Solving_an_equation_and_the_Lambert_W_function.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#Solving-an-equation,-numerically-or-with-the-Lambert-W-function\" data-toc-modified-id=\"Solving-an-equation,-numerically-or-with-the-Lambert-W-function-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Solving an equation, numerically or with the Lambert W function</a></div><div class=\"lev2 toc-item\"><a href=\"#Loading-packages-and-configuring-plot-sizes\" data-toc-modified-id=\"Loading-packages-and-configuring-plot-sizes-11\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Loading packages and configuring plot sizes</a></div><div class=\"lev2 toc-item\"><a href=\"#Plotting-the-function-first\" data-toc-modified-id=\"Plotting-the-function-first-12\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Plotting the function first</a></div><div class=\"lev2 toc-item\"><a href=\"#Solving-numerically?\" data-toc-modified-id=\"Solving-numerically?-13\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Solving numerically?</a></div><div class=\"lev2 toc-item\"><a href=\"#How-many-solutions-for-a-given-a-?\" data-toc-modified-id=\"How-many-solutions-for-a-given-a-?-14\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>How many solutions for a given a ?</a></div><div class=\"lev2 toc-item\"><a href=\"#Number-of-solutions-as-function-of-a\" data-toc-modified-id=\"Number-of-solutions-as-function-of-a-15\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>Number of solutions as function of a</a></div><div class=\"lev2 toc-item\"><a href=\"#Plot-of-solution(s)-as-function-of-a\" data-toc-modified-id=\"Plot-of-solution(s)-as-function-of-a-16\"><span class=\"toc-item-num\">1.6&nbsp;&nbsp;</span>Plot of solution(s) as function of a</a></div><div class=\"lev2 toc-item\"><a href=\"#Solving-formally-with-the-Lambert-W-function\" data-toc-modified-id=\"Solving-formally-with-the-Lambert-W-function-17\"><span class=\"toc-item-num\">1.7&nbsp;&nbsp;</span>Solving formally with the Lambert W function</a></div><div class=\"lev2 toc-item\"><a href=\"#Asymptotic-behaviors-and-approximations\" data-toc-modified-id=\"Asymptotic-behaviors-and-approximations-18\"><span class=\"toc-item-num\">1.8&nbsp;&nbsp;</span>Asymptotic behaviors and approximations</a></div><div class=\"lev2 toc-item\"><a href=\"#Conclusion\" data-toc-modified-id=\"Conclusion-19\"><span class=\"toc-item-num\">1.9&nbsp;&nbsp;</span>Conclusion</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving an equation, numerically or with the Lambert W function\n",
    "\n",
    "I want to solve the equation $\\exp(-ax^2)=x$ and find its solution(s) as a function of $a\\in\\mathbb{R}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading packages and configuring plot sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lilian Besson (Naereen) 2018-01-31T14:56:14+01:00\n",
      "\n",
      "CPython 3.6.3\n",
      "IPython 6.2.1\n",
      "\n",
      "numpy 1.14.0\n",
      "matplotlib 2.1.2\n",
      "scipy 1.0.0\n",
      "seaborn 0.8.1\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -a \"Lilian Besson (Naereen)\" -i -v -p numpy,matplotlib,scipy,seaborn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import optimize as opt\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['figure.figsize'] = (15, 8)\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import seaborn as sns\n",
    "sns.set(context=\"notebook\", style=\"darkgrid\", palette=\"hls\", font=\"sans-serif\", font_scale=1.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting the function first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def objective(x, a):\n",
    "    return np.exp(- a * x**2) - x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's have a look to its plot for some values of $a$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fd8042240>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa146bbe0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa146bcf8>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa14051d0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa14059b0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1fa1405e48>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$x$')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'$y$')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Function $\\\\exp(- a x^2) - x$ for different $a$')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1fd812df28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(-2, 2, 2000)\n",
    "for a in [0, -0.1, 0.1, -1, 1]:\n",
    "    plt.plot(X, objective(X, a), 'o-', label=f\"$a={a:.3g}$\", markevery=50)\n",
    "plt.legend()\n",
    "plt.xlabel(\"$x$\"); plt.ylabel(\"$y$\")\n",
    "plt.title(r\"Function $\\exp(- a x^2) - x$ for different $a$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that a solution to $\\exp(-a x^2) = x$ has to be positive, as $\\exp(-a x^2) > 0$ for any $x,a$.\n",
    "We also check that if $a < 0$, $\\exp(-a x^2) - x$ seems to always be positive, but if $a \\geq 0$, it seems to have a unique root.\n",
    "Let's zoom a little bit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa10bc278>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa10bc828>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa10bc9e8>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa10bce80>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa109b668>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1fa1156f28>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$x$')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'$y$')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Function $\\\\exp(- a x^2) - x$ for different $a$')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1fa1076080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(0, 1.5, 2000)\n",
    "for a in [0, -0.1, 0.1, -1, 1]:\n",
    "    plt.plot(X, objective(X, a), 'o-', label=f\"$a={a:.3g}$\", markevery=50)\n",
    "plt.legend()\n",
    "plt.xlabel(\"$x$\"); plt.ylabel(\"$y$\")\n",
    "plt.title(r\"Function $\\exp(- a x^2) - x$ for different $a$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The curve for $a=-0.1$ seems to stay negative, but that's not possible as for $a<0$ and $x\\to\\infty$, $\\exp(-a x^2)$ dominates over $-x$.\n",
    "We can check that it will have a second root:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa0ba26d8>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa0ba2c88>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa0ba2e48>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa0b65668>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1fa1053cf8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$x$')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'$y$')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Function $\\\\exp(- a x^2) - x$ for different $a$')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1fa0b69470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(0, 5, 2000)\n",
    "for a in [0, -0.1, 0.1, 1]:\n",
    "    plt.plot(X, objective(X, a), 'o-', label=f\"$a={a:.3g}$\", markevery=50)\n",
    "plt.legend()\n",
    "plt.xlabel(\"$x$\"); plt.ylabel(\"$y$\")\n",
    "plt.title(r\"Function $\\exp(- a x^2) - x$ for different $a$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving numerically?\n",
    "\n",
    "We can start to try to use [`scipy.optimize.root`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.root.html#scipy.optimize.root) to numerically solve this equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_solution(a, x0=0, verb=False):\n",
    "    sol = opt.root(objective, x0, args=(a,))\n",
    "    if verb: print(sol)\n",
    "    if sol.success:\n",
    "        return sol.x\n",
    "    else:\n",
    "        raise ValueError(f\"No solution was found for a = {a:.3g} (and starting at x0 = {x0:.3g}).\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check that there is no solution for $a < 0$ too small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    fjac: array([[-1.]])\n",
      "     fun: array([0.77291476])\n",
      " message: 'The iteration is not making good progress, as measured by the \\n  improvement from the last ten iterations.'\n",
      "    nfev: 28\n",
      "     qtf: array([-0.77291498])\n",
      "       r: array([-0.00495227])\n",
      "  status: 5\n",
      " success: False\n",
      "       x: array([0.41894532])\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "No solution was found for a = -1 (and starting at x0 = 0).",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-8-4cc3b5bba819>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mone_solution\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mverb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<ipython-input-7-c8cc0197ed60>\u001b[0m in \u001b[0;36mone_solution\u001b[0;34m(a, x0, verb)\u001b[0m\n\u001b[1;32m      5\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0msol\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"No solution was found for a = {a:.3g} (and starting at x0 = {x0:.3g}).\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: No solution was found for a = -1 (and starting at x0 = 0)."
     ]
    }
   ],
   "source": [
    "one_solution(-1, verb=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can find a solution, but only one (depending on the starting point $x_0$) and not both:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    fjac: array([[-1.]])\n",
      "     fun: array([2.22044605e-16])\n",
      " message: 'The solution converged.'\n",
      "    nfev: 8\n",
      "     qtf: array([-1.57868385e-10])\n",
      "       r: array([0.7408292])\n",
      "  status: 1\n",
      " success: True\n",
      "       x: array([1.13835649])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1.13835649])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_solution(-0.1, x0=0, verb=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    fjac: array([[-1.]])\n",
      "     fun: array([0.])\n",
      " message: 'The solution converged.'\n",
      "    nfev: 23\n",
      "     qtf: array([-2.18643326e-10])\n",
      "       r: array([-1.54264248])\n",
      "  status: 1\n",
      " success: True\n",
      "       x: array([3.56555841])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([3.56555841])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_solution(-0.1, x0=10, verb=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For $a > 0$, the equation seems to have a unique solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.65291864])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([0.65291864])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([0.65291864])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_solution(1, x0=0)\n",
    "one_solution(1, x0=-100)\n",
    "one_solution(1, x0=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can just hack and try different values for $x_0$, expecting to find all the roots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solutions(a, x0s=None, tol=1e-10, verb=False):\n",
    "    nbdigits = int(np.log10(1. / tol))\n",
    "    sols = set()\n",
    "    if x0s is None:\n",
    "        x0s = [-10, -5, -2, -1, 0, 1, 2, 5, 10]\n",
    "    for x0 in x0s:\n",
    "        sol = opt.root(objective, x0, args=(a,))\n",
    "        if sol.success:\n",
    "            approx = np.round(float(sol.x), nbdigits)\n",
    "            sols.add(approx)\n",
    "    if verb and len(sols) == 0:\n",
    "        print(f\"No solution was found for a = {a:.3g} (and starting at x0 = {x0:.3g}).\")\n",
    "    return sols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "set()"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solutions(-10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1.1383564947, 3.5655584119}"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solutions(-0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1.0}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solutions(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0.6529186404}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solutions(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0.5482170814}"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solutions(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How many solutions for a given a ?\n",
    "We can use this to try to find the threshold value for $a$ from $0$ to $2$ and from $2$ to $1$ solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def thresholds(amin=-10, amax=10, delta=0.01):\n",
    "    gap_points = dict()\n",
    "    prev_a = amin\n",
    "    prev_nb_sol = len(solutions(prev_a))\n",
    "    for a in np.arange(amin, amax, delta):\n",
    "        nb_sol = len(solutions(a))\n",
    "        if nb_sol != prev_nb_sol:\n",
    "            gap_points[(prev_nb_sol, nb_sol)] = (prev_a, a)\n",
    "            prev_nb_sol = nb_sol\n",
    "        prev_a = a\n",
    "    return gap_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(0, 1): (-0.3700000000002053, -0.3600000000002055),\n",
       " (0, 2): (-0.1900000000002091, -0.18000000000020933),\n",
       " (1, 0): (-0.3400000000002059, -0.33000000000020613),\n",
       " (2, 0): (-7.030000000000063, -7.0200000000000635),\n",
       " (2, 1): (-0.020000000000212736, -0.01000000000021295),\n",
       " (2, 3): (-0.0500000000002121, -0.04000000000021231),\n",
       " (3, 2): (-0.04000000000021231, -0.030000000000212523)}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thresholds(amin=-10, amax=10, delta=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(0, 1): (-0.37000000000016264, -0.36000000000016286),\n",
       " (0, 2): (-0.19000000000016648, -0.1800000000001667),\n",
       " (1, 0): (-0.3400000000001633, -0.3300000000001635),\n",
       " (2, 0): (-7.030000000000021, -7.020000000000021),\n",
       " (2, 1): (-0.020000000000170104, -0.010000000000170317),\n",
       " (2, 3): (-0.050000000000169464, -0.04000000000016968),\n",
       " (3, 2): (-0.04000000000016968, -0.03000000000016989)}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "thresholds(amin=-8, amax=1, delta=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I think having $3$ (or more) solutions is a numerical error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(0, 2): (-0.20000000000567297, -0.10000000000567866),\n",
       " (2, 0): (-28.20000000000408, -28.100000000004087),\n",
       " (2, 1): (-0.10000000000567866, -5.6843418860808015e-12)}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "amin = -100\n",
    "amax = 100\n",
    "gap_points = thresholds(amin=amin, amax=amax, delta=0.1)\n",
    "gap_points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we will see below, even having two solutions is nothing but a numerical error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Number of solutions as function of a\n",
    "We can plot the (estimated) number of solution as a function of $a$, to start wit, thanks to the [`matplotlib.pyplot.hlines`](https://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.hlines) function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2}\n",
      "{0: [-0.20000000000567297], 2: [-28.20000000000408, -0.10000000000567866]}\n",
      "{2: [-0.10000000000567866], 0: [-28.100000000004087], 1: [-5.6843418860808015e-12]}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1fa06e7518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_gap_points(gap_points, amin, amax):\n",
    "    ys = set()\n",
    "    for ym, yM in gap_points.keys():\n",
    "        ys.add(ym)\n",
    "        ys.add(yM)\n",
    "    print(ys)\n",
    "    xleft = dict()\n",
    "    xright = dict()\n",
    "    for (ym, yM), (xm, xM) in gap_points.items():\n",
    "        xleft[ym] = xleft.get(ym, []) + [xm]\n",
    "        xright[yM] = xright.get(yM, []) + [xM]\n",
    "    for ym, yM in gap_points.keys():\n",
    "        xleft[ym].sort()\n",
    "        xright[yM].sort()\n",
    "    print(xleft)\n",
    "    print(xright)\n",
    "    min_xleft = min(sum(list(xleft.values()), []))\n",
    "    max_xright = min(sum(list(xright.values()), []))\n",
    "    plt.figure()\n",
    "    for y in ys:\n",
    "        if y not in xleft and y in xright:\n",
    "            for x in xright[y]:\n",
    "                plt.hlines(y, x, amax)\n",
    "        if y in xleft and min_xleft in xleft[y]:\n",
    "            plt.hlines(y, amin, min_xleft)\n",
    "            del xleft[y][0]\n",
    "        #if y in xright and max_xright in xright[y]:\n",
    "        #    plt.hlines(y, max_xright, amax)\n",
    "        #    del xright[y][-1]\n",
    "        if y in xleft and y in xright:\n",
    "            for xmin, xmax in zip(xleft[y], xright[y]):\n",
    "                plt.hlines(y, xmin, xmax)\n",
    "    plt.xlabel(\"Value of $a$\")\n",
    "    plt.ylabel(\"Number of solution\")\n",
    "    plt.title(r\"Number of solutions to $\\exp(- a x^2) = x$, as function of $a$\")\n",
    "\n",
    "    return ys, xleft, min_xleft, xright, max_xright\n",
    "\n",
    "ys, xleft, min_xleft, xright, max_xright = plot_gap_points(gap_points, amin, amax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot of solution(s) as function of a\n",
    "Now we can try to use this to plot the solution(s) as function of $a$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_multivalued_function(X, f, maxnboutput=1, **kwargs):\n",
    "    Y = np.zeros((maxnboutput, len(X)))\n",
    "    Y.fill(np.nan)\n",
    "    for i, x in enumerate(X):\n",
    "        ys = sorted(list(f(x)))\n",
    "        for j, y in enumerate(ys):\n",
    "            Y[j, i] = y\n",
    "    for j in range(maxnboutput):\n",
    "        plt.plot(X, Y[j], 'o-', **kwargs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n",
      "  \n",
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1fa06891d0>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Parameter $a$')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Solution(s)')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Solution(s) to $\\\\exp(- a x^2) = x$, as function of $a$')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1fa0975358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.linspace(-100, 100, 1000)\n",
    "\n",
    "plot_multivalued_function(A, solutions, maxnboutput=2, markevery=10)\n",
    "plt.legend()\n",
    "plt.xlabel(\"Parameter $a$\"); plt.ylabel(\"Solution(s)\")\n",
    "plt.title(r\"Solution(s) to $\\exp(- a x^2) = x$, as function of $a$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No handles with labels found to put in legend.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1fa13a1e10>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Parameter $a$')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Solution(s)')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Solution(s) to $\\\\exp(- a x^2) = x$, as function of $a$')"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1fa13a1f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.linspace(0, 20, 2000)\n",
    "\n",
    "plot_multivalued_function(A, solutions, maxnboutput=2, markevery=20)\n",
    "plt.legend()\n",
    "plt.xlabel(\"Parameter $a$\"); plt.ylabel(\"Solution(s)\")\n",
    "plt.title(r\"Solution(s) to $\\exp(- a x^2) = x$, as function of $a$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows the numerical solution to the equation, and we will check below that the formal solution coincides."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving formally with the Lambert W function\n",
    "\n",
    "Luckily, we can transform this equation to solve it with the Lambert $W$ function, defined as $W(x) = z \\Leftrightarrow x = z \\mathrm{e}^{z}$.\n",
    "For more details, [please see this page](https://en.wikipedia.org/wiki/Lambert_W_function), or [this article](https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf).\n",
    "\n",
    "As for (almost) all the special function, we don't need to write it ourself: it is in scipy! [`scipy.special.lambertw`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.lambertw.html#scipy.special.lambertw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import lambertw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the only possible solution are $x>0$\n",
    "$$\n",
    "\\exp(-a x^2) = x \\Leftrightarrow\n",
    "\\left(\\exp(-a x^2)\\right)^2= \\exp(-2 a x^2) = x^2 \\Leftrightarrow\n",
    "2 a y \\exp(2 a x) = 2 a \\;\\;(\\text{with}\\;\\; y := x^2) \\Leftrightarrow \\\\\n",
    "u \\exp(u) = 2 a \\;\\;(\\text{with}\\;\\; u := 2 a y) \\Leftrightarrow\n",
    "u = W(2a) \\Leftrightarrow\n",
    "y = \\frac{W(2a)}{2a} \\Leftrightarrow\n",
    "x(a) := \\sqrt{\\frac{W(2a)}{2a}}.\n",
    "$$\n",
    "\n",
    "And so it is quite easy to compute, for $a > 0$ (the behavior at $0$ is undefined without a more careful study):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def formal_solution(a):\n",
    "    return np.sqrt(lambertw(2 * a) / (2 * a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check some values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 0.5 gives x(a) = 0.753\n",
      "a = 1 gives x(a) = 0.653\n",
      "a = 2 gives x(a) = 0.548\n",
      "a = 3 gives x(a) = 0.489\n",
      "a = 4 gives x(a) = 0.448\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:3: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:4: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  after removing the cwd from sys.path.\n"
     ]
    }
   ],
   "source": [
    "for a in [0.5, 1, 2, 3, 4]:\n",
    "    xa = formal_solution(a)\n",
    "    assert np.isclose(exp(-a * xa**2), xa)\n",
    "    print(f\"a = {a:.3g} gives x(a) = {float(xa):.3g}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Asymptotic behaviors and approximations\n",
    "\n",
    "We can try to approximate the solution for small $a$ or large $a$:\n",
    "\n",
    "- For small $a$, $W(2a) \\simeq 2a - 4a^2$ so $x(a) \\simeq 1 - a$.\n",
    "\n",
    "- For large $a$, we have [this bound](https://en.wikipedia.org/wiki/Lambert_W_function#Asymptotic_expansions):\n",
    "  $$ \\forall x \\geq \\mathrm{e},{\\displaystyle \\ln(x)-\\ln {\\bigl (}\\ln(x){\\bigr )}+{\\frac {\\ln {\\bigl (}\\ln(x){\\bigr )}}{2\\ln(x)}}\\leq W(x)\\leq \\ln(x)-\\ln {\\bigl (}\\ln(x){\\bigr )}+{\\frac {e}{e-1}}{\\frac {\\ln {\\bigl (}\\ln(x){\\bigr )}}{\\ln(x)}}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "e = np.exp(1)\n",
    "\n",
    "def upper_bound(a):\n",
    "    up_b = np.log(2*a) - np.log(np.log(2*a)) + (e / (e - 1)) * (np.log(np.log(2*a)) / np.log(2*a))\n",
    "    return np.sqrt(up_b / (2*a))\n",
    "\n",
    "def lower_bound(a):\n",
    "    lo_b = np.log(2*a) - np.log(np.log(2*a)) + np.log(np.log(2*a)) / (2 * np.log(2*a))\n",
    "    return np.sqrt(lo_b / (2*a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot all this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: RuntimeWarning: invalid value encountered in true_divide\n",
      "  \n",
      "/usr/local/lib/python3.6/dist-packages/numpy/core/numeric.py:492: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa1053ac8>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa0bb9e80>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa10a5c50>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1fa0695128>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1fa0695748>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Parameter $a$')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Solution $x(a) = \\\\sqrt{\\\\frac{W(2a)}{2a}}$')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Solution to $\\\\exp(- a x^2) = x$, as function of $a$')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1fa0c662e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.linspace(0, 20, 4000)\n",
    "A1 = A[A <= 0.5]\n",
    "A2 = A[A >= 1]\n",
    "Ae = A[A >= e]\n",
    "\n",
    "plt.plot(A, formal_solution(A), label=\"Solution\", markevery=20)\n",
    "\n",
    "plt.plot(A1, 1 - A1, 'b--', label=r\"Tangent at $0$: $x(a) \\simeq 1 - a$\", markevery=20)\n",
    "\n",
    "#plt.plot(A2, np.sqrt((np.log(2*A2) - np.log(np.log(2*A2)))/(2*A2)), 'g--', label=r\"Asymptote at $+\\infty$\", markevery=20)\n",
    "plt.plot(Ae, lower_bound(Ae), 'g--', label=r\"Lower-bound for $a \\geq e$\", markevery=20)\n",
    "plt.plot(Ae, upper_bound(Ae), 'c--', label=r\"Upper-bound for $a \\geq e$\", markevery=20)\n",
    "\n",
    "plt.legend()\n",
    "plt.xlabel(\"Parameter $a$\"); plt.ylabel(r\"Solution $x(a) = \\sqrt{\\frac{W(2a)}{2a}}$\")\n",
    "plt.title(r\"Solution to $\\exp(- a x^2) = x$, as function of $a$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And voilà."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "That's it for today, *folks*!\n",
    "\n",
    "> See [here](https://github.com/Naereen/notebooks/) for other notebooks I wrote, in Python, Julia, OCaml or other languages."
   ]
  }
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