{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pooled Classification\n",
    "\n",
    "A common workflow with longitudinal spatial data is to apply the same classification scheme to an attribute over different time periods. More specifically, one would like to keep the class breaks the same over each period and examine how the mass of the distribution changes over these classes in the different periods.\n",
    "\n",
    "The `Pooled` classifier supports this workflow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:41.941529Z",
     "start_time": "2022-11-05T19:18:40.603589Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:26.436870Z",
     "iopub.status.busy": "2025-07-11T20:09:26.436634Z",
     "iopub.status.idle": "2025-07-11T20:09:27.889059Z",
     "shell.execute_reply": "2025-07-11T20:09:27.888847Z",
     "shell.execute_reply.started": "2025-07-11T20:09:26.436845Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2.9.1.dev9+gde74d6f.d20250614'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "import mapclassify\n",
    "\n",
    "mapclassify.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample Data\n",
    "We construct a synthetic dataset composed of 20 cross-sectional units at three time points. Here the mean of the series is increasing over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:41.949728Z",
     "start_time": "2022-11-05T19:18:41.945010Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.889460Z",
     "iopub.status.busy": "2025-07-11T20:09:27.889336Z",
     "iopub.status.idle": "2025-07-11T20:09:27.891484Z",
     "shell.execute_reply": "2025-07-11T20:09:27.891297Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.889453Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 3)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 20\n",
    "data = numpy.array([numpy.arange(n) + i * n for i in range(1, 4)]).T\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:41.955945Z",
     "start_time": "2022-11-05T19:18:41.951635Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.891751Z",
     "iopub.status.busy": "2025-07-11T20:09:27.891690Z",
     "iopub.status.idle": "2025-07-11T20:09:27.893577Z",
     "shell.execute_reply": "2025-07-11T20:09:27.893379Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.891745Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20, 40, 60],\n",
       "       [21, 41, 61],\n",
       "       [22, 42, 62],\n",
       "       [23, 43, 63],\n",
       "       [24, 44, 64],\n",
       "       [25, 45, 65],\n",
       "       [26, 46, 66],\n",
       "       [27, 47, 67],\n",
       "       [28, 48, 68],\n",
       "       [29, 49, 69],\n",
       "       [30, 50, 70],\n",
       "       [31, 51, 71],\n",
       "       [32, 52, 72],\n",
       "       [33, 53, 73],\n",
       "       [34, 54, 74],\n",
       "       [35, 55, 75],\n",
       "       [36, 56, 76],\n",
       "       [37, 57, 77],\n",
       "       [38, 58, 78],\n",
       "       [39, 59, 79]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Default: Quintiles\n",
    "The default is to apply a [vec](https://en.wikipedia.org/wiki/Vectorization_(mathematics)) operator to the data matrix and treat the observations as a single collection. Here the quantiles of the pooled data are obtained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:41.965023Z",
     "start_time": "2022-11-05T19:18:41.957991Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.893896Z",
     "iopub.status.busy": "2025-07-11T20:09:27.893838Z",
     "iopub.status.idle": "2025-07-11T20:09:27.896375Z",
     "shell.execute_reply": "2025-07-11T20:09:27.896222Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.893889Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Classifier\n",
       "\n",
       "Pooled Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 31.80] |    12\n",
       "(31.80, 43.60] |     8\n",
       "(43.60, 55.40] |     0\n",
       "(55.40, 67.20] |     0\n",
       "(67.20, 79.00] |     0\n",
       "\n",
       "Pooled Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 31.80] |     0\n",
       "(31.80, 43.60] |     4\n",
       "(43.60, 55.40] |    12\n",
       "(55.40, 67.20] |     4\n",
       "(67.20, 79.00] |     0\n",
       "\n",
       "Pooled Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 31.80] |     0\n",
       "(31.80, 43.60] |     0\n",
       "(43.60, 55.40] |     0\n",
       "(55.40, 67.20] |     8\n",
       "(67.20, 79.00] |    12"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = mapclassify.Pooled(data)\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the class definitions are constant across the periods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:41.971895Z",
     "start_time": "2022-11-05T19:18:41.967042Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.896709Z",
     "iopub.status.busy": "2025-07-11T20:09:27.896648Z",
     "iopub.status.idle": "2025-07-11T20:09:27.898438Z",
     "shell.execute_reply": "2025-07-11T20:09:27.898270Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.896702Z"
    }
   },
   "outputs": [],
   "source": [
    "res = mapclassify.Pooled(data, k=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:41.978331Z",
     "start_time": "2022-11-05T19:18:41.974160Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.899550Z",
     "iopub.status.busy": "2025-07-11T20:09:27.899475Z",
     "iopub.status.idle": "2025-07-11T20:09:27.901214Z",
     "shell.execute_reply": "2025-07-11T20:09:27.901053Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.899543Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15,  5,  0,  0])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.col_classifiers[0].counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:41.984738Z",
     "start_time": "2022-11-05T19:18:41.980393Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.901580Z",
     "iopub.status.busy": "2025-07-11T20:09:27.901470Z",
     "iopub.status.idle": "2025-07-11T20:09:27.903176Z",
     "shell.execute_reply": "2025-07-11T20:09:27.903011Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.901574Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  0,  5, 15])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.col_classifiers[-1].counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:41.990334Z",
     "start_time": "2022-11-05T19:18:41.986702Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.903491Z",
     "iopub.status.busy": "2025-07-11T20:09:27.903432Z",
     "iopub.status.idle": "2025-07-11T20:09:27.905163Z",
     "shell.execute_reply": "2025-07-11T20:09:27.904974Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.903484Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15, 15, 15, 15])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.global_classifier.counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.001119Z",
     "start_time": "2022-11-05T19:18:41.997311Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.905412Z",
     "iopub.status.busy": "2025-07-11T20:09:27.905355Z",
     "iopub.status.idle": "2025-07-11T20:09:27.907365Z",
     "shell.execute_reply": "2025-07-11T20:09:27.907172Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.905405Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Classifier\n",
       "\n",
       "Pooled Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 34.75] |    15\n",
       "(34.75, 49.50] |     5\n",
       "(49.50, 64.25] |     0\n",
       "(64.25, 79.00] |     0\n",
       "\n",
       "Pooled Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 34.75] |     0\n",
       "(34.75, 49.50] |    10\n",
       "(49.50, 64.25] |    10\n",
       "(64.25, 79.00] |     0\n",
       "\n",
       "Pooled Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 34.75] |     0\n",
       "(34.75, 49.50] |     0\n",
       "(49.50, 64.25] |     5\n",
       "(64.25, 79.00] |    15"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract the pooled classification objects for each column."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.007476Z",
     "start_time": "2022-11-05T19:18:42.003714Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.907807Z",
     "iopub.status.busy": "2025-07-11T20:09:27.907737Z",
     "iopub.status.idle": "2025-07-11T20:09:27.910340Z",
     "shell.execute_reply": "2025-07-11T20:09:27.910143Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.907800Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 34.75] |    15\n",
       "(34.75, 49.50] |     5\n",
       "(49.50, 64.25] |     0\n",
       "(64.25, 79.00] |     0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c0, c1, c2 = res.col_classifiers\n",
    "c0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare to the unrestricted classifier for the first column..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.016243Z",
     "start_time": "2022-11-05T19:18:42.010510Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.910677Z",
     "iopub.status.busy": "2025-07-11T20:09:27.910620Z",
     "iopub.status.idle": "2025-07-11T20:09:27.912837Z",
     "shell.execute_reply": "2025-07-11T20:09:27.912653Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.910671Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 24.75] |     5\n",
       "(24.75, 29.50] |     5\n",
       "(29.50, 34.25] |     5\n",
       "(34.25, 39.00] |     5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapclassify.Quantiles(c0.y, k=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... and the last column comparisions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.024230Z",
     "start_time": "2022-11-05T19:18:42.018980Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.913187Z",
     "iopub.status.busy": "2025-07-11T20:09:27.913134Z",
     "iopub.status.idle": "2025-07-11T20:09:27.915033Z",
     "shell.execute_reply": "2025-07-11T20:09:27.914840Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.913181Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 34.75] |     0\n",
       "(34.75, 49.50] |     0\n",
       "(49.50, 64.25] |     5\n",
       "(64.25, 79.00] |    15"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.034362Z",
     "start_time": "2022-11-05T19:18:42.027227Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.915302Z",
     "iopub.status.busy": "2025-07-11T20:09:27.915242Z",
     "iopub.status.idle": "2025-07-11T20:09:27.917452Z",
     "shell.execute_reply": "2025-07-11T20:09:27.917276Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.915296Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[60.00, 64.75] |     5\n",
       "(64.75, 69.50] |     5\n",
       "(69.50, 74.25] |     5\n",
       "(74.25, 79.00] |     5"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapclassify.Quantiles(c2.y, k=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-default classifier: BoxPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.046090Z",
     "start_time": "2022-11-05T19:18:42.037414Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.917751Z",
     "iopub.status.busy": "2025-07-11T20:09:27.917691Z",
     "iopub.status.idle": "2025-07-11T20:09:27.920192Z",
     "shell.execute_reply": "2025-07-11T20:09:27.920005Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.917744Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Classifier\n",
       "\n",
       "Pooled BoxPlot\n",
       "\n",
       "    Interval       Count\n",
       "------------------------\n",
       "(  -inf,  -9.50] |     0\n",
       "( -9.50,  34.75] |    15\n",
       "( 34.75,  49.50] |     5\n",
       "( 49.50,  64.25] |     0\n",
       "( 64.25, 108.50] |     0\n",
       "\n",
       "Pooled BoxPlot\n",
       "\n",
       "    Interval       Count\n",
       "------------------------\n",
       "(  -inf,  -9.50] |     0\n",
       "( -9.50,  34.75] |     0\n",
       "( 34.75,  49.50] |    10\n",
       "( 49.50,  64.25] |    10\n",
       "( 64.25, 108.50] |     0\n",
       "\n",
       "Pooled BoxPlot\n",
       "\n",
       "    Interval       Count\n",
       "------------------------\n",
       "(  -inf,  -9.50] |     0\n",
       "( -9.50,  34.75] |     0\n",
       "( 34.75,  49.50] |     0\n",
       "( 49.50,  64.25] |     5\n",
       "( 64.25, 108.50] |    15"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = mapclassify.Pooled(data, classifier=\"BoxPlot\", hinge=1.5)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.054064Z",
     "start_time": "2022-11-05T19:18:42.048325Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.920544Z",
     "iopub.status.busy": "2025-07-11T20:09:27.920476Z",
     "iopub.status.idle": "2025-07-11T20:09:27.922486Z",
     "shell.execute_reply": "2025-07-11T20:09:27.922281Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.920537Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -9.5 ,  34.75,  49.5 ,  64.25, 108.5 ])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.col_classifiers[0].bins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.060428Z",
     "start_time": "2022-11-05T19:18:42.056889Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.922812Z",
     "iopub.status.busy": "2025-07-11T20:09:27.922756Z",
     "iopub.status.idle": "2025-07-11T20:09:27.924242Z",
     "shell.execute_reply": "2025-07-11T20:09:27.924055Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.922806Z"
    }
   },
   "outputs": [],
   "source": [
    "c0, c1, c2 = res.col_classifiers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.067574Z",
     "start_time": "2022-11-05T19:18:42.062869Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.924636Z",
     "iopub.status.busy": "2025-07-11T20:09:27.924571Z",
     "iopub.status.idle": "2025-07-11T20:09:27.926389Z",
     "shell.execute_reply": "2025-07-11T20:09:27.926225Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.924630Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c0.yb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.076215Z",
     "start_time": "2022-11-05T19:18:42.070735Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.926767Z",
     "iopub.status.busy": "2025-07-11T20:09:27.926702Z",
     "iopub.status.idle": "2025-07-11T20:09:27.928352Z",
     "shell.execute_reply": "2025-07-11T20:09:27.928166Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.926761Z"
    }
   },
   "outputs": [],
   "source": [
    "c00 = mapclassify.BoxPlot(c0.y, hinge=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.085022Z",
     "start_time": "2022-11-05T19:18:42.078938Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.928735Z",
     "iopub.status.busy": "2025-07-11T20:09:27.928618Z",
     "iopub.status.idle": "2025-07-11T20:09:27.930507Z",
     "shell.execute_reply": "2025-07-11T20:09:27.930321Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.928728Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c00.yb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.093521Z",
     "start_time": "2022-11-05T19:18:42.088235Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.930763Z",
     "iopub.status.busy": "2025-07-11T20:09:27.930695Z",
     "iopub.status.idle": "2025-07-11T20:09:27.933175Z",
     "shell.execute_reply": "2025-07-11T20:09:27.932986Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.930755Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BoxPlot\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "( -inf, -3.75] |     0\n",
       "(-3.75, 24.75] |     5\n",
       "(24.75, 29.50] |     5\n",
       "(29.50, 34.25] |     5\n",
       "(34.25, 62.75] |     5"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c00"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.100363Z",
     "start_time": "2022-11-05T19:18:42.095608Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.935748Z",
     "iopub.status.busy": "2025-07-11T20:09:27.935658Z",
     "iopub.status.idle": "2025-07-11T20:09:27.938444Z",
     "shell.execute_reply": "2025-07-11T20:09:27.938219Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.935741Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled BoxPlot\n",
       "\n",
       "    Interval       Count\n",
       "------------------------\n",
       "(  -inf,  -9.50] |     0\n",
       "( -9.50,  34.75] |    15\n",
       "( 34.75,  49.50] |     5\n",
       "( 49.50,  64.25] |     0\n",
       "( 64.25, 108.50] |     0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-default classifier: FisherJenks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.111872Z",
     "start_time": "2022-11-05T19:18:42.103537Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.938976Z",
     "iopub.status.busy": "2025-07-11T20:09:27.938786Z",
     "iopub.status.idle": "2025-07-11T20:09:27.941939Z",
     "shell.execute_reply": "2025-07-11T20:09:27.941747Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.938965Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Classifier\n",
       "\n",
       "Pooled FisherJenks\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 31.00] |    12\n",
       "(31.00, 43.00] |     8\n",
       "(43.00, 55.00] |     0\n",
       "(55.00, 67.00] |     0\n",
       "(67.00, 79.00] |     0\n",
       "\n",
       "Pooled FisherJenks\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 31.00] |     0\n",
       "(31.00, 43.00] |     4\n",
       "(43.00, 55.00] |    12\n",
       "(55.00, 67.00] |     4\n",
       "(67.00, 79.00] |     0\n",
       "\n",
       "Pooled FisherJenks\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 31.00] |     0\n",
       "(31.00, 43.00] |     0\n",
       "(43.00, 55.00] |     0\n",
       "(55.00, 67.00] |     8\n",
       "(67.00, 79.00] |    12"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = mapclassify.Pooled(data, classifier=\"FisherJenks\", k=5)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.119626Z",
     "start_time": "2022-11-05T19:18:42.113905Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.942365Z",
     "iopub.status.busy": "2025-07-11T20:09:27.942291Z",
     "iopub.status.idle": "2025-07-11T20:09:27.944501Z",
     "shell.execute_reply": "2025-07-11T20:09:27.944319Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.942358Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "FisherJenks\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[20.00, 23.00] |     4\n",
       "(23.00, 27.00] |     4\n",
       "(27.00, 31.00] |     4\n",
       "(31.00, 35.00] |     4\n",
       "(35.00, 39.00] |     4"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c0, c1, c2 = res.col_classifiers\n",
    "mapclassify.FisherJenks(c0.y, k=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-default classifier: MaximumBreaks\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.127177Z",
     "start_time": "2022-11-05T19:18:42.121621Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.944780Z",
     "iopub.status.busy": "2025-07-11T20:09:27.944718Z",
     "iopub.status.idle": "2025-07-11T20:09:27.946888Z",
     "shell.execute_reply": "2025-07-11T20:09:27.946706Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.944773Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20, 40, 60],\n",
       "       [10, 10, 10],\n",
       "       [22, 42, 62],\n",
       "       [23, 43, 63],\n",
       "       [24, 44, 64],\n",
       "       [25, 45, 65],\n",
       "       [26, 46, 66],\n",
       "       [27, 47, 67],\n",
       "       [28, 48, 68],\n",
       "       [29, 49, 10],\n",
       "       [30, 50, 70],\n",
       "       [31, 51, 71],\n",
       "       [32, 52, 72],\n",
       "       [33, 53, 73],\n",
       "       [34, 54, 74],\n",
       "       [35, 55, 75],\n",
       "       [36, 56, 76],\n",
       "       [37, 57, 77],\n",
       "       [38, 58, 78],\n",
       "       [39, 59, 79]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[1, 0] = 10\n",
    "data[1, 1] = 10\n",
    "data[1, 2] = 10\n",
    "data[9, 2] = 10\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.136098Z",
     "start_time": "2022-11-05T19:18:42.128885Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.947183Z",
     "iopub.status.busy": "2025-07-11T20:09:27.947120Z",
     "iopub.status.idle": "2025-07-11T20:09:27.949682Z",
     "shell.execute_reply": "2025-07-11T20:09:27.949473Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.947177Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Classifier\n",
       "\n",
       "Pooled MaximumBreaks\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 15.00] |     1\n",
       "(15.00, 21.00] |     1\n",
       "(21.00, 41.00] |    18\n",
       "(41.00, 61.00] |     0\n",
       "(61.00, 79.00] |     0\n",
       "\n",
       "Pooled MaximumBreaks\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 15.00] |     1\n",
       "(15.00, 21.00] |     0\n",
       "(21.00, 41.00] |     1\n",
       "(41.00, 61.00] |    18\n",
       "(61.00, 79.00] |     0\n",
       "\n",
       "Pooled MaximumBreaks\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 15.00] |     2\n",
       "(15.00, 21.00] |     0\n",
       "(21.00, 41.00] |     0\n",
       "(41.00, 61.00] |     1\n",
       "(61.00, 79.00] |    17"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = mapclassify.Pooled(data, classifier=\"MaximumBreaks\", k=5)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.143133Z",
     "start_time": "2022-11-05T19:18:42.138961Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.950163Z",
     "iopub.status.busy": "2025-07-11T20:09:27.950044Z",
     "iopub.status.idle": "2025-07-11T20:09:27.951905Z",
     "shell.execute_reply": "2025-07-11T20:09:27.951722Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.950156Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled MaximumBreaks\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 15.00] |     1\n",
       "(15.00, 21.00] |     1\n",
       "(21.00, 41.00] |    18\n",
       "(41.00, 61.00] |     0\n",
       "(61.00, 79.00] |     0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c0, c1, c2 = res.col_classifiers\n",
    "c0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.149335Z",
     "start_time": "2022-11-05T19:18:42.144915Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.952286Z",
     "iopub.status.busy": "2025-07-11T20:09:27.952216Z",
     "iopub.status.idle": "2025-07-11T20:09:27.953962Z",
     "shell.execute_reply": "2025-07-11T20:09:27.953796Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.952279Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 10, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,\n",
       "       37, 38, 39])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c0.y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.154525Z",
     "start_time": "2022-11-05T19:18:42.151983Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.954242Z",
     "iopub.status.busy": "2025-07-11T20:09:27.954185Z",
     "iopub.status.idle": "2025-07-11T20:09:27.955631Z",
     "shell.execute_reply": "2025-07-11T20:09:27.955443Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.954235Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.163717Z",
     "start_time": "2022-11-05T19:18:42.156794Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.955900Z",
     "iopub.status.busy": "2025-07-11T20:09:27.955844Z",
     "iopub.status.idle": "2025-07-11T20:09:27.958018Z",
     "shell.execute_reply": "2025-07-11T20:09:27.957842Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.955893Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Insufficient number of unique diffs. Breaks are random.\n"
     ]
    }
   ],
   "source": [
    "with warnings.catch_warnings():\n",
    "    warnings.filterwarnings(\"error\")\n",
    "    try:\n",
    "        mapclassify.MaximumBreaks(c0.y, k=5)\n",
    "    except UserWarning as e:\n",
    "        print(e)\n",
    "        with warnings.catch_warnings():\n",
    "            warnings.filterwarnings(\"ignore\")\n",
    "            mapclassify.MaximumBreaks(c0.y, k=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.174401Z",
     "start_time": "2022-11-05T19:18:42.166025Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.958377Z",
     "iopub.status.busy": "2025-07-11T20:09:27.958313Z",
     "iopub.status.idle": "2025-07-11T20:09:27.961102Z",
     "shell.execute_reply": "2025-07-11T20:09:27.960907Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.958370Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Classifier\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 62.80] |    20\n",
       "(62.80, 66.60] |     0\n",
       "(66.60, 71.40] |     0\n",
       "(71.40, 75.20] |     0\n",
       "(75.20, 79.00] |     0\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 62.80] |    20\n",
       "(62.80, 66.60] |     0\n",
       "(66.60, 71.40] |     0\n",
       "(71.40, 75.20] |     0\n",
       "(75.20, 79.00] |     0\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 62.80] |     4\n",
       "(62.80, 66.60] |     4\n",
       "(66.60, 71.40] |     4\n",
       "(71.40, 75.20] |     4\n",
       "(75.20, 79.00] |     4"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = mapclassify.Pooled(\n",
    "    data, classifier=\"UserDefined\", bins=mapclassify.Quantiles(data[:, -1]).bins\n",
    ")\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.181788Z",
     "start_time": "2022-11-05T19:18:42.176573Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.961595Z",
     "iopub.status.busy": "2025-07-11T20:09:27.961527Z",
     "iopub.status.idle": "2025-07-11T20:09:27.964196Z",
     "shell.execute_reply": "2025-07-11T20:09:27.964003Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.961587Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Quantiles\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 62.80] |     4\n",
       "(62.80, 66.60] |     4\n",
       "(66.60, 71.40] |     4\n",
       "(71.40, 75.20] |     4\n",
       "(75.20, 79.00] |     4"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapclassify.Quantiles(data[:, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.188254Z",
     "start_time": "2022-11-05T19:18:42.183388Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.964521Z",
     "iopub.status.busy": "2025-07-11T20:09:27.964460Z",
     "iopub.status.idle": "2025-07-11T20:09:27.966457Z",
     "shell.execute_reply": "2025-07-11T20:09:27.966222Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.964514Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([60, 10, 62, 63, 64, 65, 66, 67, 68, 10, 70, 71, 72, 73, 74, 75, 76,\n",
       "       77, 78, 79])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[:, -1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pinning the pooling\n",
    "\n",
    "Another option is to specify a specific subperiod as the definition for the classes in the pooling.\n",
    "\n",
    "### Pinning to the last period\n",
    "\n",
    "As an example, we can use the quintles from the third period to defined the pooled classifier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.198019Z",
     "start_time": "2022-11-05T19:18:42.190998Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.966763Z",
     "iopub.status.busy": "2025-07-11T20:09:27.966702Z",
     "iopub.status.idle": "2025-07-11T20:09:27.969472Z",
     "shell.execute_reply": "2025-07-11T20:09:27.969276Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.966756Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Classifier\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 62.80] |    20\n",
       "(62.80, 66.60] |     0\n",
       "(66.60, 71.40] |     0\n",
       "(71.40, 75.20] |     0\n",
       "(75.20, 79.00] |     0\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 62.80] |    20\n",
       "(62.80, 66.60] |     0\n",
       "(66.60, 71.40] |     0\n",
       "(71.40, 75.20] |     0\n",
       "(75.20, 79.00] |     0\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 62.80] |     4\n",
       "(62.80, 66.60] |     4\n",
       "(66.60, 71.40] |     4\n",
       "(71.40, 75.20] |     4\n",
       "(75.20, 79.00] |     4"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pinned = mapclassify.Pooled(\n",
    "    data, classifier=\"UserDefined\", bins=mapclassify.Quantiles(data[:, -1]).bins\n",
    ")\n",
    "pinned"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.206186Z",
     "start_time": "2022-11-05T19:18:42.200535Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.969874Z",
     "iopub.status.busy": "2025-07-11T20:09:27.969800Z",
     "iopub.status.idle": "2025-07-11T20:09:27.971653Z",
     "shell.execute_reply": "2025-07-11T20:09:27.971467Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.969867Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 62.80] |    44\n",
       "(62.80, 66.60] |     4\n",
       "(66.60, 71.40] |     4\n",
       "(71.40, 75.20] |     4\n",
       "(75.20, 79.00] |     4"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pinned.global_classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pinning to the first period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-11-05T19:18:42.215909Z",
     "start_time": "2022-11-05T19:18:42.207832Z"
    },
    "execution": {
     "iopub.execute_input": "2025-07-11T20:09:27.972019Z",
     "iopub.status.busy": "2025-07-11T20:09:27.971958Z",
     "iopub.status.idle": "2025-07-11T20:09:27.974710Z",
     "shell.execute_reply": "2025-07-11T20:09:27.974519Z",
     "shell.execute_reply.started": "2025-07-11T20:09:27.972012Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pooled Classifier\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 23.80] |     4\n",
       "(23.80, 27.60] |     4\n",
       "(27.60, 31.40] |     4\n",
       "(31.40, 35.20] |     4\n",
       "(35.20, 39.00] |     4\n",
       "(39.00, 79.00] |     0\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 23.80] |     1\n",
       "(23.80, 27.60] |     0\n",
       "(27.60, 31.40] |     0\n",
       "(31.40, 35.20] |     0\n",
       "(35.20, 39.00] |     0\n",
       "(39.00, 79.00] |    19\n",
       "\n",
       "Pooled UserDefined\n",
       "\n",
       "   Interval      Count\n",
       "----------------------\n",
       "[10.00, 23.80] |     2\n",
       "(23.80, 27.60] |     0\n",
       "(27.60, 31.40] |     0\n",
       "(31.40, 35.20] |     0\n",
       "(35.20, 39.00] |     0\n",
       "(39.00, 79.00] |    18"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pinned = mapclassify.Pooled(\n",
    "    data, classifier=\"UserDefined\", bins=mapclassify.Quantiles(data[:, 0]).bins\n",
    ")\n",
    "pinned"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the quintiles for the first period, by definition, contain all the values from that period, they do not bound the larger values in subsequent periods. Following the [mapclassify policy](https://github.com/pysal/mapclassify/blob/a7770fb98bf945dad3c62ccf2c0f8b53abb1774a/mapclassify/classifiers.py#L589), an additional class is added to contain all values in the pooled series."
   ]
  }
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