{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Produce the figures for the numerical results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This IPython notebook produces the error x distance-size ratio figures for the section \"Evaluation of the accuracy\" of the article.\n",
    "\n",
    "The data was calculated by the `tesseroid_vs_spherical_shell.ipynb` notebook and saved to CSV files in the `data` directory of the main repository."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the required libraries and set the plot defaults"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll use the pandas library to load and manipulate the data. Plots will be made with matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from __future__ import division\n",
    "from IPython.display  import set_matplotlib_formats\n",
    "set_matplotlib_formats('svg')\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.rcParams['axes.labelsize'] = 9.0  # fontsize of the x any y labels\n",
    "plt.rcParams['xtick.labelsize'] = 9.0  # fontsize of the tick labels\n",
    "plt.rcParams['ytick.labelsize'] = 9.0  # fontsize of the tick labels\n",
    "plt.rcParams['legend.fontsize'] = 9.0\n",
    "plt.rcParams['font.family'] = 'serif'\n",
    "plt.rcParams['font.serif'] = 'Computer Modern Roman'\n",
    "plt.rcParams['text.usetex'] = True  # use latex for all text handling\n",
    "plt.rcParams['text.color'] = '3a3a3a'\n",
    "plt.rcParams['figure.facecolor'] = 'white'\n",
    "plt.rcParams['axes.linewidth'] = 1\n",
    "plt.rcParams['axes.edgecolor'] = '3a3a3a'\n",
    "plt.rcParams['axes.facecolor'] = 'white'\n",
    "plt.rcParams['lines.linewidth'] = 1\n",
    "plt.rcParams['lines.markersize'] = 4\n",
    "plt.rcParams['xtick.major.size'] = 2\n",
    "plt.rcParams['ytick.major.size'] = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the spherical shell data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And load the computed shell effect per height so that we can calculate the relative difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "shell = pd.read_csv('../data/shell-per-height.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "\n",
       "            pot  height  \n",
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shell"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the error vs distance-size ratio for the 4 experiments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the computed differences between the shell and tesseroid effects for each experiment.\n",
    "We'll use the `groupby` method of the *pandas* `DataFrame` to compute the maximum absolute difference per distance-size ratio and keep that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def load_max_diff(fname):\n",
    "    data = pd.read_csv(fname)\n",
    "    return data.groupby(['size', 'ratio']).max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pole = load_max_diff('../data/difference-size-1-height-2000-pole.csv')\n",
    "equator = load_max_diff('../data/difference-size-1-height-2000-equator.csv')\n",
    "goce = load_max_diff('../data/difference-size-1-height-260000-pole.csv')\n",
    "big = load_max_diff('../data/difference-size-30-height-2000-pole.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is what the data looks like after taking the maximum difference per ratio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "            point          gx         gxx        gxy          gxz        gy  \\\n",
       "size ratio                                                                    \n",
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       "\n",
       "                   gyy        gyz          gz         gzz        pot  \n",
       "size ratio                                                            \n",
       "1    0.0    311.835644  27.800405  686.281514  782.758707  33.533012  \n",
       "     0.5     64.388814  13.539341   99.543785  128.777627   6.633058  \n",
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     },
     "execution_count": 7,
     "metadata": {},
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    }
   ],
   "source": [
    "pole.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make a plot of the maximum relative difference as a function of the distance-size ratio used in the computations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ratio = pole.index.levels[1] # Get the unique values of the distance-size ratio used"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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   "source": [
    "plotargs = dict(color='#3a3a3a', markeredgewidth=0.5, markeredgecolor='#3a3a3a')\n",
    "styles = \"-s -^ -v -o\".split()\n",
    "fig, subplots = plt.subplots(3, 1, figsize=(3.33, 5), sharex='col')\n",
    "axes = subplots.ravel()\n",
    "fields = ['pot', 'gz', 'gzz']\n",
    "titles = [r'V', r'gz', r'gzz']\n",
    "subfigure = ['(a)', '(b)', '(c)']\n",
    "for ax, f, title, sub in zip(axes, fields, titles, subfigure):\n",
    "    ax.text(-0.21, 0.9, sub, fontsize=12, fontdict={'weight': 'bold'},\n",
    "            transform=ax.transAxes)\n",
    "    ax.text(0.5, 0.9, title, fontsize=11, \n",
    "            horizontalalignment='center', verticalalignment='center',\n",
    "            bbox={'facecolor': 'w', \n",
    "                  'edgecolor': '#9b9b9b',\n",
    "                  'linewidth': 0.5, 'pad': 8}, \n",
    "            transform=ax.transAxes)\n",
    "    shell_low = np.abs(shell[shell.height == 2000][f].values)\n",
    "    shell_high = np.abs(shell[shell.height == 260000][f].values)\n",
    "    ax.plot(ratio, 100*pole[f]/shell_low, styles[0], label='pole', \n",
    "            **plotargs)\n",
    "    ax.plot(ratio, 100*equator[f]/shell_low, styles[1], label='equator', \n",
    "            **plotargs)\n",
    "    ax.plot(ratio, 100*goce[f]/shell_high, styles[2], label='260 km', \n",
    "            **plotargs)\n",
    "    ax.plot(ratio, 100*big[f]/shell_low, styles[3], label=r'$30^\\circ$ size', \n",
    "            **plotargs)\n",
    "    ax.hlines(0.1, ratio.min(), ratio.max(), colors=['#3a3a3a'], linewidth=1.5)    \n",
    "    ax.set_xlim(ratio.min(), ratio.max())\n",
    "    ax.set_yscale('log')\n",
    "    ax.set_xticks(range(11))\n",
    "    ax.set_yticks(ax.get_yticks()[2:-2])\n",
    "    ax.set_ylabel('Difference (\\\\%)')\n",
    "    ax.grid(True, linewidth=0.5, color='#aeaeae')\n",
    "    ax.set_axisbelow(True)\n",
    "    ax.minorticks_off()\n",
    "ax = axes[-1]\n",
    "ax.set_xlabel('Distance-size ratio')\n",
    "ax.legend(borderpad=0.5, numpoints=1, bbox_to_anchor=(1, 1), \n",
    "          fancybox=True, shadow=False, fontsize=9, )\n",
    "plt.tight_layout(pad=0.3, h_pad=0, w_pad=0)\n",
    "plt.subplots_adjust(hspace=0, wspace=0)\n",
    "plt.savefig('../figs/distance-size-curves.eps') # Save the figure to an EPS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the error curves for gzz for various heights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the data for the gzz difference per height. I'll use the pre-loaded spherical shell data to calculate the relative difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "gzz = pd.read_csv('../data/difference-gzz-per-height-size-1-pole.csv', \n",
    "                  index_col=0).groupby(['height', 'ratio']).max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is what the first few  lines of the data look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>gzz</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>height</th>\n",
       "      <th>ratio</th>\n",
       "      <th></th>\n",
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       "      <th rowspan=\"5\" valign=\"top\">2000</th>\n",
       "      <th>0.0</th>\n",
       "      <td> 782.758707</td>\n",
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       "    <tr>\n",
       "      <th>0.5</th>\n",
       "      <td> 128.777627</td>\n",
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       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>  32.012723</td>\n",
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       "    <tr>\n",
       "      <th>1.5</th>\n",
       "      <td>   2.289414</td>\n",
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       "    <tr>\n",
       "      <th>2.0</th>\n",
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      "text/plain": [
       "                     gzz\n",
       "height ratio            \n",
       "2000   0.0    782.758707\n",
       "       0.5    128.777627\n",
       "       1.0     32.012723\n",
       "       1.5      2.289414\n",
       "       2.0      0.283195"
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     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gzz.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "heights = gzz.index.levels[0].values # Get the unique values of the computation height"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   2000.,   10000.,   50000.,  150000.,  260000.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "heights"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we'll make the difference x ratio plot with a curve for each height."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
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   "outputs": [
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f866306f890>"
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   ],
   "source": [
    "color = '#3a3a3a'\n",
    "styles = \"-s -^ -v -o -*\".split()\n",
    "fig = plt.figure(figsize=(3.33, 3))\n",
    "ax = plt.subplot(111)\n",
    "for h, sty in zip(heights, styles):\n",
    "    shell_value = np.abs(shell[shell.height == h]['gzz'].values)\n",
    "    diff = 100*gzz.loc[int(h)]/shell_value\n",
    "    markersize = 4\n",
    "    if sty[-1] == '*':\n",
    "        markersize = 7\n",
    "    ax.plot(ratio, diff, sty, label='{:.0f} km'.format(h/1000), color=color, \n",
    "            markeredgewidth=0.5, markeredgecolor=color, markersize=markersize)\n",
    "ax.hlines(0.1, ratio.min(), ratio.max(), colors=['#3a3a3a'], linewidth=1.5)    \n",
    "ax.set_xlim(ratio.min(), ratio.max())\n",
    "ax.set_yscale('log')\n",
    "ax.set_xticks(range(11))\n",
    "ax.set_yticks(ax.get_yticks())\n",
    "ax.minorticks_off()\n",
    "ax.grid(True, linewidth=0.5, color='#aeaeae')\n",
    "ax.set_axisbelow(True)\n",
    "ax.set_ylabel('Difference (\\\\%)')\n",
    "ax.set_xlabel('Distance-size ratio')\n",
    "ax.legend(borderpad=0.5, numpoints=1, bbox_to_anchor=(1, 1), \n",
    "          fancybox=True, shadow=False, fontsize=9, )\n",
    "plt.tight_layout(pad=0.25, h_pad=0, w_pad=0)\n",
    "plt.subplots_adjust(hspace=0, wspace=0)\n",
    "plt.savefig('../figs/gzz-with-height.eps') # Save the figure to an EPS"
   ]
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