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notebooks/flow/sigma8_nonlinear.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import scipy.integrate\n",
+    "import symbolic_pofk.linear\n",
+    "import symbolic_pofk.syrenhalofit as syrenhalofit"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def compute_sigma8_from_pk(k, pk):\n",
+    "    \"\"\"Given a power spectrum P(k), compute sigma8.\"\"\"\n",
+    "    R = 8.0\n",
+    "    x = k * R\n",
+    "    W = np.zeros(x.shape)\n",
+    "    m = x < 1.e-3\n",
+    "    W[m] = 1.0\n",
+    "    W[~m] =3.0 / x[~m]**3 * (np.sin(x[~m]) - x[~m] * np.cos(x[~m]))\n",
+    "    y = pk * W**2 * k**3\n",
+    "    sigma2 = scipy.integrate.simpson(y, x=np.log(x))\n",
+    "    sigma = np.sqrt(sigma2 / (2.0 * np.pi**2))\n",
+    "\n",
+    "    return sigma\n",
+    "\n",
+    "# Cosmological parameters\n",
+    "As = 2.105  # 10^9 A_s\n",
+    "h = 0.6766\n",
+    "Om = 0.3111\n",
+    "Ob = 0.02242 / h ** 2\n",
+    "ns = 0.9665\n",
+    "tau = 0.0561\n",
+    "\n",
+    "# Define k integration range\n",
+    "\n",
+    "\n",
+    "def linear_sigma8(As, Om, Ob, h, ns):\n",
+    "    \"\"\"Calculated from Deaglan's emulator.\"\"\"\n",
+    "    return symbolic_pofk.linear.As_to_sigma8(As, Om, Ob, h, ns)\n",
+    "    # print('sigma8 from emulator', sigma8)\n",
+    "\n",
+    "# # Test linear sigma8\n",
+    "# pk_lin = symbolic_pofk.linear.plin_emulated(k, sigma8, Om, Ob, h, ns,\n",
+    "#     emulator='fiducial', extrapolate=True)\n",
+    "# new_sigma8 = compute_sigma8(k, pk_lin)\n",
+    "# print('sigma8 from integral:', new_sigma8)\n",
+    "\n",
+    "# Get non-linear sigma8\n",
+    "def nonlinear_sigma8(As, Om0, Ob, h, ns, ks):\n",
+    "    a = 1.\n",
+    "    sigma8 = linear_sigma8(As, Om0, Ob, h, ns)  # Linear sigma8\n",
+    "    pk_nl = syrenhalofit.run_halofit(\n",
+    "        ks, sigma8, Om, Ob, h, ns, a, emulator='fiducial', extrapolate=True,\n",
+    "        which_params='Bartlett', add_correction=True)\n",
+    "    return compute_sigma8_from_pk(ks, pk_nl)\n",
+    "# print('non-linear sigma8:', sigma8_nl)\n",
+    "# print('sigma8 non-linear bigger by a factor', sigma8_nl / sigma8)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "kmin, kmax, nk = 1e-4, 1e1, 256\n",
+    "ks = np.logspace(np.log10(kmin), np.log10(kmax), nk) # Wavenumber"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.825706107176727"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "linear_sigma8(As, Om, Ob, h, ns)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.9203769215120938"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "nonlinear_sigma8(As, Om, Ob, h, ns, ks)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2.1005829616811546e-09"
+      ]
+     },
+     "execution_count": 25,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    " 1e-10 * np.exp(3.0448)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "venv_csiborg",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.7"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}