBSM3snT8VvKWzErp+vloNbQKTftXwCN8OK6cuU3XqhM4tuuC1aFaT64BCyGEMJqPty9blx1i67JD/PBzavKVysaZQ1fYufoY2oUTT5DJNWAhhBBmO3PwCmcOXrE6DMfjwh9EpBqSEEIIYQEZAQshhHBcLjwClgQshBDCQcla0EIIIYT9acAm9wELIYQQ9ufCI2CZhCWEEEJYQEbAQgghHJcLj4AlAQshhHBQWhbicCTR3TS/R/ILdTtR3IxZ4i2yW+jqe34Q3s2YusJX3OOGuo0HbtEMiATeu0U0pB0fg+oKY1RdYaMu3BhW59iAgIyqlWxQO+HcDWrIoHbcvAz6pbsbU4ccX2PeLxyeBu3CxRjkGrAQQghhAacbAQshhAhD5BS0EEIIYQGZhCWEEELYmdayEIcQQghhCRceAcskLCGEEMICMgIWQgjhsLScghZCCCHsTaohCSGEEPankduQhBBCCEvISlhCCCGEMJKMgIUQQjgkDWg5BS2EEELYmdYufQpaErAQQgiH5cojYLkGLIQQQlhARsBCCCEclwufglbayW5yVko9Am6Y2EVc4LGJ7TsSOVbXJMfqmhz1WJNrreOZ0bBSaiP+xx1Sj7XWhY2Kx2hOl4DNppQ6orXObnUc9iDH6prkWF1TWDrWsEKuAQshhBAWkAQshBBCWEAS8P+aYnUAdiTH6prkWF1TWDrWMEGuAQshhBAWkBGwEEIIYYEwmYCVUjOUUg+VUme+sE8+pdQJpdRZpdROe8ZnpK8dq1IqhlJqrVLqZMCx1rF3jEZRSiVVSm1XSp0POJaWgeyjlFJjlFKXlVKnlFJZrYg1tIJ4rNUCjvGUUmqfUiqzFbGGVlCO9aN9f1JK+SmlytszRqME9Vhd5f0pzNNah7kN+A3ICpz5zOsxgXNAsoCv41sds4nH2gUYHPA4HvAUCG913CE81kRA1oDH0YBLQIZP9ikKbAAUkBM4aHXcJh5rbiBWwOMirnysAa+5A38D64HyVsdt4u/VZd6fwvoWJkfAWutd+Ceaz6kKrNBa3wzY/6FdAjNBEI5VA9GUUgqIGrCvrz1iM5rW+p7W+ljA41fAeSDxJ7uVAuZofweAmEqpRHYONdSCcqxa631a62cBXx4Aktg3SmME8fcK0BxYDjjz32tQjtVl3p/CujCZgIMgLRBLKbVDKXVUKVXT6oBMNA74DrgLnAZaau38a78ppVIAPwIHP3kpMXDro69vE/ibudP4wrF+rB7+I3+n9rljVUolBsoAkywIyxRf+L2GpfcnlyZrQQcuHJAN+B2IBOxXSh3QWl+yNixTFAJOAAWA1MAWpdRurfVLS6MKBaVUVPxHQq0COQ4VyLc47a0AXznWD/vkxz8B57FnbEb7yrGOAjpqrf38T+Y4t68ca1h6f3JpkoADdxv/NUTfAG+UUruAzPhfj3E1dYBBWmsNXFZKXQPSA4esDStklFIe+L9xzddarwhkl9tA0o++ToL/6N/pBOFYUUplAqYBRbTWT+wZn5GCcKzZgUUByTcuUFQp5au1XmW/KI0RxP/DYeX9yaXJKejArQZ+VUqFU0pFBn7G/1qMK7qJ/ydplFIJgHTAVUsjCqGA69jTgfNa6xGf2W0NUDNgNnRO4IXW+p7dgjRIUI5VKZUMWAHUcObRUVCOVWudUmudQmudAlgGNHHS5BuU/8Nh6f3JpYXJEbBSaiGQD4irlLoN9AQ8ALTWk7TW5wOqcJwCbMA0rfVnb1lyZF87VqAvMEspdRr/07MdtdaOWHElKH4BagCnlVInAp7rAiSDf493Pf4zoS8DXvifAXBGQTnWHkAcYELAyNBXO+di/kE5Vlfx1WN1pfensE5WwhJCCCEsIKeghRBCCAtIAhZCCCEsIAlYCCGEsIAkYCGEEMICkoCFEEIIC0gCFsJESqnrSqm4od1HCOF6JAELIYQQFpAELIRBlFKrAhbHP6uUavjJaymUUheUUrMD6vMuC1jF6IPmSqljSqnTSqn0Ad+TI6CO7/GAf9PZ9YCEEKaSBCy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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "x_values = par_alpha.scan_values\n", "y_values = par_beta.scan_values\n", "\n", "# plot surface\n", "im = ax.pcolormesh(x_values, y_values, stat_surface, shading=\"auto\")\n", "fig.colorbar(im, label=\"sqrt(TS)\")\n", "ax.set_xlabel(f\"{par_alpha.name}\")\n", "ax.set_ylabel(f\"{par_beta.name}\")\n", "\n", "# We choose to plot 1 and 2 sigma confidence contours\n", "levels = [1, 2]\n", "contours = ax.contour(\n", " x_values, y_values, stat_surface, levels=levels, colors=\"white\"\n", ")\n", "ax.clabel(contours, fmt=\"%.0f$\\,\\sigma$\", inline=3, fontsize=15);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that, if computed with `reoptimize=True`, this plot would be completely consistent with the third panel of the plot produced with `Fit.stat_contour` (try!)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, it is always remember that confidence contours are approximations. In particular, when the parameter range boundaries are close to the contours lines, it is expected that the statistical meaning of the contours is not well defined. That's why we advise to always choose a parameter space that com contain the contours you're interested in." ] }, { "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": "3.9.0" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": false, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1.0, "eqLabelWithNumbers": true, "eqNumInitial": 1.0, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "nbsphinx": { "orphan": true } }, "nbformat": 4, "nbformat_minor": 4 }