Generate mock data for Rh ct cosmology.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "The cosmology is Rh=ct cosmology. DL=(1+z)*(c/H0)*ln(1+z), calculate the conditonal prior DL for H_0 P(dl|H_0) and normolization;\n",
    "Given DL H0 solve z need the lamvert w function;\n",
    "c_l is the speed of light 3*10^5 km/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import bilby\n",
    "from scipy import interpolate\n",
    "from matplotlib import pyplot as plt\n",
    "import random\n",
    "from scipy import integrate\n",
    "from scipy.special import lambertw\n",
    "#####################################\n",
    "outdir='outdir'\n",
    "c_l=3*10**5\n",
    "def ogetz(dl,H0):\n",
    "    '''\n",
    "    dl is the luminosity distance\n",
    "    H0 is the Hubble constant\n",
    "    return reshift z given H0 dl\n",
    "    '''\n",
    "    t=dl*H0/(3*10**5)\n",
    "    return (np.exp(lambertw(t))-1).real\n",
    "def PDL(DL,H0):\n",
    "    '''\n",
    "    prior for DL\n",
    "    return probability\n",
    "    '''\n",
    "    z=ogetz(DL,H0)\n",
    "    return (DL*DL)/((1+z)**3)\n",
    "def normPDL(DL,H0):\n",
    "    '''\n",
    "    Normalize the prior for DL\n",
    "    Normalize area DL [0,30400Mpc]\n",
    "    '''\n",
    "    ss=np.trapz(PDL(np.arange(0,30400,100),H0),np.arange(0,30400,100))\n",
    "    return PDL(DL,H0)/ss  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "P(m1),P(m2) source frame\n",
    "the prior for m1 m2 in source frame, according Colm&Eric paper\n",
    "the ture value for parameter form Colm&Eric paper and Rory's code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [],
   "source": [
    "#mmin is the min value for m1\n",
    "alpha=1.5\n",
    "mmax=40\n",
    "lamda=0.1\n",
    "mpp=35\n",
    "deltapp=1.0\n",
    "beta=-0.2\n",
    "mmin=8\n",
    "deltam=0.1\n",
    "def fm(m):\n",
    "    return deltam/(m)-(deltam/((m-deltam)))\n",
    "def Sm(m):\n",
    "    return 1/(np.exp(fm(m-2.901))+1)\n",
    "def ppow(m):\n",
    "    return (m**(-1*alpha))*Sm(m)\n",
    "def ppp(m):\n",
    "    return np.exp(-1*(m-mpp)**2/(2*deltapp*deltapp))*Sm(m)\n",
    "def Pm1(m):\n",
    "    return ((1-lamda)*ppow(m)+lamda*ppp(m))\n",
    "def Pm2(m2,m):\n",
    "    return ((m2/m)**beta)*Sm(m2)\n",
    "def normPm1(m):\n",
    "    ss=np.trapz(Pm1(np.arange(mmin,40.5,0.5)),np.arange(mmin,40.5,0.5))\n",
    "    return (Pm1(m)/ss)\n",
    "def normPm2(m2,m):\n",
    "    ss=np.trapz(Pm2(np.arange(mmin,40.5,0.5),40),np.arange(mmin,40.5,0.5))\n",
    "    return Pm2(m2,m)/ss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the prior to generate the mock data samples DL m1 m2;\n",
    "The number of event is choiceN;\n",
    "deltadl is the step for DL; "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "choiceN=10000\n",
    "deltadl=30\n",
    "sampdl = random.choices(np.arange(1,30030,deltadl),PDL(np.arange(1,30030,deltadl),70), k=choiceN)\n",
    "sampz=ogetz(np.array(sampdl),70) #rhct cosmology\n",
    "sampm1 = random.choices(np.arange(8,40.5,0.5),Pm1(np.arange(8,40.5,0.5)), k=choiceN)\n",
    "sampm1z=(np.array(sampz)+1)*np.array(sampm1)\n",
    "temsampm2=np.zeros((choiceN,1))\n",
    "for i in range(choiceN):\n",
    "    temsampm2[i,:] = random.choices(np.arange(8,(sampm1[i]+0.5),0.5),Pm2(np.arange(8,(sampm1[i]+0.5),0.5),sampm1[i]),k=1)\n",
    "sampm2=temsampm2.flatten()\n",
    "sampm2z=np.array(sampm2)*((np.array(sampz)+1))\n",
    "sampq=sampm2/sampm1\n",
    "sampdl=np.array(sampdl)\n",
    "sampm1z=np.array(sampm1z)\n",
    "sampm2z=np.array(sampm2z)\n",
    "plt.hist(sampm2,20,alpha=0.4,density=False,label='SuorceFrame m2')\n",
    "plt.hist(sampm1,20,alpha=0.5,density=False,label='SuorceFrame m1')\n",
    "plt.legend(prop={'size': 16})\n",
    "plt.xlabel(r'$mass(M\\odot)$')\n",
    "plt.ylabel(r'$Events$')\n",
    "plt.legend(loc='upper right')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to prior for the other 12 parameters a_1 a_2 ......;\n",
    "the prior form bilby.gw.prior;\n",
    "add the samples DL m1 m2 to the other 12 parameters samples;\n",
    "return: [events x 15] array txt file, event=10000;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "label = 'samplesdata'\n",
    "bilby.core.utils.setup_logger(outdir=outdir, label=label)\n",
    "duration = 4\n",
    "sampling_frequency = 2048\n",
    "geocent_time_random=np.random.uniform(10**9,10**10,choiceN)\n",
    "a_1_prior         =bilby.gw.prior.Uniform(minimum=0, maximum=0.8, name='a_1', latex_label='$a_1$', unit=None, periodic_boundary=False)\n",
    "a_2_prior         =bilby.gw.prior.Uniform(minimum=0, maximum=0.8, name='a_2', latex_label='$a_2$', unit=None, periodic_boundary=False)\n",
    "tilt_1_prior      =bilby.core.prior.Sine(name='tilt_1', latex_label='$\\\\theta_1$', unit=None, minimum=0, maximum=3.141592653589793, periodic_boundary=False)\n",
    "tilt_2_prior      =bilby.core.prior.Sine(name='tilt_1', latex_label='$\\\\theta_1$', unit=None, minimum=0, maximum=3.141592653589793, periodic_boundary=False)\n",
    "phi_12_prior      =bilby.gw.prior.Uniform(minimum=0, maximum=6.283185307179586, name='phi_12', latex_label='$\\\\Delta\\\\phi$', unit=None, periodic_boundary=True)\n",
    "phi_jl_prior      =bilby.gw.prior.Uniform(minimum=0, maximum=6.283185307179586, name='phi_jl', latex_label='$\\\\phi_{JL}$', unit=None, periodic_boundary=True)\n",
    "theta_jn_prior    =bilby.core.prior.Sine(name='theta_jn', latex_label='$\\\\theta_{JN}$', unit=None, minimum=0, maximum=3.141592653589793, periodic_boundary=False)\n",
    "psi_prior         =bilby.gw.prior.Uniform(minimum=0, maximum=3.141592653589793, name='psi', latex_label='$\\\\psi$', unit=None, periodic_boundary=True)\n",
    "phase_prior       =bilby.gw.prior.Uniform(minimum=0, maximum=6.283185307179586, name='phase', latex_label='$\\\\phi$', unit=None, periodic_boundary=True)\n",
    "geocent_time_prior=bilby.gw.prior.Uniform(minimum=geocent_time_random- 1,maximum=geocent_time_random + 1,name='geocent_time', latex_label='$t_c$', unit='$s$')\n",
    "ra_prior          =bilby.gw.prior.Uniform(minimum=0, maximum=6.283185307179586, name='ra', latex_label='$\\\\mathrm{RA}$', unit=None, periodic_boundary=True)\n",
    "dec_prior         =bilby.core.prior.Cosine(name='dec', latex_label='$\\\\mathrm{DEC}$', unit=None, minimum=-1.5707963267948966, maximum=1.5707963267948966, periodic_boundary=False)\n",
    "kk=choiceN#number of event\n",
    "inpa=np.zeros((kk,15))\n",
    "smaples_a_1 = a_1_prior.sample(kk)\n",
    "smaples_a_2 = a_2_prior.sample(kk)\n",
    "smaples_tilt_1 = tilt_1_prior.sample(kk)\n",
    "smaples_tilt_2 = tilt_2_prior.sample(kk)\n",
    "smaples_phi_12 = phi_12_prior.sample(kk)\n",
    "smaples_phi_jl = phi_jl_prior.sample(kk)\n",
    "smaples_theta_jn = theta_jn_prior.sample(kk)\n",
    "smaples_psi = psi_prior.sample(kk)\n",
    "smaples_phase = phase_prior.sample(kk)\n",
    "smaples_geocent_time = geocent_time_prior.sample(kk)\n",
    "smaples_ra = ra_prior.sample(kk)\n",
    "smaples_dec = dec_prior.sample(kk)\n",
    "inpa[:,0]=sampm1z#samples_mass_1\n",
    "inpa[:,1]=sampm2z#smaples_mass_2\n",
    "inpa[:,2]=smaples_a_1\n",
    "inpa[:,3]=smaples_a_2\n",
    "inpa[:,4]=smaples_tilt_1\n",
    "inpa[:,5]=smaples_tilt_2\n",
    "inpa[:,6]=smaples_phi_12\n",
    "inpa[:,7]=smaples_phi_jl\n",
    "inpa[:,8]=sampdl#smaples_luminosity_distance\n",
    "inpa[:,9]=smaples_theta_jn\n",
    "inpa[:,10]=smaples_psi\n",
    "inpa[:,11]=smaples_phase\n",
    "inpa[:,12]=smaples_geocent_time\n",
    "inpa[:,13]=smaples_ra\n",
    "inpa[:,14]=smaples_dec\n",
    "np.savetxt('RHCTcosmology15p.txt',inpa)"
   ]
  }
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