{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e0bf37ee",
   "metadata": {},
   "source": [
    "# Iterated integral complementary error function\n",
    "\n",
    "Check implementation of the iterated integral complementary error function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a43941e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from bruggeman.general import ierfc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0894cfc",
   "metadata": {},
   "source": [
    "Implementation:\n",
    "\n",
    "<img src=\"_static/ierfc.png\" alt=\"Iterated integral complementary error function\" width=\"600\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05e6ceef",
   "metadata": {},
   "source": [
    "Compare to figure 3 in [Olsthoorn, (2006)](https://edepot.wur.nl/13730)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "789f447d",
   "metadata": {},
   "outputs": [],
   "source": [
    "z = np.linspace(0, 3, 51)\n",
    "ierfc_min1 = ierfc(z, -1)\n",
    "ierfc0 = ierfc(z, 0)\n",
    "plt.figure(figsize=(10, 3))\n",
    "plt.plot(z, ierfc_min1, ls=\"dashed\", label=\"ierfc(z, -1)\", lw=1.0, color=\"k\")\n",
    "plt.plot(z, ierfc0, ls=\"solid\", label=\"ierfc(z, 0)\", lw=1.0, color=\"k\")\n",
    "for n in range(1, 8):\n",
    "    plt.plot(\n",
    "        z, ierfc(z, n) / ierfc(0, n), label=f\"ierfc(z, {n}) / ierfc(0, {n})\", lw=1.0\n",
    "    )\n",
    "plt.legend()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cb40f04e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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