{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Halo profiles\n", "This example illustrates how to use CCL to calculate halo profiles (and quantities associated to them)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import pyccl as ccl\n", "import pylab as plt\n", "import matplotlib.cm as cm\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Preliminaries\n", "Generate a cosmology object and a couple of $r$ (comoving radius), $k$ (comoving wavenumber) and $M$ (halo mass) arrays." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Cosmology\n", "cosmo = ccl.Cosmology(Omega_c=0.27, Omega_b=0.045, h=0.67, sigma8=0.83, n_s=0.96)\n", "\n", "# Radius, wavenumber and mass\n", "r_arr = np.geomspace(1E-2,1E2,256)\n", "k_arr = np.geomspace(1E-2,1E2,256)\n", "m_arr = np.geomspace(1E11,1E15,32)\n", "\n", "# We will calculate everything at z=1 (scale factor = 0.5)\n", "a_sf = 0.5\n", "\n", "# We will also use a mass definition with Delta = 200, and the Duffy 2008 concentration-mass relation\n", "hmd_200c = ccl.halos.MassDef200c()\n", "cM = ccl.halos.ConcentrationDuffy08(hmd_200c)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Halo profile classes\n", "All halo profiles are sub-classes of the base `HaloProfile` class. CCL currently supports the following halo profiles:\n", "- `HaloProfileNFW`: the Navarro-Frenk-White density profile.\n", "- `HaloProfileEinasto`: the Einasto profile.\n", "- `HaloProfileHernquist`: the Hernquist profile.\n", "- `HaloProfileGaussian`: a toy Gaussian profile.\n", "- `HaloProfilePowerLaw`: a toy power-law profile.\n", "\n", "However, the API is flexible enough for you to implement your own halo profiles. See further down.\n", "\n", "For now, let's compare the first three profiles." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "profs = {}\n", "profs['NFW'] = ccl.halos.HaloProfileNFW(cM, truncated=False)\n", "profs['Einasto'] = ccl.halos.HaloProfileEinasto(cM, truncated=False)\n", "profs['Hernquist'] = ccl.halos.HaloProfileHernquist(cM, truncated=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's just plot the real-space profile for all models" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the real-space profile for a fixed mass of M = 1E14 M_sun\n", "plt.figure()\n", "for n,p in profs.items():\n", " rho_r = p.real(cosmo, r_arr, 1E14, a_sf, mass_def=hmd_200c)\n", " plt.plot(r_arr, rho_r, label=n)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.legend(loc='lower left', fontsize=15)\n", "plt.ylabel(r'$\\rho(r)\\,\\,[M_\\odot\\,{\\rm Mpc}^{-3}]$', fontsize=15)\n", "plt.xlabel(r'$r\\,\\,[{\\rm Mpc}]$', fontsize=15);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All the profile-related methods can take in an array of halo masses, and output the profile for all of them in a 2D array." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pM = profs['NFW'].real(cosmo,r_arr, m_arr, a_sf, mass_def=hmd_200c)\n", "pM.shape\n", "\n", "fig=plt.figure()\n", "cmap = plt.cm.inferno\n", "for i, p in enumerate(pM):\n", " plt.plot(r_arr, p, c=cmap((i + 0.5) / 32))\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "lm = np.log10(m_arr)\n", "sm = plt.cm.ScalarMappable(cmap=cmap,\n", " norm=plt.Normalize(vmin=lm.min(),\n", " vmax=lm.max()))\n", "sm._A = []\n", "plt.ylabel(r'$\\rho(r)\\,\\,[M_\\odot\\,{\\rm Mpc}^{-3}]$', fontsize=15)\n", "plt.xlabel(r'$r\\,\\,[{\\rm Mpc}]$', fontsize=15);\n", "cbar = fig.colorbar(sm)\n", "cbar.set_label(r'$\\log_{10}(M/M_\\odot)$', fontsize=15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Derived quantities\n", "Besides the 3D real-space profile, CCL can also calculate the Fourier-space profile ($\\rho(k)$), the 2D projected profile ($\\Sigma(R)$) and the cumulative surface density ($\\Sigma(" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the Fourier-space profile for a fixed mass of M = 1E14 M_sun\n", "plt.figure()\n", "for n,p in profs.items():\n", " rho_k = p.fourier(cosmo, k_arr, 1E14, a_sf, mass_def=hmd_200c)\n", " plt.plot(k_arr, rho_k, label=n)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.legend(loc='lower left', fontsize=15)\n", "plt.ylabel(r'$\\rho(k)\\,\\,[M_\\odot]$', fontsize=15)\n", "plt.xlabel(r'$k\\,\\,[{\\rm Mpc}^{-1}]$', fontsize=15);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Projected profile" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the projected profile for a fixed mass of M = 1E14 M_sun\n", "plt.figure()\n", "for n,p in profs.items():\n", " sig_R = p.projected(cosmo, r_arr, 1E14, a_sf, mass_def=hmd_200c)\n", " plt.plot(r_arr, sig_R, label=n)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.legend(loc='lower left', fontsize=15)\n", "plt.ylabel(r'$\\Sigma(R)\\,\\,[M_\\odot\\,{\\rm Mpc}^{-2}]$', fontsize=15)\n", "plt.xlabel(r'$R\\,\\,[{\\rm Mpc}]$', fontsize=15);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Cumulative surface density" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot the projected profile for a fixed mass of M = 1E14 M_sun\n", "plt.figure()\n", "for n,p in profs.items():\n", " sig_lR = p.cumul2d(cosmo, r_arr, 1E14, a_sf, mass_def=hmd_200c)\n", " plt.plot(r_arr, sig_lR, label=n)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.legend(loc='lower left', fontsize=15)\n", "plt.ylabel(r'$\\Sigma(" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pl = HaloProfileLorentz()\n", "rs = pl._rs(cosmo, 1E14, a_sf, hmd_200c)\n", "rho0 = 1E14 / (4 * np.pi * rs**3)\n", "\n", "# Plotting\n", "plt.figure()\n", "plt.plot(r_arr, pl.real(cosmo, r_arr, 1E14, a_sf, hmd_200c),\n", " 'k-', lw=3)\n", "# Let's compare with the expected shape\n", "plt.plot(r_arr, rho0 * np.exp(-r_arr / rs) * rs / r_arr,\n", " 'y--')\n", "plt.ylabel(r'$\\rho(r)\\,\\,[M_\\odot\\,{\\rm Mpc}^{-3}]$', fontsize=15)\n", "plt.xlabel(r'$r\\,\\,[{\\rm Mpc}]$', fontsize=15)\n", "plt.xscale('log')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fourier profile\n", "CCL can compute the Fourier-space profile automatically using FFTLog. Let us compare it with the analytical solution for this profile:\n", "\n", "\\begin{equation}\n", " \\rho(k)=\\frac{M}{1+(k r_s)^2}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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48c8iwLcNMpS/OIwxxi0/P5+1a9dy7733csopp0T9voaqZs1NfvzvkQDfIHG8oW7GGONt/vz5nHbaaezYscMz/UdtYkHCT6BMwnu0gWUSxphwTJw4kbKyMlavXl3jk/VFwoKEH+9MwR0cLJMwxtRXFiT8HD161LPsDg6WSRhj6isLEn68g4A7SFjHtanP6toIyPqoMv+GFiT8eGcS7rsgvTMJa24y9UliYmJI006Y2Hb48GESExMj+qwFCT+WSRhzTGZmJtu2bePQoUOWUdRC7puDt23bRmZmZkTHiOn7JEQkBVgEJOPUda6q3h/Nc3oHAXcmYR3Xpr5q1KgRANu3b6e4uLiGa2MikZiYSMuWLT3/luGK6SABHAHOUNVCEUkEPhWRd1X182id0DqujfHVqFGjiL9gTO0X00FCnfy20LWa6HpFNec9XnOTZRLGmPok5vskRCReRFYCecCHqvpFgH1uEJFlIrJs9+7dlTpfoOYmyySMMfVVzAcJVS1V1VOBbKC/iJwSYJ8XVDVHVXMyMjIqdb5AzU3eowKKi4spKyur1DmMMaa2iPkg4aaqBcBCYMzx9q2MQJmEiFg2YYypl2I6SIhIhog0cS2nAiOB76N5zkCZhP+yBQljTH0R0x3XQGtghojE4wS02ar6VjRPGKjj2n/ZOq+NMfVFTAcJVf0G6F2d5wzU3ATWeW2MqZ9iurmpJoTS3GSZhDGmvrAg4ccyCWOMOcaChJ9Q+iQsSBhj6gsLEn6CNTeFOhPshg0bOOOMM7jyyivJz8+PTiWNMaaaxHTHdU0I1twUaibx1FNPsXDhQgA+/vhjVq9ebfPeGGNqLcsk/FS243r9+vWe5W3btvHSSy9VcQ2NMab6WJDwU9mOa/8HtHz/fVTv/TPGmKiyIOGnsjfTFRQU+Kzv27evCmtnjDHVy4KEn1A6rivKJCxIGGPqkuN2XIvI7AiP/XtV/THCz9aYUDquK8ok9u7d67NuQcIYU5uFMrrpEmAFsD/EYwowFHgU+DGyatWcYM1NoWQSxcXFHDx40GebBQljTG0W6hDYX6rq0lB2FJEE4Ohxd4xR3s1N4Q6BDRQQLEgYY2qzUPokHgBywzhmqesz2yOqUQ2rTMe1f38EWJAwxtRux80kVPWBcA7oei51WJ+JJZXpuA4UJA4ePEhxcbHP0+2MMaa2sNFNfirTce3fae22f3+o3TnGGBNbLEj4qUzHdaBMAqzJyRhTe1mQ8BNKx3U4fRJgQcIYU3tVOkiIyGAReVtEvhCRt0RkcFVUrKZYJmGMMcdUKkiIyFnAY8AtqjoAuBV4QkTOrIrKVbeysjKKi4s96+EOgQ3WJ2FBwhhTW1U2k3gYGK+qGwBUdT1wGc6NdJUmIm1EZKGIrBaRVSJyS1UcNxjvAJGYmIiIeNatuckYUx9VNkg0UNVtItJWRA6JyEBV3Qo0rIrKASXAZFXtDgwEfi0i3avo2OUEa2qC8JubvJ8hYUHCGFNbVTZIlIpIQ2AbcBKwXEQa43y5V5qq7lDV5a7lA8AaIKsqjh1IsHsk/NdDySTatWvnWbYgYYyprSobJB4HZgDJqroZ5+a8mVRRc5M3EWkP9Aa+CFB2g4gsE5Flu3fvjvgcwe6RgPAzCe8gEawZyhhjYl2lgoSqvgzMAz4WkSXAQmC2a3uVEZEGwOvAb1W13J1pqvqCquaoak5GRkbE56mouSmUTMI7YzheJnHw4EEWLVrEoUOHIq6vMcZEW6WHwKrqy6raX1UHqeoAVX2lKirmJiKJOAHiFVWdV5XH9hfsHgkILZPw/sI/4YQTPMv+QUJVGTRoEMOGDaNr1668//77laq3McZES0zfTCfO8KJpwBpVfTLa5ws1kwglSLRq1cqz7B8kcnNz+fbbbz3LF1xwQbkpxo0xJhbEdJAAhgBXAWeIyErX6+xonSzU0U3Bmpu8n2/dsmVLz/KBAwd89vPvoygqKiI3N5yJdo0xpnqE8mS6ycA3wDequiv6VTpGVT/FeYhRtaiouSmUTMI7SLRo0cKz7N/vEOimO+vcNsbEolAeOvQ4oAAisgf4FidouN9XqWrw53nWIpXpuC4uLqakxBn5GxcXR5MmTTxl/k1JgYJEsLu1jTGmJoUSJAqAROBNYAvQE7gY+C1O8CgTkY04AeNrVf1jlOoadeFkEqrqc0e2dxaRmppKenq6Z90/SATKGixIGGNiUSh9Eh2AZ4DzcZ5d/ZiqtgOaAsOA3wALgNbA5CjVs1pUlEnEx8eTkODEVFX1mcIDKg4SoTQ3WZAwxsSi4wYJVd2nqncBnYAVwAci8h7QWVU/VdXnVPVXqjpUVZtFu8LRVNHNdFDxMFjvQBBJJuG/TVXZuHEjhYWFIdbeGGOqXsijm1Q1T1V/A5yI8/zqJSIyT0ROilrtqpl3duCfSfhv8w8S3plEWloaSUlJnsyjpKTEpykrlEzimWeeoXPnznTp0qXc6ChjjKkuYQ+BVdUtqjoJ6IEzR9M3InJPldesBnh/kQd6JnVFw2D9m5vACRZu3tnE8fokVJVbbnEmvN25cyfz588P+WcwxpiqFErHtfumto5AN5yJ/E7yWo4HTo5WBatTRR3XEHom4Q4S6enpnudbHzp0iKZNmwLHHwL7/fff+5RZJmGMqSmh3CfxDdAZSAbcM7GuAua63r9T1e3RrGR18X+ehL+KhsF690m4M4hg/RLHyyTeeecdnzKbRdYYU1NCySROAfbjBIW3cIa6rlPVsmhWrCYcL5OoqOM6WCbh5h0kjtcn4R8k9uzZ41lWVdatW0ebNm18mrOMMSYaQumTeBr4EhgFzMLJHgpF5CsRmS4ik0VklIi0jmZFq0OwR5e6VZRJhNMncbzmpq+++sqnzHv688cff5xu3brRtWtXm0HWGBN1oQyBvVVVR6pqK6AVTrC4C/gapy/iQeA9IFdEIn+YQwwIp+O6oiGwgZqbvMsram4qLS0t17zkHSTuuOMOwJkY8K233gJg7dq1PPzww6xevTrYj2aMMREJqePaTVXzgP+6XoCnU7sLzp3Yp1Rp7apZNDqu3dyZRHFxccAZX/ft20dZWVnA/gd3kNi1y3fqrAMHDqCqXHDBBXz//fdMnz6ddevWERcX6/M2GmNqi7CCRCCqqsA612tupWtUg47XcV0VQ2C9s4hmzZpRXFzs+bLft29fwKYod5BYsmSJz/affvqJvXv3ekZDbdy4kR07dpCVFbUnvBpj6pnj/skpIr8RkcxwDur6TIvj7xlbKpNJhNrc5B0EmjZt6hkWC04ACSdI7Nixgy1btvhs27Rpk6d+7mVjjIlUKO0STwHtjruXi4jEuz7TNtJK1ZTKDIENtbnJO5No0qSJT5DYu3dvwP6KwsJCioqK+Oyzz3y279y5k82bN/ts27hxIwcPHuTkk0+mU6dOPP744xw+fJjnn3/ebsozxoQtlOYmAR4RkZ9CPGa1Pf+hqlXHEFj/IFFaWupZ37t3b9CJ/nbv3s2KFSt8tgUKEps2bWL69Ols3LgRgN///vcUFxdz9913A/DFF1/QokULPvzwQ84//3yfJ+gZY4y/UILEIpy7qjPCOO4inBvvapXKDIEN1NwUqE/CfQc2QKNGjXC6dBzBmpsANm/eXK7DO1Bz08aNG1m/fr3PNneAALjvvvtYv349mzZtYubMmSxevNhTVlZWxpYtW2jXrp3PNOjGmPrruEFCVYdXQz1iQmWGwB4vk3AHEe9ZXRs2bOjzZbxv376gT6hbs2ZNuW3BMomKnpe9ePFiTx0+++wzCgsLadCgAarKWWedxcKFC7npppt45plngh7DGFN/VHp0U11SHUNgvYNEgwYNPDPFAkFHN0HgIFFQUMC6det8tn355Zc+TVj+/KceX7t2LQUFBaxYsYKFCxcCMHXqVGbPnk3v3r158803SUpKsszCmHoqpoOEiPwDOBfIU9Wo34NRmSGwoc7d5D1ZX4MGDXwCj3+QEBFPc1SgIAHwzTff+KxXFCACGTZsWMDMIy8vj/fff5+UlBRatGjB5ZdfzpdffsmECRPYt28fKSkp3HbbbcTFxXme0rdjxw7+/ve/c+DAAe68806f53wbY2qnmA4SwHRgKjCzOk5W1ZlEoD4J/+Ym975QvrnpxBNPZO3atUDwIFFZFTVNue3Zs8fT/PT55597tpeWlrJlyxamTZtGq1at2L17tyd4/u9//2PBggXk5eWxatUq4uLiaN++Pe3ataNRo0ZR+VmMMVUvpoOEqi4SkfbVca6ioq3067eOpk1BFVJS5rFly3e0aHEhaWkncvjwJrKzP2X8eKe8TZslbN36JBkZF5OS0o709J+4+GLnWElJ88nN/Y6GDdfStCns3QupqbvZtu1ZMjIWc/75zn7t2n1NcfFpAHToAJmZX5CUtI9zz3XO0bNnMk89BUVFkJCwmbFj3dfl2PuCBVBcDF26QPv2vuUA//2vs96pE7RqBaWlUFbmvJeUwNdfO/u1bg0NGzrb3fuUlMB21/y+DRo470ePOudThbvuustznq1bt/pcz6+++orGjRsHvNaNGzcmIyODZs2a0axZMzIyMsjOziYrK4vs7GzPcmZmpt09bkwNi+kgESoRuQG4AaBt28huzygq2syIERsZMcK95R9s2gSpqSeSlnYihw6tpXXr//CLX7jLF7Nx42LS03uSktKOZs0KmDTJKSktfZoNGyA+3vli3rsXMjLyWL/+Jk49FU491X2Mufz00yAA+vSBQYOcm+XcwQC+Ydo0J0gMGgTXXVe+3osXO1/aI0bA5ZeXL1+wwPlCP+88PMHJ7cgRGDPGWZ44EUaN8i0vKIALL3SWf/97GDr0WNnRo7B1K1x/vbN+221w4onO9iNHnPfNm+H5553ykSMhPR0OHoSDB/dx8OA+cnNh6dLydXZLTEwkKyuLE088ka5du3LiiSd6ltu0aWMBxJhqIN5DMEP6gEgPoD/OZH8pwE84U3J8pqqBe10rU0Enk3gr1D6JnJwcXbZsWdjnUS1j6NBBLHV9ay1cuICBAwcikkhcXAJlZSW8/PI/uPHGGxGByy8fz9///gJxcWnExSXQrVtncnM3IgJLl35B586d+fbbb+nXbzhlZdCnz8ksWbKQ66+fxPz5byECf//78zRu3JbRo88mJQVGjz6N3NxcNm/+EYBHH32EG264k7Iy5ws2PR1EoHnz5uTn5wOwe7fzV3+jRsf+2neum/O+bZvz3qIFNGkCcXFO8IqPd/b59lunvFMnyMz0LS8thUWLnPL+/aFNG0hMhKQkSE6GQ4fglVec8muugW7d4hkyJIfCwp/YseMHtm4t4fHH0xk4cCA///kXtGzp22m+ciXcequz/Je/OD/f3r3Oa/duWL0a3PcPJiQ4mY1bWloaPXv2pE+fPvTu3Zs+ffpw8sknB3zsrDGmYiLylarmBCoL9cl0HYFfAj8DWgJlQAFwBGgCpAFlIvI/4CXgtdr2vAmROIqKSnH3XSclNSA+/lh/QVxcAsnJjXH3VxcWKgkJx9rWCwuLcDfvp6e3IjGxGQ0bnkCZ6yrs21dEUlIGu3eX4O52SE9vQ+PGzQAnW9i2rYjNmwtxPz6iQ4f+ns87f4E7y/36DWL16rd86t+mzcmsWrUq6M+3Zw+e45566qmsXLnSUzZ16lTuvvtuNm70nVwwKSmJxESluLiYpUt9/+pv3749paWlzJnzJBdeeCEffPABXbt2pWPHjoDTZ7N161Zuv/0E0tLSKCs7QknJPoqL95Kfv5WCglz69TvC/PlZ5OXlkZT0IrCdrKx9dOx4iEaNilm48FiQeOMNJzvJzYUff4TNmw/x9def87e/HesjSU5Opn///gwdOpShQ4cyePBg6/8wppJCeTLdSzjB4VOcacE/A1apaqnXPi2AfsBo4DFgiohcp6qfRqXWURLNuZuCjW7ybrf3H93UpUuXgPXs37+/Z5pwt+HDh/sEieTkZIqLiylzRZkZM2YwePBgCgsL6dWrF3/+85+58847GTZsGDfeeCPjxo3jxx9/ZMCAASxdupQePXqQkJBAXFwcpaWlrFmzhh49evDJJ5/QqVMnTzBwG3usjcxz/s6dO3vW4+KSSUrKJCkpk/T0rpRvFZzks6ZaysCB+Vx55f/KOQoAABufSURBVB7WrVvD3r0vUFT0I40a7eSMMw7QoIHyyiuwcSOkpMBDD8HatUdYs+YTnn/+E/70J4iLi6Nv376MHTuWsWPH0q9fP+Lj4wNeU2NMEKpa4Qt4Bmh3vP289o8DxgPjQ/1MBcd6FdgBFAO5wHXH+0zfvn01Ut26dVNAAV21alW58nfffddTPnr0aJ+ylJQUT1lhYaGqqhYUFHi2NWjQQFVVe/Xq5dm2fPly3b59u2c9LS3Ns5yamqrFxcWede/Xe++9V27b3LlzfdZ79eqlt956q8bFxenvfvc7LSsrK/fz5OfnB9we68rKynTr1q/13Xf/pX/84x910qQx+s9/JumHH6ILFzqv115DBw3yvUbNmzfXK664QmfPnu35NzLGqALLNMh3aih3XN/sXhYRcR2wov3LgNeOd9xQqGqArtjoiTSTUFWf+yaC3UynqhVmEt7ZSNOmTUlISKBZs2b89JPvtFmnnHIKKSkpPufs3r27zz7x8fE8+eSTPPHEE0FvhGvWrFnA7bFORMjO7kl2dk9PxzvAtm2bWLr0VbZseZ/S0m/Jy3Pa9YYOhV/+EpYvz2fJkn9x9dX/Ii4ujXPOOYdLL72Us88+2+ffyhhzTLijm54AfheNisSCSOdu8l5OSkryjLpJSEggNTWVw4cPo6ocPHgw4H0SCQkJlHj3yoLnRrSMjIxyQaJFixa0bdvW525r/1Fd7mam+nSndFZWRy688G7Amavq2mv38uGHH7J8+T/ZsmUhw4Yd4ZxznL6N5csP8fDDc5gzZw5paWlcfPHFTJw4keHDh9uoKWO8hPu/4WoRmRSsUESurmR9alSkczcF6o9wa9iwoWf5wIED5TIJEQl4P0FmpvMIj4wM33kVGzVqRHJycrm/fNPT08nOzvasDxkypNwx65umTZty2WWX8eij73L77Yc44YQvWLnyaj79tBkpKccGAowZc4iffvo/LrjgTDp27Mj999/PDz/8ULOVNyZGhBskLgP+KiJDvTeKSJyI/BVnZFOtFU5zk3f2EOhuazfv0TUFBQWefUXEE1DCCRLuDCNQB+ysWbNo0KABWVlZ3H///eXK67O4uDj69OnPb387gwcfzGfUqFVMmTKF7t27M2KEc5/H66/DDTdsZtGiB+natSNjx47lrbfeCnuqE2PqkrCChKouAO4E5olIBwARaY7zzOvxOKObaq1w5m7yziQqChLemcSOHTs8y+np6Z5mjUBBwh0c/INE//79AXyyBrchQ4awa9cufvzxx3KfM766d+/O/fffz3fffcegQcv4738v4513UujcGe6/H37xC3jvvfc477zz6Ny5M3/+8589Twg0pj4J5fGlPn+yquozwL+Bt0RkBLAcaAT0U9WFUallNYm04zrU5qbt7jku/LaHk0mc77pt+uGHH/b0Nzzvvq3ZdX7vmWVNxUSEvn378tBDr/HoowXExc1i9uy+/Oc/TvlJJ8HkyT+yaNEf6Nw5i6uuuspzw6Ux9UEomcRBEflKRF4SkZtEZAhwB7AH+Aj4GBiiqlsqOkisU9WIZ4GNJJNo4HV7dEVBwn+2Wff9CCeffDIrV67kgw8+4Oc//3mQn8qEIzk5mUsuGc/f/raMBQs2cvvtt9OyZUMaNIDbb4d//auY5s1fZsKEAQwcOJBXXnnF5w8LY+qiUILEROB9oDVOU9MnQB7QHdgLbABGu+7KrrVKS0s903LHxcUFbPMPlklEEiS8twe6K9idQeTk5Pjs5x1QevbsyciRI200ThR07NiRxx57jHfe2UVc3HT+9reTWLwYzj4bnn4ali//giuvvJK2bdswZcoUn39bY+qS4367qOosVb1LVc9R1SwgE6fv4VHgHeASYDawQUT2V3ComHa8piYI3nEdSXNTqJnEBRdcwIgRI+jQoQMLFiw47s9hqlZqaipXX30Ns2ev5qKLvmTu3Mt46KEEz/Qt99yTR17eAwwe3JYrrriCzz//nOPcSmRMrRJ247Wq7sHpqP6ve5uIJAEnAz2rrmrV63hNTe7t7gcBlZSUUFpaSnx8fKUziUA3tbmDREpKigWHGJGTk0NOzmvk5eXxwgsvMH36s+zZs5OLLoLLLith+fJX+cMfXqWoqA+/+tUtjB8/3iYcNLVelbRTqOpRVV2hqjOq4ng1IZRMQkR8goA7mwg1SATLJHr2LB9bbXRS7MrMzOSee+5hzZotdO/+Gv/v//XjpZfghBNgyhRITl7ONddcQ9u2bbj33nvZ5p6K15haKJTRTVf5j3AK4TOd/e+liHWhZBLgGwTcwSHU5qZgmcTgwYN9PiMiPuUmNiUmJnLZZZfx3ntLmTx5OR9+eA333JPA4sVO+ciRu0lLe5jx49ty+eWXsXjxYmuKMrVOKJnE74CNIvKQiPQKtpOINBeRn4nIfGAlTkd3rRFKJgGBg0SomYT3o0K9M4nWrX0vlbqeGW1qj969ezNt2nTeeGM7Dz30J7Kzszl0yHli4MMPl3H++XN4/vnTOO20k3jiiSfYuXNnTVfZmJCE0nHdG2fI6whghYjsF5EvRORtEZknIgtE5AecEU9PAxuBrqo6O6o1r2LHm7fJzTsIuDOIUIOEN//O6mDTgpvaJSMjgzvvvJMffviBK66Yw7PPnsZ99znPwbjuOhg7di233XYb2dnZnHfeucydO9fn98eYWBNSn4SqvqaqpwEnArfjZAolQDqwC5gBjAFaq+pvVbXWNcIeb94mt8o0N3lzT6/hdtZZZ3mWbUhr7ZeQkMAll1zCwoWf8MwzK/n+++u4/vpkpk1zyjMzS5kw4W0++OBSBg5szuWXT+D111/3+V0yJhaENbpJVTfgDHVNA9JcI53qhOpobvLm3zE9ZcoUZs+eTX5+PtPc3ySmTujVqxcvvfQS+/c/ydy5c5kxYwbbty8iNxcuuwyuuOIwubmv8e67r/HrX6dy2mlnc/bZZzN69GiysrJquvqmngsrSIhIO+CfwOnOqhQC7wIvqup/K/xwjKtMx3UkQcI/k8jMzOSHH34gLy+PTp06hV5xU2s0atSISZMmMWnSJDZu3MjMmTP5/e9foXXrjQwf7gSM1147zOuvv86WLa8zYwYcPtyd4cPP4ayzzmLQoEE2oMFUu3Dvk3gF507re3D6HlrjNDO9LyIvAr863kOJYlVlMolImpsCDXFt2LChfQnUE506deKBBx5gypQpfPfdd8yZM4c77phFYeF6AC64AAYPhpKS1axdu5rXX3+ce+4RSkpO5bTTTmPIkCH079+f9u3b2yAHE1XhBokc4Oeq+n9e2/4qIoOBt4DtwENVVbnqFEnHdVVmEqZ+EhF69OhBjx49ePDBB1m9ejXvvPMO77//DnPmfELfviX06gWXXAJduyqTJ69gxYoV7Nv3DC+/DNu3N6BJk9707NmXXr16cdJJJ9GlS5da+9RBE3vCDRKFQIH/RlX9TETuxxkFVSuDRGU6rkN9noS35s2bR1RPU7d1796d7t27c9ttt1FYWMjHH3/M+++/z8yZ/yM391sA4uKcTKNpU4BCios/4YcfPmHePJg/3zlOnz6NSU/vSseOJ9G5c2fatm1LdnY2WVlZZGdn2+NaTcjCDRJvAjeLyFsBmpXWAU2qplrHiMgYnKG18cBLqvpoVZ8Dqq7j2r+5KTU1lbi4OM/jROHY0+WMqUiDBg0499xzOffccwHYt28fn3/+OZ9++ilTpy5m+/avaNVqPyeeCJ06gftXrEULeOKJfZSVLSUvbym7dsHatfDkk/D115CcDCed1IDU1NakpraiSZMMWrRoQYsWLWjevLnn3d386X41aNCAtLQ0a96qZ8INErcBnwFLRORB4L+qekREGgE34XRiVxnXnd7PAiOBXOBLEfmPqq6uyvNA1d1x7Z9JuO+e3rdvn2ebNTWZSDRu3JjRo0czerTzbC9VZevWraxYsYKVK1eSnPwNPXqsJzd3HQ8+eIQ2bSA7GzIz4eST4fPPneN06gRPPVUIrAfWU1gI+/bBX/4Cy5ZBu3Zwzjlw+LDziNdDh5z3FStg//44MjPTycpKJT4+lbi4VOLiUkhISCUhIYXk5BRSUlJITk4mOTnZs5yQkEBCQgLx8fHEx8d7liva5n6Pi4tDRAK+KiqrzCuY6iyL5DMtWrSgc+fOQT8XiXCHwO4VkdOAx3GyCkSkACeD2An8UkQaq+q+Cg4Tjv7ABlXd5DrXLOB8oMqDRLSGwAIWJExUiAht27albdu2nodRAZSVlbFt2zbWrVvHunXr2LhxI59/vo2jR3Pp0GEbu3Zt5f77S2jcGBo3hiZNnJf7V7RVKxg7FtLSnKYtt9/8Br79toxTTjnA3XcfwN8NN8D69TB6NPzsZ3D0KBQXQ2mp87rrLti9G846C84999j20lJn30cecYLRsGFOp31pKageez39NJSUOOW9e/uWlZXBs8869RgxArp1O1YGUFQEM2YcK+/Q4ViZKhQWwty5zvpZZznzcHkrKMDzIKrRo53A623PHnjX9Sfyuec619Pbzp3w0UfO8gUXgH9r39atsGiRs3zxxU625+2HH2DJEmd5/HjffxdwrvuyZXDVVVcxc+bMcv82lRHJLLD5wCQR+R3OX/h9gVOBXsB/ABWRzcAKVb24kvXLArZ6recCA/x3EpEbgBsA2rZtG9GJojUEFqBdu3bk5uZ61m3yPhNNcXFxtGnThjZt2nDmmWeWKy8rK2PPnj1s376d/Px88vPz2bNnD1deucezPHVqPgcPHuDIkX2UlOynrKyQLVsOAUf47jt46CFISvJ9uZ/uunOn84WWlASJiRAf73yplZQ45e4v9YQE58vQXe7+49id+SQkHPsyFIG//tVZ7tzZCRTu/UV8g0SvXjBq1LEyESf4uIPE0KFw+unOdvfxd+06FiRGjgTXU4I9fvzxWJA45xzo0cO3fPXqY0HiggucbM3bV18dCxKXXlo+CH3yybEgceWV5YPMBx8cCxKTJjnX1tu//+0EiWiI+DmXqloAzHG9ABCRVjgBozfVOG24qr4AvACQk5MT0RDcaA2BBWcCv8XuWd+wTMLUrLi4ODIzMz3T0YejuLiYgwcPcuDAAQ4fPsyRI0coKiriyJEjXHut8+69zf1eUlLCHXeUeqbY37vXeS8tPbZt4sRj2xYsKPGUlZWVoapcdJGiquzfr7zyirPsLlNVxo1z3jdsUNavV89292vUKOf9s8+UxYv9y8s4/XSnCe/tt5W33y7/s592mvM+Z44yZ45vmaoyZIgTtWbM0HJlAIMHO+XPPVdWrgyEQYOc8ieeKCs3EaQqDBzoRLQHHywtV7eyMhgwIC4q91hV6cOQVXUn8J7rVRW2AW281rNd26pctIbAAgwZMoTHH3/cs25BwtRWiYmJNGnShCb+f+qaOivWJwn6EugiIh1cDzaagNOkVeWiNQQWYNCgQT7rdsOcMaa2qNJMoqqpaomI3ITzjO144B+quioa54pmc5N/Wr9/f619yqsxpp6J9UwCVX1HVU9U1U6q+sdonSfSjuvi4mJKS502wri4uKCfveWWWzzLV1xxRWWra4wx1SKmM4nqFGkm4d/UFGz88gMPPECzZs3o2LEjffv2rYIaG2NM9FmQcIm04/p4TU1ujRs35r777qtkLY0xpnrFfHNTdYm04/p4ndbGGFObWZBwqarmJmOMqUssSLhE2nEdanOTMcbURhYkXCLNJA4ePOhZtyBhjKlrLEi4RJpJeN/zEOzZEcYYU1tZkHCJNJM4cODYbJgWJIwxdY0FCZdIh8B6ZxI23YYxpq6xIOES6hDYuLg4nyCyZ88ez7IFCWNMXWNBwiXU5ibwzSby8vI8y9bcZIypayxIuITacQ2+QWLXrl2eZcskjDF1jQUJl6rIJCxIGGPqGgsSLqF2XEPwTMKam4wxdY0FCZdQO67B96a5HTt2eJYtkzDG1DUWJFzCaW5q2rSpZ7mgoMCzbJmEMaausSDhEk7HdbNmzQJut0zCGFPXWJBwCSeTsCBhjKkvLEi4VEUmYc1Nxpi6JmaDhIhcKiKrRKRMRHKifb5I+yS8WSZhjKlrYjZIAN8BFwGLquNk4QyBDZRJJCYmkpycXOX1MsaYmhSzz7hW1TUAIlIt5wtnCGygINGwYcNqq6sxxlSXWM4kQiYiN4jIMhFZtnv37oiOUdmOa2tqMsbURTWaSYjIR0CrAEV3q+qboR5HVV8AXgDIycnRcOuhqpXuuLZOa2NMXVSjQUJVz6rJ87uVlJR4luPj44mLqzjBskzCGFNf1InmpsoKp9MaAo9usiBhjKmLYjZIiMiFIpILDALeFpH3o3WucDqtAVJSUnwm+QNrbjLG1E0xGyRU9Q1VzVbVZFVtqaqjo3WucDqt3fybnCyTMMbURTEbJKpTOJ3Wbv5Bolu3blVaJ2OMiQUWJIgsk/APJhdeeGGV1skYY2KBBQkiyySWL1/us965c+cqrZMxxsQCCxJElkmMHz8+4LIxxtQlFiQIfwgswG233UbLli055ZRTmDp1arSqZowxNSpm526qTuEOgQXIyclh27ZtxMfHR6taxhhT4yyTILLmJsAChDGmzrMgQWQd18YYUx9YkCDyTMIYY+o6CxJE1nFtjDH1gQUJIuu4NsaY+sCCBNbcZIwxwViQwDqujTEmGAsSWCZhjDHBWJDAMgljjAnGggSWSRhjTDAWJLAhsMYYE4wFCWwIrDHGBGNBAmtuMsaYYGI2SIjI4yLyvYh8IyJviEiTaJ3LOq6NMSawmA0SwIfAKaraE1gH3BmtE1kmYYwxgcVskFDVD1S1xLX6OZAdrXNZx7UxxgQWs0HCzyTg3WCFInKDiCwTkWW7d+8O++DWcW2MMYHV6JPpROQjoFWAortV9U3XPncDJcArwY6jqi8ALwDk5ORouPWwTMIYYwKr0SChqmdVVC4iE4FzgTNVNewv/1BZJmGMMYHF7DOuRWQM8HtgmKoeiua5rOPaGGMCi+U+ialAQ+BDEVkpIs9H60Q2BNYYYwKL2UxCVTtX17kskzDGmMBiOZOoNtZxbYwxgVmQwDqujTEmmJhtbqpOTZo0ITMzk6NHj5KSklLT1THGmJhhQQJ4/fXXa7oKxhgTk6y5yRhjTFAWJIwxxgRlQcIYY0xQFiSMMcYEZUHCGGNMUBYkjDHGBGVBwhhjTFASxRm4a4SI7AY2u1YbA/u8io+33gLYE6Wq+Z+rKj9T0X7BygJtt+tVuevlv82uV/jbvNftelXf9WqnqhkBS1S1zr6AF8JcX1ZddanKz1S0X7CyQNvtelXuevlvs+tVud85u16xcb3qenPT/DDXoymSc4X6mYr2C1YWaLtdr8pdL/9tdr3C31Zd18yuV4jqXHNTZYjIMlXNqel61BZ2vcJj1ys8dr3CE63rVdcziXC9UNMVqGXseoXHrld47HqFJyrXyzIJY4wxQVkmYYwxJigLEsYYY4KyIGGMMSYoCxIhEpELRORFEXlNREbVdH1inYh0FJFpIjK3pusSq0QkXURmuH6vflbT9Yl19jsVnqr6zqoXQUJE/iEieSLynd/2MSKyVkQ2iMgfKjqGqv5bVX8O/AIYH8361rQqul6bVPW66NY09oR57S4C5rp+r8ZVe2VjQDjXq77+TnkL83pVyXdWvQgSwHRgjPcGEYkHngXGAt2By0Wku4j0EJG3/F6ZXh+9x/W5umw6VXe96pvphHjtgGxgq2u30mqsYyyZTujXy0R2vSr1nVUvnnGtqotEpL3f5v7ABlXdBCAis4DzVfUR4Fz/Y4iIAI8C76rq8ujWuGZVxfWqr8K5dkAuTqBYSf35g81HmNdrdfXWLvaEc71EZA1V8J1VL38xXbI49lccOP9hsyrY/2bgLOASEflFNCsWo8K6XiLSXESeB3qLyJ3RrlyMC3bt5gEXi8hzVO8UHrEu4PWy36mggv1+Vcl3Vr3IJKqCqv4V+GtN16O2UNV8nLZQE4SqHgSurel61Bb2OxWeqvrOqs+ZxDagjdd6tmubCcyuV+Ts2oXHrld4onq96nOQ+BLoIiIdRCQJmAD8p4brFMvsekXOrl147HqFJ6rXq14ECRF5FVgCdBWRXBG5TlVLgJuA94E1wGxVXVWT9YwVdr0iZ9cuPHa9wlMT18sm+DPGGBNUvcgkjDHGRMaChDHGmKAsSBhjjAnKgoQxxpigLEgYY4wJyoKEMcaYoCxIGGOMCcqChDHGmKAsSBhTh4jIcyKyTUTsLllTJeyOa2PqEBE5HVgL7FRVqen6mNrPMglTL4jIBBE5IiKJIe7/sYio6/Vbr+1TXNvWB/ncelf5lCqqelhUdZGq7gpU5lV3FXtOtAmRBQlTX/QCVqtqcRifWQgMAmb5bS8COohIjvdGEekHtHeVx6KXcH6eFTVdEVN7WJAw9UUvwv9y/ElVP1fVnX7bDwILcKZk9jbBtf1gZFWsmIgsF5E9AV6vhPJ5Vc1V1c+B/dGon6mbLEiY+uJUnGdJAyAiZ4hIvoj8xfUg+XDNAi5zPfvc/Qz0yyifdSAi00VkmYhcICLfi0iRiHzq97B6ROR0EVkoIoUiss/V5NXbXa6qfVS1RYDXzyKovzEhsSBh6jwRyQBa4woSInIz8BbwB1X9raqWRnDYeUBL4DTX+lAgw7U9kHbAk8BDwBVAY+B9EUlx1Wk48F+gGLgGGA98QsXPXTcm6uwZ16Y+6AUosFpEXgQuAs5W1Y8jPaCqFojIezhNTJ+43t9T1X2u5MJfC+B8Vf0MQES+AjYCE4HngUeAr4HRemzI4Xvh1ktEXgLGuJZzXXW6PtzjGONmmYSpD04FfsL5K/80YEBlAoSXWcAlIpIMXEKApiYvee4AAaCqm4GvgP4ikg4MAGZoJcekq+r1qpqtquJ6twBhKsWChKkPegGC0yR0k6puqKLj/gdoAPwRSAfmV7BvXpBtrYGmrvrtqKJ6GVNlLEiY+qAX8FfgZeCfrj6KSlPVgzh9G7cC813rwWQG2bYD2AuU4QQMY2KKBQlTp7magroB3wA3AHuAOSJSVf1xz+FkEM8fZ79MERnsVa+2QB9gqSu4fAFcLUE6NIypKRYkTF3XHUgEvlXVw8CFwMnAU1VxcFX9WFUvCKGPYw/wsohcISIX4mQgecB0V/kfcDKed0XkIhEZ7bpD+tyqqKcxkbIgYeq6Xjg3t20ET4fxeOCXIjKxGuuxGbgNmILTwX0AZyRTkatei4CRQBpOs9hrwDAgtxrraEw5NsGfMQGIyMdAPk5AKa3MqCMRmQ6coqo5x9s3mkQkDucPw/8Cu1X1kpqsj6kdLJMwJriLcG5uu6WmK1JF7sP5eU6v6YqY2sNupjMmsBuBhq7lLTVZkSr0Ak5fCDj3jRhzXNbcZIwxJihrbjLGGBOUBQljjDFBWZAwxhgTlAUJY4wxQVmQMMYYE5QFCWOMMUFZkDDGGBOUBQljjDFBWZAwxhgT1P8HdgnL0T1HhnIAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# FFTLog calculation\n", "pk = pl.fourier(cosmo, k_arr, 1E14, a_sf, hmd_200c)\n", "# Analytical prediction\n", "pk_pred = 1E14 / (1 + (k_arr * rs)**2)\n", "\n", "# Plot!\n", "plt.plot(k_arr, pk,'k-', lw=3, label='FFTLog')\n", "plt.plot(k_arr, pk_pred,'y--', label='Analytic')\n", "plt.legend(loc='upper right', fontsize=15)\n", "plt.ylabel(r'$\\rho(k)\\,\\,[M_\\odot]$', fontsize=15)\n", "plt.xlabel(r'$k\\,\\,[{\\rm Mpc}^{-1}]$', fontsize=15);\n", "plt.xscale('log')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FFTLog is obviously not doing a very good job here. We can improve the result by tweaking the FFTLog precision parameters through the `update_precision_fftlog` method. This will almost always be the case when you create a new profile if you want to rely on FFTLog to produce these predictions. Below we show how we can improve the results significantly doing this (see the documentation to understand what the different precision parameters do)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Update parameters\n", "pl.update_precision_fftlog(padding_hi_fftlog=1E2,\n", " padding_lo_fftlog=1E-2,\n", " n_per_decade=1000,\n", " plaw_fourier=-2.)\n", "\n", "# Recompute fourier profile\n", "pk = pl.fourier(cosmo, k_arr, 1E14, a_sf, hmd_200c)\n", "\n", "# Replot!\n", "plt.plot(k_arr, pk,'k-', lw=3, label='FFTLog')\n", "plt.plot(k_arr, pk_pred,'y--', label='Analytic')\n", "plt.legend(loc='upper right', fontsize=15)\n", "plt.ylabel(r'$\\rho(k)\\,\\,[M_\\odot]$', fontsize=15)\n", "plt.xlabel(r'$k\\,\\,[{\\rm Mpc}^{-1}]$', fontsize=15);\n", "plt.xscale('log')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Projected profile and cumulative surface density\n", "Let's now do the same with $\\Sigma(R)$ and $\\Sigma(" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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VY3xRmTLLk1zm75/9usuzZct33eXBweHXXe6pb7/9lqNHj/Lkk09y9OhRwHXKNigoiIkTJ1KhQoVL6149MFW2bNk4e/Ys4GoJ1KpVixMnTtC7d2/uuusucuTIwTvvvHPNQPdXa9myJS+99BLDhw9n3bp17Ny581ILxBOHDx+mQIECHm+XUr52N9GrwDanQ6SFvn370rhxK0TgpZdg//6h9O3b1+lYxmQqF68NNGjQgJtvvpmbb76Z8PBwzp07x9SpU4mPj0/Wfn777Tc2bdrERx99RMuWLYmMjCQiIiJZ1/waNGhAQEAAU6ZMYezYsZQvXz5FI8jlzZuXffv2ebxdSiWrGIhIHRF5RURKXDW/fVLbeEpECgFPAZ97a5++REQYMWIEderU4eaboU0bWLu2GyNGjHA6mjGZwqlTp5g9ezaNGzdm2bJlV0yDBw9m//79LF26NFn7uvhHPygo6NK8nTt3Jnnx+HIhISE0btyY4cOHExsbS/Pmza9YfvH01cVWSFKeeOIJNm3axObNm5OVObVuWAxEpD+uT+x3AYtE5LXLFnve9knah0BnIMmT6SLSRkQ2iMiGgwcPevGt04e/vz8TJkxk/frK/Oc/0KEDTJrUzqcGuDAmo5o5cyanT5/m1VdfpVKlSldM7du3J2/evMl+5uDuu++mUKFCdOzYkblz5zJp0iSioqIICwtL1vYtW7Zk48aNqCoxMTHX7Btg6NChfP/99/z666+J7uOFF16gZMmSREVFMWLECJYtW8aYMWPo0qVLsjJ4Kjktg6eAqqr6ClAGqCUiA93LvHLCW0SeBg6o6g/XW09VR6pqhKpG5M+f3xtvne6CgoL45puZzJ5d9lLHdoMGPXvd+5eNMTc2ceJEihUrRvny5a9ZFhgYSMOGDYmNjeXcuXM33FdQUBCxsbEEBARQv359unfvzltvvUVkZGSyskRERBAWFkbdunW56aabrlj2+OOP88YbbzB06FDKly9P27ZtE91HcHAwS5cupWbNmrzzzjvUqFGDAQMGULBgwWRl8JTcaHQuEdmiqvdd9job8DVwHIhQ1VKpDiHSD3geiAOCgdxArKo+l9Q2ERERumHDhtS+tWMOHTpEVFQFWrfewYQJsHFjdpYsWXLD282MSSvbtm1L0bltc62tW7dy3333sXjxYp544ol0fe8b/RxF5AdVjbh6fnJaBvtEpOzFF6p6HmgEKHB/CrJeQ1XfUtVCqloUiAGWXq8QZAYXO7br378Qq1bB6dOnqV27Blu2bHE6mjEmhQ4fPsyaNWt4+eWXuf/++9P0uQBvS04xaMZVzwqoaoKqtgIeT4tQWUV4eDgLFiwiX758VKoEH354lGefrXKpgy1jTMYye/ZsHnvsMfbt23ep24uM4obFQFV3q+rfSSxb4+1Aqro8Mz1jcCN333033377LYcOhZArF3TseIC6dStbx3bGZEDNmjUjISGBrVu3OtrpXEp4/JyBiHyVFkGysoiICIYOncM77wQQGurq2O6ZZ6KsYztjTLpJyUNn1b2ewlClShW6d/+3Y7tGjTZTp87T1rGdMSZd+NoTyFlanTp1aN36c/r3h82bYdmyVTRq1Ii4uDino5ks4kZ3FxrflpqfnxUDH9OiRQuqVx/AF1+4Xq9dO5tWraxjO5P2AgMDrSWawZ05cybFPSJbMfBBb7zxBp07dyZfPhg1CkJCxtGpU0f71GbSVGhoKHv27OH06dP2u5bBqCqnT59mz549hIaGpmgfno5nYNJJ//79OXz4EEuXjqFRI/jssw/p3z+Ut956y+loJpPKnTs3AHv37uXChQsOpzGeCgwM5NZbb730c/TUDZ9AvmYD19Nrjt8zldGfQE6OuLg4GjVqyD33TKdqVfjgA6hZc0SSj68bY8yNpOYJ5Cv4QiHIKgICAvj66wmsW1fpUsd2I0e+yNSpU52OZozJZOw0kY8LDg4mNnYW1atHsmPHJn75BZo0aUKePHmoVq2a0/GMMZlEii4gi0gpEbl24FPXsidF5IHUxTKXy5UrFzNnLmD16hKcPw/Zsl3g9ddrsW7dOqejGWMyiZTeTTQEuLafWJcH3cuNF+XPn59FixYRHh5O587Qp89ZWreuztatW52OZozJBFJaDMoCSQ35sxbXuAfGy8LDw1m4cCGTJ+chLg66dz9G48ZV2Llzp9PRjDEZXEqLgT+QI4llOYBsKdyvuYG7776bsWMX0rNnCCEh0LHjfurWrXzDQbqNMeZ6UloMvgfaJLGsDZC57/l02IMPPsiHH86+1LFdnTp/EB0dzfHjx52OZozJoFJ6N1FPYLGIrAO+BP4GCgAvAKUAu80ljT3xxBN06zaZbt3q89dfysGDm6hVqxbz588nODjY6XjGmAwmRS0DVV0JROEavP4jYBowFNewldVU9TuvJTRJqlu3Lu3ajeLgQfDzg1y5VtC4cUPr2M4Y47EU903kHoTmESAXEA7kVtVHrRCkr5YtW/L+++8TEQEdO0Lx4rNp3bqVdWxnjPFIiouBiGQTkTbAMGAkMExEWouIXTxOZ507dyYy8g3GjoUaNSA4+EveeKOTdTZmjEm2lD50dg+wAxgO3A/Eu78OB34TkXu9ltAky/vvv4+/f3NiY6FRI9i7dwjvv/++07GMMRlESlsGI4FjwJ2q+rCq1lLVh4G7gKPACG8FNMkjInz22Uh27arNkiXQtCkMGvQWo0aNcjqaMSYDSGkxiADeUdW/Lp/pft0D11PIJp0FBAQwceIk1q6NpH17OHQIXnzxRaZNm+Z0NGOMj0tpMfgTSOr+xWDgrySWmTR2sWO7PHlcnctGRycwaFBjFi9e7HAyY4wvS2kx6AL0EZEr+icSkYeBd4E3UxvMpFzu3Ln59ttvueeeYtStC++8E0fnzjVZv36909GMMT4qpcWgG5AbWCMi+0TkJxHZh6u/otxAVxFZf3HyVliTfPnz52f+/MUMGVKAf/6BHj3O0qpVFNu2bXM6mjHGB6X0CeRf3JPxYYULF2bq1CXUr1+Bd989Svfux4iJqcysWesoUqSI0/GMMT4kRcVAVZt7O4hJG/fccw9jxy6kRYuK9O17liJF9hMVFcWqVavInz+/0/GMMT4ixQ+dmYzjwQcfZMiQ2bRqFcjs2bB9+3br2M4Yc4VktwxE5B1PdqyqvT2PY9JK1apV+eSTiTRs2JB77kmgdu2N1K37NHPmLLSO7YwxHp0m6gmcAU4BcoN1FbBi4GPq1avHiBEjmDSpDRUrgsh3PPtsI6ZM+YaAABsO25iszJPTRP8DAoEfgE7AHaqaP4kpNE3SmlRr3bo11ar1Y9gwePxxKFZsFm3atLZ+jIzJ4pJdDFS1GFAB2ILrWYL9IhIrIg1EJCStAhrve/PNN7nzzk6XOrbLlm0sb77Z2elYxhgHeXQBWVU3qGonVS0MROMa1OZj4ICIfC0iFVMSQkSC3c8k/CQiW0SkV0r2Y5JHRBgwYAB+fs2IjYUCBWDQoA+sYztjsrDUjGewUlVfwjWWwQigEfBaCnd3DqiiqqWA0kC0+2lmk0ZEhJEjR/HXX7Xo3RsSEqBr1y7WsZ0xWVRqxjN4VEQ+AnYC7fh3tDOPqctJ98tA92QnsdNYQEAAkyZNpmLFStx8M4wcCRMmtOWbb75xOpoxJp15VAxEpKyIDBCRncASXK2CDkCoqsao6oqUBhERfxH5ETgALFLVdYms00ZENojIhoMHD6b0rcxlgoODmTlzJsWLl+bMGXjrLWXgwBiWLFnidDRjTDpKdjEQkV+B/wAP4OqmOlRVn1HVSap6OrVBVDVeVUsDhYCHROT+RNYZqaoRqhphT896T+7cuZk1awGjR9/J7t3Qo0ccb7xRk++//97paMaYdOJJy6AYrgHvywEDcI1odiCpKaWBVPUosAzXBWqTTkJDQ5kxYwmDB9/m7tjuDK1aVbOO7YzJIjx50ijN7vARkfzABVU96r5NtRpgt7aksyJFijBliqtju+bNj7F79zGioqJYvXo1hQsXdjqeMSYNiS88bCQiDwBfAv64WitTbtSdRUREhG7YsCE94mU569evp0qVKpw6dQo/PyhV6i4WLFhjHdsZkwmIyA+qGnH1fJ/oqE5VN6tqGVV9QFXvt36NnPXQQw8xY8YMAgMDeestaNv2N555JooTJ044Hc0Yk0Z8ohgY31O1alUmTJjAkiVw551Qr96P1K37NGfPnnU6mjEmDVgxMEmqX78+zZt/xvvvQ9myULHiSp59thFxcXFORzPGeJkVA3Ndbdq0oUqVvnz0katju8KFZ9G2bVvr2M6YTMaKgbmhLl26ULTo63z2GSxcCGPGjKFLly5OxzLGeJEVA3NDIsIHH3xAcHAzLj52EBs7gAEDBjgbzBjjNV4tBiJSQUTmisg6EZkjIhW8uX/jHBFh1KhR1KpVi8ceg1GjYMWKNxk5cqTT0YwxXuC1YiAiVXE9mfyqqpbH1WfRIBF5wlvvYZwVEBDA5MmTyZatIuvWweuvw9dft2Xy5MlORzPGpJI3WwZ9gEaq+huAqu4AGgL9vfgexmHBwcFMnz6bmTPLsG0bvP02DBrUhPnz5zsdzRiTCt4sBjlVdY+IFBaR0yLysKruAnJ58T2MD3B1bLeQL74o5u7YLp7mzeuwatUqp6MZY1LIm6Ogx4tILmAPcA+wT0RuwtW5nclk8uXLx8yZS3nqqYfJm3cPf/99lqeffprly5dTunRpp+MZYzzkzZbBQFz9CwWp6k5chWYcdpoo0ypUqBDTpi1j69ZbAShS5BjPPvsE27dvdziZMcZTXmsZqOp4EQFYLiLxuArNMFX92lvvYXxPsWLFWLBgAVFRkXTvfoyzZ49Qr14V5s1bS3h4uNPxjDHJ5NVbS1V1vKo+pKqPqGp5KwRZQ6lSpZg+fR79+gWRNy+8+uoeateugo1GZ0zGYQ+dGa+oUKECffvOpFcvf4oUgRYtfqNWrWocO3bM6WjGmGSwYmC8pnr16nTsOJH33hPuuQcKF/6JWrVqcebMGaejGWNuINnXDESkI7AZ2Kyq+9MuksnIGjRowLFjx3j11dZs3QqqK2nQoAHTp08nMDDQ6XjGmCR40jIYCMwH9orIfhFZLCKDRaS5iJQTkeA0ymgymFatWtGs2UBU4dZbITR0Ls2aNSUhIcHpaMaYJHhSDI4Cp4GJwGjgLFDP/f164ISI/FdEpojI215PajKUTp060bVrVypWhBdegDx5JtK+/f9Z19fG+ChPisHtwEdAbeBxYICqFgFuBiKBV4ClQAGgo5dzmgyoT58+5Mv3IrGx0KABnDw5gm7dujkdyxiTiGQXA1U9pqpdgTuBTcBCEZkP3KWqq1T1U1V9SVUfV9Vb0iqwyThEhI8/Hs6hQzEsWAAtWsC2bX354IMPnI5mjLmKx3cTqeoBVX0FKA7sBdaKSKyI3OP1dCbD8/Pz48svx/HLLzVYtQqqV4cuXd5g9OjRTkczxlwmxbeWqupfqtoCKImr/6HNImLnAMw1AgMDmTLlG5Yte4yOHSE+3jWc5rRp05yOZoxx86gYiMudIvKUiHQSkdHAGKAq4A/clxYhTcYXEhLC9OlzKVGiLEFB0KNHAgMGxLBgwQKnoxlj8KAYiMhm4BSwHfga151ECkwDYoBCqto4LUKazCF37tzMnz+fe++9i0KFoFeveLp0qc2aNWucjmZMludJy+B+4DyuQtAGaA60UdUhqrpQVfemRUCTueTPn5+ZM5fy4YdhHDkCPXueo127aDZv3ux0NGOyNE+KwVDgeyAKmARsAU6KyA8iMlZEOopIlIgUSIugJvMIDw9n2rSl9OuXl/PnoXv3Ezz3XBV27NjhdDRjsixPbi3toKrVVPU24DZcRaEr8BOuawW9cT2hvFtErLtKc13Fixdn/PjF9O6dk5Mn4fTpw1SrVo3du3c7Hc2YLClF4xmo6gFgiXsCXBeXgWLAA7hOKRlzXaVLl2bEiPlUr16VU6fOAjt58smqLF26inz58jkdz5gsxWu9lqrLdlWdpqo9vbVfk7k9+uijTJvm6sSuaVNo1+5XnnkmiuPHjzsdzZgsxZO7iV4RkVBPdu7exj7imeuKjo5m/Pjx7NgBxYtD3bqbqFv3aev62ph05EnLYAhQJPhwkLAAABq+SURBVLkri4i/e5vCnoYyWU/Dhg1p1mwk/ftD2bJQqdJ3NGxYj/PnzzsdzZgswZNrBgL0E5EjHqyfvBVFwoFxwK24nl0YqapDPchmMoHWrVvzzz//MHTom7z6Kpw8+S3PP/88EyZMwN/f3+l4xmRqnhSDlbieMs7v4TYnkrFeHNBRVTeKSC7gBxFZpKpbPXgvkwl07tyZt98+xsiRfdm/H5YunUL27NkZPXo0fn42MJ8xaSXZxUBVK6VVCFXdB+xzf39CRLYBYYAVgyyoT58+vPbaSSZOHAbAokVjefXVnAwbNgzXTWvGGG/zuY9aIlIUKAOsczaJcYqIMGTIEFq0aEHx4vDFF3DkyMe8/baNmWRMWvGpYiAiOYFvgNdU9Zp7C0WkjYhsEJENBw/ac22ZmZ+fHyNHjqRs2QasWAGtW8Ovv/ajb9++TkczJlPymWIgIoG4CsHXqhqb2DqqOlJVI1Q1In9+Ty5dmIzI39+fceO+5uefn2LlSnj5ZVi9+m2GDRvmdDRjMh2fKAbup5dHA9tUdbDTeYzvCAwMZPLkaaxeXZn166FjRxgx4lXGjBnjdDRjMhWfKAbAo8DzQBUR+dE9Pel0KOMbgoODiY2dzbx55Rk2DLZtg1atWjFp0iSnoxmTaaSobyIAESkJPISr07pg4AiusQ7WqOo/nuxLVVfhwXMJJuvJkSMHM2bMp0qVKsAmChRQBg1qQo4cOahZs6bT8YzJ8DwqBiJyB9AOaILrAbEE4ChwDsgDZAcSRGQF8DkwWVUTvJrYZFl58uRh4cKFREZG8sILWylVKoG3365HSMg8qlat6nQ8YzI0T/om+hzXGAalcXVXXQYIVtX8qlpIVXMCoUBN4GdgALBNRB7zfmyTVeXLl49FixYxeXIRDhyA3r0v0LHj06xevdrpaMZkaJ5cMzgD3O0e02CEqm5W1fjLV1DVQ6r6raq+hqsfo3dwPTxmjNcULFiQ2NjlfPDBbRw7Br17n6Ndu+ps3LjR6WjGZFieDG7zsqru9GD9BFWdrKqTUxbNmKQVLVqUadNW0Leva7S0Bg1OERUVxZYtW5yOZkyGlOILyMY4rXjx4kyYsJRGjR7nzz+Pc/asa7S07777jjvvvNPpeMZkKL5ya6kxKfLAAw/w5ZeLCAjISUgIPP/8PurVi2TXrl1ORzMmQ/HkAvItIjJBRA6KyN8iMlJEbr5qnYdE5B0RWeP9qMYk7qGHHmLu3LnccUcQkZHw2mt7qF07kn379jkdzZgMw9PBbRoCa4DZQAVgjoiEisgwEfkbWIvrorHdTmrSVcWKFRk0aCbdu/tToAC0a/cHTz9diQMHDjgdzZgMwZNiUB3ooqq1VbU1UBJXF9PfA+2BjUBT4FZVtdtJTbqrXr063bpNpWdPP4oWhZYtt/P005U5dOiQ09GM8XmeFINQYNXFF6qqwLtAOPCOqj6pquNV9bCXMxqTbHXq1KFDh4n07i3ccgvs3buVatWqceRIcgfoMyZr8vRuovirXu9xf13khSzGeEXDhg25cOECTZs+x/nzsGfPjzz5ZDXmz19Cnjx5nI5njE/ytBh8KCI/ANvc0//c823UcuNTmjRpwoULF2jevDlt20Lx4hupVSuKOXMWkzt3bqfjGeNzPCkGQ4H7cV1EDsU1cP1FH7vvINoE/Aj81/okMk5r1qwZ58+fZ+rUtjRsCPHx31O7dg1mz15Azpw5nY5njE/xZAzkDhe/F5FQXBeQSwIPuL++BIS4VzkN2P8247g2bdpw4cIFBgxoT+fOkJCwhmeeeYpZs74le/bsTsczxmek6AlkVT0ALHFPwKUBaorhKg73eyWdMV7wf//3f5w/f55Bg17njTfg3LmV1K5di9mz5xAcHOx0PGN8gte6o3DfXbTdPU3z1n6N8YYOHTpw4cIFBg9+k3/+gVWrllC3bl2mT59OUFCQ0/GMcZx1R2GyjM6dO/PQQ++yyn2D9F9/fUvDhvU4f97ufzDGioHJUrp160b37t0pVAiGDoWSJefSuHEjKwgmy7NiYLKcXr168dxzXfj8c6haFUqUmEGjRg2sIJgszeNiICJ3iEiciEQlsqyJiJwTkfzeiWeM94kIffv2JSysI6NHQ1QU3H33LBo0qMe5c+ecjmeMIzwuBqr6O7ASaJnI4mbAXFU9mMpcxqQpEWHgwIEUKPAGY8ZA9epw4sQc6tevbwXBZEkpPU00GqglIpee7ReRwkAVYJQ3ghmT1kSE999/n7CwLnTsCMuWwZw5c6hbty5nz551Op4x6SqlxWAarjGRm1w2rymwG5if2lDGpJeLp4yio7sCUKQIFC8+j3r1altBMFlKioqBqp4DJgAtLpvdDBjrft7AmAxDROjTpw/dunWjVCmoXRvKl19InTo1OXPmjNPxjEkXqbmbaDRQWkRKikgkUAQY451YxqQvEaF3796ULv0OH38MFSvCo48utoJgsowUFwNV3YSrY7qWuFoFS1V1p5dyGZPuRIRevXpRsmRPhg6Fxx6Dxx9fwjPPPMWpU6ecjmdMmkrtcwajgeeA+sDnqY9jjPN69OhB2bK9GTIEQkJgxYplREdHc+zYMaejGZNmUlsMvgay47qYPD31cYzxDd27d6d8+ffcHdvBpk2rqFGjMocP20B+JnNKVUd1qnpcROoA51T1gpcyGeMTunbtSvbs2Xn99Q689x6IbCI6+nFmz17Kbbfd5nQ8Y7wq1d1RqOoCVV3uhSzG+JzXXnuNESM+Y8YMuPdeaNVqG08++Si7du1yOpoxXmV9ExlzA23atKFVq/G8844fRYvCK6/8ztNPP8L//ve/G25rTEbhM8VARMaIyAER+cXpLMZcrUmTJrzxxjTeftuf0FBo2nQPjz/+OFu3bnU6mjFe4TPFABgLRDsdwpik1KlThz595tC1azYGD4Z9+/YRGRnJhg0bnI5mTKr5TDFQ1ZXAEadzGHM90dHRDB26kGPHXEN816lziObNK7J48WKHkxmTOskuBiLyvIj4e7JzEblLRB73PJYxvisyMpLFixdz++15qFoV+vU7w5tvRjN58mSnoxmTYp60DF4H/ici74pIqaRWEpG87nENZgM/AgVSG/KyfbcRkQ0isuHgQesl2zinfPnyzJ27hr59b+PIEejXL57hw2P46KOPnI5mTIqIJ/3KiUgj4GWgAnAS2AYcAs4BeYDbgcLAP8B4YKCq7vFg/0WBOap6/43WjYiIUDtXa5y2a9cu6tZ9gubNd1CiBAweDGXKvM27776LiDgdz5hriMgPqhpx9XyPrhmo6mRVfQwoBryB65N/HJAD2A98iesicAFVfc2TQmBMRhQeHs78+WuZNOlB1q6Fgwfhvffeo02bNsTFxTkdz5hk86hlkJZEZCJQCciHq7D0UNXRSa1vLQPjS06dOkXDhg2ZN28eAKVKwR131ObrrycSEhLicDpj/pXqloGIvCAieZOxXpiIvONpQFVtrKoFVDVQVQtdrxAY42ty5MjBjBkzeOGFFyha1HW6qHTpmVSvHsmBAwecjmfMDXlymugL4M5krFcI6JGyOMZkXIGBgXzxxRfUr9+J4cNdXWA3bvw9UVERbNu2zel4xlyXJ8XgiqthIhIgIl1EpKCXMxmTYfn5+TFw4EAiI4fSo4dQtCh06bKLhg0fYunSpU7HMyZJKXroTERuA1YAfYFfRKSpV1MZk8G98sordO48ky5dggkMhBIlTlK9enXGjLHBAI1v8rgYiMgjwEZct5I+DMwAvhCR2e4iYYwBatasydixa3jrrdv45huIi4ujc+eWdO3alYSEBKfjGXMFT4tBS2AZ8B+gvKquV9UWwNNAGWALEOPdiMZkXGXKlGHp0u8pVaoUBQvC2LFw5Eg/6tWrw/Hjx52OZ8wlnhaDFsC7qlpXVU9enKmq84D7gXnAq17MZ0yGV6hQIb777jvKlIlm8WKIiYFHHplFlSoPsn37dqfjGQN4Vgx6AdGq+l5iC1X1qKo+D9QEensjnDGZRa5cuZgxYzZ+fh344AMoUwY6dNhOgwblmDt3rtPxjEl+MVDVXqq6JBnrzVXVXqmLZUzmExAQwODBg4mJ+Yo338xGcDBUrnySmjVr8t577+ErD4CarMlnnkD2lD2BbDKyjRs30rRpTX79dS8XLsAtt0CVKnUZPfoLcufO7XQ8k4l5pW8iY4x3lC1bliVLNlGhQiTBwTB0KDz4YCyRkaXZtGmT0/FMFmTFwBiHhIaGsmjRIlq3bs+UKVC6NHTt+getWj3EJ598YqeNTLqyYmCMgwIDAxk27CMaN55Ap04hnD0LAwbEsWbN/9GwYQOOHTvmdESTRVgxMMYHNG7cmGnTfmT48JIsXw4PPwzTp39D6dKl+e6775yOZ7IAKwbG+IjixYuzfPl6jhxpxxtvQHw8HD36J2+9VZHOnTtz7tw5pyOaTMyKgTE+JDg4mOHDP+Grr6aSJ08eGjWCPn3Az28gjz1Whh9//NHpiCaTsmJgjA+qX78+v/zyCzt3VmXcOKhWDTp12kabNhG8++67nD9/3umIJpOxYmCMjwoLC2PevIVERAynU6cgzp2DAQPiWb36HcqUKcOqVaucjmgyESsGxvgwEeGll15i8uTNjBoVwddfw7p1sHXrVqKjH6dt2zb8888/Tsc0mYAVA2MygOLFi7Ns2Vruu28IFy7kwM8PBgyAO+4YRcWKxfnyyy+tW2yTKlYMjMkgAgICeO2119i2bRs1a9Zk6VIoWRIGDjzEihXNePTRsqxYscLpmCaDsmJgTAYTHh7O9OkzadIkli5dbmX1anjhBejU6SdatKhE3bp1+e2335yOaTIYKwbGZEAiQp06dVi9egfQjQ4dsvHzz7BrF0yfPp0KFe6mTZvW/Pnnn05HNRmEFQNjMrBcuXLx7rvvMmvWb/z2WxMuXIDAQPj443juv/9zGja8k9atW/HHH384HdX4OCsGxmQC4eHhjB8/nnXr1vHoo48ycSIUKAADBiRQqtRoGje+i+bNm/HTTz85HdX4KCsGxmQiDz30EEuXfscrryzl008fY8gQCA2F/v0T+OGHLyldujSVKlUiNjaWuLg4p+MaH2KD2xiTiS1fvpw+fXogspIlS0AVnn0WgoLghx8K0qBBO5577jmKFi3qdFSTTmxwG2OyoEqVKrF48Qp6915Do0YxBAQEULgwPPccDBq0F+hO06a3U7nyY4waNYqjR486Hdk4xFoGxmQhe/bsYcSIEcyY8QmPPnqEatUgb16YORM+/BCCgrJRrVpVataszdNPP03BggWdjmy8LKmWgRUDY7Kgs2fPMn36dMaP/5LDhxexf38Cf/4J99zj6iV13TpYvRoSEspQvXptKleuTPny5QkKCnI6ukklKwbGmETt37+fiRMn8tVXX3Hs2EYaN4by5SFnTjh/Hn78EQYOhBMngnj44YeJjIzkscceo2zZsuTNm9fp+MZDVgyMMTf0+++/M3v2bObMmcHRoyspXz6B0qXhpZfgwgV4/nl44AH45RfYsQPOnCnE7bc/SNmy5ShZsiQlSpTgjjvuIDAw0Ol/ikmCFQNjjEeOHj3KggULWLx4MStWrGDHjh3Uqwc1akDRouDv71rvjz+gRQvX9+XKQUKCP35+RShY8F6KFr2d8PBwChcuTHh4OOHh4RQoUICAgADH/l1Znc8XAxGJBoYC/sDnqtr/eutbMTAmfe3du5eVK1eycuVKfvppHadP/0zRohcIDISpU13rfPGFq1AAnDwJ+/e7rj+MGuWa9/DDcOaMIJKHwMB8hITcSr58oeTLl+/SdNNNN5EzZ05y5cp1abr8dXBwMCLiyDHIDHy6GIiIP7AdqAbsBr4HGqvq1qS2sWJgjLMuXLjA1q1b2bhxIxs3buS///0vhw5tITBwH4ULQ6FCkD8//PknfP65a5vZs13XIi5KSIA5c2DIENfrHj1c1ylOn3ZNZ864Tkn9+CP4+UFEBJw7B6qB+PkFIZKNM2eCiYvLTnBwNnLlyoa/fzCBgcEEBQUTGBiIv78//v7+BAQEXPf7q+f5+fkhIh5NgMfbJLaPi5J6HRAQQNOmTVP0c/P1YvAI0FNVq7tfvwWgqv2S2saKgTG+6dSpU2zfvp0dO3awa9cu/vrrL/fXncTH/4mf3xFuuolL0x9/wMqVEBAAI0ZA9uyuKSQEsmWDiRNh5EhXEZk9+9r3GzMGvvrKVXimTHHNS0hwXeOIi3NtO2uWqzgNHuxaFh/v+pqQAKNHu96/aFHo3Pnf5aquaexY+OknKFYM2rb9d/5Fn38O27fDvfe6nt+4evmoUbBzJ5QqBXXrXrlcFT77zNWCKlcOoqP/3e7iOp98AkePwiOPQKVKsGwZbN6cnVOnTqXo55NUMfCVE3dhwK7LXu8Gyl+9koi0AdoAFC5cOH2SGWM8kiNHDsqUKUOZMmUSXX7+/HkOHz7MoUOHLk0xMa6vmzcf4vjx45w4cYKTJ09y+vQxTp48QdGipzhz5gQdOhzHz891auridLEPvtOn4dNPXQUkMND11d/f9YcY4OxZWL/e1cLw93dNfn5w/LhreUICHDt25TIR1wSu15ffWXtx2cXLH9myuZ7ZuHr5xWvpOXJAePi/+7u4PFs21+ubb4a77/532UUXl+fLB/fdBz//7OEPJJl8pWVQH4hW1Vbu188D5VW1fVLbWMvAmKwpISGBc+fOce7cOc6ePXvp+8Rex8XFERcXR3x8PPHx8Ze+T2ze1d/Hx8ejqh5NgMfbXL39Rdd7nS1bNj799NMUHT9fbxnsAcIve13IPc8YY67g5+dHSEgIISEhTkfJVHylb6LvgWIicruIZANigFkOZzLGmCzDJ1oGqhonIu2BBbhuLR2jqlscjmWMMVmGTxQDAFWdB8xzOocxxmRFvnKayBhjjIOsGBhjjLFiYIwxxoqBMcYYfOShs5QQkYOA+9lCbgKOXbXK1fMuf50POJRG0RLL4q1trrdeUsuSc2wSm2fHy7N5vny8krudt45XYvOz2vG63nJPf5+ufp3a41VEVfNfMzc1T8v5ygSMvNG8y18DG9Izi7e2ud56SS1LzrGx45W5j1dyt/PW8brR8ckKx8vTY+YLxyuznCZKpPuqa+Yltk5aSMn7JHeb662X1LLkHJvE5tnx8myeLx+v5G7nreOV2Pysdryutzwlv09pfrwy7Gmi1BCRDZpI3xwmcXa8PGPHyzN2vDyTVscrs7QMPDXS6QAZjB0vz9jx8owdL8+kyfHKki0DY4wxV8qqLQNjjDGXsWJgjDHGioExxhgrBtcQkWdEZJSITBaRKKfz+DoRuUNERovINKez+CoRySEiX7p/r5o4ncfX2e+UZ7z1NytTFQMRGSMiB0Tkl6vmR4vIryLym4h0ud4+VHWGqrYGXgQapWVep3npeP2uqi3TNqnv8fDY1QWmuX+vaqV7WB/gyfHKqr9Tl/PweHnlb1amKgbAWCD68hki4g8MB2oA9wKNReReESkpInOumkIv27Sbe7vMbCzeO15ZzViSeexwDeO6y71afDpm9CVjSf7xMik7Xqn6m+Uzg9t4g6quFJGiV81+CPhNVX8HEJFJQG1V7Qc8ffU+RESA/sC3qroxbRM7yxvHK6vy5NgBu3EVhB/JfB/AksXD47U1fdP5Hk+Ol4hswwt/s7LCL2YY/34qA9d/zLDrrP8yUBWoLyIvpmUwH+XR8RKRvCIyAigjIm+ldTgfl9SxiwXqicinpF83DBlBosfLfqeSlNTvl1f+ZmWqloE3qOowYJjTOTIKVT2M61ylSYKqngKaO50jo7DfKc94629WVmgZ7AHCL3tdyD3PJM6OV8rZsfOMHS/PpOnxygrF4HugmIjcLiLZgBhglsOZfJkdr5SzY+cZO16eSdPjlamKgYhMBNYCJURkt4i0VNU4oD2wANgGTFHVLU7m9BV2vFLOjp1n7Hh5xonjZR3VGWOMyVwtA2OMMSljxcAYY4wVA2OMMVYMjDHGYMXAGGMMVgyMMcZgxcAYYwxWDIwxxmDFwGQhIjJERPSyab+IjBORvDfYbvll27x22fye7nk7kthuh3t5Ty//O3pelsdGAzNeYcXAZCUlgf8AjwCPAoOAJiRvQJBl7u0mXTX/LHC7iERcPlNEHgSKupd72+fuLJvSYN8mi7IurE1WUhKYqqr/cb9eIyKPAdWSse2Ry7a73ClgI65OwzZcNj8GWAqUS0XeRKnqbmC3iBz39r5N1mUtA5MliMitQCiuDr4ud4DUD0U5CWjoHiXv4mh5Dbm2FYGIjBWRDeIaxPy/InJWRFZdPdyjiFQUkWUiclJEjrlPVZVJZU5jkmTFwGQVJd1f/3txhoj44TrdktrRx2KBW4HH3K8fB/K75yemCDAYeBd4FrgJWCAiwe5clYAlwAWgKa5Bzr/j+iP0GZMqdprIZBUXi8FvIhIAFAS6A8eBzqnZsaoeFZH5uE4Nfef+Ol9Vj7kbC1fLh2tc6TUAIvID8D+gGTAC6Af8BFTXf7sVnp+ajMbciLUMTFbxgPvrn7g+ce8EooE67mEWU2sSrjFog4D6JHKK6DIHLhYCAFXdCfwAPCQiOYDywJdq/cubdGTFwGQVF+8kehCoAPTANWxgNy/tfxaQE3gPyMH1Tz0dSGJeAeBmQIB9XsplTLJYMTCZnvvawL3AGlXdoKprVbU3rlMvDd3LU8U96P0coAMw2/06KaFJzNsH/AMk4CoMxqQbKwYmKygGhHDtffkTcF3ofchL7/MprhbBiBusFyoiFS6+EJHCQFlgvbuIrANekCQuOBiTFuwCsskKLl48/vGq+d/i+hQejesUUqqo6nJgeTJWPQSMF5FuwBmgF67TRGPdy7sAi4FvRWQkrmcZHgE2qOqc1OY0JjHWMjBZQUlcTwL/9/KZqnoI16fw6HTOsxPoBPTEdaH5BK47h866c63E9SBcdmA8MBmIBHanc06ThYjdsGDM9YnIcuAwrvv941Nzl4+IjAXuV9WIG617nX344fogtwQ4qKr1U7ovYy6yloExyVMX1y2przodBHgHV5aKTgcxmYddMzDmxtoCudzf/+VkELeRuO5cAjjiZBCTedhpImOMMXaayBhjjBUDY4wxWDEwxhiDFQNjjDFYMTDGGIMVA2OMMVgxMMYYgxUDY4wxwP8DzFFzwD5gV58AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.special import kn\n", "\n", "# Predictions\n", "x = r_arr / rs\n", "sR_pred = 1E14 / (2 * np.pi * rs**2) * kn(0, x)\n", "slR_pred = 1E14 / (2 * np.pi * rs**2) * (2 / x**2) * (1 - x * kn(1, x))\n", "\n", "# FFTlog calculation\n", "sR = pl.projected(cosmo, r_arr, 1E14, a_sf, hmd_200c)\n", "slR = pl.cumul2d(cosmo, r_arr, 1E14, a_sf, hmd_200c)\n", "\n", "# Projected profile\n", "plt.figure()\n", "plt.plot(r_arr, sR,'k-', lw=3, label='FFTLog')\n", "plt.plot(r_arr, sR_pred,'y--', label='Analytic')\n", "plt.legend(loc='upper right', fontsize=15)\n", "plt.ylabel(r'$\\Sigma(R)\\,\\,[M_\\odot\\,{\\rm Mpc}^{-2}]$', fontsize=15)\n", "plt.xlabel(r'$R\\,\\,[{\\rm Mpc}]$', fontsize=15);\n", "plt.xscale('log')\n", "\n", "# Cumulative surface density\n", "plt.figure()\n", "plt.plot(r_arr, slR,'k-', lw=3, label='FFTLog')\n", "plt.plot(r_arr, slR_pred,'y--', label='Analytic')\n", "plt.legend(loc='upper right', fontsize=15)\n", "plt.ylabel(r'$\\Sigma(