p3_err_p.ipynb

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    "# Error Propagation in the calculation of SFRD\n",
    "\n",
    "It is important to propagate uncertainties in the $M^*$, $\\phi^*$ and $\\alpha$ properly in final computed star formation rate density. We used Monte-Carlo methods to achieve this goal. We generate a random normal distribution of each parameters around its mean value and standard deviation equal to the uncertainty in the parameter (to reduce the computing time, we are currently using each array of size 50). Later we used this random normal distributions in $M^*$, $\\phi^*$ and $\\alpha^*$ to calculate the Schechter function (for each combination of values for these parameters from the distribution). Then we integrate the Schechter function accordingly (again, for each combination of values of parameters). Doing so, we would have an array of integration values (each value corresponds to the different Schechter function). We then measure the mean and standard deviation of this array to find the uncertainty in the luminosity density --- once, we got the errors in luminosity density, it is fairly easy to propogate this errors in the calculation of the star formation rate density since the conversion factor ($\\kappa$) does not have any uncertainty.\n",
    "\n",
    "We implement this whole procedure to calculate the Star Formation Rate Density in `sfr` function from `util.py` file. Interested use can visit the same file for the code. In the present notebook, we directly use the `utils.sfr` function to compute SFRD."
   ],
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import astropy.constants as con\n",
    "import os\n",
    "import utils as utl"
   ]
  },
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   "execution_count": 2,
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   "source": [
    "# Redshift\n",
    "z_bou = np.array([4,5,6,7,8])\n",
    "\n",
    "# Characteristic absolute magnitude\n",
    "mst_bou = np.array([-20.98, -20.60, -20.37, -20.14, -20.10])\n",
    "msterr_bou = np.array([0.10, 0.23, 0.30, 0.26, 0.52])\n",
    "\n",
    "# Characteristic luminosity\n",
    "lst_bou = np.array([])\n",
    "lsterr_bou = np.array([])\n",
    "\n",
    "for i in range(len(mst_bou)):\n",
    "    mst1 = np.random.normal(mst_bou[i], msterr_bou[i], 10000)\n",
    "    lst1 = utl.m_to_l_wave(mst1, 1500)\n",
    "    lst_bou = np.hstack((lst_bou, np.mean(lst1)))\n",
    "    lsterr_bou = np.hstack((lsterr_bou, np.std(lst1)))\n",
    "\n",
    "\n",
    "# Normalisation constant\n",
    "phi_bou = np.array([1.3, 1.4, 1.4, 0.86, 0.59])*0.001\n",
    "phierr_bou = np.array([0.2, 0.6, 0.85, 0.545, 0.69])*0.001\n",
    "\n",
    "# Alpha\n",
    "alp_bou = np.array([-1.73, -1.79, -1.73, -2.01, -1.91])\n",
    "alperr_bou = np.array([0.005, 0.12, 0.20, 0.21, 0.32])\n",
    "\n",
    "# Kappas\n",
    "sol_lum = (con.L_sun*1e7).value\n",
    "kap_uv = 2.2e-10/sol_lum\n",
    "kap_ir = 4.5*10**(-44)\n",
    "\n",
    "# Range of Luminosities (or absolute magnitudes) used\n",
    "mags_bou = np.linspace(-24, -13, 1000)\n",
    "lums_bou = utl.m_to_l_wave(mags_bou, 1500)\n",
    "\n",
    "#print(np.log10(lst_bou))\n",
    "#print(np.log10(lsterr_bou))\n",
    "#print(np.log10(lums_bou))"
   ]
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   "execution_count": 3,
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   "source": [
    "# SFRD without error propagation\n",
    "sfrd_wo_errs = np.zeros(z_bou.shape)\n",
    "\n",
    "for i in range(len(z_bou)):\n",
    "    sfrd_wo_errs[i] = utl.sfrd_wo_err(lum=lums_bou, lum1=lst_bou[i], phi1=phi_bou[i], alpha=alp_bou[i], kappa=kap_uv, limit=0.03, Auv=0.0)"
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   "execution_count": 4,
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     "text": [
      "100%|██████████| 10000/10000 [01:41<00:00, 98.32it/s]\n",
      "100%|██████████| 10000/10000 [01:44<00:00, 96.15it/s]\n",
      "100%|██████████| 10000/10000 [01:42<00:00, 97.48it/s]\n",
      "100%|██████████| 10000/10000 [01:45<00:00, 94.48it/s]\n",
      "100%|██████████| 10000/10000 [01:39<00:00, 100.04it/s]\n"
     ]
    }
   ],
   "source": [
    "sfrd_bou, sfrd_err_bou = np.zeros(z_bou.shape), np.zeros(z_bou.shape)\n",
    "\n",
    "for i in range(len(z_bou)):\n",
    "    sfrd_bou[i], sfrd_err_bou[i] = utl.sfrd_w_err(lum=lums_bou, lum1=lst_bou[i], lum1err=lsterr_bou[i], phi1=phi_bou[i], phi1err=phierr_bou[i], alpha=alp_bou[i], alphaerr=alperr_bou[i], kappa=kap_uv)"
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "log_sfrd_bou, log_sfrd_bou_err =  utl.log_err(sfrd_bou, sfrd_err_bou)\n",
    "log_sfrd_wo_bou = np.log10(sfrd_wo_errs)\n",
    "\n",
    "# Comparing values from Madau&Dickinson paper\n",
    "z_mad, log_sfrd_mad, log_sfrd_mad_perr, log_sfrd_mad_nerr = np.loadtxt('madau_bou.dat', usecols=(0,1,2,3), unpack=True)\n",
    "\n",
    "plt.figure(figsize=(15,7.5))\n",
    "plt.errorbar(z_bou, log_sfrd_bou, yerr=log_sfrd_bou_err, fmt='.', marker='o', c='cornflowerblue')\n",
    "plt.errorbar(z_mad, log_sfrd_mad, yerr=[log_sfrd_mad_perr, log_sfrd_mad_nerr], marker='X', fmt='.', lw=3, c='grey', label='From Madau & Dickinson paper')\n",
    "plt.scatter(z_bou, log_sfrd_wo_bou, marker='D', c='orangered', label='Without errors', alpha=0.7)\n",
    "plt.xlabel('Redshift')\n",
    "plt.ylabel('SFRD')\n",
    "plt.legend(loc='best')\n",
    "plt.ylim([-2.7, -0.5])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "--------------------------------------------------------------------------------\nAt redshift 4:\nValue of SFRD (wo error propagation) is: 3.07e-02\nValue of log(SFRD) (wo error propagation) is: -1.51e+00\n--------------------------------------------------------------------------------\nValue of SFRD is: 3.08e-02 +/- 5.83e-03\nValue of log(SFRD) is: -1.51e+00 +/- 8.20e-02\n--------------------------------------------------------------------------------\n--------------------------------------------------------------------------------\nAt redshift 5:\nValue of SFRD (wo error propagation) is: 2.59e-02\nValue of log(SFRD) (wo error propagation) is: -1.59e+00\n--------------------------------------------------------------------------------\nValue of SFRD is: 2.68e-02 +/- 1.48e-02\nValue of log(SFRD) is: -1.57e+00 +/- 2.41e-01\n--------------------------------------------------------------------------------\n--------------------------------------------------------------------------------\nAt redshift 6:\nValue of SFRD (wo error propagation) is: 1.95e-02\nValue of log(SFRD) (wo error propagation) is: -1.71e+00\n--------------------------------------------------------------------------------\nValue of SFRD is: 2.06e-02 +/- 1.73e-02\nValue of log(SFRD) is: -1.69e+00 +/- 3.63e-01\n--------------------------------------------------------------------------------\n--------------------------------------------------------------------------------\nAt redshift 7:\nValue of SFRD (wo error propagation) is: 1.52e-02\nValue of log(SFRD) (wo error propagation) is: -1.82e+00\n--------------------------------------------------------------------------------\nValue of SFRD is: 1.70e-02 +/- 1.55e-02\nValue of log(SFRD) is: -1.77e+00 +/- 3.96e-01\n--------------------------------------------------------------------------------\n--------------------------------------------------------------------------------\nAt redshift 8:\nValue of SFRD (wo error propagation) is: 9.21e-03\nValue of log(SFRD) (wo error propagation) is: -2.04e+00\n--------------------------------------------------------------------------------\nValue of SFRD is: 1.26e-02 +/- 2.75e-02\nValue of log(SFRD) is: -1.90e+00 +/- 9.47e-01\n--------------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# Saving all of these values\n",
    "f23 = open(os.getcwd() + '/Results/Bou12_w_wo.dat','w')\n",
    "f23.write('#Redshift\\tSFRD(wo)\\tSFRD(w)\\tErr\\n')\n",
    "\n",
    "for i in range(len(sfrd_bou)):\n",
    "    print('--------------------------------------------------------------------------------')\n",
    "    print('At redshift {:d}:'.format(z_bou[i]))\n",
    "    print('Value of SFRD (wo error propagation) is: {:.2e}'.format(sfrd_wo_errs[i]))\n",
    "    print('Value of log(SFRD) (wo error propagation) is: {:.2e}'.format(log_sfrd_wo_bou[i]))\n",
    "    print('--------------------------------------------------------------------------------')\n",
    "    print('Value of SFRD is: {:.2e} +/- {:.2e}'.format(sfrd_bou[i], sfrd_err_bou[i]))\n",
    "    print('Value of log(SFRD) is: {:.2e} +/- {:.2e}'.format(log_sfrd_bou[i], log_sfrd_bou_err[i]))\n",
    "    print('--------------------------------------------------------------------------------')\n",
    "    f23.write(str(z_bou[i]) + '\\t' + str(sfrd_wo_errs[i]) + '\\t' + str(sfrd_bou[i]) + '\\t' + str(sfrd_err_bou[i]) + '\\n')\n",
    "f23.close()"
   ]
  }
 ]
}