From be94cd178d49cc30872aba6b445d6c14adde3b4b Mon Sep 17 00:00:00 2001 From: Maxime Lucas Date: Thu, 2 May 2024 17:39:48 +0200 Subject: [PATCH] removed unused files --- notebooks/correctness_identify.ipynb | 1137 ---------------- .../figure_1_linear_stability-harmonics.ipynb | 642 --------- notebooks/hid.simulate-ring-Copy1.ipynb | 1151 ----------------- notebooks/simulate-ring.ipynb | 985 -------------- 4 files changed, 3915 deletions(-) delete mode 100644 notebooks/correctness_identify.ipynb delete mode 100644 notebooks/figure_1_linear_stability-harmonics.ipynb delete mode 100644 notebooks/hid.simulate-ring-Copy1.ipynb delete mode 100644 notebooks/simulate-ring.ipynb diff --git a/notebooks/correctness_identify.ipynb b/notebooks/correctness_identify.ipynb deleted file mode 100644 index dcb1e53..0000000 --- a/notebooks/correctness_identify.ipynb +++ /dev/null @@ -1,1137 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "3b2ad256", - "metadata": {}, - "outputs": [], - "source": [ - "import sys\n", - "from itertools import combinations\n", - "from math import sin\n", - "from pathlib import Path\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import pandas as pd\n", - "import seaborn as sb\n", - "from tqdm import tqdm\n", - "\n", - "sys.path.append(\"../code/\")\n", - "\n", - "import xgi\n", - "from hypersync_draw import *\n", - "from hypersync_generate import *\n", - "from hypersync_identify import *\n", - "from hypersync_integrate import *\n", - "\n", - "sb.set_theme(style=\"ticks\", context=\"notebook\")\n", - "\n", - "results_dir = \"../results/\"\n", - "data_dir = \"../data/\"\n", - "\n", - "Path(results_dir).mkdir(parents=True, exist_ok=True)\n", - "Path(data_dir).mkdir(parents=True, exist_ok=True)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "c2f1f091", - "metadata": {}, - "outputs": [], - "source": [ - "run_dir = f\"{results_dir}run_k1_1_k2s_ic_random_tend_600.0_nreps_10001_ringSC_sym/\"\n", - "file_name = f\"{run_dir}thetas_arr_k1_1_k2s_ic_random_tend_600.0_nreps_10001_ringSC_sym.npy\"\n", - "\n", - "data = np.load(file_name) # end states\n", - "\n", - "#file_name = f\"{run_dir}df_long_ring_k1_1_k2s_ic_random_tend_500.0_nreps_1000_di.csv\"\n", - "\n", - "#df = pd.read_csv(file_name, index_col=0)\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "ab3098a0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(9, 10001, 42)" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "data.shape" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "9a476e4f", - "metadata": {}, - "outputs": [], - "source": [ - "k2s = np.arange(0, 4.5, 0.5)\n", - "results = {}\n", - "\n", - "thetas_arr = data.swapaxes(0, 1) # get (n_rep, k2s)\n", - "thetas_arr = thetas_arr[:, :, :, None]\n", - "for j, k2 in enumerate(k2s):\n", - " states = [identify_state(thetas, atol=0.05) for thetas in thetas_arr[:, j]]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "b16604e4", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c8e1d067", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 75, - "id": "ed86c349", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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k2stateproba
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" - ], - "text/plain": [ - " k2 state proba\n", - "216 0.00 2-cluster NaN\n", - "217 0.25 2-cluster NaN\n", - "218 0.50 2-cluster NaN\n", - "219 0.75 2-cluster NaN\n", - "220 1.00 2-cluster NaN\n", - "221 1.25 2-cluster NaN\n", - "222 1.50 2-cluster NaN\n", - "223 1.75 2-cluster NaN\n", - "224 2.00 2-cluster 0.001\n", - "225 2.25 2-cluster 0.002\n", - "226 2.50 2-cluster NaN\n", - "227 2.75 2-cluster 0.001\n", - "228 3.00 2-cluster NaN\n", - "229 3.25 2-cluster NaN\n", - "230 3.50 2-cluster 0.002\n", - "231 3.75 2-cluster 0.001\n", - "232 4.00 2-cluster 0.003\n", - "233 4.25 2-cluster NaN" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df[df.state == \"2-cluster\"]" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "b4b797ae", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(1000, 100)" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "data[-2].shape" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "bd60a6d6", - "metadata": {}, - "outputs": [], - "source": [ - "n_reps = 1000\n", - "i = -2\n", - "\n", - "states = [identify_state(thetas[:, None], atol=0.05) for thetas in data[i]]\n", - "states_unique, counts = np.unique(states, return_counts=True)\n", - "probs = counts / n_reps" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "26aeff9d", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array(['-1-twisted', '-2-twisted', '-3-twisted', '-4-twisted',\n", - " '-5-twisted', '0-twisted', '2-cluster', '2-twisted', '3-twisted',\n", - " '4-twisted', '5-twisted', '6-twisted', 'other'], dtype='" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "j = 530\n", - "plot_phases(data[i, j, :, None], it=-1)" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "id": "aa5d0d51", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'2-cluster'" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "identify_state(data[i, j, :, None], atol=0.05)" - ] - }, - { - "cell_type": "code", - "execution_count": 159, - "id": "ef9a35d4", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 159, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N = 100\n", - "#psi = generate_k_clusters(N, k=2, ps=[0.3, 0.7], noise=0.05)\n", - "psi = generate_state(N, kind=\"sync\")\n", - "\n", - "plot_phases(psi[:, None], it=-1)" - ] - }, - { - "cell_type": "code", - "execution_count": 160, - "id": "5636dace", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0 1\n" - ] - }, - { - "ename": "TypeError", - "evalue": "unsupported operand type(s) for -: 'list' and 'int'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn [160], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m idenfity_k_clusters(psi[:, \u001b[38;5;28;01mNone\u001b[39;00m], k\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m2\u001b[39m, t\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m, atol\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0.01\u001b[39m)\n", - "Cell \u001b[0;32mIn [114], line 34\u001b[0m, in \u001b[0;36midenfity_k_clusters\u001b[0;34m(thetas, k, t, atol)\u001b[0m\n\u001b[1;32m 32\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m n_clust \u001b[38;5;241m==\u001b[39m \u001b[38;5;28mlen\u001b[39m(clusters):\n\u001b[1;32m 33\u001b[0m sizes \u001b[38;5;241m=\u001b[39m [\u001b[38;5;28mlen\u001b[39m(cluster) \u001b[38;5;241m/\u001b[39m N \u001b[38;5;28;01mfor\u001b[39;00m cluster \u001b[38;5;129;01min\u001b[39;00m clusters]\n\u001b[0;32m---> 34\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m n_clust \u001b[38;5;241m==\u001b[39m \u001b[43mclusters\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1\u001b[39;49m:\n\u001b[1;32m 35\u001b[0m sizes \u001b[38;5;241m=\u001b[39m [\u001b[38;5;28mlen\u001b[39m(cluster) \u001b[38;5;241m/\u001b[39m N \u001b[38;5;28;01mfor\u001b[39;00m cluster \u001b[38;5;129;01min\u001b[39;00m clusters[:\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m]]\n\u001b[1;32m 36\u001b[0m sizes[\u001b[38;5;241m0\u001b[39m] \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(clusters[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m]) \u001b[38;5;66;03m# 0th and last clusters are the same\u001b[39;00m\n", - "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for -: 'list' and 'int'" - ] - } - ], - "source": [ - "idenfity_k_clusters(psi[:, None], k=2, t=-1, atol=0.01)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "bc4719d6", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 102, - "id": "895e2410", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 102, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(np.sin(psi), \"o\")\n", - "plt.plot(np.cos(psi), \"x\")" - ] - }, - { - "cell_type": "code", - "execution_count": 103, - "id": "0dddc2f7", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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KiiRJbdq08WgPDQ11952vbdu2atu2rUfbyy+/rKCgICUkJEiS8vPzVVFRoREjRig3N1dhYWF64IEHdOedd1ZbR2pqarV9hYWFXvUBAHA+nwfkmTNnJEkBAQEe7YGBgTp58uQFl1+xYoXeeOMNTZ48Wa1bt5Z07iQel8ultLQ0hYeHa8OGDZo4caLOnj2ru+++29cvAQAA3wdk1a5Sp9PpsdvU4XAoODi42uWMMZo3b54WLVqkRx55REOGDHH3ffjhh6qsrHQfc4yOjtbhw4e1dOnSagNy/fr11T5XTVuXAABIdXAMsmrXZUlJiUd7SUmJwsLCrMucPXtW48aN0+LFizVx4kQ9/vjjHv1BQUFeJ+RERkZad9kCAOALPg/I6OhoNWvWTFlZWe620tJS7dy5031M8cfGjx+vv//973r++ef14IMPevSVlpYqMTFRq1at8mjfsWOHOnTo4OvyAQCQVAe7WAMCAjR48GA999xzat26tX79619rzpw5Cg8PV+/evVVZWaljx46pefPmCgoK0qpVq7Ru3TqNHz9eiYmJOnLkiHuu5s2bq0WLFurWrZvmzp2rK6+8Utdcc40++eQTvf/++3rppZd8XT4AAJIkP2OM8fWklZWVysjI0KpVq1ReXq6EhARNmTJFbdu2VUFBgVJTUzVr1izdddddGj58uP75z39a56kaU1ZWpvnz5+vjjz/W0aNHFRERoccee0y9evW6pPqqjkHWdJwSAHD5qo/P8ToJyMsdAQkAP2/18TnOzcoBALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALAgIAEAsCAgAQCwICABALCok4B0uVx68cUX1b17d8XGxuqhhx7SoUOHqh1//PhxjR07VgkJCUpMTNS0adN05swZjzEfffSRbrvtNsXExKhv377atGlTXZQOAICkOgrIhQsXauXKlZoxY4befvttuVwujRw5Uk6n0zo+LS1NBw8e1GuvvaZ58+Zpw4YNmjp1qrs/MzNT48aN04ABA7R69WolJydr1KhR2rt3b12UDwCA7wPS6XTq1VdfVVpamnr27Kno6GjNnTtXRUVF+uSTT7zGb9u2TZs3b9bs2bPVqVMnJScna/r06XrvvfdUXFwsSVqyZIl69eqloUOHKiIiQk899ZQ6deqk5cuX+7p8AAAk1UFA5ubm6tSpU0pOTna3tWjRQh07dlR2drbX+JycHIWEhCgiIsLdlpiYKD8/P23ZskUul0tbt271mE+SkpKSrPMBAOALjX09YVFRkSSpTZs2Hu2hoaHuvvMVFxd7jQ0ICFDLli1VWFio0tJSnT59WuHh4Rc1X5XU1NRq+woLC72eEwCA8/l8C7Lq5JqAgACP9sDAQDkcDuv4H489f3x5eXmt5gMAwBd8vgUZFBQk6dyxyKp/S5LD4VBwcLB1vO3kHYfDoSZNmigwMNA934/7bfNVWb9+fbV9NW1dAgAg1cEWZNWuy5KSEo/2kpIShYWFeY0PDw/3Gut0OnXixAmFhoaqZcuWatKkyUXPBwCAL/g8IKOjo9WsWTNlZWW520pLS7Vz504lJCR4jU9ISFBRUZEOHjzobtu8ebMkqWvXrvLz81NcXJy7rUpWVpbi4+N9XT4AAJLqYBdrQECABg8erOeee06tW7fWr3/9a82ZM0fh4eHq3bu3KisrdezYMTVv3lxBQUG64YYbFBcXpyeeeEJTp07V6dOnNWXKFPXt29e9hThs2DCNGjVKHTt2VI8ePfS3v/1Nu3bt0jPPPOPr8gEAkFRHNwpIS0vT3XffrcmTJ+v+++9Xo0aNtHTpUvn7+6uwsFApKSlat26dJMnPz08LFixQ27Zt9cADD+jxxx9Xjx49PG4UkJKSopkzZ+qtt95Sv379lJmZqcWLF3tcGgIAgC/5GWNMQxdR36pO0qnpRB4AwOWrPj7HuVk5AAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWPg9Ih8OhadOmKTk5WV26dNHYsWN17NixGpfZunWrhgwZoq5du6p79+6aNGmSTpw44e4vLi5WVFSU12PVqlW+Lh8AAEl1EJBTp07Vxo0bNX/+fC1fvlz79u1TWlpateP379+vESNGKCoqSn/96181d+5cbd++XWPGjHGPyc3NVWBgoL788ktt3LjR/bjtttt8XT4AAJKkxr6crLi4WGvWrNHixYsVHx8vScrIyNAtt9yibdu2qUuXLl7LrFmzRqGhoZo0aZL8/PwkSU8//bQGDRqkQ4cO6Te/+Y3y8/P129/+VqGhob4sFwCAavl0C3LLli2SpG7durnb2rVrp7CwMGVnZ1uXueOOOzR79mx3OEpy//vkyZOSpLy8PEVERPiyVAAAauTzLchWrVopMDDQoz00NFRFRUXWZWzBt2TJEoWEhCgqKkqSlJ+fr1atWmnQoEHav3+/rrnmGj3yyCPq0aNHtbWkpqZW21dYWKg2bdpczEsCAPxC1SogCwoKagyeMWPGKCAgwKs9MDBQDofjop5j9uzZ+uKLL7RgwQL5+/uroqJC+/btU/v27TVhwgQ1a9ZMa9eu1ahRo7Rs2TIlJyfX5iUAAHBRahWQYWFhWrduXbX9GzZskNPp9Gp3OBwKDg6uce6zZ89qypQpWrNmjWbMmKFevXqdK7BxY2VlZalRo0YKCgqSJHXu3Fm7d+/W0qVLqw3I9evXV/tcNYU8AABSLQPS39+/xmOBeXl5OnHihJxOp8eWZElJicLCwqpdrqysTI899phycnKUkZGhW2+91aO/adOmXst06NBBGzdurE35AABcNJ+epNO1a1e5XC73yTrSucs4iouLlZCQYF3G6XTq4Ycf1vbt27V06VKvcNy9e7fi4uKUlZXl0f7NN9+offv2viwfAAA3nwZkWFiY/vCHP2jy5MnKysrS9u3b9eSTTyoxMVGxsbGSzgXikSNH3LtiX3rpJW3ZskUzZszQtddeqyNHjrgfTqdTERERuvbaazV9+nTl5ORo7969mjVrlv7nf/5HjzzyiC/LBwDAzc8YY3w54enTpzVz5kx9/PHHkqQePXpo8uTJatWqlSQpKytLQ4cO1euvv66kpCT16dNHBw4csM5VNeaHH37Q888/ry+//FKlpaXq2LGj/vznP7uvtaytqmOQNR2nBABcvurjc9znAflzQEACwM9bfXyOc7NyAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsfB6QDodD06ZNU3Jysrp06aKxY8fq2LFjNS6zaNEiRUVFeT3O9+abbyo1NVUxMTEaOHCgdu7c6evSAQBw83lATp06VRs3btT8+fO1fPly7du3T2lpaTUuk5eXpzvvvFMbN270eFRZvXq10tPTNWbMGK1atUpt27bVsGHDLhi8AABcKp8GZHFxsdasWaPJkycrPj5eMTExysjIUHZ2trZt21btcvn5+erYsaNCQkI8HlUWL16swYMH64477lD79u01c+ZMBQcH69133/Vl+QAAuPk0ILds2SJJ6tatm7utXbt2CgsLU3Z2tnUZp9OpAwcO6Nprr7X2Hz16VAcOHFBycrK7rXHjxoqPj692TgAAfqrGvpysuLhYrVq1UmBgoEd7aGioioqKrMvs2bNHlZWV+vjjj/XMM8/I4XAoISFB48aN81iuTZs2XnPm5uZWW0tqamq1fYWFhV7zAQBwvloFZEFBQY3BM2bMGAUEBHi1BwYGyuFwWJfJz8+XJAUHB2vevHk6evSoMjIyNHToUK1Zs0ZnzpyRJK95a5oTAICfqlYBGRYWpnXr1lXbv2HDBjmdTq92h8Oh4OBg6zJ9+/ZVjx491Lp1a3dbhw4d1KNHD/3jH//Q1VdfLUle89Y0pyStX7++2r6aQh4AAKmWAenv76+IiIhq+/Py8nTixAk5nU6PLb6SkhKFhYVVu9z54Sid233asmVLFRUVKSkpyT3H+c99oTkBAPgpfHqSTteuXeVyudwn60jS/v37VVxcrISEBOsyc+fOVZ8+fWSMcbcVFBTo+PHjat++va688kq1a9dOWVlZ7v6Kigrl5ORUOycAAD+VTwMyLCxMf/jDHzR58mRlZWVp+/btevLJJ5WYmKjY2FhJ53aVHjlyxL3L9Pe//72+//57TZ06Vfv371d2drZGjx6tuLg4de/eXZI0fPhwLVu2TKtXr9aePXv0l7/8ReXl5br77rt9WT4AAG4+v1HAjBkzlJycrMcee0wjRozQtddeqxdffNHdv23bNqWkpLivi+zcubOWLFmivLw83XXXXXrsscd03XXXafHixfLz85Mk3XvvvUpLS9MLL7yg/v376/vvv9eyZcu8ds0CAOArfub8fZu/EFUn6dR0Ig8A4PJVH5/j3KwcAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAAALAhIAAAsCEgAACwISAACLxr6e0OFw6Nlnn9Xf//53lZeX6+abb9akSZPUunVr6/gJEyZo9erV1r7Ro0frsccekyT17t1bBw8e9Ojv16+fnn32Wd++AAAAVAcBOXXqVOXk5Gj+/PkKCAjQ008/rbS0NL3xxhvW8ZMmTdLYsWM92mbNmqXNmzfrnnvukSSdPn1ahw4d0ksvvaROnTq5xwUFBfm6fAAAJPk4IIuLi7VmzRotXrxY8fHxkqSMjAzdcsst2rZtm7p06eK1TPPmzdW8eXP33//4xz+0bt06LV++XGFhYZKkPXv2yOVyqUuXLrriiit8WTIAAFY+PQa5ZcsWSVK3bt3cbe3atVNYWJiys7MvuLzD4dAzzzyj/v37Kykpyd2el5enq666inAEANQbnwZkcXGxWrVqpcDAQI/20NBQFRUVXXD5d999Vz/88IMef/xxj/a8vDw1adJEaWlpSklJ0e23367XXntNLpfLl+UDAOBWq12sBQUFSk1NrbZ/zJgxCggI8GoPDAyUw+GocW6Xy6Xly5frnnvuUUhIiEff7t27VVpaqj59+uhPf/qTtmzZojlz5ujkyZMaM2aMdb6a6iwsLFSbNm1qrAcA8MtWq4AMCwvTunXrqu3fsGGDnE6nV7vD4VBwcHCNc2/dulXfffed7r//fq++JUuWyOFwuI9VRkVFqaysTIsWLdLo0aP1q19xtQoAwLdqFZD+/v6KiIiotj8vL08nTpyQ0+n02JIsKSlxn3BTnU8//VQdO3a0zh8QEOC1ZRoZGanTp0/r5MmTatWqldcy69evr/a5atq6BABA8vExyK5du8rlcrlP1pGk/fv3q7i4WAkJCTUum52dreTkZK92Y4x69eqlBQsWeLTv2LFDISEh1nAEAOCn8mlAhoWF6Q9/+IMmT56srKwsbd++XU8++aQSExMVGxsrSXI6nTpy5IjHrtjKykrl5+crOjraa04/Pz/9/ve/19KlS7Vu3Tp99913euedd/TKK68oLS3Nl+UDAODm8xsFzJgxQzNnznTfAadHjx6aPHmyu3/btm0aOnSoXn/9dfelHCdOnNDZs2fVsmVL65xjx45Vs2bNlJGRoaKiIrVt21aTJk3Svffe6+vyAQCQJPkZY0xDF1Hfqo5B1nScEgBw+aqPz3FO/wQAwIKABADAgoAEAMCCgAQAwIKABADAgoAEAMCCgAQAwIKABADAgoAEAMCCgAQAwIKABADAgoAEAMCCgAQAwMLnP3cFAP+Ovv6mRJOXbXL//fuktvq/d3VRQGO2M/5dEZAAcAG3j33Pq+3TrAJ9mlWgu3pGaNjtnRugKtQ1vvoAQA1s4Xi+VV/s1bIPvqmnalCfCEgAqMaFwrHKqi/2ylnhquNqUN8ISACw2P/dyVqN/+if++uoEjQUAhIALNLmfVGr8YVHT9VNIWgwBCQA+ECbK5s2dAnwMQISAHzg1hvbNXQJ8DECEgAsXhzT86LHxkW34nrIf0P8FwUAi3ZXX3HRY6c91KMOK0FDISABoBofPH+nT8bg54k76QBADT54/k7t/+6k11mtf+7fRb/7P1c3TFGoFwQkAFxAu6uvYEvxF4hdrAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFjUaUBOmTJFEyZMuOC4goICPfzww4qLi1NKSopeeOEFVVZWeox58803lZqaqpiYGA0cOFA7d+6sq7IBAKibgHS5XMrIyNA777xzwbFnz57ViBEjJElvv/22pk6dqrfeekv/9V//5R6zevVqpaena8yYMVq1apXatm2rYcOG6dixY3VRPgAAvg/IvXv3auDAgXr33Xf1H//xHxcc//HHH+vw4cNKT09XZGSkevXqpSeffFLLly+X0+mUJC1evFiDBw/WHXfcofbt22vmzJkKDg7Wu+++6+vyAQCQVAcBmZmZqYiICH344Ydq27btBcfn5OSoU6dOuuKK//3ttW7duqmsrEy7du3S0aNHdeDAASUnJ7v7GzdurPj4eGVnZ/u6fAAAJNXBr3kMGjSoVuOLiooUHh7u0RYaGipJKiwsVOPG50ps06aN15jc3Nxq501NTa22r6CgQI0aNapxDADg8lVYWKhGjRrV6XPUKiALCgpqDJVNmzapdevWtSqgvLxcLVq08GgLDAyUJDkcDp05c0aSFBAQ4DXG4XDU6rnO9+OTgH4OCgsLJXl/Wbjc/Vzrln6+tVN3/aLu+ldZWSmXy1Wnz1GrgAwLC9O6deuq7T9/N+nFCgoKch9rrFIVfE2aNFFQUJAkWccEBwdXO+/69eur7asK+ZrGXI6ou/79XGun7vpF3fWvPvYA1iog/f39FRER4dMCwsPDlZ+f79FWUlIi6VwgV32zKSkp8XjukpIShYWF+bQWAACqNPiNAhISErRz506VlZW52zIzM9W0aVNFR0fryiuvVLt27ZSVleXur6ioUE5OjhISEhqiZADAL0C9B6TT6dSRI0fcu0x79eqlkJAQPf7448rNzdVnn32mjIwMDR8+3H3ccfjw4Vq2bJlWr16tPXv26C9/+YvKy8t1991313f5AIBfiHoPyG3btiklJUXbtm2TdO5km1deeUUul0v33nuvpk2bpoEDB+rRRx91L3PvvfcqLS1NL7zwgvr376/vv/9ey5Ytq/UJQQAAXCyfX+ZxvhUrVni1JSUlKS8vz6Ptmmuu0auvvlrjXCNGjHDfcQcAgLrW4McgAQC4HPkZY0xDFwEAwOWGLUgAACwISAAALAhIAAAsCEgAACz+7QNyypQpmjBhwgXHFRQU6OGHH1ZcXJxSUlL0wgsveN3Q/M0331RqaqpiYmI0cOBA7dy506e1OhwOTZs2TcnJyerSpYvGjh1b449CT5gwQVFRUdbHggUL3ON69+7t1X8x66Su6pakRYsWWes+3+W2viVp69atGjJkiLp27aru3btr0qRJOnHihLu/uLjY+rpWrVp1yXW6XC69+OKL6t69u2JjY/XQQw/p0KFD1Y4/fvy4xo4dq4SEBCUmJmratGnum/5X+eijj3TbbbcpJiZGffv21aZNmy65Pl/Wvnv3bo0aNUpJSUlKTk5WWlqaDh8+7O6vrKxUTEyM1/qdP39+g9b9/vvvW/+7FxQUuMfUxzqvTd3z58+v9vNj4sSJ7nHDhg3z6h8yZIjPa6/y0ksvXXD+enuPm39TlZWV5vnnnzeRkZHmqaeeqnGs0+k0vXv3NqNGjTJ5eXnm008/NYmJiWbevHnuMatWrTIxMTHmvffeM7t37zbjxo0ziYmJ5ujRoz6recKECaZXr14mOzvbfP3116Zv375m0KBB1Y4vLS01JSUlHo8nnnjC3HjjjaaoqMgYY8ypU6dMdHS0+fzzzz3GlZaWNljdxhgzZswYM27cOK/6q1yO63vfvn0mNjbWzJgxw+zZs8dkZ2ebP/7xj2bo0KHuMV988YW5/vrrTXFxscfrOnPmzCXXOX/+fJOUlGQ+//xzs2vXLjN8+HDTu3dv43A4rOMHDx5s+vfvb7755hvz1VdfmZtuusmMHz/e3b9p0ybTqVMns3z5crNnzx7z7LPPms6dO5s9e/Zcco2+qP3YsWPmxhtvNKNHjzZ5eXlmx44dZtCgQebWW2815eXlxhhj9uzZYyIjI82uXbs81m9ZWVmD1W2MMenp6Wbw4MFe7+eKigpjTP2t89rUXVZW5lXv7NmzTWxsrMnNzXWPS05ONitXrvQYd/z4cZ/WXeWNN94w0dHRZvDgwTWOq6/3+L9lQO7Zs8fcd999plu3bqZnz54XDMgPPvjAdO7c2Zw4ccLd9vbbb5u4uDj3G6t3794mPT3d3X/27Fnzu9/9zixevNgnNRcVFZno6GjzxRdfuNv27dtnIiMjzdatWy9qjvXr15uoqCiTmZnpbvv6669NZGSkx2vzpUut+9ZbbzXLli2rtv9yXN8ZGRmmd+/exuVyuduys7NNZGSk+e6774wxxrz88svm9ttv90mNxhjjcDhMly5dzJtvvuluO3nypImJiTEffPCB1/itW7eayMhIjw+CL7/80kRFRbm/NA0fPtyMGTPGY7n77rvP/Od//qfP6r6U2v/617+aLl26eHyZOHz4sImMjDRfffWVMcaYtWvXmri4OJ/W+VPrNsaYkSNHmhkzZlQ7Z32s80up+3zffvut6dSpk1m1apW77YcffjCRkZHm22+/9VmdNkVFRebhhx82sbGx5pZbbqkxIOvzPf5vuYs1MzNTERER+vDDD9W2bdsLjs/JyVGnTp08fq6rW7duKisr065du3T06FEdOHBAycnJ7v7GjRsrPj5e2dnZPql5y5Yt7uet0q5dO4WFhV3UczgcDj3zzDPq37+/kpKS3O15eXm66qqrLumnyC7GpdTtdDp14MABXXvttdb+y3V933HHHZo9e7b8/PzcbVX/PnnypKRz69uXv3iTm5urU6dOeayLFi1aqGPHjtY6c3JyFBIS4lFDYmKi/Pz8tGXLFrlcLm3dutVjPuncHa58tW4vtfbk5GQtXLjQ/RN3kvSrX537iCotLZXk+/Xri7ovVFd9rfNLqft806dPV3x8vPr16+duy8vLk5+fn9q1a+ezOm2+/fZb+fv76/3339cNN9xQ49j6fI/X6a3mGsqgQYNqNb6oqEjh4eEebaGhoZLO/aBo48bnVtOPf1Q0NDRUubm5P6HS/1VcXKxWrVq5fyz6/OcoKiq64PLvvvuufvjhBz3++OMe7Xl5eWrSpInS0tK0detWtWrVSv3799fQoUPdHz71XfeePXtUWVmpjz/+WM8884wcDocSEhI0btw4j+Uut/Vt+wBcsmSJQkJC3MdP8/Pz1apVKw0aNEj79+/XNddco0ceeUQ9evS4pDprWhe2OouLi73GBgQEqGXLliosLFRpaalOnz5tfb9fzPusLmtv27at1xfal19+WUFBQe5f7snPz1dFRYVGjBih3NxchYWF6YEHHtCdd97ZYHWfPHlSxcXFysnJ0cqVK3X8+HHFxMRo3LhxateuXb2t89rWfb7PP/9c27Zt05o1azza8/Pz1bx5c02fPl3//Oc/1aRJE91yyy169NFHvX7E/qe4+eabdfPNN1/U2Pp8j//sArKgoKDGH8rctGlTrW9iXl5erhYtWni0VX1wOhwO98HfH78hAgMD3T/ufCEXqnvMmDHWN9zFPIfL5dLy5ct1zz33KCQkxKNv9+7dKi0tVZ8+ffSnP/1JW7Zs0Zw5c3Ty5EmNGTOmQequ+v3P4OBgzZs3T0ePHlVGRoaGDh2qNWvWXPbru8rs2bP1xRdfaMGCBfL391dFRYX27dun9u3ba8KECWrWrJnWrl2rUaNGadmyZV7faC9GTeuiaqv1x+Nrel3l5eXVznexr/ti1bb2H1uxYoXeeOMNTZ482f3/9O7du+VyuZSWlqbw8HBt2LBBEydO1NmzZ3326z61rXv37t2SJGOMZs2apfLyci1atEgDBw7UBx98oIqKimrn8+U6/ynre9myZbrpppt03XXXebTn5+fL4XAoJiZGw4YN065du5Senq7Dhw8rPT3dZ7XXRn2+x392ARkWFqZ169ZV238puxKDgoLcP79VpWpFNmnSxL3LxzYmODj4op7jQnVv2LDBa/6LfY6tW7fqu+++0/333+/Vt2TJEjkcDjVv3lySFBUVpbKyMi1atEijR4++4FZkXdTdt29f9ejRw+OLTIcOHdSjRw/94x//0NVXXy3p8l3fZ8+e1ZQpU7RmzRrNmDFDvXr1knRuN3BWVpYaNWrkfs907txZu3fv1tKlSy8pIM9/752/67G6Om3v5arxTZo0cX/x+ynr9mLVtvYqxhjNmzdPixYt0iOPPOJxRuOHH36oyspKNW3aVJIUHR2tw4cPa+nSpT4LyNrWHR8fr02bNqlVq1buXe4LFixQz549tWrVKt1zzz3u+c7n63V+qev78OHDysrK0ssvv+zVN336dD311FPuz9XIyEj5+/vriSee0Pjx43XVVVf5rP6LVZ/v8Z9dQPr7+/v8GER4eLh7q6ZKSUmJpHMftFWb8yUlJR7PXVJSorCwsIt6jgvVnZeXpxMnTsjpdHp887mY5/j000/VsWNH6/wBAQFe36QiIyN1+vRpnTx5Uq1atWqQun+8lR8aGqqWLVuqqKjIfQz1clzfZWVleuyxx5STk6OMjAzdeuutHv1VH9zn69ChgzZu3HhRdf/Y+e+9qi8OVX//+LIY6dx7+bPPPvNoczqdOnHihHsdN2nSxP3+Pn++i123dVW7dO7Lx8SJE/Xhhx9q4sSJevDBBz36z//grxIZGan333+/Qev+8fs5ODhYbdu2VXFxcb2t80upW5I+++wztW7dWjfeeKNXX+PGjb02Ojp06CDp3C7dhgjI+nyP/1uepFNbCQkJ2rlzp8rKytxtmZmZatq0qaKjo3XllVeqXbt2ysrKcvdXVFQoJyfHfWzkp+ratatcLpf75BFJ2r9/v4qLiy/4HNnZ2datE2OMevXq5XFNpCTt2LFDISEhFwzHuqp77ty56tOnj8x598kvKCjQ8ePH1b59+8t2fTudTj388MPavn27li5d6hWOu3fvVlxcnEfdkvTNN9+offv2l1RndHS0mjVr5jFnaWmpdu7caa0zISFBRUVFOnjwoLtt8+bNks69Zj8/P8XFxbnbqmRlZSk+Pv6SavRV7ZI0fvx4/f3vf9fzzz/vFY6lpaVKTEz0uqZ0x44d7g/thqj7nXfeUVJSkk6fPu1uKysr04EDB9S+fft6W+eXsr6lcye9JCYmus+1ON+QIUM8romUzq1vf39//fa3v/VZ7bVRr+/xWp3z+jM0ePBgr8s8HA6HKSkpcV/CUV5ebnr16mVGjBhhdu3a5b4Ocv78+e5l3nnnHRMTE2NWrVrlvi4vKSnJp9flPfnkk+bmm282mZmZ7uvyzj/d+cd1G2NMRUWF6dSpk3nvvfescz777LMmNjbWrF271hw8eNC8/fbbJiYmxrzzzjsNVveOHTtMp06dzJQpU8y+ffvM5s2bTd++fc2AAQPcl1Bcjuv7xRdfNFFRUebDDz/0un7M4XCYyspK079/f3PbbbeZ7Oxss2fPHjNz5kzTuXNnk5eXd8l1ZmRkmMTERPPZZ595XNvmdDpNRUWFx3WWLpfLDBgwwPTr1898/fXXZtOmTeamm24yEyZMcM/35Zdfmuuuu868+uqrZs+ePWb27NkmJiamTq6DrE3tf/vb30xkZKR55ZVXvNZv1ZjRo0eblJQU88UXX5j9+/ebl156yVx33XXmv//7vxus7sOHD5v4+Hjzpz/9yeTn55vt27ebBx980PTq1ct9/WZ9rfPa1F0lNTXVLFy40DrfihUrzHXXXWdWrlxpvvvuO7N27VqTlJRkMjIyfFr3+Z566imP/w8b8j3+iwzIzMxMExkZ6XG94IEDB8ywYcPM9ddfb1JSUswLL7xgKisrPZZ75ZVXTI8ePUxMTIwZOHCg2blzp09rPXXqlJk0aZKJj4838fHx5sknnzTHjh2rse6q65Q2bNhgnfPs2bNmwYIFJjU11XTq1Mn06dPHp+F4qXV/9dVX5r777jOxsbEmMTHRTJw40etazcttfffu3dtERkZaH1Vjjhw5YiZMmGBuvPFGc/3115v77rvPZGdn/6Q6KyoqTHp6uunWrZuJjY01Dz30kDl06JAxxphDhw6ZyMhI87e//c09/ocffjCjR482sbGxJikpyTz99NPuD+oqq1evNr///e/N9ddfb/r16+e+ztDXalP7sGHDql2/VWP+9a9/mZkzZ5rf/e53pnPnzubOO+80n376aYPWbYwx33zzjRk2bJjp2rWriYuLM6NHjzaHDx/2mLM+1nlt6zbGmJiYGLNy5cpq53zjjTfMrbfeajp37mxuuukms2jRIq/PRl/6cUA25Huc34MEAMCCY5AAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABYEJAAAFgQkAAAWBCQAABY/H8YZ1U6lc3/ggAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(np.cos(psi), np.sin(psi), \"o\")\n", - "\n", - "plt.ylim([-1, 1])\n", - "plt.xlim([-1, 1])\n", - "plt.gca().set_aspect(\"equal\")" - ] - }, - { - "cell_type": "code", - "execution_count": 104, - "id": "0a59231b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 104, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(psi)" - ] - }, - { - "cell_type": "code", - "execution_count": 106, - "id": "4a8e03e0", - "metadata": {}, - "outputs": [ - { - "ename": "IndexError", - "evalue": "index 1 is out of bounds for axis 0 with size 1", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn [106], line 12\u001b[0m\n\u001b[1;32m 9\u001b[0m idcs \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mwhere(diff \u001b[38;5;241m>\u001b[39m dist \u001b[38;5;241m/\u001b[39m \u001b[38;5;241m2\u001b[39m)[\u001b[38;5;241m0\u001b[39m]\n\u001b[1;32m 11\u001b[0m clust_1 \u001b[38;5;241m=\u001b[39m psi[:idcs[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m]\n\u001b[0;32m---> 12\u001b[0m clust_2 \u001b[38;5;241m=\u001b[39m psi[idcs[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m:idcs[\u001b[38;5;241m1\u001b[39m]\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m 13\u001b[0m clust_3 \u001b[38;5;241m=\u001b[39m psi[idcs[\u001b[38;5;241m1\u001b[39m]\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m:]\n\u001b[1;32m 15\u001b[0m \u001b[38;5;28mprint\u001b[39m(np\u001b[38;5;241m.\u001b[39mmean(np\u001b[38;5;241m.\u001b[39mdiff(clust_1)))\n", - "\u001b[0;31mIndexError\u001b[0m: index 1 is out of bounds for axis 0 with size 1" - ] - } - ], - "source": [ - "n_clust = 2\n", - "dist = 2*np.pi / n_clust\n", - "\n", - "\n", - "psi = psi % (2*np.pi)\n", - "psi = np.sort(psi)\n", - "\n", - "diff = np.diff(psi)\n", - "idcs = np.where(diff > dist / 2)[0]\n", - "\n", - "clust_1 = psi[:idcs[0]+1]\n", - "clust_2 = psi[idcs[0]+1:idcs[1]+1]\n", - "clust_3 = psi[idcs[1]+1:]\n", - "\n", - "print(np.mean(np.diff(clust_1)))\n", - "print(np.mean(np.diff(clust_2)))\n", - "print(np.mean(np.diff(clust_3)))\n", - "\n", - "print(np.mean(clust_1) - np.mean(clust_2))\n", - "print(np.mean(clust_1) - np.mean(clust_3))\n", - "\n", - "print(np.mean(clust_2) - np.mean(clust_3))\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 114, - "id": "5b0d4d13", - "metadata": {}, - "outputs": [], - "source": [ - "def idenfity_k_clusters(thetas, k, t, atol=1e-1):\n", - " \n", - " n_clust = k\n", - " dist = 2 * np.pi / n_clust\n", - " N = len(thetas)\n", - "\n", - " psi = thetas[:, t] % (2 * np.pi)\n", - " psi = np.sort(psi)\n", - "\n", - " diff = np.diff(psi)\n", - " idcs = np.where(diff > dist / 2)[0]\n", - "\n", - " clusters = []\n", - " n_changes = len(idcs)\n", - " for i in range(n_changes + 1):\n", - " start = idcs[i - 1] + 1 if i > 0 else None\n", - " end = idcs[i] + 1 if i < n_changes else None\n", - " clusters.append(psi[start:end])\n", - "\n", - " for i in range(n_changes + 1):\n", - " if np.mean(np.diff(clusters[i])) > atol: # cluster is not compact\n", - " print(f\"cluster {i} not compact: {np.mean(np.diff(clusters[i]))}\")\n", - " return False\n", - "\n", - " for i in range(n_changes):\n", - " dist_ij = abs(np.mean(clusters[i]) - np.mean(clusters[i+1]))\n", - " if abs(dist_ij - dist) > atol:\n", - " print(f\"cluster {i} and {i+1} wrong distance by: {abs(dist_ij - dist)}\")\n", - " return False # clusters have wrong distance between them\n", - " \n", - " print(n_changes, len(clusters))\n", - " if n_clust == len(clusters):\n", - " sizes = [len(cluster) / N for cluster in clusters]\n", - " elif n_clust == clusters - 1:\n", - " sizes = [len(cluster) / N for cluster in clusters[:-1]]\n", - " sizes[0] += len(clusters[-1]) # 0th and last clusters are the same\n", - " else: \n", - " raise ValueError(\"n_changes must be equal to or one unit above n_clust\")\n", - " \n", - " return True, sizes" - ] - }, - { - "cell_type": "code", - "execution_count": 92, - "id": "b0e1e57f", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.2379991410381057" - ] - }, - "execution_count": 92, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.mean(clusters[0])" - ] - }, - { - "cell_type": "code", - "execution_count": 94, - "id": "b8228f34", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "6.174050046924062" - ] - }, - "execution_count": 94, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.mean(clusters[-1])" - ] - }, - { - "cell_type": "code", - "execution_count": 93, - "id": "668cc306", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 93, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(clusters[0])\n", - "plt.plot(clusters[1])\n", - "plt.plot(clusters[2])\n" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "id": "98f49496", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "100" - ] - }, - "execution_count": 58, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(psi)" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "id": "3124e1ef", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "100" - ] - }, - "execution_count": 59, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(clust_1) + len(clust_2)+ len(clust_3)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "08c094c2", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "b6b7f9e4", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 34, - "id": "4c585e34", - "metadata": {}, - "outputs": [], - "source": [ - "n_clust = 2\n", - "dist = 2*np.pi / n_clust\n", - "\n", - "idcs = np.where(diff > dist / 2)" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "d2184564", - "metadata": {}, - "outputs": [], - "source": [ - "clust_1 = diff[:idcs[0][0]]\n", - "clust_2 = diff[:idcs[0][1]]" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "id": "61780762", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.01717383636837027" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.mean(clust_1)" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "id": "15415df4", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.04106689446248958" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.mean(clust_2)" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "id": "4ec49f37", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 28, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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+JsxwAMTDOtHxbxdmohNAYALYYB1IAqcLsyYMIHbmrhyX06xZa2E8MRGYADZ4rduFW5ExARAPb6gjLljKMRGYADZ4zKUcWTImDCQAYhfU+ZXi13YITAAbvJ5AQyQ/BhIA8fAGFb/6a0xYyvEjMAFssLaQ9iNjAiAetB+IjMAEsMHcleNwmC3pGUgAxMN6xAVLOe0RmAA2WDs1mtcYSADEwWMuDVtOF6b41URgAtjAUg6ARPGE2JXDeBJAYALYYF3K8e/KIWMCIB5ey0THyVk57RCYADYEGqwFduUwwwEQD7P41cF24VAITAAbvGanRke7awAQi+AGa77JTgs1JqaEni4MnIwMw5B/MuNyOnw7cyR5Dd/nACAW/mUbp8tpqTFhouNHYAJEYV2ycVo6Nbb9HADYEar4laWcAAITIArrgGEdSNp+DgDssAYm/uJXw2Ci40dgAkThaZMx8S/lSAwkAGLntZxW7nJxzEVbBCZAFN62GRMXGRMA8bN2fk0KysBSZyKxKweIKjhj4vTlXEN8DgDsMItfqVkLicAEiMI6i3E6JLGUA6ADrKcLOzmxvB2WcoAorIOIo7XzK90aAcTLesSFZSWH83JaEZgAUVgr6P3MXibEJQBiZB1THA7rlmEGFInABIjKGyIwCbSRZiABEJu2Y4oZmJAxkURgAkRlXcrxC2RMGEgAxMY/ofG3o+e8nGAEJkAUoZZy6NYIIF7+zIh/suMvgCUD60NgAkRh7Tng55/hkDEBECuvEWYph/FEEoEJEFVgKSdwLXCQHwMJgNh42iwPBw7yYzyRCEyAqALNkCwZE4rVAMTJ42mTMWltS8944kNgAkQRcrsw2/sAxMncldMakLBdOBiBCRBFqF05/noTxhEAsQrsyqHGJBQCEyAKMiYAEqntmMJ24WAEJkAUXk/4wITiVwCxal/82pqBpcZEEoEJEFXI7cIUvwKIU9vlYf9/W8jASiIwAaLyZ0WCtguzJgwgTu2WchhPghCYAFF4PMHto31/ZykHQOwMw7CcldNmVw4ZWEkEJkBUbdeDJQYSAPGxNlHzF736tw3TYM2HwASIIrCUE6L4lYEEQAysyzXtl3KoMZEITICo2nZp9P2dGQ6A2FkDk7Yt6akx8SEwAaII3cfE/zlmOADs84bKmNCSPgiBCRBFxM6vFL8CiEFwxqRtS3rGE4nABIgqVB8TJ8WvAOJgzbL65zqBmjUysBKBCRCVf7DwV9BLzHAAxMdrWRp2OKgxCYXABIjCXMpx0JIeQMdEKqZvIQMricAEiCpU8St9TADEwxxPrBlYF0s5VgQmQBRmgzUXGRMAHeOvMXGGOnuLpRxJBCZAVKGWcsiYAIhHpKVhAhMfAhMgitB9TOjUCCB2IZdymOgEITABoggMJNbUK31MAMQu1EQnyd9gjYmOJAITICr/YBGq+NXLDAdADLwRMrAcceFDYAJEEarzq7mUQ8YEQAwC24Upfg2HwASIItQMx8UMB0AcArtyrNuF/Us5jCcSgQkQVcTiV5ZyAMTAX5fmDDHRafFQYyIRmABRhT7Ejz4mAGIXuvMrGVgrAhMgCk+kGhMGEgAxCLVdmAxsMAITIIpIpwszwwEQi9A1a2wXtiIwAaIILOUErgUGEgITAPYF2g9YduW4yMBaEZgAUYQaSPx/9VCsBiAGoZaG2S4cjMAEiCL06cJ0fgUQu5DFr63bhVka9iEwAaKItCuHGQ6AWETaLkzxqw+BCRBFpD4mzHAAxCLSdmGKX30ITIAoInV+JWMCIBahdvkxngQjMAGiiHRWDhkTALHw+ovpXSG2C7OUI6mDgcnjjz+uq666KuJjjh07pp///OcqKirS5MmTNW/ePDU0NHTkZYHjKnTxK4EJgNiFbNjoYinHKineJz733HNauHChJk2aFPFxN910kxoaGvT000+rurpad911l+rr6/Wb3/wm3pcGjiv/lmAnqVcAHRRposN44hNzYFJWVqZ7771Xq1ev1rBhwyI+dv369fr000+1bNkyjRgxQpL0q1/9Stdee61uueUWDRo0KK6bBo6nUFX0LOUAiAc1a9HFHJhs2rRJycnJWrJkiR555BEdPHgw7GOLi4s1cOBAMyiRpMmTJ8vhcGjt2rX66le/2u45s2bNCvv1SkpKlJeXF+stAx0SelcOLaQBxC50g7XWPibUmEiKIzCZOXOmZs6caeuxZWVl7QKJlJQU9e3bVyUlJbG+NNAlQm7vczDDARC7kC3p2S4cJO4aEzsaGhqUkpLS7npqaqqamppCPmfFihVhv16kbArQWUKlXv3FaizlAIiFN2TnVyY6Vp26XTgtLU1ut7vd9aamJvXq1aszXxpIGE+kTo0MJABiEOmIC8YTn04NTHJzc1VeXh50ze12q7KyUjk5OZ350kDCBGY41kP8CEwAxM6sMXGRMQmnUwOToqIilZaWat++fea1Tz/9VJI0ceLEznxpIGECa8L0MQHQMaE6v5q7/DitXFKCAxOPx6OKigo1NjZKksaNG6fCwkLdfPPN2rhxo1atWqV77rlH3/zmN9kqjBNGyO3CDgITALEzO0kHhhNzotPCeCIpwYFJSUmJpk6dqmXLlkmSHA6HFi9erPz8fH3/+9/Xz372M02fPl1z585N5MsCncq/K8dJsRqADjIzsK4Qu3LYLiypg7ty5s+fH/Rxfn6+tm3bFnStf//+WrRoUUdeBuhSZuo1xNkWXrb3AYhByOJXF+OJFYf4AVGYSzmO9ks5ZEwAxILOr9ERmABRhGywRh8TAHEItTTMLr9gBCZAFOYMx7ImTMYEQDwid35lPJEITICoPKGq6MmYAIiDv4wkdM2aIcNgTCEwAaLwhqiiJ/UKIB7+jIm1Zi3JEqQw2SEwAaIKebowSzkA4hBql5+13oQxhcAEiCrQEIniVwAdE3JXjiUbS2BCYAJEFamPCYMIgFiEPsTPkjGhLT2BCRCJYRiB4lda0gPoIH/g4XS23+UnMdmRCEyAiKxjRND2PnMph9kNAPtC1qw5HeauPwITAhMgImtGJGTGxBDb+wDY5u8kbV0algIZFM7LITABIvJYMiKhOr9KLOcAsM/s/OoIDkwCB4OShSUwASKwBh1hi9UITADYFGpXjvVjJjoEJkBE0ZZy2j4GACLxhGjYKNGW3orABIjAOkiE6mPS9jEAEEmoXX5SIFBhPCEwASKynpMTLmPCQALArlC7cqwf08eEwASIyBtmdmP9mKUcAHZFqzFhokNgAkQUSLsG/6g4HA7LQX7McADYE3Yph+3CJgITIAKzUK3NICJZu78e11sCcAILt5TDRCeAwASIINxSjkTfAQCx83r8k502u3JcLOX4EZgAEYSb3UiclwMgdqEOBZWoMbEiMAEiCFeoZr3GQALArvA1Jkx0/AhMgAjCDSKS9SA/BhIA9oTfLuwvfmVpmMAEiCBSxiRwkB+BCQB7AmNK8K9fJxlYE4EJEIF/617bQcR3zRH0GACIJlwWNonOryYCEyACfzYkRFzC9j4AMfOGaUFAzVoAgQkQgT/oaNtgTQpkUYhLANgVto+Jf7swNSYEJkAkgaWcEDUmZEwAxMDrNeQvSQu3K4eMCYEJEFG4ngMSxWoAYmMdK/ynCZsfM56YCEyACMwaE0f4PiZsFwZgh3UHX7jtwl6WcghMgEjsLeUQmACIzlo/QvFreAQmQARmzwFX+O3C9DEBYIc1u9q2xsTJWTkmAhMgAvMQvwhLOfQxAWCHNehoO6aQMQkgMAEi8ITpOSAFZjzUmACww2yu5gi1K8ffYI0aEwITIAJzIAmxKyfQx4TABEB0/uxqyL5I/rO3yMASmACRRFrK8Y8tzHAA2GFmYENOdFjK8SMwASII16XRd601Y0LxKwAb/GNFpPGkhe3CBCZAJLYarJF6BWCDuZQTqZiejAmBCRCJrV05DCQAbPBGmOiYNSaMJwQmQCSBpZz2PypO+pgAiEGkpWEaNgYQmAAReCMUq7GUAyAWdk4rJzAhMAEi8thYyiFjAsCOyMX0/okOxa8EJkAEEdeEyZgAiIHXTmBCxoTABIjEzJhEXBNmhgMguki7/Ch+DSAwASKgjwmARPFG3C5MjYkfgQkQgTdCxsSsMWEpB4ANkXb5uVxkYP0ITIAI7GwX9pAxAWCDuSuHmrWICEyACCKdLuzidGEAMbC1K4fxhMAEiCTSUg59TADEInKDtdYaE7YLE5gAkdiZ4VD8CsAOb6QaEzImJgITIIJIfQdoIQ0gFhEnOi7GEz8CEyACO0s51JgAsMNrtqSnZi0SAhMgAjt9TJjhALDDX48WOjDxjyfUmBCYABEEBpJQ24X9j2EgARAdpwvbQ2ACROAvbA0Rl9D5FUBMIrWkT3Kxy8+PwASIINDHhCp6AB0TeVcOS8N+BCZABP7ZS6TUKy3pAdhhaymHpWECEyCSwFJOhE6NLOUAsCHirhy2C5sITIAI7Mxw2N4HwA5a0ttDYAJE4I2wlEPfAQCx8EToi2QW07NdmMAEiMTWUg6BCQAbItWsMZ4ExByYeL1eLVq0SNOmTdP48eN13XXXaf/+/WEfv2TJEp155pnt/hw4cKBDNw4cD54IVfQUqwGIhbnLzxVpPCEwSYr1CX/4wx/0/PPPa/78+crNzdUDDzyga6+9VkuXLlVKSkq7x2/btk2TJ0/WggULgq5nZ2fHf9fAceIPOkK3pKePCQD7Ip29RfFrQEwZE7fbraeeeko33XSTZsyYoYKCAj300EMqLS3Vm2++GfI527dv15lnnqmBAwcG/XG5XAn5BwCdKVJDJJeDgQSAfRxxYU9MGZOtW7eqrq5O5557rnmtT58+Gj16tNasWaOLL7643XO2bdummTNn2n6NWbNmhf1cSUmJ8vLyYrlloEPMGhNHiIyJi+JXAPZFOhQ0yRxPWBqOKWNSWloqSe2Cg5ycHPNzVlVVVSorK1NxcbG+/vWva+rUqbrhhhu0Z8+eDtwycPxQrAYgUSLtyvFfa/EYMnr48nBMGZOGhgZJaldLkpqaqqqqqnaP37FjhyTJMAzdf//9amxs1KOPPqorrrhCS5cu1YABA9o9Z8WKFWFfP1I2BegMkZZyOHQLQCwiFdNbr3kNKcSQ02PEFJikpaVJ8tWa+P8uSU1NTUpPT2/3+EmTJmnlypXq16+fHK2p8MWLF2vGjBl6+eWX9aMf/agj9w50OjP1GmIphz4mAGLhL6aPlIGVfMs5LmfPrcOMaSnHv4RTXl4edL28vFyDBg0K+Zzs7GwzKJGk9PR05efnq6ysLNZ7BY67SIdu+YMVAhMAdvhr1qIFJj19y3BMgUlBQYEyMzO1evVq81p1dbU2b96soqKido9/4YUXdM4556i+vt68Vltbq7179+r000/vwG0Dx0eg7wDb+wB0TMRdfpZrPX1MiSkwSUlJ0ZVXXqkHH3xQK1as0NatW3XzzTcrNzdXs2fPlsfjUUVFhRobGyVJ06dPl9fr1e23364dO3bo888/14033qjs7GxdeumlnfIPAhIp8lIOLaQB2Oc/4iJSXySJwCTmzq833XSTLrvsMt19992aM2eOXC6XnnzySSUnJ6ukpERTp07VsmXLJPmWfp5++mnV19drzpw5+sEPfqDevXvrmWeeUWpqasL/MUCiRSx+pY8JgBiY40mo9gMO6+N69mQn5s6vLpdLt912m2677bZ2n8vPz9e2bduCro0ZM0ZPPfVU/HcIdKGIh27RxwRADPwBhzNES3qHwyGX0yGP1+jxYwqH+AERRFrKIWMCIBaROr9ar1P8CiAsO8VqPX12A8CeqIGJi7b0EoEJEJGt04V7+CACwJ5Ih/hZr7f08BPLCUyACFjKAZAokfoiSWRh/QhMgAi8NvqY9PRBBIA9kYrpJc7f8iMwAcLweg35xweOKQfQUf6W9OECE6c5prCUAyAEr+WEz5ANkWhJDyAGkYrpJTImfgQmQBjWgCNkxsRcyunZsxsA9rBd2B4CEyAM66wlYsbEkAyjZw8kAKKLuiuHujVJBCZAWJ6gjEn7HxVrOranDyQAoovUfsB6nRoTACF5o2RMgo4pJzABEIV/2Td88Ss1JhKBCRCWddYSahyx9jYhYwIgmmg1JkkuAhOJwAQIy7oe7AjRYM26lNPTBxIA0UXvY9K6lEPnVwChRBtErBkTAhMA0fh324TLmLCU40NgAoQRrYLeGrCwlAMgGnNMcYUrfmW7sERgAoQVbT3Y4XBYZjg9O/UKIDrbfUx6+ESHwAQIwxtlKUfiID8A9plnb4XtY+IMelxPRWAChBGt54BEQyQA9nGInz0EJkAY0Q7ckjgvB4B9UQvqCUwkEZgAYfkP8YsUmDDDAWAXZ+XYQ2AChBFtEJFYygFgj2EYlp1+0VrS9+zxhMAECCNazwGJ4lcA9gSdVu4KV/zKieUSgQkQVixLOWRMAETitZxAHm0pp4WlHACheO1kTOhjAsAGa91I2F05LpZyJAITICxb24Wd/r4Dx+WWAJygrMFG9AZrPXtAITABwvAPDs4w68ESGRMA9lgDE2fY4leWhiUCEyAss4I+xMnCfvQdAGCHdfISbnXYyXZhSQQmQFjRmiFJzHAA2GM9FNQRZrJDXyQfAhMgDLPGxNZSTs8eSABEZq8vkr/4tWcvDROYAGGYh/hFWMoxMyYGgQmA8Lw2JjpkTHwITIAwbM1wWBMGYENgaTjSLj+WhiUCEyAs84hyV/gfEycDCQAbzENBI2Vg/Us5PXyiQ2AChNE6jkRZyvH3MenZAwmAyOzUrJmdX6kxARBKIGMSqfjV99+eXqwGILJYloa9ZEwAhGJvu3BrxoTiVwAReGOpWevhGVgCEyCMmBqs9fAZDoDIvDaOuHCyXVgSgQkQlpkxYXsfgA6KpWFjTx9PCEyAMOysCTvpYwLABo+NmjUCEx8CEyAMOw3WWMoBYId/jIg0nqQkuyRJR6saj8s9dVcEJkAYge19NhoikTEBEIGd7cJnnz5ALqdDe0uqtedQ1fG6tW6HwAQIw0y90vkVQAfZ2ZWTlZmqyWNyJUlvf/rFcbmv7ojABAjDa6NYLXCIX8+uogcQmcfGrhxJmn3OqZKkd9fuV3OLp9PvqzsiMAHCsNd3gD4mAKKzM9GRpAln5qh/Vppq6pu16t+lx+PWuh0CEyAMOjUCSBQ7S8P+z88qOkWS9NbqfZ1+X90RgQkQhp2+A+ZSDhkTABHYGU/8vjzZF5h8tqNC5UfrO/W+uiMCEyAMO6lXjikHYIe/QD5axkSScvtn6OzTB8gwpBVrel4RLIEJEIadYjX6mACww27xq58/a/L2mi963MQnqatvAOgutuw5qoMVNWpye9To9mjH/mOSbNaYsJQDIAI7p5VbnXv2YGW8vFHlxxq0cWeFxo/M6czb61YITABJuw9W6fbFH4b8XEZa+B8TJy2kAdhgd1eOX2qyS9ML8/X6J3v11uovCEyAnuajDQclSYOye+n0/L5KTXEpLcWl7D5pmjFxaNjnBZZy6GMCnIxqG5rV0uJV396pHfo6dnb5tTV78ql6/ZO9WvnvEtXUu9W7V0qH7uFEQWACSGa/gKu+MkrnF+bbfl6gj0mn3BaALuTxGrpt0Qc6VtOkR2+fqX590jr0taTYApMR+Vk6bXCWdh+q0rJP9ujbF54Z9+ufSCh+RY93sKJW+8tqlORyaNKoQTE911/HRsYEOPls2n1YB8prVdfQrPfWHejQ14plu7Cfw+HQJRecLkl69f1dqm9s7tA9nCgITNDjrf53iSRp7IgBykhPjum5dH4FTl4ffnbI/Ps7xfs79LUCDdZi+7U7bfwQDRmYqZr6Zv3roz0duocTBYEJejz/Ms6UsXkxP9dF8StwUvJ4vPpkYyAw6eiJv94Y+phYuZwOfWe2bwnnlfd39oisCYEJerRj1Y3auu+oJOmc1lM9Y+GkJT1wUtqw87Cq69zKykzRlLN8Y0NHsib+7tCxBiZSz8uaEJigR/t0c6kMQzpjaF/1z0qP+fnJSb4focNVDYm+NQBd6KPPfDv1vjR2sL482Xfi73vrDsRdT2ZuF7bZx8Sqp2VNCEzQo5nLOGfFvowjSRMLBsnldGjznqPatPtI3PdhGIbeXL1Pr6/cKyOGehWP19C/Ptqt4i1lcb82cDJqbom/IL25xatPPvfVnk0dP1iFBTnKykxRZU2T1m+viOtrupvjqzHx60lZEwIT9Fj1jc36rHWQ8adqYzUou5cubG0d/fzyrXF9DcMw9PS/Nuvhf3ymP7y4QR+2ztTseP2TPXr8fz/XvCdW6dk3tsQU1AAnq+Wr9uk7dy/TIy9uiOtn4rPt5apraFa/3qkac9oAJbmcOn+Cr41ArMs59Y3NeuLVf2vpR7slSekprpjvR0pM1uRQRW2HArbjhcAE3VZVbZPZFr4jyo/V67GXN+rznYeDrq/bVq4Wj1eDB2Ro6KDecX/9yy8cqSSXQxt3Htbnuw5Hf4KFYRj66+tb9PJ7O81rj738uSprmqI+92h1o/76+hbz4xfe2q4Hnl2rpmZPTPcAnCwMw9A/V2zX4n9+JnezR2+s3Ks3V8d+CJ5/cnDe2YPNmpALJvkaLa76d4lqG6IHBYZh6IP1B/R/f7NCr36wS16voXPH5ulrU0+L+X784s2aVNU26TfPrNH181foloXv62h1Y9z3cDwQmJwgDMPQK+/v1H898E6PSNt/vuuwbvjtO7pl4Qd65MUNam6J75ftsZpG/fKxT/Tax3v0y8c/0dufBgapVZ8HlnEcjtjXff1y+vXSl8/xrUE/98bWmGZozy3fqn+u2CFJuuYbZ2lYXh/V1Lv12P9ujPrcp5ZsUn1ji84Y2lf/9a3xcjkd+vCzg7rr0Y91rCb2gcfrNXrcYWHoXkoO1+n9dQfimtV7vYaeXLJJzyzzBeujhmVLkv74vxu1r6Ta9tdxN3vMJd6p44eY10cMydIpub3V3OLVxxsOhXu6Gpta9N7a/brzDx/rgWfX6mh1k/L6Z2judVP0ix9MVp+M+Lu3WrMm/1yxPerEzTAMfbj+oG747Tv6qPWe95ZU647FH6rkcF3c99HZYg5MvF6vFi1apGnTpmn8+PG67rrrtH9/+NTWsWPH9POf/1xFRUWaPHmy5s2bp4YGCgVjKaAyDEN/eW2znlyySftKa/TrP6/Wytb1z5PRGyv36pePfaLqOrf58Z1/+FhHYiwwrWto1tw/rtKhw3VKSXLK4zX0+xfW64W3tqm5xaviLR2rL7G6fNZIJbmc2rT7iDbutJc1+dub2/TCW9sl+YKSb54/Qj/9zgQ5nQ59vOGQPt4YfvDbsKNC768/IIdDuuH/jNN/TDlVv7r+XGWmJ2vbvmO69fcfaFvrbqNQNu0+onse/0Q/eeAd/fC+N/Xtu17TN29fou/PW65PN5XG9o/vQnUNzfrtX4t11dw39Pu/r9farWVqodndCemjDQd10+/e1YPPrdXND72n7V/Yz5a2eLxa+Pd1evWDXZJ8P0/zfzJVEwty5G7x6jd/XaPGphZbX2vt1nI1NLWof1aaGdxIvmZnM1uPp3h3bfDvPI/X0IbtFXrob+v0vXlv6HfPr9Om3UeUnOTUFf9RoMW3XaCJBbE1bwxn2vghGj9yoBrdHs17YpUOVdSGfNyx6kbd/5c1+u2zxaquc2tYXh/94geTldu/l0qP1Ov2xR9q98H4tz93JocR4wLc4sWL9eyzz2r+/PnKzc3VAw88oAMHDmjp0qVKSWkfCV511VVqaGjQvHnzVF1drbvuuktFRUX6zW9+E/PNzpo1S5K0YsWKmJ/bXRypatBzb2zVO8X7Nea0/vr2l0dq7IgBYWfsHq+hR1/aoOWr9knytSjedaBKLqdDt145UVPHDQn5vOOltt6tytom5Q3IjGkbXGNTixqaWtS3d6r5b2/xePXkq//Wvz72pSinjx+i88YN1qJ/fKa6hmb17Z2q//e9Io05rX/0r+9u0dw/rdKm3UfUNzNV8/9rqt5avU8vvetbMhlzWn/f53qn6ul7/iOuLXxtPf7yRv3r4z0aNSxbv/mvqea/y+M1tHFHhfYcqlbpkbrWP/UqOeKbsfzw4jG6tLW7oyT99fUt+sfb29U3M1WLb7tAWZnBZ3Q0t3h144Pv6mBFrb523nD9+NKzzc8drKjVvCdWqeRwnZwO6T/PP13fvahAqcm+de2mZo+efX2LXv1gl8L95DsdvoH969NO61AmqbPtOlCp+c+sUemR+qDrmenJOndsnmZMzI/4s3UiMgxDBytqleRyKrd/Rtxfx+s19N66/fpkY4mmjR+iaeOHhOxIur+sRh9+dlC5/TP0pbF5SktN/CkmHo9Xf319i/mz6XQ65PUa7b5/vV5De0uqtX5bubZ9cUwNjS1qdLeo0e1RTb1bR6oa5XI69NPvTNAFrQFEVW2Tbvrdezpa3aiZk4bq5jmFUe/ngb8W64PPDuo/p4/Qtf95VtDnjlQ16If3vSnDkBb9fIYOHa7Tp5tKtXZrmapq3ebjBmX30sxJQ3Vh0SnKye6VwHfLp76xWXc9+rF2HqjSoOxeeuDGaWa7fMMw9NanX+ippZtU19Asl9Ohyy8cqW/NGqnkJKeOVTfq3j+t1J5D1eqVlqQ7vleknH7pOlbdpKPVjaqqbdLo4f11+tC+Cb3nWH5/xxSYuN1uTZkyRbfeequuuOIKSVJ1dbWmTZumX//617r44ouDHr9+/Xp95zvf0bJlyzRixAhJ0kcffaRrr71W77//vgYNii2C7MzAZN4Tq1R2tE6TR+fqvHGDdXp+34QOaHUNzXrp3R169YPdcrepARg1LFvf/vJIFZ6ZE/SaLR6vHnp+nT747KAcDuknl43XhUVDtfCF9Xpv7QE5HdLNcwrNQ+YMw1DZ0XodrKjVwL7pGpLT2/Yv3MamFpUdq5fXa8jjNWQYvrR+WkqSsrPSlJmebN7bsepGrdpUqpUbD2njzsPyeA31SktSwbBsjR6WrdHD++uMU/oqLaX9IHawolZLPtilFcX71eT2KCXZpdz+vZSbnaGq2iZta50lXfmVAl0+a6QcDocOHa7V/U+v0d6SarmcDk05K0/pqUlKSXYqJdmlXqlJGpKTqVNz+2jwwEw5HNKv//ypireUqVdaku6/YapOG5IlSXrto916/JXPzV/K/zHlVP3Xt8bH9P8ynCNVDbruf95Wc4tXv/rRuSoYlq23P/1CSz/cbQYhVk6HdNVXR+uymWcEXW9u8ehnD72vL0prdP6EfN165cSgz//j7e366+tb1DczVY/+v1nKbNOttqberT++8rneW+troT14QIZu+vYEuVwOLfzbOh2s8N3LhUWnaEZhvtLTkpSRnqz01CQ9v3yrGQR/7bzhuu4/z5LLldgV3xaPV+u3lWvl5yVKcjl1+tC+OmNoX50yqLet1zIMQ8tX7dMfX/lczS1e5fRL11VfGaWt+47p442HgupzTsntrYvPG64ZE4cqPcZfql6voV0HK1V+rEGnDOqtwQNjC76t93u4slH7y2vUv0+a8nMybb+nhmGoorJBG3cc1oadFdq447BZHzB+5EBdcv7pmnDmwJjGqg3bK/TU0k3abWkWNnxwH131lVGaNGqQHA6H9pVW6x9vbdeHGw6aPytpKS596ezBmlU0VGedNiCm1upS61KhYSjJ8m+vqm3SA88Wa8MOX5bx0hmn65vnj9CTSzbp/fW+79+8ARk6Y2hfbdhREfTLv63UFJf+3/eK2h0r8fmuw7r70Y/lNaSffWeCCgtyVHakXqVH6lR2tF5pqUk6bXCWhg/uo6Qkp6669w01uj168KZpOvPU7Hav88vHPzGL5q0y0pM1ddxgzZw0VKOGZXd6QFxZ06TbH/5QJUfqdNrgLN3/k/N0tLpRj7y4Qf/e5dshOCI/Sz/99gQNH5wV9Ny6hmbd99TqsDsJhw7K1B9un5XQ++20wGTjxo361re+pTfeeEPDhw83r8+ZM0cjR47UvHnzgh7/pz/9SX/5y1/00UcfmdfcbrfGjRun3/3ud/rqV79q96UldW5gcsNv39H+shrz45x+6Tp37GDlDchQRnqyMtOT1SstSanJLhmSZPjakBuGocqaJh2ubFBFZYMqjjWoqq5JyUm+02lTU1xKcjn1yUbf6ZCSLxC5bNYZWre1XG+u3meup+b276V+vdOUluJSWmqSjlQ1aPsXlUpyOXTLFRM1rXW90+M1tPgfn+ntNV/I4ZAumDhUFccatPtQleosRVmpKS4Nz+ujEfl9NXhghpJcTjkcDjlbf2DKj9VrX0m1viitUenRurAzaElKSXKqf1a60lJd2ltSHfTYlCSn3G3WhF1Oh4YP7qOCU7NVMCxbGenJev2TvVqzpTTi66SluPTz705st7zS2NSiRf/4LOqOlSSXQ1mZqTpS1aiUJKd+df2X2mVYVn5+SA8+u1buFq/mXXeuCgsSd5z4n179XEs+2K2B/dJV39CsukZf+jgjPVmFZ+Yot38v5fXPUG7/DOXnZIY9FGz7F8d026IP5DWkL08+RcPy+ii3f4bS05I090+r5G726JYrCs2ZYSifbi7VI//cYP4iczp8hw1m90nTjZePD3kukGEY+t/3dunp1zbJMKTCghxdcv4I7S2p1u6DVdp9sEplR+vVJyNF2X3S1D8rXf2z0pSWmqTmFq+aWzxqbvGqxeNV38xUDezXSzn90pWT3Ut1Dc16f90BfbThkLlMZ5WS7NKwvN7KSEtWSrJLqckupSS7lJzsVHKSU8kup5KSnNpfVqNPNvqWMotGD9LNcwrNU1c9XkObdx/R++sP6P11B9To9k0CMtKSNG1CvpJcDtXUNaumwa2aOreSk5w6JbePTs3trVNz+2hQdi9t339MxVvKtHZreVCQ4/95Om1IltJTk1Tb0Kza+mbVNTSr0d2ijPRk9clIUZ+MVPXJSFF9Y7N2tb5n1n9vSpJTwwdn6bQhWcoflKlkl1NOp+/n0uFw6Gh1ow5W1Opgea0OlNeY30N+yUlOeTxe8+DIU3J76xvTTjO/749UNehIVaNvOaJPmvr39f0/6t0rRa99vMesUeuVlqTzzh6sjzceUn3ra4walq1+fVLN91eSCs/MUcnhuqDgum9mqnKy09Wvd5r69k5Vv95pyspMUWavFPXu5Rsvk1xO7Sut0a4Dla3vQ6UamjxKcjmVnpqk9LQkNTQ2q6a+WWkpLv30OxOCMsCfbirVIy9uCCrUTEtx6awRA3T26QPUt3dq6xibpLQUl4YMzGyXXfT7+1vb9Nwb0XfN9clIUXWdWznZvfTELy4MGVx8vOGQ5j+zRpIv6J88JldFowdp9PD+QUHX8VByuE63P/yhKmubNHRQb5UcrlOLx6vUFJeuvKhAX596WtgguKnZo0V/X68PNxz0TUD7pKpfnzRl907T9AlDdE4ClritOi0wefPNN3XjjTdqw4YNSksLDKg//elP1djYqMcffzzo8f/93/+tDRs26J///GfQ9XPPPVfXXnutrrnmmrA3H0pJSYny8vI6JTBpbGrRmi1l+njjIRVvKVOTO/E7G/JzMvX9r43WOWNyzW/4I1UNeuX9XXp95d6Qr5mS7NKd328/C/B6DT368ka9sXJv0PUkl0O5/TNUUdkQ878hMz1ZKcmtwYvTN0g2NLaYAZXVGUP76ktnD9a5Y/OUm91Le0uqtXnPUW3Z6+vnEanqu2j0IP3n9BEaPby/KirrVXqkXmVH6lRd59aXzh4cdoeMYRgq3lKmksN1amr2yN3slbvZl8bdX1ajfaU1amhdR3Y5Hbrrh5NVNDr0NuC9JdXaW1Kt8ycMSejM5lh1o679n7fNrNjgARn6xvQRmjkp9hn70//aZKa32xo7YoB+/X+/FPXeaxua9eelm/Tmal8W5IKJ+frRN8cqM8rx6Ss/P6QHn1vXLruXKH0zUzV1/GClJLm080ClduyvNP/f2eF0OnTVV0bp0hmnh5251zY06501X+hfH++Ju9AvPdWlwQMztb+stkPvhdPpUF7/DB2tblBDU2xfx+mQzhjaT2efMUDjzhioUcOydaymSUs+3KW3Vu+L+eu5nA599bzh+vaFI5WVmaqaerdeemeHln64O2iCcd7Zg/XtL4/U8MFZMgxDW/Ye1TvF+/XRZwfbBUsdMXhAhn7xw8k6NbdPu8/VNTTrXx/tVrPHq/FnDNSZp2abTQ1j4fEa+tUTq7RuW7kcDmlA33TlZmdoUHYv1Ta4tftQtcqPBpYEL79wpK76yqiwX8+/DDxkYGbM95Jouw5U6s4/fGz+/BQW5OiG/zNOg2wuITW3eON6T2PVaYHJq6++qttvv11btmyR09Ik5vbbb1d5ebmefvrpoMffdddd2rt3r5577rmg6zNmzNDll1+uG264IezNh9KZgYlVo7tF67eVa922ClXVNqm+0TcrqmtsUZPbI4fDVwjlcEgO+aLsgf16aWDfdA3sl66szFS1tHjV6PaoqdmjRneLBg/I1PkThoSNXqvr3Np1oFKN7hY1NPme4272qPDMHJ0S4gdW8v2ifvWDXao41mDOwIYO6u2bUXkNHaqo1a6DVdp1oFIVlQ3m8ozRmu3J7pOmU3P76NQ832wx3GzD3ezR0epGHalqVHVdk0bk91VOv/Df9P7087a9x7R1ny9YOVzZoHPH5ukb00d02g+z/3W/KK1Rdp80c/nmeHtv7X6t2VymGRPzNbFgUMwpbz+v19DHGw5p18FKsyal9EidklxOzf/J1Ji2OG/bd1TNLV6dNWKA7efs2H9Mi/+5QXUNzTptSJZGDMnS8CFZGjwgQ7UNzebs/GhVo5rcHiUnu5SS5MtuOJ0OVdY0qexovSqONaj8WL28hqEpZ+Xp/MJ8jTt9QNDPgtfrq534oqxGTe4WNbUGne7WALTF4zUzMYZhaEbhUI0a3j7NHu59XL+9XOu2lis1xaU+GSnKTE/xZTWaWvRFqS9ruK+0WqVH6pWfk6lJowZpUsEgjT6tf7ufpz0Hq+TxGsrslayMtGRl9kpWWopLdQ3Nqq5zq7rOrapat5KTnRoxxPdzeWpuH6W01kmUHKnT7gNVvv+vR+vN3VCe1v/2yUxR/sBM5ef01pCcTOUNyDBrhNqqa2jWm6v36b21B+RyOdQ/y5LFSknSsRrfz+3hygYdrW7U8MFZuvKiAg0O8TN4pKpBL7+7U/WNLfrm+SN0al7ocaep2aN9JdU6Vt2oozVNqmz9b02dWzX17tZMkltNzR7l5/TWiCFZGpGfpRFD+io7K00NrfVlDU0tam7x6oyhoZd9E63F49Xhygb1z0pTclL797OuoVl7S6p1tLpR54zJVUqY97w72rT7iF58Z4dmFOZreoInW4nSaYHJ8uXLddNNN4XMmLjdbj366KNBj7/vvvu0cePGkBmT66+/Xj/4wQ/svrSkk6P4FegI/49rdxx4ojEMo9vft8drJKQQGkCwWH5/x5S/ycvzrTmVl5cHXS8vLw9ZyJqbm9vusW63W5WVlcrJSdy6PtBTOFrrEE5EJ8J9E5QAXS+mwKSgoECZmZlavXq1ea26ulqbN29WUVFRu8cXFRWptLRU+/btM699+umnkqSJEye2ezwAAOjZYlrYS0lJ0ZVXXqkHH3xQ2dnZGjJkiB544AHl5uZq9uzZ8ng8Onr0qHr37q20tDSNGzdOhYWFuvnmmzV37lzV19frnnvu0Te/+c2YtwoDAICTX8yluDfddJMuu+wy3X333ZozZ45cLpeefPJJJScnq6SkRFOnTtWyZcsk+VK3ixcvVn5+vr7//e/rZz/7maZPn665c+cm+t8BAABOAjF3fu1KFL8CAHDi6bTiVwAAgM5EYAIAALoNAhMAANBtEJgAAIBug8AEAAB0GwQmAACg2yAwAQAA3QaBCQAA6DYITAAAQLcR01k5Xa28vFwej8fsIAcAALq/kpISuVwuW489oTImqampSkrqnFiqpKREJSUlnfK10R7v9/HF+3188X4fX7zfx1c873dSUpJSU1NtPfaEOiunM3EOz/HF+3188X4fX7zfxxfv9/HV2e/3CZUxAQAAJzcCEwAA0G0QmAAAgG6DwAQAAHQbBCYAAKDbIDABAADdBtuFAQBAt0HGBAAAdBsEJgAAoNsgMAEAAN0GgQkAAOg2CEwAAEC30eMDE6/Xq0WLFmnatGkaP368rrvuOu3fv7+rb+ukUVlZqXvuuUfTp09XYWGh5syZo+LiYvPzK1eu1KWXXqpx48bpoosu0muvvdaFd3ty2bNnjyZMmKCXX37ZvLZlyxZdeeWVGj9+vGbOnKlnnnmmC+/w5PDKK6/oq1/9qsaOHauvfe1rev31183PHThwQNdff70KCws1depULVy4UB6Ppwvv9sTW0tKi3//+97rgggs0YcIEffe739Vnn31mfp7v78R5/PHHddVVVwVdi/b+Juz3qdHDPfzww8Y555xjvPvuu8aWLVuMq6++2pg9e7bR1NTU1bd2UvjhD39oXHzxxcaaNWuM3bt3G/PmzTPOPvtsY9euXcbOnTuNsWPHGgsWLDB27txpPPHEE8bo0aONTz75pKtv+4TndruNSy+91Bg5cqTx0ksvGYZhGEePHjXOOecc48477zR27txpvPjii8bYsWONF198sYvv9sT1yiuvGKNHjzaeffZZY9++fcYf/vAHo6CgwFi3bp3hdruN2bNnGz/60Y+Mbdu2GW+99ZYxefJk4/e//31X3/YJa9GiRcZ5551nfPjhh8bevXuNu+66y5g4caJRVlbG93cCPfvss0ZBQYFx5ZVXmtfsvL+J+n3aowOTpqYmY8KECcZzzz1nXquqqjLOPvtsY+nSpV14ZyeHvXv3GiNHjjSKi4vNa16v17jwwguNhQsXGr/85S+Nyy67LOg5t9xyi3H11Vcf71s96fzud78zvve97wUFJo899pgxdepUo7m5Oehxs2fP7qrbPKF5vV7jggsuMObPnx90/eqrrzYee+wxY+nSpcZZZ51lVFZWmp/7+9//bhQWFjLxidM3vvEN4/777zc/rqmpMUaOHGksX76c7+8EKC0tNa6//npj/PjxxkUXXRQUmER7fxP5+7RHL+Vs3bpVdXV1Ovfcc81rffr00ejRo7VmzZouvLOTQ79+/fTHP/5RY8eONa85HA45HA5VV1eruLg46L2XpClTpmjt2rUy6PsXtzVr1uiFF17Q/Pnzg64XFxdr8uTJSkpKMq9NmTJFe/fu1eHDh4/3bZ7w9uzZo4MHD+rrX/960PUnn3xS119/vYqLizVmzBhlZWWZn5syZYpqa2u1ZcuW4327J4X+/fvr3Xff1YEDB+TxePTCCy8oJSVFBQUFfH8nwKZNm5ScnKwlS5Zo3LhxQZ+L9v4m8vdpjw5MSktLJUl5eXlB13NycszPIX59+vTR+eefr5SUFPPa8uXLtW/fPk2bNk2lpaXKzc0Nek5OTo4aGhp07Nix4327J4Xq6mrdfvvtuvvuu9t9X4d7vyWppKTkuN3jyWLPnj2SpPr6el1zzTU699xz9a1vfUvvvPOOJN7vznDXXXcpOTlZs2bN0tixY/XQQw9p0aJFOuWUU3i/E2DmzJl6+OGHNXTo0Hafi/b+JvL3aY8OTBoaGiQp6BenJKWmpqqpqakrbumktm7dOt15552aPXu2ZsyYocbGxnbvvf9jt9vdFbd4wps7d64mTJjQbhYvKeT7nZqaKkl8v8ehtrZWknTHHXfo4osv1lNPPaXzzjtPN9xwg1auXMn73Ql27typ3r1765FHHtELL7ygSy+9VLfeequ2bNnC+93Jor2/ifx9mhT9ISevtLQ0Sb5fgv6/S743OT09vatu66T09ttv69Zbb1VhYaEefPBBSb5v2LYBiP9j3v/YvfLKKyouLtbSpUtDfj4tLa3d++0fMHr16tXp93eySU5OliRdc801uuSSSyRJo0aN0ubNm/XnP/+Z9zvBSkpK9POf/1xPP/20Jk2aJEkaO3asdu7cqYcffpj3u5NFe38T+fu0R2dM/Cmn8vLyoOvl5eUaNGhQV9zSSenZZ5/VjTfeqAsuuECPPfaYGWXn5eWFfO979eql3r17d8WtntBeeuklHTlyRDNmzNCECRM0YcIESdK9996ra6+9Vrm5uSHfb0l8v8fB/56NHDky6Prpp5+uAwcO8H4n2IYNG9Tc3BxUsyZJ48aN0759+3i/O1m09zeRv097dGBSUFCgzMxMrV692rxWXV2tzZs3q6ioqAvv7OTx/PPP67777tN3v/tdLViwICjNN2nSJH366adBj1+1apUKCwvldPbob824PPjgg1q2bJleeeUV848k3XTTTfr1r3+toqIirV27NqiPxqpVqzR8+HD179+/i+76xDVmzBhlZGRow4YNQde3b9+uU045RUVFRdq8ebO55CP53u+MjAwVFBQc79s94fnrG7Zt2xZ0ffv27Ro2bBjf350s2vub0N+nHdtcdOJbsGCBMXnyZOPtt98O2nftdru7+tZOeLt37zbGjBlj/OQnPzHKy8uD/lRXVxvbt283xowZYzzwwAPGzp07jSeffJI+Jglm3S58+PBho6ioyLjjjjuMHTt2GC+99JIxduxY4+WXX+7iuzxxPfLII8aECROMpUuXBvUxWbVqldHY2GhceOGFxjXXXGNs2bLF7GPy8MMPd/Vtn5A8Ho8xZ84c46KLLjJWrlxp7Nmzx3jooYeMUaNGGZ999hnf3wl2xx13BG0XtvP+Jur3aY8PTFpaWozf/va3xpQpU4zx48cb1113nbF///6uvq2TwqOPPmqMHDky5J877rjDMAzDeP/9942LL77YOOuss4yLLrrIeO2117r4rk8u1sDEMAxjw4YNxuWXX26cddZZxgUXXGD89a9/7cK7Ozk89dRTxsyZM40xY8YY3/jGN4y33nrL/NzevXuNH/7wh8bYsWONqVOnGgsXLjQ8Hk8X3u2JrbKy0pg7d64xY8YMY8KECca3v/1tY/Xq1ebn+f5OnLaBiWFEf38T9fvUYRg0jAAAAN0DC/kAAKDbIDABAADdBoEJAADoNghMAABAt0FgAgAAug0CEwAA0G0QmAAAgG6DwAQAAHQbBCYAAKDbIDABAADdBoEJAADoNv4/47ykWrpDsBYAAAAASUVORK5CYII=\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "\n", - "\n", - "diff = np.diff(np.sort(psi% (2*np.pi)))\n", - "\n", - "plt.plot(diff)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "38aee163", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 30, - "id": "8687499b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(np.sort(psi) )" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4bebadcd", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "435b3855", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "venv_xgi", - "language": "python", - "name": "venv_xgi" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13" - }, - "toc": { - "base_numbering": 1, - "nav_menu": {}, - "number_sections": true, - "sideBar": true, - "skip_h1_title": false, - "title_cell": "Table of Contents", - "title_sidebar": "Contents", - "toc_cell": false, - "toc_position": {}, - "toc_section_display": true, - "toc_window_display": false - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/figure_1_linear_stability-harmonics.ipynb b/notebooks/figure_1_linear_stability-harmonics.ipynb deleted file mode 100644 index 6665a42..0000000 --- a/notebooks/figure_1_linear_stability-harmonics.ipynb +++ /dev/null @@ -1,642 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "c05e6c8b", - "metadata": {}, - "source": [ - "# Figure 1: linear stability" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "add533e0", - "metadata": {}, - "outputs": [], - "source": [ - "import sys\n", - "from math import cos, exp, pi, sin\n", - "from pathlib import Path\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import seaborn as sb\n", - "from mpl_toolkits.axes_grid1.inset_locator import inset_axes, mark_inset\n", - "from numba import jit\n", - "\n", - "sys.path.append(\"../code/\")\n", - "\n", - "import xgi\n", - "from hypersync_draw import *\n", - "from hypersync_generate import *\n", - "from hypersync_identify import *\n", - "from hypersync_integrate import *\n", - "\n", - "sb.set_theme(style=\"ticks\", context=\"paper\")\n", - "\n", - "results_dir = \"../results/\"\n", - "data_dir = \"../data/\"\n", - "\n", - "Path(results_dir).mkdir(parents=True, exist_ok=True)\n", - "Path(data_dir).mkdir(parents=True, exist_ok=True)" - ] - }, - { - "cell_type": "markdown", - "id": "7e56dd9a", - "metadata": {}, - "source": [ - "## Spectrum" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "id": "1e15cac6", - "metadata": {}, - "outputs": [], - "source": [ - "@jit\n", - "def lambda2(N, K1, K2, q, r):\n", - " \"\"\"\n", - " Computes the lambda_max from Eq 5\n", - "\n", - " Parameters\n", - " ----------\n", - " N : int\n", - " Number of nodes\n", - " K1 : float\n", - " Pairwise coupling strength\n", - " K2 : float\n", - " Triadic coupling strength\n", - " q : int\n", - " Winding number (number of twists of twisted state)\n", - " r : int\n", - " Coupling range (for ring structure)\n", - "\n", - " Returns\n", - " -------\n", - " lambda_2 : float\n", - " Maximum non-zeros Lyapunov exponent\n", - " \"\"\"\n", - " a2 = K1 * cos(2 * np.pi * q / N) / (2 * r)\n", - " a3 = K1 * cos(4 * np.pi * q / N) / (2 * r)\n", - " a1 = -2 * (a2 + a3)\n", - " \n", - " # sym\n", - " #b2 = K2 * (1 + cos(2 * np.pi * q / N) + cos(6 * np.pi * q / N)) / (r * (2 * r - 1))\n", - " #b3 = K2 * (1 + cos(2 * np.pi * q / N) + cos(6 * np.pi * q / N)) / (r * (2 * r - 1))\n", - " \n", - " # asym\n", - " #b2 = K2 * (2 * cos(8 * np.pi * q / N) + + 2 - cos(10 * np.pi * q / N)) / (r * (2 * r - 1))\n", - " #b3 = K2 * (cos(12 * np.pi * q / N) + 2 * cos(10 * np.pi * q / N) - \n", - " # cos(8 * np.pi * q / N) + 2 * cos(6 * np.pi * q / N) - 1) / (r * (2 * r - 1))\n", - " \n", - " # sym SC\n", - " b2 = 2 * K2 * (cos(6 * np.pi * q / N)) / (r * (2 * r - 1))\n", - " b3 = 2 * K2 * (1 + cos(6 * np.pi * q / N)) / (r * (2 * r - 1))\n", - " \n", - " b1 = -2 * (b2 + b3)\n", - "\n", - " A1 = a1 + b1\n", - " A2 = a2 + b2\n", - " A3 = a3 + b3\n", - "\n", - " Lambda = np.zeros(N, dtype=np.complex_)\n", - " for i in range(N):\n", - " Lambda[i] = (\n", - " A1\n", - " + A2 * np.exp(2j * np.pi * i / N)\n", - " + A3 * np.exp(2j * np.pi * i * 2 / N)\n", - " + A2 * np.exp(2j * np.pi * i * (N - 1) / N)\n", - " + A3 * np.exp(2j * np.pi * i * (N - 2) / N)\n", - " )\n", - "\n", - " Lambda = np.real(Lambda)\n", - " lambda_2 = np.sort(Lambda[1:])[-1]\n", - "\n", - " return lambda_2" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "id": "9c6ac762", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/maxime/.pyenv/versions/venv_xgi/lib/python3.9/site-packages/labellines/core.py:148: UserWarning: Tried to label line Line2D(_child5), but could not find a label for it.\n", - " warnings.warn(\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "suf = \"ring_sym_SC\"\n", - "#suf = \"ring_asym\"\n", - "\n", - "m = 5\n", - "N = 83\n", - "r = 2\n", - "r1 = 1\n", - "r2 = range(m)\n", - "Lambda_2 = np.zeros((N, m), dtype=np.complex_)\n", - "\n", - "for q in range(N):\n", - " for j in range(m):\n", - " Lambda_2[q, j] = lambda2(N, r1, r2[j], q, r)\n", - "\n", - "fig, (ax, axins1) = plt.subplots(\n", - " 2, 1, figsize=(3.4, 2.4), height_ratios=[4, 1], sharex=True\n", - ")\n", - "\n", - "ax.set_xlabel(r\"$q$, winding number\")\n", - "ax.set_ylabel(r\"$\\lambda_\\mathrm{max}$\")\n", - "\n", - "markers = [\"o\", \"s\", \"p\", \"h\", \"d\"]\n", - "labels = [rf\"$\\sigma_\\Delta={i}$\" for i in range(5)]\n", - "colors = [\"silver\"] + sb.color_palette(\"Reds\", n_colors=len(labels) - 1)\n", - "\n", - "for i in range(m):\n", - " ax.plot(\n", - " Lambda_2.real[:, i],\n", - " linestyle=\"-\",\n", - " # linewidth=3,\n", - " marker=markers[i],\n", - " ms=2,\n", - " color=colors[i],\n", - " # alpha=0.6,\n", - " label=labels[i],\n", - " )\n", - "\n", - "ax.axhline(0, linestyle=\"--\", alpha=0.6, c=\"grey\", zorder=-2)\n", - "\n", - "\n", - "from labellines import labelLine, labelLines\n", - "\n", - "legs = labelLines(\n", - " ax.get_lines(),\n", - " zorder=2.5,\n", - " xvals=[40] * 5,\n", - " yoffsets=[0.3] + [0.05] * 5,\n", - " fontsize=\"x-small\",\n", - " align=False,\n", - ")\n", - "x_offset = 15\n", - "for leg in legs:\n", - " x, y = leg.get_position()\n", - " leg.set_position((x + x_offset, y))\n", - "\n", - "\n", - "for i in range(m):\n", - " axins1.plot(\n", - " Lambda_2.real[:, i],\n", - " linestyle=\"-\",\n", - " # linewidth=3,\n", - " marker=markers[i],\n", - " ms=2,\n", - " color=colors[i],\n", - " # alpha=0.6,\n", - " label=labels[i],\n", - " )\n", - "\n", - "axins1.set_ylim(ymax=0.01, ymin=-0.025)\n", - "axins1.axhline(0, linestyle=\"--\", alpha=0.6, c=\"grey\", zorder=-2)\n", - "axins1.set_ylabel(\"\")\n", - "\n", - "mark_inset(ax, axins1, loc1=2, loc2=4, ec=\"0.5\", ls=\":\")\n", - "\n", - "sb.despine()\n", - "\n", - "#plt.savefig(\"lambda2.pdf\")" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "id": "21fc6ae1", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([ 0, 1, 2, 3, 4, 5, 6, 7, 21, 22, 23, 24, 25, 26, 27, 28, 29,\n", - " 30, 31, 32, 33, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62,\n", - " 76, 77, 78, 79, 80, 81, 82]),)" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.where(Lambda_2.real[:, 4] < 0 )" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "id": "638bf0a1", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 72, 73, 74, 75, 76,\n", - " 77, 78, 79, 80, 81, 82]),)" - ] - }, - "execution_count": 33, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.where(Lambda_2.real[:, 0] < 0 )" - ] - }, - { - "cell_type": "markdown", - "id": "184cafb5", - "metadata": {}, - "source": [ - "## Fraction of stable states" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "id": "f700f191", - "metadata": {}, - "outputs": [], - "source": [ - "m = 50\n", - "N1 = 83\n", - "N2 = 830\n", - "r = 2\n", - "k1 = 1\n", - "k2 = np.linspace(0, 10, num=m)\n", - "\n", - "Lambda_2 = np.zeros((N1, m), dtype=np.complex_)\n", - "for q in range(N1):\n", - " for j in range(m):\n", - " Lambda_2[q, j] = lambda2(N1, k1, k2[j], q, r)\n", - "stable_fraction1 = np.mean(Lambda_2 < 0, axis=0)\n", - "\n", - "Lambda_2 = np.zeros((N2, m), dtype=np.complex_)\n", - "for q in range(N2):\n", - " for j in range(m):\n", - " Lambda_2[q, j] = lambda2(N2, k1, k2[j], q, r)\n", - "stable_fraction2 = np.mean(Lambda_2 < 0, axis=0)" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "id": "9faec1e1", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(figsize=(3.4, 2.4))\n", - "\n", - "ax.set_xlabel(r\"$\\sigma_\\Delta$\")\n", - "ax.set_ylabel(r\"$p_\\mathrm{stable}$\")\n", - "\n", - "\n", - "ax.plot(\n", - " k2,\n", - " stable_fraction1,\n", - " linestyle=\"--\",\n", - " color=\"grey\",\n", - " alpha=0.6,\n", - " label=r\"$n=83$\",\n", - ")\n", - "ax.plot(\n", - " k2,\n", - " stable_fraction2,\n", - " linestyle=\"-\",\n", - " color=\"k\",\n", - " alpha=0.6,\n", - " label=r\"$n=830$\",\n", - ")\n", - "\n", - "# ax.set_xticks([0, 2, 4])\n", - "#ax.set_yticks([0.2, 0.5, 0.8])\n", - "#ax.set_ylim(ymin=0.18)\n", - "\n", - "\n", - "ax.legend(loc=\"lower right\", frameon=False, ncol=1)\n", - "\n", - "sb.despine()\n", - "\n", - "#plt.savefig(\"stable_fraction.pdf\")" - ] - }, - { - "cell_type": "markdown", - "id": "c880bc9e", - "metadata": {}, - "source": [ - "## All together" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "d462eaab", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/maxime/.pyenv/versions/venv_xgi/lib/python3.9/site-packages/labellines/core.py:148: UserWarning: Tried to label line Line2D(_child5), but could not find a label for it.\n", - " warnings.warn(\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "m = 5\n", - "N = 83\n", - "r = 2\n", - "r1 = 1\n", - "r2 = range(m)\n", - "Lambda_2 = np.zeros((N, m), dtype=np.complex_)\n", - "\n", - "for q in range(N):\n", - " for j in range(m):\n", - " Lambda_2[q, j] = lambda2(N, r1, r2[j], q, r)\n", - "\n", - "# figure setup\n", - "fig = plt.figure(figsize=(7, 2.1), layout=\"constrained\")\n", - "subfigs = fig.subfigures(1, 3, wspace=0.05, width_ratios=[1, 3, 2.5])\n", - "\n", - "ax1 = subfigs[0].subplots(1, 1)\n", - "(ax, axins1) = subfigs[1].subplots(2, 1, height_ratios=[2, 1], sharex=False)\n", - "ax2 = subfigs[2].subplots(1, 1)\n", - "\n", - "\n", - "markers = [\"o\", \"s\", \"p\", \"h\", \"d\"]\n", - "labels = [rf\"$\\sigma_\\Delta={i}$\" for i in range(5)]\n", - "colors = [\"darkgrey\"] + sb.color_palette(\"Reds\", n_colors=len(labels) - 1, desat=0.8)\n", - "\n", - "# plot full spectrum\n", - "#####################\n", - "\n", - "for i in range(m):\n", - " ax.plot(\n", - " Lambda_2.real[:, i],\n", - " linestyle=\"-\",\n", - " # linewidth=3,\n", - " marker=\"o\", # \"markers\"[i],\n", - " ms=1.5,\n", - " color=colors[i],\n", - " # alpha=0.6,\n", - " label=labels[i],\n", - " )\n", - "\n", - "ax.axhline(0, linestyle=\"--\", alpha=0.6, c=\"k\", zorder=-2, lw=0.5)\n", - "ax.set_ylabel(r\"$\\lambda_\\mathrm{max}$\")\n", - "\n", - "\n", - "from labellines import labelLine, labelLines\n", - "\n", - "legs = labelLines(\n", - " ax.get_lines(),\n", - " zorder=2.5,\n", - " xvals=[40] * 5,\n", - " yoffsets=[0.29] * 6, # [0.3] + [0.05] * 5,\n", - " fontsize=\"x-small\",\n", - " align=False,\n", - " outline_width=0.5,\n", - " clip_on=False,\n", - ")\n", - "x_offset = 15\n", - "for leg in legs:\n", - " x, y = leg.get_position()\n", - " leg.set_position((x + x_offset, y))\n", - "\n", - "\n", - "# plot zoom in\n", - "##############\n", - "\n", - "for i in range(m):\n", - " axins1.plot(\n", - " Lambda_2.real[:, i],\n", - " linestyle=\"-\",\n", - " # linewidth=3,\n", - " marker=\"o\", # \"markers\"[i],\n", - " ms=1,\n", - " color=colors[i],\n", - " # alpha=0.6,\n", - " label=labels[i],\n", - " )\n", - "\n", - "axins1.set_ylim(ymax=0.01, ymin=-0.04)\n", - "axins1.axhline(0, linestyle=\"--\", alpha=1, c=\"silver\", zorder=-1, lw=1)\n", - "axins1.set_ylabel(\"\")\n", - "axins1.set_xlabel(r\"$q$, winding number\")\n", - "\n", - "mark_inset(ax, axins1, loc1=2, loc2=4, ec=\"lightgrey\", ls=\":\")\n", - "\n", - "# plot Porder\n", - "#############\n", - "\n", - "m = 50\n", - "N1 = 83\n", - "N2 = 830\n", - "r = 2\n", - "r1 = 1\n", - "r2 = np.linspace(0, 4, num=m)\n", - "\n", - "Lambda_2 = np.zeros((N1, m), dtype=np.complex_)\n", - "for q in range(N1):\n", - " for j in range(m):\n", - " Lambda_2[q, j] = lambda2(N1, r1, r2[j], q, r)\n", - "stable_fraction1 = np.mean(Lambda_2 < 0, axis=0)\n", - "\n", - "Lambda_2 = np.zeros((N2, m), dtype=np.complex_)\n", - "for q in range(N2):\n", - " for j in range(m):\n", - " Lambda_2[q, j] = lambda2(N2, r1, r2[j], q, r)\n", - "stable_fraction2 = np.mean(Lambda_2 < 0, axis=0)\n", - "\n", - "\n", - "ax2.set_xlabel(r\"$\\sigma_\\Delta$, triadic coupling strength\")\n", - "ax2.set_ylabel(r\"$P_\\mathrm{stable}$\")\n", - "\n", - "\n", - "ax2.plot(\n", - " r2,\n", - " stable_fraction1,\n", - " linestyle=\"-.\",\n", - " color=\"g\",\n", - " # alpha=0.6,\n", - " label=r\"$n=83$\",\n", - " zorder=2\n", - ")\n", - "ax2.plot(\n", - " r2,\n", - " stable_fraction2,\n", - " linestyle=\"-\",\n", - " color=\"k\",\n", - " alpha=0.8,\n", - " label=r\"$n=830$\",\n", - ")\n", - "\n", - "ax2.set_yticks([0.2, 0.5, 0.8])\n", - "#ax2.set_ylim(ymin=0.18)\n", - "axins1.set_yticks([0, -0.02])\n", - "\n", - "ax.set_xticklabels([])\n", - "\n", - "ax2.legend(loc=\"upper right\", frameon=False, ncol=1)\n", - "\n", - "# plot twisted states\n", - "#####################\n", - "\n", - "N = 20\n", - "\n", - "for q in range(3):\n", - " psi = generate_q_twisted_state(N, q)\n", - " H = xgi.trivial_hypergraph(N)\n", - "\n", - " pos = xgi.circular_layout(H, center=[0, -7.5 * q], radius=2.8)\n", - " psi = psi % (2 * np.pi)\n", - " _, im = xgi.draw_nodes(\n", - " H,\n", - " pos=pos,\n", - " ax=ax1,\n", - " node_fc=psi,\n", - " vmin=0,\n", - " vmax=2 * np.pi,\n", - " node_fc_cmap=\"twilight\",\n", - " node_size=4,\n", - " node_lw=0.3,\n", - " )\n", - "\n", - " ax1.text(0, -7.5 * q, f\"$q={q}$\", fontsize=\"x-small\", va=\"center\", ha=\"center\")\n", - "\n", - "\n", - "ax1.set_aspect(\"equal\")\n", - "\n", - "cbar = plt.colorbar(\n", - " im,\n", - " aspect=5,\n", - " shrink=0.3,\n", - " label=r\"$\\theta_i$\",\n", - " orientation=\"horizontal\",\n", - " location=\"bottom\",\n", - ")\n", - "cbar.set_ticks(\n", - " ticks=[0, np.pi, 2 * np.pi], labels=[0, r\"$\\pi$\", r\"$2\\pi$\"], fontsize=\"x-small\"\n", - ")\n", - "cbar.outline.set_visible(False)\n", - "\n", - "ax.text(0.03, 0.98, \"(b)\", transform=ax.transAxes, va=\"top\", ha=\"left\")\n", - "axins1.text(0.03, 1.1, \"(c)\", transform=axins1.transAxes, va=\"top\", ha=\"left\")\n", - "ax2.text(0.04, 0.98, \"(d)\", transform=ax2.transAxes, va=\"top\", ha=\"left\")\n", - "ax1.text(-0.5, 0.98, \"(a)\", transform=ax1.transAxes, va=\"top\", ha=\"left\")\n", - "\n", - "fig.suptitle(suf)\n", - "\n", - "sb.despine()\n", - "\n", - "plt.savefig(f\"../results/figure_1_v5_{suf}.pdf\", dpi=250, bbox_inches=\"tight\", pad_inches=0)" - ] - }, - { - "cell_type": "markdown", - "id": "44251267", - "metadata": {}, - "source": [ - "## Haromnics" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "289d8f4c", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c6a48c36", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "venv_xgi", - "language": "python", - "name": "venv_xgi" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13" - }, - "toc": { - "base_numbering": 1, - "nav_menu": {}, - "number_sections": true, - "sideBar": true, - "skip_h1_title": false, - "title_cell": "Table of Contents", - "title_sidebar": "Contents", - "toc_cell": false, - "toc_position": {}, - "toc_section_display": true, - "toc_window_display": true - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/hid.simulate-ring-Copy1.ipynb b/notebooks/hid.simulate-ring-Copy1.ipynb deleted file mode 100644 index b08b903..0000000 --- a/notebooks/hid.simulate-ring-Copy1.ipynb +++ /dev/null @@ -1,1151 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "417f4911", - "metadata": {}, - "source": [ - "# Simulate Kuramoto on a hypergraph ring" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "8da1197d", - "metadata": {}, - "outputs": [], - "source": [ - "import sys\n", - "from pathlib import Path\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import pandas as pd\n", - "import seaborn as sb\n", - "from tqdm import tqdm\n", - "\n", - "sys.path.append(\"../code/\")\n", - "\n", - "import xgi\n", - "from hypersync_draw import *\n", - "from hypersync_generate import *\n", - "from hypersync_identify import *\n", - "from hypersync_integrate import *\n", - "\n", - "sb.set_theme(style=\"ticks\", context=\"notebook\")\n", - "\n", - "results_dir = \"../results/\"\n", - "data_dir = \"../data/\"\n", - "\n", - "Path(results_dir).mkdir(parents=True, exist_ok=True)\n", - "Path(data_dir).mkdir(parents=True, exist_ok=True)" - ] - }, - { - "cell_type": "markdown", - "id": "9775a80e", - "metadata": {}, - "source": [ - "## Generate structure" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "7ece7682", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Unnamed Hypergraph with 83 nodes and 0 hyperedges\n" - ] - } - ], - "source": [ - "N = 83\n", - "H = xgi.trivial_hypergraph(N)\n", - "\n", - "r1 = 2\n", - "r2 = 2\n", - "\n", - "print(H)" - ] - }, - { - "cell_type": "markdown", - "id": "388376d1", - "metadata": {}, - "source": [ - "## Dynamics" - ] - }, - { - "cell_type": "code", - "execution_count": 158, - "id": "91f4e739", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Set parameters\n", - "\n", - "# dynamical\n", - "k1 = 1 # pairwise coupling strength\n", - "k2 = 4.5 # triplet coupling strength\n", - "omega = 0 # 1 * np.ones(N) # np.random.normal(size=N) #1 * np.ones(N)\n", - "\n", - "ic = \"random\" # initial condition type, see below\n", - "noise = 0 # noise strength\n", - "\n", - "psi_init = generate_state(N=83, kind=ic,noise=noise)\n", - "\n", - "# integration\n", - "t_end = 400\n", - "dt = 0.01\n", - "times = np.arange(0, t_end + dt / 2, dt)\n", - "integrator = \"RK45\"\n", - "\n", - "tag_params = f\"k1_{k1}_k2_{k2}_ic_{ic}\"\n", - "\n", - "fig, ax = plt.subplots(figsize=(1, 1))\n", - "plot_phases(psi_init, it=None, ax=ax)\n", - "plt.show()\n" - ] - }, - { - "cell_type": "code", - "execution_count": 159, - "id": "88c5c993", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|███████████████████████████████████████████| 20/20 [00:06<00:00, 3.09it/s]\n" - ] - } - ], - "source": [ - "n_reps = 20\n", - "\n", - "# simulate\n", - "\n", - "thetas_arr = np.zeros((n_reps, N, len(times)))\n", - "\n", - "for i in tqdm(range(n_reps)):\n", - " psi_init = generate_state(N, kind=\"random\", noise=noise)\n", - "\n", - " thetas, times = simulate_kuramoto(\n", - " H,\n", - " k1=k1,\n", - " k2=k2,\n", - " omega=omega,\n", - " theta_0=psi_init,\n", - " t_end=t_end,\n", - " dt=dt,\n", - " rhs=rhs_ring_nb,\n", - " integrator=integrator,\n", - " args=(r1, r2),\n", - " t_eval=False,\n", - " )\n", - "\n", - " thetas_arr[i] = thetas" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "df36a858", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(-2, False)\n", - "other\n" - ] - }, - { - "data": { - "image/png": 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\n", 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot the last repetition\n", - "i = 4\n", - "fig, axs = plot_sync(thetas_arr[i], times)\n", - "\n", - "axs[0, 1].set_title(f\"$t={times[0]}$s\", fontsize=\"x-small\")\n", - "axs[1, 1].set_title(f\"$t={times[-1]}$s\", fontsize=\"x-small\")\n", - "\n", - "axs[0, 0].set_xlabel(\"\")\n", - "axs[1, 0].legend(loc=\"best\", fontsize=\"x-small\")\n", - "\n", - "plt.subplots_adjust(hspace=0.5, top=0.8)\n", - "\n", - "fig.suptitle(tag_params, fontsize=\"small\")\n", - "\n", - "# only to viz twisted states\n", - "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(4, 1), width_ratios=[2, 1])\n", - "\n", - "ax1.plot(thetas_arr[i, :, -1] % (2 * np.pi), \"o\", mfc=\"w\", alpha=0.5)\n", - "ax1.plot(thetas_arr[i, :, -10000] % (2 * np.pi), \"o\", mfc=\"w\", alpha=0.5)\n", - "ax1.set_ylabel(\"phases\")\n", - "ax1.set_xlabel(\"node idx\")\n", - "\n", - "ax1.set_title(identify_state(thetas_arr[i], atol=0.01))\n", - "\n", - "pos = xgi.circular_layout(H)\n", - "ax2, ims = xgi.draw_nodes(\n", - " H,\n", - " pos=pos,\n", - " node_fc=thetas_arr[i, :, -1] % (2 * np.pi),\n", - " node_fc_cmap=\"twilight\",\n", - " node_size=5,\n", - " node_lw=0.1,\n", - " vmin=0,\n", - " vmax=6.28,\n", - ")\n", - "plt.colorbar(ims, label=\"phase value\")\n", - "\n", - "#ax2.plot(thetas_arr[i, :, -10000] % (2 * np.pi), \"o\", mfc=\"w\", alpha=0.5)\n", - "\n", - "\n", - "print(identify_winding_number(thetas_arr[i], t=-1))\n", - "# print(winding_number(thetas_arr[i].T, N, -1, atol=0.5))\n", - "print(identify_state(thetas_arr[i], atol=0.001))" - ] - }, - { - "cell_type": "code", - "execution_count": 167, - "id": "f27f545c", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/wm/5gv37br900l73y63tjf8sr1r0000gn/T/ipykernel_43997/2012031778.py:20: UserWarning: This figure was using a layout engine that is incompatible with subplots_adjust and/or tight_layout; not calling subplots_adjust.\n", - " plt.subplots_adjust(hspace=0.5, top=0.8)\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(-2, False)\n", - "other\n" - ] - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot the last repetition\n", - "i = 4\n", - "fig, axs = plt.subplots(2, 3, width_ratios=[3, 1, 3], figsize=(7, 3), layout=\"constrained\")\n", - "\n", - "\n", - "plot_series(thetas_arr[i], times, ax=axs[0,0])\n", - "plot_order_param(thetas_arr[i], times, order=1, ax=axs[1,0])\n", - "plot_order_param(thetas_arr[i], times, order=2, ax=axs[1,0], ls=\"--\", color=\"b\")\n", - "\n", - "\n", - "plot_phases(thetas_arr[i], it=0, ax=axs[0,1])\n", - "plot_phases(thetas_arr[i], it=-1, ax=axs[1,1])\n", - "\n", - "axs[0, 1].set_title(f\"$t={times[0]}$s\", fontsize=\"x-small\")\n", - "axs[1, 1].set_title(f\"$t={times[-1]}$s\", fontsize=\"x-small\")\n", - "\n", - "axs[0, 0].set_xlabel(\"\")\n", - "axs[1, 0].legend(loc=\"best\", fontsize=\"x-small\")\n", - "\n", - "plt.subplots_adjust(hspace=0.5, top=0.8)\n", - "\n", - "fig.suptitle(tag_params, fontsize=\"small\")\n", - "\n", - "# only to viz twisted states\n", - "#fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(4, 1), width_ratios=[2, 1])\n", - "\n", - "ax1, ax2 = axs[0, 2], axs[1, 2]\n", - "\n", - "ax1.plot(thetas_arr[i, :, -1] % (2 * np.pi), \"o\", alpha=0.5, ms=3)\n", - "ax1.plot(thetas_arr[i, :, -10000] % (2 * np.pi), \"x\", alpha=0.5, ms=3)\n", - "ax1.set_ylabel(\"phases\")\n", - "ax1.set_xlabel(\"node idx\")\n", - "ax1.set_ylim([0, 2*np.pi])\n", - "\n", - "ax1.set_title(identify_state(thetas_arr[i], atol=0.01))\n", - "\n", - "pos = xgi.circular_layout(H)\n", - "ax2, ims = xgi.draw_nodes(\n", - " H,\n", - " pos=pos,\n", - " node_fc=thetas_arr[i, :, -1] % (2 * np.pi),\n", - " node_fc_cmap=\"twilight\",\n", - " node_size=5,\n", - " node_lw=0.1,\n", - " vmin=0,\n", - " vmax=6.28,\n", - ")\n", - "plt.colorbar(ims, label=\"phase value\")\n", - "ax2.set_aspect(\"equal\")\n", - "\n", - "\n", - "#ax2.plot(thetas_arr[i, :, -10000] % (2 * np.pi), \"o\", mfc=\"w\", alpha=0.5)\n", - "\n", - "\n", - "print(identify_winding_number(thetas_arr[i], t=-1))\n", - "# print(winding_number(thetas_arr[i].T, N, -1, atol=0.5))\n", - "print(identify_state(thetas_arr[i], atol=0.001))\n", - "state = identify_state(thetas_arr[i], atol=0.001)\n", - "\n", - "sb.despine(ax=axs[0,0])\n", - "sb.despine(ax=axs[1,0])\n", - "sb.despine(ax=axs[0, 2])\n", - "\n", - "fig_name = f\"ring_N_{N}_r_{r2}_k1_{k1}_k2_{k2}_ic_{ic}_{state}\"\n", - "\n", - "#plt.savefig(f\"{fig_name}.png\", dpi=250, bbox_inches=\"tight\")\n" - ] - }, - { - "cell_type": "code", - "execution_count": 168, - "id": "97d27f10", - "metadata": {}, - "outputs": [], - "source": [ - "np.savez(\n", - " f\"{fig_name}.npz\",\n", - " thetas=thetas_arr[i],\n", - " times=times,\n", - " state=state,\n", - " ic=ic,\n", - " k1=k1,\n", - " k2=k2,\n", - " dt=dt,\n", - " t_end=t_end\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "id": "c4e2e853", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(10, 83, 40001)" - ] - }, - "execution_count": 43, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "thetas_arr.shape" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1c282ecd", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": 104, - "id": "098fa4f4", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'-1-twisted',\n", - " '-2-twisted',\n", - " '-3-twisted',\n", - " '-4-twisted',\n", - " '0-twisted',\n", - " '1-twisted',\n", - " '2-twisted',\n", - " 'other'}" - ] - }, - "execution_count": 104, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "states = [identify_state(thetas, atol=0.01) for thetas in thetas_arr]\n", - "set(states)" - ] - }, - { - "cell_type": "code", - "execution_count": 105, - "id": "6af16e8c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array(['-1-twisted', '-2-twisted', '-3-twisted', '-4-twisted',\n", - " '0-twisted', '1-twisted', '2-twisted', 'other'], dtype='" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "###### Set parameters\n", - "\n", - "# dynamical\n", - "k1 = 1 # pairwise coupling strength\n", - "k2 = 0 # triplet coupling strength\n", - "omega = 1 * np.ones(N) # np.random.normal(size=N) #1 * np.ones(N)\n", - "\n", - "ic = \"random\" # initial condition type, see below\n", - "noise = 0 # noise strength\n", - "\n", - "psi_init = generate_state(N, kind=ic, noise=noise)\n", - "\n", - "# integration\n", - "t_end = 200\n", - "dt = 0.01\n", - "times = np.arange(0, t_end + dt / 2, dt)\n", - "\n", - "tag_params = f\"k1_{k1}_k2_{k2}_ic_{ic}\"\n", - "\n", - "fig, ax = plt.subplots(figsize=(1, 1))\n", - "plot_phases(psi_init, it=None, ax=ax)\n", - "plt.show()\n", - "\n", - "# only to viz twisted states\n", - "fig, ax = plt.subplots(figsize=(2, 2))\n", - "ax, ims = xgi.draw(\n", - " H, pos=pos, node_fc=psi_init % (2 * np.pi), node_fc_cmap=\"twilight\", node_size=5\n", - ")\n", - "plt.colorbar(ims[0], label=\"phase value\")" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "281fcca2", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 25.16it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 19.15it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 17.40it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 14.19it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 12.03it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 10.57it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:01<00:00, 9.34it/s]\n" - ] - } - ], - "source": [ - "n_reps = 10\n", - "\n", - "k2s = [0, 0.5, 1, 1.5, 2, 2.5, 3]\n", - "\n", - "# simulate\n", - "\n", - "thetas_arr = np.zeros((n_reps, len(k2s), N, len(times)))\n", - "\n", - "for j, k2 in enumerate(k2s):\n", - " for i in tqdm(range(n_reps)):\n", - " psi_init = generate_state(N, kind=\"random\", noise=noise)\n", - "\n", - " thetas, times = simulate_kuramoto(\n", - " H,\n", - " k1=k1,\n", - " k2=k2,\n", - " omega=omega,\n", - " theta_0=psi_init,\n", - " t_end=t_end,\n", - " dt=dt,\n", - " rhs=rhs_ring_nb,\n", - " integrator=integrator,\n", - " args=(r1, r2),\n", - " t_eval=False,\n", - " )\n", - "\n", - " thetas_arr[i, j] = thetas" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "82eace5c", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|█████████████████████████████████████████████| 7/7 [00:03<00:00, 2.05it/s]\n" - ] - } - ], - "source": [ - "results = {}\n", - "\n", - "for j, k2 in enumerate(tqdm(k2s)):\n", - " states = [identify_state(thetas, atol=0.5) for thetas in thetas_arr[:, j]]\n", - " states_unique, counts = np.unique(states, return_counts=True)\n", - " probs = counts / n_reps\n", - "\n", - " results[k2] = {}\n", - " for state, prob in zip(states_unique, probs):\n", - " results[k2][state] = prob" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "e808a398", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{0: {'-1-twisted': 0.1,\n", - " '-2-twisted': 0.2,\n", - " '0-twisted': 0.2,\n", - " '1-twisted': 0.3,\n", - " 'other': 0.1,\n", - " 'sync': 0.1},\n", - " 0.5: {'-1-twisted': 0.3,\n", - " '0-twisted': 0.3,\n", - " '1-twisted': 0.1,\n", - " '2-twisted': 0.3},\n", - " 1: {'-1-twisted': 0.5, '0-twisted': 0.4, '3-twisted': 0.1},\n", - " 1.5: {'-1-twisted': 0.3,\n", - " '-2-twisted': 0.1,\n", - " '-3-twisted': 0.1,\n", - " '0-twisted': 0.2,\n", - " '1-twisted': 0.1,\n", - " '2-twisted': 0.1,\n", - " '3-twisted': 0.1},\n", - " 2: {'-1-twisted': 0.2,\n", - " '-4-twisted': 0.1,\n", - " '0-twisted': 0.1,\n", - " '1-twisted': 0.2,\n", - " 'other': 0.4},\n", - " 2.5: {'-1-twisted': 0.2,\n", - " '-2-twisted': 0.2,\n", - " '-4-twisted': 0.1,\n", - " '3-twisted': 0.1,\n", - " 'other': 0.4},\n", - " 3: {'-2-twisted': 0.1, '-4-twisted': 0.1, 'other': 0.8}}" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "f8800cb0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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k2-1-twisted-2-twisted0-twisted1-twistedothersync2-twisted3-twisted-3-twisted-4-twisted
00.00.10.20.20.30.10.1NaNNaNNaNNaN
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21.00.5NaN0.4NaNNaNNaNNaN0.1NaNNaN
31.50.30.10.20.1NaNNaN0.10.10.1NaN
42.00.2NaN0.10.20.4NaNNaNNaNNaN0.1
52.50.20.2NaNNaN0.4NaNNaN0.1NaN0.1
63.0NaN0.1NaNNaN0.8NaNNaNNaNNaN0.1
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" - ], - "text/plain": [ - " k2 -1-twisted -2-twisted 0-twisted 1-twisted other sync 2-twisted \\\n", - "0 0.0 0.1 0.2 0.2 0.3 0.1 0.1 NaN \n", - "1 0.5 0.3 NaN 0.3 0.1 NaN NaN 0.3 \n", - "2 1.0 0.5 NaN 0.4 NaN NaN NaN NaN \n", - "3 1.5 0.3 0.1 0.2 0.1 NaN NaN 0.1 \n", - "4 2.0 0.2 NaN 0.1 0.2 0.4 NaN NaN \n", - "5 2.5 0.2 0.2 NaN NaN 0.4 NaN NaN \n", - "6 3.0 NaN 0.1 NaN NaN 0.8 NaN NaN \n", - "\n", - " 3-twisted -3-twisted -4-twisted \n", - "0 NaN NaN NaN \n", - "1 NaN NaN NaN \n", - "2 0.1 NaN NaN \n", - "3 0.1 0.1 NaN \n", - "4 NaN NaN 0.1 \n", - "5 0.1 NaN 0.1 \n", - "6 NaN NaN 0.1 " - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df = pd.DataFrame.from_dict(results, orient=\"index\").reset_index(names=\"k2\")\n", - "df" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "0858afc2", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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k2stateproba
00.0-1-twisted0.1
10.5-1-twisted0.3
21.0-1-twisted0.5
31.5-1-twisted0.3
42.0-1-twisted0.2
............
651.0-4-twistedNaN
661.5-4-twistedNaN
672.0-4-twisted0.1
682.5-4-twisted0.1
693.0-4-twisted0.1
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70 rows × 3 columns

\n", - "
" - ], - "text/plain": [ - " k2 state proba\n", - "0 0.0 -1-twisted 0.1\n", - "1 0.5 -1-twisted 0.3\n", - "2 1.0 -1-twisted 0.5\n", - "3 1.5 -1-twisted 0.3\n", - "4 2.0 -1-twisted 0.2\n", - ".. ... ... ...\n", - "65 1.0 -4-twisted NaN\n", - "66 1.5 -4-twisted NaN\n", - "67 2.0 -4-twisted 0.1\n", - "68 2.5 -4-twisted 0.1\n", - "69 3.0 -4-twisted 0.1\n", - "\n", - "[70 rows x 3 columns]" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df_long = df.melt(id_vars=\"k2\", var_name=\"state\", value_name=\"proba\")\n", - "df_long" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "39040506", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(figsize=(3.4, 2.4))\n", - "g = sb.lineplot(\n", - " data=df_long,\n", - " x=\"k2\",\n", - " y=\"proba\",\n", - " hue=\"state\",\n", - " markers=True,\n", - " ax=ax,\n", - " alpha=0.7,\n", - " style=\"state\",\n", - " # hue_order=[\"sync\", \"2-cluster\", \"other\"]\n", - " legend=True,\n", - ")\n", - "\n", - "g.set(yscale=\"log\")\n", - "\n", - "ax.set_xlabel(\"k2, triplet coupling strength\")\n", - "\n", - "title = f\"all-to-all, {ic} ic, {n_reps} reps \\n rhs_pairwise_triplet_all_asym\"\n", - "ax.set_title(title)\n", - "\n", - "sb.move_legend(g, loc=\"center left\", bbox_to_anchor=(1, 0.5))\n", - "\n", - "\n", - "sb.despine()\n", - "ax.set_ylim(ymax=1.1)\n", - "\n", - "fig_name = f\"basin_size_a2a_ic_{ic}_nreps_{n_reps}_rhs_pairwise_triplet_all_asym\"\n", - "\n", - "# plt.savefig(f\"{results_dir}{fig_name}.png\", dpi=300, bbox_inches=\"tight\")" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "6c59dd93", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0-twisted'" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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v5bXXXuv14IYTwlefKeTC3y4sc3FDiMViuhALMVcUBUVRdPdPWVmZnhpZTNSK1A0iIgjQbyRim9vtxuv1EovFqK+vZ+vWrUNyPSSSkcgHm+tYu62F+tYElftibKtuG+ohHRa/185Zn5/MF44fz7hcG0klzo697b2O2OmR4F911VXMnz+f8847j9/+9rc0NDQctr3IETMaEGmNMxFJ0kQETjKZJBQKEY1GdfeOz+fT20ajUT0mv7i4WI/Ogc+ycVqtVn1VrbD2AX2f1WrF7XZjt9v1GP39+/cP3oWQSEYo7cE4H1c2EFPSqBhQUirReHKoh9Utfq+dGROL8Tgt5LpM7N7XRm1TuFd99WjS1mQy8dBDD/HII4/whz/8gVWrVjFlyhQMBgNr1qwhlUrpicMqKir44x//yGmnndargQ03MidtxSQskCXIIm2CiLN3u926hS4WZDmdTkpLS0kmk3q4pgjDFD9FygZAbyMWZ4lJ3ZycHNra2ggGg2zcuBGv16tn7ZRIJAcTjCRIJZN4HCYSKY1xRQ6mlPmGelhHRI7bhsvlYOueViwWhV21Hb3Ko9/jOHyj0chVV13FRRddxMsvv8ybb75JbW0tf/jDH3j44YcBdH/06aefzi9/+cueHmJYkkwmdRHOzIufSqVQVVV37YgVtGazGZPJpAt9PB7HbDaTl5dHYWEh8Xhcz8EjnhKE315k5oxGo1lPFeL4VqsVVVXx+Xy0trbS2trKxo0bWbx4sT45LJFIsmlsDdEeSqCqUOB3s2zxhCEvOXik+L12Zk0qpHp/O7keE+GoQjCqDLzgC9xuNxdffDEXX3wxqqqyd+9e6urq9JS+M2bMGJIlygOFCLXMJNPyFrVoRRlDs9mM3W4nmUwSDodJJBLYbDYKCgr0VbnpdJpgMKhP0iqKkmXli6cK8WQgJn7F3IGouBWJRKitrcXn83Wb30giGYu0B+Os3dJAeziF1WLGbjOS47IN9bB6RJ7fTVo1sKc+RnE63KvJ234xB41GIxMnTmTixIn90d0RoaoqDz74IM899xyhUIhFixZx++23U15ePiDHs9lsB6VDEH59Icoi3FL478Uq23C409/mdrvJzc3F7XaTSCSw2+3YbDY9D49w6wC6q0c8RWRuB/RJXq/Xqx9jx44d5Obmyvh8ieQAglGFhtYQAJoGBgzAyFqtbjIZKfQ7yfcmSaTThKM9n38YsTl3H3roIZ555hl+8Ytf8Oc//xlVVbniiitQlN7HqHZHZqikQLh0xKIrIMv/nkwm9apXJSUl+Hw+3YIXVr74nIjQEU8O4oaiKEqWr1+8RBhoTk4OJpOJUCjEhg0bCIVCA3YNJJKRSEcoTm1zhEAkRTCapDjfSVnhyJrz8jqt5Ljt1DTFaGiPsmlXc4+jdXok+GeeeSYvvfRSj0RVURT++te/cuaZZ/ZoYN31+dhjj3Hddddx6qmnMnPmTH7zm9/Q0NDA66+/3m/HyURV1axC5MLKTyQSRCKRrH2pVIpkMkk6nSYej2M0GnG73ZSXl2M2m/VkacKyN5lMutgLERfiLo6bKfSZbcXiLp/PRyqVor29nQ0bNuiLvyQSCWyuaiUYSWMAUikNh9UyLNIo9AS/105Jgbtz/BYjextC1Db1zLjrkUvnq1/9KnfffTd33nknS5Ys4fjjj+eoo46irKwMh8MBQDQapba2ls2bN/P+++/z9ttvY7FYuPzyy3s0sMOxfft2IpEIxx9/vL7N6/Uye/Zs1q5dy/Lly/vtWJmYTCZd7IULBtBdOmazmUQioT8BqKqqh2L6fD69MIoI4xQ+e/ESNwwh6KKcYuYqXnHDgM7JXTFhDJ1PFMFgkPr6ejZu3MjRRx8tC6dIJEBMUcAAVrORtAbGkeXN0fG5HZjNBpRkGksqTU/dUj0S/CuvvJILL7yQ559/nhdffJGXX345y6cMn4UpaprGtGnTuPbaaznvvPP6NWRQxP8f6KsuLCzsdm1AX8iMpAF0oYbPYuZFqgSR/0ZVVWw2GyUlJVkrcMPhsO7WEatvRd8ip45IqyySsx24X+QCSaVSWCwWXC6X7s+vrq7G4/EwY8aMAbseEslIYd6kPCo21hJVVPJzXCycOTA1Ywcar8eOwQAdYQWXy43b2bOVwj2etHW73XzrW9/iW9/6FrW1tXz00Ufs3r1bLw3m8/mYPHkyCxYsGLAJ1FgsBnBQbn6bzUYgEOjyM0uXLj1kf/X19T2e6MzMbqmqKvF4PCvFQqa/3263U1jY+QemKIo+setwOPSYe03TdLcQkBWpIyaEXS6XfkyRnE20V1UVh8OhT/IGAgG2bNmC3W4f1WmrJZIjYc6UXM46roDWsMqx8yYPWJHwgSYaT6FqkOMyo2lqjydu+xSlU1ZWRllZWV+66BXChaEoiv47dOasEa6lgThmpsCKOHwRJy8qVgnXi8lk0mPtPR4PDoeDSCSiT/LabDbdLSRCMkUMvVjAJVbfihuE6B/IcieJFbui35ycHNrb2+no6GDjxo3YbDaKi4sH5LpIJCOFIr8Vv9fI+CLvUA+l1xiNRtDAYBRRRj0Lzey3VTqRSIRgMHhQrDpAaWlpfx0G+MyV09TUxPjx4/XtTU1Nh3RhrF69+pD9Hc76F2QWP8ksaC7CMzNdMpBdySonJ4dgMKiLu6hqFQwGdZeM8M87nc6DrH2Rn8fj8ehCL2LyM8M1RYgooE/gtrS0sG7dOhYtWkRRUVG35ymRjEYCkSTbayPEFUgYGlk0u2jETdoC2K1GbBYDoZhKrs+Eu4cFW/ok+IlEggcffJDnn39ed+l0xbZt2/pymIOYOXMmbrebiooKXfCDwSBbt27lkksu6ddjCRRFyZpwhc/SLQjrXlj8mf58u92O2+3WPyueQESBcxGSKXz2AA6Hg1gspgt6Op0mGo1mpXE1m81Z6ZRFH2JcYs6ktbWVpqYm1q5dK0VfMmaJJVSicZVCn5VgNNGrVarDATWdJt9rZWqpDavTjbGHs899Evyf/vSnvPTSS5x++ukcc8wx5OQMzjJlq9XKJZdcwn333Udubi7jxo3j3nvvpbi4mGXLlg3IMTPz22Tm0clcFJWZbyczJ35eXp4+0Zrprxcv0U4cRwi9CM8UmTYzXUDiCePApwsxBtFGVVU6Ojpoamrigw8+YOHChVlPRRLJWMDnsWMyGtjdEGPyhJwhL2XYWxKKgsloIJJQKRvn6vF59Enw33jjDb7+9a/z85//vC/d9IrrrruOVCrFbbfdRjweZ9GiRTz66KO6cPY3wpIXvvtMMq174eLJtO49Hg/pdDortXIkEtHj90WaBLGyVsxNRCIRLBYLiqLoKZedTifpdFovuSieOMSNJPPmY7fb9QneQCBAc3MzFRUVJBIJpk6dKuviSsYMBoMBk9mEpiVJJUdmDYn2YJyNO5oJRJP4PFamjfcNXi4d6LyIs2fP7ksXvcZkMnHTTTdx0003DcrxxMSpsKaFeGcuwspMqwCdTyIFBQW6qMdiMVRVJRQK6TVtRXZRYfUDejy/KK4iJnvFMcSNIXMRmLgJiacQEeEDnZFVRqORjo4OOjo6WL9+PaFQiHnz5slka5IxQTCqYDJbmFJiJJLoXeKxoaa2KcTmPW1oqkoinSDci8pXfVqVs3TpUt5///2+dDFiEIuhMielhUWfGbEjXCpGoxGXy4XP59NDKw0GA4FAQPfP2+12PbpGhFMKV0xm2mVxrEAg0KXYZ67AzXxZLBY91t/tduPz+TAYDHR0dLB161b+/e9/EwwGh+R6SiSDiddpJdfrpKlDwWxMjUiXTiCcoCOUIBBJEYqlCQ12Lp3vfve71NbW8pOf/ITNmzfT1tamW5GZr9FApq/8wDTJQvCFmwXQ8+EXFBQAnS6cQCCgl4j0er34fL6D3EROp1MvdpIZcplMJolGo1k5dcRxMnPviJ+ijcVi0W8sTqcTv9+PzWYjFAqxe/du3nzzTbZt25blbpJIRht+r50TFo5nZrmLKUVWXPaRtwI9kYhjNRtxO83keR14erjoCvro0hETpFu3buX5558/ZLv+jtIZCjJdNZmrXoVQZ1r+YvGVCKOMxWKEQiE99NLtduuCnhnH73Q6dQEXufKtVquedVO4gYQbJtN9I9I0iCpcmQuzRH5+cQ7iFYlEaGhoIBwOs2/fPubMmdPvIbQSyXChwO9m0jgfjZ8WMZ9QNnJCM9uDcTbtbERJqRhNZqaW+ygr9PS4nz4J/ve+970xM/GXTCZ1l02mlS8mRUXOG2Gti+vS2tqqi7rIqZOZ5178LpKhic+m02lsNhvJZFIvhhKNRonFYni93oNcSzabTRd9cSMRwm6xWLLcP/BZycRQKERHRweRSITGxkbKy8uZPXu2vjJYIhlNGCwuPt5dRzgWZEqTwmlHl48I0d9c1cT2mgCqComURoHf0atx90nwr7322r58fEQhQirFK1PU4bNcOsINY7VasVgsRCKRLNcOoEfxxONx3d8u8uJnJmAT8f0i2kYkR8vJydFvNMJ6z7TsxVOAiBgS7ppMSz/zSSIYDBKJRGhrayMUCrF3716Ki4uZNWsWpaWlWfH/EslIJhQ3sK85gcVkYPPORqaV9TzSZShoam4nndbwuqwkVBPGXhraMkTjCLHZbDidTn01cWZkTKYPXljrTqeTgoICPd2xy+UiHo/rE7TxeGcea1HOUFj84ilCzA9kljVMp9MEAgE9R5Hw1YvJ3swQzczQ0cwsnAKRy0f4/G02G7FYjGg0SktLC8FgkJqaGnw+H5MmTWLq1Kl6QXaJZKRiMBixWm1oaYVQOE5DS4SyQs+wFn1FUcixpyj0WVBUM+X57l7X4u2R4O/fvx/4LFWCeN8do8EvLFwomblsMi3nzEVXJpMJr9eL3+/X98fjcaxWK+FwOEvshbtFURR9Ra7L5dJFXFEUbDYbNpuNYDBIOBwmFovpKRiE1S4mj4Xln+l6EjeQzBDMzGybop3Iry+EX8w9NDY2smHDBvx+P+PGjaO8vJyioqKDktdJJMOdskI386YXsXVnHamowvub9tHcEeNLn580bEW/oaGB4lwbX1o8DovTT1Geq9e1eHsk+EuWLMFgMLBx40asVqv+vjtGw6StqFcr3CFGo1HPU39gWKbZbMbn82XVCBDpEUSsvclkwm63YzQasypeCb+9pml6WGVmIrV4PE4wGMThcGSlXhDHFaIPZPWduRI3M5Inc19mcRWr1aov+IpEIoTDYTo6OqitrWXDhg160ZXi4mLKysooLCwcsMR1Ekl/4ffaOe2Y8SQSCarX7iUcC1HfGiff72TZ4uGXVTYQCOih08fOm9zn/7EeCf5dd92l+30z348FMiN0RIy7SNOc6doB9AgdYX1bLBY6Ojqy3mdG6aTTaV3cTSaTHsoqYvUVRdGjddLpNC0tLZSUlOhuICHU4saTmVkzM50yZNfjzUwVkZmpMzMcVLh6EomEHhoKnX+ITU1NVFVV6TcJp9OJx+MhNzcXv99Pfn4+ubm5WUnfJJKhxu+1U5DrQcNAWtWIhONs3d3KolnDK2qnsTXE1so92M0weUJJvxhUPRL8c88997DvRzNCoA98n2lhCxeJ1WrF4/EQjUb1iVcRPSN8+iLHPZAl9iKFAnSmZE4kErr/3m63Ew6HCQaDBINBPB4PFoslay0AkDWhm/k+c1Wu+Jl5I8islSsQnxFjUBSFZDKpl3EUTyMAHR0dWU8LmQvC7Ha7niXU5XLhcrlwu904nU68Xq/+XqwZkEgGkillfkoLvFTXd+B1mQiFwuxrDA0bwW/piPDG+9sIhBLkeOxMn97zEMyu6NOk7bZt26iqqsoqKfjvf/+blStXoigKy5cv55vf/GafBzkcyLSYxWKmzMlRYRmLBVdutztrgtfr9Wbl24nFYrpQivq2IkzzwNq1wiIXOfVjsRhNTU14PJ6s8oeZUTqZ48qM9RfnkhlldGCqCPEUkzkXkLlP3ABEuodUKqW7uzITy2Uu5hJPBr257pkLyQ5cYSyS2oltB5aMzNwmzkHcXDMLxh947pkur8zJ7swxiFXPmcXlu3rizbypZob2Zm7PvMbibyCzilxmjeLMFB7i5p253iJzbimzH1EbWYxJTNZn/n1kZnkVaTwy/17mzZvXq+9xuDGpNIfzlk7njQ/2UNvYQUc4zhtrdhCKKsyelDekwq+qKjt27SUQSlCcaydt8hCOp8jrh777JPj33nsvdrtdF/x9+/bx/e9/H5/PR2FhIffccw92u51vfOMb/TDUoUX8YwvBED71TCsZOq313Nxc3SIXFrqoPSsmXTPTJbe3t2f54TNfRqORcDisT7LabDai0SiNjY0UFBToMfmZNxMxpszJ5MxtB/4uooMEmf7+AzNzivMXriTBgQnkDkww15frDmTdPCRDx4svvsgdd9wx1MPoF+ZPK8RoMPDGmipaO8JsrQnQ2F5JY3v5kMXnp9Np9u7di0FN4HKYSRpc5Hoc/ZYKok+O1e3bt3PMMcfo719++WWMRiMvvvgizz33HF/4whf485//3OdBDgeElSQsJpvNllWBSiCibMRiqPz8fD1fTjAYzPKxi6cEUexErK4VE7zCR2+1WnVrVsTkx2IxGhoadMEW1nZXIi+sbdHuwEpd8NnaAOGqEe1En6IPYW2KNuIlau+KBWoSyUigrNBDSaGPWNqI3WLAbExTXdtERyg+6GNRFIU9e/YQiUTIcVs54/gZHD+/rF+LtfTJwg+FQlmx2e+++y4nnHACubm5AJxwwgm89957fRrgcEG4ADJdDMLqFpa/eAoQMffCF22xWAgEAnqMvFiUJQRS3EzMZjPhcFgX6UQikZU3R0yMirDJuro6XC4XeXl5WeKe6c4RNwJxExA3gsybROYNQXw+U8yF4CuKkmXFi/DSgSAzBUSmu6SrvEHiJnzg9kNFIonvMbN9V8cV11Q8zR04PtHfgfMWwgV34NPUgZ/NXFyX6Q7L/D2Trrb1hL5+HuBrX/tan/sYTvi9dj43t4SYkmRPXQdJJY7DrFKzdy+KolCY5x0USz8QCLB//3590eSECRMGJOqtT4JfUFBAVVUV0FlecMuWLVkTuZFIZMCjM26//XYUReGee+4Z0ONkLm7KjFQSZPpLhQtHWPQizDGRSOgTtCIvDqBPvCqKgtFo1PPhCx9zKpXSSyGmUindrRONRqmpqcFms+kFzDMFPVOcMyd2xb5Miz5zu1jpK3zzmW0OXHMA2RFMmaKcGeJptVr1xWsil1BOTo5eM8Dr9eoJ3g4UYYlkIJlUmoPPPY3aps41MqFAC3vqQ2zZE6Awz8vRR5VjNpvxOq39Lv6KotDQ0KCHXjocDsaPHz9ggQt9EvylS5fy1FNPoSiKHpt/xhln6PsrKyv1VaH9jaqqPPDAAzz77LN89atfHZBjZCKsZ0C34g+Mbc+MrRdVqgA9r73b7SaZTOqCCugRO6LfaDSqf97pdOqWYWYpRFVVcTgchEIh2tra2LZtG1OmTNH7yhT6TAs902rPnHDNFHYRhXNgkXbBgRPKdrtdD8f0er3k5eXh8/nIzc3F6XTKxVmSEYHfa9fFfHetiz1Nuyj0qexr6KC6voNk2oTdYWfpovHMn9b3PFONrSH21TWRSoRxOzqfQgsKCigoKBhQY6dPgv+DH/yAtrY2Xn75ZTweD3fffTf5+fkAhMNh/vnPf3LxxRf3y0Azqaqq4sc//jE1NTWDtopXhFCKiVWXy5UVuw7ofnnh3xbiKEQ1Eonobgar1aqHYZpMJhKJhB7GKSZ6I5GI7tMXk6JCwIXoxuNxFEUhEolQVFSkl5kUFrnwuR/on1cURXcpZS4gy4z4EW6rTOs8NzeX/Px8CgoKKCoq0mvnSiSjBb/XQXlJIS3tITSDQnVDhHA0jZJqo6E5iOnMmTgcDpo74hTlOo941Ws6nWZffSu7aprYua8dVQWn3cjR0wuYMXU8dvvAu476JPgul4tf//rXXe5zOp289957A3ISH3zwAVOmTOH//t//yw9+8IN+778rbDYbmqZhs9n01a92u51QKKT7bMVkbqbFL0Q00y1yYHnCeDyuh90J61+EMWbm3lEUhXg8fpCrRVEUgsEgzc3NmM1mHA6H7qfOFP3MSdjMyVpxY8oUd6/Xq4t6UVERubm5MomaZEzg99pZNLuIYNRPbaOffS2VpNQodquJcDTBf9bvpr5dIZbU8LntnLKwlDyfE5/HQa7XTnV9kKraADYzTCxx4bB0/j83tYbYXhuhqSNJeyjJwum5pA02fPnFgyL2MIDJ04xGIx5P/ywWOJDePDUsXbr0kPvq6+spKSk57OdVVcXr9eo+aaPRSEFBAe3t7UDn+TqdTmw2m754KNNiFjcDYVkLd4r4rHDjiGyZIo8OkLXY6cAJQIvFoi/6yoyYgcP71jP96jk5OeTl5VFcXExpaSl+v3/MrKCWSLpCuHi8TitzpxayflsDaVWjILfzfz8cTTEu38bepjDvrNuDz2XBaTfid1n4cEeAxo4kJiPMHu9i8YwcPE4z0YSKkjYyfUIeW2vChBQr44s8g1p9a9hly6ytrT2sOK9Zs0aPAhpMHA4HkydPpqmpicLCQvLy8vB6vUQiEZqamvB6vZSWljJx4kS8Xm+W5ZwZ8w6fZdcUkTiZlrdYwJS5KlZMlAr3S2YxFHEDURSFaDSqPwEIhK89c8I0NzeXoqIiCgoKyM3NlROkEskh8HvtnHvqVGZNzCUaTzKlrLOeRfDtHbQEY7icVmxWC6X5DurbYiRTCqGoisdhJpHUCMY0rA4PZWV5FJSYSFvaCEUVjprsYEpZzqBn6hx2gl9UVMRrr712yP3CR91TVq9efch9c+fOpb6+/rA3GolE0j319fWjzvXn99r5/LzsucKvLZlBY1sUh81EY2uMUFRh6sR8ivIctMeq2dcUxmozMGV8EZMnjMP3qagvslgIRpUBifg5Eoad4FssFqZMmTKoxxSulu6or68H6Nb9IxkY5PUfWo7k+guX52hnUmmOPlnbXhTPEnGvy0ZVbQCn3cSsidlpGjKjgYaCYSf4Q8G6deuOqJ14Ajjc04Jk4JDXf2iR179rDhTxzJvBcEM6byUSiWSMIAVfIpFIxggj3qXz5JNPDvUQJBKJZEQgLXyJRCIZI0jBl0gkkjGCFHyJRCIZIxi0/kiSLZFIJJJhj7TwJRKJZIwgBV8ikUjGCFLwJRLJqEZVVebPn084HO51H4qicOutt3LyySdzzDHHsGLFCnbu3Knvb21t5fLLL2f+/PksX76cjz/+OOvz3e3vbdueIgVfIpGMampqavD7/X0q1pNKpSgrK+Mvf/kLH374IUuWLOF73/uevv+OO+6gvLyciooKLr/8cq699tqs/Fzd7c+kJ217jCaRSCSjlB07dmhz5szRZs+erS1YsEBbsWJFv/SbSCS0GTNmaG1tbVooFNKOOuoorbm5Wd//hS98QXvvvfc0TdO63Z9JT9r2hhG/0lYikUgOxbRp07jmmmsIh8PcfPPNWfuuvvpq1q9f3+XnrrrqKq666qpD9vvxxx+Tl5eH3+9ny5YteDwevbwrwPTp06mqquKkk06ipqbmsPszOVzbOXPmcOONN9LW1oamaZx//vlcdNFFPboeUvAlEsmoprKykiVLlhy0fdWqVb3qLxgM8pOf/IQf/vCHQGe96wPdRW63m0gkckT7Mzlc21dffZWysjIeffRR2trauPPOO7nwwgt7VJ1O+vAlEsmoprKykmnTpvVLX4lEgu9+97ucdtppnHfeeUBnNbwDxTscDuNyuY5ofyaHa7t48WLeeOMNrrnmGl577TVuvfXWHpcilYIvkUhGLYlEgrq6OqZOnXrQviuuuIKFCxd2+Vq5cuVB7dPpND/84Q8pLi7Ocg9NmDCBYDBIS0uLvm3nzp16Iafu9mdyuLYzZszgjTfe4Nxzz2XHjh2cc845elGaI0W6dCQSyaglFAphMplIJpPYbLasfY888kiP+rrttttIJBL89re/zbKs3W43p556Kg899BA333wz//jHPwiHwyxevPiI9mdyuLYrV64kEAhw8803s2TJEioqKmhoaOhRBTiZWkEikYxqbrzxRlavXs38+fN54oknetVHXV0dS5YswWazZdXsffjhhzn22GNpaWnh5ptvZt26dZSVlXHnnXeyYMECvd3h9l9xxRWcffbZnH322Ydt297ezk033URjYyMmk4kTTjiBm266qUfnIQVfIpFIxgjShy+RSCRjBCn4EolEMkYYFYK/atUqVqxYMdTDkEgkkmHNiBf8p59+mgceeGCohyGRSCTDnhEbltnY2Mgdd9xBRUUFEydOHOrhSCQSybBnxFr4W7ZswWKx8MorrzB//vyhHo5EIpEMe0ashb9kyZIu82P0hmOPPRZFUSgoKOiX/iSSsUpzczNWq5V169YN9VAkXTBiBb+nLF269JD7xGo8STZaOp39UlVQVTRVRVM10D79iVzKMVYwms1Y8/IOuT+VSiGX9gxfxozgHw6TyURJSQmrV68e6qEMGclQiODmLQQ2byGyew+R6hrS0WjPOjEaMTnsGK020FSSHYFDNrWPK8VeVITBaCQZDhPdvQeMxs4l6+KnwQAGsBeXYMvvFJlUNEK0Zi9gwGCgsw3ipwFbYQH2ggIwQDoWI7Kn+oAjf7Yk3pafj62w86kunUgQqdp9qKZYc3OxFxUBoCpJwlVVhzw3q8+HvaS4s20qRXjnrkO2teR4cZSWAqCpKqHKHYdu6/HgKBunvw9u237ItmaXC+f4cv19qLLy05vzwZicDlwTJnzWdsdOtHT6oHZGs5kJ31xB3uJFhzzu4Qyr0YamaaRSKRKJBMlkknQ6rd/sjEYjJpMJq9WK1WrFbB4eUjs8RjEIHE7Mx9IfaSaJ1jZa/vNfWv7z305ROsAyM5jN2IsKsRV2vow2K9E9NURqakgFgwf1N+HiCyk771wA4k1NtPznfax+H1a/H5PLhcnhwOxyYnI6MVqtPc70J5EMNclkklAoRDgcJhKJkO7ixtgVFosFl8uF2+3G4/EMmUdhzAi+5DNClTuoe/FlWis+BFXVtzvKysiZNwfP9Gm4Jk3EMW4cRotF3x+prubj/3MDAEarFe/sWXhmTMczYzrOiROx5vr1tvbCQsrOPWfQzkkiGSg0TSMUCtHa2tplDnur1YrFYsFsNutGjKqqpFIpksmk/uro6KCjowODwYDX6yUvLw+HwzGoho8U/DFEdO8+9jz2BB0ffaxv88ycQcHJJ5H7ucXY8nL17Zqm0fz2uyRaWyn/+tcAcE2cSPkF5+OaPBnfgnmYDsg+KJGMJjRNIxAI0NTUlFVT1uFw4PF4cLvd2O12jMbDBzum02mi0SiRSIRgMIiiKAQCAQKBAE6nk6Kioi5z4w8EUvDHAGoyyd4/PUvdiy+DqmIwmyk49WTGfeXLOMePP6h9rL6BqodWEtj0CQazmcJTT8FW0FlybfyF3xjs4Y940uk0yWRyqIfRr5hMpiyLdrQRj8epq6sjFosBnefr9/vJzc3FarX2qC+TyYTH48Hj8VBUVEQ8Hqe1tZVAIEA0GmXPnj3k5ORQUlIy4L7+USH499xzz1APYdgSb2xk+69+TeTTScbcxccx8dvfxPHppOKBtK75gB0P/B41HsdotVL+ja9j9noGc8ijinA4TG1t7aiMXHE6nZSUlPRYAIczmqbR0tJCU1MTmqZhNBrJz88nLy+vX/zuBoMBh8NBWVkZRUVFNDU10d7eTiAQIBwOM27cOLxebz+cSdeMCsGXdE1ox062/fIukoEgZrebKd+7hvzPH99lW03T2Pfsc+z707MAeGfPYup13z/kjUHSPel0mtraWpxOJwUFBaPGGtY0DUVRaG5uZs+ePUybNq1bt8ZIQHxfoVAIAI/HQ2lpKZaMeaz+xGKxMG7cOHJzc6mrqyMej7N3714KCgooLCwckL8XKfijlMAnm9n68ztRFQXXpEnM+vEtulumK6qf+CP7X3oFgNKzlzPhmyswDpNQspFKMplE0zQKCgpwOBxDPZx+xeFwYLFYqKmpQVEU7Hb7UA+pT6RSKWpqaojFYhgMBkpKSvD7/YNyk3Y4HEyePJnGxkZaW1tpbm5GURTKysr6/fjyP3oUEqrcwdZf3o2qKPgWLmDG/9yI2Xl4wbH6OyNsJl15OaXLzxyMYY4ZRotlfyCjwaqHTrGvrq4mHo9jMpmYMGECTqdzUMdgNBopKSnBbrdTV1dHIBBA0zTKy8v79e9HCv4oI97YyNZf3Ikaj5Mzby6zfnQzxiPwsY4752xy5s3BPXnyIIxSIhkeqKpKTU0N8Xgcs9nMpEmTDqp9O5j4/X7MZjN79+4lGAyyf/9+SktL+030R8ctWgJ0rhbdfve9pEJh3FOnMOvHtxxW7GP796NmhJtJsZeMJTRN0yNxjEYjEydOHFKxF3g8HsrLO1dJt7e309bW1m99S8EfRex5+DEie/ZgyfEy85b/wXQYv2oqHGHL7T9j0//8iHhT0yCOUjJc2L17NzNnzmThwoUsWLCAr3zlK2zatGmohzVoiOgYgPHjxw+reQiv10txcWfARH19vR4e2lek4I8S2jd8ROMbbwIw/cbrDztBC1C16g8kmltIx6KY3e7BGKJkmLF9+3Zmz57NRx99xIYNGzjmmGO46667hnpYg4KiKDQ0NABQVFSEexj+D+Tl5ekhmrW1tagZq+J7ixT8UUAqEmHXg/8PgJLlZ+KbN/ew7ds3fETLe/8Bo5HpN/wQ8yBPUEmGB5WVlcycORPonDRcuHAh7e3tQzyqwaGhoQFVVXE6neTnH944GioMBgOlpaWYzWYSiQStra197lNO2o4Cap/7K0prK/biYiasuPiwbdOJBLtXPQxA6fIz8UyfNhhDlNDpM1YTiQHr32iz9Whyr7KykhNOOAGAuro6nnjiCZYtWzZQwxs2iBQHQL9OiA4EZrOZoqIi6urqaG5u1id1e91fP45NMgTEGxrY/+rfAZh05WWH9dsD7H/5VeINjVjzcim/8ILBGKKETrH/5JYfE9peOWDH8Myaydy7f3nEArZjxw4qKiq4//77iUajXHbZZfzgBz9AURQuueQSdu7cyUsvvcSEjNTJo4GmT+es/H7/sPLbHwqfz0drayvxeJyWlhbdt98bpEtnhFP9v0+hpVL4FszHf8zRh22bCoepe+llACZ+89JuY/Ml/cwwsiRDoRD79+/n3//+N+vXr+e73/0umzdv1nPkPPTQQ3zhC18Y6mH2O/F4XM94OVIq3BkMBgoLC4HOiea++PKlhT+CiVRX0/r+GjAYmPjtb3Zr2SVDYVwTJ5IKh8k/6YRBGqUEOv9p5979y2Hj0qmsrKS0tFSfrLz88st55JFH9Ljv4erX7isixNHr9Y6oHEAejweLxUIymSQQCOD3+7v/UBdIwR/B1D73AgD5J3we18TuH7sdJcXMufPnpEJhDKNkleRIwmAwdOtyGywqKyuZOnWq/t7tdrNgwQLeeecdLrrooiEc2cAh0h0DvRbMocJgMOD3+2lqauqT4Mv/+hFKtLaOlv++D0DZ18894s8ZDAYsMvvlmKeyspJp07In7E844QTee++9IRrRwBOLxUin0xiNxmEZhtkdOTk5AD2qtHUg0sIfZLR0mvaPPibwyWbUeBzXlMkUnnZqVmWpI2H/S6+AppF73CJcEycetq2qKOx/5W8Unr4Uqy+n94OXjBp+/vOfH7TtmmuuGYKRDB7hcBjofJoZzpE5h0JU1komk0SjUTyenhtuUvAHkUjNXnb8+jefFuH+jI4NHzPzlpuOuJ9UOELzu52WWOk5Z3fbvvm9f1Pz5NM0rn6Lox/6/Yj8Y5cMLt/97nfZtGkT1dXVfPOb3+RLX/rSUA+pz0SjUYBBqy7V3xgMBlwuFx0dHVLwhzvh3bvZfNsdpCOdK1vzT/w8JoeD/a/8jdY1H9C+4SP8Ry88or6a3nobVVFwThiPd/asw7bVNI36v70GQPGyM6TYS46Ihx56aKiH0O/E43GAEZ2q2uFw0NHRoZ9LTxkwwU8mkzz44IO89tprhEIh5s2bxw9+8ANmz56d1W737t28++67vPfeezz++OMDNZwhJRUOs/3u/490JIpn1kxm/ehmLJ8umdZUlf0vv8qeR5/AO3tWt5N6mqpS/49/AlD8pS92K+CRqt1E9lRjsFgoOmNp/5yQRDLCEEXFgWGRIK23iMiizBq7PWHABH/VqlWsWrWK/Px8SktLqaio4JJLLuGZZ57B4/HwzDPP8Prrr+vl30biJMqRsvdPz5JoasZeXMTs227Nyl1Tfv55NL/zHrHaWnb+7kFm3HTDYUU8sHkL8f31mBwOCk45udtjN765GoC84xfLnDmSMYuoKWwwGEZ0Hn9RfUvcvHrKgAn+K6+8wgknnMDKlSuxWCw0NjZy9dVXc/fdd7NlyxbC4TBz5szhrLPO4sQTT2TBggUDNZQhJd7QQP1rnRb5lO9crYuumkzS9PY7oGnMuOl6tvz0F7T+dw0Nc1+n5EuHXvDS/Pa7AOSffGK3C6fSiQTN7/0bgKLTpXUvGbuIxUomk2lEuzVFXd10Oo2maT0+lwET/P3793PllVfqd6SioiJuuOEGrrzySqZNm8YDDzzAlClTBurww4b9f/sHqCq+BfPxLZgPdEbqbPvl3XR8vBGAsvPPY+I3V7Dn0cfZ9+e/UHjqyZi68DOmEwla13wAcETWfeuaCtKRKLbCQnLmzunHs5JIRhZC8EeydQ99H/+AnX0qlTooT4XIzHf11VePCbFPx2I0rX4LgNKvfFnfXvfyq7rYAzS+sZqiL5yBvbiIZEcHjavf7rK/9nXrScdi2Ary8c6a2e3xE83NGCwWCpecKhdaScY0whLWNG2IR9I3hOD39kllQFWgvb096wKLLG95eXkDedhhQ9va9aSjUezFRbp1n4pEqP3L80Cni8fkcJBsbydas5fSsztvCg2v/aPLP0wRipl/8klHJODlX/8ax/3xcUq/fFZ/nZJEMiIRQtkfOeWHEjEX0dsb14CGZd59993cf//9TJ06lVmzZjFu3DgMBkOvJxxGGq3vd66EzT/xBF2gtVSKglNPJryriqIvnEFo5y7SsSgGs4mC006l5smnidXtJ1S5A2uun91/eJSZt9xEOhajff1HwJG5cwQyQZpE8pmxmU6nUVV1xLp2hOALX35PGTDBf+SRR9i+fTuVlZVs376dF198URf6q666itLSUqZPn66/pk2bxvTp0wdqOINOOh7XBTrv88fr2y05OUy55io0VcVgMDDt2u9mfc539AJa/7uGjo83Et27l/a166j/+z8w2W1oqRTOiRNwTRjf7fGVtnasuSMrX4hEMlCYTCaMRiOqqqIoyohIi9wVIhyzt4nfBkzwTzzxRE488UT9fTKZpKqqSr8JVFZWsmnTJt5+u9NfbTAY2LZt20ANZ9AJbtuOqijYCvJxTZ500P5DuWRy5s6l9b9rCHyyWc+d7ps3l90PPwpA7uLjuj12Khxm3ZXX4CwvZ85dP5cVrSRjHoPBgM1mIxaLEY/HR6zgiwVXvV1LMGgrbS0WCzNnztQnbgUtLS1s27aNHTt2DNZQBoXg1s6bl/eo2frkStvadZjdbjwzph8k+LG6/dS/9g8KTjsFgNCOnWipFK5JkzC73QS3bAUg/Wku78PR9uE6tFQKTU1LsZcckt27d3PmmWficDjQNI0JEybwi1/8gnnz5g310AYEp9NJLBYjGo3i8/mGeji9QqSHcPby/3rIHVn5+fmcdNJJXH755UM9lH5FF/yM1Ad7n/4Tn9zyYz20UpBOJPjk1h9T/7fXCG2rxGi1on366OZbOF+PpQdoff8DtG4mnto3bACO7GlAMnYZa0XMRQ4dkURtpJFKpYjFYkDv8wENueCPRtRkkvCOnQB4Z3UKfjIQILKnunPbUUdltTfZbJR/43wA9j7zZ5wZPnrvrJl6dI7RakVpayNUeeinIS2d1kM+jzQ3j2RsMtaKmLtcLgwGA4qi9DoXzVASCoUAsNvt+vqmniIFvxfE6htQDxNpFNm9B1VRMHs8OMrLgM6UCADOCeO7TFFc/MVlOMrLSEejWaXwTC4X0Zq9GMxm/MceA9BZ5eoQhHdVkQqFMblcskD5MCQdjx/ypR6QH+VwbdMHVM5K90LAKisrmfWpQTIWipibTCY9w+RIvLGJMYu8+L1BZsvsIY1vrmbX7x+iZPmZTL7y8k+3vUXtc39lwoqLyD/xhM/cObNm6v77wKZPAMiZN7fLfg0mEyVnfYndKx/Wnw4MFgst//kvAP5jjqbglJNofX8NrR9UMPGyb3W58KJ9Q2dkkG/BPAy9DN2SDBwffOPiQ+7zH3M0s2//sf7+w0svO2RJRO+co5h752c57ddd+R0WP9mz5IOHKmL+4Ycfct9992EymZg7dy4/+tGPetTvcMbn8xEMBuno6KCoqGjEhGfG43Hdf9+X+YeRcbbDiP2v/A1ATzmsqSrV//sk8YYGKu+9n0RzS5f+e+GGyTnAnZNJwSmnZKVU0JJJGj7Nw1Ny5hfxLVyAwWIh0dRMrLauyz5EKKj/6MMXNJeMbQ5XxHzChAk89dRT/OlPf6K1tZXKysqhHm6/4fF4sFqtpNNpvb7tSKC5uRnorMXbW3cOSAu/x6RCnRM+omBJpLqGVDCo72/94AOC27YDnwl+OpEg8mnRE/fUQ6eUMDsd5J98Io3/egOT201aVOiZNpWc+fMwGAx4Z88isHETHR9/jPNTd1Em4776FdrXrce3cEHfT1bS73zu2acPue/AyK3j/vjYoTs64Onu2If/X4/G0V0Rc4HZbO71Ip/hiMFgoKCggLq6Opqbm/H7/cP+/GKxmF6Lt7CwsE99ScHvAZqmkfxU3OONTez7y/NwwArn/X97jVQohMFk0uPvo9U1oKpYcnKw5h8+rUTOnKMIbNxE3vGfo+mddzFarUy77vu6+6b07OUUnnoKvkNMyOafcDz5Jxzf5T7J0NOTIuYD1RaOrIj51q1baW9vz2o3GvD5fLS0tJBIJGhsbMy6wQ03NE1j//79QKfvvq/rB6Tg9wBVUdA+nazd9+xfSEdj5CzIjllONDQCndEyiZZWHCXFuCZNZO6v7iIZCHSb8Cj/hM+Tf9KJGAwGJnxzBUDWZ3I/nbiVSPrC4YqYX3TRRbS2tvLLX/6S3/3ud0M0woHDYDBQUlJCdXU1bW1teL3eYVuPo6WlhVgshtFopLi4uM/9ScHvAelI9LPfo53xsNGafYds3/rf9yk771yMVivemTOO6BiZE609yYanqSp1L72Cb95cXJMnyeyYksNyuCLmiqJwww038KMf/Yj8/PzBHtqg4Ha78fv9tLe3U1tby5QpU/rkGx8IotEojY2dBmRxcXG/jE+qQg9Ix2IYzNn3yOSnvjXojKrJJPDJ5gEZR7yxidoXXqLh9Tf1bZE91dT875N88uPb0dLpATmuZGzw0ksvsWPHDn71q1+xYsUKPvroo6Ee0oBQUlKCzWYjlUqxd+/eYZVJU1EUampqgM6JWr+/f/JiSQu/BxjtdopOX0LDP1//bGPGH4lzwngiu6owmM1oqRTBbdtJRSLUPPUM7qlTKDytf/LShyorqfnfJ3FOnEDxstOBjHDMeXMxDjNLRTKyOP/88zn//POHehgDjtFoZPz48ezevZtYLMbevXsZP378kIdqfvmGl/Xff/Odo/Qsw/2BtPCPEE1V2XTLj7LF/lOsebmc8PJfmX79/yH3c4uZcctNmN1u1ESCprfepuG1f1Lz5DP95mbxLZgPBgPR6hqUts7FGB1C8OXqWonkiLHZbEyYMAGj0Ug4HKampob0ED4hZ4o9wA//35Z+jSKSgn+EBDZvRWlq7nKfY9w4APb96VnCu6rQEgmKv7iMsvPOJd7Y+Rn31Mn9NhaL14t7Smd/HR9/TCocIfhpZk3/0Qv67TgSyVjA6XTqoh+JRNi9ezeJQyx4G0hE6oSBRAr+EaKmkofcZy8tJRWN0VaxFqWlBYPFwoQVFzNhxcWkRCx9P4e2iTj79o8+pmPTJlBVHONKsRcV9etxJJKxgMvlYtKkSZjNZhKJBFVVVbS1tQ1KSURVVWloaNB99gOJFPwjxDMtQ7ANBowZlaQa//U62+68W8+FYi/6bHFEpKoKQLfI+wsh+B0fb6J97brObdKdI5H0GofDwZQpU3C5XKiqyv79+9mzZ4+eobK/0TSNYDDIrl27aGlpAWDl9cdmtXn111/p12OO2ElbVVV58MEHee655wiFQixatIjbb7+d8vLyATme5dOkSwAGsxlHSQmRqt2dGzQNe3ERwU8TpNkKO63seGMj0b2dYZvufi7a7pkxHZPDQSoYpOmtdwAZoz9cGemFsw/FcIpq6S8sFgsTJ06ktbWVxsZGotEoVVVVeL1e8vPzcTgcfZ5A1TSNUChEc3OzfjMxm82Ulpbi9Xp59dfj+uNUumTECv5DDz3EM888wz333ENxcTH33nsvV1xxBa+++mqvy391h3f2LIJbt5F3/GK0dPozwQc806bR9OZbwGd1ZCvvvR/oTGvc3+UGjWYzOfPm0PHRRqZ852qs+Xl4Z83s/oOSQcNisWAwGGhubqagoKDfIi2GGk3TUBSF5uZmjEbjgP2/DRUGg4H8/Hy8Xi+NjY0EAgGCwSDBYBCbzUZOTg4ejwe73X7E36mmaUSjUUKhEB0dHXq5V4PBQF5eHgUFBYOS4mFECr6iKDz22GPceOONnHrqqQD85je/4aSTTuL1119n+fLlA3Lc6TdeT8t//kPR0qXsefx/s/YVnHoy7Rs24D/2s0ey8vPPo+bpPzH+ogsGZDyTr74Si8eDcZT9w40WTCYTZWVl1NbWUl1dPdTD6XecTuewCGMcKKxWK+Xl5RQUFNDS0kIgECCRSNDU1ERTUxMmkwmHw4HNZsNisWA2mzEajWiahqqqpFIpkskk8XicWCyW9aRnMpnw+/3k5eUN6oKvESn427dvJxKJcPzxn+WM8Xq9zJ49m7Vr1w6Y4Nvychn3lbOBznj3pjdX6/tMdjuzfnRLVvvc4xaRe9yiARlL53gOn5dHMvS43W6mTZtGMnnoSf+RiMlkwmw2j5qnlsNht9spKyujpKSEQCBAKBQiHA6TTqcJh8NHXEHLZDLhdrvJycnB7XYPyY1yRAp+Q0MD0LlSLpPCwkJ930CT9/nP4X51KuGdu/DOOXTKY4nEZDIN+4yMku4xmUzk5uaSm5uLqqrE43Hi8TiJRIJkMkk6ndateIPBgNlsxmKxYLPZ9CeBob5BjkjBFxMdB/oObTabnkb0QJYuXXrI/mprazGZTIdt0xVaOk06FsMUbMPQw89KJKOR+vr6MXFzMxqNOJ3OXhcTHypGpPNNpAhVDigJl0gkcGQUEDlSxN24O+rr66mvr//scyYTZrdbJiobJA68/pLB5Uiuv9lsxmazDdKIJD1lRFr4wpXT1NTE+PGfFfxuampixoyus1KuXr26y+09QTwB9Edfkp4jr//QIq//yGdEmqYzZ87E7XZTUVGhbwsGg2zdupVFiwZuklQikUhGMiPSwrdarVxyySXcd9995ObmMm7cOO69916Ki4tZtmzZUA9PIpFIhiUjUvABrrvuOlKpFLfddhvxeJxFixbx6KOPDrsiBhKJRDJcGLGCbzKZuOmmm7jpppuGeigSiUQyIhiRPnyJRCKR9Bwp+BKJRDJGMGijNZWfRCKRSLKQFr5EIpGMEaTgSyQSyRhBCr5EIpGMEaTgSyQSyRhBCr5EIpGMEaTgHwGqqvK73/2Ok046iQULFnDllVeyb9++oR7WqGTVqlWsWLEia9u2bdu45JJLWLBgAUuWLOGPf/xj1n75/fSNjo4Obr/9dk4++WSOPvpoLrzwQtatW6fvX7NmDeeeey7z58/ni1/8In//+9+zPp9IJPjZz37G8ccfz8KFC7nhhhtoa2sb7NOQHAmapFt+//vfa4sXL9befvttbdu2bdpll12mLVu2TEskEkM9tFHFU089pc2cOVO75JJL9G1tbW3a4sWLtVtvvVXbtWuX9vzzz2tz587Vnn/+eb2N/H76xre//W1t+fLl2tq1a7Xdu3drP/vZz7R58+ZpVVVV2q5du7S5c+dq999/v7Zr1y7tkUce0WbPnq29//77+udvueUW7fTTT9fWrl2rbdy4UTvnnHO0iy++eAjPSHIopOB3QyKR0BYuXKg9/fTT+rZAIKDNmzdPe/XVV4dwZKOHhoYG7eqrr9YWLFigffGLX8wS/JUrV2onnniilkwm9W2//vWvtWXLlmmaJr+fvlJdXa1Nnz5dW7dunb5NVVXt9NNP1x544AHtJz/5iXbeeedlfeb666/XLrvsMk3TOr+7mTNnau+8846+f/fu3dr06dO1DRs2DM5JSI4Y6dLphu7q50r6zpYtW7BYLLzyyivMnz8/a9+6des47rjjsgrUfO5zn6O6upqWlhb5/fQRv9/PH/7wB+bOnatvMxgMGAwGgsEg69aty7q20Hn9169fj6ZprF+/Xt8mmDRpEkVFRfL6D0Ok4HfDcKifO9pZsmQJv//97ykvLz9oX0NDA8XFxVnbCgsLgc4KTPL76Rter5dTTjklq1zov/71L2pqajjppJMOef1jsRjt7e00Njbi9/sPqnIlr//wRAp+Nxyufm4ikRiKIY0p4vF4l9ceOicL5ffTv2zYsIFbb72VZcuWceqpp3Z5/cV7RVGIxWIH7Qd5/YcrUvC7ob/r50p6ht1u7/LaAzidTvn99CNvvvkml112GQsWLOC+++4DOoX7wGsr3jscji6/H5DXf7giBb8bMuvnZtLU1ERRUdFQDGlMUVxc3OW1BygqKpLfTz/x1FNPce2113LaaaexcuVK/SmqpKSky2vrdDrxeDwUFxfT0dFxkOjL6z88kYLfDbJ+7tCyaNEi1q9fTzqd1rd98MEHTJo0iby8PPn99APPPPMMv/jFL7j44ou5//77s1w0xx57LB9++GFW+w8++ICjjz4ao9HIMcccg6qq+uQtwJ49e2hsbJTXfxgiBb8bMuvnrl69mu3bt/PDH/5Q1s8dJL72ta8RDof58Y9/zK5du3jhhRd44oknuPrqqwH5/fSVPXv2cNddd3HGGWdw9dVX09LSQnNzM83NzYRCIVasWMGmTZu47777qKqq4rHHHuOf//wnV1xxBdD5lHXWWWdx2223UVFRwaZNm7j++us57rjjWLBgwdCenOQgZD78IyCdTnP//ffzwgsv6PVzb7/9dsrKyoZ6aKOOW265hbq6Op588kl926ZNm7jzzjvZunUrBQUFXHbZZVxyySX6fvn99J6VK1fym9/8pst9X/3qV7nnnnt47733uPfee6murqasrIxrr72WM888U28XjUa56667+Ne//gXAySefzG233Ybf7x+Uc5AcOVLwJRKJZIwgXToSiUQyRpCCL5FIJGMEKfgSiUQyRpCCL5FIJGMEKfgSiUQyRpCCL5FIJGMEKfgSiUQyRjB330Qi6Tu33HILL7744mHbjBs3jrq6OlavXi0XTUkkA4BceCUZFPbu3ZtV5/Shhx5i69atPPjgg/o2RVGwWq3Mnj27y5S7Eomkb0gLXzIojB8/nvHjx+vvc3NzsVqtMt+KRDKISB++ZNjwwgsvMGPGDGpra4FON9Dll1/Os88+y+mnn868efO44IIL2LNnD2+//TZf/vKXmT9/Pl//+tfZtm1bVl/r1q3jkksuYf78+Rx33HHcfPPNWU8YEslYRFr4kmHNRx99RFNTE7fccguJRIKf/vSnXHXVVRgMBq677jocDgd33HEHN954I3//+98BWLt2Ld/+9rf53Oc+xwMPPEAgEOC3v/0tl156Kc8//7xeNEUiGWtIwZcMayKRCA888ABTpkwB4MMPP+TPf/4zTzzxhF5cu6amhl/96lcEg0G8Xi+//vWvmTRpEqtWrcJkMgEwf/58zjrrLP76179y8cUXD9n5SCRDiXTpSIY1OTk5utgD5OfnA50CLvD5fEBn4ZNYLMbGjRs55ZRT0DSNVCpFKpWivLycKVOm8N///ndQxy+RDCekhS8Z1rjd7i63O53OLrcHg0FUVeXhhx/m4YcfPmi/KN0nkYxFpOBLRhUulwuDwcC3vvUtzjrrrIP2y8LakrGMFHzJqMLtdjN79mx2797N3Llz9e3xeJzrrruOU045halTpw7hCCWSoUP68CWjjuuvv57//Oc/3HDDDbz77ru89dZbXHHFFaxZs4ajjjpqqIcnkQwZUvAlo44TTzyRRx99lIaGBq677jr+53/+B5PJxOOPPy4XeknGNDK1gkQikYwRpIUvkUgkYwQp+BKJRDJGkIIvkUgkYwQp+BKJRDJGkIIvkUgkYwQp+BKJRDJGkIIvkUgkYwQp+BKJRDJGkIIvkUgkYwQp+BKJRDJGkIIvkUgkYwQp+BKJRDJG+P8BVcZhol2AUnYAAAAASUVORK5CYII=\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot the last repetition\n", - "i = 5\n", - "j = 3\n", - "fig, axs = plot_sync(thetas_arr[i, j], times)\n", - "\n", - "axs[0, 1].set_title(f\"$t={times[0]}$s\", fontsize=\"x-small\")\n", - "axs[1, 1].set_title(f\"$t={times[-1]}$s\", fontsize=\"x-small\")\n", - "\n", - "axs[0, 0].set_xlabel(\"\")\n", - "axs[1, 0].legend(loc=\"best\", fontsize=\"x-small\")\n", - "\n", - "plt.subplots_adjust(hspace=0.5, top=0.8)\n", - "\n", - "identify_state(thetas_arr[i, j])\n", - "\n", - "# fig.suptitle(tag_params, fontsize=\"small\")\n", - "\n", - "# only to viz twisted states\n", - "# fig, ax = plt.subplots(figsize=(3, 3))\n", - "# ax, ims = xgi.draw(\n", - "# H, pos=pos, node_fc=thetas_arr[i,j,-1] % (2 * np.pi), node_fc_cmap=\"twilight\", node_size=5\n", - "# )\n", - "# plt.colorbar(ims[0], label=\"phase value\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6b401ca1", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "venv_xgi", - "language": "python", - "name": "venv_xgi" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13" - }, - "toc": { - "base_numbering": 1, - "nav_menu": {}, - "number_sections": true, - "sideBar": true, - "skip_h1_title": false, - "title_cell": "Table of Contents", - "title_sidebar": "Contents", - "toc_cell": false, - "toc_position": {}, - "toc_section_display": true, - "toc_window_display": true - }, - "vscode": { - "interpreter": { - "hash": "78db47bee367e3fae825d59af43d695909ce208402094df58551906768c6e91c" - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/notebooks/simulate-ring.ipynb b/notebooks/simulate-ring.ipynb deleted file mode 100644 index 358db99..0000000 --- a/notebooks/simulate-ring.ipynb +++ /dev/null @@ -1,985 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "417f4911", - "metadata": {}, - "source": [ - "# Simulate Kuramoto on a hypergraph ring" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "8da1197d", - "metadata": {}, - "outputs": [], - "source": [ - "import sys\n", - "from pathlib import Path\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import pandas as pd\n", - "import seaborn as sb\n", - "from tqdm import tqdm\n", - "\n", - "sys.path.append(\"../code/\")\n", - "\n", - "import xgi\n", - "from hypersync_draw import *\n", - "from hypersync_generate import *\n", - "from hypersync_identify import *\n", - "from hypersync_integrate import *\n", - "\n", - "sb.set_theme(style=\"ticks\", context=\"notebook\")\n", - "\n", - "results_dir = \"../results/\"\n", - "data_dir = \"../data/\"\n", - "\n", - "Path(results_dir).mkdir(parents=True, exist_ok=True)\n", - "Path(data_dir).mkdir(parents=True, exist_ok=True)" - ] - }, - { - "cell_type": "markdown", - "id": "9775a80e", - "metadata": {}, - "source": [ - "## Generate structure" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "7ece7682", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Unnamed Hypergraph with 83 nodes and 0 hyperedges\n" - ] - } - ], - "source": [ - "N = 83\n", - "H = xgi.trivial_hypergraph(N)\n", - "\n", - "r1 = 2\n", - "r2 = 2\n", - "\n", - "print(H)" - ] - }, - { - "cell_type": "markdown", - "id": "388376d1", - "metadata": {}, - "source": [ - "## Dynamics" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "91f4e739", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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yaubJd3km4an/JSZOhKdp/IK7ePb/fmlO6Kg92qpBJBQYS5ph1Ey0CJeFyc+mXQKmIkwAUxEmgKkIE8BUhAlgKsIEMBVhApiKMAFMRZgApiJMAP8Dh3hrnwK0BOcAAAAASUVORK5CYII=\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Set parameters\n", - "\n", - "# dynamical\n", - "k1 = 1 # pairwise coupling strength\n", - "k2 = 1 # triplet coupling strength\n", - "omega = 0 # 1 * np.ones(N) # np.random.normal(size=N) #1 * np.ones(N)\n", - "\n", - "ic = \"random\" # initial condition type, see below\n", - "noise = 0 # noise strength\n", - "\n", - "psi_init = generate_state(N=83, kind=ic,noise=noise)\n", - "\n", - "# integration\n", - "t_end = 400\n", - "dt = 0.01\n", - "times = np.arange(0, t_end + dt / 2, dt)\n", - "integrator = \"RK45\"\n", - "\n", - "tag_params = f\"k1_{k1}_k2_{k2}_ic_{ic}\"\n", - "\n", - "fig, ax = plt.subplots(figsize=(1, 1))\n", - "plot_phases(psi_init, it=None, ax=ax)\n", - "plt.show()\n" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "88c5c993", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|███████████████████████████████████████████| 10/10 [00:01<00:00, 5.97it/s]\n" - ] - } - ], - "source": [ - "n_reps = 10\n", - "\n", - "# simulate\n", - "\n", - "thetas_arr = np.zeros((n_reps, N, len(times)))\n", - "\n", - "for i in tqdm(range(n_reps)):\n", - " psi_init = generate_state(N, kind=\"random\", noise=noise)\n", - "\n", - " thetas, times = simulate_kuramoto(\n", - " H,\n", - " k1=k1,\n", - " k2=k2,\n", - " omega=omega,\n", - " theta_0=psi_init,\n", - " t_end=t_end,\n", - " dt=dt,\n", - " rhs=rhs_ring_nb,\n", - " integrator=integrator,\n", - " args=(r1, r2),\n", - " t_eval=False,\n", - " )\n", - "\n", - " thetas_arr[i] = thetas" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "df36a858", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "(-2, True)\n", - "-2-twisted\n" - ] - }, - { - "data": { - "image/png": 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\n", 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot the last repetition\n", - "i = 4\n", - "fig, axs = plot_sync(thetas_arr[i], times)\n", - "\n", - "axs[0, 1].set_title(f\"$t={times[0]}$s\", fontsize=\"x-small\")\n", - "axs[1, 1].set_title(f\"$t={times[-1]}$s\", fontsize=\"x-small\")\n", - "\n", - "axs[0, 0].set_xlabel(\"\")\n", - "axs[1, 0].legend(loc=\"best\", fontsize=\"x-small\")\n", - "\n", - "plt.subplots_adjust(hspace=0.5, top=0.8)\n", - "\n", - "fig.suptitle(tag_params, fontsize=\"small\")\n", - "\n", - "# only to viz twisted states\n", - "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(4, 1), width_ratios=[2, 1])\n", - "\n", - "ax1.plot(thetas_arr[i, :, -1] % (2 * np.pi), \"o\", mfc=\"w\", alpha=0.5)\n", - "ax1.plot(thetas_arr[i, :, -10000] % (2 * np.pi), \"o\", mfc=\"w\", alpha=0.5)\n", - "ax1.set_ylabel(\"phases\")\n", - "ax1.set_xlabel(\"node idx\")\n", - "\n", - "ax1.set_title(identify_state(thetas_arr[i], atol=0.01))\n", - "\n", - "pos = xgi.circular_layout(H)\n", - "ax2, ims = xgi.draw_nodes(\n", - " H,\n", - " pos=pos,\n", - " node_fc=thetas_arr[i, :, -1] % (2 * np.pi),\n", - " node_fc_cmap=\"twilight\",\n", - " node_size=5,\n", - " node_lw=0.1,\n", - " vmin=0,\n", - " vmax=6.28,\n", - ")\n", - "plt.colorbar(ims, label=\"phase value\")\n", - "\n", - "print(identify_winding_number(thetas_arr[i], t=-1))\n", - "# print(winding_number(thetas_arr[i].T, N, -1, atol=0.5))\n", - "print(identify_state(thetas_arr[i], atol=0.001))" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "098fa4f4", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'-1-twisted',\n", - " '-2-twisted',\n", - " '0-twisted',\n", - " '1-twisted',\n", - " '2-twisted',\n", - " '3-twisted'}" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "states = [identify_state(thetas, atol=0.01) for thetas in thetas_arr]\n", - "set(states)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "6af16e8c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(array(['-1-twisted', '-2-twisted', '0-twisted', '1-twisted', '2-twisted',\n", - " '3-twisted'], dtype='" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "###### Set parameters\n", - "\n", - "# dynamical\n", - "k1 = 1 # pairwise coupling strength\n", - "k2 = 0 # triplet coupling strength\n", - "omega = 1 * np.ones(N) # np.random.normal(size=N) #1 * np.ones(N)\n", - "\n", - "ic = \"random\" # initial condition type, see below\n", - "noise = 0 # noise strength\n", - "\n", - "psi_init = generate_state(N, kind=ic, noise=noise)\n", - "\n", - "# integration\n", - "t_end = 200\n", - "dt = 0.01\n", - "times = np.arange(0, t_end + dt / 2, dt)\n", - "\n", - "tag_params = f\"k1_{k1}_k2_{k2}_ic_{ic}\"\n", - "\n", - "fig, ax = plt.subplots(figsize=(1, 1))\n", - "plot_phases(psi_init, it=None, ax=ax)\n", - "plt.show()\n", - "\n", - "# only to viz twisted states\n", - "fig, ax = plt.subplots(figsize=(2, 2))\n", - "ax, ims = xgi.draw(\n", - " H, pos=pos, node_fc=psi_init % (2 * np.pi), node_fc_cmap=\"twilight\", node_size=5\n", - ")\n", - "plt.colorbar(ims[0], label=\"phase value\")" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "281fcca2", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 25.16it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 19.15it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 17.40it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 14.19it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 12.03it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:00<00:00, 10.57it/s]\n", - "100%|███████████████████████████████████████████| 10/10 [00:01<00:00, 9.34it/s]\n" - ] - } - ], - "source": [ - "n_reps = 10\n", - "\n", - "k2s = [0, 0.5, 1, 1.5, 2, 2.5, 3]\n", - "\n", - "# simulate\n", - "\n", - "thetas_arr = np.zeros((n_reps, len(k2s), N, len(times)))\n", - "\n", - "for j, k2 in enumerate(k2s):\n", - " for i in tqdm(range(n_reps)):\n", - " psi_init = generate_state(N, kind=\"random\", noise=noise)\n", - "\n", - " thetas, times = simulate_kuramoto(\n", - " H,\n", - " k1=k1,\n", - " k2=k2,\n", - " omega=omega,\n", - " theta_0=psi_init,\n", - " t_end=t_end,\n", - " dt=dt,\n", - " rhs=rhs_ring_nb,\n", - " integrator=integrator,\n", - " args=(r1, r2),\n", - " t_eval=False,\n", - " )\n", - "\n", - " thetas_arr[i, j] = thetas" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "82eace5c", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "100%|█████████████████████████████████████████████| 7/7 [00:03<00:00, 2.05it/s]\n" - ] - } - ], - "source": [ - "results = {}\n", - "\n", - "for j, k2 in enumerate(tqdm(k2s)):\n", - " states = [identify_state(thetas, atol=0.5) for thetas in thetas_arr[:, j]]\n", - " states_unique, counts = np.unique(states, return_counts=True)\n", - " probs = counts / n_reps\n", - "\n", - " results[k2] = {}\n", - " for state, prob in zip(states_unique, probs):\n", - " results[k2][state] = prob" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "e808a398", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{0: {'-1-twisted': 0.1,\n", - " '-2-twisted': 0.2,\n", - " '0-twisted': 0.2,\n", - " '1-twisted': 0.3,\n", - " 'other': 0.1,\n", - " 'sync': 0.1},\n", - " 0.5: {'-1-twisted': 0.3,\n", - " '0-twisted': 0.3,\n", - " '1-twisted': 0.1,\n", - " '2-twisted': 0.3},\n", - " 1: {'-1-twisted': 0.5, '0-twisted': 0.4, '3-twisted': 0.1},\n", - " 1.5: {'-1-twisted': 0.3,\n", - " '-2-twisted': 0.1,\n", - " '-3-twisted': 0.1,\n", - " '0-twisted': 0.2,\n", - " '1-twisted': 0.1,\n", - " '2-twisted': 0.1,\n", - " '3-twisted': 0.1},\n", - " 2: {'-1-twisted': 0.2,\n", - " '-4-twisted': 0.1,\n", - " '0-twisted': 0.1,\n", - " '1-twisted': 0.2,\n", - " 'other': 0.4},\n", - " 2.5: {'-1-twisted': 0.2,\n", - " '-2-twisted': 0.2,\n", - " '-4-twisted': 0.1,\n", - " '3-twisted': 0.1,\n", - " 'other': 0.4},\n", - " 3: {'-2-twisted': 0.1, '-4-twisted': 0.1, 'other': 0.8}}" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "results" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "f8800cb0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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k2-1-twisted-2-twisted0-twisted1-twistedothersync2-twisted3-twisted-3-twisted-4-twisted
00.00.10.20.20.30.10.1NaNNaNNaNNaN
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21.00.5NaN0.4NaNNaNNaNNaN0.1NaNNaN
31.50.30.10.20.1NaNNaN0.10.10.1NaN
42.00.2NaN0.10.20.4NaNNaNNaNNaN0.1
52.50.20.2NaNNaN0.4NaNNaN0.1NaN0.1
63.0NaN0.1NaNNaN0.8NaNNaNNaNNaN0.1
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" - ], - "text/plain": [ - " k2 -1-twisted -2-twisted 0-twisted 1-twisted other sync 2-twisted \\\n", - "0 0.0 0.1 0.2 0.2 0.3 0.1 0.1 NaN \n", - "1 0.5 0.3 NaN 0.3 0.1 NaN NaN 0.3 \n", - "2 1.0 0.5 NaN 0.4 NaN NaN NaN NaN \n", - "3 1.5 0.3 0.1 0.2 0.1 NaN NaN 0.1 \n", - "4 2.0 0.2 NaN 0.1 0.2 0.4 NaN NaN \n", - "5 2.5 0.2 0.2 NaN NaN 0.4 NaN NaN \n", - "6 3.0 NaN 0.1 NaN NaN 0.8 NaN NaN \n", - "\n", - " 3-twisted -3-twisted -4-twisted \n", - "0 NaN NaN NaN \n", - "1 NaN NaN NaN \n", - "2 0.1 NaN NaN \n", - "3 0.1 0.1 NaN \n", - "4 NaN NaN 0.1 \n", - "5 0.1 NaN 0.1 \n", - "6 NaN NaN 0.1 " - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df = pd.DataFrame.from_dict(results, orient=\"index\").reset_index(names=\"k2\")\n", - "df" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "0858afc2", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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k2stateproba
00.0-1-twisted0.1
10.5-1-twisted0.3
21.0-1-twisted0.5
31.5-1-twisted0.3
42.0-1-twisted0.2
............
651.0-4-twistedNaN
661.5-4-twistedNaN
672.0-4-twisted0.1
682.5-4-twisted0.1
693.0-4-twisted0.1
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70 rows × 3 columns

\n", - "
" - ], - "text/plain": [ - " k2 state proba\n", - "0 0.0 -1-twisted 0.1\n", - "1 0.5 -1-twisted 0.3\n", - "2 1.0 -1-twisted 0.5\n", - "3 1.5 -1-twisted 0.3\n", - "4 2.0 -1-twisted 0.2\n", - ".. ... ... ...\n", - "65 1.0 -4-twisted NaN\n", - "66 1.5 -4-twisted NaN\n", - "67 2.0 -4-twisted 0.1\n", - "68 2.5 -4-twisted 0.1\n", - "69 3.0 -4-twisted 0.1\n", - "\n", - "[70 rows x 3 columns]" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df_long = df.melt(id_vars=\"k2\", var_name=\"state\", value_name=\"proba\")\n", - "df_long" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "39040506", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(figsize=(3.4, 2.4))\n", - "g = sb.lineplot(\n", - " data=df_long,\n", - " x=\"k2\",\n", - " y=\"proba\",\n", - " hue=\"state\",\n", - " markers=True,\n", - " ax=ax,\n", - " alpha=0.7,\n", - " style=\"state\",\n", - " # hue_order=[\"sync\", \"2-cluster\", \"other\"]\n", - " legend=True,\n", - ")\n", - "\n", - "g.set(yscale=\"log\")\n", - "\n", - "ax.set_xlabel(\"k2, triplet coupling strength\")\n", - "\n", - "title = f\"all-to-all, {ic} ic, {n_reps} reps \\n rhs_pairwise_triplet_all_asym\"\n", - "ax.set_title(title)\n", - "\n", - "sb.move_legend(g, loc=\"center left\", bbox_to_anchor=(1, 0.5))\n", - "\n", - "\n", - "sb.despine()\n", - "ax.set_ylim(ymax=1.1)\n", - "\n", - "fig_name = f\"basin_size_a2a_ic_{ic}_nreps_{n_reps}_rhs_pairwise_triplet_all_asym\"\n", - "\n", - "# plt.savefig(f\"{results_dir}{fig_name}.png\", dpi=300, bbox_inches=\"tight\")" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "6c59dd93", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0-twisted'" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot the last repetition\n", - "i = 5\n", - "j = 3\n", - "fig, axs = plot_sync(thetas_arr[i, j], times)\n", - "\n", - "axs[0, 1].set_title(f\"$t={times[0]}$s\", fontsize=\"x-small\")\n", - "axs[1, 1].set_title(f\"$t={times[-1]}$s\", fontsize=\"x-small\")\n", - "\n", - "axs[0, 0].set_xlabel(\"\")\n", - "axs[1, 0].legend(loc=\"best\", fontsize=\"x-small\")\n", - "\n", - "plt.subplots_adjust(hspace=0.5, top=0.8)\n", - "\n", - "identify_state(thetas_arr[i, j])\n", - "\n", - "# fig.suptitle(tag_params, fontsize=\"small\")\n", - "\n", - "# only to viz twisted states\n", - "# fig, ax = plt.subplots(figsize=(3, 3))\n", - "# ax, ims = xgi.draw(\n", - "# H, pos=pos, node_fc=thetas_arr[i,j,-1] % (2 * np.pi), node_fc_cmap=\"twilight\", node_size=5\n", - "# )\n", - "# plt.colorbar(ims[0], label=\"phase value\")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6b401ca1", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "venv_xgi", - "language": "python", - "name": "venv_xgi" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13" - }, - "toc": { - "base_numbering": 1, - "nav_menu": {}, - "number_sections": true, - "sideBar": true, - "skip_h1_title": false, - "title_cell": "Table of Contents", - "title_sidebar": "Contents", - "toc_cell": false, - "toc_position": {}, - "toc_section_display": true, - "toc_window_display": true - }, - "vscode": { - "interpreter": { - "hash": "78db47bee367e3fae825d59af43d695909ce208402094df58551906768c6e91c" - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -}