development/test_iparam.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "28809747-f341-4852-a3db-6034e0e483ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "%matplotlib widget\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "db937dee-0cb5-4f36-b5c6-aa18359ef0eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "Rsun = 696000.#  Sun radius in km\n",
    "d2s = 86400 \n",
    "n_sample = 1000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "e20570d9-1845-4356-a5e2-20142a9d8a40",
   "metadata": {},
   "outputs": [],
   "source": [
    "rot_period = np.random.normal(7.5, 0.5, n_sample)\n",
    "r_star =  np.random.normal(1.0, 0.02, n_sample)\n",
    "v_eq =  2* np.pi * r_star * Rsun / (rot_period * d2s )\n",
    "i_star = np.random.normal(98, 15, n_sample)\n",
    "veq_sini = v_eq * np.sin(i_star / 180. * np.pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "1020be15-4d44-4b33-87a2-df0dc9c8f40e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e2f807cc03414f9c89ce5c92dda8c672",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": "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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,4))\n",
    "plt.hist(v_eq, bins=50)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b63fcef-94dd-45d5-a159-caa61d42930e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cea62ba3-a563-4285-b306-342365e78f96",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "0724984f-2029-4a30-862b-48064d465065",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ffb972f394394c188b75463abee527e0",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": "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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAlgAAAGQCAYAAAByNR6YAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAmG0lEQVR4nO3df1BV953/8ReC3CALZ0kIkKtsNLuWyJK4W9ggullsFUwrsvljR2dIbsOuZZPFSFl0jSY7jXF2wBhLupFq25lsnEmNZFpLp/NVWRi3xbBKgizMiibdTqsVyi+T4AUpAYKf7x9ZzvaKQcUPoPB8zNw/OPd97/1cTi3PfO7lEmSMMQIAAIA1s6Z6AQAAANMNgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGAZgQUAAGBZyFQv4E5x5coVtbW1KSIiQkFBQVO9HAAA7hjGGPX29srr9WrWrJmxt0Ng3aC2tjbFx8dP9TIAALhjtbS0aN68eVO9jElBYN2giIgISZ/9jyMyMnKKVwMAwJ2jp6dH8fHx7s/SmYDAukEjLwtGRkYSWAAAjMNMeovNzHghFAAAYBIRWAAAAJYRWAAAAJYRWAAAAJYRWAAAAJYRWAAAAJYRWAAAAJYRWAAAAJYRWAAAAJYRWAAAAJYRWAAAAJYRWAAAAJbxx54BAJhB5m89fN2Z8ztXT8JKpjd2sAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACwjsAAAACyzElglJSUKCgpSYWGhe8wYo+3bt8vr9SosLEzLly/XmTNnAm43MDCgjRs3Kjo6WuHh4crOzlZra2vATHd3t3w+nxzHkeM48vl8unTpUsDMhQsXtGbNGoWHhys6OloFBQUaHBwMmDl9+rTS09MVFhamuXPnaseOHTLG2Hj6AAAAAW45sOrr6/X9739fDz/8cMDxXbt2qbS0VGVlZaqvr1dcXJwyMjLU29vrzhQWFqqiokLl5eWqra3V5cuXlZWVpeHhYXcmJydHTU1NqqysVGVlpZqamuTz+dzrh4eHtXr1avX19am2tlbl5eU6dOiQNm3a5M709PQoIyNDXq9X9fX12rNnj3bv3q3S0tJbffoAAACjmVvQ29trFi5caKqrq016err5xje+YYwx5sqVKyYuLs7s3LnTnf3kk0+M4zjmu9/9rjHGmEuXLpnZs2eb8vJyd+a3v/2tmTVrlqmsrDTGGHP27FkjydTV1bkzJ0+eNJLMBx98YIwx5siRI2bWrFnmt7/9rTtz8OBB4/F4jN/vN8YYs3fvXuM4jvnkk0/cmZKSEuP1es2VK1du6Ln6/X4jyb1PAADuRPc/9/+ue7FtJv4MvaUdrA0bNmj16tVauXJlwPFz586po6NDmZmZ7jGPx6P09HSdOHFCktTQ0KChoaGAGa/Xq6SkJHfm5MmTchxHqamp7sySJUvkOE7ATFJSkrxerzuzatUqDQwMqKGhwZ1JT0+Xx+MJmGlra9P58+dv5VsAAAAwSsh4b1heXq7/+q//Un19/ajrOjo6JEmxsbEBx2NjY/Wb3/zGnQkNDVVUVNSomZHbd3R0KCYmZtT9x8TEBMxc/ThRUVEKDQ0NmJk/f/6oxxm5bsGCBaMeY2BgQAMDA+7XPT09o2YAAACuZVw7WC0tLfrGN76hH/zgB7rrrrs+dy4oKCjga2PMqGNXu3rmWvM2Zsz/vsH989ZTUlLivrHecRzFx8ePuW4AAIAR4wqshoYGdXV1KTk5WSEhIQoJCVFNTY1ee+01hYSEBOwO/b6uri73uri4OA0ODqq7u3vMmc7OzlGPf/HixYCZqx+nu7tbQ0NDY850dXVJGr3LNmLbtm3y+/3upaWl5frfGAAAAI0zsFasWKHTp0+rqanJvaSkpOiJJ55QU1OTHnjgAcXFxam6utq9zeDgoGpqarR06VJJUnJysmbPnh0w097erubmZncmLS1Nfr9f7733njvz7rvvyu/3B8w0Nzervb3dnamqqpLH41FycrI7c/z48YCPbqiqqpLX6x310uEIj8ejyMjIgAsAAMCNGNd7sCIiIpSUlBRwLDw8XPfcc497vLCwUMXFxVq4cKEWLlyo4uJizZkzRzk5OZIkx3G0fv16bdq0Sffcc4/uvvtubd68WQ899JD7pvlFixbpscceU15enr73ve9Jkv7+7/9eWVlZSkhIkCRlZmYqMTFRPp9Pr7zyij7++GNt3rxZeXl5bhTl5OTopZdeUm5urp5//nn98pe/VHFxsb75zW9e9yVLAACAmzXuN7lfz5YtW9Tf36/8/Hx1d3crNTVVVVVVioiIcGdeffVVhYSEaO3aterv79eKFSu0f/9+BQcHuzMHDhxQQUGB+9uG2dnZKisrc68PDg7W4cOHlZ+fr2XLliksLEw5OTnavXu3O+M4jqqrq7VhwwalpKQoKipKRUVFKioqmqinDwAAZrAgY/g48xvR09Mjx3Hk9/t5uRAAcMeav/XwdWfO71xt9TFn4s9Q/hYhAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZQQWAACAZeMKrH379unhhx9WZGSkIiMjlZaWpqNHj7rXG2O0fft2eb1ehYWFafny5Tpz5kzAfQwMDGjjxo2Kjo5WeHi4srOz1draGjDT3d0tn88nx3HkOI58Pp8uXboUMHPhwgWtWbNG4eHhio6OVkFBgQYHBwNmTp8+rfT0dIWFhWnu3LnasWOHjDHjeeoAAADXNa7Amjdvnnbu3KlTp07p1KlT+vKXv6y//uu/diNq165dKi0tVVlZmerr6xUXF6eMjAz19va691FYWKiKigqVl5ertrZWly9fVlZWloaHh92ZnJwcNTU1qbKyUpWVlWpqapLP53OvHx4e1urVq9XX16fa2lqVl5fr0KFD2rRpkzvT09OjjIwMeb1e1dfXa8+ePdq9e7dKS0vH89QBAACuK8hY2sq5++679corr+jv/u7v5PV6VVhYqOeee07SZ7tVsbGxevnll/X000/L7/fr3nvv1Ztvvql169ZJktra2hQfH68jR45o1apVev/995WYmKi6ujqlpqZKkurq6pSWlqYPPvhACQkJOnr0qLKystTS0iKv1ytJKi8vV25urrq6uhQZGal9+/Zp27Zt6uzslMfjkSTt3LlTe/bsUWtrq4KCgm7o+fX09MhxHPn9fkVGRtr4lgEAMOnmbz183ZnzO1dbfcyZ+DP0lt+DNTw8rPLycvX19SktLU3nzp1TR0eHMjMz3RmPx6P09HSdOHFCktTQ0KChoaGAGa/Xq6SkJHfm5MmTchzHjStJWrJkiRzHCZhJSkpy40qSVq1apYGBATU0NLgz6enpblyNzLS1ten8+fOf+7wGBgbU09MTcAEAALgR4w6s06dP6w/+4A/k8Xj0zDPPqKKiQomJiero6JAkxcbGBszHxsa613V0dCg0NFRRUVFjzsTExIx63JiYmICZqx8nKipKoaGhY86MfD0ycy0lJSXue78cx1F8fPzY3xAAAID/Ne7ASkhIUFNTk+rq6vQP//APeuqpp3T27Fn3+qtfejPGXPfluKtnrjVvY2bkVdGx1rNt2zb5/X730tLSMubaAQAARow7sEJDQ/Unf/InSklJUUlJiRYvXqx//dd/VVxcnKTRu0NdXV3uzlFcXJwGBwfV3d095kxnZ+eox7148WLAzNWP093draGhoTFnurq6JI3eZft9Ho/H/S3JkQsAAMCNsPY5WMYYDQwMaMGCBYqLi1N1dbV73eDgoGpqarR06VJJUnJysmbPnh0w097erubmZncmLS1Nfr9f7733njvz7rvvyu/3B8w0Nzervb3dnamqqpLH41FycrI7c/z48YCPbqiqqpLX69X8+fNtPX0AAADXuALr+eef1zvvvKPz58/r9OnTeuGFF/Tzn/9cTzzxhIKCglRYWKji4mJVVFSoublZubm5mjNnjnJyciRJjuNo/fr12rRpk44dO6bGxkY9+eSTeuihh7Ry5UpJ0qJFi/TYY48pLy9PdXV1qqurU15enrKyspSQkCBJyszMVGJionw+nxobG3Xs2DFt3rxZeXl57o5TTk6OPB6PcnNz1dzcrIqKChUXF6uoqOiGf4MQAADgZoSM50adnZ3y+Xxqb2+X4zh6+OGHVVlZqYyMDEnSli1b1N/fr/z8fHV3dys1NVVVVVWKiIhw7+PVV19VSEiI1q5dq/7+fq1YsUL79+9XcHCwO3PgwAEVFBS4v22YnZ2tsrIy9/rg4GAdPnxY+fn5WrZsmcLCwpSTk6Pdu3e7M47jqLq6Whs2bFBKSoqioqJUVFSkoqKi8Tx1AACA67L2OVjT3Uz8DA8AwPTD52BNDv4WIQAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGUEFgAAgGXjCqySkhL9xV/8hSIiIhQTE6PHH39cv/jFLwJmjDHavn27vF6vwsLCtHz5cp05cyZgZmBgQBs3blR0dLTCw8OVnZ2t1tbWgJnu7m75fD45jiPHceTz+XTp0qWAmQsXLmjNmjUKDw9XdHS0CgoKNDg4GDBz+vRppaenKywsTHPnztWOHTtkjBnP0wcAABjTuAKrpqZGGzZsUF1dnaqrq/Xpp58qMzNTfX197syuXbtUWlqqsrIy1dfXKy4uThkZGert7XVnCgsLVVFRofLyctXW1ury5cvKysrS8PCwO5OTk6OmpiZVVlaqsrJSTU1N8vl87vXDw8NavXq1+vr6VFtbq/Lych06dEibNm1yZ3p6epSRkSGv16v6+nrt2bNHu3fvVmlp6XiePgAAwJiCjIVtnIsXLyomJkY1NTX6q7/6Kxlj5PV6VVhYqOeee07SZ7tVsbGxevnll/X000/L7/fr3nvv1Ztvvql169ZJktra2hQfH68jR45o1apVev/995WYmKi6ujqlpqZKkurq6pSWlqYPPvhACQkJOnr0qLKystTS0iKv1ytJKi8vV25urrq6uhQZGal9+/Zp27Zt6uzslMfjkSTt3LlTe/bsUWtrq4KCgq77HHt6euQ4jvx+vyIjI2/1WwYAwJSYv/XwdWfO71xt9TFn4s9QK+/B8vv9kqS7775bknTu3Dl1dHQoMzPTnfF4PEpPT9eJEyckSQ0NDRoaGgqY8Xq9SkpKcmdOnjwpx3HcuJKkJUuWyHGcgJmkpCQ3riRp1apVGhgYUENDgzuTnp7uxtXITFtbm86fP2/jWwAAAOC65cAyxqioqEh/+Zd/qaSkJElSR0eHJCk2NjZgNjY21r2uo6NDoaGhioqKGnMmJiZm1GPGxMQEzFz9OFFRUQoNDR1zZuTrkZmrDQwMqKenJ+ACAABwI245sJ599ln993//tw4ePDjquqtfejPGXPfluKtnrjVvY2bkldHPW09JSYn7xnrHcRQfHz/mugEAAEbcUmBt3LhRP/3pT/Wzn/1M8+bNc4/HxcVJGr071NXV5e4cxcXFaXBwUN3d3WPOdHZ2jnrcixcvBsxc/Tjd3d0aGhoac6arq0vS6F22Edu2bZPf73cvLS0tY3wnAAAA/s+4AssYo2effVY//vGP9R//8R9asGBBwPULFixQXFycqqur3WODg4OqqanR0qVLJUnJycmaPXt2wEx7e7uam5vdmbS0NPn9fr333nvuzLvvviu/3x8w09zcrPb2dnemqqpKHo9HycnJ7szx48cDPrqhqqpKXq9X8+fPv+Zz9Hg8ioyMDLgAAADciHEF1oYNG/SDH/xAb731liIiItTR0aGOjg719/dL+uxlt8LCQhUXF6uiokLNzc3Kzc3VnDlzlJOTI0lyHEfr16/Xpk2bdOzYMTU2NurJJ5/UQw89pJUrV0qSFi1apMcee0x5eXmqq6tTXV2d8vLylJWVpYSEBElSZmamEhMT5fP51NjYqGPHjmnz5s3Ky8tzoygnJ0cej0e5ublqbm5WRUWFiouLVVRUdEO/QQgAAHAzQsZzo3379kmSli9fHnD8jTfeUG5uriRpy5Yt6u/vV35+vrq7u5WamqqqqipFRES486+++qpCQkK0du1a9ff3a8WKFdq/f7+Cg4PdmQMHDqigoMD9bcPs7GyVlZW51wcHB+vw4cPKz8/XsmXLFBYWppycHO3evdudcRxH1dXV2rBhg1JSUhQVFaWioiIVFRWN5+kDAACMycrnYM0EM/EzPAAA0w+fgzU5+FuEAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAlhFYAAAAloVM9QIAAIA987cenuolQOxgAQAAWEdgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWEZgAQAAWDbuwDp+/LjWrFkjr9eroKAg/eQnPwm43hij7du3y+v1KiwsTMuXL9eZM2cCZgYGBrRx40ZFR0crPDxc2dnZam1tDZjp7u6Wz+eT4zhyHEc+n0+XLl0KmLlw4YLWrFmj8PBwRUdHq6CgQIODgwEzp0+fVnp6usLCwjR37lzt2LFDxpjxPn0AAIDPNe7A6uvr0+LFi1VWVnbN63ft2qXS0lKVlZWpvr5ecXFxysjIUG9vrztTWFioiooKlZeXq7a2VpcvX1ZWVpaGh4fdmZycHDU1NamyslKVlZVqamqSz+dzrx8eHtbq1avV19en2tpalZeX69ChQ9q0aZM709PTo4yMDHm9XtXX12vPnj3avXu3SktLx/v0AQAAPleQsbCNExQUpIqKCj3++OOSPtu98nq9Kiws1HPPPSfps92q2NhYvfzyy3r66afl9/t177336s0339S6deskSW1tbYqPj9eRI0e0atUqvf/++0pMTFRdXZ1SU1MlSXV1dUpLS9MHH3yghIQEHT16VFlZWWppaZHX65UklZeXKzc3V11dXYqMjNS+ffu0bds2dXZ2yuPxSJJ27typPXv2qLW1VUFBQdd9jj09PXIcR36/X5GRkbf6LQMAYELM33r4lu/j/M7VFlbyf2biz9AJeQ/WuXPn1NHRoczMTPeYx+NRenq6Tpw4IUlqaGjQ0NBQwIzX61VSUpI7c/LkSTmO48aVJC1ZskSO4wTMJCUluXElSatWrdLAwIAaGhrcmfT0dDeuRmba2tp0/vz5az6HgYEB9fT0BFwAAABuxIQEVkdHhyQpNjY24HhsbKx7XUdHh0JDQxUVFTXmTExMzKj7j4mJCZi5+nGioqIUGho65szI1yMzVyspKXHf9+U4juLj46//xAEAACSFTOSdX/3SmzHmui/HXT1zrXkbMyOvjH7eerZt26aioiL3656eHiILADClbLz8h8kxITtYcXFxkkbvDnV1dbk7R3FxcRocHFR3d/eYM52dnaPu/+LFiwEzVz9Od3e3hoaGxpzp6uqSNHqXbYTH41FkZGTABQAA4EZMSGAtWLBAcXFxqq6udo8NDg6qpqZGS5culSQlJydr9uzZATPt7e1qbm52Z9LS0uT3+/Xee++5M++++678fn/ATHNzs9rb292ZqqoqeTweJScnuzPHjx8P+OiGqqoqeb1ezZ8/3/43AAAAzGjjDqzLly+rqalJTU1Nkj57Y3tTU5MuXLigoKAgFRYWqri4WBUVFWpublZubq7mzJmjnJwcSZLjOFq/fr02bdqkY8eOqbGxUU8++aQeeughrVy5UpK0aNEiPfbYY8rLy1NdXZ3q6uqUl5enrKwsJSQkSJIyMzOVmJgon8+nxsZGHTt2TJs3b1ZeXp6765STkyOPx6Pc3Fw1NzeroqJCxcXFKioquqHfIAQAALgZ434P1qlTp/SlL33J/Xrk/UpPPfWU9u/fry1btqi/v1/5+fnq7u5WamqqqqqqFBER4d7m1VdfVUhIiNauXav+/n6tWLFC+/fvV3BwsDtz4MABFRQUuL9tmJ2dHfDZW8HBwTp8+LDy8/O1bNkyhYWFKScnR7t373ZnHMdRdXW1NmzYoJSUFEVFRamoqCjgPVYAAAC2WPkcrJlgJn6GBwDg9jJZb3Lnc7BuHX+LEAAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwDICCwAAwLKQqV4AAAD4zPyth6d6CbCEHSwAAADLCCwAAADLCCwAAADLCCwAAADLCCwAAADLCCwAAADLCCwAAADLCCwAAADLCCwAAADLCCwAAADL+FM5AABMEv4UzszBDhYAAIBlBBYAAIBlBBYAAIBlBBYAAIBlBBYAAIBlBBYAAIBlBBYAAIBlBBYAAIBlfNAoAAAW8CGi+H3sYAEAAFhGYAEAAFhGYAEAAFhGYAEAAFhGYAEAAFjGbxECAHAD+C1B3Ax2sAAAACwjsAAAACwjsAAAACzjPVgAgBmP91fBNnawAAAALCOwAAAALOMlQgDAtMdLgJhs7GABAABYRmABAABYxkuEAIA7Gi//4XbEDhYAAIBl7GABAG5r7FDhTkRgAQCmDPGE6WpGBdbevXv1yiuvqL29XX/6p3+qb3/723r00UenelkAMG0RUJipZkxgvf322yosLNTevXu1bNkyfe9739NXvvIVnT17Vn/0R3801csDgDsSAQVcW5Axxkz1IiZDamqqvvjFL2rfvn3usUWLFunxxx9XSUnJdW/f09Mjx3Hk9/sVGRk5kUsFgElBHOHznN+52ur9zcSfoTNiB2twcFANDQ3aunVrwPHMzEydOHHimrcZGBjQwMCA+7Xf75f02f9IAOBWJL3471O9BGBMtn/WjdzfDNnTkTRDAuvDDz/U8PCwYmNjA47Hxsaqo6PjmrcpKSnRSy+9NOp4fHz8hKwRAIDbhfPtibnf3t5eOY4zMXd+m5kRgTUiKCgo4GtjzKhjI7Zt26aioiL36ytXrujjjz/WPffc87m3uR319PQoPj5eLS0tM2Zb9nbFubi9cD5uH5yL28tEnA9jjHp7e+X1eq3c351gRgRWdHS0goODR+1WdXV1jdrVGuHxeOTxeAKO/eEf/uFELXHCRUZG8n9ctwnOxe2F83H74FzcXmyfj5myczViRnySe2hoqJKTk1VdXR1wvLq6WkuXLp2iVQEAgOlqRuxgSVJRUZF8Pp9SUlKUlpam73//+7pw4YKeeeaZqV4aAACYZmZMYK1bt04fffSRduzYofb2diUlJenIkSO6//77p3ppE8rj8ejFF18c9XInJh/n4vbC+bh9cC5uL5wPO2bM52ABAABMlhnxHiwAAIDJRGABAABYRmABAABYRmABAABYRmBNA3v37tWCBQt01113KTk5We+8887nzv74xz9WRkaG7r33XkVGRiotLU3//u/8XTRbbuZc/L7//M//VEhIiP7sz/5sYhc4w9zs+RgYGNALL7yg+++/Xx6PR3/8x3+sf/u3f5uk1U5vN3suDhw4oMWLF2vOnDm677779Ld/+7f66KOPJmm109fx48e1Zs0aeb1eBQUF6Sc/+cl1b1NTU6Pk5GTdddddeuCBB/Td73534hc6DRBYd7i3335bhYWFeuGFF9TY2KhHH31UX/nKV3ThwoVrzh8/flwZGRk6cuSIGhoa9KUvfUlr1qxRY2PjJK98+rnZczHC7/fra1/7mlasWDFJK50ZxnM+1q5dq2PHjun111/XL37xCx08eFAPPvjgJK56errZc1FbW6uvfe1rWr9+vc6cOaMf/vCHqq+v19e//vVJXvn009fXp8WLF6usrOyG5s+dO6evfvWrevTRR9XY2Kjnn39eBQUFOnTo0ASvdBowuKM98sgj5plnngk49uCDD5qtW7fe8H0kJiaal156yfbSZpzxnot169aZf/7nfzYvvviiWbx48QSucGa52fNx9OhR4ziO+eijjyZjeTPKzZ6LV155xTzwwAMBx1577TUzb968CVvjTCTJVFRUjDmzZcsW8+CDDwYce/rpp82SJUsmcGXTAztYd7DBwUE1NDQoMzMz4HhmZqZOnDhxQ/dx5coV9fb26u67756IJc4Y4z0Xb7zxhn71q1/pxRdfnOglzijjOR8//elPlZKSol27dmnu3Ln6whe+oM2bN6u/v38yljxtjedcLF26VK2trTpy5IiMMers7NSPfvQjrV69ejKWjN9z8uTJUedu1apVOnXqlIaGhqZoVXeGGfNJ7tPRhx9+qOHh4VF/sDo2NnbUH7b+PN/61rfU19entWvXTsQSZ4zxnItf/vKX2rp1q9555x2FhPBP0abxnI9f//rXqq2t1V133aWKigp9+OGHys/P18cff8z7sG7BeM7F0qVLdeDAAa1bt06ffPKJPv30U2VnZ2vPnj2TsWT8no6Ojmueu08//VQffvih7rvvvila2e2PHaxpICgoKOBrY8yoY9dy8OBBbd++XW+//bZiYmImankzyo2ei+HhYeXk5Oill17SF77whcla3oxzM/82rly5oqCgIB04cECPPPKIvvrVr6q0tFT79+9nF8uCmzkXZ8+eVUFBgb75zW+qoaFBlZWVOnfuHH87dopc69xd6zgC8Z/Nd7Do6GgFBweP+q/Arq6uUf/FcbW3335b69ev1w9/+EOtXLlyIpc5I9zsuejt7dWpU6fU2NioZ599VtJnP+CNMQoJCVFVVZW+/OUvT8rap6Px/Nu47777NHfuXDmO4x5btGiRjDFqbW3VwoULJ3TN09V4zkVJSYmWLVumf/qnf5IkPfzwwwoPD9ejjz6qf/mXf2HXZBLFxcVd89yFhITonnvumaJV3RnYwbqDhYaGKjk5WdXV1QHHq6urtXTp0s+93cGDB5Wbm6u33nqL9zRYcrPnIjIyUqdPn1ZTU5N7eeaZZ5SQkKCmpialpqZO1tKnpfH821i2bJna2tp0+fJl99j//M//aNasWZo3b96Ernc6G8+5+N3vfqdZswJ/PAUHB0v6v90TTI60tLRR566qqkopKSmaPXv2FK3qDjFlb6+HFeXl5Wb27Nnm9ddfN2fPnjWFhYUmPDzcnD9/3hhjzNatW43P53Pn33rrLRMSEmK+853vmPb2dvdy6dKlqXoK08bNnour8VuEdt3s+ejt7TXz5s0zf/M3f2POnDljampqzMKFC83Xv/71qXoK08bNnos33njDhISEmL1795pf/epXpra21qSkpJhHHnlkqp7CtNHb22saGxtNY2OjkWRKS0tNY2Oj+c1vfmOMGX0ufv3rX5s5c+aYf/zHfzRnz541r7/+upk9e7b50Y9+NFVP4Y5BYE0D3/nOd8z9999vQkNDzRe/+EVTU1PjXvfUU0+Z9PR09+v09HQjadTlqaeemvyFT0M3cy6uRmDZd7Pn4/333zcrV640YWFhZt68eaaoqMj87ne/m+RVT083ey5ee+01k5iYaMLCwsx9991nnnjiCdPa2jrJq55+fvazn435M+Ba5+LnP/+5+fM//3MTGhpq5s+fb/bt2zf5C78DBRnDfisAAIBNvAcLAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAMgILAADAsv8PdHAHxQFETmkAAAAASUVORK5CYII=' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ratio = veq_sini / v_eq\n",
    "plt.figure(figsize=(6,4))\n",
    "plt.hist(ratio, bins=50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f2a15456-de4b-4642-b297-9ca7b93c4019",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "ratio = veq_sini / v_eq\n",
    "sel = (ratio > 1.)\n",
    "ratio[sel] -= 2. \n",
    "i_star_derived = np.arcsin(ratio) / np.pi * 180.\n",
    "print(np.sum(sel))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "14ac6cc5-b8e1-46e6-81ff-0070460204cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2ef2d25f47724e35aa4cf19add15710f",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": "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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img src='data:image/png;base64,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' width=600.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,4))\n",
    "plt.hist(i_star, bins=50)\n",
    "plt.hist(i_star_derived, bins=50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4d924fa1-de4d-4f9b-b9be-d05f27988888",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.17"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}