{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tests of the code\n",
    "This notebook is designed to document some simple tests of the photon-ALP propagation code ALPro. Most of these tests can be run by running \n",
    "\n",
    "```\n",
    "python -m unittest alpro.test\n",
    "```\n",
    "\n",
    "from the command line. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import alpro \n",
    "import matplotlib.pyplot as plt\n",
    "alpro.util.set_default_plot_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Single Domain Test\n",
    "First, let's compare an idealised pure polarization state solution to the analytic solution given by\n",
    "\n",
    "$$ \n",
    "P_{\\gamma \\rightarrow a} = \n",
    "\\frac{\\Theta^2}{1+\\Theta^2} \n",
    "\\sin^2 (\\Delta_{\\rm eff} \n",
    "\\sqrt{1+\\Theta^2} L),\n",
    "$$\n",
    "where\n",
    "$$\n",
    "\\Theta=2B_\\perp E g_{a \\gamma}/m_{\\rm eff}^2\n",
    "$$\n",
    "and \n",
    "$$\n",
    "\\Delta_{\\rm eff}=m_{\\rm eff}^2 L / (4E)\n",
    "$$\n",
    "where $m_{\\rm eff}^2=m_a^2-\\omega_{\\rm pl}^2$.\n",
    "\n",
    "The model here is a single domain of width $10~{\\rm kpc}$, with uniform field $B=10 \\mu{\\rm G}$ oriented along the $y$-axis. The polarization state is $(0,1,0)$ and we use energies from $1-10~{\\rm keV}$. \n",
    "\n",
    "This test also checks for agreement within a relative tolerance of $10^{-6}$ between the theoretical and numerical calculations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = alpro.test.RunTest()\n",
    "test.test_analytic(subplot=111)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Discretisation Test\n",
    "In our second test, we repeat the above test, but now compare a single domain to a discretised uniform field. Specifically the result from 1 uniform cell of size $L$ to $10$ uniform cells of size $L/10$. This should give an identical result. The parameters and procedure are identical to our first test. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test.test_discretise(subplot=111)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Libanov field model v Marsh \n",
    "This tests a uniform field model from [Libanov \\& Troitsky (2021)](https://www.sciencedirect.com/science/article/pii/S0370269320300563?via%3Dihub), which is originally described by [Gourgouliatos et al. (2010)](https://arxiv.org/abs/1008.5353), against M. C. David Marsh's code. This test uses a large scale uniform field and energies in the GeV regime. The field components are given by \n",
    "\n",
    "$$\n",
    "B_r = \\frac{2 \\cos\\theta}{r^2} f(r) \\\\\n",
    "B_\\theta = - \\frac{\\sin \\theta}{r} f'(r)  \\\\\n",
    "B_\\phi = \\frac{\\alpha \\sin \\theta}{r} f(r) \\, ,\n",
    "$$\n",
    "\n",
    "where $\\alpha$ solves a transcendental equation and is approximately given by  $\\alpha= 5.76$. The function $f(r)$ is given by\n",
    "\n",
    "$$\n",
    "f(r) =c_1\\Big(\n",
    "\\alpha \\cos (\\alpha u) - \\frac{\\sin(\\alpha u)}{u}\n",
    "- u^2\\left(\n",
    "\\alpha \\cos\\alpha - \\sin \\alpha\n",
    "\\right)\n",
    "\\Big) \\, .\n",
    "$$\n",
    "\n",
    "The form of the field is plotted below, before we plot the ALP result. Note that this is now the **survival** probability on a linear axis. We find cosmetically perfect agreement between our results and Marsh. the Libanov results are smoothed with the Fermi response which is presumably the reason for the difference, but the overall form is similar. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test.test_marsh(subplot=111)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Massive Fourier Formalism"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/matthews/Library/Python/3.7/lib/python/site-packages/alpro/test.py:153: RuntimeWarning: invalid value encountered in greater\n",
      "  select = (P1 > 1e-7)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test.test_fourier_massive(subplot=111)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Massless Fourier Formalism"
   ]
  },
  {
   "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test.test_fourier_massless(subplot=111)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Domain Field Test v Analytic \n",
    "This tests a cell-based domain model against an analytic solution computed by Pierluca Carenza. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Custom model specified - make sure get_B & density methods are populated or domain set manually!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x13763a890>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np \n",
    "def setup_carenza_model():\n",
    "    s = alpro.Survival(\"custom\")\n",
    "    s.init_model()\n",
    "    r, f = np.genfromtxt(\"../data/Bfield_Carenza.dat\", unpack=True)\n",
    "    s.set_params(g=1e-12 * 1e-9, mass=1e-11)\n",
    "    s.domain.deltaL = r[1:] - r[:-1]\n",
    "    s.domain.r = r[:-1]\n",
    "    s.domain.rcen = 0.5 * (r[1:] + r[:-1])\n",
    "    s.domain.ne = np.zeros_like(s.domain.r) \n",
    "    s.domain.Bx = f[:-1] * 1e-6\n",
    "    s.domain.By = np.zeros_like (s.domain.Bx)\n",
    "    s.domain.B = np.sqrt(s.domain.Bx**2  + s.domain.By **2)\n",
    "    s.domain.phi = np.arctan2(s.domain.Bx,s.domain.By)\n",
    "    return (s) \n",
    "\n",
    "energies,P = np.genfromtxt(\"../data/Prob_Carenza.dat\", unpack=True)\n",
    "\n",
    "s = setup_carenza_model()\n",
    "Pcode, _ = s.propagate(s.domain, energies, pol=\"x\")\n",
    "\n",
    "# make the default plot and overplot Pierluca's solution\n",
    "s.default_plot()\n",
    "plt.plot(energies, P, c=\"C1\", ls=\"--\", label=\"Carenza analytic\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Additional Tests\n",
    "I've done a number of other tests - using the code in various regimes in terms of density, energy, magnetic field strength. I've also tested alpro against [gammaALPs](https://github.com/me-manu/gammaALPs), with near identical results in the X-ray regime, but these are not documented here for the moment.  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
