{ "cells": [ { "cell_type": "markdown", "source": [ "# 2D Histograms in physt" ], "metadata": { "collapsed": true } }, { "cell_type": "code", "source": [ "# Necessary import evil\n", "import physt\n", "from physt import h1, h2, histogramdd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "%matplotlib inline\n", "\nnp.random.seed(42)" ], "outputs": [], "execution_count": 1, "metadata": { "collapsed": false } }, { "cell_type": "code", "source": [ "# Some data\n", "x = np.random.normal(100, 1, 1000)\n", "y = np.random.normal(10, 10, 1000)" ], "outputs": [], "execution_count": 2, "metadata": { "collapsed": true } }, { "cell_type": "code", "source": [ "# Create a simple histogram\n", "histogram = h2(x, y, [8, 4], name=\"Some histogram\", axis_names=[\"x\", \"y\"])\n", "histogram" ], "outputs": [ { "output_type": "execute_result", "execution_count": 3, "data": { "text/plain": [ "Histogram2D(bins=(8, 4), total=1000, dtype=int64)" ] }, "metadata": {} } ], "execution_count": 3, "metadata": { "collapsed": false } }, { "cell_type": "code", "source": [ "# Frequencies are a 2D-array\n", "histogram.frequencies" ], "outputs": [ { "output_type": "execute_result", "execution_count": 4, "data": { "text/plain": [ "array([[ 0, 2, 4, 0],\n", " [ 3, 26, 20, 5],\n", " [ 17, 78, 104, 10],\n", " [ 26, 163, 147, 17],\n", " [ 17, 136, 96, 17],\n", " [ 6, 41, 38, 6],\n", " [ 1, 11, 7, 0],\n", " [ 0, 1, 0, 1]])" ] }, "metadata": {} } ], "execution_count": 4, "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## Multidimensional binning\n", "\nIn most cases, binning methods that apply for 1D histograms, can be used also in higher dimensions. In such cases, each parameter can be either scalar (applies to all dimensions) or a list/tuple with independent values for each dimension. This also applies for *range* that has to be list/tuple of tuples." ], "metadata": {} }, { "cell_type": "code", "source": [ "histogram = h2(x, y, \"fixed_width\", (2, 10), name=\"Fixed-width bins\", axis_names=[\"x\", \"y\"])\n", "histogram.plot();\n", "histogram.numpy_bins" ], "outputs": [ { "output_type": "execute_result", "execution_count": 5, "data": { "text/plain": [ "[array([ 96., 98., 100., 102., 104.]),\n", " array([-20., -10., 0., 10., 20., 30., 40., 50.])]" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEYCAYAAABLOxEiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XuUHVWZ9/HvLwmE+3CJjZhEiRCwgaWIkUEugglIQIag\n", "AwrLkSjMm1cHFS/IRXxlXCMOeENZOmoLSFjDECKCZLySdC4MAwQS5ZKQaAIo9BDJxEAQYYJJnveP\n", "2r049Jzuruqcc6pO5/dZ66w+tWufqqeLcJ7eu3btrYjAzMwsrxFlB2BmZu3FicPMzApx4jAzs0Kc\n", "OMzMrBAnDjMzK8SJw8zMCnHisKaQ9FpJz0sa2YRjh6T9t/IY75d0xwD7F0r6+wH2Xy/piznPtW+K\n", 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axis_names=[\"x\", \"y\"])\n", "histogram.plot(cmap_min=0);\n", "histogram.numpy_bins" ], "outputs": [ { "output_type": "execute_result", "execution_count": 6, "data": { "text/plain": [ "[array([ 96.75873266, 99.54993453, 100.40825276, 103.85273149]),\n", " array([-19.40388635, 3.93758311, 10.63077132, 17.28882177, 41.93107568])]" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAZMAAAEYCAYAAACZaxt6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAGWxJREFUeJzt3X2wZHV95/H3Z2YgyMjDAIIIKBhZHxYVzQgTNcYFk4Ba\n", "oq5YupZgJM6yKwaNMaBJxbLUXTAmqNFsGAXFrCso0YL1GXnQuCIyKCpPBkSBWQaQFRSxUIHv/tHn\n", "xma4d6bnnr59Tt/7flV13T6/Pn36O5dhPv17OOekqpAkqY1lXRcgSZp+hokkqTXDRJLUmmEiSWrN\n", "MJEktWaYSJJaM0wkSa0ZJlrykvw8yaOb5x9J8o55HqeSPGaO116R5Ett6pT6zDDRxCV5VZLvJflF\n", "kluS/EOSnSb02Rcl+ZPhtqp6aFVdv5CfW1Ufq6o/XMjPkLpkmGiikrwROBl4E7ATsAbYF/hSkm06\n", 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colorbar\n", "import matplotlib.cm as cm\n", "fig, ax = plt.subplots()\n", "ax = histogram.plot(ax=ax, cmap=cm.copper, show_colorbar=False, grid_color=cm.copper(0.5))\n", "ax.set_title(\"Custom colormap\");" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAF7VJREFUeJzt3XmUZGWd5vHvU1WyWSCFyF4MdIsLzYAtiNoiKriArYAO\n", "2qjHRuV0jY7aKqMNqON0T7sA2ugZlzPWEUdslEVkKUVRxAV7WBQUFEQFEaQEKUGQpQUp+M0fcatJ\n", "ykxqgcz3zczv55w4EXHve288GRTxxL1x40aqCkmSejOndQBJksZjQUmSumRBSZK6ZEFJkrpkQUmS\n", "umRBSZK6ZEFJ01iS7ZJUknmts0gPNwtKM0KSVya5KMkdSW5I8tUkezzEdf5jkuMfroyS1owFpWkv\n", "yaHAR4D3A5sD2wKfAPZvmat3bnWpdxaUprUkjwL+F/DGqjq1qu6sqnuq6ktV9Y5hzGeSvHfMMs9O\n", "snTM/cOS/DrJ7Ul+lmTvJPsA7wT+Ztgqu3QYu1WSJUl+l+SqJH83Zj3/mOQLSY4f1vXjJI9LckSS\n", "ZUmuS/L8B/lbFiY5Nclvk9yc5GPD9DlJ3p3k2mE9nx3+7vHWsap8pwz5bgNes6aZk7w2yRXD2KuT\n", 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"collapsed": false } }, { "cell_type": "code", "source": [ "# Show labels (and hide zero bins), no grid(lw=0)\n", "ax = histogram.plot(show_values=True, show_zero=False, cmap=cm.RdBu, format_value=float, lw=0)" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEYCAYAAABLOxEiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3XecFdX5x/HPd3eBRYpUAVmair0LaMQCGBWMihoLahDb\n", "DxNLTGzYokYlthhjVxQDJoogimIl2DUqAjZAQJoKSO9NYHef3x8z4IJb7i5377l393m/XvPi3pnZ\n", "mW827n3uOTNzjswM55xzLlFZoQM455zLLF44nHPOlYsXDuecc+XihcM551y5eOFwzjlXLl44nHPO\n", "lYsXDlflSOosaZqk1ZJOKmGfNyT1qYRzt5VkknLi9+9JurACxzlX0kelbK+U/M4lwguH+wVJ30n6\n", "9VbrSv0gSzO3Ag+ZWV0ze6m4Hcysh5kNTnGupMn0/C6zeeFwVVEbYFJxGxTx/+6d2wb+B+QqJO6O\n", "2aXI+0GSbo9fd5E0R9I1khZKmifpJEnHSfpW0lJJ1xf52U6SPpG0PN73IUk1tzrX7+Pup2WSHpak\n", "EnLNAHYCXom7qmrF3UX9Jf0PWAvstHUXkqTzJU2Ojz9KUptEzi8pW9LfJS2WNBP4TQm5asX/u/cp\n", 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"cell_type": "markdown", "source": [ "### Large histograms as images\n", "\n", "Plotting histograms in this way gets problematic with more than roughly 50x50 bins. There is an alternative, though, partially inspired by the `datashader` project - plot the histogram as bitmap, which works very fast even for very large histograms.\n", "\n**Note**: This method does not work for histograms with irregular bins." ], "metadata": {} }, { "cell_type": "code", "source": [ "x = np.random.normal(100, 1, 1000000)\n", "y = np.random.normal(10, 10, 1000000)" ], "outputs": [], "execution_count": 12, "metadata": { "collapsed": false } }, { "cell_type": "code", "source": [ "fig, axes = plt.subplots(1, 3, figsize=(12, 4))\n", "h2(x, y, 20, name=\"20 bins - map\").plot(\"map\", cmap=\"rainbow\", lw=0, alpha=1, ax=axes[0], show_colorbar=False)\n", "h2(x, y, 20, name=\"20 bins - image\").plot(\"image\", cmap=\"rainbow\", alpha=1, ax=axes[1])\n", "h2(x, y, 500, name=\"500 bins - image\").plot(\"image\", cmap=\"rainbow\", alpha=1, ax=axes[2]);" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ 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Therefore, it may be of some use to transform the values by a function, e.g. logarithm." ], "metadata": {} }, { "cell_type": "code", "source": [ "fig, axes = plt.subplots(1, 3, figsize=(12, 4))\n", "h2(x, y, 20, name=\"20 bins - map\").plot(\"map\", alpha=1, lw=0, show_zero=False, cmap=\"rainbow\", ax=axes[0], show_colorbar=False, cmap_normalize=\"log\")\n", "h2(x, y, 20, name=\"20 bins - image\").plot(\"image\", alpha=1, ax=axes[1], cmap=\"rainbow\", cmap_normalize=\"log\")\n", "h2(x, y, 500, name=\"500 bins - image\").plot(\"image\", alpha=1, ax=axes[2], cmap=\"rainbow\", cmap_normalize=\"log\");" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAA1cAAAEYCAYAAACwUwxgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvXl4W9d5r/sucQLnwSAp0RxAWpMp2WSsIW5Ct4rkOq6k\n", "NLTbm5smauWTnqZpjm9PnfSkUq5rUT6uxT7tjc7pTU9z3MSNEtXN0DpsSquOazuqzTSOBoeyJGqw\n", 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plt.subplots(figsize=(8, 7))\n", "h_2 = h2(x, y, 30)\n", "h_2.plot(\"map\", lw=0, alpha=0.9, cmap=\"Blues\", ax=ax, cmap_normalize=\"log\", show_zero=False)\n", "# h2(x, y, 300).plot(\"image\", alpha=1, cmap=\"Greys\", ax=ax, transform=lambda x: x > 0);\n", "# Not working currently" ], "outputs": [ { "output_type": "execute_result", "execution_count": 15, "data": { "text/plain": [ "" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAhkAAAHwCAYAAAALuX1cAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X2w3Ndd3/HP5z5LupJt+cqJsRzbFOPgMAlQxUkJ5AEC\n", "VSDFgQnU5iGmuPGEkjT0iTiFCWU6mSbQSSGDCSOw69AJcU2SOqbj1JgMwU2Jg+WQgh3HRHUerNjY\n", "upEfdKX7fL/9Y1fJtbiS9ny1v3v2/u77pdmRdu+e/Z09d3f13e/vnPN1RAgAAKDfhmp3AAAAtBNB\n", "BgAAaARBBgAAaARBBgAAaARBBgAAaARBBgAAaARBBgAAaARBBgAAaARBBgAAaMRI7Q70w9TUVFx8\n", "8cW1uwGkZTbetQf/WMBGdt99901HxK6mjzO846KIpdm+P27MHrozIvb2/YELtCLIuPjii7V///7a\n", 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"code", "source": [ "proj1 = histogram.projection(\"x\", name=\"Projection to X\")\n", "proj1.plot(errors=True)\n", "proj1" ], "outputs": [ { "output_type": "execute_result", "execution_count": 18, "data": { "text/plain": [ "Histogram1D(bins=(4,), total=1000, dtype=int64)" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAFZdJREFUeJzt3XuU5GV95/H3J4x4AcIwMCDMjA6JY6LrUUNGlijREbKJ\n", "4GXILmQ1WZko2TkmyHqJWdHjbnYTTSDRlWPORg8rruNd1htjJG5YEE1WIQ6KXAIJIwsyDjKjXKJh\n", "vaDf/aOeXouhe7p6prvr6e7365w69aunnvrVp4uhP/386tfVqSokSerNT4w7gCRJk7GgJEldsqAk\n", "SV2yoCRJXbKgJEldsqAkSV2yoKQ9JHl9knculP1Ki1X8PSgtBkluA44Cfgj8E3ApcE5VfWdMeTYA\n", "76uq1fPwXL8J/FZVnbiPj38L8KSq+pWhsQuAx1XV82YnpTRzrqC0mDy/qg4GjgOeBrxhzwkZ8N/9\n", "g/0H4KeTvAQgyS8Am4CXjTWVljz/R9WiU1VfB/4SeBJAkiuTvCnJ/wbuB34qyTFJtia5O8n2JP92\n", 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dtype=int64)" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAFyVJREFUeJzt3X+0XWWd3/H3ZwDBChWQgJCkE5zJtKJLgyvDpHVW5w7Y\n", "kR9qsEumaKvo0Il2YauragV1VW0HB1dVWmeNzsoIY/wtVRlRsSMijMtOhQkakRgoEaOJieTKL2Ho\n", "oMC3f5x95RhPcn/f+5xz36+1zjpnP/vZe38fuMkne+/n7pOqQpKk1vzKYhcgSdIgBpQkqUkGlCSp\n", "SQaUJKlJBpQkqUkGlCSpSQaUtB9J3pTkA8OyX2nUGFAaKUl2JPl/SR5IcmeSv0hy+Ez2VVXvqKp/\n", "O8t6xpLsmuv97udYL0/ytRlu+y+6/17H9LUdmmRbklfOXZXS1BlQGkXPr6rDgWcBvwm8Zd8O6fHn\n", "v1NV1wCfB/5HX/NbgD3AxkUpSkuef0A1sqrqh8AXgacDJLk+ycVJ/jfwIPCUJCckuSrJ3Um2J/nD\n", "ie2TvC3JR/qW1yX5myT3JvlWkrG+dUd3Z2u7k9yT5C+TPKE7/gndGd0D3fH23e8Lkmzt9nt9kqf2\n", "rduR5PVJbk5yX5JPJjls37F22/wZ8E+749zbtT8xyYeSjCf5fpK3HCCY/yPwO0nOSvJ04NXAH5aP\n", "m9EiMaA0spKsBM4EvtnX/FJgA3AE8H3g48Au4ATgRcA7kpw2YF/LgS8AfwQcDbwe+HSSZV2XDwP/\n", 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19, "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## Adaptive 2D histograms" ], "metadata": {} }, { "cell_type": "code", "source": [ "# Create and add two histograms with adaptive binning\n", "height1 = np.random.normal(180, 5, 1000)\n", "weight1 = np.random.normal(80, 2, 1000)\n", "ad1 = h2(height1, weight1, \"fixed_width\", 1, adaptive=True)\n", "ad1.plot(show_zero=False)\n", "\n", "height2 = np.random.normal(160, 5, 1000)\n", "weight2 = np.random.normal(70, 2, 1000)\n", "ad2 = h2(height2, weight2, \"fixed_width\", 1, adaptive=True)\n", "ad2.plot(show_zero=False)\n", "\n(ad1 + ad2).plot(show_zero=False);" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEYCAYAAABPzsEfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X101Nd95/H3F0k8yBiMg23AGBvb4BjHQG0lJsZO8FOK\n", "u2fjptu0Tk5qdpOWttvWjne7abLbxm3SnpMmaXOy3T3pko3dZJs4j47tNonjJEACMghLAgwyBmMT\n", 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Warning: be aware that the memory consumption can be significant." ], "metadata": {} }, { "cell_type": "code", "source": [ "# Create a 4D histogram\n", "data = [np.random.rand(1000)[:, np.newaxis] for i in range(4)]\n", "data = np.concatenate(data, axis=1)\n", "h4 = histogramdd(data, [3, 2, 2, 3], axis_names=\"abcd\")\n", "h4" ], "outputs": [ { "output_type": "execute_result", "execution_count": 21, "data": { "text/plain": [ "HistogramND(bins=(3, 2, 2, 3), total=1000, dtype=int64)" ] }, "metadata": {} } ], "execution_count": 21, "metadata": { "collapsed": false } }, { "cell_type": "code", "source": [ "h4.frequencies" ], "outputs": [ { "output_type": "execute_result", "execution_count": 22, "data": { "text/plain": [ "array([[[[31, 28, 33],\n", " [21, 22, 22]],\n", "\n", " [[25, 29, 28],\n", " [29, 35, 28]]],\n", "\n\n", " [[[20, 25, 20],\n", " [28, 32, 31]],\n", "\n", " [[30, 28, 24],\n", " [29, 21, 27]]],\n", "\n\n", " [[[27, 26, 33],\n", " [21, 35, 30]],\n", "\n", " [[38, 30, 32],\n", " [25, 30, 27]]]])" ] }, "metadata": {} } ], "execution_count": 22, "metadata": { "collapsed": false } }, { "cell_type": "code", "source": [ "h4.projection(\"a\", \"d\", name=\"4D -> 2D\").plot(show_values=True, format_value=int, cmap_min=\"min\");" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAZgAAAEYCAYAAABhi+CNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X28VWWd9/HPFwQJTQROEA8+d0SNlxljqJFEIgRkiAbe\n", "YCaOMsxoVMaYwnhjPpbmPWPN+BSJgaakUgKlpQyjYQoKiiLCbSI5eZSBjgLSDajQ7/5jr0Obwzln\n", "b3Svs9fZ5/t+vdbrrHXta1/rt0DPj+ta17qWIgIzM7NSa1PuAMzMrDI5wZiZWSqcYMzMLBVOMGZm\n", "lgonGDMzS4UTjJmZpcIJxszMUuEEY5kjqVrSdkk/yys7T9JOSX9Jtj9K+qmkI5shnm6SZkt6U9Jm\n", "SU9KOiELsZllmROMZdEtwNIGyhdHxP5AJ+BUYBvwrKS+xTYsqfsHiGf/JJ6/A7oAs4CHJO1fytjM\n", "Ko0TjGWKpLHAJmBhY3UiYmdEvBoRFwG/A67ci1PMlPSMpAslHVjMFyJibUT8W0SsS849HWgP9Clx\n", 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"AAAASUVORK5CYII=\n" ] }, "metadata": {} } ], "execution_count": 24, "metadata": { "collapsed": false, "scrolled": true } }, { "cell_type": "markdown", "source": [ "## Support for pandas DataFrames (without pandas dependency ;-))" ], "metadata": {} }, { "cell_type": "code", "source": [ "# Load notorious example data set\n", "iris = sns.load_dataset('iris')" ], "outputs": [], "execution_count": 25, "metadata": { "collapsed": false } }, { "cell_type": "code", "source": [ "iris = sns.load_dataset('iris')\n", "iris_hist = physt.h2(iris[\"sepal_length\"], iris[\"sepal_width\"], \"human\", (12, 7), name=\"Iris\")\n", "iris_hist.plot(show_zero=False, cmap=cm.gray_r, show_values=True, format_value=int);" ], "outputs": [ { "output_type": "display_data", "data": { "text/plain": [ "" ], "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEYCAYAAABGJWFlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzt3X141OWZ6PHvnRCTQFBS0opNjIlCydUFSg3VtFoPUlto\n", 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