voigt.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.special import wofz\n",
    "from scipy.optimize import curve_fit\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "init_printing(use_unicode=False, wrap_line=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lorentz"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def lorentz(x, gamma):\n",
    "    return 1 / (gamma**2 + x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAAAvBAMAAAAbRlkCAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHaZq4lU72YizbtEMt0MBTtrAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABxklEQVRIDe2VvUvDUBTFT5K2NtTYoHUSIai7CoIiftSvqYNF7aCDFP8BxUFHdXK0g7g42P9ABVehk7hVEQQHpUJndRWUmJe+tLevT3069w3pvb9zTtJ3eWkBlfVkq7hEjzZz+q8c0N/MicP0++ZcpGP573lJ7ZQd+Q2bVJyA1usgIUKFPhzZwAHzTbywVVaI+JYjI4+Uqpn47BYHm6RnZdz9bb0BRdv6FHJK7Sj0DWb84/5wgVhS6QGCaQjFXQHxtnNpSiZomVn2c5pYmMzJZGAAEzLBgFHy+YpM9dgHTm4kUrxgeoM08tqWRGRoT56L2izX5oTS3+SAVa5c1zvCJSDSM1YPSWc982aNQK/87W/tmM2NrfqceV6hjdfI6zlabTNp8UkHufa+7kwWh3hojPhkf66MMI4f7/gDg9yAPm2UzMvHQXnOPEPs5h47rst1novm9PfQbovrvslzug3NSQead3C3Ky+mhVg+oN99LjtECb4n4pQSQ63M8K35pJor5jTKa/ZqtVitvILnugrz3rh+XuNU5rn122FcUS6pk5TxXEdPZCRLuaROUlbdH4XS2nIoFs41lYRaLwhAsQ0p+kSbKQKh/wI7enn3IXcXsQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$y = \\frac{1}{\\gamma^{2} + x^{2}}$$"
      ],
      "text/plain": [
       "         1     \n",
       "y = -----------\n",
       "         2    2\n",
       "    gamma  + x "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, x, gamma = symbols(\"y x gamma\", real=True)\n",
    "Eq(y, lorentz(x, gamma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f9e353d3c8>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-12.0, 12.0, 0.01)\n",
    "yL = lorentz(x, 1.0)\n",
    "plt.plot(x, yL, \"-r\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00689655, 0.00690798, 0.00691944, ..., 0.00693092, 0.00691944,\n",
       "       0.00690798])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$$\\int_{-\\infty}^{\\infty} \\frac{1}{\\gamma^{2} + x^{2}}\\, dx = \\begin{cases} \\frac{\\pi}{\\gamma} & \\text{for}\\: \\left(\\pi > 2 \\left|{\\arg{\\left (\\gamma \\right )}}\\right| \\wedge \\pi \\neq 2 \\left|{\\arg{\\left (\\gamma \\right )}}\\right| \\wedge \\frac{1}{\\gamma^{2}} \\neq 0\\right) \\vee \\pi > 2 \\left|{\\arg{\\left (\\gamma \\right )}}\\right| \\\\\\int_{-\\infty}^{\\infty} \\frac{1}{\\gamma^{2} + x^{2}}\\, dx & \\text{otherwise} \\end{cases}$$"
      ],
      "text/plain": [
       "                     /        pi                /   /                                             1        \\                     \\\n",
       "                     |      -----         for Or|And|pi > 2*|arg(gamma)|, pi != 2*|arg(gamma)|, ------ != 0|, pi > 2*|arg(gamma)||\n",
       "                     |      gamma               |   |                                                2     |                     |\n",
       " oo                  |                          \\   \\                                           gamma      /                     /\n",
       "  /                  |                                                                                                            \n",
       " |                   | oo                                                                                                         \n",
       " |       1           |  /                                                                                                         \n",
       " |  ----------- dx = < |                                                                                                          \n",
       " |       2    2      | |       1                                                                                                  \n",
       " |  gamma  + x       | |  ----------- dx                                         otherwise                                        \n",
       " |                   | |       2    2                                                                                             \n",
       "/                    | |  gamma  + x                                                                                              \n",
       "-oo                  | |                                                                                                          \n",
       "                     |/                                                                                                           \n",
       "                     \\-oo                                                                                                         "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# in case we'll need to normalize\n",
    "x, gamma = symbols(\"x gamma\", real=True)\n",
    "L_norm = Integral(lorentz(x, gamma), (x, -oo, oo))\n",
    "Eq(L_norm, L_norm.doit())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gauss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gauss_(x, sigma):\n",
    "    return np.exp(-np.square(x) / (2 * np.square(sigma)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Mul' object has no attribute 'exp'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-58-d0e27e02dc5f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msigma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msymbols\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'y x sigma'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mreal\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mEq\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mgauss_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0msigma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m<ipython-input-57-4cda65c42dc1>\u001b[0m in \u001b[0;36mgauss_\u001b[1;34m(x, sigma)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mgauss_\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msigma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[1;33m(\u001b[0m \u001b[1;33m-\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msquare\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msquare\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msigma\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAttributeError\u001b[0m: 'Mul' object has no attribute 'exp'"
     ]
    }
   ],
   "source": [
    "y, x, sigma = symbols(\"y x sigma\", real=True)\n",
    "Eq(y, gauss_(x, sigma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f9e3896630>]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "yG = gauss_(x, 1.0)\n",
    "plt.plot(x, yL, \"-r\")\n",
    "plt.plot(x, yG, \"-b\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$e^{\\left[\\begin{array}-72.0 & -71.88005 & -71.7602 & -71.64045 & -71.5208 & -71.40125 & -71.2818 & -71.16245 & -71.0432 & -70.92405 & -70.805 & -70.68605 & -70.5672 & -70.44845 & -70.3298 & -70.21125 & -70.0928 & -69.97445 & -69.8562 & -69.73805 & -69.62 & -69.5020500000001 & -69.3842 & -69.2664500000001 & -69.1488000000001 & -69.0312500000001 & -68.9138000000001 & -68.7964500000001 & -68.6792000000001 & -68.5620500000001 & -68.4450000000001 & -68.3280500000001 & -68.2112000000001 & -68.0944500000001 & -67.9778000000001 & -67.8612500000001 & -67.7448000000001 & -67.6284500000001 & -67.5122000000001 & -67.3960500000001 & -67.2800000000001 & -67.1640500000001 & -67.0482000000001 & -66.9324500000001 & -66.8168000000001 & -66.7012500000001 & -66.5858000000001 & -66.4704500000001 & -66.3552000000001 & -66.2400500000001 & -66.1250000000001 & -66.0100500000001 & -65.8952000000001 & -65.7804500000001 & -65.6658000000001 & -65.5512500000001 & -65.4368000000001 & -65.3224500000001 & 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-4.08979999999909 & -4.11844999999909 & -4.14719999999909 & -4.17604999999908 & -4.20499999999908 & -4.23404999999908 & -4.26319999999907 & -4.29244999999907 & -4.32179999999906 & -4.35124999999906 & -4.38079999999906 & -4.41044999999905 & -4.44019999999905 & -4.47004999999904 & -4.49999999999904 & -4.53004999999904 & -4.56019999999903 & -4.59044999999903 & -4.62079999999903 & -4.65124999999902 & -4.68179999999902 & -4.71244999999901 & -4.74319999999901 & -4.77404999999901 & -4.804999999999 & -4.836049999999 & -4.86719999999899 & -4.89844999999899 & -4.92979999999899 & -4.96124999999898 & -4.99279999999898 & -5.02444999999897 & -5.05619999999897 & -5.08804999999897 & -5.11999999999896 & -5.15204999999896 & -5.18419999999896 & -5.21644999999895 & -5.24879999999895 & -5.28124999999894 & -5.31379999999894 & -5.34644999999894 & -5.37919999999893 & -5.41204999999893 & -5.44499999999892 & -5.47804999999892 & -5.51119999999892 & -5.54444999999891 & -5.57779999999891 & -5.6112499999989 & -5.6447999999989 & -5.6784499999989 & -5.71219999999889 & -5.74604999999889 & -5.77999999999888 & -5.81404999999888 & -5.84819999999888 & -5.88244999999887 & -5.91679999999887 & -5.95124999999886 & -5.98579999999886 & -6.02044999999886 & -6.05519999999885 & -6.09004999999885 & -6.12499999999884 & -6.16004999999884 & -6.19519999999884 & -6.23044999999883 & -6.26579999999883 & -6.30124999999882 & -6.33679999999882 & -6.37244999999881 & -6.40819999999881 & -6.44404999999881 & -6.4799999999988 & -6.5160499999988 & -6.55219999999879 & -6.58844999999879 & -6.62479999999879 & -6.66124999999878 & -6.69779999999878 & -6.73444999999877 & -6.77119999999877 & -6.80804999999877 & -6.84499999999876 & -6.88204999999876 & -6.91919999999875 & -6.95644999999875 & -6.99379999999875 & -7.03124999999874 & -7.06879999999874 & -7.10644999999873 & -7.14419999999873 & -7.18204999999872 & -7.21999999999872 & -7.25804999999872 & -7.29619999999871 & -7.33444999999871 & -7.3727999999987 & -7.4112499999987 & 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-11.8097999999983 & -11.8584499999983 & -11.9071999999982 & -11.9560499999982 & -12.0049999999982 & -12.0540499999982 & -12.1031999999982 & -12.1524499999982 & -12.2017999999982 & -12.2512499999982 & -12.3007999999982 & -12.3504499999982 & -12.4001999999982 & -12.4500499999982 & -12.4999999999982 & -12.5500499999982 & -12.6001999999982 & -12.6504499999982 & -12.7007999999982 & -12.7512499999982 & -12.8017999999982 & -12.8524499999982 & -12.9031999999982 & -12.9540499999981 & -13.0049999999981 & -13.0560499999981 & -13.1071999999981 & -13.1584499999981 & -13.2097999999981 & -13.2612499999981 & -13.3127999999981 & -13.3644499999981 & -13.4161999999981 & -13.4680499999981 & -13.5199999999981 & -13.5720499999981 & -13.6241999999981 & -13.6764499999981 & -13.7287999999981 & -13.7812499999981 & -13.8337999999981 & -13.8864499999981 & -13.9391999999981 & -13.992049999998 & -14.044999999998 & -14.0980499999981 & -14.151199999998 & -14.204449999998 & -14.257799999998 & -14.311249999998 & -14.364799999998 & -14.418449999998 & -14.472199999998 & -14.526049999998 & -14.579999999998 & -14.634049999998 & -14.688199999998 & -14.742449999998 & -14.796799999998 & -14.851249999998 & -14.905799999998 & -14.960449999998 & -15.015199999998 & -15.0700499999979 & -15.1249999999979 & -15.180049999998 & -15.2351999999979 & -15.2904499999979 & -15.3457999999979 & -15.4012499999979 & -15.4567999999979 & -15.5124499999979 & -15.5681999999979 & -15.6240499999979 & -15.6799999999979 & -15.7360499999979 & -15.7921999999979 & -15.8484499999979 & -15.9047999999979 & -15.9612499999979 & -16.0177999999979 & -16.0744499999979 & -16.1311999999979 & -16.1880499999978 & -16.2449999999978 & -16.3020499999979 & -16.3591999999978 & -16.4164499999978 & -16.4737999999978 & -16.5312499999978 & -16.5887999999978 & -16.6464499999978 & -16.7041999999978 & -16.7620499999978 & -16.8199999999978 & -16.8780499999978 & -16.9361999999978 & -16.9944499999978 & -17.0527999999978 & -17.1112499999978 & 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      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$$\\int_{-\\infty}^{\\infty} e^{- \\frac{x^{2}}{2 \\gamma^{2}}}\\, dx = \\begin{cases} \\sqrt{2} \\sqrt{\\pi} \\gamma & \\text{for}\\: \\frac{\\pi}{2} \\geq 2 \\left|{\\arg{\\left (\\gamma \\right )}}\\right| \\\\\\int_{-\\infty}^{\\infty} e^{- \\frac{x^{2}}{2 \\gamma^{2}}}\\, dx & \\text{otherwise} \\end{cases}$$"
      ],
      "text/plain": [
       " oo                /  ___   ____            pi                  \n",
       "  /                |\\/ 2 *\\/ pi *gamma  for -- >= 2*|arg(gamma)|\n",
       " |                 |                        2                   \n",
       " |       2         |                                            \n",
       " |     -x          |  oo                                        \n",
       " |   --------      |   /                                        \n",
       " |          2      |  |                                         \n",
       " |   2*gamma       |  |       2                                 \n",
       " |  e         dx = <  |     -x                                  \n",
       " |                 |  |   --------                              \n",
       "/                  |  |          2                              \n",
       "-oo                |  |   2*gamma                               \n",
       "                   |  |  e         dx          otherwise        \n",
       "                   |  |                                         \n",
       "                   | /                                          \n",
       "                   | -oo                                        \n",
       "                   \\                                            "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# in case we'll need to normalize\n",
    "x, sigma = symbols(\"x sigma\", real=True)\n",
    "G_norm = Integral(gauss_(x, gamma), (x, -oo, oo))\n",
    "Eq(G_norm, G_norm.doit())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "So a normalized Gaussian is:\n",
       "$$ G(x; \\sigma) = \\frac{1}{\\sigma \\sqrt{2 \\pi}} e^{-\\frac{x^2}{2 \\sigma^2}} $$\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "So a normalized Gaussian is:\n",
    "$$ G(x; \\sigma) = \\frac{1}{\\sigma \\sqrt{2 \\pi}} e^{-\\frac{x^2}{2 \\sigma^2}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "The Voigt profile is defined by by a convolution of a Cauchy-Lorentz distribution and a Gaussian distribution:\n",
       "$$ V(x;\\sigma,\\gamma) \\equiv \\int_{-\\infty}^\\infty G(x';\\sigma)L(x-x';\\gamma)\\, dx' $$\n",
       "this can be evaluated by a special case of the Faddeeva function w(z):\n",
       "$$ V(x;\\sigma,\\gamma)=\\frac{\\operatorname{Re}[w(z)]}{\\sigma\\sqrt{2 \\pi}} $$\n",
       "where:\n",
       "$$ z=\\frac{x+i\\gamma}{\\sigma\\sqrt{2}} $$\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "The Voigt profile is defined by by a convolution of a Cauchy-Lorentz distribution and a Gaussian distribution:\n",
    "$$ V(x;\\sigma,\\gamma) \\equiv \\int_{-\\infty}^\\infty G(x';\\sigma)L(x-x';\\gamma)\\, dx' $$\n",
    "this can be evaluated by a special case of the Faddeeva function w(z):\n",
    "$$ V(x;\\sigma,\\gamma)=\\frac{\\operatorname{Re}[w(z)]}{\\sigma\\sqrt{2 \\pi}} $$\n",
    "where:\n",
    "$$ z=\\frac{x+i\\gamma}{\\sigma\\sqrt{2}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "def voigt(x, sigma, gamma):\n",
    "    return np.real(wofz((x + 1j * gamma) / (sigma * np.sqrt(2)))) / (\n",
    "        sigma * np.sqrt(2 * np.pi)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-12.0, 12.0, 0.01)\n",
    "yL = lorentz(x, 1.0)\n",
    "yG = gauss(x, 1.0)\n",
    "yV = voigt(x, 1.0, 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "x and y must have same first dimension, but have shapes (2400,) and (1,)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-45-4e5257f1f4da>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;31m#ax.set_ylim()\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     10\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0myL\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'-r'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 11\u001b[1;33m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0myG\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'-b'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     12\u001b[0m \u001b[0max\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0myV\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'-g'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     13\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\matplotlib\\__init__.py\u001b[0m in \u001b[0;36minner\u001b[1;34m(ax, data, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1808\u001b[0m                         \u001b[1;34m\"the Matplotlib list!)\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mlabel_namer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1809\u001b[0m                         RuntimeWarning, stacklevel=2)\n\u001b[1;32m-> 1810\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0max\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1811\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1812\u001b[0m         inner.__doc__ = _add_data_doc(inner.__doc__,\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_axes.py\u001b[0m in \u001b[0;36mplot\u001b[1;34m(self, scalex, scaley, *args, **kwargs)\u001b[0m\n\u001b[0;32m   1609\u001b[0m         \u001b[0mkwargs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmlines\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mLine2D\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_alias_map\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1610\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1611\u001b[1;33m         \u001b[1;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1612\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1613\u001b[0m             \u001b[0mlines\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mline\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_grab_next_args\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m    391\u001b[0m                 \u001b[0mthis\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    392\u001b[0m                 \u001b[0margs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 393\u001b[1;33m             \u001b[1;32myield\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    394\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    395\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[1;34m(self, tup, kwargs)\u001b[0m\n\u001b[0;32m    368\u001b[0m             \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtup\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    369\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 370\u001b[1;33m         \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_xy_from_xy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    371\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    372\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcommand\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m'plot'\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\Anaconda3\\lib\\site-packages\\matplotlib\\axes\\_base.py\u001b[0m in \u001b[0;36m_xy_from_xy\u001b[1;34m(self, x, y)\u001b[0m\n\u001b[0;32m    229\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    230\u001b[0m             raise ValueError(\"x and y must have same first dimension, but \"\n\u001b[1;32m--> 231\u001b[1;33m                              \"have shapes {} and {}\".format(x.shape, y.shape))\n\u001b[0m\u001b[0;32m    232\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    233\u001b[0m             raise ValueError(\"x and y can be no greater than 2-D, but have \"\n",
      "\u001b[1;31mValueError\u001b[0m: x and y must have same first dimension, but have shapes (2400,) and (1,)"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.close(\"all\")\n",
    "fig, ax = plt.subplots(figsize=(14, 8))\n",
    "ax.grid(b=True, which=\"both\", axis=\"both\")\n",
    "ax.minorticks_on()\n",
    "ax.set_title(\"Gaussian, Lorentzian and Voiget\", fontsize=16)\n",
    "ax.set_xlabel(\"x\", fontsize=14)\n",
    "# ax.set_xlim()\n",
    "ax.set_ylabel(\"y\", fontsize=14)\n",
    "# ax.set_ylim()\n",
    "ax.plot(x, yL, \"-r\")\n",
    "ax.plot(x, yG, \"-b\")\n",
    "ax.plot(x, yV, \"-g\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}