{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import smpl\n",
    "from smpl import plot\n",
    "print(smpl.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gompertz(n,a,b):\n",
    "    return -a * n * np.log(b*n)\n",
    "\n",
    "def solution_gompertz(t,a,b,c):\n",
    "    return 1/b*np.exp(np.exp(-t*a)*c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multi Plot\n",
    "## Different color\n",
    "\n",
    "\n",
    "Separation of Variables:\n",
    "\n",
    "$$\\int \\frac{1}{N \\ln (bN)} dN = \\ln(\\ln(bN)) +c= -adt =-at$$\n",
    "\n",
    "$$\\implies N(t) =  \\frac{1}{b} \\exp (c \\exp (-t a))$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for a in [1,2]:\n",
    "    for b in [1,0.5]:\n",
    "        plot.function( gompertz, a,b, xaxis=\"$N$\", yaxis=\"$\\\\dot N$\",xmin=0.1, xmax=3 ,init=False )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "for a in [1,2]:\n",
    "    for b in [1,1/8]:\n",
    "        for c in [1,2]:\n",
    "            plot.function( solution_gompertz, a,b,c, xaxis=\"$t$\", yaxis=\"$N$\",xmin=0.1, xmax=3,init=False,lpos=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Same color"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for a in [1,2]:\n",
    "    for b in [1,0.5]:\n",
    "        plot.function( gompertz, a,b, xaxis=\"$N$\", yaxis=\"$\\\\dot N$\",xmin=0.1, xmax=3 ,init=False,next_color=a == b )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "file_extension": ".py",
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   "pygments_lexer": "ipython3",
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