Quadrupole Testing of MMT.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Make Quadrupole Field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from TestModules import *\n",
    "from MMTModules import *\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "N = 1024\n",
    "beam_map = np.zeros((N,N))\n",
    "rotation_angle = np.pi/4\n",
    "\n",
    "beam_map = quadrupole_field(beam_map, 10., rotation_angle=rotation_angle)\n",
    "#beam_map = beam_map\n",
    "\n",
    "vmin = -1\n",
    "vmax = 1\n",
    "eta = 0.00001\n",
    "plt.imshow(beam_map[502:522,502:522],vmin=vmin,vmax=vmax)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Store Fields in Beam Matrix and Show for pure T sky"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#rotation_angle for dipole is 0 for y-axis, pi/4 for b-axis, pi/2 for x-axis, -pi/4 for a-axis\n",
    "#rotation_angle for quadrupole is 0 for U-axes and pi/4 for Q-axis\n",
    "\n",
    "#interface\n",
    "N=1024\n",
    "pixel_size = 0.25/60.\n",
    "inst_beam_width = 1.5\n",
    "p = 10.\n",
    "Q = 10.\n",
    "delta_ell = 50.\n",
    "ell_max = 5000    #maximum ell of Fourier Transform\n",
    "pix_size = pixel_size*60.    #pixel size for Fourier Transform in arcmin\n",
    "beam_map = np.zeros((N,N))\n",
    "empty_map = np.zeros((N,N))\n",
    "choose_normalization = 'TT'\n",
    "\n",
    "#T is gaussian\n",
    "inst_beam_1 = offset_2d_gaussian_beam(N, pix_size, inst_beam_width, 0,0)\n",
    "\n",
    "#Q is dipole\n",
    "#dipole_beam_Q  = 0.02*inst_beam_1\n",
    "dipole_beam_Q = 0.02*quadrupole_field(beam_map, p, rotation_angle=np.pi/4)\n",
    "\n",
    "#U is dipole\n",
    "#dipole_beam_U = 0.02*inst_beam_1\n",
    "dipole_beam_U = 0.02*quadrupole_field(beam_map, p, rotation_angle=0)\n",
    "\n",
    "#############################################Plot Beam Matrix##############################################################\n",
    "\n",
    "beam_matrix = {}\n",
    "beam_matrix['II'] = inst_beam_1\n",
    "beam_matrix['IQ'] = empty_map\n",
    "beam_matrix['IU'] = empty_map\n",
    "beam_matrix['QI'] = dipole_beam_Q\n",
    "beam_matrix['QQ'] = inst_beam_1\n",
    "beam_matrix['QU'] = empty_map\n",
    "beam_matrix['UI'] = dipole_beam_U\n",
    "beam_matrix['UQ'] = empty_map\n",
    "beam_matrix['UU'] = inst_beam_1\n",
    "\n",
    "#Plot beam maps in 3x3 matrix\n",
    "fig, ax = plt.subplots(3,3, figsize=(20,20))\n",
    "vmin = -1\n",
    "vmax = 1\n",
    "\n",
    "#II\n",
    "ax[0,0].imshow(beam_matrix['II'][502:522,502:522],vmin=vmin,vmax=vmax)\n",
    "ax[0,0].set_title('II Beam')\n",
    "\n",
    "#IQ\n",
    "ax[0,1].imshow(beam_matrix['IQ'][502:522,502:522],vmin=vmin,vmax=vmax)\n",
    "ax[0,1].set_title('IQ Beam')\n",
    "\n",
    "#IU\n",
    "ax[0,2].imshow(beam_matrix['IU'][502:522,502:522],vmin=vmin,vmax=vmax)\n",
    "ax[0,2].set_title('IU beam')\n",
    "\n",
    "#QI\n",
    "ax[1,0].imshow(beam_matrix['QI'][502:522,502:522],vmin=0.02*vmin,vmax=0.02*vmax)\n",
    "ax[1,0].set_title('QI beam')\n",
    "\n",
    "#QQ\n",
    "ax[1,1].imshow(beam_matrix['QQ'][502:522,502:522],vmin=vmin,vmax=vmax)\n",
    "ax[1,1].set_title('QQ beam')\n",
    "\n",
    "#QU\n",
    "ax[1,2].imshow(beam_matrix['QU'][502:522,502:522],vmin=vmin,vmax=vmax)\n",
    "ax[1,2].set_title('QU beam')\n",
    "\n",
    "#UI\n",
    "ax[2,0].imshow(beam_matrix['UI'][502:522,502:522],vmin=0.02*vmin,vmax=0.02*vmax)\n",
    "ax[2,0].set_title('UI beam')\n",
    "\n",
    "#UQ\n",
    "ax[2,1].imshow(beam_matrix['UQ'][502:522,502:522],vmin=vmin,vmax=vmax)\n",
    "ax[2,1].set_title('UQ beam')\n",
    "\n",
    "#UU\n",
    "ax[2,2].imshow(beam_matrix['UU'][502:522,502:522],vmin=vmin,vmax=vmax)\n",
    "ax[2,2].set_title('UU beam')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beam_matrix['II'][512,512]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the TFs for a pure T sky"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "###########################################################################################################################\n",
    "\n",
    "\n",
    "#Generate 2D power spectra from beam maps\n",
    "Imap = inst_beam_1\n",
    "Qmap = dipole_beam_Q\n",
    "Umap = dipole_beam_U\n",
    "binned_spectra_dict = calculate_2d_spectra(Imap=Imap, Qmap=Qmap, Umap=Umap, delta_ell=delta_ell, ell_max=ell_max, pix_size=pix_size, N=N)\n",
    "beam_spectrum = calculate_2d_spectra(Imap=inst_beam_1, delta_ell=delta_ell, ell_max=ell_max, pix_size=pix_size, N=N)\n",
    "\n",
    "\n",
    "sky_decomp = [1,0,0]\n",
    "beam_fwhm = inst_beam_width\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#combine to detector IQU array maps and make 2d FFTs and bin to 1d leakage spectra\n",
    "binned_ell, binned_spectra = get_leakage_spectra(beam_matrix, pixel_size, N, inst_beam_width, sky_decomp, delta_ell, ell_max, choose_normalization)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Zoom in"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/ipykernel_launcher.py:12: UserWarning: Attempted to set non-positive bottom ylim on a log-scaled axis.\n",
      "Invalid limit will be ignored.\n",
      "  if sys.path[0] == '':\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "zero_line = np.zeros(len(binned_spectra['TE']))\n",
    "ell_convert = binned_ell[1:]*(binned_ell[1:] + 1)/(2*np.pi)\n",
    "plt.semilogy( binned_ell[1:], binned_spectra['TE'])#/(norm_fac*binned_spectra_dict['TT']) )\n",
    "plt.semilogy(binned_ell[1:], binned_spectra['EB'])#/(norm_fac*binned_spectra_dict['EE']) )\n",
    "plt.semilogy(binned_ell[1:], binned_spectra['TB'])#/(norm_fac*binned_spectra_dict['TT']))\n",
    "plt.semilogy(binned_ell[1:], zero_line, color='gray')\n",
    "cross_labels = ['T->E','E->B','T->B']\n",
    "plt.legend(cross_labels)\n",
    "plt.title('Leakage Spectra')\n",
    "plt.ylabel('Spectra $uK^2$')\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylim(0,5e-2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Run Quadrupole Through Cobaya Central Value Shift:\n",
    "\n",
    "Questions:\n",
    "\n",
    "1.) Is the offset when using pure unbiased fiducial spectra from the gaussian likelihood approximation\n",
    "\n",
    "2.) Should I do anything about 1.)?\n",
    "\n",
    "3.) How should I weight the points?\n",
    "\n",
    "\n",
    "Going to define the leakage TF TE as the measured TE and run through simulator, calling EE zero and TT is the LCDM fiducial spectrum\n",
    "\n",
    "Assumptions:\n",
    "\n",
    "1.) gaussian likelihood\n",
    "\n",
    "2.) full sky survey"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### First fit the TFs to a Polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Transfer Function')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#define 9th order polynomial\n",
    "def polynomial_9(x, a, b, c, d, e, f, g, h, i, j):\n",
    "    return a*x**9. + b*x**8. + c*x**7. + d*x**6. + e*x**5. + f*x**4. + g*x**3. + h*x**2. + i*x + j\n",
    "\n",
    "#For TE\n",
    "import scipy.optimize as optimization\n",
    "\n",
    "#ell_set is the range of ell values the binned spectrum goes over\n",
    "ell_set = binned_ell[1:]\n",
    "initial_guess = np.array([0.,0.,0.,0.,0.,0.,0.,0.,0.,0.])\n",
    "\n",
    "#right now for one simulation just take the std of the dataset. If it's necessary, multiple simulations can be run\n",
    "#to make the weighting in the optimization more accurate, but for now I don't care as much\n",
    "sigma = np.sqrt(np.var(binned_spectra['TE']))\n",
    "errors = sigma*np.ones(len(binned_spectra['TE']))\n",
    "curve_fit = optimization.curve_fit(polynomial_9, ell_set, binned_spectra['TE'], initial_guess, errors)\n",
    "\n",
    "parameters = curve_fit[0]\n",
    "ell = np.arange(ell_max+101)\n",
    "tf_fit = polynomial_9(ell,parameters[0],parameters[1],parameters[2],\n",
    "                      parameters[3],parameters[4],parameters[5],\n",
    "                      parameters[6],parameters[7],parameters[8],parameters[9])\n",
    "plt.semilogy(binned_ell[1:],binned_spectra['TE'])\n",
    "plt.semilogy(ell,tf_fit)\n",
    "plt.title('Curve Fit of TT->TE Transfer Function')\n",
    "plt.xlabel('$\\ell$')\n",
    "plt.ylabel('Transfer Function')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define Simulation Parameters and Gaussian Likelihood\n",
    "\n",
    "measured spectra with TE leakage (dividing out the beam), for pure fiducial sky\n",
    "\n",
    "TT = TT\n",
    "\n",
    "TE = TE + leakage*TT\n",
    "\n",
    "EE = EE\n",
    "\n",
    "leakage = (TT->TE)/beam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[prior] *WARNING* No sampled parameters requested! This will fail for non-mock samplers.\n",
      "[camb] Importing *auto-installed* CAMB (but defaulting to *global*).\n",
      "[camb] Initialized!\n"
     ]
    }
   ],
   "source": [
    "from CobayaModules import *\n",
    "import numpy as np\n",
    "\n",
    "#parameters\n",
    "lmax = 5100    #for accuracy to lmax of 5000\n",
    "packages_path = '/path/to/your/packages'\n",
    "ell = np.arange(lmax+1)\n",
    "\n",
    "#Define transfer functions\n",
    "#TF_eff_dict = {}\n",
    "#TF_eff_dict['TE'] = tf_fit[10:]\n",
    "TF_eff_dict = None\n",
    "\n",
    "#calculate fiducial spectra\n",
    "Cl_fid = generate_fiducial(lmax = lmax)\n",
    "\n",
    "#Define leakage spectrum as measured spectrum and assume the sky is pure T\n",
    "Cl_fid['TE'] = Cl_fid['TE'] + Cl_fid['TT']*tf_fit[10:lmax+1]\n",
    "Cl_fid['EE'] = Cl_fid['EE']\n",
    "\n",
    "#parameter initialization\n",
    "As_lower = 1e-9\n",
    "As_upper = 4e-9\n",
    "As_fid = 2.2e-9\n",
    "\n",
    "ns_lower = 0.9\n",
    "ns_upper = 1.1\n",
    "ns_fid = 0.96\n",
    "\n",
    "nnu_lower = 3.03\n",
    "nnu_upper = 3.06\n",
    "nnu_fid = 3.046\n",
    "\n",
    "#define gaussian likelihood\n",
    "#including TT, TE, EE in likelihood\n",
    "def my_like_multi_spectra(\n",
    "        # Parameters that we may sample over (or not)\n",
    "        Cl_fid=Cl_fid,\n",
    "        #TF_eff = TF_mag[8:l_max-1],\n",
    "        TF_eff_dict = TF_eff_dict,\n",
    "        # Keyword through which the cobaya likelihood instance will be passed.\n",
    "        _self=None):\n",
    "    import numpy as np\n",
    "    \n",
    "    # Cl of the map: data + noise\n",
    "    Cl_map = {}\n",
    "    if TF_eff_dict is not None:\n",
    "        Cl_map = Cl_fid\n",
    "        for tf_key in TF_eff_dict.keys():\n",
    "            if tf_key is 'TT':\n",
    "                Cl_map['TT'] = TF_eff_dict['TT']*Cl_fid['TT']\n",
    "            elif tf_key is 'TE':\n",
    "                Cl_map['TE'] = TF_eff_dict['TE']*Cl_fid['TE']\n",
    "            elif tf_key is 'EE':\n",
    "                Cl_map['EE'] = TF_eff_dict['EE']*Cl_fid['EE']\n",
    "            else:\n",
    "                print(str(tf_key) + ' spectrum not included')\n",
    "    else:\n",
    "        Cl_map = Cl_fid\n",
    "    \n",
    "    # Request the Cl from the provider\n",
    "    # I believe what this is is a snapshot of what the theoretical spectrum is at that particular set of sampled LCDM model\n",
    "    Cl_theo_tt = _self.provider.get_Cl(ell_factor=False, units=\"muK2\")['tt'][10:lmax+1]\n",
    "    Cl_theo_ee = _self.provider.get_Cl(ell_factor=False, units=\"muK2\")['ee'][10:lmax+1]\n",
    "    Cl_theo_te = _self.provider.get_Cl(ell_factor=False, units=\"muK2\")['te'][10:lmax+1]\n",
    "    \n",
    "    #Cl_map['TT'] = Cl_theo_tt\n",
    "    #Cl_map['EE'] = Cl_theo_ee\n",
    "    #Cl_map['TE'] = Cl_theo_te\n",
    "    \n",
    "    Cl_map_theo = {}\n",
    "    Cl_map_theo['TT'] = Cl_theo_tt\n",
    "    Cl_map_theo['EE'] = Cl_theo_ee\n",
    "    Cl_map_theo['TE'] = Cl_theo_te\n",
    "    \n",
    "    #covariance matrix is the inverse of the wishart curvature\n",
    "    Cov_inv = np.asarray( ( (2*ell[8:lmax-1]+1) ) / ( 2*(Cl_map['TT']*Cl_map['EE'] - Cl_map['TE']**2.)**2. ) * [[Cl_map['EE']**2., -2*Cl_map['TE']*Cl_map['EE'], Cl_map['TE']**2.],\n",
    "       [-2*Cl_map['EE']*Cl_map['TE'], 2*(Cl_map['TT']*Cl_map['EE']+Cl_map['TE']**2.), -2*Cl_map['TT']*Cl_map['TE']],\n",
    "      [Cl_map['TE']**2., -2*Cl_map['TE']*Cl_map['TT'],Cl_map['TT']**2.]])\n",
    "    \n",
    "    #approximating the likelihood as gaussian\n",
    "    d = np.asarray([Cl_map['TT'], Cl_map['TE'], Cl_map['EE']])\n",
    "    m = np.asarray([Cl_map_theo['TT'], Cl_map_theo['TE'], Cl_map_theo['EE']])\n",
    "    curv = np.asarray([np.sum(Cov_inv[0,0]*(d-m)[0])+np.sum(Cov_inv[0,1]*(d-m)[1])+np.sum(Cov_inv[0,2]*(d-m)[2]), \n",
    "                   np.sum(Cov_inv[1,0]*(d-m)[0])+np.sum(Cov_inv[1,1]*(d-m)[1])+np.sum(Cov_inv[1,2]*(d-m)[2]), \n",
    "                   np.sum(Cov_inv[2,0]*(d-m)[0])+np.sum(Cov_inv[2,1]*(d-m)[1])+np.sum(Cov_inv[2,2]*(d-m)[2])])\n",
    "    \n",
    "    logp = ( np.matmul(np.transpose(np.sum(d-m,axis=1)), curv) )\n",
    "            \n",
    "    # Set our derived parameter\n",
    "    derived = {'Map_Cl_at_500': Cl_map['TT'][500]}\n",
    "    return logp, derived"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finalize Simulation and Calculate the Shift in $N_\\nu$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[camb] Importing *auto-installed* CAMB (but defaulting to *global*).\n",
      "[camb] Initialized!\n",
      "[my_cl_like] Initialized external likelihood.\n",
      "nnu has been shifted by 0.014000000000000234 by noise and systematics.\n",
      "The new maximum liklihood is given by 3.06\n"
     ]
    }
   ],
   "source": [
    "\n",
    "#use above leakage spectra calculation (TE,TB,EB) to bias fiducial spectra\n",
    "#TF_TE = binned_spectra['TE']\n",
    "#TF_TB = binned_spectra['TB']\n",
    "#TF_EB = binned_spectra['EB']\n",
    "\n",
    "#initialize\n",
    "#info = initialize_simulation(Nl=None, TF_eff=None, As_lower=1e-9, As_upper=4e-9, As_fid = 2.2e-9, ns_lower=0.9, ns_upper=1.1, ns_fid=0.96, nnu_lower=3.04, nnu_upper=3.05, nnu_fid=3.046)\n",
    "\n",
    "info = {\n",
    "        'params': {\n",
    "            # Fixed\n",
    "            'ombh2': 0.022, 'omch2': 0.12, 'H0': 68, 'tau': 0.07,\n",
    "            'mnu': 0.06,\n",
    "            # Sampled\n",
    "            'As': {'prior': {'min': As_lower, 'max': As_upper}, 'latex': 'A_s'},\n",
    "            'ns': {'prior': {'min': ns_lower, 'max': ns_upper}, 'latex': 'n_s'},\n",
    "            'nnu': {'prior': {'min': nnu_lower, 'max': nnu_upper}, 'latex': 'nnu'},\n",
    "            # Derived\n",
    "            'Map_Cl_at_500': {'latex': r'C_{500,\\,\\mathrm{map}}'}},\n",
    "        'likelihood': {'my_cl_like': {\n",
    "            \"external\": my_like_multi_spectra,\n",
    "            # Declare required quantities!\n",
    "            \"requires\": {'Cl': {'tt': lmax}},\n",
    "            # Declare derived parameters!\n",
    "            \"output_params\": ['Map_Cl_at_500']}},\n",
    "        'theory': {'camb': {'stop_at_error': True}},\n",
    "        'packages_path': packages_path}\n",
    "\n",
    "\n",
    "#calculate\n",
    "from cobaya.model import get_model\n",
    "model = get_model(info)\n",
    "\n",
    "\n",
    "#get shift\n",
    "num_nnu_samples = 500\n",
    "nnu_max_shift = calculate_shift(model, nnu_lower, nnu_upper, num_nnu_samples, nnu_fid, As_fid, ns_fid)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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