kingjr/for_theo_nonlin_cmap.ipynb

## for_theo_nonlin_cmap.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: MacOSX\n",
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "([], <a list of 0 Text yticklabel objects>)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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M2z5k+wSwE9jSVWcL8OVq/kngZkmqazTHxBENPLhLTKuBwx3LM8CmXnVsn5L0GvAO4GivRhPiiBqvc3z3U35y1Ty+slzS3o7lSduT1fxcPWr3GLyfOudIiCNq2N48wOZmgLUdy2uAIz3qzEgaA64AjtU1mmPiiItnD7BO0rWSJoCtwFRXnSng49X8R4Fv2PUXqtMTR1wk1THuNmA3MAo8Ynu/pO3AXttTwJeAxyRN0+6Btza1q4aQR8SQy3A6onAJcUThEuKIwiXEEYVLiCMKlxBHFC4hjihcQhxRuP8Hpqh+KCZauxAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Rfspx14EtI+PTBtKv+O/WSP9xYvpA+rtH4z4AntB4gD0H0vvPGEgX8IGnrC3+G4Le3AQ2szpzE9jMakkB2uoM0MxqyhmgmdWXb4KYWS2FM0Azq7G6BMB6fOHPzKwDZ4Bm1ipA23Z2JcaHA6CZtRD1aQI7AJpZO98FNrNaCn8X2MzqzE1gM6srZ4BmVl8OgGZWS34MxszqzE1gM6uvmgRAfxXOzFrFDrwqkLRQ0o2S1ko6rcP8fSR9R9K1kq6T9NL+bMjoHADNrIXIP4pa4TXquqQBYCmwCJgPLJE0v1TsvcAlEXEwsBj4TF83qAcHQDNr068ACBwCrI2IdRGxBbgYOLZUJoDd8vDuwIZ+bcdo3AdoZu2q9wHOkLSmML4sIpYVxvcG1hfGh4BDS+s4A/impL8BpgJH7VBdHwEHQDNrtWM/iLoxIhb0mN/pn4uUw+sS4PyI+Lik5wEXSjooIsb8+yhuAptZu/7dBBkCZhfGZ9HexD0RuAQgIn4ETAFmPOy67wAHQDNr08c+wNXAPElzJU0i3eRYUSrzG+BIAEkHkALgHf3bmu7cBDazdn16DjAitko6GVgFDABfiIjrJZ0JrImIFcDbgfMkvTW/8wkRMS5PIjoAmlmbfn4TJCJWAitL004vDN8APL9/71idA6CZtdqBh5wf6xwAzaydA6CZ1ZH/J4iZ1ZrG5x7ETucAaGatatQH6OcAzay2nAGaWRv/IKqZ1ZcDoJnVlTNAM6unHfs1mMc03wQxs9pyBmhm7dwENrM6av5PkDpwADSzdv4miJnVlTNAM6unGn0VzgHQzNrU5TEYB0Aza1eTDNDPAZpZbTkDNLM2vgliZvUU1OYxGDeBzay2nAGaWZu63AV2BmhmteUM0Mxa+LvAZlZfEb4JYmY20TkDNLM2bgKbWX05AJpZXdUlA3QfoJnVljNAM2sVwHA9UkAHQDNrV4/45yawmdWXM0Aza+ObIGZmfSBpoaQbJa2VdFqXMq+SdIOk6yUtH6+6OQM0szbq000QSQPAUuBFwBCwWtKKiLihUGYe8C7g+RGxSdKT+vLmFTgDNLOxdAiwNiLWRcQW4GLg2FKZNwJLI2ITQETcPl6VcwA0s1axA6/R7Q2sL4wP5WlF+wH7SfqhpKslLXwk1d8RbgKb2SMxQ9KawviyiFhWGFeHZcqhcxCYBxwOzAJ+IOmgiLi7rzXtwAHQzFqk3wOs3Ae4MSIW9Jg/BMwujM8CNnQoc3VEPATcLOlGUkBcXbUSD5ebwGY2llYD8yTNlTQJWAysKJX5GnAEgKQZpCbxuvGonAOgmbUbrvgaRURsBU4GVgG/Ai6JiOslnSnpmFxsFXCnpBuA7wDvjIg7+7o9XbgJbGZtdqAJPKqIWAmsLE07vTAcwNvya1w5AzSz2nIGaGatqj/i8pjnDNDMassZoJmV1Oe/wjkAmlmbuvwajAOgmbWrSQboPkAzqy0HQDOrLTeBzaxVgCp8y2MicAZoZrXlDNDM2vkmiJnZxOYM0Mza1SMBdAA0s3b9/DWYRzM3gc2stpwBmlk7Z4BmZhObM0AzaxVU+rn7icAZoJnVljNAM2shwneBzcwmOmeAZtbOGaCZ2cTmDNDM2jkDNDOb2BwAzay23AQ2s1Y1ehDaAdDM2vg5QDOzCc4ZoJm1cwZoZjaxOQCaWW25CWxmJVGbJrADoJm1CmoTAN0ENrPacgA0s9pyADSzdsMVXxVIWijpRklrJZ3Wo9wrJYWkBY+w9pU5AJrZmJE0ACwFFgHzgSWS5ncoNx04BfjxeNbPAdDMxtIhwNqIWBcRW4CLgWM7lPsAcBbwwHhWzgHQzNoootKrgr2B9YXxoTxt+3tJBwOzI+KK/m1BNX4MxszaVX8MZoakNYXxZRGxrDCuTmsfmSk1gLOBE3a0iv3gAGhmj8TGiOh102IImF0YnwVsKIxPBw4CvisJYC9ghaRjIqIYWMeEm8BmNpZWA/MkzZU0CVgMrGjOjIh7ImJGRMyJiDnA1cC4BD9wADSzsgCGo9prtFVFbAVOBlYBvwIuiYjrJZ0p6Zix3ZDRuQlsZmMqIlYCK0vTTu9S9vDxqFOTM0Azqy1ngGZWUp9fg3EGaGa15QzQzNo5AzQzm9gcAM2sttwENrN2bgKbmU1szgDNrFXzmyA14AzQzGrLGaCZlQRExd+7f4xzBmhmteUAaGa15SawmbXzYzBmZhObA6CZ1ZabwGbWys8BmplNfA6AZlZbbgKbWTvfBTYzm9gcAM2sttwENrN2bgKbmU1szgDNrMT/FtPMbMJzADSz2nIT2MxaBTDsH0Q1M5vQHADNrLbcBDazdr4LbGY2sTkAmlltuQlsZu3cBDYzm9gcAM2sthwAzawk0v8EqfKqQNJCSTdKWivptA7z3ybpBknXSbpK0r5936QuHADNbMxIGgCWAouA+cASSfNLxa4FFkTEM4HLgLPGq34OgGY2lg4B1kbEuojYAlwMHFssEBHfiYj78ujVwKzxqpzvAptZq4CIyt8FniFpTWF8WUQsK4zvDawvjA8Bh/ZY34nA16u++SPlAGhmj8TGiFjQY746TOvYeSjpeGABcFg/KlaFA6CZjaUhYHZhfBawoVxI0lHAe4DDIuLBcaqbA6CZdVDxDm8Fq4F5kuYC/wcsBo4rFpB0MHAusDAibu/XG1fhmyBmNmYiYitwMrAK+BVwSURcL+lMScfkYv8ETAMulfQzSSvGq37OAM1sTEXESmBladrpheGjxr1SmQOgmbXzd4HNzCY2B0Azqy0HQDOrLfcBmlmrCP9XODOzic4B0Mxqy01gM2vnx2DMzCY2B0Azqy0HQDOrLfcBmlmb8GMwZmYTmwOgmdWWm8BmVhJ+DMbMbKJzBtjDvWza+K247NaWf+GybadVx+yRGLd/Nv5Y4gDYQ0TsubPrYGZjxwHQzFoF/fynSI9q7gM0s9pyADSz2nIT2Mzahb8JYmY2oTkAmlltuQlsZi0CCN8FNjOb2BwAzay2HADNrLbcB2hmrSL8GIyZ2UTnAGhmteUmsJm18WMwZmYTnAOgmdWWA6CZ1ZYDoJmNKUkLJd0oaa2k0zrMnyzpK3n+jyXNGa+6OQCaWbsYrvYahaQBYCmwCJgPLJE0v1TsRGBTRDwdOBv4aJ+3pisHQDMbS4cAayNiXURsAS4Gji2VORb4Yh6+DDhSksajcg6AZjaW9gbWF8aH8rSOZSJiK3AP8MTxqJyfAzSzFveyadW34rIZFYtPkbSmML4sIpYVxjtlcuWHDKuUGRMOgGbWIiIW9nF1Q8DswvgsYEOXMkOSBoHdgbv6WIeu3AQ2s7G0Gpgnaa6kScBiYEWpzArgdXn4lcC3I8IZoJk9tkXEVkknA6uAAeALEXG9pDOBNRGxAvg8cKGktaTMb/F41U/jFGjNzB513AQ2s9pyADSz2nIANLPacgA0s9pyADSz2nIANLPacgA0s9pyADSz2vp/AyQKbZbKYq0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%pylab\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from matplotlib.colors import LinearSegmentedColormap\n",
    "\n",
    "\n",
    "class Logcmap(LinearSegmentedColormap):\n",
    "    # Authors: Jean-Remi King, <jeanremi.king@gmail.com>\n",
    "    #          Clement Levrard <clement.levrard@gmail.com>\n",
    "    #\n",
    "    # License: BSD (3-clause)\n",
    "    \"\"\"\n",
    "    Creates colormap with a logarithmic scale \n",
    "\n",
    "    The center and bounds define \n",
    "    where the color mass is spread such that:\n",
    "        f(0, center) = 0\n",
    "        f(1, center) = 1\n",
    "        f(center, center) = .5\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    cmap : str, matplotlib cmap\n",
    "    center : float, defaults to 0.5\n",
    "    clim : tuple, shape(2,), default to [0, 1]\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    cmap : matplotlib cmap\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, cmap='viridis', center=.5, clim=[0, 1]):\n",
    "        if isinstance(cmap, str):\n",
    "            self.cmap = plt.get_cmap(cmap)\n",
    "            self.clim = clim\n",
    "            self.center = center\n",
    "            for attr in self.cmap.__dict__.keys():\n",
    "                setattr(self, attr, self.cmap.__dict__[attr])\n",
    "\n",
    "    def __call__(self, value, alpha=1., **kwargs):\n",
    "        center = (self.center - self.clim[0]) / np.diff(self.clim)\n",
    "        value = (value - self.clim[0]) / np.diff(self.clim)\n",
    "        value = np.clip(value, 0, 1)\n",
    "        ilogval = self.transform(x=value, inverse=True)\n",
    "        return self.cmap(ilogval, alpha=alpha, **kwargs)\n",
    "    \n",
    "    def transform(self, x=None, inverse=False):\n",
    "        \"\"\"\n",
    "        Transforms data with a logarithmic scale such that:\n",
    "        f(0, center) = 0\n",
    "        f(1, center) = 1\n",
    "        f(center, center) = .5\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        x : float | np.array | None\n",
    "            If float or np.array, 0. < x < 1.\n",
    "            If None, set to np.linspace(0., 1., 256).\n",
    "            Defaults to None.\n",
    "        center : float\n",
    "            0. < center < 1.\n",
    "        Returns\n",
    "        -------\n",
    "        y : float | np.array\n",
    "        \"\"\"\n",
    "\n",
    "        from numpy import exp, log\n",
    "        if x is None:\n",
    "            x = np.linspace(0., 1., 256)\n",
    "        if self.center >= 1. or self.center <= 0.:\n",
    "            raise ValueError('center must be between 0 and 1')\n",
    "        if self.center == .5:\n",
    "            y = x\n",
    "        else:\n",
    "            n = 1. / self.center\n",
    "            if inverse is False:\n",
    "                y = (exp(2 * log(n - 1) * x) - 1) / (n * (n - 2))\n",
    "            else:\n",
    "                y = log(x * (n * (n - 2)) + 1) / (2 * log(n - 1))\n",
    "        return y\n",
    "\n",
    "\n",
    "# imaging a dataset where most of the variation is between 90% and 100%\n",
    "X = np.array([np.r_[np.linspace(0, .9, 50), \n",
    "                    np.linspace(.9, 1, 50)]]*100)\n",
    "\n",
    "# by default it will be difficult to notice the difference above 90%\n",
    "plt.matshow(X, cmap='viridis')\n",
    "plt.colorbar()\n",
    "plt.title('default')\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "\n",
    "# we thus use this non linear colormap\n",
    "plt.matshow(X, cmap=Logcmap('viridis', .90))\n",
    "plt.colorbar()\n",
    "plt.title('emphasize variation of color around 90% accuracy')\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "\n",
    "\n",
    "# for more colorvariation, but less intuitive colors use a larger spectrum\n",
    "plt.matshow(X, cmap=Logcmap('rainbow', .90))\n",
    "plt.colorbar()\n",
    "plt.title('emphasize variation of color around 90% accuracy')\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "\n",
    "# On the contrary, when we want to emphasize below chance results,:\n",
    "chance = 1./10.\n",
    "plt.matshow(X, cmap=Logcmap('RdBu_r', chance))\n",
    "plt.colorbar()\n",
    "plt.axvline(np.where(X[0]>=chance)[0][0], color='k', label='chance')\n",
    "plt.title('make below chance level as blue as accuracy can be');\n",
    "plt.xticks([])\n",
    "plt.yticks([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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