{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Quick-start notebook for the axion module"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#start by importing the controller and manipulate modules\n",
    "from analytical.controller import *\n",
    "from numerical.manipulate import *\n",
    "#reimport numpy (though it is pulled by numerical) for smarter syntax highlighting in vscode\n",
    "import numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analytical part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "axion_analytical=analytical_pipeline(\"../../MyModels/axion/axionSM.cfg\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numerical part"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "first create the NumRate class object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "axion_rate=NumRate(*axion_analytical,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now all methods of the class are available. For illustration purposes we output the full rate at 10 values of k/T for an axion-gluon coupling only. We rescale $f_\\mathrm{PQ}$ by setting its value to 1 and we use a strong coupling $g_3$ corresponding to $\\alpha_s=0.06$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "k=numpy.linspace(1,10,10)\n",
    "#the tuple for the couplings is the union of the gauge and other couplings\n",
    "#from the output of the analytical pipeline we have \n",
    "# {'gauge': ('g1', 'g2', 'g3'), 'noneq': ('fPQ',), 'others': ('c1', 'c2', 'c3', 'ct', 'ht')}\n",
    "rate = axion_rate.rate(k,1.,(0.,0.,numpy.sqrt(4.*numpy.pi*0.06),0,0,1.,0,0),0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Strict LO-scheme rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.24468720482499e-6, 2.48806377023693e-5, 3.35216329472938e-5,\n",
       "       3.89866431064388e-5, 4.30820774272845e-5, 4.64391827454089e-5,\n",
       "       4.93197028763330e-5, 5.18530080251627e-5, 5.41151703842284e-5,\n",
       "       5.61573931901464e-5], dtype=object)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rate[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Subtracted-scheme rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.32458357276370e-5, 2.68517915080078e-5, 3.44196852859558e-5,\n",
       "       3.94963238927934e-5, 4.34096375330550e-5, 4.66671741757908e-5,\n",
       "       4.94874378831309e-5, 5.19815453260401e-5, 5.42167932436927e-5,\n",
       "       5.62397439824078e-5], dtype=object)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rate[2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tuned-scheme rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.13516715648551e-5, 3.50716746267359e-5, 4.25672158519041e-5,\n",
       "       4.74800571298319e-5, 5.12012593583113e-5, 5.42733060334197e-5,\n",
       "       5.69285281412678e-5, 5.92808393892183e-5, 6.13957319484079e-5,\n",
       "       6.33165674566682e-5], dtype=object)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rate[3]"
   ]
  }
 ],
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