Permutation Records Test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Notebook Setup\n",
    "\n",
    "Once you have downloaded all the data onto your local machine, you can continue with this notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports\n",
    "\n",
    "In the first step, we only important some Python packages and create a Spark session."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os.path\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import statsmodels as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Directories\n",
    "\n",
    "Here we setup the directories which point to the source data and to intermediate directories. Note that we also set a `spark_tempdir` directory where Spark can spill data to. That directory should have at least 150GB of free space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Source directory where all downloaded data is stored in\n",
    "weather_basedir = \"file:///dimajix/data/weather-noaa\"\n",
    "\n",
    "# Output directory for intermediate results and aggregations\n",
    "structured_basedir = \"file:///srv/ssd/dimajix/weather-dwh\"\n",
    "\n",
    "# Temporary directory for Spark\n",
    "spark_tempdir = \"/srv/ssd/tmp/jupyter-spark\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The intermediate directories are located below the `structured_basedir` path and will contain derived data. Since our data set is rather large, persisting intermediate transformations and preaggregates will speed up our work significantly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "hourly_weather_location = os.path.join(structured_basedir, \"weather-measurements\")\n",
    "stations_location = os.path.join(structured_basedir, \"weather-stations\")\n",
    "daily_weather_location = os.path.join(structured_basedir, \"daily-weather-measurements\")\n",
    "daily_country_weather_location = os.path.join(structured_basedir, \"daily-country-weather-measurements\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spark Session\n",
    "\n",
    "Finally a Spark session is created. You might want to adjust the settings, I used Spark local mode with 48GB RAM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <div>\n",
       "                <p><b>SparkSession - in-memory</b></p>\n",
       "                \n",
       "        <div>\n",
       "            <p><b>SparkContext</b></p>\n",
       "\n",
       "            <p><a href=\"http://192.168.110.55:4040\">Spark UI</a></p>\n",
       "\n",
       "            <dl>\n",
       "              <dt>Version</dt>\n",
       "                <dd><code>v3.0.0</code></dd>\n",
       "              <dt>Master</dt>\n",
       "                <dd><code>local[*]</code></dd>\n",
       "              <dt>AppName</dt>\n",
       "                <dd><code>pyspark-shell</code></dd>\n",
       "            </dl>\n",
       "        </div>\n",
       "        \n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "<pyspark.sql.session.SparkSession at 0x7fc4f1813d90>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pyspark.sql import SparkSession\n",
    "import pyspark.sql.functions as f\n",
    "\n",
    "if not 'spark' in locals():\n",
    "    spark = SparkSession.builder \\\n",
    "        .master(\"local[*]\") \\\n",
    "        .config(\"spark.driver.memory\",\"48G\") \\\n",
    "        .config(\"spark.local.dir\", spark_tempdir) \\\n",
    "        .getOrCreate()\n",
    "\n",
    "spark"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Load Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "country = \"GM\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "root\n",
      " |-- CTRY: string (nullable = true)\n",
      " |-- STATE: string (nullable = true)\n",
      " |-- date: date (nullable = true)\n",
      " |-- min_temperature: double (nullable = true)\n",
      " |-- max_temperature: double (nullable = true)\n",
      " |-- avg_temperature: double (nullable = true)\n",
      " |-- min_wind_speed: double (nullable = true)\n",
      " |-- max_wind_speed: double (nullable = true)\n",
      " |-- avg_wind_speed: double (nullable = true)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Read in data again and filter for selected country\n",
    "daily_country_weather = spark.read.parquet(daily_country_weather_location).filter(f.col(\"CTRY\") == country)\n",
    "daily_country_weather.printSchema()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Yearly Average Temperature\n",
    "\n",
    "Now we can calculate the average temperature per year of the selected country."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "yearly_weather = daily_country_weather \\\n",
    "    .withColumn(\"year\", f.year(f.col(\"date\"))) \\\n",
    "    .groupBy(\"year\").agg(\n",
    "        f.avg(f.col(\"avg_temperature\")).alias(\"avg_temperature\"),\n",
    "        f.avg(f.col(\"avg_wind_speed\")).alias(\"avg_wind_speed\"),\n",
    "        f.avg(f.col(\"max_wind_speed\")).alias(\"max_wind_speed\")\n",
    "    )\\\n",
    "    .orderBy(f.col(\"year\")).toPandas()\n",
    "\n",
    "yearly_weather.set_index(\"year\", drop=True, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='year', ylabel='avg_temperature'>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1728x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(24,6))\n",
    "sns.regplot(x=yearly_weather.index, y=yearly_weather[\"avg_temperature\"], color=\"r\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Identifying new Records"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc4f15a4c90>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1728x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "running_max = yearly_weather[\"avg_temperature\"].expanding().max()\n",
    "running_min = yearly_weather[\"avg_temperature\"][::-1].expanding().min()[::-1]\n",
    "\n",
    "plt.figure(figsize=(24,6))\n",
    "sns.relplot(x=yearly_weather.index, y=yearly_weather[\"avg_temperature\"], color=\"r\", aspect=4)\n",
    "plt.plot(running_max)\n",
    "plt.plot(running_min)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Number of Records"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def count_max_records(series):\n",
    "    running_max = series.expanding().max()\n",
    "    records = running_max > running_max.shift(1)\n",
    "    return records.sum() + 1\n",
    "\n",
    "def count_min_records(series):\n",
    "    running_min = series.expanding().min()\n",
    "    records = running_min < running_min.shift(1)\n",
    "    return records.sum() + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "94"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(yearly_weather.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_max_records(yearly_weather[\"avg_temperature\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count_min_records(yearly_weather[\"avg_temperature\"][::-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Expected Number of Mimima / Maxima"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.125820165099301"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def harmonic_sum(n): \n",
    "    i = 1\n",
    "    s = 0.0\n",
    "    for i in range(1, n+1): \n",
    "        s = s + 1/i; \n",
    "    return s; \n",
    "  \n",
    "harmonic_sum(len(yearly_weather.index))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of Number of Minima using Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_samples = 10000\n",
    "permutation_size = len(yearly_weather.index)\n",
    "\n",
    "samples = np.zeros(num_samples, dtype=int)\n",
    "\n",
    "\n",
    "for i in range(0,num_samples):\n",
    "    p = np.random.permutation(permutation_size)\n",
    "    num_maximums = count_max_records(pd.Series(p))\n",
    "    samples[i] = num_maximums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Count'>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.histplot(data=samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.distributions.empirical_distribution import ECDF\n",
    "\n",
    "ecdf = ECDF(samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability of having 12 or more Maximums/Minimums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0012999999999999678"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - ecdf(11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'ECDF' object has no attribute 'mean'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-35-21acab0fec73>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mecdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: 'ECDF' object has no attribute 'mean'"
     ]
    }
   ],
   "source": [
    "ecdf.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 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": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}