{ "cells": [ { "cell_type": "markdown", "id": "82a950e2", "metadata": {}, "source": [ "# 02 Validation Iwabuchi\n", "\n", "- see: Iwabuchi, H., & Suzuki, T. (2009). Fast and accurate radiance calculations using truncation approximation for anisotropic scattering phase functions. Journal of Quantitative Spectroscopy and Radiative Transfer, 110(17), 1926-1939." ] }, { "cell_type": "code", "execution_count": 1, "id": "5a2572b3", "metadata": { "execution": { "iopub.execute_input": "2026-02-10T07:55:04.731340Z", "iopub.status.busy": "2026-02-10T07:55:04.731164Z", "iopub.status.idle": "2026-02-10T07:55:05.777630Z", "shell.execute_reply": "2026-02-10T07:55:05.776660Z" } }, "outputs": [], "source": [ "%reload_ext autoreload\n", "%autoreload 2\n", "\n", "import os\n", "from pathlib import Path\n", "import numpy as np\n", "from scipy.integrate import simpson, trapezoid\n", "from pytrunc.phase import calc_moments\n", "from pytrunc.truncation import delta_m_phase_approx, gt_phase_approx\n", "from pytrunc.utils import integrate_lobatto\n", "\n", "import matplotlib.pyplot as plt\n", "import xarray as xr\n", "\n", "from pytrunc.constant import DIR_ROOT\n", "\n", "save_fig = False" ] }, { "cell_type": "markdown", "id": "2fd6b88d", "metadata": {}, "source": [ "## Truncation approximation for the anisotropic phase function" ] }, { "cell_type": "markdown", "id": "c682271f", "metadata": {}, "source": [ "### Get realistic water cloud phase function from mie calculation" ] }, { "cell_type": "code", "execution_count": 2, "id": "624ae711", "metadata": { "execution": { "iopub.execute_input": "2026-02-10T07:55:05.779935Z", "iopub.status.busy": "2026-02-10T07:55:05.779586Z", "iopub.status.idle": "2026-02-10T07:55:06.219694Z", "shell.execute_reply": "2026-02-10T07:55:06.218813Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Phase function []')" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# in the paper (Iwabuchi et al. 2009) water cloud at wl = 500 nm and reff = 8 um\n", "\n", "# wc available in smartg auxdata: https://github.com/hygeos/smartg\n", "# Follow smartg README to download auxdata, \n", "# then create environemnt variable 'SMARTG_DIR_AUXDATA' where auxdata have been downloaded\n", "# wc_path = Path(os.environ['SMARTG_DIR_AUXDATA']) / Path('clouds/wc_sol.nc')\n", "# ds = xr.open_dataset(wc_path)\n", "# pha_exact = ds['phase'].interp(reff=8, wav=500, method='linear').values[0, :]\n", "\n", "# wc at the correct wavelength and effective radius avaible in pytrunc/data\n", "ds = xr.open_dataset(DIR_ROOT / 'pytrunc' / 'data' / 'wc_wl500_reff8.nc')\n", "\n", "theta = ds['theta'].values\n", "pha_exact = ds[\"phase\"].values[0,:]\n", "\n", "method = 'lobatto'\n", "# method = 'trapezoid'\n", "# method = 'simpson' # use pair number for theta\n", "\n", "INTEGRATORS = {\n", " \"simpson\": simpson,\n", " \"trapezoid\": trapezoid,\n", " \"lobatto\": integrate_lobatto\n", " }\n", "integrate_m = INTEGRATORS[method]\n", "\n", "# theta = np.linspace(0., 180., 18000)\n", "# pha_exact = np.interp(theta, ds.theta.values, pha_exact)\n", "\n", "# theta, _ = quadrature_lobatto(0., 180., 7201)\n", "# pha_exact = np.interp(theta, ds.theta.values, pha_exact)\n", "\n", "mu = np.cos(np.deg2rad(theta))\n", "idmu = np.argsort(mu)\n", "# renormalize depending on the chosen integration method\n", "if method == 'lobatto':\n", " sin_th = np.sin(np.deg2rad(theta))\n", " pha_exact = (2. * pha_exact) / integrate_m(pha_exact*sin_th, np.deg2rad(theta))\n", "else:\n", " pha_exact = (2. * pha_exact) / integrate_m(pha_exact[idmu], mu[idmu])\n", "\n", "plt.figure(figsize=(6,5))\n", "plt.plot(theta, pha_exact, c='k', lw=3)\n", "plt.yscale('log')\n", "plt.ylim(ymin=1e-3, ymax=1e4)\n", "plt.xlim(xmin=0, xmax=180)\n", "plt.xlabel('Scattering angle [°]')\n", "plt.ylabel('Phase function []')" ] }, { "cell_type": "markdown", "id": "aa19f75f", "metadata": {}, "source": [ "### Plot exact and approximated phase functions\n", " - Reproduce Fig.1a" ] }, { "cell_type": "code", "execution_count": 3, "id": "af0da140", "metadata": { "execution": { "iopub.execute_input": "2026-02-10T07:55:06.221968Z", "iopub.status.busy": "2026-02-10T07:55:06.221747Z", "iopub.status.idle": "2026-02-10T07:55:13.213459Z", "shell.execute_reply": "2026-02-10T07:55:13.212426Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "integral(P_exact)= 2.0\n", "integral(P_approx_dm)= 2.0000675723515875\n", "f = 0.43294807007378455\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m_max = 20\n", "ds_dm = delta_m_phase_approx(pha_exact, theta, m_max, method=method)\n", "f = float(ds_dm['f'].values)\n", "ds_gt = gt_phase_approx(pha_exact, theta, f, method=method, th_tol=12)\n", "\n", "plt.figure(figsize=(6,5))\n", "plt.plot(theta, pha_exact, 'k', lw=3, label='original')\n", "plt.plot(theta, ds_dm['phase_approx'], 'g:', lw=2, label=f'DM, M={m_max}')\n", "plt.plot(theta, ds_gt['phase_approx'], 'r', lw=2, label=f'GT, M={m_max}')\n", "plt.yscale('log')\n", "plt.ylim(ymin=1e-3, ymax=1e3)\n", "plt.xlim(xmin=0, xmax=180)\n", "plt.legend()\n", "plt.ylabel(\"Phase Function []\")\n", "plt.xlabel(\"Scattering Angle [°]\")\n", "if save_fig:\n", " plt.savefig(\"iwabuchi_fig1a.png\", dpi=200)\n", "\n", "mu = np.cos(np.deg2rad(theta))\n", "idmu = np.argsort(mu)\n", "if method == 'lobatto':\n", " print(\"integral(P_exact)=\", integrate_m(pha_exact*np.sin(np.deg2rad(theta)),\n", " np.deg2rad(theta)))\n", " print(\"integral(P_approx_dm)=\", integrate_m(ds_dm['phase_approx'].values*np.sin(np.deg2rad(theta)), \n", " np.deg2rad(theta)))\n", "else:\n", " print(\"integral(P_exact)=\", integrate_m(pha_exact[idmu], mu[idmu]))\n", " print(\"integral(P_approx_dm)=\", integrate_m(ds_dm['phase_approx'].values[idmu], mu[idmu]))\n", "print(\"f =\",f)" ] }, { "cell_type": "markdown", "id": "2adf8ce0", "metadata": {}, "source": [ "### Zoom of previous plot\n", "- Fig.1b" ] }, { "cell_type": "code", "execution_count": 4, "id": "ee188b0a", "metadata": { "execution": { "iopub.execute_input": "2026-02-10T07:55:13.215417Z", "iopub.status.busy": "2026-02-10T07:55:13.215218Z", "iopub.status.idle": "2026-02-10T07:55:13.413224Z", "shell.execute_reply": "2026-02-10T07:55:13.412269Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,5))\n", "plt.plot(theta, pha_exact, 'k', lw=3, label='original')\n", "plt.plot(theta, ds_dm['phase_approx'], 'g:', lw=2, label=f'DM, M={m_max}')\n", "plt.plot(theta, ds_gt['phase_approx'], 'r', lw=2, label=f'GT, M={m_max}')\n", "plt.yscale('log')\n", "plt.ylim(ymin=2, ymax=100)\n", "plt.xlim(xmin=0, xmax=30)\n", "plt.legend()\n", "plt.ylabel(\"Phase Function []\")\n", "plt.xlabel(\"Scattering Angle [°]\")\n", "if save_fig:\n", " plt.savefig(\"iwabuchi_fig1b.png\", dpi=200)" ] }, { "cell_type": "markdown", "id": "22a0fe13", "metadata": {}, "source": [ "### Plot exact and approximated phase moments\n", "- Fig.2a" ] }, { "cell_type": "code", "execution_count": 5, "id": "6a70c48c", "metadata": { "execution": { "iopub.execute_input": "2026-02-10T07:55:13.415155Z", "iopub.status.busy": "2026-02-10T07:55:13.414950Z", "iopub.status.idle": "2026-02-10T07:55:13.671269Z", "shell.execute_reply": "2026-02-10T07:55:13.670305Z" } }, "outputs": [ { "data": { "image/png": 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/gy4xhKCqXYgRYFsKdASQmshuukRED5OysjIolUpUVlYiKysLUVFRWLx4MZ566imMHTu2zn38/Pxw8+ZNmJjo7lHQq6++ihdeeAEdOnSod5vGPI755JNPMH/+fPz0009wd3cX23lUN2KVyWSYPn06PvroI3h7e8PDwwPz5s2Ds7Mzhg8f3szfpvkYQlAVQuyA8KreWGVXGEKIiB4mUVFRcHJygr6+PqysrBAUFISvvvoK48aNg1xef0dRGxubex53/PjxSEtLw6FDhxpUh76+PmxtbRtT+j2tWrUKKpUKzz//vNbyBQsWYOHChQCAd999F0VFRXjttdeQm5uLfv36ISoqqlW0G5EJgiBIXcSDlJ+fD0tLS+Tl5Ym3tGJjY/Hb8BB8mK7Z5jkX4IekYhgbG0tYKRFR61JaWorU1FR4eHi0ii+w1mDAgAEYNGiQ+IX/MLjXn3Nd36HN0e7HCQE0t76Sbt6Z974GpKSkSFcQERG1enl5eUhJScHbb78tdSltFkMINM/ObhvfuT3GF9kREdH9WFpa4urVq/ftzUL1YwipIvPxET/zRXZEREQtjyGkSkc/P1SPHccQQkRE1PIYQqp4e3uL75BxBJCRcEHSeoiIiB52DCFVvL29kVRj5OCKzEvSFUNERNQOMIRUufttunalucjPz5euICIiooccQ0gVT09PxKnuvMSoXyZw+PBhCSsiIiJ6uDGEVDE2NobKIxzlVfNDK4Hdu3ZJWhMREdHDjCGkhgHDhuFI1WdPAJd+/x3tbEBZIiKiB4YhpIYnnngCu2vMB167hoSEBMnqISIi3VAqlZg2bRq8vLxgZGQEBwcH9O3bF6tWrUJxcTEGDhwImUxW7zRw4MAGnSctLQ0ymQx6enq4du2a1rrMzEzo6+tDJpMhLS2tSb/HmjVr0L9/f1hZWcHKygoRERE4ceKE1jaCIGD+/PlwcnKCsbExIiIiWu2wEwwhNQQGBuKMvb04P9QM2L179z32ICKi1u7y5csICQnB3r17sWjRIsTExCA6OhrvvvsuduzYgf3792PLli3IzMxEZmam+KW+f/9+cdmWLVsadU4XFxd8//33Wss2btwIFxeXevZomEOHDmHkyJE4ePAgoqOj4erqisGDB2sFnqVLl+Krr77C6tWrcfz4cZiamiIyMhKlpaXNOneLENqZvLw8AYCQl5dX5/qXJ04UrphAEAChRA/C0IgBD7ZAIqJWqqSkRIiLixNKSkqkLqVRIiMjhY4dOwqFhYV1rler1VrzqampAgAhJiam0eeq3nfu3LmCt7e31jofHx9h3rx5AgAhNTW10ceuS0VFhWBubi5s3LhREATN7+Lo6Ch8+umn4ja5ubmCQqEQ/vvf/zbomPf6c77fd2hj6UuagFqhoU88gd371+HVDMCoEtBL+AtFRUUwNTWVujQiotYnNBRQKu+/na45OgKnTt13s1u3bol3QOr7d1wmk9W5vDmefvpprF69GkeOHEG/fv1w5MgR3L59G8OGDcOHH36ote393j0zevRorF69us51xcXFKC8vh7W1NQAgNTUVSqUSERER4jaWlpYICwtDdHQ0XnrppWb+ZrrFEHKXiIgIvFwpw6vQNEgdrFTj4MGDeOqppySujIioFVIqgbvaPrQmycnJEAQBXbp00Vpua2srPp6YPHkyPvnkE52e18DAAKNHj8a6devQr18/rFu3DqNHj4aBgUGtbWNjY+95LAsLi3rXzZo1C87OzmLoUFYFQgcHB63tHBwcxHWtCUPIXSwtLVHkFo7ya8dgAGBoOfDF7t0MIUREdXF0bJPnPXHiBNRqNUaNGoWysjIdFaVt4sSJ6NOnDxYtWoRffvkF0dHRqKioqLWdl5dXk46/ZMkSbNq0CYcOHYKRkVFzy5UEQ0gdBgwbhiPHjmEQAC8A8du3Q1i5skVu2RERtWkNeCQiJS8vL8hkslo9HTt37gxAM0ZUSwkMDISvry9GjhwJPz8/dO3atc67Hk15HPPZZ59hyZIl2L9/P7p16yYud6wKZ1lZWXBychKXZ2VlITg4uOm/TAthCKnD0KFD8eOcORhUNd/16lUkJibWup1HREStm42NDR5//HGsXLkSU6dOfeDt+yZOnIg333wTq1atqnebxj6OWbp0KT7++GPs2bMHoaGhWus8PDzg6OiIAwcOiKEjPz8fx48fx6RJk5r0O7QkhpA6dOvWDTPt7IAbNwAAQ401XXUZQoiI2p5vvvkGffv2RWhoKBYuXIhu3bpBLpfj5MmTuHTpEnr06NFi53711VfxwgsvoEOHDvVu05jHMZ988gnmz5+Pn376Ce7u7mI7DzMzM5iZmUEmk2H69On46KOP4O3tDQ8PD8ybNw/Ozs4YPnx4M38b3eM4IXWQyWRwf+opXK26SzewHNi763/SFkVERE3i6emJmJgYREREYM6cOQgKCkJoaChWrFiBt99+u1ZvlXsZP358gwcuAwB9fX3Y2tpCX183/+dftWoVVCoVnn/+eTg5OYnTZ599Jm7z7rvvYurUqXjttdfQs2dPFBYWIioqqlW2G5EJQvsalzw/Px+WlpbIy8u7Z4vjX3/9Fbf/9QJezdDMP+Uqx8+XCmBiYvKAKiUial1KS0uRmpoKDw+PVvmF9iAMGDAAgwYNwsKFC6UupcXc68+5od+hDcU7IfWIiIjAHvWdhqiDszVddYmIqH3Ky8tDSkoK3n77balLeWgwhNSjQ4cOKHTtfeetumUcwp2IqD2ztLTE1atX79ubhRqOIeQeBgwbhqNVn70BxG3fzrfqEhER6QhDyD0MHTpU6626AVeutNo3ERIREbU1DCH3EBQUhFO2tuL8UAUfyRAR8Y7ww+1B/vkyhNyDTCaD21NP4WpV4+BBleyqS0Ttl56eHgBApVJJXAm1pOo/3+o/75Yk+WBlX3/9NT799FMolUoEBQVhxYoV6NWrV73bL1++HKtWrUJGRgZsbW3x/PPPY/HixS3WXWzoE08g6o8NeCUDMK4AEH8YxcXF7KpLRO2Ovr4+TExMcOPGDRgYGEAu5/9jHzZqtRo3btyAiYmJzsY2uRdJQ8jmzZsxc+ZMrF69GmFhYVi+fDkiIyORkJAAe3v7Wtv/9NNPmD17NtatW4c+ffogMTER48ePh0wmw+eff94iNT7++ON4VZDhleq36t5S49ChQ3jiiSda5HxERK2VTCaDk5MTUlNTkZ6eLnU51ELkcjk6der0QN6XJulgZWFhYejZsydWrlwJQJPAXF1dMXXqVMyePbvW9lOmTEF8fDwOHDggLvvXv/6F48eP48iRIw06Z1MGWokM740dfx+HAYBEACumTMGKFSsatC8R0cNGrVbzkcxDzNDQsN67XLoerEyyOyEqlQqnT5/GnDlzxGVyuRwRERGIjo6uc58+ffrghx9+wIkTJ9CrVy9cvnwZu3btwpgxY+o9T1lZmdZrmvPz8xtd64BhT+PY38cxAIAPgIvbtwMMIUTUTsnl8nY7YirplmQP9G7evInKyko4ODhoLXdwcBBfyHO3f/7zn/jggw/Qr18/GBgYwNPTEwMHDsS///3ves+zePFiWFpaipOrq2uja727q65/Rga76hIRETVTm2pVdOjQISxatAjffPMNzpw5gy1btmDnzp33fPnQnDlzkJeXJ05Xrlxp9HmDg4Nx0sZGnB9qwK66REREzSVZCLG1tYWenh6ysrK0lmdlZcHR0bHOfebNm4cxY8bglVdeQWBgIJ599lksWrQIixcvhlqtrnMfhUIBCwsLramxZDIZOj31FK4pNPODBGDvTnbVJSIiag7JQoihoSF69Oih1chUrVbjwIEDCA8Pr3Of4uLiWo1lqvsxt3T72iFDh2JvVYcdkwqgJPFvDthDRETUDJI+jpk5cybWrFmDjRs3Ij4+HpMmTUJRUREmTJgAABg7dqxWw9Vhw4Zh1apV2LRpE1JTU7Fv3z7MmzcPw4YNa/FBVUJDQxFb42q55xUjOzu7Rc9JRET0MJN0nJARI0bgxo0bmD9/PpRKJYKDgxEVFSU2Vs3IyNC68zF37lzIZDLMnTsX165dg52dHYYNG4aPP/64xWt1d3dH0nUDoOq9ugG3gbi4uFoNa4mIiKhhJB0nRArN6eM8ODAQey9cAABEAUhesQJTpkxpgSqJiIhaH12PE9KmesdIzSEoCLerPgcAuHjxopTlEBERtWkMIY3gHxCA6tjhCiD93DkpyyEiImrTGEIaISAgABdr3H1SXT/LHjJERERNxBDSCAEBAbhodWfeTV3EHjJERERNxBDSCO7u7khS3+lQFFDJdiFERERNxRDSCHp6elBZeYvzAdc03XSJiIio8RhCGsk5sDtyqj77g3dCiIiImoohpJECunZF9b0PVwBpZ89KWQ4REVGbxRDSSP7+/qh570N94QJ7yBARETUBQ0gjBQQE4KLBnfmOigL2kCEiImoChpBG8vDwQJJjjR4ypmwXQkRE1BQMIY0kl8tRZu8lzgeoGEKIiIiagiGkCZx9uyOn6mZIgJLddImIiJqCIaQJunYNRFyF5nNHgT1kiIiImoIhpAkCarzIDmAPGSIioqZgCGmCu7vpuhYUICsrS7J6iIiI2iKGkCbw8PBAsqGhOO9vynYhREREjcUQ0gRyuRylXTuL8wEW7CFDRETUWAwhTeTs1x05RprPAQUMIURERI3FENJEXbsG4qKJ5nPHQiD9HHvIEBERNQZDSBMFBAQgLufOvPrCRfaQISIiagSGkCa6u5sue8gQERE1DkNIE7m7u2v1kAkA24UQERE1BkNIE8nlclR26SLO+8vYTZeIiKgxGEKawSEoCDlVN0P4Nl0iIqLGYQhpBv+AAFy00nzuWAikXDgtbUFERERtCENIMwQEBOCiosaC5Dj2kCEiImoghpBmCAgIQNyVO/NuWcXsIUNERNRADCHN4O7ujmQD9pAhIiJqCoaQZpDL5aio0UOGIYSIiKjhGEKayTEoCNUDp/qD3XSJiIgaiiGkmQK6dsVFY83njmAPGSIiooZiCGkmf39/XLS7My9cYw8ZIiKihmAIaaaAgADEye7Mu5ezhwwREVFDMIQ0k7u7O5JyDcT5gGtsnEpERNQQDCHNJJfLUdnJV5xnDxkiIqKGYQjRgZo9ZBhCiIiIGoYhRAcCunZFdexwAZBx7pyU5RAREbUJDCE64O/vj4v6d+Yr0s+xhwwREdF9MIToQEBAAC4635l3NyiGUqmUriAiIqI2gCFEB9zd3ZEs3Okh4y/jyKlERET3wxCiA3K5HCo7b3Ge3XSJiIjujyFER1z8u+NW1eegCuDMaQ7fTkREdC8MIToS2rMnjld9dgBwNSqKjVOJiIjugSFERwYPHoy9NeaDsrPZLoSIiOgeGEJ0pEuXLjjn6CjODzYD9u7de489iIiI2jeGEB2RyWTwfPJJXDHVzD9SCuyP+l3aooiIiFoxhhAdGhwZiT02ms/GFYAQ/ydKS0ulLYqIiKiVYgjRocceewz7KmrMZ1bir7/+kq4gIiKiVowhRIesra1x26kH1FXzgyvYLoSIiKg+DCE61vuJJ3Cy6nMggNidO6Ush4iIqNViCNGxyMhI7Kkx7xIfj8zMTMnqISIiaq0YQnSsV69eOGpiIs5HmgL79u2TsCIiIqLWiSFExwwMDGD+eATyqt5n97ga2BO1W9qiiIiIWiGGkBYQMWQo/rDXfLYtAa7/vQNqtfreOxEREbUzDCEtIDIyEntqXNnw64WIjY2VrB4iIqLWiCGkBXh4eCBR7ibOR5axqy4REdHdGEJaiP9TTyGp6nMfAH+yqy4REZEWhpAWUvOtugYAjKKjUVhYKGVJRERErQpDSAsZOHAg9svvXN5HDStx+PBhCSsiIiJqXRhCWoiFhQVKeoehXKaZjzQE9uzZc++diIiI2hGGkBbU/4kncayqq653HnD2j63SFkRERNSKMIS0oMjISOw1ujPvm3IV6enp0hVERETUijCEtKCQkBD8nWshzkeWsqsuERFRNYaQFqSnpweHyCG4WTX/GIB9uzmEOxEREcAQ0uIeHzIE1a+vswSQv28fKioqpCyJiIioVZA8hHz99ddwd3eHkZERwsLCcOLEiXtun5ubi8mTJ8PJyQkKhQI+Pj7YtWvXA6q28WqOFwIA4apCnDx5UrJ6iIiIWgtJQ8jmzZsxc+ZMLFiwAGfOnEFQUBAiIyORnZ1d5/YqlQqPP/440tLS8OuvvyIhIQFr1qyBi4vLA6684VxcXJDaxUucj7RkuxAiIiJA4hDy+eef49VXX8WECRPg7++P1atXw8TEBOvWratz+3Xr1iEnJwfbtm1D37594e7ujgEDBiAoKOgBV944PZ58GhesNZ973gSO7NkubUFEREStgGQhRKVS4fTp04iIiLhTjFyOiIgIREdH17nP9u3bER4ejsmTJ8PBwQFdu3bFokWLUFlZWe95ysrKkJ+frzU9aIMHD8Yec81nPQGwPh+D3NzcB14HERFRayJZCLl58yYqKyvh4OCgtdzBwQFKpbLOfS5fvoxff/0VlZWV2LVrF+bNm4dly5bho48+qvc8ixcvhqWlpTi5urrq9PdoiP79++Nglr44P6xQwJYtWx54HURERK2J5A1TG0OtVsPe3h7fffcdevTogREjRuC9997D6tWr691nzpw5yMvLE6crV648wIo1TExMoP/Io8ipmn8RwA9LlkCtVj/wWoiIiFoLyUKIra0t9PT0kJWVpbU8KysLjo6Ode7j5OQEHx8f6Onpicv8/PygVCqhUqnq3EehUMDCwkJrksKrb72Fb6o+GwIYmpTUqnv1EBERtTTJQoihoSF69OiBAwcOiMvUajUOHDiA8PDwOvfp27cvkpOTte4gJCYmwsnJCYaGhi1ec3MMHToU+7p0QWnV/Oty4KslH0haExERkZQkfRwzc+ZMrFmzBhs3bkR8fDwmTZqEoqIiTJgwAQAwduxYzJkzR9x+0qRJyMnJwbRp05CYmIidO3di0aJFmDx5slS/QoPJ5XJMnDMHG8w08xZqIOTqSfz999/SFkZERCQR/ftvAlhbWzfqoDKZDGfOnIGbm9s9txsxYgRu3LiB+fPnQ6lUIjg4GFFRUWJj1YyMDMjld3KSq6sr9uzZgxkzZqBbt25wcXHBtGnTMGvWrEbVJ5WRI0fikQ9n4rXCHMgBTL8JvPXJIvyylV12iYio/ZEJgiDcbyO5XI7ly5fD0tLyvgcUBAFvvvkmLly4gM6dO+ukSF3Kz8+HpaUl8vLyJGkfsmzZMrgtfxvPX9XMvwxgVkICfHx8HngtREREjaHr79AGhxClUgl7e/sGHdTc3Bxnz55lCKnn/MM7OuGPgmIAwCUAy199Fau/++6B10JERNQYuv4ObVCbkOqusQ1VUFDQKgNIa2BhYYFeb07Foap5XwA316+vd2wUIiKih1WbGifkYfHWW2/hC/07zXFmVFRgxYoVElZERET04DUohGzfvh3l5eUNPuiuXbtQUlLS5KIeds7OzrAbOxbnq+b7Ajjx4xcoKCiQsiwiIqIHqkEh5Nlnn23Uu05eeuklZGZmNrWmduHtd97BpzWecE0tL8HatWulK4iIiOgBa1AXXUEQMH78eCgUigYdtLS09P4btXO+vr4o7P0krvyxE66FwNPXgUFfLMGUKVNgYGAgdXlEREQtrkEhZNy4cY066KhRoyQbHr0teXvWv/HFqZ34vFAzP+ZKNjZv3ozRo0dLWxgREdED0KAuug8Tqbvo3u3x3r3x8/HjsAKgAvCEry/2xcVBJpNJXRoREZEWSbroUsuZMmeO1ovtBl+6hD179khZEhER0QPBECKxYcOGYbenp/hiuzcAfLmYL7YjIqKHH0OIxORyOSbMmYONVX8SFgB6pkXj4MGDktZFRETU0hhCWoHRo0djnbs1yqv+NN5RAh/OfgvtrLkOERG1M40OId9//z3KyspqLVepVPj+++91UlR7o1AoMOGdj7HWVTNvrgKejrmArVu3SlsYERFRC2p07xg9PT1kZmbWepfMrVu3YG9vj8rKSp0WqGutrXdMtfLycvTt1hkHE67CVADKADzRuTP2JCRAX79BPamJiIhalOS9YwRBqLP76NWrV2FpadnsgtorAwMD/GvhZ1heFQkVAMZdvowNGzZIWRYREVGLafCdkJCQEMhkMpw9exYBAQFa/zuvrKxEamoqhgwZgp9//rnFitWF1nonBNC8rXhQ9+7YcvYsbACoAUTa22N7WhqMjY2lLo+IiNo5XX+HNvg+//DhwwEAsbGxiIyMhJmZmbjO0NAQ7u7ueO6555pdUHsml8sx99NPsWjwYCyD5jbVtIpsrFy5Eu+8847U5REREelUo9uEbNy4ESNGjICRkVFL1dSiWvOdkGpDBw3Ct38fQqeqwUMi3YyxOfY6OnToIGldRETUvkneJmTcuHEwMjKCSqXC1atXkZGRoTVR832wdCkWONyZX1BQgk+WLJGuICIiohbQ6BCSlJSE/v37w9jYGG5ubvDw8ICHhwfc3d3h4eHREjW2Oz179kRh6LO42EEz3ycHSPniC1y/fl3SuoiIiHSp0X0/x48fD319fezYsQNOTk580VoL+XjREszy+x+2Qg0AWKBS4aOFC/HNd99JXBkREZFuNDqExMbG4vTp0/D19W2JeqiKj48P7F9+GUfXrEFfAAEAVGvXIvHtt+Hj4yN1eURERM3W6Mcx/v7+uHnzZkvUQndZsHAhFhga3pkXBCycM0vCioiIiHSn0SHkk08+wbvvvotDhw7h1q1byM/P15pId5ydnRE6YwZ2VD3xcgXgfHIboqOjJa2LiIhIFxrdRVcu1+SWu9uCVI+kymHbdev27dsYEuKC6PQSyAHkGwLTBX34f7wI02fM4JDuRET0wEg2WFk1vmL+wbKyssJzby7E99/Mwvh0wEIFrEMFdr/7Lv7xww/4+IcfEBgYKHWZREREjdboOyFtXVu7EwIAJSUlGDwoHFPSzmJE1p3lhQDek8vQ4d//xnvz5sOwRvsRIiIiXZN8sDIA+OuvvzB69Gj06dMH165dAwD83//9H44cOdLsgqg2Y2Nj7N5/BEdfnIpnAFyrWm4G4Eu1gMjVH2N4dx+cOHFCwiqJiIgap9Eh5LfffkNkZCSMjY1x5swZlJWVAQDy8vKwaNEinRdIGmZmZvjqq6/w7pEjeMbLC6trrOtzE9h6KR07+4dh1owZ4p8JERFRa9boEPLRRx9h9erVWLNmDQwMDMTlffv2xZkzZ3RaHNXWt29fHDl/Hhlz5mCQowyJVprlikrgfRUwYvlyvBQSgsTERGkLJSIiuo9Gh5CEhAQ88sgjtZZbWloiNzdXFzXRfRgZGWHRokX4fNdp/LOzPxZ7ABVV67oD+CE+Hl8EBuL7jRulLJOIiOieGh1CHB0dkZycXGv5kSNH0LlzZ50URQ0TEhKC6OhY4NVF6GdggPiq5aYAVqlUMJw1Hq+MeB4FBQUSVklERFS3RoeQV199FdOmTcPx48chk8lw/fp1/Pjjj3j77bcxadKklqiR7sHAwABz5szB2jNnMMbXFzXfLPNSFjB3128YH+yD06dPS1YjERFRXRrdRVcQBCxatAiLFy9GcXExAEChUODtt9/Ghx9+2CJF6lJb7KLbUMXFxZg+fTpyfl+DNbmAValmeQWAD+Ry2Hz6Kd6aMYMvHSQioibR9Xdok8cJUalUSE5ORmFhIfz9/WFmZtbsYh6EhzmEVPv555+xYNZ4rCkpQb8a44ocBLC+d2/M+OYbhISESFYfERG1Ta0mhLRV7SGEAEBqaipGvTQCg0+cxDwAelXLKwCstQPO9n0a736+HB4eHhJWSUREbYnkIaS0tBQrVqzAwYMHkZ2dDbVarbW+tXfTbS8hBADKy8sxb948HP3kE/wIoFONdSV6wEojOW6PeQ0zP/wQtra2UpVJRERthOQhZNSoUdi7dy+ef/55ODg41GpfsGDBgmYX1ZLaUwiptnfvXkwZPx4j8jPxTrnm/TPVbgP4UqGAyezZmPLuuzAxMZGsTiIiat0kDyGWlpbYtWsX+vbt2+yTS6E9hhBA02j1q6++wqo1H+Ito2JMiQcUNf7krwP4j5URylzdYdjRA6Y+XWDt749OnTvDzc0Nrq6uUCgUktVPRETSkzyE+Pv7Y9OmTejWrVuzTy6F9hpCqt26dQsfffwRtq9ciffKKzAOd9qL3K0SgBLAVQBXTYEEeyd0+fBTPDtyJOTyJr12iIiI2jDJX2C3bNkyzJo1C+np6c0+OT14NjY2+OLzL3AgMQl/jBqFQABb6tlWD4ALgDAAzxUB/07NRO+XR+MTj07Y+/vvaGdtmomISMcafSfkxo0bePHFF/Hnn3/CxMRE6/0xAJCTk6PTAnWtvd8JuVtMTAxmz56Nq+l70d1EEzo6XgY65lV9BuCA2mk1HcDPPj7ov3Ytevfv/6DLJiIiCUj+OCYiIgIZGRl4+eWX62yYOm7cuGYX1ZIYQup26dIlnD9/Hunp6bWmouI8dOsBvJcD/OOu9+KlANgeHISIdesRyLFHiIgeapKHEBMTE0RHRyMoKKjZJ5cCQ0jj5eXlYd++fZjz0RxYnE3GBwCevGubRAWQqDAH9A0AQ0PA0BAyQ0NAoYBcoYCsQwdYPvEEgl55BSaWllL8GkRE1EySh5Du3bvjm2++Qe/evZt9cikwhDRdRUUFvv/+eyxcuBAuV67gAwCPN/IYhQDibG1RGh4O13Hj4P7MM5Dp67dAtUREpGuSh5C9e/fi/fffx8cff4zAwMBabUJa+xc7Q0jzlZaWYvXq1fjo448QEHALH6QBA5rYTvm2ngxprm7Qe/RRuL30EiwHDNDcSSEiolZH8hBS3TXz7rYggiBAJpOhsrKy2UW1JIYQ3SkoKMDnn3+OpT8uhYlLMcyOAYYqwBCAAQBDZ8CwF2AgB9z/AAblAo8CcL7HMctkMlxzdERlaCgchw+H+eDBQMeOD+T3ISKie5M8hBw+fPie6wcMGNCsgloaQ4ju5efn4/jx47h9+zaKi4tRVFRUazp//jyio6OhVqvRBcCj9sCjNsCgNMCm5N7HzzU1RZm9PWQmJpAbG0PP1BT6pqYwMDODobk55ObmQPfuwKBBDCxERC1I8hDS1jGESOf27ds4cOAAoqKisPPPnVBaKyHzBLr9BfS5AoQD6A3AuxnnULm7w3DIEODRR4GBAwE7O90UT0RErSOE5Obm4j//+Q/i4+MBAAEBAZg4cSIs20CvB4aQ1kEQBFy8eBFRUVGIiorCsWPHUFKiuSViaw+EPQb0vgr0TgB6ZgNN/ZslBAZC9sgjQKdOgIMD4Oh456edHaBX33ixRER0N8lDyKlTpxAZGQljY2P06tULAHDy5EmUlJRg79696N69e7OLakkMIa1TWVkZTp48icOHD+PA4QM4mnEUKieVZtz4S4AMgKJqMhoNKGwBIxVg9A1gB+ARaNqbhEHTHqVB5HLA1lYTRqysNFOHDrU/+/pqHvcYNPjIREQPJclDSP/+/eHl5YU1a9ZAv6prZUVFBV555RVcvnwZf/75Z7OLakkMIW2DSqUSQ0l0dDSys7ORm5uL3Nxc3DK9hUqTSk3aiNXez/RZoJ8J8Ggq8OhJoHt5E95NUBcTE6BPH+CRR4ABA4BevQAjI10cmYiozZA8hBgbGyMmJga+vr5ay+Pi4hAaGori4uJmF9WSGELaPkEQUFpaitu3byM3NxeJiYnYuXMnduzYAaW7EggAYAVgGWAlaGYdATg4A46egEMR4HgZcMjVLLcBYNrYIgwNgbAwTTAxMgJKS+ue9PWBrl2BkBAgOFjzWOiunmVERG2Frr9DGz1KlIWFBTIyMmqFkCtXrsDc3LzZBRHdj0wmg7GxMYyNjeHs7Ax/f38MHz4carUaMTEx2LFjB7bt2oZYIRa3ARyp3tEHwMCqz/8FkHvnmIbGQIfJQIdSwCoJ6LBHk2PsoHnEM0AOdFTXKEKlAv76SzPdz2+/3flsba0JI8HBmmDSpYv24x+2USGidqTRd0LeeustbN26FZ999hn69OkDADh69CjeeecdPPfcc1i+fHlL1KkzvBPSfly/fh27d+/GmTNnkJKSgvjr8bhacRXqDmrgAoCCGhs7AXi96vNpAL/fdbAxgLs18Egc8MhB4JGK5vXiqZeFhXa7FAsLwMwMMDfX/Kw5WVgArq6Ahwfg7Kxp40JEuiUIQGUlUF6umSoqtD9XVGjW1zep1fX/VKs1x7/78/1+qmv8j0gmq3u6H5lM85+e+iaZTPNvSvXxqj7nl5TAcsgQ6R7HqFQqvPPOO1i9ejUqKioAAAYGBpg0aRKWLFkChULR7KJaEkNI+1ZRUYGMjAwkJycjJSUFycnJSE9PR9r1NKQWpyKnMgfIA3Clxk5GAN4BoAcgB8BXmsVOAIIAqL2BUjOgVADKzgGlaqAUmsnMAhji6YBBxh3Qu8wIzteyIFMqdf+LGRoC7u5A586AhwcumpWg2MEaRiYWCHQO1jwWqpoSc1OQWXIDlcYK9OwaCXMnN03IkcmQXZSNw2masYB8bX0R6BCodZrtCdtRUl4CYwNjPN3laa11scpYxN2IAwA85vEYHMwcxHW5pbn4PUGT7LysvRDuGq617+8JvyOnJAdymRxjgsZorbuYfREnr58EAAxwGwAPKw9xXWlFKTZd2AQAcLVwxWOdH9Pad1/KPlwvuA4AGBk4EoZ6d0bjvXz7Mo5kaO6T9XLpBV9b7bu7P5z7AQBga2KLIV5DtNYdu3IMablpAIBhPsNgrrhzFzizIBOH0zXXMMAuoNY13HZpG8oqymBmaIYnfbTfwhSrjEXiLc1bIh/1eBS2Jrbiutslt7H/8n4AgKe1J7o7aXcC2JuyF/ll+dCX62O473CtdZduXsKF7AuQQYZw13A4m98ZMrC4vBi7k3YDAFwsXNC7o/YrOf5M/xM3i28CAJ7p8gz05Hfu1qXlpuFM5hkAQIhjiNafTaW6EtsTtgMAbExs8IjbI5ov7NJSoKwMZ1KjkX0rA3JVOfo794axzED8Yr+Zl4m4zHOQVVTCw6wjOhrYACUl4nQx/RRkZWUwLgc8TJy1vvBvFmShoCQPMrUaTqaOUKhl4uPR8uIC5OVlQ09VDuMKGYwqoBUiVKoSoLISsko1DATZnfBBonxoeitKPk5IcXExUlJSAACenp4wMTFpdjEPAkMI3UtZWRmuXr2KjIwMZGRkID4+Hr/v/R1xBnFAF2h66+y7a6cJANyqPn8AoOZjm56487a/LYAiQYEnQ0PxgpcXehrpY/eZ/8CqFPCW2aKXiRdw+/ad6UH+46enB1hbo9jcCDHlV5BjDLi4dUX3gAjNIyRra8DGBqMOTUWC+iaMbB1wZOIRrf8Jrji6HD/EbIC+Gljx1NfoHjxU0xXa2BgXsy+i66quAICXQ17G2qfXap2++7fdEaOMgaGeIcrmlmmt+yL6C8zcOxMAsPn5zXgx4EVx3Y2iG7D/zB6AJgxsH7lda9/IHyKxN2UvACB3Vi4sje509v7h3A8Ys1UTeFYOXYnJvSZr7St7X/O/yd4deyP65WitdWO2jhFDStLUJHhZe4nr9iTvwZAfNaFlwYAFWDhwoda+9p/a40bxDXS26oyUt1K01s3cMxNf/P0FAODYxGNaYS0mMwbdv9MEj0mhk/DNk9/c2VEQELQyAIlZ8eigb4bMGVe1/je+IvpLfPbnEhhVAKsjlmOQcx+grAwoK8PN29fw6q/jYFQB9HMIxeTAl7XaNf10ch2yb12BgRp4vdtE6FeqNY8jy8uRdiMZF67FwLASCOzgAyf9DprjlpZCKCuF8mY6FBWAiVqu+cKv+T94apNaTQhpqxhCqCnS0tKwY8cO/G/7/3D40GGU1wwIr0EzFn0lgA/v2vGuEIJzNdYpAMzRfHQodMArilfg4+MDHx8feHt5YdKOcTh8cRfMy4ATIw/AutIQKCwECgtx8tIf+OnIKrjlAsMM/OF5WwakpgKtsWG4pSXK7K1xtDwVSjPA1rMrBnd7VvwfMUpL8fu5X1FckAOTShmGuQ3W3Nmpegx1Oj8BOzIPo9AQeCnsZfTwGaC5qyOXI6+8CBN+fxmVcqBHx16YP2iB5tZx1ZfvB38swPnMs9BTA+ue/A4megrNekNDHL4ejaWnvkSZHvBm3+n4R9AITTdsQQDKy/HId31goAa6Wfvii0eXat1+X3Xia/ydfgx6amDJox/D3shGc05BQNzNeKw4+TUEAE/6PIlhvk/fuZ1dXo6FO94GCovgomeJV31Gav5Mi4qAoiIk3LiEtPwMVMqA8E59YGVqowmIcjlul+UhOuEAzFSAu4EtOulZ39m3sFBzfmqQEn0ACgWMTS01f+ZVjyDSCq6gBBWAnh78HAI0yw0MAAMDpBZdQ3J+GsrlQKhbb9h3cBHvLhZUFOOXhK2olAOdbb3wmNdgrUcbP1z4CVeKMqGWAe8NnKf5u1A1/X39BP6X+DvUMuDFriPQwyVUfPRRqlbh3f2zIciALna+mBI2VesRyTcnvsY5peYflU8jPoG5oZnm7y+AM9dP4z+x6wEA//B7Fo95aN8lnLF7GoSKSnQyc8bMXtO0Quv2uG04q4yFTABeD3kFdia24qOgi9nJ6Lpx64MPIRMnTmzQAdetW9esgloaQwg1V35+Pvbu3Yvff/8dp06dQo5hDkpkJSgtL0V5XDnUNf+35wTAs+pzIoDsGgfSg2aYWEDTSPaC9nnMepmhg2cHWFtbY4jVEPh5+sHT0xOenp64rXcb2xM1/+t/1ONRhHUM0/wjkZ0NpKZix+6vYHwrDxYGZuhpH6x1x+LyjUTcylPCoKwcfnoOUOQVATk5QE4O1Dm3IM8vAFGTGRkBCgUEhQL5MhUqDfQhNzJGhw4OgEKhmYyMkFmeg9tCKSoN9dHFMQCGRqbil/rtikIk5KVAra8HV2sPuDp4A8bG4rTzyh8oNZDB2MIGT3QdfucLXy7H8cxTuHQ7CYJchqd8n4GtpeZuHBQKZJbfxq/J2wGZDMGOwejv1l+r9B/O/YD8snwY6RthYoj2d96p66dwJvMMZJBhiNcQuFq6iuvyy/Lxa9yvAABPK08McNd+fcnOxJ24UXwDADAuaJzWu9cSbibg+LXjAIC+rn3hae0prlNVqrD5wmYAgJO5EyI6R2gd91DaIVzNvwoAeN7/eRjp3xk2IC03DX+ma4bM6OHUAwH2AVr7bojdgEp1JayNrfGs37O1jnvp5iUAwIsBL8La2FpcF381Hv6u/g8+hMjlcri5uSEkJAT32mXr1q3NLqolMYRQSxIEAeXl5SgpKUFJSQkSEhKwf/9+7N+/HydPntTZCx6NjY3RuXNnBAcHo0+fPujbty+6du0KPV30rikv1zwOqgomyMkBbt3S/pybq/kfWY22JlqTSgUolZopM1MzFRU1vzbS0NPTtOMxNb3TUNnYWHPtq76MazU0NDAQA4LWVL2s5s/qqeZyQ0PNMap/3v3ZyEjzk13QH2qSjRMyefJk/Pe//4WbmxsmTJiA0aNHw9ra+v47tjIMISSVvLw8HD58GPv378eBAwcQFxen0+Obm5ujd+/e6NOnD/r06YPevXu3rr/jBQV3Qklpad1fdkZGmi82lUp89KQ1FRRowsy9eh8Iwr1b/QuC5vg1p7KyO5/l8jtfrHdP1SHr7i/56nm5XHP8mr0Zak76+ndCQ80AYWqqmfT07t2TwsREs72hIb/sSRKSDlZWVlaGLVu2YN26dTh27BiefPJJvPzyyxg8eLDW7aXWjCGEWousrCzExcUhMTERiYmJSEpKQmJiIlJSUsSeZ81lb2+PTp06wc3NrdZPDw8PWFlZ6eQ8RNQ+SD5iarX09HRs2LAB33//PSoqKnDx4kWYmZk1u6CWxhBCrV1FRQXS0tKQlJSElJQUreny5csoLS3V2blcXV0RFBSkNXl6eurmsQ4RPXQkHzG1mlwuh0wmgyAIOnvOTUSAvr4+vLy84OXlVWudWq2GUqlESkoKLly4gOjoaBw9ehSXL19u0rmuXLmCK1euYMeOHeIyExMTBAYGIjg4GCEhIQgJCUFgYCCMjY2b/DsREdWlyY9jjhw5gqeeegoTJkzAkCFDIG8jozXyTgg9jJRKpRhIjh07htOnT0OlUuns+Hp6evD19UVISIgYTry8vODs7Cy+yJKIHn6SPY558803sWnTJri6umLixIkYNWoUbG1t779jK8MQQu1BaWkpkpOTxUHX0tPTxZ/p6em4fv26dlfiJpLL5XBycoKrq6vW5Obmhp49e6Jjx446+G2IqLWQLITI5XJ06tQJISEh92yEumXLlkYX8fXXX+PTTz+FUqlEUFAQVqxYgV69et13v02bNmHkyJF45plnsG3btgadiyGESPP6hYSEBJw9exZnz57FuXPncPbsWWRlZen0PJ06dUK/fv3Qt29f3XYjJiJJSBZCxo8f36AeMOvXr29UAZs3b8bYsWOxevVqhIWFYfny5fjll1+QkJAAe3v7evdLS0tDv3790LlzZ1hbWzOEEOlAVlYWzp49i9jYWMTGxiImJgYJCQn3HBuoMSwsLBAeHo6ePXvCzc1N6+4J38JN1Pq1mt4xuhIWFoaePXti5cqVADQN71xdXTF16lTMnj27zn0qKyvxyCOPYOLEifjrr7+Qm5vLEELUQoqKinDu3DnExMSI08WLF3XaSwcALC0t0bFjR7i6usLHxwfdu3dHjx494Ovry3YnRK1Eq+kdowsqlQqnT5/GnDlzxGVyuRwRERGIjo6ud78PPvgA9vb2ePnll/HXX3/d8xxlZWUoK7vzQqz8/PzmF07UjpiamiI8PBzh4XdepiYIAm7duiX2rrl7On/+PHJzcxt1nry8POTl5eHixYuIiooSlxsZGSEoKAg9evRA9+7d0b17d/j7+7f6N3YT0f1JGkJu3ryJyspKODg4aC13cHDApUuX6tznyJEj+M9//oPY2NgGnWPx4sV4//33m1sqEdUgk8lga2sLW1tbhISE1FqvVqsRHx+PI0eO4OjRozhy5AhSU1ObdK7S0lIcP34cx48fF5fJ5XJ4eXkhICAA/v7+8Pf3R0BAALp06QIjI6N7HI2IWpM2dY+zoKAAY8aMwZo1axrcM2fOnDmYOXOmOJ+fnw9XV9d77EFEzSWXyxEQEICAgAC8/vrrAIDMzEyxC3FycrJ41+TWrVuNPr5arRZHmq35viq5XI7OnTujS5cu4huJqz87Ozu3mZGdidoLSduEqFQqmJiY4Ndff8Xw4cPF5ePGjUNubi7+97//aW0fGxuLkJAQrdb11d0M5XI5EhIS4OnpiXthmxCi1qWkpARXr17FlStXcPXqVaSmpuLs2bM4c+YM0tPTdXYeU1NT+Pj4wNfXV2sgtrY41ACRVB7Khqm9evXCihUrAGhCRadOnTBlypRaDVOrxz6oae7cuSgoKMCXX34JHx8fGBoa3vN8DCFEbcfNmzcRExODM2fO4MyZMzh9+jRSUlJ0eo6OHTtqDcIWGBgId3d3NoYlqsNDF0I2b96McePG4dtvv0WvXr2wfPly/Pzzz7h06RIcHBwwduxYuLi4YPHixXXuP378ePaOIWpHCgoKEB8fj7i4OFy8eFH8qcu7JoaGhvD09ESXLl1qTTY2Njo7D1Fb81D1jgGAESNG4MaNG5g/fz6USiWCg4MRFRUlNlbNyMhoM0PCE1HLMzc3R69evWoNaFhYWIj4+HgkJCQgISFBbDOSmJiI4uLiRp1DpVIhPj4e8fHxtdbZ29uLDWFr/rSzs2vW70XUHkl+J+RB450QovZFEARcv35dDCfVY56cO3cOJSUlOjuPnZ0dAgIC0K1bN/GNxAEBAeytQw+Vh+5xzIPGEEJEAFBRUYHExEStQdjOnj3bpN469dHT00OXLl0QFBSE4OBgdO3aFV5eXnB3d79v+zWi1oghpJkYQojoXm7evCneNak5paSkoLy8XCfnqH4Xl6enJ7y8vODp6QlPT0/4+/vD29ub79ehVoshpJkYQoioKSoqKnD58uVaDWIvXbqkNSpzc5mamiI4OFgcHbZ79+7w8/ODgYGBzs5B1FQMIc3EEEJEulRZWYnLly/j4sWLuHDhAmJjY3H27Nlawwk0h0KhQLdu3eDn5wdvb294eXmJPy0tLXV2HqL7YQhpJoYQInoQCgsLcf78efGtxGfPnkVSUpJO25wAgK2tLby9veHt7Y2uXbuiW7duCAwMhJOTE0eIJZ1jCGkmhhAiklJubi5SUlKQnJyMlJQU8XNiYiKUSqXOzmNjY4PAwEAxlAQGBsLPz4//7lGzMIQ0E0MIEbVWSqVSa4TYM2fOIC0tTafncHFxgb+/P/z8/LR+cvh6agiGkGZiCCGitiQnJ0cc1yQ5ORnJyclISkpCenq6+O4sXbC1tYWfn1+tydXVlY91SMQQ0kwMIUT0MFCpVEhNTRVDSXx8PM6fP4/z58+jsLBQZ+cxNTWFr6+v+Fbkrl27IiAgAJ06dWI4aYcYQpqJIYSIHmZqtRppaWk4f/48zp07J/5MTk5GZWWlzs5jbm4Of39/MZRUP9rhnZOHG0NIMzGEEFF7VFZWJt4xiYuLE38mJCRApVLp7DzVd05qtjnx8/ODp6cn30z8EGAIaSaGECKiOyoqKpCamiq+sK86nFy6dAkFBQU6O4+BgQG8vb3h5+cnhhQ/Pz906dIFpqamOjsPtSyGkGZiCCEiuj9BEHDt2jUxlFy8eFEckC0/P1+n53J3dxcf63Tt2hVdu3aFr68vX/7XCjGENBNDCBFR01WHkwsXLoihpPrxji7vnMjlcnh5eYmBxMfHB126dIGPjw+sra11dh5qHIaQZmIIISLSPUEQcP36da02J9VTdna2Ts9lY2MjBpIuXbqId1Dc3Nwgl8t1ei7SxhDSTAwhREQPVk5OjlYoqZ7S09Ohy68gMzMzrUc61Y94HB0d2WNHRxhCmokhhIiodSguLkZCQoL4WKf6p65HibWwsNB6nFP908fHh41iG4khpJkYQoiIWrfCwkKtxrCJiYlITExESkoKKioqdHouV1dX+Pv7i2OdVE98O3HdGEKaiSGEiKhtKi8vR1paGhISEpCYmIiEhARxpNjc3FydnqvmO3Z8fX3h6+uLLl26tPu3EzOENBNDCBHRw0UQBGRmZuL8+fO4cOGCOF28eBElJSU6PZe5ublWKKk5GJuhoaFOz9UaMYQ0E0MIEVH7oFarceXKFfGuSfXPhIQEZGRk6LRRrL6+Pjw9PcVQUj0gm6+vL8zNzXV2HqkxhDQTQwgREZWUlGgNY3/x4kXExcUhKSlJ5+1OXFxcaoUTPz8/ODg4tLlHOwwhzcQQQkRE9VGpVEhKSkJcXJz4bp1Lly4hISEBxcXFOj1Xhw4dtEJJ9WcPDw/o6enp9Fy6whDSTAwhRETUWGq1GlevXhVDSfUUHx+PzMxMnZ5LoVDAx8dH65FO9aixUncpZghpJoYQIiLSpdzcXDGQ1JxSU1OhVqt1eq5OnTqJoaT6TcX+/v6wtbXV6XnqwxDSTAwhRET0IJSWlortTmqGlISEBJSWlur0XLa2tmKX4ppdizt27KjTdicMIc3EEEJERFJSq9VIT0+vFU7i4+ORk5Oj03OZmpqiS5cu4t2T6snb27tJbylmCGkmhhAiImqNBEHAjRs3xGBS3f6kJd6zI5fL4enpqTVKrL+/P3x9fWFiYlLvfgwhzcQQQkREbU1xcTGSkpLEUFIzqJSVlensPDKZDO7u7loNYqsnOzs7hpDmYgghIqKHRWVlJVJTUxEXFyeOeRIXF4dLly6hsLBQp+eysbGBl5cXjh8/zhDSVAwhRET0sBMEAdevX9fqTlw9Xb16tdnHZwhpIoYQIiJqzwoKCnDp0iXxrkn1aLGpqakNPgZDSBMxhBAREdVWVFSEhIQE8XFO9ZSUlASVSqW1LUNIEzGEEBERNVxFRQXS0tJw6dIlxMbGYt68eQwhTcUQQkRE1DS6/g6V66AmIiIiokZjCCEiIiJJMIQQERGRJBhCiIiISBIMIURERCQJhhAiIiKSBEMIERERSYIhhIiIiCTBEEJERESSYAghIiIiSTCEEBERkSQYQoiIiEgSDCFEREQkCYYQIiIikgRDCBEREUmCIYSIiIgkwRBCREREkmAIISIiIkkwhBAREZEkGEKIiIhIEgwhREREJAmGECIiIpIEQwgRERFJgiGEiIiIJMEQQkRERJJgCCEiIiJJMIQQERGRJBhCiIiISBIMIURERCQJhhAiIiKSBEMIERERSaJVhJCvv/4a7u7uMDIyQlhYGE6cOFHvtmvWrEH//v1hZWUFKysrRERE3HN7IiIiap0kDyGbN2/GzJkzsWDBApw5cwZBQUGIjIxEdnZ2ndsfOnQII0eOxMGDBxEdHQ1XV1cMHjwY165de8CVExERUXPIBEEQpCwgLCwMPXv2xMqVKwEAarUarq6umDp1KmbPnn3f/SsrK2FlZYWVK1di7Nix990+Pz8flpaWyMvLg4WFRbPrJyIiai90/R0q6Z0QlUqF06dPIyIiQlwml8sRERGB6OjoBh2juLgY5eXlsLa2rnN9WVkZ8vPztSYiIiKSnqQh5ObNm6isrISDg4PWcgcHByiVygYdY9asWXB2dtYKMjUtXrwYlpaW4uTq6trsuomIiKj5JG8T0hxLlizBpk2bsHXrVhgZGdW5zZw5c5CXlydOV65cecBVEhERUV30pTy5ra0t9PT0kJWVpbU8KysLjo6O99z3s88+w5IlS7B//35069at3u0UCgUUCoVO6iUiIiLdkfROiKGhIXr06IEDBw6Iy9RqNQ4cOIDw8PB691u6dCk+/PBDREVFITQ09EGUSkRERDom6Z0QAJg5cybGjRuH0NBQ9OrVC8uXL0dRUREmTJgAABg7dixcXFywePFiAMAnn3yC+fPn46effoK7u7vYdsTMzAxmZmaS/R5ERETUOJKHkBEjRuDGjRuYP38+lEolgoODERUVJTZWzcjIgFx+54bNqlWroFKp8Pzzz2sdZ8GCBVi4cOGDLJ2IiIiaQfJxQh40jhNCRETUNA/VOCFERETUfjGEEBERkSQYQoiIiEgSDCFEREQkCYYQIiIikgRDCBEREUmCIYSIiIgkwRBCREREkmAIISIiIkkwhBAREZEkGEKIiIhIEgwhREREJAmGECIiIpIEQwgRERFJgiGEiIiIJMEQQkRERJJgCCEiIiJJMIQQERGRJBhCiIiISBIMIURERCQJhhAiIiKSBEMIERERSYIhhIiIiCTBEEJERESSYAghIiIiSTCEEBERkSQYQoiIiEgSDCFEREQkCYYQIiIikgRDCBEREUmCIYSIiIgkwRBCREREkmAIISIiIkkwhBAREZEkGEKIiIhIEgwhREREJAmGECIiIpIEQwgRERFJgiGEiIiIJMEQQkRERJJgCCEiIiJJMIQQERGRJBhCiIiISBIMIURERCQJhhAiIiKSBEMIERERSYIhhIiIiCTBEEJERESSYAghIiIiSTCEEBERkSQYQoiIiEgSDCFEREQkCYYQIiIikgRDCBEREUmCIYSIiIgkwRBCREREkmAIISIiIkkwhBAREZEkGEKIiIhIEgwhREREJAmGECIiIpIEQwgRERFJgiGEiIiIJMEQQkRERJJgCCEiIiJJMIQQERGRJFpFCPn666/h7u4OIyMjhIWF4cSJE/fc/pdffoGvry+MjIwQGBiIXbt2PaBKiYiISFckDyGbN2/GzJkzsWDBApw5cwZBQUGIjIxEdnZ2ndsfO3YMI0eOxMsvv4yYmBgMHz4cw4cPx4ULFx5w5URERNQcMkEQBCkLCAsLQ8+ePbFy5UoAgFqthqurK6ZOnYrZs2fX2n7EiBEoKirCjh07xGW9e/dGcHAwVq9efd/z5efnw9LSEnl5ebCwsNDdL0JERPSQ0/V3qL4OamoylUqF06dPY86cOeIyuVyOiIgIREdH17lPdHQ0Zs6cqbUsMjIS27Ztq3P7srIylJWVifN5eXkANBeSiIiIGq76u1NX9y8kDSE3b95EZWUlHBwctJY7ODjg0qVLde6jVCrr3F6pVNa5/eLFi/H+++/XWu7q6trEqomIiNq3W7duwdLSstnHkTSEPAhz5szRunOSm5sLNzc3ZGRk6OQCthf5+flwdXXFlStX+BirgXjNmobXrfF4zZqG163x8vLy0KlTJ1hbW+vkeJKGEFtbW+jp6SErK0treVZWFhwdHevcx9HRsVHbKxQKKBSKWsstLS35l64JLCwseN0aidesaXjdGo/XrGl43RpPLtdNvxZJe8cYGhqiR48eOHDggLhMrVbjwIEDCA8Pr3Of8PBwre0BYN++ffVuT0RERK2T5I9jZs6ciXHjxiE0NBS9evXC8uXLUVRUhAkTJgAAxo4dCxcXFyxevBgAMG3aNAwYMADLli3Dk08+iU2bNuHUqVP47rvvpPw1iIiIqJEkDyEjRozAjRs3MH/+fCiVSgQHByMqKkpsfJqRkaF126dPnz746aefMHfuXPz73/+Gt7c3tm3bhq5duzbofAqFAgsWLKjzEQ3Vj9et8XjNmobXrfF4zZqG163xdH3NJB8nhIiIiNonyUdMJSIiovaJIYSIiIgkwRBCREREkmAIISIiIkm0uxDy9ddfw93dHUZGRggLC8OJEyekLqlV+fPPPzFs2DA4OztDJpPVeiePIAiYP38+nJycYGxsjIiICCQlJUlTbCuxePFi9OzZE+bm5rC3t8fw4cORkJCgtU1paSkmT54MGxsbmJmZ4bnnnqs16F57smrVKnTr1k0cJCo8PBy7d+8W1/N63d+SJUsgk8kwffp0cRmvW20LFy6ETCbTmnx9fcX1vGZ1u3btGkaPHg0bGxsYGxsjMDAQp06dEtfr6rugXYWQzZs3Y+bMmViwYAHOnDmDoKAgREZGIjs7W+rSWo2ioiIEBQXh66+/rnP90qVL8dVXX2H16tU4fvw4TE1NERkZidLS0gdcaetx+PBhTJ48GX///Tf27duH8vJyDB48GEVFReI2M2bMwO+//45ffvkFhw8fxvXr1/GPf/xDwqql1bFjRyxZsgSnT5/GqVOn8Oijj+KZZ57BxYsXAfB63c/Jkyfx7bffolu3blrLed3qFhAQgMzMTHE6cuSIuI7XrLbbt2+jb9++MDAwwO7duxEXF4dly5bByspK3EZn3wVCO9KrVy9h8uTJ4nxlZaXg7OwsLF68WMKqWi8AwtatW8V5tVotODo6Cp9++qm4LDc3V1AoFMJ///tfCSpsnbKzswUAwuHDhwVB0FwjAwMD4ZdffhG3iY+PFwAI0dHRUpXZ6lhZWQlr167l9bqPgoICwdvbW9i3b58wYMAAYdq0aYIg8O9ZfRYsWCAEBQXVuY7XrG6zZs0S+vXrV+96XX4XtJs7ISqVCqdPn0ZERIS4TC6XIyIiAtHR0RJW1nakpqZCqVRqXUNLS0uEhYXxGtaQl5cHAOILnk6fPo3y8nKt6+br64tOnTrxugGorKzEpk2bUFRUhPDwcF6v+5g8eTKefPJJresD8O/ZvSQlJcHZ2RmdO3fGqFGjkJGRAYDXrD7bt29HaGgoXnjhBdjb2yMkJARr1qwR1+vyu6DdhJCbN2+isrJSHIm1moODA5RKpURVtS3V14nXsH5qtRrTp09H3759xVF8lUolDA0N0aFDB61t2/t1O3/+PMzMzKBQKPDGG29g69at8Pf35/W6h02bNuHMmTPiayxq4nWrW1hYGDZs2ICoqCisWrUKqamp6N+/PwoKCnjN6nH58mWsWrUK3t7e2LNnDyZNmoS33noLGzduBKDb7wLJh20nephMnjwZFy5c0HrmTHXr0qULYmNjkZeXh19//RXjxo3D4cOHpS6r1bpy5QqmTZuGffv2wcjISOpy2oyhQ4eKn7t164awsDC4ubnh559/hrGxsYSVtV5qtRqhoaFYtGgRACAkJAQXLlzA6tWrMW7cOJ2eq93cCbG1tYWenl6tVs9ZWVlwdHSUqKq2pfo68RrWbcqUKdixYwcOHjyIjh07issdHR2hUqmQm5urtX17v26Ghobw8vJCjx49sHjxYgQFBeHLL7/k9arH6dOnkZ2dje7du0NfXx/6+vo4fPgwvvrqK+jr68PBwYHXrQE6dOgAHx8fJCcn8+9aPZycnODv76+1zM/PT3yMpcvvgnYTQgwNDdGjRw8cOHBAXKZWq3HgwAGEh4dLWFnb4eHhAUdHR61rmJ+fj+PHj7fraygIAqZMmYKtW7fijz/+gIeHh9b6Hj16wMDAQOu6JSQkICMjo11ft7up1WqUlZXxetXjsccew/nz5xEbGytOoaGhGDVqlPiZ1+3+CgsLkZKSAicnJ/5dq0ffvn1rDTOQmJgINzc3ADr+Lmhq69m2aNOmTYJCoRA2bNggxMXFCa+99prQoUMHQalUSl1aq1FQUCDExMQIMTExAgDh888/F2JiYoT09HRBEARhyZIlQocOHYT//e9/wrlz54RnnnlG8PDwEEpKSiSuXDqTJk0SLC0thUOHDgmZmZniVFxcLG7zxhtvCJ06dRL++OMP4dSpU0J4eLgQHh4uYdXSmj17tnD48GEhNTVVOHfunDB79mxBJpMJe/fuFQSB16uhavaOEQRet7r861//Eg4dOiSkpqYKR48eFSIiIgRbW1shOztbEARes7qcOHFC0NfXFz7++GMhKSlJ+PHHHwUTExPhhx9+ELfR1XdBuwohgiAIK1asEDp16iQYGhoKvXr1Ev7++2+pS2pVDh48KACoNY0bN04QBE3XrHnz5gkODg6CQqEQHnvsMSEhIUHaoiVW1/UCIKxfv17cpqSkRHjzzTcFKysrwcTERHj22WeFzMxM6YqW2MSJEwU3NzfB0NBQsLOzEx577DExgAgCr1dD3R1CeN1qGzFihODk5CQYGhoKLi4uwogRI4Tk5GRxPa9Z3X7//Xeha9eugkKhEHx9fYXvvvtOa72uvgtkgiAITbpfQ0RERNQM7aZNCBEREbUuDCFEREQkCYYQIiIikgRDCBEREUmCIYSIiIgkwRBCREREkmAIISIiIkkwhBAREZEkGEKIqEVt2LCh1qvSWzt3d3csX75c58fdsGEDZDIZZDIZpk+fLi4fOHCguDw2Nlbn5yVqrRhCiFqp8ePHi19MNachQ4ZIXVqjjBgxAomJiVKX0WpYWFggMzMTH374obhsy5YtOHHihIRVEUlDX+oCiKh+Q4YMwfr167WWKRQKiappGmNjYxgbG0tdRi2VlZWQyWSQy3X/fzGVSgVDQ8M618lkslqvO7e2tkZ+fr7O6yBq7XgnhKgVUygUcHR01JqsrKwAAIcOHYKhoSH++usvcfulS5fC3t4eWVlZADS3+adMmYIpU6bA0tIStra2mDdvHmq+Mur//u//EBoaCnNzczg6OuKf//wnsrOzxfWHDh2CTCbDgQMHEBoaChMTE/Tp00frVd9nz57FoEGDYG5uDgsLC/To0QOnTp0CUPfjmFWrVsHT0xOGhobo0qUL/u///k9rvUwmw9q1a/Hss8/CxMQE3t7e2L59+z2v1e3btzF27FhYWVnBxMQEQ4cORVJSkri+uo7t27fD398fCoUCGRkZyM7OxrBhw2BsbAwPDw/8+OOPtY6dm5uLV155BXZ2drCwsMCjjz6Ks2fPiusXLlyI4OBgrF27Fh4eHjAyMrpnrUSkwRBC1EYNHDgQ06dPx5gxY5CXl4eYmBjMmzcPa9euhYODg7jdxo0boa+vjxMnTuDLL7/E559/jrVr14rry8vL8eGHH+Ls2bPYtm0b0tLSMH78+Frne++997Bs2TKcOnUK+vr6mDhxorhu1KhR6NixI06ePInTp09j9uzZMDAwqLPurVu3Ytq0afjXv/6FCxcu4PXXX8eECRNw8OBBre3ef/99vPjiizh37hyeeOIJjBo1Cjk5OfVej/Hjx+PUqVPYvn07oqOjIQgCnnjiCZSXl4vbFBcX45NPPsHatWtx8eJF2NvbY/z48bhy5QoOHjyIX3/9Fd98841WCAOAF154AdnZ2di9ezdOnz6N7t2747HHHtOqJzk5Gb/99hu2bNnCdh1EDaWLV/4Ske6NGzdO0NPTE0xNTbWmjz/+WNymrKxMCA4OFl588UXB399fePXVV7WOMWDAAMHPz09Qq9XislmzZgl+fn71nvfkyZMCAKGgoEAQBEE4ePCgAEDYv3+/uM3OnTsFAEJJSYkgCIJgbm4ubNiwoc7jrV+/XrC0tBTn+/TpU6vOF154QXjiiSfEeQDC3LlzxfnCwkIBgLB79+46z5GYmCgAEI4ePSouu3nzpmBsbCz8/PPPYh0AhNjYWHGbhIQEAYBw4sQJcVl8fLwAQPjiiy8EQRCEv/76S7CwsBBKS0u1zunp6Sl8++23giAIwoIFCwQDAwMhOzu7zvrquxY1paamCgCEmJiYex6D6GHCOyFErdigQYMQGxurNb3xxhviekNDQ/z444/47bffUFpaii+++KLWMXr37g2ZTCbOh4eHIykpCZWVlQCA06dPY9iwYejUqRPMzc0xYMAAAEBGRobWcbp16yZ+dnJyAgDxjsHMmTPxyiuvICIiAkuWLEFKSkq9v1N8fDz69u2rtaxv376Ij4+v93ympqawsLCodYei5jH19fURFhYmLrOxsUGXLl20jmtoaKh13Or9evToIS7z9fXVenx09uxZFBYWwsbGBmZmZuKUmpqq9Xu6ubnBzs6u3t+biGpjw1SiVszU1BReXl733ObYsWMAgJycHOTk5MDU1LTBxy8qKkJkZCQiIyPx448/ws7ODhkZGYiMjIRKpdLatubjlepQo1arAWjaRPzzn//Ezp07sXv3bixYsACbNm3Cs88+2+Ba7nb34xyZTCaer6mMjY21AllDFBYWwsnJCYcOHaq1rmZYacx1JyIN3gkhasNSUlIwY8YMrFmzBmFhYRg3blytL+rjx49rzf/999/w9vaGnp4eLl26hFu3bmHJkiXo378/fH19673bcD8+Pj6YMWMG9u7di3/84x+1evVU8/Pzw9GjR7WWHT16FP7+/k06b/UxKyoqtH7XW7duISEh4Z7H9fX1RUVFBU6fPi0uS0hIQG5urjjfvXt3KJVK6Ovrw8vLS2uytbVtcs1ExBBC1KqVlZVBqVRqTTdv3gSg6WI6evRoREZGYsKECVi/fj3OnTuHZcuWaR0jIyMDM2fOREJCAv773/9ixYoVmDZtGgCgU6dOMDQ0xIoVK3D58mVs375da/yKhigpKcGUKVNw6NAhpKen4+jRozh58iT8/Pzq3P6dd97Bhg0bsGrVKiQlJeHzzz/Hli1b8PbbbzfhCml4e3vjmWeewauvvoojR47g7NmzGD16NFxcXPDMM8/Uu1+XLl0wZMgQvP766zh+/DhOnz6NV155RatLcUREBMLDwzF8+HDs3bsXaWlpOHbsGN577z2xBxARNQ1DCFErFhUVBScnJ62pX79+AICPP/4Y6enp+PbbbwFo2ml89913mDt3rlb30bFjx6KkpAS9evXC5MmTMW3aNLz22msAADs7O2zYsAG//PIL/P39sWTJEnz22WeNqlFPTw+3bt3C2LFj4ePjgxdffBFDhw7F+++/X+f2w4cPx5dffonPPvsMAQEB+Pbbb7F+/XoMHDiwCVfojvXr16NHjx546qmnEB4eDkEQsGvXrnp76dTcz9nZGQMGDMA//vEPvPbaa7C3txfXy2Qy7Nq1C4888ggmTJgAHx8fvPTSS0hPT9fqhUREjScThBoDBhDRQ2XgwIEIDg5ukSHIqfE2bNiA6dOnaz3uqZaWlgYPDw/ExMQgODj4gddGJAXeCSEieoDy8vJgZmaGWbNmicuGDh2KgIAACasikgZ7xxARPSDPPfec+DitZs+atWvXoqSkBICmnQ5Re8HHMURERCQJPo4hIiIiSTCEEBERkSQYQoiIiEgSDCFEREQkCYYQIiIikgRDCBEREUmCIYSIiIgkwRBCREREkvh/2dNCUjGjB1oAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_expan = 60\n", "chi_exact = calc_moments(phase=pha_exact, theta=theta, m_max=n_expan, method=method, normalize=True)\n", "chi_approx_dm = calc_moments(phase=ds_dm['phase_approx'].values, theta=theta, m_max=n_expan, method=method, normalize=True)\n", "chi_approx_gt = calc_moments(phase=ds_gt['phase_approx'].values, theta=theta, m_max=n_expan, method=method, normalize=True)\n", "\n", "exp_order = np.arange(61)\n", "plt.figure(figsize=(6,5))\n", "plt.plot(chi_exact, 'k', lw=3, label='original')\n", "plt.plot(chi_approx_dm, 'g:', lw=2, label=f'DM, M={m_max}')\n", "plt.plot(chi_approx_gt, 'r', lw=2, label=f'GT, M={m_max}')\n", "plt.xlim(xmin=0, xmax = 60)\n", "plt.ylim(ymin=0, ymax=1)\n", "plt.legend()\n", "plt.ylabel(\"Moment []\")\n", "plt.xlabel(\"Expansion order []\")\n", "if save_fig:\n", " plt.savefig(\"iwabuchi_fig2a.png\", dpi=200)" ] }, { "cell_type": "markdown", "id": "5ff51783", "metadata": {}, "source": [ "### Plot moment ratio\n", "- Fig.2b" ] }, { "cell_type": "code", "execution_count": 6, "id": "b64d6142", "metadata": { "execution": { "iopub.execute_input": "2026-02-10T07:55:13.673324Z", "iopub.status.busy": "2026-02-10T07:55:13.673117Z", "iopub.status.idle": "2026-02-10T07:55:13.816101Z", "shell.execute_reply": "2026-02-10T07:55:13.815203Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "exp_order = np.arange(61)\n", "plt.figure(figsize=(6,5))\n", "plt.plot(chi_approx_dm/chi_exact, 'g:', lw=2, label=f'(DM)/exact, M={m_max}')\n", "plt.plot(chi_approx_gt/chi_exact, 'r', lw=2, label=f'(GT)/exact, M={m_max}')\n", "plt.xlim(xmin=0, xmax = 40)\n", "plt.ylim(ymin=0.95, ymax=1.15)\n", "plt.legend()\n", "plt.ylabel(\"Moment ratio approx/exact []\")\n", "plt.xlabel(\"Expansion order []\")\n", "if save_fig:\n", " plt.savefig(\"iwabuchi_fig2b.png\", dpi=200)" ] } ], "metadata": { "kernelspec": { "display_name": "default", "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": "3.13.11" } }, "nbformat": 4, "nbformat_minor": 5 }