HajimeKawahara/exojax

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documents/tutorials/Cross_Section_using_Discrete_Integral_Transform.ipynb

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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cross section computation using the Discrete Integral Transform (DIT) for rapid spectral synthesis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We demonstarte the Discrete Integral Transform (DIT) method proposed by D.C.M van den Bekerom and E.Pannier. DIT takes advantage especially for the case that the number of the molecular line is large (typically > 10,000). We here compare the results by DIT with the direct computation (LPF).  \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:02:46.217211Z",
     "iopub.status.busy": "2023-03-14T12:02:46.215520Z",
     "iopub.status.idle": "2023-03-14T12:02:46.461449Z",
     "shell.execute_reply": "2023-03-14T12:02:46.461096Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we use FP64, but if you want you can use FP32 (but slightly large errors):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:02:46.463799Z",
     "iopub.status.busy": "2023-03-14T12:02:46.463512Z",
     "iopub.status.idle": "2023-03-14T12:02:46.876882Z",
     "shell.execute_reply": "2023-03-14T12:02:46.877117Z"
    }
   },
   "outputs": [],
   "source": [
    "from jax import config\n",
    "\n",
    "config.update(\"jax_enable_x64\", True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:02:46.881094Z",
     "iopub.status.busy": "2023-03-14T12:02:46.880800Z",
     "iopub.status.idle": "2023-03-14T12:02:51.079548Z",
     "shell.execute_reply": "2023-03-14T12:02:51.079232Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xsmode =  dit\n",
      "xsmode assumes ESLIN in wavenumber space: xsmode=dit\n",
      "======================================================================\n",
      "The wavenumber grid should be in ascending order.\n",
      "The users can specify the order of the wavelength grid by themselves.\n",
      "Your wavelength grid is in ***  descending  *** order\n",
      "======================================================================\n",
      "radis engine =  vaex\n"
     ]
    }
   ],
   "source": [
    "from exojax.spec.hitran import line_strength\n",
    "from exojax.spec.hitran import doppler_sigma\n",
    "from exojax.spec.hitran import gamma_hitran\n",
    "from exojax.spec.hitran import gamma_natural\n",
    "from exojax.utils.grids import wavenumber_grid\n",
    "from exojax.utils.constants import Tref_original\n",
    "from exojax.spec import api\n",
    "\n",
    "# Setting wavenumber bins and loading HITRAN database\n",
    "nus, wav, resolution = wavenumber_grid(\n",
    "    1900.0, 2300.0, 350000, unit=\"cm-1\", xsmode=\"dit\"\n",
    ")\n",
    "mdbCO = api.MdbHitran(\n",
    "    \"CO\", nus, isotope=1, gpu_transfer=True\n",
    ")  # here we use the isotope=1 (12C16O) in DIT.\n",
    "\n",
    "# set T, P and partition function\n",
    "Mmol = mdbCO.molmass\n",
    "Tfix = 1000.0  # we assume T=1000K\n",
    "Pfix = 1.0e-3  # we compute P=1.e-3 bar\n",
    "Ppart = Pfix  # partial pressure of CO. here we assume a 100% CO atmosphere.\n",
    "qt = mdbCO.qr_interp_lines(\n",
    "    Tfix, Tref_original\n",
    ")  # use all isotopes as a partition function\n",
    "\n",
    "# compute Sij, gamma_L, sigmaD\n",
    "Sij = line_strength(\n",
    "    Tfix, mdbCO.logsij0, mdbCO.nu_lines, mdbCO.elower, qt, Tref_original\n",
    ")\n",
    "gammaL = gamma_hitran(\n",
    "    Pfix, Tfix, Ppart, mdbCO.n_air, mdbCO.gamma_air, mdbCO.gamma_self\n",
    ") + gamma_natural(mdbCO.A)\n",
    "sigmaD = doppler_sigma(mdbCO.nu_lines, Tfix, Mmol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DIT uses a grid of sigmaD, gammaL, and wavenumber. set_ditgrid.ditgrid_log_interval makes a 1D grid for sigmaD and gamma."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:02:51.085989Z",
     "iopub.status.busy": "2023-03-14T12:02:51.085640Z",
     "iopub.status.idle": "2023-03-14T12:02:51.225382Z",
     "shell.execute_reply": "2023-03-14T12:02:51.225067Z"
    }
   },
   "outputs": [],
   "source": [
    "from exojax.spec.set_ditgrid import ditgrid_log_interval\n",
    "\n",
    "sigmaD_grid = ditgrid_log_interval(sigmaD)\n",
    "gammaL_grid = ditgrid_log_interval(gammaL)\n",
    "\n",
    "# we can change the resolution using res option\n",
    "# sigmaD_grid=set_ditgrid(sigmaD,res=0.1)\n",
    "# gammaL_grid=set_ditgrid(gammaL,res=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:02:51.241333Z",
     "iopub.status.busy": "2023-03-14T12:02:51.232890Z",
     "iopub.status.idle": "2023-03-14T12:02:51.583509Z",
     "shell.execute_reply": "2023-03-14T12:02:51.583158Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# show the grids\n",
    "plt.plot(sigmaD, gammaL, \".\")\n",
    "for i in sigmaD_grid:\n",
    "    plt.axvline(i, lw=1, alpha=0.5, color=\"C1\")\n",
    "for i in gammaL_grid:\n",
    "    plt.axhline(i, lw=1, alpha=0.5, color=\"C1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to precompute the contribution for wavenumber. Also, pmarray is needed. These can be computed using init_dit. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:02:51.586306Z",
     "iopub.status.busy": "2023-03-14T12:02:51.585989Z",
     "iopub.status.idle": "2023-03-14T12:02:51.724879Z",
     "shell.execute_reply": "2023-03-14T12:02:51.723727Z"
    }
   },
   "outputs": [],
   "source": [
    "from exojax.spec import initspec\n",
    "\n",
    "cnu, indexnu, pmarray = initspec.init_dit(mdbCO.nu_lines, nus)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then, let's compute a cross section!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:02:51.733878Z",
     "iopub.status.busy": "2023-03-14T12:02:51.732601Z",
     "iopub.status.idle": "2023-03-14T12:02:53.823792Z",
     "shell.execute_reply": "2023-03-14T12:02:53.824059Z"
    }
   },
   "outputs": [],
   "source": [
    "from exojax.spec.dit import xsvector\n",
    "\n",
    "xs = xsvector(cnu, indexnu, pmarray, sigmaD, gammaL, Sij, nus, sigmaD_grid, gammaL_grid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also, we here try the direct computation using Direct-LPF for the comparison purpose"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:02:53.826846Z",
     "iopub.status.busy": "2023-03-14T12:02:53.826541Z",
     "iopub.status.idle": "2023-03-14T12:03:01.877225Z",
     "shell.execute_reply": "2023-03-14T12:03:01.876924Z"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from exojax.spec.opacalc import OpaDirect\n",
    "opa = OpaDirect(mdbCO, nus)\n",
    "xsv = opa.xsvector(Tfix, Pfix, Ppart)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The difference is <~ 1%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-03-14T12:03:01.887461Z",
     "iopub.status.busy": "2023-03-14T12:03:01.886148Z",
     "iopub.status.idle": "2023-03-14T12:03:02.182257Z",
     "shell.execute_reply": "2023-03-14T12:03:02.182483Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_809841/4022811313.py:11: UserWarning: No artists with labels found to put in legend.  Note that artists whose label start with an underscore are ignored when legend() is called with no argument.\n",
      "  plt.legend(loc=\"upper left\")\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 5))\n",
    "ax = fig.add_subplot(211)\n",
    "plt.plot(nus, xs, lw=1, alpha=0.5, label=\"DIT\")\n",
    "plt.plot(nus, xsv, lw=1, alpha=0.5, label=\"Direct LPF\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.ylabel(\"Cross Section (cm2)\")\n",
    "ax = fig.add_subplot(212)\n",
    "# plt.plot(nus,xsv-xs,lw=2,alpha=0.5,label=\"precomputed\")\n",
    "plt.plot(nus, xsv - xs, lw=2, alpha=0.5)\n",
    "plt.ylabel(\"LPF - DIT (cm2)\")\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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