From 733fb5de39496f76711fbdf8a4c23b990ed6b515 Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Wed, 9 Sep 2026 15:13:12 +0200 Subject: [PATCH 1/9] =?UTF-8?q?docs(guides):=20expliquer=20densit=C3=A9=20?= =?UTF-8?q?et=20largeur=20des=20classes?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/_static/css/custom.css | 47 +++++++ docs/conf.py | 4 +- docs/counts_vs_density.ipynb | 254 +++++++++++++++++++++++++++++++++++ docs/demo.ipynb | 11 +- docs/index.rst | 18 +++ 5 files changed, 326 insertions(+), 8 deletions(-) create mode 100644 docs/counts_vs_density.ipynb diff --git a/docs/_static/css/custom.css b/docs/_static/css/custom.css index d03f79a..9f0afde 100644 --- a/docs/_static/css/custom.css +++ b/docs/_static/css/custom.css @@ -40,6 +40,53 @@ img.sidebar-logo { box-shadow: 0 4px 16px rgba(0, 0, 0, 0.12) !important; } +@media (prefers-reduced-motion: reduce) { + .sd-card { + transition: none; + } +} + +.histogram-guide-card { + border-color: #4170d8 !important; + background: #4170d8 !important; + color: #ffffff !important; +} + +.histogram-guide-card .sd-card-title, +.histogram-guide-card .sd-card-text { + color: #ffffff; +} + +[data-theme="dark"] .histogram-guide-card { + border-color: #6699ff !important; + background: #6699ff !important; + color: #000000 !important; +} + +[data-theme="dark"] .histogram-guide-card .sd-card-title, +[data-theme="dark"] .histogram-guide-card .sd-card-text { + color: #000000; +} + +.histogram-guide-card:hover { + border-color: #f16e00 !important; +} + +[data-theme="dark"] .histogram-guide-card:hover { + border-color: #ff7900 !important; +} + +.histogram-guide-card:focus-within { + outline: 3px solid #000000; + outline-offset: 2px; + box-shadow: 0 0 0 2px #ffffff !important; +} + +[data-theme="dark"] .histogram-guide-card:focus-within { + outline-color: #ffffff; + box-shadow: 0 0 0 2px #000000 !important; +} + /* Gallery images */ .sd-card img { border-radius: 4px; diff --git a/docs/conf.py b/docs/conf.py index 81de350..38c45d1 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -80,7 +80,7 @@ "color-highlighted-background": "#FFD200", "color-admonition-title--note": "#FF7900", "color-admonition-title-background--note": "#FFF0E2", - "font-stack": "Helvetica Neue, Helvetica, sans-serif", + "font-stack": "Helvetica Neue, Helvetica, Arial, sans-serif", }, "dark_css_variables": { "color-brand-primary": "#FF7900", @@ -90,7 +90,7 @@ "color-highlighted-background": "#FFD200", "color-admonition-title--note": "#FF7900", "color-admonition-title-background--note": "#CC6100", - "font-stack": "Helvetica Neue, Helvetica, sans-serif", + "font-stack": "Helvetica Neue, Helvetica, Arial, sans-serif", }, # Sets the Github Icon (the SVG is embedded, copied from furo's repo) "footer_icons": [ diff --git a/docs/counts_vs_density.ipynb b/docs/counts_vs_density.ipynb new file mode 100644 index 0000000..b7dca37 --- /dev/null +++ b/docs/counts_vs_density.ipynb @@ -0,0 +1,254 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "178ae8be", + "metadata": {}, + "source": [ + "# Counts, density, and variable-width bins\n", + "\n", + "Khisto chooses adaptive bins, so their widths can differ. That makes one\n", + "distinction essential: **counts describe how many observations fall in a bin;\n", + "density describes how concentrated those observations are over the bin's\n", + "width**.\n", + "\n", + "By the end of this guide, you will know what bar height and bar area mean in\n", + "each view, and which view to choose for your question." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8e971340", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Observations: 10,000\n", + "Adaptive bins: 23\n", + "Sum of density areas: 1.000000\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from khisto import histogram\n", + "\n", + "SEED = 42\n", + "rng = np.random.default_rng(SEED)\n", + "data = np.concatenate([\n", + " rng.normal(0, 0.35, 6000),\n", + " rng.normal(2.5, 1.0, 3000),\n", + " rng.exponential(2.0, 1000) + 4,\n", + "])\n", + "\n", + "counts, bin_edges = histogram(data, density=False)\n", + "density, density_edges = histogram(data, density=True)\n", + "\n", + "np.testing.assert_array_equal(bin_edges, density_edges)\n", + "widths = np.diff(bin_edges)\n", + "probabilities = counts / counts.sum()\n", + "\n", + "assert counts.sum() == data.size\n", + "assert np.isclose(np.sum(density * widths), 1.0)\n", + "\n", + "print(f\"Observations: {int(counts.sum()):,}\")\n", + "print(f\"Adaptive bins: {len(counts)}\")\n", + "print(f\"Sum of density areas: {np.sum(density * widths):.6f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "f94cd2b9", + "metadata": {}, + "source": [ + "## One histogram, two questions\n", + "\n", + "For bin $i$, let:\n", + "\n", + "- $c_i$ be its count,\n", + "- $w_i$ be its width,\n", + "- $N$ be the total number of observations.\n", + "\n", + "The relative frequency is $p_i = c_i / N$. The density is\n", + "\n", + "$$d_i = \\frac{c_i}{N w_i} = \\frac{p_i}{w_i}.$$\n", + "\n", + "A count bar's **height** answers \"how many observations?\" A density bar's\n", + "**area** answers \"what fraction of observations?\" because\n", + "\n", + "$$d_i w_i = p_i,$$\n", + "\n", + "and all density-bar areas sum to 1. Dividing by width is what makes bins of\n", + "different widths comparable." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1cdc39a4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=(12, 4.5))\n", + "\n", + "axes[0].bar(\n", + " bin_edges[:-1], counts, width=widths, align=\"edge\",\n", + " color=\"#52789c\", edgecolor=\"white\",\n", + ")\n", + "axes[0].set_title(\"Counts: height = observations\")\n", + "axes[0].set_xlabel(\"Value\")\n", + "axes[0].set_ylabel(\"Count\")\n", + "\n", + "axes[1].bar(\n", + " bin_edges[:-1], density, width=widths, align=\"edge\",\n", + " color=\"#f16e00\", edgecolor=\"white\",\n", + ")\n", + "axes[1].set_title(\"Density: area = probability\")\n", + "axes[1].set_xlabel(\"Value\")\n", + "axes[1].set_ylabel(\"Density\")\n", + "\n", + "fig.suptitle(\"Same adaptive bins, different questions\")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "2bce5d17", + "metadata": {}, + "source": [ + "With unequal widths, raw count heights are not directly comparable: a wide bin\n", + "has more room to collect observations. Density corrects for that extra width.\n", + "\n", + "Use **counts** when totals matter, such as workload or sample size. Use\n", + "**density** when reading distribution shape or comparing samples of different\n", + "sizes.\n", + "\n", + "## The key example: equal counts, unequal widths\n", + "\n", + "Imagine two bins that each contain 50 of 100 observations. Their widths are 1\n", + "and 4. Both count heights are 50, but their densities are 0.5 and 0.125. Values\n", + "are therefore **four times more concentrated** in the narrow bin.\n", + "\n", + "In the density view, the bars have different heights but equal areas:\n", + "\n", + "- narrow bin: $0.5 \\times 1 = 0.5$,\n", + "- wide bin: $0.125 \\times 4 = 0.5$.\n", + "\n", + "Each area correctly shows that the bin contains half of the observations." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c5fe66ce", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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DQy0dnkmXLl1Us2ZNS4cBC+BnDwDW48UXX5SNjY3p5eTkJE9PT7Vv314zZsxQZGSkpUO8r+7duz/SFwUAkFkkQoBMGjdunFq3bq2SJUtq/fr1ioqK0rFjxzRq1CjNmTNHo0ePtnSIyKWWLVumf/75x9JhAAAeUzdu3JBhGIqIiNDu3bvVt29fzZgxQ9WqVdP+/fstHZ4kacmSJTp79qylwwBg5UiEAJnwww8/6IsvvtC0adP09ddfq1atWrK3t1exYsU0ePBgHT16VE899ZSlwwQAAFasQIECKl++vIYPHy5/f385OTmpa9euuf7KEADIKSRCgAwyDEOTJ09WxYoV9corr6TZxsXFRa+//rpZ2ZIlS9SwYUM5OTmpUKFCatOmjXbt2mXWpmrVqurevXuq/saMGSNnZ2ezspR1Iq5du6Zu3brJ2dlZxYsX12uvvabExERTu5o1a2rt2rU6ceKE6VLZ/Pnzm+r9/f3VpUsXlShRQs7OznryySf13XffmfXx559/ysbGRp9++mmGxmjXrl3q0KGD3Nzc5ODgoCeffFK//fZbqnazZs1S5cqV5eDgoPr162vbtm169dVX5eDg8NDjMmbMGNN52traqkiRIurUqZMOHjyYodjT86Bxzsy5p7dGyNdff61KlSo9cDwyGlNW/OwBAI+HwoULa+LEibpx44bmzZtnVrdnzx517NhRhQsXloODg+rWratffvnFrE2HDh1Ut25dhYSEqEePHipUqJCKFSumV155RXfv3jVrGxAQoK5du5p9vnz77bdmny//XSOkbt268vPz06lTp8xu75Gk1157Tfb29rp+/Xqq83rrrbeUP39+Xbt2TR999JFsbGy0efPmDI3J4sWL1bhxYxUsWFDOzs5q06aN/vrrL7M2CQkJGjdunDw8PFSwYEG1a9dOZ8+e1dNPP62nn37a1C4mJkY2Njb66KOPUh2nSZMmatmyZaqyf382e3h46LnnntOVK1cyFHtax8hIf25ubnrxxRe1b98+NW3aVI6Ojvrggw8kSZGRkfrf//6nihUrqkCBAvLw8NBLL72k8PBw0/5nz541+/k4ODioRo0amjp1qpKTk83G7Z133lHlypXl5OSk8uXLa8iQIbpw4cJDnR+QXUiEABl04sQJXblyRR06dDB9QD/I119/rQEDBqh9+/Y6f/68jh49qpIlS6p169bauHHjQ8eSkJCgl19+WW+99ZauXbumL7/8Ul9//bWmT59uanP8+HF17txZNWrUkGEYMgzDNBGJiIiQj4+PXFxcdPDgQd28eVMLFizQsWPHHvrS2RUrVqhVq1aqUKGCAgICFBISohEjRui5557Tjz/+aGr3+eefa+zYsfL19dWVK1e0ZMkSTZ8+XadOnXro8ZCkmTNnms7zzp072rdvnwoVKqT27dvr6tWrD9VnRsZZyvi5p+XTTz/Va6+9phdffFHBwcH67bffNGvWrHTHIzf+7AEAuVu7du0kSTt27DCV+fn5qWXLlipTpoz8/f0VEhKil156SUOGDNF3331ntv+dO3f08ssv64033tDVq1c1Y8YMzZo1S19++aWpTVRUlHx8fOTk5KQDBw7o5s2b+umnnxQYGKg9e/akG9vff/+tbt26qUqVKqbPLMMwJEmjRo3S3bt3U32WJiQkaN68eerYsaM8PDwyNRbvvfeehg4dqr59++rcuXM6e/asateurRYtWph9Dg4ePFhz5szRjBkzdO3aNX344YcaM2aMYmNjM3W8//rrr79M5xgTE6NVq1bp1KlT6tq1a6rEUlb3d/78eU2ZMkU//PCDzpw5oyeffFLR0dFq1qyZ/Pz89P333+vWrVtat26d/vrrL7Vt21Z37tyRJFWqVMns53Pt2jW99dZbmjx5sj777DPTMcaPH685c+bo+++/V1hYmPbs2aO2bdvq66+/fqRxA7KcASBD1qxZY0gyPv300wy1j4mJMQoVKmR06tTJrDwxMdHw8vIyatSoYSqrUqWK0a1bt1R9jB492ihYsKBZWZs2bQxJhr+/v1l5x44djcqVK5uVde7c2ew4KbZv325IMnbs2JGhc3mQhIQEo0SJEkabNm1S1b344ouGu7u7cffuXSMmJsZwdnY2+vXrZ9YmIiLCcHV1Nezt7c3KMzMuaYmPjzfs7OyM6dOnm8p69eplVKlS5YH7ZnScM3ruaR07OjracHZ2NgYMGGC2X3R0tFG4cOFU45Ebf/YAAMsbOXKkIcm4ceNGum3y589vNGzY0DAMw7hz545RqlQpo0WLFqnajRkzxihSpIiRkJBgGIZhtG/f3pBkHDhwwKxd165djQoVKpi2d+/ebUgytmzZct9Y+/XrZ3h5eZmVdevWLd3PZh8fH6NcuXJGUlKSqWzRokWGJGPlypX3PdZ/nT592rC1tTXeeuutVHUNGzY0fZb7+/sbkozPP//crM2hQ4cMSUbTpk1NZdHR0YYk48MPP0zVZ+PGjdMc4//666+/DEnG7t27TWXlypUzBg4cmNFTe2B/rq6uRsGCBY2wsDCztpMmTTJsbGyMI0eOmJUHBgYaNjY2xvz58+97rDFjxhjly5c3bdetW9fo0aPHQ8UN5CSuCAGyycGDBxUdHa2ePXualefLl0/du3fXiRMnHvoJMx4eHnryySfNymrWrKkLFy6YXZ6YnieeeEKOjo567bXXtHLlyke+Z/jgwYMKDQ1Vnz59UtW1bdtWN2/e1IkTJ3TgwAHFxMTomWeeMWvj6uqqVq1aPVIM169f1+jRo1WhQgUVKFBANjY2cnR01N27dx96UbaMjHNGzz0tBw8eVExMjLp27WpW7uzsnO545LafPQAg70i5ovXw4cO6evVqup9dt27d0rFjx0xlxYoVU8OGDc3a1axZU5cuXTJdcZhyK8Qbb7yhFStWZNnny+jRo3Xx4kWtXbvWVPbtt9+qRIkS6tKlS6b6WrdunZKTk9M875Rblw3D0JYtWyQp1Xylfv368vT0fIiz+P9Onjypvn37ysPDQ/nz55eNjY2aNGkiSQ81X8lMf08//bSKFCliVrZ69WpVqVJFtWvXNiuvWrWqSpcubXYV0aJFi/TUU0/JxcXFdIvMzJkzdfHiRdPVJ3Xq1NG6dev08ccfs0A8cjUSIUAGlStXTpJ06dKlDLUPCwuTJJUsWTJVXUrZzZs379uH8X+Xhv5XWpeBuri46O7du4qLi3tgbB4eHlq3bp2cnZ3Vt29fFSlSRA0bNtS3336rpKSkB+7/XyEhIZLuXcKaP39+5cuXT/ny5ZOtra169+4t6d54pIxJiRIlUvWRVll6/jsuycnJ8vHx0Z9//ql58+bpxo0bSk5OlmEYcnBweKhLTaWMjXNGzz0tKeXFixdPVZdWWUZjetA5ZeXPHgCQ+4WEhCgxMVGlSpUybUvS2LFjU312pazN9e/PrvQ+e5KSkhQTEyPp3ufWn3/+KTc3N/Xr109FihRRgwYN9M033zzS50uXLl1UtmxZzZ49W5J05MgR7du3T4MHDzZb/yojUs67cePGpvO2tbWVra2tPv30U925c0fR0dHZNl8JCQlR06ZNdfPmTa1bt05RUVEyDEPHjx+XpEzPVzLbX+nSpdPs49SpU8qfP7/ZmNjY2OjKlSumsfjxxx81ePBgderUScePH9fdu3dlGIbGjx8vwzBMP+MZM2ZoxIgR+vrrr1WtWjWVLFlSw4cPZ40Q5DokQoAMqlGjhjw9PbVhw4Z0ExT/lpJxT+uqj5Qyd3d3SfeuiIiOjk7VLjg4OM2+M7pGyf20bNlSO3bsUHh4uDZs2KBq1app9OjR+vzzzzPdV8p5LFy4UImJiUpKSlJSUpIpGWEYhlq3bq2iRYtKuv+Y/FtGx+Xvv//W0aNHNXHiRLVq1Uqurq6ysbFRSEiIbt++nenzSZGRcc7ouaclZTzSWgQurbKMxvQgWfmzBwDkfinrkqUs3Jny2TVv3rx0P7tS1hWRMv7Z06xZM23btk0RERHauHGjatWqpbFjx2rKlCkPHXu+fPk0cuRIbdiwQUFBQfr2228lScOGDct0XynnfeLECdN5Jycnm523i4tLpuYrTk5OsrOzy9B85Y8//lBERIRmzpypevXqycnJSdK9tTseRmb7s7OzS1Xm7u6u+vXrKzEx0WxMUsbjjz/+kHRvnlOvXj29++67Klu2rCkJ9d9jubq66ptvvlFISIhOnjypt99+W2vWrFHz5s1N640AuQGJECCDbGxs9P777+vcuXOaOXNmmm2ioqI0bdo0SVKjRo1UqFAhrVy50qxNUlKS/Pz8VKNGDdO3Cl5eXgoMDDT7xiQqKirV02Uyq2DBgkpISLhvG2dnZ7Vt21YLFy6Up6endu7cmenjNG7cWMWKFdPvv/9+33YNGzaUs7OzVq9ebVYeFRWl7du3p2qf2XGxt7c32164cGEGz+DhZfTc05IyHv++3FeSYmNj0xyPzMipnz0AIHcLDw/X5MmTVaJECVPyoGHDhipRosRDfXZlRMGCBdWmTRvNnz9f5cuXf+Dny4M+s3x9fZU/f3599tln+uWXX9S0adM0n8L2IJ07d5atrW2aT7T7t5QvMP47Xzl8+HCqp7HY2tqqfPnypqswUgQEBKS7WHtWz1cepb+uXbvqyJEjOn36dKaPc+vWrVRzmBQ2NjaqVq2axo4dq3Hjxuny5ctcFYJchUQIkAkjRozQG2+8oVdffVWvvvqqTpw4oYSEBN28eVOLFi1S7dq1tXfvXkn3PtQnTZqkNWvWaOLEiQoNDdXFixc1ZMgQBQUF6YsvvjDr99q1a5o4caIiIiJ06tQpDRs2zHSP58NKuX/377//Nls/YtmyZfL19dWePXsUERGh6Oho/fzzz7p27ZrZ2hQZfXyug4ODvvvuO61bt04vvPCC/vnnH92+fVtBQUH6+eefTd8qOTs7691339Xvv/+uzz//XGFhYTp79qyef/75NM81o+NSs2ZNVaxYUVOmTFFgYKAiIiI0f/587dmzR66uro8yhA+U0XNPi7Ozs9555x0tWbJE06ZN061bt3Tu3DkNHTpUjRo1eqS4HvVnDwDIu+7cuaOLFy9q7ty5ql+/vuLj47V69WoVKlRIklSgQAHNmTNHGzdu1PDhwxUYGKj4+HidP39eixcvVtu2bTN9zJUrV2rYsGHavXu3wsPDFRMTo19//VVXrlx54OdLzZo1deXKFR0+fDjN9a6KFy+u3r17a86cOYqJidHw4cPN6jP6+NyqVavqnXfe0UcffaQpU6bo4sWLio+P18mTJ/XVV19p5MiRku6tBdK7d29NnjxZS5cuVVRUlA4cOKB33nlHdevWTdXviBEjtGHDBi1evFjR0dHau3evJk+enGrdDR8fHzk6OurNN99USEiIQkJC9N5779035vvJiv7GjRun6tWrq0uXLlq9erVu3bql8PBw7d27Vy+88IKWLVsm6d56Kfv379e8efMUGxuro0ePqkePHmrTpo1Zf+3atdOiRYt0/vx5JSQkKDAwUMuWLVP58uVVoUKFhz5XIMvl7NqswONh69atRu/evY1SpUoZdnZ2RvHixY3GjRsbn3zyiRESEmLW9ueffzbq169vODg4GAULFjRatWplbNu2LVWfM2fONMqVK2fY29sbjRs3Nvbv35/uU2Pq16+fav8PP/zQkGRER0ebyiIjI40ePXoYrq6uhiQjX758hmEYxu3bt4158+YZzZo1M9zc3AxXV1ejQYMGxnfffWckJyeb9l+/fr0hyZgyZUqGxmX//v1Gjx49jGLFihkFChQwKlWqZAwZMsQICAgwa/f1118bFStWNAoUKGDUqVPH2LRpk/HKK6+kekpKZsbl5MmTRrt27QwXFxejaNGixrBhw4zIyEjD1dXVGDlypKldZp4ak9Fxzui5p3fsGTNmGBUrVjTs7e2NevXqGVu3bjVefPFFw8XF5aFjetSfPQAg70h5akzKy8HBwShVqpTRrl07Y/r06UZERESa+x08eNDo2bOn6bPLy8vLGDx4sHH48GFTm/bt2xt16tRJte+UKVMMSUZ4eLhhGPeeorZgwQKjefPmRuHChQ0XFxfjySefNL799luzz5e0nhoTFRVl9OrVy/SZldafKHv27DEkGYUKFTJiYmLM6lI+Bzdt2pSh8Vq+fLnRsmVLw9XV1XBycjJq1KhhjBs3zrh06ZKpze3bt43XX3/dKFGihOHo6Gi0bt3aOHXqlNG0aVOzp8YYxr2n8Lz22muGu7u74eTkZHTu3Nm4cuVKmk+N2bRpk9GgQQPD0dHR8PT0ND744APj1KlThiTjhx9+MLXL6FNjMtrff+dD/xYTE2O89957RrVq1Qx7e3vD3d3daNasmTF37lzj9u3bhmHce+rh+++/b5QtW9ZwdHQ0GjZsaGzevNmYOHGiIcmIj483DMMwAgICjKFDh5rmNWXLljVGjBhhXLhw4YHnAuQkG8PIwGIHAJDNXn31VX333XePtKbH46Rr1646ffq0Tp06ZelQAACwuOPHj6tWrVry9fXVDz/8YLE4nn76aUnS7t27LRYDgEfHrTEAkMvcunVL27dvV4sWLSwdCgAAuULKuh4jRoywcCQAHgckQgDAgvz9/TVu3DidPHlScXFx8vf3Nz26cNy4cZYNDgCAXOD06dP6/vvv1bZt20deQwsAJClzD9/OBsnJydq/f7/Onz+vunXrqnr16qnaXLlyRbt27ZKDg4Nat26d7YsfAkBOqVOnjnbs2KFnn31Wp0+flr29vZo1a6bdu3ercuXKlg4PeKwcPnxYJ0+elIeHh1q0aGF6/OP9xMXFaefOnYqOjlazZs1UsmTJHIgUQAp3d3fFxMToqaee0rx58ywdDoDHhEXXCLl69aq6deum69evq1mzZjp9+rTatm2rTz75xNRm4cKFeumll9SsWTOFh4crKChI69evV4MGDSwVNgAAyGNGjBihZcuWqVWrVgoICJC7u7s2bdokNze3dPfZtm2bBgwYoLJly6pKlSry9/fX1KlT1bVr15wLHAAAZDmLJUIMw5C3t7ccHR21fv16OTg4SJK2bNliegxTSEiIKlasqM8++0xjxoyRJA0YMEDHjh1L9axuAACAtKxYsUL9+vXT4cOHVatWLUVGRqp+/frq3LmzZsyYkeY+wcHBql69usaOHasPP/xQ0r2rQ44cOSJvb++cDB8AAGQxiyVCtm/frlatWunAgQNq2LBhmm3mzJmj1157TWFhYXJ0dJQk7d27V02bNtWRI0dSPZsbAADgv/r06aOIiAht2rTJVDZ58mTNnDlT169fT3Ofd999V3PmzNHVq1dlZ2eXU6ECAIAcYLE1Qnbv3i1XV1fVqlVLa9euVVxcnOrWrWt2T/zx48dVoUIFUxJEkmrUqGGqSysRkpCQoISEBNN2cnKybt26paJFi8rGxiYbzwgAABiGoejoaJUqVUq2trljTfbjx4+rXbt2ZmU1atTQjRs3dP36dRUvXjzVPrt371aLFi0UERGhLVu2yNnZWY0bN1axYsXSPQ5zEAAALCczcxCLJULCwsLk7OysZs2aqVixYnJwcNDzzz+vUaNG6YsvvpAkRUVFqXDhwmb7ubq6Kl++fIqKikqz3ylTpmjSpEnZHj8AAEjf5cuX5enpaekwJKU9nyhSpIipLq1ESFhYmO7cuaMmTZqofv36Cg0NVUBAgObPn69evXqleRzmIAAAWF5G5iAWS4Q4ODgoODhYH374oYYOHSpJ2rp1q9q0aaMePXqoadOmcnR0VHR0tNl+8fHxSkpKMrtK5N8mTJig119/3bQdGRmpsmXL6vLly3Jxccm+EwIAAIqKilKZMmVUqFAhS4diktZ8ImU7vfmEg4ODDh8+rGPHjpmuVn377bc1bNgwde3aVQUKFEi1D3MQAAAsJzNzEIslQlImFZ07dzaVtW7dWo6Ojvr777/VtGlTVapUSb///ruSk5NNl7YEBQVJkipVqpRmv/b29rK3t09V7uLiwiQEAIAckptuBalUqZIuXLhgVnb+/Hk5OTnJw8MjzX0qV66shIQEs1t2O3furClTpuj8+fOqUqVKqn2YgwAAYHkZmYNY7Obdjh07qkCBAjp69Kip7MyZM4qPj1eFChUk3ZtwRERE6M8//zS1+eWXX1S8eHE1atQox2MGAAB5T9euXbVx40aFhYVJurd2x5IlS9S5c2fTFy0XLlzQjz/+qLi4OElS9+7ddfHiRUVGRpr6OXr0qPLnz68yZcrk/EkAAIAsY7ErQjw8PPTRRx9p4MCBGj16tBwcHPTdd9+pQ4cO6tChgySpWrVqeuWVV/Tcc89p7NixunXrlr799lstWrSIFdwBAECG+Pr6asGCBWrdurUGDRqknTt36vTp01q4cKGpzaFDhzRixAh16NBBTk5O6t27t+bPn69WrVrpueeeU2hoqGbNmqWPP/5YTk5OFjwbAADwqCz2+NwU27dv1+rVq2Vra6uGDRuqd+/eqVZ49fPz09atW2Vvb68+ffqk+7jdtERFRcnV1VWRkZFclgoAQDbLrZ+78fHxmj9/vk6cOCEPDw8NHTpUpUuXNtX7+/tr9uzZ+vzzz00LqyYlJWnx4sU6ePCgChcurI4dO8rb2zvDx8ytYwEAwOMoM5+7Fk+EZDcmIQAA5Bw+d/8/xgIAgJyTmc9di60RAgAAAAAAkNNIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWI7+lA0DGXblyRYcOHUpV3rlzZ9nZ2ZmVBQUF6dSpUypTpoxq1qyZUyECyGJbt25VVFSUWVmFChVUp04ds7I7d+5o//79un37tho1aiRXV9ecDBNAHmUYhg4fPqwbN26odu3aKlWq1H3b+/v76/Lly2ZlRYoUUfPmzTPdb2aPDQBAViERkods375dvr6+6tChg1m5j4+PWSJk7Nixmjt3rho0aKBjx46padOmWrZsmezt7XM6ZACPaOzYsbKxsZGXl5eprEOHDmaJkMDAQHXs2FF2dnZydXXV6dOntWjRInXr1s0SIQPII8LDw9WxY0ddvHhRXl5eOnz4sD744AO9+eab6e7z1VdfaefOnXryySdNZVWqVDFLhGSk34c5NgAAWYVESB7j5uamVatWpVu/dOlSzZkzR3/99Zfq1aun4OBgPfnkk/riiy/0zjvv5FygALLM8OHD9eqrr6Zb/9xzz6lu3bpauXKlbGxs9OGHH2rw4ME6f/68ihQpknOBAshT/ve//yk6OlqnT59WoUKFtHr1aj3zzDNq3bq1GjRokO5+rVu31oIFCx6p34c9NgAAWYE1QvKYpKQk7dixQzt27NCNGzdS1S9atEht27ZVvXr1JEmlS5fWgAEDtHDhwpwOFUAWuXLlitavX69jx44pMTHRrO7kyZPy9/fXG2+8IRsbG0nSK6+8otu3b8vPz88S4QLIA+7evavffvtNL774ogoVKiRJ6tq1q6pWrapFixbdd9/w8HBt2LBBBw8eVFxcXKb7fZRjAwCQFUiE5DFRUVGaMGGCxo0bJ09PT40fP96s/siRI6nWDqhbt67OnDmj+Pj4nAwVQBb59ddf9eWXX6p9+/aqWbOm/P39TXVHjhyRJLP/9y4uLqpQoYKOHj2a47ECyBvOnj2r2NjYVHOGOnXqPPB3x86dO/XZZ59pwIABKl++vFauXJmpfh/l2AAAZAUSIXlI9erVdfr0ae3du1cHDhzQn3/+qS+//NLs8tTIyEgVLlzYbL+iRYvKMIxUCy4CyP0+/vhjXb58WZs3b9b58+dVs2ZN9e7d25TYjIyMVL58+eTi4mK2X9GiRRUREWGBiAHkBZGRkZKU5pzhfr87nnvuOV29elVbtmzRmTNnNHLkSA0cOFBBQUEZ7vdhjw0AQFYhEZKHPPnkkypXrpxpu1WrVurYsaPZNzEFChRIdZlqTEyMJLFYKpAHdevWTba2935V29vba/Lkybpw4YL+/vtvSff+zyclJSkhIcFsv5iYGP7PA0hXgQIFJCnNOcP9fne0b99ejo6OkiQbGxt98MEHkqQNGzZkuN+HPTYAAFmFREge5+bmpuvXr5u2K1asmOqxdpcvX5abm5vc3NxyODoAWS3l/3HK//uKFStKktn/++TkZAUHB6tChQo5Hh+AvCHl90Nac4bM/O7Ily+fnJ2dTb+TMtJvVh0bAICHRSIkD7l586bZdkxMjLZu3Wr2CLuOHTtq3bp1un37tiTJMAwtX75cHTt2zNFYATy6yMhI3b1716zMz89Ptra2qlu3riSpSZMmcnNz0/Lly01ttm3bprCwsFSP2gaAFIULF1aTJk3MfneEhIRo9+7dZnOGQ4cOaefOnZLuLXKacltLin379unGjRumuUhG+s3osQEAyC42hmEYlg4iO0VFRcnV1VWRkZGp7qHPa3r06KFixYrJ29tbt2/f1uzZsxUdHa3du3erdOnSku6t5F6/fn1VqFBBgwYN0oYNG/Tnn3/qwIEDeuKJJyx8BgAyw9/fX76+vurXr5/Kli2rQ4cO6dtvv9X//vc/ffTRR6Z2c+bM0dixY/Xee++pcOHC+uSTT9SuXTvNnz/fgtHDWj1On7uPKrePxa5du9S2bVuNGDFC9erV08yZM2VnZ6e9e/cqf/78kqT+/fvrwoUL+uuvvxQVFaXGjRurd+/eqlq1qs6fP6+vvvpKTz/9tFatWmV6clVG+s1IGwAAMiMzn7skQvKQpKQk/fLLL9qxY4dsbGxUp04dDR8+3HSvboqbN2/q66+/1qlTp+Tp6alRo0bJy8vLQlEDeBTnz5/X/PnzdfbsWXl6eqpHjx7y9vZO1W7Dhg367bfflJCQoNatW2vo0KGmtUWAnPQ4fe4+qrwwFgEBAfrxxx8VFhamevXqacyYMSpYsKCp/ssvv9T169c1depUSdKtW7f0448/6ujRoypatKhat26tbt26ZbrfjLYBACCjSIT8S16YhAAA8Ljgc/f/YywAAMg5mfnc5etCAAAAAABgNSx2E+adO3f0/vvvpyrv06eP6tevb1a2d+9ebdmyRQ4ODurevbsqV66cU2ECAIDHQFJSkpYvX66TJ0/Kw8ND/fr1u+/T1E6ePKmFCxemKn/77be5ugMAgDzOYleE3LlzR1OnTlV0dLTp0a5ubm6mZ8un+Oijj9S+fXuFhobq77//Vq1atbR27VoLRQ0AAPKaxMREtW/fXhMmTFBcXJwWLVqkWrVqpXp867+dPn1aX331ldkcxc3NzbQgKAAAyLssviz3c889pyZNmqRZFxQUpA8++EC//vqr+vTpI0lyd3fXSy+9pAsXLrAQIAAAeKCFCxdq7969OnPmjEqXLq27d++qUaNGevfdd/XTTz+lu5+dnZ3Gjx+fg5ECAICcYPFMwm+//aZJkybp559/VlRUlFndH3/8oYIFC6pHjx6msqFDh+ry5cs6ePBgTocKAADyoBUrVqht27amR83b2dlp4MCBWrVqle63ZnxiYqI+//xzTZkyRWvWrFFycnJOhQwAALKRRRMhhQoVUnh4uG7fvq1p06apatWq+vvvv031p0+fVrly5cyeJ1+pUiVTXVoSEhIUFRVl9gIAANbr9OnTpvlDikqVKikqKkohISHp7ufh4aHg4GCFhoZqxIgRatq0qWJjY9NtzxwEAIC8wWKJEHt7ex0/flwLFizQlClTdOjQIdWuXVu+vr6mNrGxsakWJHN2dla+fPnSnYhMmTJFrq6upleZMmWy7Rz4Zuj+GJ8HY4wAWJo1/B5Kaz7h6upqqktLw4YNFRgYqOnTp2v69Ok6evSogoKC9OGHH6Z7nJycgxjJSdnW9+OA8QEA3I/F1gixs7NT2bJlTdu2trYaMmSInn32WcXExMjZ2VnOzs6KjIw02y86OlpJSUlydnZOs98JEybo9ddfN21HRUVl20TE1tZW03/brivXI7Kl/7zMs7ibXu3X0tJh5Hq8hwBYkrX8rk5rPhEREWGqS0vKbTQpihUrpq5du2rnzp3pHicn5yA2tvkUt3CgkkMDs6X/vMy2RDU5DV5s6TAAALmYxRdL/bekpCQZhqE7d+5IkqpVq6aFCxfqzp07pqfJnDp1ylSXFnt7e9nb2+dMwJKuXI/Q+athOXY8PH54DwFA9qpWrZpp/pDi1KlTcnNzU8mSJTPcT1JSkm7fvp1ufU7PQZJDA5V8JSDHjgcAwOPCYrfGHDlyRDExMabtO3fu6Pvvv1fdunVVpEgRSVK3bt2UkJCgX3/91dRuzpw5qlixop588skcjxkAAOQ9ffr00datWxUUFCRJio+P16JFi0xPpJOk48ePa/z48aZ1Pfbs2WO2kOrly5fl5+enNm3a5GzwAAAgy1nsipDg4GD1799f9erVk5ubmzZv3izDMLRs2TJTmzJlyujzzz/XSy+9pM2bN+vWrVvasWOHVq9eLRsbG0uFDgAA8pABAwZo2bJlatasmbp06aL9+/fr7t27Zut9/PPPP5o6darGjBkjFxcXbdy4UaNGjVLjxo119+5drVq1So0bN9Z7771nwTMBAABZwWKJkE6dOsnb21ubNm3SjRs31LVrV7Vt21Z2dnZm7V555RW1bt1a27dvl729vX744QeVKlXKQlEDAIC8xtbWVitWrNCmTZt04sQJtWrVSs8884ycnJxMbWrVqmVa7FSSJk2apMGDB2vHjh1KTk7WyJEj1aRJE0udAgAAyEIWXSOkcOHC6tu37wPb1apVS7Vq1cqBiAAAwOPIxsZG7dq1U7t27dKsr1KlisaPH29W5uXlJS8vr5wIDwAA5CCLrRECAAAAAACQ00iEAAAAAAAAq0EiBAAAAAAAWA0SIQAAAAAAwGqQCAEAAAAAAFaDRAgAAAAAALAaJEIAAAAAAIDVIBECAAAAAACsBokQAAAAAABgNUiEAAAAAAAAq0EiBAAAAAAAWA0SIQAAAAAAwGqQCAEAAAAAAFaDRAgAAAAAALAaJEIAAAAAAIDVIBECAAAAAACsBokQAAAAAABgNUiEAAAAAAAAq0EiBAAAAAAAWA0SIQAAAAAAwGqQCAEAAAAAAFaDRAgAAAAAALAaJEIAAAAAAIDVIBECAAAAAACsBokQAAAAAABgNUiEAAAAAAAAq0EiBAAAAAAAWA0SIQAAAAAAwGqQCAEAAAAAAFaDRAgAAAAAALAaJEIAAAAAAIDVIBECAAAAAACsBokQAAAAAABgNUiEAAAAAAAAq0EiBAAAAAAAWA0SIQAAAAAAwGqQCAEAAAAAAFaDRAgAAAAAALAaJEIAAAAAAIDVIBECAAAAAACsBokQAAAAAABgNUiEAAAAAAAAq5ErEiHJycl6+eWX1bt3b926dStV3cKFC/X8889r5MiR2rJli4WiBAAAeVVUVJQ++eQTDRo0SOPGjdOZM2cyvO+1a9fUr18/vfLKK9kYIQAAyCm5IhHyySefaM2aNVq+fLni4uLM6kaOHKnx48erXr16KlmypDp27Kgff/zRQpECAIC8Ji4uTk899ZTWrFmj5s2b6+rVq6pfv76OHz/+wH2Tk5M1aNAgHThwQBs2bMiBaAEAQHbLb+kA9uzZox9//FGff/65+vbta1Z39OhR/fjjj9q6datatWolScqfP7/eeustDR48WAUKFLBEyAAAIA+ZM2eOrly5osuXL6tQoUJ64YUX1LJlS7377rtatWrVfff95JNP5OzsrH79+j2wLQAAyBssekVIeHi4Bg0apHnz5qlw4cKp6tevXy93d3e1bNnSVNa3b1/dunVLf/31Vw5GCgAA8qp169apffv2KlSokKmsT58+2rBhg5KSktLdb8+ePZozZw5XogIA8JixaCJk+PDh6tOnj1q3bp1mfVBQkDw9PWVjY2MqK1eunKkuLQkJCYqKijJ7AQAA6xUUFKSyZcualZUtW1a3b9/WtWvX0twnPDxcAwcO1A8//KBixYpl6DjMQQAAyBsslgiZNWuWzp8/r48++ijdNgkJCXJycjIrc3BwUL58+XT79u0095kyZYpcXV1NrzJlymRp3AAAIG9Jaz7h7OwsSenOJ4YPH65u3bqpQ4cOGT4OcxAAAPIGiyVCvvzyS9nZ2enZZ59V7969NXnyZEn3FkddsGCBJMnV1VXh4eFm+0VERCgpKUlubm5p9jthwgRFRkaaXpcvX87O0wAAALlcWvOJsLAwSUpzPhEUFKSVK1fq3Llz6t27t3r37q1Vq1bp6tWr6t27t/z9/dM8DnMQAADyBostljpr1izFxsaato8dO6Zdu3apW7duqlevniSpdu3amjNnjmJiYkzf3Bw9etRUlxZ7e3vZ29tnc/QAACCvqF27tmn+kOLo0aMqWbKk3N3dU7UvUaKEli5dala2ePFiRUdHq3///ipdunSax2EOAgBA3mCxREjHjh3NtlO+kenUqZM8PT0lSd26ddOrr76qWbNm6a233pJhGJo2bZrq1aun6tWr53TIAAAgDxo0aJC6deumAwcOqFGjRrp586YWLFig5557ztTmr7/+0hdffKHvv/9eRYoUUe/evc36OHTokAIDA1OVAwCAvMeii6U+iLu7u3766Sd99NFH8vb2VvXq1eXv76+FCxdaOjQAAJBHdO7cWa+++qpat26tNm3aqEaNGvLy8tL7779vanPlyhUtX75ccXFxFowUAADkBItdEfJftWvX1tKlS1W0aFGz8p49e6ply5bav3+/7O3t9dRTT8nBwcFCUQIAgLzoiy++0EsvvaSTJ0/Kw8ND9evXN3sqnbe3d5rzkBSDBg1K9yl3AAAgb8k1iZDixYune7lpkSJFUt1KAwAAkBleXl7y8vJKs6506dL3ve2lZs2aqlmzZnaFBgAAclCuvjUGAAAAAAAgK5EIAQAAAAAAVoNECAAAAAAAsBokQgAAAAAAgNUgEQIAAAAAAKwGiRAAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAVoNECAAAAAAAsBokQgAAAAAAgNUgEQIAAAAAAKwGiRAAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAVoNECAAAAAAAsBokQgAAAAAAgNUgEQIAAHKlffv2KS4uztJhAACAxwyJEAAAkCt9/PHH8vDw0MiRI7V//35LhwMAAB4TJEIAAECutHTpUs2aNUtnzpyRt7e3atSooS+//FLXr1+3dGgAACAPIxECAAByJUdHRw0aNEhbt27VuXPn1KtXL3399dfy9PRUz549tWbNGiUlJVk6TAAAkMeQCAEAALlehQoV9N577+nLL79U8eLFtXLlSvXs2VNPPPGEVq1aZenwAABAHpLpREhwcLAuXLiQ6ToAAICHcezYMb322msqVaqUXnzxRfXu3VvHjx9XaGioRowYoQEDBujSpUuWDhMAAOQRmU6E/Prrr5o5c2am6wAAADJj6dKlatiwoerUqaOjR4/q66+/VnBwsKZPn64aNWqocOHCGj9+vJo0aaJ//vnH0uECAIA8In9WdhYRESEXF5es7BIAAFip9evXy8fHR7/99psqVqyYbrtPPvlEXl5eORgZAADIyzKcCFm3bp1++eUXBQYGKj4+XiEhIWb1sbGx2rRpk1asWJHlQQIAAOtTokQJ9ezZM80kyIQJE9SrVy81aNBA3t7eFogOAADkVRm+NcbW1lb58+eXra2t6d//fpUpU0Y//fST2rVrl53xAgAAKxEQEKCbN2+mWefv76/w8PAcjggAADwOMnxFSIcOHdShQwft2LFD0dHR6tKlS3bGBQAArNS1a9cUGxuruLg4Xbt2TWfPnjWrDw0N1ZEjR1S6dGkLRQgAAPKyTK8R0qJFi+yIAwAAQJI0dOhQbdiwQZK0a9euNNsMHDhQ1atXz8mwAADAY+KhFksNCAjQzJkzdf78ed25c8esbsCAARo9enSWBAcAAKzPTz/9pPj4eD3//PMaNmyY2Zcwtra2cnd3l5OTkwUjBAAAeVmmEyEXL15Us2bN1KxZM3l7e8vOzs6svnLlylkWHAAAsD4lSpSQJG3YsEF2dnbKly+fhSMCAACPk0wnQjZv3qxmzZpp/fr12REPAACwYleuXFFMTIzKlCmj8PBwxcTEpNu2TJkyKliwYA5GBwAAHgeZToQ4OTmpTJky2RELAACwcr6+vtqwYYPWr1+v6dOnm9YKScv69evVoUOHHIwOAAA8DjKdCGnevLkmTZqksLAwFS1aNDtiAgAAVurnn3/W7du3VaxYMTVo0EC3b99Ot22xYsVyMDIAAPC4yHQi5MSJE7KxsVHVqlXVunVrFSpUyKy+ffv26tOnT5YFCAAArIe7u7vp3/b29qnqb9y4IcMwVLx48ZwMCwAAPEZsM7vDnTt3VKdOHbVp00Y2NjaKiYkxe/33KTIAAAAPIy4uTr1791ZkZKSke0+T8fDwUIkSJfTZZ59ZODoAAJBXZfqKkC5duqhLly7ZEQsAAIDJN998o6pVq8rV1VWS9M4772jWrFny8vJSz549NWLECBUuXNjCUQIAgLwm01eEAAAA5IRDhw6pfv36kqSTJ08qKSlJI0eOVNu2bVW7dm39888/Fo4QAADkRZm+IsTPz0/z589Pt7579+4aMmTIo8QEAAAgZ2dnXbhwQZK0Zs0atWrVylQXGRkpZ2dnC0UGAADyskwnQpydneXp6WlWFhsbqy1btihfvnyZSoIcP35cs2bN0rFjx+Tm5qbOnTvL19dXdnZ2pjZxcXH69NNPtWXLFjk4OKhfv34aMWKEbGxsMhs6AADIQ3r37q3+/fvrr7/+0rp167R06VJJ0qVLl3T79m1Vq1Ytw32dP39eH374oU6ePCkPDw+98soratmy5X33WbNmjRYvXqyLFy+qTJkyGjZsmNq3b/8opwQAAHKBTCdC2rRpozZt2qQqj4uLk7e3typWrJihfgIDAzVixAj5+vpq8ODBOnv2rN566y0dPnxYP/zwg6ld7969dfHiRU2dOlXh4eEaM2aMQkJC9P7772c2dAAAkId07txZixcv1tatWzV37lx16NBBkrR792599dVXyp8/Y9OYmzdvqmnTpmratKk++eQTbd++XT4+PtqyZYuaN2+e5j6zZ8/Wzp071atXL5UqVUo7duwwxdOvX78sO0cAAJDzMp0ISY+Tk5O6deumzZs3q3bt2g9s7+Xlpb1795qu7PD29lZoaKimTJliSoTs2bNH69evV0BAgOrWrSvp3qWwb775pl5//XUuiQUA4DH3zDPP6JlnnjEre/bZZzPVx6xZs5ScnKxff/1V+fPnV+vWrXX06FF98MEH2rp1a5r7DBs2TC+99JJp+6mnntKOHTu0YsUKEiEAAORxWbpYalBQUIYfn1ugQAGz21sSEhK0Y8cONWjQwFS2ZcsWeXh4mJIg0r2n1sTHx2vfvn1ZFjcAAMidkpOTFRgYqK1bt2rz5s1mr7CwsAz1sWXLFrVr187sCpIuXbpo165d6c5b7O3tzbavXr2q48ePm81TAABA3pTpK0J27dqltWvXmpUlJSXp2LFj2r59uyZMmJCp/l588UXt3btXFy9elLe3t+n+X0m6fPmyPDw8zNqXKlXKVJeWhIQEJSQkmLajoqIyFQ8AAMgdQkJC1K5dOx07dizN+vXr15tul7mfy5cvy9vb26ysVKlSSkxMVEhIiMqWLZvuvnXr1lVCQoIuXLig//3vf/rf//6XblvmIAAA5A2ZToSEhITo0KFD5p3kz6+yZctq9+7dqlGjRqb6GzdunG7duqXjx4/r3Xff1TvvvKNvvvlGknT37t1U38jY2dnJ1tZWd+/eTbO/KVOmaNKkSZmKAQAA5D6fffaZ3N3dFRQUpPLlyz/0QulpzSdSttObT6RYsGCB4uLitHXrVn3yySeqU6eOevfunWZb5iAAAOQNmU6E9OnTR3369MmyALy8vOTl5aWGDRuqcOHC6tGjh9566y15enqqaNGiqS57DQ8PV3JysooWLZpmfxMmTNDrr79u2o6KilKZMmWyLF4AAJAzLl68qNGjR6tChQqP1E9a84mU7fTmEylSbs996qmnFBISovfeey/dRAhzEAAA8oYsXSPkURUrVkySFBERIUmqX7++zp07ZzZ5SVkbpH79+mn2YW9vLxcXF7MXAADIe6pWraoLFy48cj/169fXgQMHzMr27dunihUrys3NLcP9FCtWTOHh4enWMwcBACBveKhEyN27d/XNN9+oXbt2ql69utq0aaMpU6YoPj4+w30sW7bMbMHT8PBwffLJJ6pYsaKqVasm6d5K8e7u7po0aZIMw1B8fLw++eQTtWnT5pG/HQIAALnbwIEDNXPmTC1evFhBQUG6cuWK2evf63Hcj6+vr/z9/bVq1SpJ0pkzZ7Rw4UKNGDHC1Gbz5s2qW7eurl+/LkmaNm2arly5Yqr/559/NHfuXHXp0iXrThAAAFhEphMhhmGoffv2mjhxoipWrKiBAweqevXq+vrrr+Xt7Z3hSUmNGjU0ceJEubu764knnlCpUqWUnJysdevWKV++fJIkZ2dnrVy5Un/88YdKlCih4sWLKzk5WQsXLsxs2AAAII95/fXXdeHCBQ0aNEheXl4qU6aM2Wvbtm0Z6uepp57SrFmzNGjQIJUrV041a9ZUjx49NG7cOFObiIgIHTlyxPQUmcqVK8vHx0dly5ZV+fLlVb9+fXXt2lUzZszIlnMFAAA5J9NrhGzatElnzpxRYGCgSpQoYSr/+OOP5e3trd9++02DBw9+YD/VqlXTxo0bFRUVpdDQUJUuXVpOTk6p2nl7eysoKEjnzp2Tvb39fVd2BwAAj48ff/xRMTEx6dZnZv2Nl156Sc8//7wuXryoEiVKqEiRImb1Pj4+CggIMM1tunbtqq5du+ratWtKSEiQp6en2eN3AQBA3pXpT/R//vlHHTp0MEuCSJKLi4t69uypU6dOZaq/jNxDa2trq8qVK2c2VAAAkId5enpmaX9OTk6m22//y9XV1bQw6r95eHhkaQwAAMDyMn1rTPHixXX06FElJyenqjt8+LBpwVMAAICssGPHDn377bemhVODg4Pve6UIAADA/WQ6EdK5c2ddvnxZXbt21R9//CF/f3+tW7dOffv21e7du9W3b9/siBMAAFiZu3fvqn379urcubPefPNN/fPPP5Kk7du3a8yYMRaODgAA5FWZToQUKlRI27dvl2EY6tmzpxo0aKCuXbsqNDRU27dvV6lSpbIjTgAAYGVmz56t2NhYXb16Vc2aNTOVP/vss/rzzz8VGhpqwegAAEBe9VCrfj3xxBNat26d7t69q6tXr6pkyZKyt7fP6tgAAIAV27dvn8aMGZNqLTEbGxtVqlRJJ0+eTLVmGQAAwINkKhESGxsrwzDk7OwsSbKzs1O5cuUkSXFxcUpKSlKhQoWyPkoAAGB1kpOTTY+ztbGxMZUbhqFLly7J1dXVUqEBAIA8LFO3xnTt2lX+/v5p1l28eFFPP/20DMPIksAAAIB18/HxMd0ek5IISUxM1DvvvKPExETVrl3bwhECAIC8KMNXhBw7dkwRERFq0aJFmvXVqlVT6dKltXnzZvn4+GRZgAAAwDoNGTJEf/zxhypUqKDk5GSFhoZq+PDhunXrlpYvX678+R/qDl8AAGDlMjyDOHLkiGrVqnXfNjVr1tTRo0dJhAAAgEeWP39++fn5yc/PT5s3b1ZkZKQ6deqkwYMHq1KlSpYODwAA5FEZToREREQ8cP2PQoUKKTw8/JGDAgAAkO6tDdK9e3d1797d0qEAAIDHRIYTIeXKldPChQvv2+bAgQNMVAAAQJa4c+eONm7cqOPHjysuLk4lS5ZU69atVbVqVUuHBgAA8rAMJ0JatWqlwYMH64cfftCIESNS1a9atUpbtmzR999/n6UBAgAA6xMQEKAePXro4sWLKlCggBwcHBQdHS1JGj58uGbPns0aIQAA4KFkeAbh7OysGTNmaMiQIfrll1/UoUMHlS5dWiEhIdq+fbvWrl2rL7/8Uh4eHtkZLwAAeMzFxcWpW7duql27tlatWqU6derIxsZG0dHRWrlypV599VVVrFhREyZMsHSoAAAgD8rUVymDBw+Wu7u7Jk6cqAkTJpgelVuzZk0tWbJE/fr1y5YgAQCA9Vi5cqUKFy6sVatWmV31UahQIQ0ePFjFihXTsGHDNH78eNNjdQEAADIq09eUdurUSZ06dVJ0dLRu3bolNzc3ubq6ZkdsAADACu3bt0+DBw9O99aXjh07Kl++fAoKCpKXl1cORwcAAPI624fdsVChQipXrhxJEAAAkKWCg4Mf+HjcSpUq6erVqzkUEQAAeJw8dCIEAAAgO9y+fVv29vb3bePg4KC4uLgciggAADxOWG4dAADkKoZhaPfu3YqJiUm3TWhoqGmtMgAAgMwgEQIAAHKdjz/+2NIhAACAxxSJEAAAkKusWrVKiYmJD2zn6OiYA9EAAIDHDYkQAACQqzg4OFg6BAAA8BhjsVQAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAVoNECAAAAAAAsBokQgAAAAAAgNUgEQIAAAAAAKwGiRAAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAVoNECAAAAAAAsBokQgAAAAAAgNUgEQIAAAAAAKwGiRAAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAVoNECAAAAAAAsBoWS4Tcvn1bM2fOlLe3t0qUKKEGDRpozpw5qdqFhITo2WefVYkSJVSuXDm9+eabunPnjgUiBgAAedVff/2l5s2by93dXbVq1dKCBQvu2/7atWsaN26catasqVKlSsnHx0c7duzImWABAEC2ym+pA3///fc6c+aMvvrqK1WoUEG7du3S888/r5iYGL3xxhuSpOTkZHXu3Fmurq7asWOHwsPD1bdvX0VHR2v27NmWCh0AAOQhFy5ckI+Pj1588UX9/PPP2r59u4YPH65ChQqpV69eae4zfvx41alTR0uWLFGRIkU0e/Zs+fj4aO/evWrQoEEOnwEAAMhKFkuEjB071my7d+/e2rZtmxYvXmxKhGzcuFGHDx/W2bNn5eXlJUn6+OOPNXz4cH300UcqWrRojscNAADylpkzZ6pYsWL6/PPPJUmDBw/W5s2b9emnn6abCPnpp5/Mtj/88EMtXbpUv//+O4kQAADyuFy1RkhUVJScnJxM27t371a5cuVMSRBJ8vHxUWJiov766y9LhAgAAPKY3bt3q3Xr1mZlPj4+Onz4sOLj4zPUR3JysmJiYszmKQAAIG/KNYmQAwcOaMmSJRoyZIip7OrVqypevLhZu2LFisnGxkbXrl1Ls5+EhARFRUWZvQAAgPVKaz5RvHhxJScnKzQ0NEN9fPnll7p586YGDBiQbhvmIAAA5A25IhFy9uxZde/eXQMGDJCvr69Zna2teYg2NjaSJMMw0uxrypQpcnV1Nb3KlCmTPUEDAIA847/ziZTt9OYT/7ZixQq9/fbb+u6771SlSpV02zEHAQAgb7B4IiQoKEitW7dW8+bNNX/+fLO64sWL68aNG2ZlYWFhMgwj1Tc7KSZMmKDIyEjT6/Lly9kWOwAAyP3Smk/cuHFDNjY2Klas2H33/eOPPzRgwAB98803ZletpoU5CAAAeYNFEyHnz59Xq1at5O3trcWLFytfvnxm9d7e3jp//ryuXLliKtu2bZtsbW3VqFGjNPu0t7eXi4uL2QsAAFgvb29v7dy506xs27ZtqlGjhpydndPdb/Xq1erbt6+++uorvfjiiw88DnMQAADyBoslQi5evKhWrVqpSZMmaSZBJKljx46qXLmyxo4dq/DwcJ0/f14ffPCB+vbtKw8PDwtEDQAA8pqXXnpJQUFB+uKLL3T79m1t2rRJixcv1quvvmpqs2rVKjk7O+vq1auSpHXr1qlPnz6aNm2aRo0aZaHIAQBAdrBYIuS7777TxYsXtWbNGrm5ucnZ2VnOzs7y9PQ0tSlQoIDWrl2r8PBwFS9eXNWqVVODBg30/fffWypsAACQx1SvXl0rV67U999/r4IFC2rAgAF6//33NXz4cFObxMRExcbGKjk5WZI0ceJE3blzR2+++aZpjuLs7KznnnvOUqcBAACySH5LHXjSpEl65513UpWnLIaaolKlStq2bZsSExOVL1++VPUAAAAP0qlTJ3Xq1El3796VnZ1dqvoePXooOjpaBQsWlCTt3LlTSUlJqdrlz2+xqRMAAMgiFvs0L1CggAoUKJDh9kw8AADAo0orCSJJ+fLlM1svxNHRMadCAgAAOcziT40BAAAAAADIKSRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBq5Ld0AAAAAACAnHHz5k0dOHBABQsWlLe3twoUKPDAfeLi4rRlyxa5uLioRYsWqeoNw1BgYKAuXryo8uXLq1q1amb1CQkJWr16dar9vL29Vbp06Yc/GeAhkQgBAAAAACuwePFijRw5UnXq1NH169eVlJSkjRs3qlKlSmm2v3Pnjt588039/vvvMgxDVapU0fbt283a7NmzR2PGjNGdO3dUtmxZHTp0SDVr1tTKlSvl5uYmSQoPD1efPn3k4+MjFxcX076enp4kQmARJEIAAAAA4DEXHBwsX19fffHFFxo9erSSkpLUoUMHDR8+XDt27Ehzn4SEBJUvX14nTpzQuHHjdPbs2VRtoqOj9dNPP6l27dqSpIiICDVs2FBvvfWW5syZY9Z22rRpqlmzZtafHJBJJEIAAAAA4DG3bNkyFShQQCNGjJAk5cuXT6+99po6d+6sixcvqly5cqn2KVSokF599dX79tuhQwezbTc3N/n4+OjQoUOp2h4+fFiXLl1SpUqV9MQTTzz8yQCPiMVSAQAAAOAxd/ToUVWpUsVsTZCUqziOHTuWZcdJSkrSzp07VaNGjVR106ZN07Rp09SgQQO1b99eN2/ezLLjAplBIgQAAAAAHnORkZEqXLiwWVnRokUl3budJau88847unjxot5++21TmaOjo3bs2KG///5bmzdv1unTp3Xu3Dm9/PLLWXZcIDNIhAAAAADAY87e3l5xcXFmZTExMZIkBweHLDnGl19+qRkzZmjFihWqXLmyqdzV1VXNmzc3bZcsWVJjx47V6tWrZRhGlhwbyAwSIQAAAADwmKtYsaIuXbpkVpayXbFixUfuf/r06Xr33Xe1cuVK+fj4PLC9q6urYmNjUyVngJxAIgQAAAAAHnMdO3bUpUuXdPDgQVPZ77//Lg8PD9WtW1eSFB8fr2XLlik4ODhTfX/99deaMGGCVqxYkWrxVEkKDQ1NVbZq1SpVrVpVBQsWzNyJAFmAp8YAAAAAwGPuqaeeUr9+/dS7d2+NGzdOV69e1bRp07Rw4ULZ2t77fjwsLEx9+vTR0qVL1bt3b0nS+vXrFRsbqwsXLujGjRtatmyZJJnqf/75Z73yyivy9fVVbGysqd7JyUmdOnWSJC1ZskRr165Vp06dVKhQIfn5+Wnr1q1asWJFTg8DIIlECAAAAABYhcWLF2v+/PnauXOnnJyctGXLFrO1O5ycnNSrVy95enqaylavXq3r16/Lzc1Nbm5uWrJkiaT/nwhJSEhQr169FB4ebqqT7i3EmpIIeeWVV9SgQQOtXLlSYWFhatKkib777juVKlUqJ04bSIVECAAAAABYgXz58snX11e+vr5p1hcpUsR0RUeKb7/99r59Dh8+XMOHD3/gsZs2baqmTZtmPFggG7FGCAAAAAAAsBokQgAAAAAAgNUgEQIAAAAAAKwGiRAAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAgJUxkpMsHQIAK2bp30H5LXp0AAAAADnOxjaf4hYOVHJooKVDAWBlbEtUk9PgxRaNgUQIAAAAYIWSQwOVfCXA0mEAQI7j1hgAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAViNXJELCw8MVFhZ23zbR0dG6fft2DkUEAAAeRxEREUpKSsrUPtevX1dMTEw2RQQAAHKaRRMhfn5+6tChg4oXL6727dun2ebkyZNq1KiR3N3d5eLiop49eyoiIiJnAwUAAHna8uXLVbp0aXl4eMjNzU3vvvvufdvHxsZq1qxZqlmzpjw8PPTRRx/lUKQAACC7WSwRkpCQoHnz5mns2LF66aWX0m3TpUsXVa5cWeHh4bp8+bLOnj2rYcOG5XC0AAAgrzp69Kj69++v9957T7GxsdqwYYNmzJihb7/9Nt19Dh48qBMnTujXX39VtWrVcjBaAACQ3fJb6sD29vby8/OTJG3cuDHNNmvWrNGFCxe0Z88eOTk5ycnJSRMnTlSfPn0UHBys0qVL52TIAAAgD5o9e7aqVq2qF198UZL01FNPadCgQZo5c6ZGjRqV5j4tW7ZUy5YtczBKAACQU3LFGiHpOXDggLy8vOTh4WEqa968uQzD0MGDBy0YGQAAyCsOHDigp59+2qysefPmCgwMVHR0tIWiAgAAlmKxK0Iy4saNG3J3dzcrK1q0qGxtbXX9+vU090lISFBCQoJpOyoqKltjBAAAuVta84lixYqZ6goVKpQlx2EOAgBA3pCrrwixsbFRYmKiWVlycrKSk5OVL1++NPeZMmWKXF1dTa8yZcrkRKgAACCXSms+kbKd3nziYTAHAQAgb8jViZDSpUsrNDTUrCxlu1SpUmnuM2HCBEVGRppely9fzvY4AQBA7pXefMLW1lYlSpTIsuMwBwEAIG/I1YmQ5s2b6/Llyzp16pSpbMOGDbKzs1OTJk3S3Mfe3l4uLi5mLwAAYL2aN2+uLVu2yDAMU9mGDRvUqFEjOTg4SLp3W0tISIiSk5Mf+jjMQQAAyBssmggJCwtTSEiI4uLilJiYqJCQEIWEhJgmKm3atJG3t7eGDh0qf39/bdq0SW+//bZGjx6twoULWzJ0AACQR4wZM0aRkZEaPXq0AgMDNXv2bP3+++965513TG1Wr14tDw8PXb16VdK9W3FT5iWJiYmKjY1VSEiIbt26ZanTAAAAWcSii6X26tVL//zzj2m7bt26kqSgoCA5OTnJxsZGq1ev1vjx49W3b1/Z29vrpZdeMpu4AAAA3I+np6e2b9+ut99+Wx06dJCHh4d+/fVXdenSxdTGwcFBJUqUMK0ZEhYWZpqXSNLSpUu1dOlS1a9fX2vXrs3pUwAAAFnIoomQ7du3P7BN0aJF9cMPP2R/MAAA4LFVt25drVu3Lt36Ll26KCQkxLRdrFgxs20AAPD4yNVrhAAAAAAAAGQlEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBqkAgBAAAAAABWg0QIAAAAAACwGiRCAAAAAACA1SARAgAAAAAArAaJEAAAAAAAYDVIhAAAAAAAAKtBIgQAAAAAAFgNEiEAAAAAAMBq5IlEyN27dxUQEKDAwEBLhwIAAPKoiIgIHTp0SFeuXMnWfQAAQO6W6xMh27ZtU5kyZdSzZ081a9ZMderU0cWLFy0dFgAAyEO++OILeXh4aPDgwXriiSfUv39/3blzJ8v3AQAAuV+uToRERUWpT58+ev7553X+/Hldu3ZNRYsW1XPPPWfp0AAAQB6xY8cOvfnmm/Lz89PJkyf1zz//aNu2bfr000+zdB8AAJA35OpEiJ+fn6KiojRhwgRJkp2dnd566y3t2rVLZ8+etXB0AAAgL5g3b54aN26sdu3aSZLKli2rwYMHa968eVm6DwAAyBvyWzqA+wkICFDFihXl5uZmKmvUqJGprlKlSqn2SUhIUEJCgmk7MjJS0r2rS7KDu7OdEgo7ZkvfeZm7s122jfnjhvcQAEvJjt/VKf0ZhpGl/T6KgIAANW/e3KysUaNG+uKLLxQeHq7ChQtnyT45PQeJc6mkZPekbOk7L7N1qaRk5iAZwnsIgCVk1+/pzMxBcnUi5NatWypatKhZmZubm2xtbXXr1q0095kyZYomTZqUqrxMmTLZEiPSN2GYpSMAADxIdv2ujo6Olqura/Z0nklpzSdStm/dupVmUuNh9mEOklsclV5caukgAADpyt7f0xmZg+TqRIidnZ1u375tVnbnzh0lJyerQIECae4zYcIEvf7666bt5ORk02TGxsYmy2KLiopSmTJldPnyZbm4uGRZv48LxufBGKP7Y3wejDG6P8bnwbJjjAzDUHR0tEqVKpUl/WWFtOYT8fHxkpTufOJh9mEOkjswPg/GGN0f43N/jM+DMUb3l13jk5k5SK5OhJQrV06rV682KwsODpZ0717dtNjb28ve3t6s7N+31mQ1FxcX3tz3wfg8GGN0f4zPgzFG98f4PFhWj1FuuRIkRbly5UzzhxTBwcGys7NTyZIls2wf5iC5C+PzYIzR/TE+98f4PBhjdH/ZMT4ZnYPk6sVSfXx8FBoaqgMHDpjK/Pz85OzsLG9vbwtGBgAA8gofHx9t3LjRbP0OPz8/tWzZUnZ2dpKksLAw7d692/R43IzsAwAA8qZcnQhp3LixevTooYEDB+q3337T7Nmz9d577+n999+Xk5OTpcMDAAB5wKhRo+To6KiePXtq9erVeuONN7R582ZNnjzZ1Gbbtm1q1qyZrl+/nuF9AABA3pSrEyGS9Ouvv8rX11fz5s3T+vXrNWfOHI0bN87SYcne3l4TJ05MdQks7mF8Howxuj/G58EYo/tjfB7MWsaocOHC2rt3r7y8vDR9+nSFhoZq586datKkiamNu7u7mjZtahqLjOxjKdbyc3tYjM+DMUb3x/jcH+PzYIzR/eWG8bExctPz7QAAAAAAALJRrr8iBAAAAAAAIKuQCAEAAAAAAFaDRAgAAAAAALAa+S0dQF50584dHT9+XAULFlSVKlUsHU6udOXKFV24cEF169aVs7OzpcPJdUJDQ3Xt2jVVqFAhw8+6tiZJSUk6ffq0bGxsVKFCBRaaSodhGNq3b58cHR1Vr149S4eTaxw6dEi3b982K/P09FT58uUtE1Audvr0aSUlJalq1aqysbGxdDjIgFu3buncuXPy9PSUh4eHpcPJlY4dO6a4uDg1btzY0qHkOoZh6Ny5c7p7964qVqzI52sa4uPjderUKbm5ualcuXL8bkxHZGSkjh07ptKlS6tChQqWDidXiI+Pl7+/f6ryWrVqMd//j4SEBAUGBqpYsWIqXbq0ZYIwkCkbNmww3N3djQoVKhhFihQx6tWrZ1y5csXSYeUae/fuNZ555hnD3d3dkGQcPHjQ0iHlKjt37jSaNGlilChRwqhTp47h6OhojBo1ykhMTLR0aLnGzJkzjdKlSxs1a9Y0KlasaBQtWtSYP3++pcPKlb788kvD1tbWqFGjhqVDyVXKlStnVKpUyWjatKnpNXPmTEuHlavs3bvXqFKlilGqVCmjXr16Rr169YxTp05ZOiw8wKRJkwx7e3ujevXqhr29vTFkyBA+P/5l3rx5Rt26dY3ChQsbRYsWtXQ4uc63335rlC1b1vDy8jKeeOIJo0iRIsaCBQssHVauERUVZYwaNcooUqSI8eSTTxru7u5GjRo1jICAAEuHluskJycbnTt3NmxtbY1XXnnF0uHkGoGBgYYko2HDhmZzEP4eMvftt98arq6uRrVq1YwnnnjC6N+/vxEfH5/jcXBrTCbcunVLffv21ahRoxQUFKSrV6/KyclJQ4cOtXRoucaxY8c0dOhQbd++3dKh5EpnzpzR9OnTFRISor///lsHDx7Uzz//rBkzZlg6tFzj9u3bOnbsmI4dO6Zz587p/fff1/DhwxUcHGzp0HIVf39/zZgxQ4MGDbJ0KLnSW2+9pd27d5teo0ePtnRIucaFCxfUvn17de/eXZcvX9bhw4f1888/838sl1u7dq0+/PBDbdq0SSdOnNCxY8e0atUqPj/+5fTp05o7d67ef/99S4eSK924cUN79+7V2bNnderUKU2dOlXDhw/XsWPHLB1arnDjxg01btxYoaGh8vf319WrV1WpUiUNGTLE0qHlOl999ZWSkpJUs2ZNS4eSK61YscJsDtKgQQNLh5RrLF68WK+88oqWLFmikydP6tSpU+rVq5ciIyNzPBYSIZmwfPlyJSQkaNy4cZLuPf943Lhx2rRpky5fvmzh6HKHF154Qd27d1e+fPksHUquNGzYMLNLdWvUqKHmzZtr9+7dFowqd3njjTdUuHBh03arVq2UnJyskJAQC0aVu0RHR2vAgAGaM2eOihUrZulwcqWwsDAdOnRIoaGhlg4l1/nss8/k7u6ujz/+WLa296YB1atXV6tWrSwcGe5n3rx5atmypZo1ayZJqly5svr376958+ZZOLLcY8qUKXryySctHUau9f7775tdgj58+HDZ2tpq3759Fowq96hYsaIGDx6s/PnvrRxgZ2enpk2bkiT+D39/f02bNk3z58/ntqF0nD9/XgEBAYqOjrZ0KLnO+++/r6FDh6pDhw6mst69e6tEiRI5HguJkEwICAhQlSpVzNa8aNSokSTp77//tlBUyMvu3Lmjo0ePqlKlSpYOJVcJDg7W7t27tWLFCo0cOVK9e/dmcvsvL774ojp06GD2IQJzH3/8sXx9feXl5aXmzZsrKCjI0iHlGlu2bFGnTp2UmJiow4cP6+LFizIMw9Jh4QECAgJUv359s7JGjRopMDBQCQkJFooKedmRI0d09+5d5iD/cfz4ce3cuVM//vijZsyYoQ8//NDSIeUa0dHR6t+/v2bNmqWSJUtaOpxca8CAARo0aJCKFi2qF198kd/R/+f8+fMKCgpS165dFRYWJn9/f928edNi8bBYaibcunVLRYsWNStL2b5165YlQkIe9+abbyoqKkovv/yypUPJVXbt2qVvvvlGwcHBsrGx0QcffMC3Dv9n/vz5OnLkiA4dOmTpUHKtiRMnatCgQbKzs1NYWJh69OihPn366MCBA1ytJunq1asKCwtTtWrV5OrqqitXrqhMmTJasmSJnnjiCUuHh3SkNwdJTk5WRESERb5NQ94VFxenYcOG6emnn+ZqsP+YO3eu6RaiJ598Uu3bt7d0SLnGSy+9pDZt2qhbt26WDiVXcnZ21po1a9S5c2dJ95KNrVq1kqurq6ZOnWrh6Czv6tWrkqQNGzZo+PDhKlWqlE6dOqVu3bppwYIFOb54M1eEZIKdnV2qJxHEx8dLkgoUKGCJkJCHTZ06Vd9//72WL1+uMmXKWDqcXKV///7as2ePLly4oHfeeUedOnXS0aNHLR2Wxd24cUMvv/yyRo0apUOHDmn37t0KDg5WXFycdu/erYiICEuHmCsMHTpUdnZ2ku79ofjJJ5/o8OHDOn36tIUjyx3s7Oy0Zs0arV27VgEBAbp06ZKKFCmi559/3tKh4T6YgyCrJCQkqGfPnoqNjdWyZcv4ouE/vvrqK+3fv19Xr15V8eLF1bZtW929e9fSYVncH3/8oTVr1qhnz56mtS9iY2N19epVbvH+P56enqYkiCTVqVNHo0aN0pIlSywYVe6RMjc7ePCgzp07p4CAAJ08eVKbNm3Sp59+muPxcEVIJpQrV067du0yK0u5b7Bs2bKWCAl51BdffKFJkybJz89PrVu3tnQ4uZqvr6/efPNNbdy4UbVr17Z0OBYVHx+vunXr6pdfftEvv/wi6d7Cl+Hh4Ro/fry+/PJLHheZhpRvyoODg1WtWjULR2N55cuXl4eHh2ksHB0d9fzzz2vIkCFKSEjgcZq5VLly5VKtVRAcHKxChQqZrasE3M+dO3fUs2dPBQUFafv27VxJdB/29vYaO3asfvnlF506dcrqFwZNTExUzZo1NXnyZFPZtWvXFBcXp6tXr2rHjh1cdZmGEiVKsM7M/ylfvrwkaeDAgaalJsqXL6/27dun+hs7J5AIyQQfHx99/PHHOnr0qOkPMj8/P7m5ualhw4YWjg55xbRp0/Tee+/Jz89PPj4+lg4nV4mPj5e9vb1pAUdJun79uqKiolJdEm6NypYtm+pbl//973/6888/+Tbm/8TGxqpgwYJmZRs3bpStrS1JkP/Tvn17rV+/3qzsypUrcnFxIQmSi/n4+OiXX35RYmKiaTFHPz8/tW3b1sKRIa9ISYKcOXNG27ZtU6lSpSwdUq6S1ufH2bNnJYk5iKSePXuqZ8+eZmV169ZVy5YtNX36dMsElcuk9R7atGmT1SfRUhQvXlx169ZNlRi6cuWKRX4fkQjJhBYtWqhjx47q16+fJk+erNDQUE2ePFmfffYZl6X+n2vXruncuXO6dOmSpHv3xt2+fVsVKlQwW6ncWs2ZM0dvvPGG3n//fTk5OZn+eHVxcbH6qx2ke48XHjlypIYOHaqKFSvqypUrmjZtmqpUqaK+fftaOjzkAfv27dPHH3+s5557TqVLl9Zff/2lqVOn6o033uB30P95/fXXtWjRIr3wwgvq1auXzpw5o08//VQTJkywdGi4j1dffVULFixQv379NGTIEK1fv14HDx7kiR//cvLkSd26dUvnz59XYmKi6TP2ySeflJOTk4Wjs7z+/ftrx44dmjt3rs6fP6/z589Lupdk58rme3M0f39/de7cWe7u7vr777/16aefauTIkfLw8LB0eMgDPvzwQ4WFhaldu3ZycHDQ77//rg0bNsjPz8/SoeUan332mXr16qVixYqpVq1aWr9+vfbt22eRL/RsDJaKz5T4+HhNmzZNO3bskJOTkwYMGKB+/fpZOqxcY8WKFZo2bVqq8jFjxqh///4WiCh3efvtt7Vz585U5TVq1NCcOXMsEFHuc/LkSX333Xf6559/VLRoUT399NMaNmyYHB0dLR1arjRr1izt379fCxcutHQoucaBAwc0d+5cXbhwQWXKlFG/fv24+uo/goOD9dlnn+nEiRMqUaKE+vTpo+7du1s6LDzAxYsXNXXqVJ06dUqenp569dVXVa9ePUuHlWu89dZb2rNnT6ryRYsWqUKFChaIKHdp06ZNmk+vGDZsmIYNG2aBiHKfP/74Q8uXL1dISIg8PT3Vs2dPszUfYG7o0KGqV6+exo4da+lQcgXDMPTrr79q9erVioqKUpUqVTR69Gh5eXlZOrRcZffu3Zo9e7auX78uLy8vvfzyy6pRo0aOx0EiBAAAAAAAWA2eGgMAAAAAAKwGiRAAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAVoNECAAAAAAAsBokQgDkSsePH9eWLVssHQYAALAymzdv1smTJy0dBoBsRCIEQJYJCAjQ6tWr063fsmWL9u7dm6G+li1bpokTJ2ZVaAAA4DG2fv16HTp0KM26xMRE/fbbbzp//nyG+nr33Xe1YsWKrAwPQC5DIgRAlgkODla3bt107ty5VHURERHq0qWLjh07ZoHIAADA42zt2rUaOHBgunUDBgzI4YgA5GYkQgBkmY4dO8rDw0Pz5s1LVffLL7/I1tZWAwYM0Llz57RkyRItWbJEa9eu1YULFx7Y9/79+/XXX3+ZlQUGBmrjxo2p2v7zzz9atWqV9u/fr7t37z70+QAAgLzB19dXp0+f1q5du1LVzZ07V61bt1aFChW0e/duLVmyRL/99pu2bdum8PDwB/bt5+enixcvmpVt3bo11Zc7SUlJ2rdvn/z8/BQYGPhoJwQgW+W3dAAAHh/58uXTkCFD9NNPP2ny5MnKly+fqW7u3Lnq06ePXFxcdODAAa1atUqSFBUVpV27dmn06NH69NNP0+179uzZSkxMVJMmTUxlfn5+WrZsmdq1aydJSkhI0ODBg7Vjxw41bNhQFy5cUHJyslavXq2KFStmz0kDAACLq1u3rp588knNmzdPzZo1M5Vfu3ZN69ev16JFiyTd+2Ll4MGDkqTLly/rxIkTWrRokbp27Zpu3yNHjtQXX3yhcuXKmcomT56sp59+WrVq1ZIkBQUFmfrw8vLSoUOH1LRpU/3666/Kn58/uYDchitCAGSp4cOH6+rVq2ZXavz99986fPiwfH19JUlt27Y1XRGybt06BQQE6JtvvpG/v/8jHXvy5Mm6fPmygoKCtHr1ah07dkxNmzbVqFGjHqlfAACQ+/n6+mrp0qWKjo42lf30009ycXFRjx49JElvvPGGaQ6yZ88eTZs2TS+88IKSkpIe6dh9+/bVM888oxMnTuiPP/7Q6dOndfz4cc2cOfOR+gWQPUiEAMhSFStWVMuWLTV37lxT2dy5c1WlShU9/fTTprK4uDjt3r1by5Yt06FDh1SiRAkdOHDgkY49f/581a5dW+vWrdPSpUv1+++/q3jx4tqxY4eSk5MfqW8AAJC7Pfvss0pOTtZvv/1mKps3b54GDRoke3t7U1lISIg2b96s3377TUlJSQoJCdGlS5ce+rhHjx6Vv7+/ypUrp2XLlmnp0qVat26dKlWqpG3btj3SOQHIHlynBSDL+fr6aujQobp586YKFSqkX375RePHjzfVb968Wf3791epUqVUsWJFOTg4KDo6WtevX3/oY965c0fXrl1TYGCgIiIizOq6deum27dvy8nJ6aH7BwAAuZurq6t69+6tefPmydfXV7t27dKZM2e0fPlyU5vJkydr6tSpql+/vooXL24qv379uipUqPBQx01Z62zbtm2ysbExlRcsWFCVK1d+uJMBkK1IhADIcj179tSYMWP0888/q2TJkoqKitLgwYNN9a+//rpGjx6tSZMmmcqqVq0qwzDS7dPW1jbVVR23b982/dvOzk4ODg7q168ft8IAAGClhg8frpYtWyowMFBz585Vw4YNTet4BAcHa+LEidq7d6+8vb0l3UtiLF++/JHmIC4uLpKkKVOmsCYZkEdwawyALOfg4KCBAwdq7ty5mjt3rrp27aoSJUqY6kNCQlSlShXT9tGjR3XmzJn79lm6dGmdPXvWrGz79u2mf9vY2Kh9+/b68ccfU93nGxwc/AhnAwAA8ooWLVqocuXKmjFjhpYuXWpan0ySQkNDJclsDrJs2bIH9vnfOciNGzd04sQJ03ajRo1UuHBhfffdd2b7GYaha9euPfS5AMg+XBECIFv4+vpq5syZOn78uNauXWtW1717d7399tuKiIhQbGysvvrqKzk7O9+3vwEDBujTTz/VqFGjVL9+fa1du1YnT55U2bJlTW2mTZumFi1a6KmnntKgQYNkGIZ27typAgUK6JdffsmW8wQAALnL8OHDNX78eDk5OWnAgAGm8ho1aqhSpUrq27evnn32WR0/ftz0NJn7GTx4sN555x0VLFhQzs7Omjt3rtmTYJycnPTDDz/o2WefVXBwsFq1aqXQ0FD5+fnppZde0tChQ7PlPAE8PBIhALJFnTp1NHbsWEVGRqp9+/ZmdTNnztT333+vgwcPysXFRUuXLtWmTZtUs2ZNU5t//1uSqlevrn379unnn39WQECABg4cqCFDhmj//v2mNhUrVtSxY8f0008/6fDhw3Jzc9OgQYPUrVu37D1ZAACQazz//PMKCAhQw4YNVahQIVO5vb29du3apZkzZ2r79u0qX7689u3bp3fffVfu7u6mdj4+PqpRo4Zp++WXX1axYsW0detWFSlSRD/++KPWrFmjqlWrmtr06tVLR48e1c8//6xdu3apbNmy+v7771W3bt0cOWcAmWNj3O+GOAAAAAAAgMcIa4QAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAVoNECAAAAAAAsBokQgAAAAAAgNUgEQIAAAAAAKwGiRAAAAAAAGA1SIQAAAAAAACrQSIEAAAAAABYDRIhAAAAAADAapAIAQAAAAAAVuP/AVHinIPhucb1AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "example_left_edges = np.array([0.0, 2.0])\n", + "example_widths = np.array([1.0, 4.0])\n", + "example_counts = np.array([50, 50])\n", + "example_density = example_counts / (example_counts.sum() * example_widths)\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(11, 4.5), sharex=True)\n", + "\n", + "count_bars = axes[0].bar(\n", + " example_left_edges, example_counts, width=example_widths, align=\"edge\",\n", + " color=\"#52789c\", edgecolor=\"white\",\n", + ")\n", + "axes[0].bar_label(count_bars, labels=[\"50\", \"50\"], padding=3)\n", + "axes[0].set_title(\"Counts: equal heights\")\n", + "axes[0].set_xlabel(\"Value\")\n", + "axes[0].set_ylabel(\"Count\")\n", + "axes[0].set_ylim(0, 60)\n", + "\n", + "density_bars = axes[1].bar(\n", + " example_left_edges, example_density, width=example_widths, align=\"edge\",\n", + " color=\"#f16e00\", edgecolor=\"white\",\n", + ")\n", + "axes[1].bar_label(density_bars, labels=[\"0.500\", \"0.125\"], padding=3)\n", + "axes[1].set_title(\"Density: equal areas\")\n", + "axes[1].set_xlabel(\"Value\")\n", + "axes[1].set_ylabel(\"Density\")\n", + "axes[1].set_ylim(0, 0.6)\n", + "\n", + "fig.suptitle(\"Two bins, 50 observations each\")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "e3adade6", + "metadata": {}, + "source": [ + "## Reading variable-width histograms\n", + "\n", + "| Question | Use | What to compare |\n", + "| --- | --- | --- |\n", + "| How many observations? | Counts (`density=False`) | Bar heights |\n", + "| What fraction of observations? | Counts divided by $N$, or density | Bar areas |\n", + "| Where are values concentrated? | Density (`density=True`, the Khisto default) | Bar heights |\n", + "\n", + "Before interpreting a histogram:\n", + "\n", + "1. Notice whether bin widths differ.\n", + "2. Identify whether the y-axis shows count or density.\n", + "3. For density, read each bar's **area** as probability.\n", + "\n", + "## Go further\n", + "\n", + "Continue with [Histograms - Khiops](https://khiops.org/learn/histograms/) for\n", + "the principles behind Khiops histograms, from the simplest to the most complex." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "khisto-python (3.12.3)", + "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": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/demo.ipynb b/docs/demo.ipynb index c20702e..852181b 100644 --- a/docs/demo.ipynb +++ b/docs/demo.ipynb @@ -25,8 +25,8 @@ "short-but-wide bin can hold the *same* number of points, so only the density\n", "(count divided by bin width) shows the true shape of the distribution.\n", "\n", - "> 📚 For a didactic walk-through of optimal histograms — from the simplest to the\n", - "> most complex — see the histogram documentation in [Khiops fundations](https://khiops.org/learn/understand/)" + "> 📚 Go further with [Histograms - Khiops](https://khiops.org/learn/histograms/),\n", + "a didactic walk-through from the simplest histogram to the most complex." ] }, { @@ -302,7 +302,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": null, "id": "d0e40b1c", "metadata": {}, "outputs": [ @@ -322,7 +322,7 @@ } ], "source": [ - "hist_counts, bin_edges = histogram(data)\n", + "hist_counts, bin_edges = histogram(data, density=False)\n", "\n", "print(f\"Number of bins: {len(hist_counts)}\")\n", "print(f\"Bin edges: {bin_edges}\")\n", @@ -542,8 +542,7 @@ "3. **`khisto.core.compute_histograms`** — full control over the granularity\n", " series, with `HistogramResult` exposing counts, probabilities and densities.\n", "\n", - "To go further, the\n", - "[Khiops histograms guide](https://github.com/KhiopsML/khiops-doc/blob/dev/docs/learn/histograms.md)\n", + "To go further, [Histograms - Khiops](https://khiops.org/learn/histograms/)\n", "builds the intuition from the simplest histogram to the most complex." ] } diff --git a/docs/index.rst b/docs/index.rst index f9709e7..ec58a9d 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -74,6 +74,23 @@ Get started A runnable notebook tour covering all features. +.. grid:: 1 1 2 2 + :gutter: 3 + :class-container: sd-mt-3 + + .. grid-item-card:: :octicon:`law;1.5em` Counts or density? + :link: counts_vs_density + :link-type: doc + + Learn how bin width changes the meaning of bar height and area. + + .. grid-item-card:: :octicon:`info;1.5em` Histograms - Khiops + :link: https://khiops.org/learn/histograms/ + :link-type: url + :class-card: histogram-guide-card + + Go further, from the simplest histogram to the most complex. + .. toctree:: :maxdepth: 2 :caption: API Reference @@ -89,3 +106,4 @@ Get started :hidden: Demo + Counts, density, and bin widths From 50c0e07a42e6e5a6268901c48263eafb23fc5440 Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Wed, 9 Sep 2026 15:21:23 +0200 Subject: [PATCH 2/9] =?UTF-8?q?chore(release):=20pr=C3=A9parer=20la=20vers?= =?UTF-8?q?ion=201.0.2?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- CHANGELOG.md | 11 +++++++++++ pyproject.toml | 2 +- 2 files changed, 12 insertions(+), 1 deletion(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index 663d9d4..c576703 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,6 +2,16 @@ All notable changes to Khisto are documented in this file. +## [1.0.2] - 2026-09-09 + +### Added + +- Explain counts, densities, and variable-width bins in a dedicated guide. + +### Changed + +- Highlight and update links to the official Khiops histogram documentation. + ## [1.0.1] - 2026-09-07 ### Fixed @@ -20,4 +30,5 @@ First stable release. - Prebuilt wheels for Linux, macOS, and Windows. - Public API documentation and usage examples. +[1.0.2]: https://github.com/KhiopsML/khisto-python/compare/v1.0.1...v1.0.2 [1.0.1]: https://github.com/KhiopsML/khisto-python/compare/v1.0.0...v1.0.1 diff --git a/pyproject.toml b/pyproject.toml index 6e723c7..e7ce6fe 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -1,6 +1,6 @@ [project] name = "khisto" -version = "1.0.1" +version = "1.0.2" description = "Optimal histogram visualization using the Khiops algorithm" readme = "README.md" license = "BSD-3-Clause-Clear" From 990bed077889e91152ddc70caba8635f70b68ef0 Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Wed, 9 Sep 2026 15:25:12 +0200 Subject: [PATCH 3/9] =?UTF-8?q?ci(docs):=20publier=20un=20aper=C3=A7u=20pa?= =?UTF-8?q?r=20pull=20request?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .github/workflows/docs.yaml | 57 ++++++++++++++++++++++++++----------- 1 file changed, 40 insertions(+), 17 deletions(-) diff --git a/.github/workflows/docs.yaml b/.github/workflows/docs.yaml index 701d1ad..412c730 100644 --- a/.github/workflows/docs.yaml +++ b/.github/workflows/docs.yaml @@ -9,23 +9,18 @@ on: type: boolean default: false pull_request: + types: [opened, reopened, synchronize, closed] paths: - - docs/**.rst - - docs/conf.py - - docs/make.bat - - docs/Makefile - - docs/requirements.txt - - docs/_static/**.css - - src/khisto/**.py + - docs/** + - pyproject.toml + - src/khisto/**/*.py - .github/workflows/docs.yaml push: tags: ['*'] -# Sets permissions of the GITHUB_TOKEN to allow deployment to GitHub Pages +# Keep default workflow permissions read-only; deployment jobs elevate explicitly. permissions: contents: read - id-token: write packages: read - pages: write # Allow only one concurrent deployment, skipping runs queued between the run in-progress and latest # queued. However, do NOT cancel in-progress runs as we want to allow these production deployments # to complete. @@ -34,6 +29,7 @@ concurrency: cancel-in-progress: false jobs: build: + if: github.event_name != 'pull_request' || github.event.action != 'closed' runs-on: ubuntu-22.04 steps: - name: Checkout khisto-python @@ -61,7 +57,34 @@ jobs: with: name: khisto-python-docs path: ./docs/_build/html/ - # Publish to GH pages on Git tag push + preview: + if: >- + always() && + github.event_name == 'pull_request' && + github.event.pull_request.head.repo.full_name == github.repository && + (github.event.action == 'closed' || needs.build.result == 'success') + needs: build + runs-on: ubuntu-22.04 + permissions: + contents: write + pull-requests: write + steps: + - name: Checkout khisto-python + uses: actions/checkout@v4 + - name: Download the docs artifact + if: github.event.action != 'closed' + uses: actions/download-artifact@v4 + with: + name: khisto-python-docs + path: ./docs/_build/html + - name: Deploy PR preview + uses: rossjrw/pr-preview-action@v1 + with: + source-dir: ./docs/_build/html + preview-branch: gh-pages + wait-for-pages-deployment: true + qr-code: false + # Publish production docs to GitHub Pages on manual request. publish: if: github.event_name == 'workflow_dispatch' && inputs.deploy-gh-pages == true needs: build @@ -77,9 +100,9 @@ jobs: name: khisto-python-docs path: ./docs/_build/html - name: Deploy web site - run: | - # Install tool for pushing to GH pages - pip install ghp-import - - # Push built site directory contents to GH pages - ghp-import -m "Deployed ${GITHUB_SHA:0:7}" --push --force --no-jekyll ./docs/_build/html/ \ No newline at end of file + uses: JamesIves/github-pages-deploy-action@v4 + with: + folder: ./docs/_build/html + branch: gh-pages + clean-exclude: pr-preview + force: false From 6547014d38fba496c6ea502c57958dca70b5251f Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Wed, 9 Sep 2026 15:54:02 +0200 Subject: [PATCH 4/9] =?UTF-8?q?docs(dev):=20pr=C3=A9ciser=20le=20compilate?= =?UTF-8?q?ur=20requis=20sous=20Windows?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- README.md | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/README.md b/README.md index 05fa3e3..d9c58d4 100644 --- a/README.md +++ b/README.md @@ -54,6 +54,11 @@ plt.show() ## Development +On Windows, install [Visual Studio Build Tools 2022](https://visualstudio.microsoft.com/visual-cpp-build-tools/) +with the **Desktop development with C++** workload. Then run the commands below +from an **x64 Native Tools Command Prompt for VS 2022** and verify that the +compiler is available with `where cl`. + ```bash # Clone repository git clone https://github.com/KhiopsML/khisto-python.git From 4b20bf78664ecc8f66891af9ef3c005d216f2ce2 Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Fri, 11 Sep 2026 10:44:11 +0200 Subject: [PATCH 5/9] =?UTF-8?q?docs(guides):=20ajouter=20le=20guide=20sur?= =?UTF-8?q?=20la=20densit=C3=A9=20des=20histogrammes?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/counts_vs_density.ipynb | 254 ---------------------- docs/counts_vs_density.rst | 16 ++ docs/images/counts-vs-density.png | Bin 0 -> 109041 bytes docs/index.rst | 8 +- scripts/generate_distribution_examples.py | 83 +++++++ 5 files changed, 106 insertions(+), 255 deletions(-) delete mode 100644 docs/counts_vs_density.ipynb create mode 100644 docs/counts_vs_density.rst create mode 100644 docs/images/counts-vs-density.png diff --git a/docs/counts_vs_density.ipynb b/docs/counts_vs_density.ipynb deleted file mode 100644 index b7dca37..0000000 --- a/docs/counts_vs_density.ipynb +++ /dev/null @@ -1,254 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "178ae8be", - "metadata": {}, - "source": [ - "# Counts, density, and variable-width bins\n", - "\n", - "Khisto chooses adaptive bins, so their widths can differ. That makes one\n", - "distinction essential: **counts describe how many observations fall in a bin;\n", - "density describes how concentrated those observations are over the bin's\n", - "width**.\n", - "\n", - "By the end of this guide, you will know what bar height and bar area mean in\n", - "each view, and which view to choose for your question." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "8e971340", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Observations: 10,000\n", - "Adaptive bins: 23\n", - "Sum of density areas: 1.000000\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "from khisto import histogram\n", - "\n", - "SEED = 42\n", - "rng = np.random.default_rng(SEED)\n", - "data = np.concatenate([\n", - " rng.normal(0, 0.35, 6000),\n", - " rng.normal(2.5, 1.0, 3000),\n", - " rng.exponential(2.0, 1000) + 4,\n", - "])\n", - "\n", - "counts, bin_edges = histogram(data, density=False)\n", - "density, density_edges = histogram(data, density=True)\n", - "\n", - "np.testing.assert_array_equal(bin_edges, density_edges)\n", - "widths = np.diff(bin_edges)\n", - "probabilities = counts / counts.sum()\n", - "\n", - "assert counts.sum() == data.size\n", - "assert np.isclose(np.sum(density * widths), 1.0)\n", - "\n", - "print(f\"Observations: {int(counts.sum()):,}\")\n", - "print(f\"Adaptive bins: {len(counts)}\")\n", - "print(f\"Sum of density areas: {np.sum(density * widths):.6f}\")" - ] - }, - { - "cell_type": "markdown", - "id": "f94cd2b9", - "metadata": {}, - "source": [ - "## One histogram, two questions\n", - "\n", - "For bin $i$, let:\n", - "\n", - "- $c_i$ be its count,\n", - "- $w_i$ be its width,\n", - "- $N$ be the total number of observations.\n", - "\n", - "The relative frequency is $p_i = c_i / N$. The density is\n", - "\n", - "$$d_i = \\frac{c_i}{N w_i} = \\frac{p_i}{w_i}.$$\n", - "\n", - "A count bar's **height** answers \"how many observations?\" A density bar's\n", - "**area** answers \"what fraction of observations?\" because\n", - "\n", - "$$d_i w_i = p_i,$$\n", - "\n", - "and all density-bar areas sum to 1. Dividing by width is what makes bins of\n", - "different widths comparable." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "1cdc39a4", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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3z7i5uaX5Xjl//nxOrUq2+frrr829995rAgICTKlSpdKNKVy4sKlWrZrDun3//feZLnfXrl2mbNmyplSpUiY0NNRUrFjR/PnnnzmxCoDd7RzP8vMx8KOPPjIlS5Y0VapUMRUqVDDFixc38+bNy7RPfjoG3iw8PNxIMg899JDD+u3ZsyfTfjNnznQ43jVt2tTExMTkUtY559ChQ2mOW1WqVDGSzLJlyzLsV6NGDVO+fHmHfh999FEuZp59nDkG3s7x7G49Bu7YscM8/fTTJiQkxEgy69evTxPz7rvvmuLFi5tq1aqZcuXKmVKlSpklS5ZkutyBAweaoKAgh32mZ8+eObQW2ScmJsaMGjXKlCpVyhQuXNj069cvTczmzZuNJPPII484rN+hQ4cyXfa3335rChUqZKpUqWIKFy5sWrdubS5fvpxTq5ItKEzBbsiQIaZChQrm3LlzxhhjvvvuO2O1WjP9orudPneLr776yoSHh9unf/vtN+Pt7W2mTJmSYZ/UwlR+Vbx4cfPdd985HZ+SkmJq1KhhOnXqZGw2mzHGmN69e5uyZcuahISEnErTZRYvXmwkmZ07d2YY88orr5iWLVvmYlY554svvjBLly4127dvz7Aw1adPH1O9enX7SfbEiRONh4eHOXz4cIbLvZ0+ecHWrVvNp59+ai5cuGCqVKmSbmFq/Pjx5q+//rJPr1u3zri7u5v58+dnuNx58+YZf3//nEg5x7322mvmjz/+MOPGjcu0MPXTTz85vczExERToUIF07t3b2OMMTabzXTu3NlUrVrVpKSkZEPWQFq3czzL78fA//znPyYqKso+/dFHHxlPT09z9OjRDPvkp2PgzVILU6nnxM44dOiQ8fDwsP/Id/HiRVOlShXz3HPP5VSaLvXiiy+aEiVKmKSkpAxjatSoYT799NPcSyoH3eoYeDvHs7v5GDht2jQzd+5cc/To0XQLU8nJyeaNN95w+OFtzJgxplChQubMmTMZLnfgwIHm6aefzqm0c8z+/fvN2LFjTWRkpGncuHGmhamrV686vdw9e/YYq9VqZs2aZYwx5uzZs6ZcuXKZ/nCeF+Tf/0EjS5KSkoyfn5/5+OOPHdrLly9vXnnllWzrc7dr2LBhpicLqYWpAwcOmD/++MPEx8fnYnY5r3jx4ua///2v2bFjh8PJaEZ+/fVXI8ns3r3b3nb48GEjyaxYsSInU3WJ9u3bm/vvvz/TmFdeecU0bdrU7Nq1yxw6dMgkJyfnUnY5Z8eOHekWpuLj4423t7eZNGmSvS0lJcUUL17cjBkzJt1l3U6fvCijwlR6atasaf71r39lOH/evHnGz8/P7Nu3z/z5559ZOjnJK25VmJo0aZLZsWOHU/+hW716tZHkUKjcvXu3kWQ2b96cbTkDN7qd41lBOwZevnzZSDJz5szJMCY/HgNTpRamtm3bZsLDw82lS5du2Wf06NGmRIkS9sKlMcZMmDDBeHt757tzyKtXr5qAgADz73//O9O4GjVqmNGjR5vffvvNnD59Opeyy1kZHQNv53iWH46BERERGV4xdbPIyMhbXmU3cOBA06ZNG7Nz505z+PDhPF+gS8+tClN//PGH2b17t7ly5cotlzV8+HBTqVIlh7b333/f+Pv75+nv3LvnZlTkqKNHjyouLk4PPPCAQ3u9evUyvD/8dvrcza5cuaL9+/enufc3Pa1bt1anTp1UtGhR/fvf/5YxJhcyzB1vvfWW+vfvr/Lly+uxxx7TiRMnMowNDw+Xu7u7atWqZW+rWLGiAgMD890+EhUVpWXLlmnAgAG3jN20aZN69eqlRo0aqXTp0lqwYEEuZJj79u/fr2vXrjl8R1itVj3wwAMZfv630+dudv78eR07duyW3ytxcXFq37692rdvr8DAQL333nu5lGHuGDlypPr166ewsDC1bt1ap0+fzjA2PDxc/v7+DuON1K5dW56envlyH0HecDvHs4J0DJSkHTt2SNItv8/y+zGwU6dO6tatmwIDAzV06FAlJSVlGBseHq77779fFovF3vbggw/q2rVrOnDgQG6km2vmz5+v2NhY9evX75axn3zyiQYMGKDKlSvroYceynfbItXtHM8K2jEw9XvlVmOMrVq1Sn369FH9+vVVtmxZLV++PDfSyzXt2rXTM888o6JFi+q1115LMzbnjcLDw9P8//zBBx9UbGysjh49mtOp3jYKU5AkXbhwQZIUFBTk0B4UFGSflx197maDBw+Wu7u7nn/++Qxjihcvrl9++UVHjx7V33//rZUrV+q///2vJkyYkIuZ5pz33ntP58+f1+7du3X8+HHFx8era9euGRbeLly4oMDAQIcTLil/7iPTp0+Xp6enunfvnmlc48aNFRERoT///FOnTp3SoEGD1K1bN+3bty+XMs09fK9kzhijAQMGKCQkRD179swwrmzZstq1a5cOHTqkI0eOaO7cuRo9erS+++67XMw254wfP17nz5/XH3/8oaNHj+rMmTOZbo8LFy6k2T+k/LmPIO+4neNZQToGxsbGatCgQXriiSd0//33ZxiXn4+B/v7+WrVqlSIiIrR//35t3bpVM2bM0Lvvvpthn/S+z1Kn89s+MmXKFDVr1uyWg7u/9tpr9nPNkydPyt/fXx07dkz3YTN3u9s5nhWkY2B0dLSGDh2qZ555JsOHCklSy5YtderUKe3Zs0dnzpxRt27d1LlzZx05ciQXs80ZwcHB2rhxo44fP66DBw9q3bp1+vLLL/Xf//43wz536/cKhSlIkv0pKteuXXNov3r1qjw9PbOtz91q1KhR+umnn7R48WIFBwdnGHfvvffqkUcesU83adJEXbt21ezZs3MjzRzXt29f+5MxQkJC9O6772rbtm06fvx4uvEeHh5p9g8pf+4jU6dOVZcuXW755J0nn3xSJUqUkHT9SqDRo0crKCgo3/1iLPG9ciuDBw/Wpk2btGTJkkyf+FmvXj2HJ8u0bdtWbdu2zTffK/3797c/TahEiRJ66623tG7dOp07dy7d+IL0vYK843b2u4Kyr165ckVt27aVj4+Pvv/++0xj8/MxsHz58mrRooV9+oEHHtCAAQMy/a5Obx+5evWqJOWrfeTo0aPasGGDU1eV9+7dW15eXpKuF/s+/PBD7d+/X3/88UdOp5nr+F7JWGxsrFq1aqXQ0FBNnjw509innnrK/pRHNzc3jRs3Th4eHlq8eHFupJqjqlatqkcffdQ+3aBBA/Xq1Stffq9QmIKk67/IS9KpU6cc2k+dOpXh485vp8/d6D//+Y++/PJLrVy5Ug8++GCW+xcvXjzNNsovihcvLintPpCqbNmyiouL06VLl+xtiYmJOnfuXL7aR7Zs2aKDBw86dcJ1M4vFopCQkHy5j/C9krGhQ4dq7ty5Wrt2rWrWrJnl/gX9eyU6Otrh1/MrV64oNjY2X+0jyFtu53hWEI6BV65cUZs2bRQXF6c1a9aoaNGiWeqfn4+B0q2/q8uWLZvu8U5SvtlHpOs/3gUFBalDhw5Z7nurY8Ld7HaOZwXhGBgXF6cWLVrIzc1NK1euzPTHu/S4ubkpKCgoX+4zUv79XqEwBUnXLxO87777HCrLFy9e1KZNm9S8eXN728GDB7Vnz54s9bmbjR49Wp9//rlWrlyp+vXrp5kfExOjLVu22KvQV65ccZhvs9lu+z+eec3N6yZJq1evlru7u6pWrWpv2759u/755x9JUtOmTeXu7q4lS5bY569atUqJiYl6/PHHcz7pXDJ58mTVqFEj3X3k2LFj+v333+3TN2/Hf/75RwcPHswX+8jNypUrp0qVKjl8R5w5c0a//fabw3fEX3/9pb1792apz93spZde0qxZs7RmzRrVrl07zfzo6Ght2bLFPi7JzftMUlKSNm7cmC/2mYy+V7y9vR3Gqfn111918uRJSVKzZs2UlJSklStX2ucvXrxYVqtVjz32WM4njQLJ2eNZQToGxsfHq02bNrp48aLWrl2b7u1FBekYmN732c8//+ywbpcvX9aWLVsUFxcnSWrevLm2b9+us2fP2mMWLVqke+65x/5Dzd0uJSVF//vf/9S7d+90r9bYtWuX/Zar+Pj4NMNDrF69WpJUo0aNnE82lzl7PCtIx8DUopR0/bP39/dPE3P48GH7eFrGGPv/w1IdOnRIJ06cyJffK8YYrVmzxmHdYmNjtWXLFnts8+bNtWnTJsXGxtpjFi1apDp16qT7PZ1nuHLkdeQty5cvN25ubmbMmDFm4cKFplGjRqZ69eoOT4Dq0qWLeeihh7LU5271wQcfGIvFYj744AOzefNm+2vv3r32mBUrVjg8jaxPnz7m5ZdfNj/99JNZsGCBadOmjSlSpIj5/fffXbUa2Wbp0qXm8ccfN1OnTjUrV640b775pvH29jZvvvmmQ1xQUJDD08hee+01ExQUZKZOnWq+++47U6JECfP888/ndvo5Ji4uzhQqVMiMHz8+3fnDhg0zZcuWtU/XqFHDfPjhh2bFihVm6tSp5p577jH33nuvuXz5ci5lnH0iIiLM5s2bzeTJk40kM3PmTLN582aHR/r++OOPxt3d3YwdO9YsWLDAPPjgg+b+++93eFR0mzZtTLNmzbLUJy9KSEiwf0+UKVPG9OrVy2zevNns2bPHHjNq1Cjj5uZmvvjiC4fvlQMHDthjfvjhByPJvh2ffvppM2LECLNo0SIzb94807RpUxMYGJjmKYh50Z9//mk2b95sBg0aZEJCQuzrm3qMmD17tnniiSfM//73P7NixQozYsQI4+npaT744AOH5Xh5eZlx48bZp1944QUTGhpqZsyYYaZNm2aCgoLM8OHDc3XdUPA4czwrKMfAlJQU06xZM1O0aFGzcOFCh++zU6dO2ePy8zHwZi+//LIZOHCgmTdvnlm0aJHp0qWL8fLyMmvXrrXHpD7FNvXpaUlJSeb+++83Dz/8sFmwYIEZO3ascXNzMz/++KOrViPbLV26NN0n96aqUqWKGThwoDHm+pMsGzRoYL799luzatUqM3bsWFOkSBHzwgsv5GbK2eZWx0BjnDue5ZdjYFRUlNm8ebNZsGCBkWQ+//xzs3nzZnPixAljjDGJiYnmkUceMcWKFTNLly51+F6JjIy0L6dfv36mRo0axpjr517VqlUzn3zyiVm5cqX55ptvTLly5Uy9evXMtWvXXLKeWZG6fvfdd59p27at2bx5s8P/G59//nkzdOhQM3/+fPPTTz+Z9u3bm0KFCplff/3VHrN+/XojyYSHhxtjrj8Bs3r16ubRRx81CxcuNKNHjzZubm55/mmwFmPy0ePCcMfWr1+vSZMm6fz586pTp45GjBjhMKbSW2+9pTNnzujrr792us/daujQoek+3eLhhx/Wxx9/LOn6L6OvvPKKZs2apTJlyigpKUlTp07Vzz//rMTERNWoUUMvvfSSfTyFu92vv/6qadOm6Z9//lGZMmXUvXt3NW3a1CGmbdu2at++vf22NpvNpsmTJ2vRokWy2Wx64okn9MILL9jHqrrb/fzzz3rnnXe0cOFCBQYGppn/+eefa/PmzZo3b54k6dy5c/riiy/0+++/y8/PT4888ogGDhxoH0/hbjJz5kxNnDgxTftrr72m9u3b26dXrVqlyZMn6+LFi6pXr55GjBihgIAA+/wRI0YoMTFRn376qdN98qJz587pqaeeStNeq1YtffXVV5Kk5557TocOHUoT8/jjj+utt96SJK1du1ZjxozR4sWLFRgYqISEBH399ddav369jDGqVauWXnrppbvie/Zf//qX/Yk6N5ozZ45KlSolSdqwYYO+++47nTx5UuXKlVOvXr3UoEEDh/hmzZqpb9++6tGjh6Trv8BPnDhRy5Ytk8ViUbt27fT888/bx6oCcoIzx7OCcgxMTEzM8OqMYcOGqXPnzpLy9zHwZjabTd9//72WLVumK1euqGrVqhoyZIjKlStnjzl48KD69euniRMn6t5775V0/er7Dz74QDt27FDRokXVv39/tWzZ0kVrkf3effddHT16VFOnTk13fo8ePVSnTh29+uqrkq4/Uezbb7/V4cOHVbp0aXXs2FFt27bNzZSzjTPHQGeOZ/nlGLhixQqNHTs2TXvfvn3Vt29fxcbGqk2bNun2HTlypH0/+OCDD7Rv3z7NmDFD0vUr67/44guFh4eraNGiatSokfr3728ftzSvSklJUePGjdO0ly5d2j6GVHJysqZPn66VK1fq2rVrql69uoYOHarSpUvb48PDwzV06FD973//s19tHh0drQ8++EDh4eEKCgrSoEGD0vyfLa+hMAUAAAAAAACXyNtlVQAAAAAAAORbFKYAAAAAAADgEhSmAAAAAAAA4BIUpgAAAAAAAOASFKYAAAAAAADgEhSmAAAAAAAA4BIUpgAAAAAAAOASFKYAIItmz56tqKgoV6cBAACQp0RGRmru3LmuTgPAXYbCFIB8LykpSXPmzNGxY8fSnR8VFaXZs2crLi7OqeV169ZNf/75Z3amCAAA4BIRERGaPXu2rl27lu783bt3a8mSJU4ta/fu3erevXt2pgegAKAwBSDf8/Dw0EcffaQxY8akO3/8+PF69dVXVbhw4VzODAAAwLU8PDzUs2dPLViwIN35zz33XIbzACA7UJgCUCD069dPP/74Y5qrolJSUjR9+nT16dNHbm5uWrRokWbPnq25c+dq69atGf56mOrKlSuaPXu2Ll++7NA+b948nT592qEtPj5ea9as0fLly3Xy5MnsWTEAAIA7EBoaqieeeEJTpkxJM2/Xrl3avXu3+vXrp5iYGM2ePVuzZ8/WTz/95NTV40eOHNGyZcsc2s6ePavZs2fLGOPQfubMGS1ZskQbNmxw+ip2APkDhSkABUL37t1lsVj0ww8/OLQvX75ckZGR6tu3ryRpxYoVWrhwoebNm6f+/furRo0aOnDgQIbLPXfunLp166bIyEiH9p49e2rXrl326TVr1qhcuXIaM2aMvvzyS91777169913s3ENAQAAbk///v21fv16HT9+3KF9ypQpqlq1qho2bKjY2FgtXLhQCxcu1PTp09W8eXO1atVKiYmJGS73559/1rBhwxza/vrrL3Xr1k0pKSn2tnfeeUfVqlXTl19+qdGjR6tSpUpas2ZNtq4jgLzL3dUJAEBu8Pf3V6dOnTR16lQNHDjQ3j5lyhQ99thjqlChgiRp0qRJDv0GDhyo1157zemxFdITHR2tp59+WtOnT1eHDh0kSX///bfuv/9+NWvWTPXr17/tZQMAANypJ554QiVKlNC0adP09ttvS5KuXbumWbNm6Y033pAklS1bVrNnz7b3uXLliurVq6dvv/1WgwcPvu33XrJkiSZMmKA9e/aoTJkykq6fn/Xs2VPHjh2Tt7f3HawZgLsBhSkABUa/fv3UuHFj7d27VzVr1lRUVJSWLVumGTNmOMQdOnRIhw4dUlxcnPz9/bVw4cI7et8FCxbIzc1NycnJmjdvniTJGKPSpUtrw4YNFKYAAIBLubm5qXfv3vrf//6nMWPGyGq1av78+bpy5Yp69eplj7PZbNq1a5ciIiKUkJCgsLAw/fbbb3dUmJo2bZpq1Kih3377Tdu3b5cxRu7u7oqMjNT+/ftVp06d7FhFAHkYhSkABcajjz6qypUra+rUqfrvf/+rGTNmyNfXVx07dpQkJScnq0uXLlqzZo0eeughBQQE6Ny5czp79uwdve/x48dlsVj0448/OrTfd999KlWq1B0tGwAAIDv069dP77//vtasWaMWLVpo6tSpevLJJ1WsWDFJ0okTJ9S8eXMlJiaqRo0a8vX11YkTJ2S13tnoMMePH1dCQkKa86QuXbrc8bIB3B0oTAEoUPr27atPPvlE77//vqZOnapnn31WXl5ekqTFixdr/fr1Onr0qIKCgiRJs2fP1oYNGzJcXuoJk81ms7clJycrOTnZPu3n5yc3NzeHy98BAADykooVK6px48aaOnWq7rnnHq1fv15Lly61zx87dqwqVKigFStWyGKxSJL69OmTZpzNG1mtVodzJElpHizj5+enMmXKpLmCHUDBQQkaQIHSp08fXbx4USNHjtSBAwfUv39/+7zIyEgFBwfbi1KS0vx6d7PQ0FBZrVYdPnzY3rZ582aHAT1btmypc+fOpXnU8rVr13ThwoU7XSUAAIBs0b9/fy1cuFAff/yxSpUqpZYtW9rnRUZGqnLlyvai1OXLl7Vq1apMl1eqVCmdOXNGV65csbetX7/eIaZVq1ZatGiRzpw549B+6tSpO10dAHcJrpgCUKAUL15cbdu21aeffqp69eqpVq1a9nktW7bUq6++qgEDBujhhx/WqlWrtHbt2kyX5+npqa5du+qll17SP//8o5iYGE2fPt3h0vM6dero3//+t7p3767BgwerevXqOnr0qH788UfNnj1bgYGBOba+AAAAznr66ac1ZMgQffXVV3rzzTfl5uZmn9ehQwe99NJLCg0NVUBAgL755ps0Vz/drGnTpgoODlbnzp3VqVMn7d69O82PfsOGDdPSpUv10EMP6cUXX1RgYKB27dqlTZs26a+//sqR9QSQt3DFFIACZ/jw4erSpYv9KTOpKlasqK1bt6pw4cLavHmz6tevrxUrVqhLly4OcV26dFFoaKh9etq0aRoyZIh27NihpKQkrV27Vj169HAYP2rs2LFavXq1jDHasmWLfP+/du7YxkEgCKDoXGaQXIA7IHRAAXRBbpfhEIkGqIAmHEJKhEQF0AmXneQGbk6699LdYDdbfa3meo1pmgz0BAD+jMvlEl3XRdu28Xw+P9Yej0eM4xjHccS2bfF6vWIYhmia5mfP7Xb7eDeVZRnLssT9fo9lWaKqqni/3x/zo4qiiHmeo+/72Pc91nWNuq5jXddfuTOQ7+s8zzP7EAAAAAD8P35MAQAAAJBCmAIAAAAghTAFAAAAQAphCgAAAIAUwhQAAAAAKYQpAAAAAFIIUwAAAACkEKYAAAAASCFMAQAAAJBCmAIAAAAghTAFAAAAQAphCgAAAIAU32OwEUf8fQ6NAAAAAElFTkSuQmCC", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, axes = plt.subplots(1, 2, figsize=(12, 4.5))\n", - "\n", - "axes[0].bar(\n", - " bin_edges[:-1], counts, width=widths, align=\"edge\",\n", - " color=\"#52789c\", edgecolor=\"white\",\n", - ")\n", - "axes[0].set_title(\"Counts: height = observations\")\n", - "axes[0].set_xlabel(\"Value\")\n", - "axes[0].set_ylabel(\"Count\")\n", - "\n", - "axes[1].bar(\n", - " bin_edges[:-1], density, width=widths, align=\"edge\",\n", - " color=\"#f16e00\", edgecolor=\"white\",\n", - ")\n", - "axes[1].set_title(\"Density: area = probability\")\n", - "axes[1].set_xlabel(\"Value\")\n", - "axes[1].set_ylabel(\"Density\")\n", - "\n", - "fig.suptitle(\"Same adaptive bins, different questions\")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "2bce5d17", - "metadata": {}, - "source": [ - "With unequal widths, raw count heights are not directly comparable: a wide bin\n", - "has more room to collect observations. Density corrects for that extra width.\n", - "\n", - "Use **counts** when totals matter, such as workload or sample size. Use\n", - "**density** when reading distribution shape or comparing samples of different\n", - "sizes.\n", - "\n", - "## The key example: equal counts, unequal widths\n", - "\n", - "Imagine two bins that each contain 50 of 100 observations. Their widths are 1\n", - "and 4. Both count heights are 50, but their densities are 0.5 and 0.125. Values\n", - "are therefore **four times more concentrated** in the narrow bin.\n", - "\n", - "In the density view, the bars have different heights but equal areas:\n", - "\n", - "- narrow bin: $0.5 \\times 1 = 0.5$,\n", - "- wide bin: $0.125 \\times 4 = 0.5$.\n", - "\n", - "Each area correctly shows that the bin contains half of the observations." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "c5fe66ce", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "example_left_edges = np.array([0.0, 2.0])\n", - "example_widths = np.array([1.0, 4.0])\n", - "example_counts = np.array([50, 50])\n", - "example_density = example_counts / (example_counts.sum() * example_widths)\n", - "\n", - "fig, axes = plt.subplots(1, 2, figsize=(11, 4.5), sharex=True)\n", - "\n", - "count_bars = axes[0].bar(\n", - " example_left_edges, example_counts, width=example_widths, align=\"edge\",\n", - " color=\"#52789c\", edgecolor=\"white\",\n", - ")\n", - "axes[0].bar_label(count_bars, labels=[\"50\", \"50\"], padding=3)\n", - "axes[0].set_title(\"Counts: equal heights\")\n", - "axes[0].set_xlabel(\"Value\")\n", - "axes[0].set_ylabel(\"Count\")\n", - "axes[0].set_ylim(0, 60)\n", - "\n", - "density_bars = axes[1].bar(\n", - " example_left_edges, example_density, width=example_widths, align=\"edge\",\n", - " color=\"#f16e00\", edgecolor=\"white\",\n", - ")\n", - "axes[1].bar_label(density_bars, labels=[\"0.500\", \"0.125\"], padding=3)\n", - "axes[1].set_title(\"Density: equal areas\")\n", - "axes[1].set_xlabel(\"Value\")\n", - "axes[1].set_ylabel(\"Density\")\n", - "axes[1].set_ylim(0, 0.6)\n", - "\n", - "fig.suptitle(\"Two bins, 50 observations each\")\n", - "plt.tight_layout()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "e3adade6", - "metadata": {}, - "source": [ - "## Reading variable-width histograms\n", - "\n", - "| Question | Use | What to compare |\n", - "| --- | --- | --- |\n", - "| How many observations? | Counts (`density=False`) | Bar heights |\n", - "| What fraction of observations? | Counts divided by $N$, or density | Bar areas |\n", - "| Where are values concentrated? | Density (`density=True`, the Khisto default) | Bar heights |\n", - "\n", - "Before interpreting a histogram:\n", - "\n", - "1. Notice whether bin widths differ.\n", - "2. Identify whether the y-axis shows count or density.\n", - "3. For density, read each bar's **area** as probability.\n", - "\n", - "## Go further\n", - "\n", - "Continue with [Histograms - Khiops](https://khiops.org/learn/histograms/) for\n", - "the principles behind Khiops histograms, from the simplest to the most complex." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "khisto-python (3.12.3)", - "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": "3.12.3" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/docs/counts_vs_density.rst b/docs/counts_vs_density.rst new file mode 100644 index 0000000..a7d4fd6 --- /dev/null +++ b/docs/counts_vs_density.rst @@ -0,0 +1,16 @@ +Counts can mislead with variable-width bins +=========================================== + +Both columns show the same 500 observations with two different binning schemes. +With equal-width bins, counts and density have the same shape. With variable-width +bins, raw counts favor wider intervals and can distort the visual comparison. + +.. image:: images/counts-vs-density.png + +With equal-width bins, taller bars indicate a greater probability of falling +within that interval. When bin widths vary, height alone is not enough: +probability is represented by the bar's area, calculated as density multiplied +by bin width. + +For a detailed introduction to density and variable-width bins, see the +`Khiops histogram tutorial `_. \ No newline at end of file diff --git a/docs/images/counts-vs-density.png b/docs/images/counts-vs-density.png new file mode 100644 index 0000000000000000000000000000000000000000..c5f57a9cd77ae04eff06429bc33edb4e211700b0 GIT binary patch literal 109041 zcmdqJXH=D0*DZ*pXsM`WDPjV(1QAeBL6B^fWjG+Bg)Hr-TkLWkK1?j8E@4q)bTv$*?aA^=A3J;=kfJxm$z-%zlDZ| zW*gvEa5uK$5g*=%}6(SnBNKoa?9o!b5v z2Wi&P&`|#TUB)(Gq{GH`cf(4_M0KQm?av#2elyqUe)ysr?e$-1H*g$}ww-DHCAX~+x!#zzkjB=_RDpA%fDZy_wJB& zT6^8uwE^q&&nw_?$WQ!>ZCR{cyVuiBqGhqc} zo{x+ej&>EQ`}3JJ7C0?hQY&7&8P{Ia>#qt_$}|oXccJA|P|@D&`ixO9vT$WV{IUm= zth2LoOxs{-PFbxRJx6_vG^^E6Jw@GR+3F(Sriiz?)l3$L3Kqw5={pXpgb2+mo4#T4 zV$jbmm)2eie($`VhGs0}5!SfxI4kSrV8_YFBCAUl3F?JvEiEl_gDWd5`W-pxoY}p< 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100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -28,6 +28,12 @@ Khisto — Histograms that fit your data Get started ----------- +.. admonition:: Density by default + :class: important + + Unlike NumPy and Matplotlib, Khisto uses density by default. + :doc:`Learn how to read variable-width histograms `. + .. div:: install-cmd .. code-block:: bash @@ -82,7 +88,7 @@ Get started :link: counts_vs_density :link-type: doc - Learn how bin width changes the meaning of bar height and area. + See why counts mislead when bins have different widths. .. grid-item-card:: :octicon:`info;1.5em` Histograms - Khiops :link: https://khiops.org/learn/histograms/ diff --git a/scripts/generate_distribution_examples.py b/scripts/generate_distribution_examples.py index 9942102..7a57ab6 100644 --- a/scripts/generate_distribution_examples.py +++ b/scripts/generate_distribution_examples.py @@ -42,6 +42,85 @@ def save_gaussian_figure(data: np.ndarray, output_path: Path) -> None: plt.close(fig) +def save_counts_density_comparison_figure(output_path: Path) -> None: + equal_edges = np.array([0, 10, 20, 30, 40]) + equal_counts = np.array([90, 110, 100, 200]) + variable_edges = np.array([0, 30, 40]) + variable_counts = np.array([300, 200]) + total_count = equal_counts.sum() + + fig, axes = plt.subplots(2, 2, figsize=(9, 5.5), sharex=True) + configurations = ( + (equal_edges, equal_counts, "Equal-width bins"), + (variable_edges, variable_counts, "Variable-width bins"), + ) + for column, (edges, counts, title) in enumerate(configurations): + widths = np.diff(edges) + densities = counts / (total_count * widths) + colors = ["darkorange" if edge >= 30 else "steelblue" for edge in edges[:-1]] + count_bars = axes[0, column].bar( + edges[:-1], counts, width=widths, align="edge", color=colors, + edgecolor="white", + ) + density_bars = axes[1, column].bar( + edges[:-1], densities, width=widths, align="edge", color=colors, + edgecolor="white", + ) + axes[0, column].bar_label(count_bars, labels=[str(count) for count in counts], padding=3) + axes[1, column].bar_label( + density_bars, + labels=[f"{density:.3f}" for density in densities], + padding=3, + ) + axes[0, column].set_title(title) + for row in range(2): + axes[row, column].set_xticks([0, 10, 20, 30, 40]) + axes[row, column].tick_params(axis="x", labelbottom=True) + axes[row, column].set_xlabel("Value") + axes[0, column].set_ylim(0, 350) + axes[1, column].set_ylim(0, 0.048) + + axes[0, 0].set_ylabel("Count") + axes[1, 0].set_ylabel("Density") + axes[0, 0].text( + 15, + 165, + "Small local fluctuation", + ha="center", + ) + axes[0, 1].text( + 15, + 245, + "Counts suggest\nthis bin dominates", + color="white", + ha="center", + va="center", + weight="bold", + ) + axes[1, 1].text( + 15, + 0.012, + "Fluctuation smoothed out\nin the wider bin", + color="white", + ha="center", + va="center", + weight="bold", + ) + axes[1, 1].annotate( + "30–40 is twice \nas dense as 0-30", + xy=(35, 0.034), + xytext=(15, 0.034), + arrowprops={"arrowstyle": "->", "color": "#333333"}, + ha="center", + va="center", + weight="bold", + ) + fig.suptitle("Same 500 observations, two binning choices") + fig.tight_layout() + fig.savefig(output_path, dpi=180) + plt.close(fig) + + def save_pareto_figure(data: np.ndarray, output_path: Path) -> None: fig, ax = plt.subplots(figsize=(7, 4.5)) hist(data, density=True, ax=ax, color="darkorange", edgecolor="white", linewidth=0.8) @@ -64,6 +143,9 @@ def main() -> None: pareto_data = generate_pareto_data() save_gaussian_figure(gaussian_data, images_dir / "gaussian-quick-start.png") + save_counts_density_comparison_figure( + images_dir / "counts-vs-density.png" + ) save_pareto_figure(pareto_data, images_dir / "pareto-quick-start.png") print(f"Gaussian sample: size={gaussian_data.size}, mean={gaussian_data.mean():.4f}, std={gaussian_data.std():.4f}") @@ -72,6 +154,7 @@ def main() -> None: f"size={pareto_data.size}, min={pareto_data.min():.4f}, max={pareto_data.max():.4f}, shape={PARETO_SHAPE:.1f}" ) print(f"Wrote {images_dir / 'gaussian-quick-start.png'}") + print(f"Wrote {images_dir / 'counts-vs-density.png'}") print(f"Wrote {images_dir / 'pareto-quick-start.png'}") From d1060c826e99a8a54455f98f56d2c3f0ab724235 Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Fri, 11 Sep 2026 10:48:59 +0200 Subject: [PATCH 6/9] =?UTF-8?q?docs:=20relier=20les=20pages=20sources=20?= =?UTF-8?q?=C3=A0=20GitHub?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/conf.py | 3 +++ 1 file changed, 3 insertions(+) diff --git a/docs/conf.py b/docs/conf.py index 38c45d1..62ed8d2 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -72,6 +72,9 @@ html_theme = 'furo' html_theme_options = { + "source_repository": "https://github.com/KhiopsML/khisto-python/", + "source_branch": "main", + "source_directory": "docs/", "light_css_variables": { "color-brand-primary": "#FF7900", "color-brand-content": "#F16E00", From e0a71a499bc4545cd0de81bfb49cf51fb887ac13 Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Mon, 14 Sep 2026 15:10:55 +0200 Subject: [PATCH 7/9] fix(review): appliquer les retours de la PR 31 --- CHANGELOG.md | 11 ----------- README.md | 5 ++--- docs/counts_vs_density.rst | 19 +++++++++++++++---- docs/images/counts-vs-density.png | Bin 109041 -> 124084 bytes docs/index.rst | 2 +- pyproject.toml | 5 ++--- scripts/generate_distribution_examples.py | 22 +++++++++++++++++----- 7 files changed, 37 insertions(+), 27 deletions(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index c576703..663d9d4 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,16 +2,6 @@ All notable changes to Khisto are documented in this file. -## [1.0.2] - 2026-09-09 - -### Added - -- Explain counts, densities, and variable-width bins in a dedicated guide. - -### Changed - -- Highlight and update links to the official Khiops histogram documentation. - ## [1.0.1] - 2026-09-07 ### Fixed @@ -30,5 +20,4 @@ First stable release. - Prebuilt wheels for Linux, macOS, and Windows. - Public API documentation and usage examples. -[1.0.2]: https://github.com/KhiopsML/khisto-python/compare/v1.0.1...v1.0.2 [1.0.1]: https://github.com/KhiopsML/khisto-python/compare/v1.0.0...v1.0.1 diff --git a/README.md b/README.md index d9c58d4..64bff31 100644 --- a/README.md +++ b/README.md @@ -55,9 +55,8 @@ plt.show() ## Development On Windows, install [Visual Studio Build Tools 2022](https://visualstudio.microsoft.com/visual-cpp-build-tools/) -with the **Desktop development with C++** workload. Then run the commands below -from an **x64 Native Tools Command Prompt for VS 2022** and verify that the -compiler is available with `where cl`. +with the **Desktop development with C++** workload before running the commands +below. ```bash # Clone repository diff --git a/docs/counts_vs_density.rst b/docs/counts_vs_density.rst index a7d4fd6..508a447 100644 --- a/docs/counts_vs_density.rst +++ b/docs/counts_vs_density.rst @@ -1,5 +1,5 @@ -Counts can mislead with variable-width bins -=========================================== +Understanding counts with variable-width bins +============================================= Both columns show the same 500 observations with two different binning schemes. With equal-width bins, counts and density have the same shape. With variable-width @@ -12,5 +12,16 @@ within that interval. When bin widths vary, height alone is not enough: probability is represented by the bar's area, calculated as density multiplied by bin width. -For a detailed introduction to density and variable-width bins, see the -`Khiops histogram tutorial `_. \ No newline at end of file +Note that variable-width bins are ideal for unbalanced distributions and outliers, +as shown in `Histograms - Khiops `_. + +Reading variable-width histograms +--------------------------------- + +.. csv-table:: + :header: "Question", "Use", "What to compare" + :widths: 35, 35, 30 + + "How many observations?", "Counts (``density=False``)", "Bar heights" + "What fraction of observations?", "Counts divided by :math:`N`, or density", "Bar areas" + "Where are values concentrated?", "Density (``density=True``, the Khisto default)", "Bar heights" \ No newline at end of file diff --git a/docs/images/counts-vs-density.png b/docs/images/counts-vs-density.png index 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a/docs/index.rst b/docs/index.rst index 8c2a9c9..cc53208 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -112,4 +112,4 @@ Get started :hidden: Demo - Counts, density, and bin widths + Counts vs density diff --git a/pyproject.toml b/pyproject.toml index e7ce6fe..2479c45 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -1,6 +1,6 @@ [project] name = "khisto" -version = "1.0.2" +version = "1.0.1" description = "Optimal histogram visualization using the Khiops algorithm" readme = "README.md" license = "BSD-3-Clause-Clear" @@ -131,7 +131,6 @@ ignore = [ [tool.scikit-build] wheel.py-api = "py3" # We specify full compatibility with all Python 3 releases cmake.version = "CMakeLists.txt" # Read CMake minimal version from file -cmake.args = ["-G", "Ninja"] # Generator specification and build configuration # CMake variables # Build khisto binary in Release mode for better performance, as it is not intended for debugging @@ -143,7 +142,7 @@ cmake.define.BUILD_LEX_YACC = false cmake.define.BUILD_JARS = false cmake.define.GENERATE_VIEWS = false cmake.define.C11 = true -ninja.make-fallback = false +ninja.make-fallback = true build.targets = ["khisto"] # Build only khisto install.components = ["KHISTO"] # Only install KHISTO component in wheel diff --git a/scripts/generate_distribution_examples.py b/scripts/generate_distribution_examples.py index 7a57ab6..ed5cf40 100644 --- a/scripts/generate_distribution_examples.py +++ b/scripts/generate_distribution_examples.py @@ -8,10 +8,10 @@ import matplotlib.pyplot as plt import numpy as np +from matplotlib.lines import Line2D from khisto.matplotlib import hist - SEED = 42 SAMPLE_SIZE = 10_000 PARETO_SHAPE = 3.0 @@ -51,8 +51,8 @@ def save_counts_density_comparison_figure(output_path: Path) -> None: fig, axes = plt.subplots(2, 2, figsize=(9, 5.5), sharex=True) configurations = ( - (equal_edges, equal_counts, "Equal-width bins"), - (variable_edges, variable_counts, "Variable-width bins"), + (equal_edges, equal_counts, "Without Khisto\nEqual-width bins"), + (variable_edges, variable_counts, "With Khisto\nVariable-width bins"), ) for column, (edges, counts, title) in enumerate(configurations): widths = np.diff(edges) @@ -91,11 +91,12 @@ def save_counts_density_comparison_figure(output_path: Path) -> None: axes[0, 1].text( 15, 245, - "Counts suggest\nthis bin dominates", + "Counts apply to the whole interval;\ndo not rely on rectangle area", color="white", ha="center", va="center", weight="bold", + fontsize=9, ) axes[1, 1].text( 15, @@ -107,7 +108,7 @@ def save_counts_density_comparison_figure(output_path: Path) -> None: weight="bold", ) axes[1, 1].annotate( - "30–40 is twice \nas dense as 0-30", + "bin 30–40 is twice \nas dense as bin 0-30", xy=(35, 0.034), xytext=(15, 0.034), arrowprops={"arrowstyle": "->", "color": "#333333"}, @@ -117,6 +118,17 @@ def save_counts_density_comparison_figure(output_path: Path) -> None: ) fig.suptitle("Same 500 observations, two binning choices") fig.tight_layout() + left_column_right = axes[0, 0].get_position().x1 + right_column_left = axes[0, 1].get_position().x0 + separator_x = (left_column_right + right_column_left) / 2 + fig.add_artist(Line2D( + [separator_x, separator_x], + [axes[1, 0].get_position().y0, axes[0, 0].get_position().y1], + transform=fig.transFigure, + color="#777777", + linewidth=1, + linestyle="--", + )) fig.savefig(output_path, dpi=180) plt.close(fig) From bc514f57481420ffeb67a28e53a76ab927e77e64 Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Mon, 14 Sep 2026 15:51:43 +0200 Subject: [PATCH 8/9] =?UTF-8?q?docs(demo):=20tracer=20les=20r=C3=A9solutio?= =?UTF-8?q?ns=20avec=20hist?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/demo.ipynb | 66 ++++++++++++++++++++++++++++++------------------- 1 file changed, 40 insertions(+), 26 deletions(-) diff --git a/docs/demo.ipynb b/docs/demo.ipynb index 852181b..f9e75e5 100644 --- a/docs/demo.ipynb +++ b/docs/demo.ipynb @@ -43,7 +43,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 28, "id": "d9b9b33b", "metadata": {}, "outputs": [], @@ -70,7 +70,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 29, "id": "9e8eff47", "metadata": {}, "outputs": [ @@ -112,7 +112,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 30, "id": "e8a48420", "metadata": {}, "outputs": [ @@ -161,7 +161,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 31, "id": "8b183e7b", "metadata": {}, "outputs": [ @@ -202,7 +202,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 32, "id": "c8ed6f75", "metadata": {}, "outputs": [ @@ -250,7 +250,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 33, "id": "48c3b0aa", "metadata": {}, "outputs": [ @@ -302,7 +302,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 34, "id": "d0e40b1c", "metadata": {}, "outputs": [ @@ -331,7 +331,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 35, "id": "55ee75b7", "metadata": {}, "outputs": [ @@ -354,7 +354,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 36, "id": "33828aaa", "metadata": {}, "outputs": [ @@ -398,7 +398,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 37, "id": "247c1571", "metadata": {}, "outputs": [ @@ -408,7 +408,7 @@ "Text(0, 0.5, 'Cumulative probability')" ] }, - "execution_count": 22, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" }, @@ -446,7 +446,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 38, "id": "03285190", "metadata": {}, "outputs": [ @@ -486,13 +486,13 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 39, "id": "b93b2015", "metadata": {}, "outputs": [ { "data": { - "image/png": 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" ] @@ -502,25 +502,39 @@ } ], "source": [ - "# Each level carries densities, so we visualize the series as densities\n", - "n_levels = min(6, len(results))\n", + "# Visualize selected resolutions through the public plotting API\n", + "best_result = next(result for result in results if result.is_best)\n", + "coarser_limits = sorted(\n", + " {\n", + " len(result)\n", + " for result in results\n", + " if result.granularity < best_result.granularity\n", + " and len(result) < len(best_result)\n", + " }\n", + ")\n", + "max_bins_values = coarser_limits[-5:] + [None]\n", + "\n", "fig, axes = plt.subplots(2, 3, figsize=(15, 8))\n", "axes = axes.flatten()\n", "\n", - "for i, result in enumerate(results[n_levels:]):\n", - " ax = axes[i]\n", - " ax.stairs(result.densities, result.bin_edges, fill=True, alpha=0.7,\n", - " color=\"steelblue\")\n", - " title = f\"Granularity {result.granularity} ({len(result.frequencies)} bins)\"\n", - " if result.is_best:\n", - " title += \" — BEST\"\n", + "for ax, max_bins in zip(axes, max_bins_values, strict=False):\n", + " density, _, _ = hist(\n", + " data,\n", + " max_bins=max_bins,\n", + " density=True,\n", + " ax=ax,\n", + " color=\"steelblue\",\n", + " alpha=0.7,\n", + " )\n", + " if max_bins is None:\n", + " ax.set_title(f\"Best histogram ({len(density)} bins)\")\n", " ax.set_facecolor(\"aliceblue\")\n", - " ax.set_title(title)\n", + " else:\n", + " ax.set_title(f\"max_bins={max_bins} ({len(density)} bins selected)\")\n", " ax.set_xlabel(\"Value\")\n", " ax.set_ylabel(\"Density\")\n", "\n", - "# Hide any unused axes\n", - "for ax in axes[n_levels:]:\n", + "for ax in axes[len(max_bins_values):]:\n", " ax.set_visible(False)\n", "\n", "plt.tight_layout()\n", From e8636d9e7fb48489e5da86972714fe1dabb5a00f Mon Sep 17 00:00:00 2001 From: Elouen Ginat Date: Mon, 14 Sep 2026 18:28:10 +0200 Subject: [PATCH 9/9] =?UTF-8?q?docs(histogramme):=20retirer=20le=20s=C3=A9?= =?UTF-8?q?parateur=20du=20graphique?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/counts_vs_density.rst | 4 ++-- docs/images/counts-vs-density.png | Bin 124084 -> 121414 bytes scripts/generate_distribution_examples.py | 12 ------------ 3 files changed, 2 insertions(+), 14 deletions(-) diff --git a/docs/counts_vs_density.rst b/docs/counts_vs_density.rst index 508a447..a0cbf6a 100644 --- a/docs/counts_vs_density.rst +++ b/docs/counts_vs_density.rst @@ -1,5 +1,5 @@ -Understanding counts with variable-width bins -============================================= +Counts vs Density +================= Both columns show the same 500 observations with two different binning schemes. With equal-width bins, counts and density have the same shape. 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save_counts_density_comparison_figure(output_path: Path) -> None: ) fig.suptitle("Same 500 observations, two binning choices") fig.tight_layout() - left_column_right = axes[0, 0].get_position().x1 - right_column_left = axes[0, 1].get_position().x0 - separator_x = (left_column_right + right_column_left) / 2 - fig.add_artist(Line2D( - [separator_x, separator_x], - [axes[1, 0].get_position().y0, axes[0, 0].get_position().y1], - transform=fig.transFigure, - color="#777777", - linewidth=1, - linestyle="--", - )) fig.savefig(output_path, dpi=180) plt.close(fig)