HajimeKawahara/exojax

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why we multiply the factor of 4/3 to C_gamma for a 2D case"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's simulate the residual grids of delta log gamma and (logT - logTref) delta n (as a normalized one to -0.5 to 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "N=10000\n",
    "x=np.linspace(-0.5,0.5,N)\n",
    "y=np.linspace(-0.5,0.5,N)\n",
    "g=np.meshgrid(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the error is not root sum, but absolute of |dlog gamma - (log T - log Tref) delta n| "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = np.abs(g[0] - g[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "rf=r.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For comparison, in the case of 1D, we use |x| as a uniform distribution of the error of gamma. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(rf,bins=100,density=True)\n",
    "plt.hist(np.abs(x),density=True,alpha=0.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The factor is defined by the mean of both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3333333200000026"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fac=np.mean(rf)/np.mean(np.abs(x))\n",
    "fac #4/3\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The factor using median is less than that for mean. But we use the mean version as a fiducial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1715999999999998"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fac2=np.median(rf)/np.median(np.abs(x))\n",
    "fac2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(rf/fac,bins=100,density=True, label=\"2D applied factor 4/3\")\n",
    "plt.hist(np.abs(x),density=True,alpha=0.4, label=\"1D\")\n",
    "plt.legend()\n",
    "plt.savefig(\"diff2D1D_broadening.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.8 ('base')",
   "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": "3.8.8"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "72bc7f8b1808a6f5ada3c6a20601509b8b1843160436d276d47f2ba819b3753b"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}