Using Fisher Matrix to calculate err.ipynb

{
 "cells": [
  {
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   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import bilby\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "duration = 4\n",
    "sampling_frequency = 2048.\n",
    "outdir = 'outdir'\n",
    "label = 'fishermatrixerr'\n",
    "bilby.core.utils.setup_logger(outdir=outdir, label=label)\n",
    "\n",
    "\n",
    "#waveform_generator\n",
    "# Create the waveform_generator using a LAL BinaryBlackHole source function\n",
    "waveform_arguments = dict(waveform_approximant='IMRPhenomPv2',\n",
    "                          reference_frequency=50., minimum_frequency=20.)\n",
    "waveform_generator = bilby.gw.WaveformGenerator(\n",
    "        duration=duration, sampling_frequency=sampling_frequency,\n",
    "        frequency_domain_source_model=bilby.gw.source.lal_binary_black_hole,\n",
    "        waveform_arguments=waveform_arguments)\n",
    "\n",
    "#calculate the polorization signal with 15 parameter and waveform_generator\n",
    "#return h+ hx data array\n",
    "def insig(mass_1,mass_2, a_1, a_2, tilt_1, tilt_2,phi_12, phi_jl, luminosity_distance, theta_jn, psi,phase, geocent_time, ra, dec,waveform_generator=waveform_generator):\n",
    "    injection_parameters=dict(mass_1=mass_1,mass_2=mass_2, a_1=a_1, a_2=a_2, tilt_1=tilt_1, tilt_2=tilt_2,phi_12=phi_12,\\\n",
    "                              phi_jl=phi_jl, luminosity_distance=luminosity_distance, theta_jn=theta_jn, psi=psi,phase=phase, geocent_time=geocent_time, ra=ra, dec=dec)\n",
    "    ifos = bilby.gw.detector.InterferometerList(['ET'])\n",
    "    ifos.set_strain_data_from_power_spectral_densities( ##power spectral\n",
    "        sampling_frequency=sampling_frequency, duration=duration,\n",
    "        start_time=injection_parameters['geocent_time'] - 3)\n",
    "    return ifos.inject_signal(waveform_generator=waveform_generator,parameters=injection_parameters)\n",
    "\n",
    "#calculate the derivative for dl m1 m2 l\n",
    "#return dh/dDL, dh/dm1,dh/dm2,dh/dl \n",
    "def derivative(table,param,tol):\n",
    "    h_pola=insig(table['mass_1'],table['mass_2'],table['a_1'],table['a_2'],table['tilt_1'],table['tilt_2'],table['phi_12'],\\\n",
    "          table['phi_jl'],table['luminosity_distance'],table['theta_jn'],table['psi'],table['phase'],\\\n",
    "          table['geocent_time'],table['ra'],table['dec'],waveform_generator=waveform_generator)\n",
    "    if param =='mass_1':\n",
    "         h_pola_new=insig(table['mass_1']+tol,table['mass_2'],table['a_1'],table['a_2'],table['tilt_1'],table['tilt_2'],table['phi_12'],\\\n",
    "          table['phi_jl'],table['luminosity_distance'],table['theta_jn'],table['psi'],table['phase'],\\\n",
    "          table['geocent_time'],table['ra'],table['dec'],waveform_generator=waveform_generator) \n",
    "    elif param =='mass_2':\n",
    "         h_pola_new=insig(table['mass_1'],table['mass_2']+tol,table['a_1'],table['a_2'],table['tilt_1'],table['tilt_2'],table['phi_12'],\\\n",
    "          table['phi_jl'],table['luminosity_distance'],table['theta_jn'],table['psi'],table['phase'],\\\n",
    "          table['geocent_time'],table['ra'],table['dec'],waveform_generator=waveform_generator) \n",
    "    elif param =='luminosity_distance':\n",
    "         h_pola_new=insig(table['mass_1'],table['mass_2'],table['a_1'],table['a_2'],table['tilt_1'],table['tilt_2'],table['phi_12'],\\\n",
    "          table['phi_jl'],table['luminosity_distance']+tol,table['theta_jn'],table['psi'],table['phase'],\\\n",
    "          table['geocent_time'],table['ra'],table['dec'],waveform_generator=waveform_generator) \n",
    "    elif param=='theta_jn':\n",
    "        h_pola_new=insig(table['mass_1'],table['mass_2'],table['a_1'],table['a_2'],table['tilt_1'],table['tilt_2'],table['phi_12'],\\\n",
    "          table['phi_jl'],table['luminosity_distance'],table['theta_jn']+tol,table['psi'],table['phase'],\\\n",
    "          table['geocent_time'],table['ra'],table['dec'],waveform_generator=waveform_generator)       \n",
    "    else:\n",
    "        raise ValueError('Parameter not supported!')\n",
    "    return (h_pola_new[0]['plus']- h_pola[0]['plus']) / tol\n",
    "\n",
    "#calculate the inner_product for two derivative <dh/dxi|dh/dxj> adding the ET psd\n",
    "def inner_product(aa, bb, power_spectral_density, duration):\n",
    "    integrand = np.conj(aa) * bb / power_spectral_density\n",
    "    return 4 / duration * np.sum(integrand)\n",
    "\n",
    "#using inner_product to calculate the fisher information matrix(fim)\n",
    "#return 4x4 matrix\n",
    "def calculate_fisher(parameters,table,tolerance,power_spectral_density,duration):\n",
    "    '''\n",
    "    parameters = array of the name of the waveform parameters to be included in the analysis\n",
    "    table = dictionary of waveform parameters\n",
    "    tolerance = step of the waveform derivative   \n",
    "    returns the errors on the input parameters 4x4 parameters\n",
    "    '''\n",
    "    fim = np.zeros([len(parameters),len(parameters)])\n",
    "    for i,val1 in enumerate(parameters):\n",
    "        for j,val2 in enumerate(parameters):\n",
    "            fim[i][j] = inner_product(derivative(table,val1,tolerance),derivative(table,val2,tolerance),\\\n",
    "                             ifos[0].power_spectral_density_array, duration).real\n",
    "    return fim \n",
    "\n",
    "#calculate the mock data's fim\n",
    "#15 parameter + snr for mock data\n",
    "inpa=np.loadtxt('LCDMcosmology15p.txt')\n",
    "mockdata=np.zeros((len(inpa),22))\n",
    "for i in range(len(inpa)):\n",
    "    injection_parameters_k= dict(\n",
    "        mass_1=inpa[i,0], mass_2=inpa[i,1], a_1=inpa[i,2], a_2=inpa[i,3], tilt_1=inpa[i,4], tilt_2=inpa[i,5],\n",
    "        phi_12=inpa[i,6], phi_jl=inpa[i,7], luminosity_distance=inpa[i,8], theta_jn=inpa[i,9], psi=inpa[i,10],\n",
    "        phase=inpa[i,11], geocent_time=inpa[i,12], ra=inpa[i,13], dec=inpa[i,14])\n",
    "    ifos = bilby.gw.detector.InterferometerList(['ET'])\n",
    "    ifos.set_strain_data_from_power_spectral_densities( ##power spectral\n",
    "        sampling_frequency=sampling_frequency, duration=duration,\n",
    "        start_time=injection_parameters_k['geocent_time'] - 3)\n",
    "    ifos.inject_signal(waveform_generator=waveform_generator,\n",
    "                   parameters=injection_parameters_k)\n",
    "    table = {}\n",
    "    table['mass_1']             =inpa[i,0]\n",
    "    table['mass_2']             =inpa[i,1]\n",
    "    table['a_1']                =inpa[i,2]\n",
    "    table['a_2']                =inpa[i,3]\n",
    "    table['tilt_1']             =inpa[i,4]\n",
    "    table['tilt_2']             =inpa[i,5]\n",
    "    table['phi_12']             =inpa[i,6]\n",
    "    table['phi_jl']             =inpa[i,7]\n",
    "    table['luminosity_distance']=inpa[i,8]\n",
    "    table['theta_jn']           =inpa[i,9]\n",
    "    table['psi']                =inpa[i,10]\n",
    "    table['phase']              =inpa[i,11]\n",
    "    table['geocent_time']       =inpa[i,12]\n",
    "    table['ra']                 =inpa[i,13]\n",
    "    table['dec']                =inpa[i,14]\n",
    "\n",
    "    h_pola=insig(table['mass_1'],table['mass_2'],table['a_1'],table['a_2'],table['tilt_1'],table['tilt_2'],table['phi_12'],\\\n",
    "          table['phi_jl'],table['luminosity_distance'],table['theta_jn'],table['psi'],table['phase'],\\\n",
    "          table['geocent_time'],table['ra'],table['dec'],waveform_generator=waveform_generator)\n",
    "    #step for derivative\n",
    "    tol = 10**(-11)\n",
    "    #calculate the m1 m2 DL l derivative\n",
    "    params = ['mass_1','mass_2','luminosity_distance','theta_jn']\n",
    "    fim = calculate_fisher(params,table,tol,ifos[0].power_spectral_density_array,duration)\n",
    "    #[fimatrix]^-1 \n",
    "    Sigma = np.linalg.inv(fim) \n",
    "    #Sqrt the Diagonal \n",
    "    sqrtt=np.sqrt(np.diag(Sigma))\n",
    "    #save fisher matrix err for dl m1 m2 l\n",
    "    mockdata[i,15]=sqrtt[0]\n",
    "    mockdata[i,16]=sqrtt[1]\n",
    "    mockdata[i,17]=sqrtt[2]\n",
    "    mockdata[i,18]=sqrtt[3]\n",
    "    #save 15 injection parameters\n",
    "    mockdata[i,0] =inpa[i,0]\n",
    "    mockdata[i,1] =inpa[i,1]\n",
    "    mockdata[i,2] =inpa[i,2]\n",
    "    mockdata[i,3] =inpa[i,3]\n",
    "    mockdata[i,4] =inpa[i,4]\n",
    "    mockdata[i,5] =inpa[i,5]\n",
    "    mockdata[i,6] =inpa[i,6]\n",
    "    mockdata[i,7] =inpa[i,7]\n",
    "    mockdata[i,8] =inpa[i,8]\n",
    "    mockdata[i,9] =inpa[i,9]\n",
    "    mockdata[i,10]=inpa[i,10]\n",
    "    mockdata[i,11]=inpa[i,11]\n",
    "    mockdata[i,12]=inpa[i,12]\n",
    "    mockdata[i,13]=inpa[i,13]\n",
    "    mockdata[i,14]=inpa[i,14]\n",
    "    mockdata[i,19]=ifos[0].meta_data['matched_filter_SNR']\n",
    "    mockdata[i,20]=ifos[0].meta_data['optimal_SNR']\n",
    "    mockdata[i,21]=sqrtt[2]/inpa[i,8]\n",
    "np.savetxt('LCDMmockdata_fim_snr.txt',mockdata)"
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