hr8799_replicate.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: rebound in /Users/hurum/.pyenv/versions/3.9.18/lib/python3.9/site-packages (4.3.2)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m23.0.1\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.0\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "!pip install rebound"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import rebound\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "from scipy.interpolate import CubicSpline\n",
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def integrate_to_mean_anomaly_16pi(sim, body_index):\n",
    "    target_mean_anomaly = 16 * np.pi\n",
    "    initial_time_step = 0.02\n",
    "    time_step = initial_time_step\n",
    "    M=[0]\n",
    "    time=[sim.t]\n",
    "    current_mean_anomaly = 0\n",
    "    N_peri=0\n",
    "    while True:\n",
    "        sim.integrate(sim.t + time_step)\n",
    "        current_mean_anomaly = sim.particles[1].M +N_peri*np.pi\n",
    "        if current_mean_anomaly  - M[len(M)-1] < 0:\n",
    "          N_peri = N_peri+ 2\n",
    "          current_mean_anomaly = current_mean_anomaly +2*np.pi\n",
    "          time.append(sim.t)\n",
    "          M.append(sim.particles[1].M+ N_peri*np.pi)\n",
    "        else:\n",
    "          time.append(sim.t)\n",
    "          M.append(sim.particles[1].M+ N_peri*np.pi)\n",
    "          \n",
    "        if current_mean_anomaly  > target_mean_anomaly:\n",
    "          f = CubicSpline(M, time)\n",
    "          sim.integrate(f(target_mean_anomaly))\n",
    "          break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimizing_function(theta):\n",
    "  initial_e_1,initial_e_2, initial_e_3,initial_e_4,mean_anomaly_2, mean_anomaly_3,mean_anomaly_4, X_5,X_6,pomega_2, pomega_3, pomega_4 =theta\n",
    "  pomega_1 =0\n",
    "  kappa=2.035\n",
    "  rho = 1\n",
    "  ini_param = [initial_e_1,initial_e_2, initial_e_3,initial_e_4,mean_anomaly_2, mean_anomaly_3,mean_anomaly_4, X_5,X_6, pomega_2, pomega_3, pomega_4]\n",
    "  C_0 = 0.5\n",
    "  C_1 = 0.5\n",
    "  mean_anomaly_1 = 0\n",
    "  a_1=  rho*1\n",
    "  a_2=  a_1*kappa**(2/3)\n",
    "  pd_pc_nom = (1+C_0*(1-kappa))**(-1)\n",
    "  pe_pd_nom = (1+C_1*(1-pd_pc_nom))**(-1)\n",
    " \n",
    "  a_3=  a_2*(X_5+pd_pc_nom)**(2/3)\n",
    "  a_4=  a_3*(X_6+pe_pd_nom)**(2/3)\n",
    "\n",
    "  \n",
    "  sim = rebound.Simulation()\n",
    "  sim.add(m=2)\n",
    "  sim.add(m=3e-5, a=a_1, e=initial_e_1, M=mean_anomaly_1, pomega=pomega_1)\n",
    "  sim.add(m=5e-5, a=a_2, e=initial_e_2, M=mean_anomaly_2, pomega=pomega_2)\n",
    "  sim.add(m=7e-5, a=a_3, e=initial_e_3, M=mean_anomaly_3, pomega=pomega_3)\n",
    "  sim.add(m=9e-4, a=a_4, e=initial_e_4, M=mean_anomaly_4, pomega=pomega_4)\n",
    "  sim.move_to_com()\n",
    "\n",
    "  integrate_to_mean_anomaly_16pi(sim, 1)\n",
    "\n",
    "\n",
    "  sim.move_to_com()\n",
    "\n",
    "\n",
    "  end_param = [sim.particles[1].e,sim.particles[2].e,sim.particles[3].e,sim.particles[4].e, sim.particles[2].M,sim.particles[3].M,sim.particles[4].M, (sim.particles[3].a)**(3/2)/(sim.particles[2].a)**(3/2) - pd_pc_nom, (sim.particles[4].a)**(3/2)/(sim.particles[3].a)**(3/2) - pe_pd_nom, sim.particles[1].pomega,sim.particles[2].pomega, sim.particles[3].pomega,  sim.particles[4].pomega]\n",
    "  difference =[]\n",
    "  \n",
    "\n",
    "  for i in range(0,8):\n",
    "    difference.append(ini_param[i]-end_param[i])\n",
    "  difference.append((pomega_1-ini_param[9])-(end_param[9]-end_param[10]))\n",
    "  difference.append((ini_param[9]-ini_param[10])-(end_param[10]-end_param[11]))\n",
    "  difference.append((ini_param[10]-ini_param[11])-(end_param[11]-end_param[12]))\n",
    "\n",
    "  return np.sqrt(difference[0]**2+difference[1]**2+difference[2]**2+difference[3]**2+difference[4]**2+difference[5]**2+difference[6]**2+difference[7]**2+difference[8]**2+difference[9]**2+difference[10]**2)\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "ini_guess=[ 0.03,0.05,0.05,0.08, 1 ,0.5,0.5, 0.01 , 0.01,  1,1,1]\n",
    "\n",
    "bounds = [ (0, 0.99),(0, 0.99),(0, 0.99),(0, 0.99), (None, None), (None, None), (None, None),  (-.5, .5), (-.5, .5),  (None, None), (None, None), (None, None)]\n",
    "result = minimize(optimizing_function, ini_guess, bounds=bounds, tol=1e-6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.74232758e-01  8.18687387e-01  5.67820900e-01  5.81138501e-02\n",
      "  9.17489880e-01  4.82999517e-01  3.47675095e-01 -6.24625847e-04\n",
      "  1.61905447e-03  1.05840082e+00  1.03243636e+00  8.65807475e-01]\n"
     ]
    }
   ],
   "source": [
    "print(result.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([0.27423276, 0.81868739, 0.5678209 , 0.05811385])]\n"
     ]
    }
   ],
   "source": [
    "kappa_list=[2]\n",
    "e_list=[]\n",
    "e_list.append(result.x[:4])\n",
    "print(e_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1.5874010519681994 2.5193174196415953 4.00132512088794\n"
     ]
    }
   ],
   "source": [
    "initial_e_1,initial_e_2, initial_e_3,initial_e_4,mean_anomaly_2, mean_anomaly_3,mean_anomaly_4, X_5,X_6,pomega_2, pomega_3, pomega_4 =(result.x)\n",
    "\n",
    "C_0 = 0.5\n",
    "C_1 = 0.5\n",
    "mean_anomaly_1 = 0\n",
    "rho=1\n",
    "kappa = 2\n",
    "a_1=  rho*1\n",
    "a_2=  a_1*kappa**(2/3)\n",
    "pd_pc_nom = (1+C_0*(1-kappa))**(-1)\n",
    "pe_pd_nom = (1+C_1*(1-pd_pc_nom))**(-1)\n",
    "a_3=  a_2*(X_5+pd_pc_nom)**(2/3)\n",
    "a_4=  a_3*(X_6+pe_pd_nom)**(2/3)\n",
    "\n",
    "print(a_1,a_2,a_3,a_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.999999999999999"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.9240177382128656**(3/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<rebound.plotting.OrbitPlot at 0x16983ac10>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_e_1,initial_e_2, initial_e_3,initial_e_4,mean_anomaly_2, mean_anomaly_3,mean_anomaly_4, X_5,X_6,pomega_2, pomega_3, pomega_4 =(result.x)\n",
    "\n",
    "sim = rebound.Simulation()\n",
    "pomega_1=0\n",
    "C_0 = 0.5\n",
    "C_1 = 0.5\n",
    "mean_anomaly_1 = 0\n",
    "a_1=  rho*1\n",
    "a_2=  a_1*kappa**(2/3)\n",
    "pd_pc_nom = (1+C_0*(1-kappa))**(-1)\n",
    "pe_pd_nom = (1+C_1*(1-pd_pc_nom))**(-1)\n",
    " \n",
    "a_3=  a_2*(X_5+pd_pc_nom)**(2/3)\n",
    "a_4=  a_3*(X_6+pe_pd_nom)**(2/3)\n",
    "\n",
    "sim.add(m=2)\n",
    "sim.add(m=3e-5, a=a_1, e=initial_e_1, M=mean_anomaly_1, pomega=pomega_1)\n",
    "sim.add(m=5e-5, a=a_2, e=initial_e_2, M=mean_anomaly_2, pomega=pomega_2)\n",
    "sim.add(m=7e-5, a=a_3, e=initial_e_3, M=mean_anomaly_3, pomega=pomega_3)\n",
    "sim.add(m=9e-4, a=a_4, e=initial_e_4, M=mean_anomaly_4, pomega=pomega_4)\n",
    "\n",
    "sim.move_to_com()\n",
    "\n",
    "rebound.OrbitPlot(sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.44308444039416\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_e_1,initial_e_2, initial_e_3,initial_e_4,mean_anomaly_2, mean_anomaly_3,mean_anomaly_4, X_5,X_6,pomega_2, pomega_3, pomega_4 =(result.x)\n",
    "\n",
    "sim = rebound.Simulation()\n",
    "\n",
    "C_0 = 0.5\n",
    "C_1 = 0.5\n",
    "mean_anomaly_1 = 0\n",
    "a_1=  rho*1\n",
    "a_2=  a_1*kappa**(2/3)\n",
    "pd_pc_nom = (1+C_0*(1-kappa))**(-1)\n",
    "pe_pd_nom = (1+C_1*(1-pd_pc_nom))**(-1)\n",
    " \n",
    "a_3=  a_2*(X_5+pd_pc_nom)**(2/3)\n",
    "a_4=  a_3*(X_6+pe_pd_nom)**(2/3)\n",
    "\n",
    "sim.add(m=2)\n",
    "sim.add(m=3e-5, a=a_1, e=initial_e_1, M=mean_anomaly_1, pomega=pomega_1)\n",
    "sim.add(m=5e-5, a=a_2, e=initial_e_2, M=mean_anomaly_2, pomega=pomega_2)\n",
    "sim.add(m=7e-5, a=a_3, e=initial_e_3, M=mean_anomaly_3, pomega=pomega_3)\n",
    "sim.add(m=9e-4, a=a_4, e=initial_e_4, M=mean_anomaly_4, pomega=pomega_4)\n",
    "sim.move_to_com()\n",
    "integrate_to_mean_anomaly_16pi(sim, 1)\n",
    "rebound.OrbitPlot(sim)\n",
    "print(sim.particles[1].P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.838709851113629e-07\n",
      "6.11172679172604e-07\n",
      "1.1138893017205625e-05\n"
     ]
    }
   ],
   "source": [
    "sim = rebound.Simulation()\n",
    "sim.add(m=2)\n",
    "sim.add(m=3e-5, a=a_1, e=initial_e_1, M=mean_anomaly_1, pomega=0)\n",
    "sim.add(m=5e-5, a=a_2, e=initial_e_2, M=mean_anomaly_2, pomega=pomega_2)\n",
    "sim.add(m=7e-5, a=a_3, e=initial_e_3, M=mean_anomaly_3, pomega=pomega_3)\n",
    "sim.add(m=9e-4, a=a_4, e=initial_e_4, M=mean_anomaly_4, pomega=pomega_4)\n",
    "sim.move_to_com()\n",
    "ab_cart_initial= [sim.particles[1].x- sim.particles[2].x, sim.particles[1].y-sim.particles[2].y]\n",
    "bc_cart_initial= [sim.particles[2].x-sim.particles[3].x, sim.particles[2].y- sim.particles[3].y]\n",
    "cd_cart_initial= [sim.particles[3].x- sim.particles[4].x, sim.particles[3].y-sim.particles[4].y]\n",
    "\n",
    "integrate_to_mean_anomaly_16pi(sim, 1)\n",
    "sim.move_to_com()\n",
    "ab_cart_final= [sim.particles[1].x- sim.particles[2].x, sim.particles[1].y-sim.particles[2].y]\n",
    "bc_cart_final= [sim.particles[2].x-sim.particles[3].x, sim.particles[2].y- sim.particles[3].y]\n",
    "cd_cart_final= [sim.particles[3].x-sim.particles[4].x, sim.particles[3].y- sim.particles[4].y]\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "print(sum((x - y) ** 2 for x, y in zip(ab_cart_initial, ab_cart_final)))\n",
    "print(sum((x - y) ** 2 for x, y in zip(bc_cart_initial, bc_cart_final)))\n",
    "print(sum((x - y) ** 2 for x, y in zip(cd_cart_initial, cd_cart_final)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "N= 1000\n",
    "transittimes = np.zeros(N)\n",
    "p = sim.particles\n",
    "i = 0\n",
    "while i<N:\n",
    "    y_old = p[1].y - p[0].y\n",
    "    t_old = sim.t\n",
    "    sim.integrate(sim.t+0.5)\n",
    "    t_new = sim.t\n",
    "    if y_old*(p[1].y-p[0].y)<0. and p[1].x-p[0].x>0.:\n",
    "        while t_new-t_old>1e-7:\n",
    "            if y_old*(p[1].y-p[0].y)<0.:\n",
    "                t_new = sim.t\n",
    "            else:\n",
    "                t_old = sim.t\n",
    "            sim.integrate( (t_new+t_old)/2.)\n",
    "        transittimes[i] = sim.t\n",
    "        i += 1\n",
    "        sim.integrate(sim.t+0.05)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.vstack([np.ones(N), range(N)]).T\n",
    "c, m = np.linalg.lstsq(A, transittimes, rcond=-1)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure(figsize=(10,5))\n",
    "ax = plt.subplot(111)\n",
    "\n",
    "ax.set_xlabel(\"Transit number\")\n",
    "ax.set_ylabel(\"TTV [hours]\")\n",
    "plt.scatter(range(N), (transittimes-m*np.array(range(N))-c)*(24.*365./2./np.pi));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting ttvfaster\n",
      "  Downloading ttvfaster-0.1.0.tar.gz (62 kB)\n",
      "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m62.5/62.5 kB\u001b[0m \u001b[31m118.5 kB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0ma \u001b[36m0:00:01\u001b[0m\n",
      "\u001b[?25h  Installing build dependencies ... \u001b[?25ldone\n",
      "\u001b[?25h  Getting requirements to build wheel ... \u001b[?25ldone\n",
      "\u001b[?25h  Preparing metadata (pyproject.toml) ... \u001b[?25ldone\n",
      "\u001b[?25hCollecting Cython\n",
      "  Using cached Cython-3.0.10-py2.py3-none-any.whl (1.2 MB)\n",
      "Requirement already satisfied: numpy in /Users/hurum/.pyenv/versions/3.9.18/lib/python3.9/site-packages (from ttvfaster) (1.26.4)\n",
      "Building wheels for collected packages: ttvfaster\n",
      "  Building wheel for ttvfaster (pyproject.toml) ... \u001b[?25ldone\n",
      "\u001b[?25h  Created wheel for ttvfaster: filename=ttvfaster-0.1.0-cp39-cp39-macosx_13_0_arm64.whl size=38902 sha256=adf6780a751596dd3a18b869636438ae1ad05fa30177a6c02a355ed7e98bb858\n",
      "  Stored in directory: /Users/hurum/Library/Caches/pip/wheels/4f/7c/73/ba6b355ced124003a57f2cb2e62fcf4ed36b74bd3f59d521da\n",
      "Successfully built ttvfaster\n",
      "Installing collected packages: Cython, ttvfaster\n",
      "Successfully installed Cython-3.0.10 ttvfaster-0.1.0\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m23.0.1\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.0\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "!pip install ttvfaster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ttvfaster import run_ttvfaster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}