whittakerw-for-tikz.ipynb

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whittakerw-for-tikz.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "whittakerw-for-tikz.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/kpym/41d4723d06bec948638602fd7f6922c0/whittakerw-for-tikz.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "metadata": {
        "id": "H7b5gscx_v28",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from mpmath import whitw # the Whittaker W function"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "JPbpHFVoAOHt",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# generate data points\n",
        "x = range(-100,0,1)\n",
        "y = [whitw(1, x_i,10) for x_i in x]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "4hxmTXG2__MQ",
        "colab_type": "code",
        "outputId": "b4d9c04d-c859-42e3-a941-bbc3970b3e90",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "cell_type": "code",
      "source": [
        "# output tuples ready to be plot by tikz\n",
        "print(\"\\\\addplot coordinates {\"+\" \".join(\"(%.1f,%.2E)\" % xy for xy in list(zip(x,y)))+\"};\") # or '{'+str(list(zip(x,y))).strip('[]')+'}'"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\\addplot coordinates {(-100.0,1.31E+118) (-99.0,3.28E+116) (-98.0,8.29E+114) (-97.0,2.12E+113) (-96.0,5.45E+111) (-95.0,1.42E+110) (-94.0,3.73E+108) (-93.0,9.93E+106) (-92.0,2.67E+105) (-91.0,7.25E+103) (-90.0,1.99E+102) (-89.0,5.53E+100) (-88.0,1.55E+99) (-87.0,4.41E+97) (-86.0,1.27E+96) (-85.0,3.68E+94) (-84.0,1.08E+93) (-83.0,3.22E+91) (-82.0,9.70E+89) (-81.0,2.96E+88) (-80.0,9.12E+86) (-79.0,2.85E+85) (-78.0,9.02E+83) (-77.0,2.89E+82) (-76.0,9.38E+80) (-75.0,3.08E+79) (-74.0,1.03E+78) (-73.0,3.47E+76) (-72.0,1.19E+75) (-71.0,4.12E+73) (-70.0,1.45E+72) (-69.0,5.18E+70) (-68.0,1.88E+69) (-67.0,6.90E+67) (-66.0,2.57E+66) (-65.0,9.74E+64) (-64.0,3.74E+63) (-63.0,1.46E+62) (-62.0,5.80E+60) (-61.0,2.34E+59) (-60.0,9.57E+57) (-59.0,3.99E+56) (-58.0,1.69E+55) (-57.0,7.27E+53) (-56.0,3.19E+52) (-55.0,1.42E+51) (-54.0,6.46E+49) (-53.0,2.99E+48) (-52.0,1.41E+47) (-51.0,6.77E+45) (-50.0,3.32E+44) (-49.0,1.66E+43) (-48.0,8.45E+41) (-47.0,4.39E+40) (-46.0,2.34E+39) (-45.0,1.27E+38) (-44.0,7.04E+36) (-43.0,4.00E+35) (-42.0,2.32E+34) (-41.0,1.38E+33) (-40.0,8.40E+31) (-39.0,5.24E+30) (-38.0,3.36E+29) (-37.0,2.21E+28) (-36.0,1.49E+27) (-35.0,1.03E+26) (-34.0,7.36E+24) (-33.0,5.40E+23) (-32.0,4.08E+22) (-31.0,3.18E+21) (-30.0,2.56E+20) (-29.0,2.13E+19) (-28.0,1.83E+18) (-27.0,1.63E+17) (-26.0,1.51E+16) (-25.0,1.44E+15) (-24.0,1.44E+14) (-23.0,1.49E+13) (-22.0,1.62E+12) (-21.0,1.83E+11) (-20.0,2.17E+10) (-19.0,2.69E+09) (-18.0,3.52E+08) (-17.0,4.85E+07) (-16.0,7.08E+06) (-15.0,1.10E+06) (-14.0,1.81E+05) (-13.0,3.19E+04) (-12.0,6.04E+03) (-11.0,1.24E+03) (-10.0,2.75E+02) (-9.0,6.69E+01) (-8.0,1.80E+01) (-7.0,5.36E+00) (-6.0,1.80E+00) (-5.0,6.90E-01) (-4.0,3.05E-01) (-3.0,1.58E-01) (-2.0,9.76E-02) (-1.0,7.26E-02)};\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "m-1TgtzJB8H-",
        "colab_type": "code",
        "outputId": "2cfa29ff-de64-4c37-8190-259a37f1594e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 358
        }
      },
      "cell_type": "code",
      "source": [
        "# check the result before to plot it\n",
        "import matplotlib.pyplot as plt\n",
        "_ = plt.plot(x, y, 'o')"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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1JsvtTuzgclvm93uMnq+vYo5mMEczmKMZzNGMeM0xZoQ/y3GcyK8vXLig4uJivfTSS6qp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\nD49HW29dHgX0AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}

WhittakerW_plot.tex

% https://tex.stackexchange.com/a/480433
\documentclass[tikz,border=7pt]{standalone}
\usepackage{pgfplots}
\begin{document}
  \begin{tikzpicture}
    \begin{semilogyaxis}
      % data generated with iPython : https://colab.research.google.com/gist/kpym/41d4723d06bec948638602fd7f6922c0/whittakerw-for-tikz.ipynb
      \addplot coordinates {(-100.0,1.31E+118) (-99.0,3.28E+116) (-98.0,8.29E+114) (-97.0,2.12E+113) (-96.0,5.45E+111) (-95.0,1.42E+110) (-94.0,3.73E+108) (-93.0,9.93E+106) (-92.0,2.67E+105) (-91.0,7.25E+103) (-90.0,1.99E+102) (-89.0,5.53E+100) (-88.0,1.55E+99) (-87.0,4.41E+97) (-86.0,1.27E+96) (-85.0,3.68E+94) (-84.0,1.08E+93) (-83.0,3.22E+91) (-82.0,9.70E+89) (-81.0,2.96E+88) (-80.0,9.12E+86) (-79.0,2.85E+85) (-78.0,9.02E+83) (-77.0,2.89E+82) (-76.0,9.38E+80) (-75.0,3.08E+79) (-74.0,1.03E+78) (-73.0,3.47E+76) (-72.0,1.19E+75) (-71.0,4.12E+73) (-70.0,1.45E+72) (-69.0,5.18E+70) (-68.0,1.88E+69) (-67.0,6.90E+67) (-66.0,2.57E+66) (-65.0,9.74E+64) (-64.0,3.74E+63) (-63.0,1.46E+62) (-62.0,5.80E+60) (-61.0,2.34E+59) (-60.0,9.57E+57) (-59.0,3.99E+56) (-58.0,1.69E+55) (-57.0,7.27E+53) (-56.0,3.19E+52) (-55.0,1.42E+51) (-54.0,6.46E+49) (-53.0,2.99E+48) (-52.0,1.41E+47) (-51.0,6.77E+45) (-50.0,3.32E+44) (-49.0,1.66E+43) (-48.0,8.45E+41) (-47.0,4.39E+40) (-46.0,2.34E+39) (-45.0,1.27E+38) (-44.0,7.04E+36) (-43.0,4.00E+35) (-42.0,2.32E+34) (-41.0,1.38E+33) (-40.0,8.40E+31) (-39.0,5.24E+30) (-38.0,3.36E+29) (-37.0,2.21E+28) (-36.0,1.49E+27) (-35.0,1.03E+26) (-34.0,7.36E+24) (-33.0,5.40E+23) (-32.0,4.08E+22) (-31.0,3.18E+21) (-30.0,2.56E+20) (-29.0,2.13E+19) (-28.0,1.83E+18) (-27.0,1.63E+17) (-26.0,1.51E+16) (-25.0,1.44E+15) (-24.0,1.44E+14) (-23.0,1.49E+13) (-22.0,1.62E+12) (-21.0,1.83E+11) (-20.0,2.17E+10) (-19.0,2.69E+09) (-18.0,3.52E+08) (-17.0,4.85E+07) (-16.0,7.08E+06) (-15.0,1.10E+06) (-14.0,1.81E+05) (-13.0,3.19E+04) (-12.0,6.04E+03) (-11.0,1.24E+03) (-10.0,2.75E+02) (-9.0,6.69E+01) (-8.0,1.80E+01) (-7.0,5.36E+00) (-6.0,1.80E+00) (-5.0,6.90E-01) (-4.0,3.05E-01) (-3.0,1.58E-01) (-2.0,9.76E-02) (-1.0,7.26E-02)};
    \end{semilogyaxis}
  \end{tikzpicture}
\end{document}