ScaDaMaLe Course site and book

Utilities Needed for Financial Data

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

Here, certain delta.io tables are loaded. These tables have been prepared already.

You will not be able to load them directly but libraries used in the process are all open-sourced.

object TrendUtils {
  private val fx1mPath = "s3a://XXXXX/findata/com/histdata/free/FX-1-Minute-Data/"
  private val trendCalculusCheckpointPath = "s3a://XXXXX/summerinterns2020/trend-calculus-blog/public/"
  private val streamableTrendCalculusPath = "s3a://XXXXX/summerinterns2020/johannes/streamable-trend-calculus/"
  private val yfinancePath = "s3a://XXXXX/summerinterns2020/yfinance/"
  
  def getFx1mPath = fx1mPath
  def getTrendCalculusCheckpointPath = trendCalculusCheckpointPath
  def getStreamableTrendCalculusPath = streamableTrendCalculusPath
  def getYfinancePath = yfinancePath
}

defined object TrendUtils

class TrendUtils:
  
  def getTrendCalculusCheckpointPath():
    return "s3a://XXXXX/summerinterns2020/trend-calculus-blog/public/"
  
  def getYfinancePath():
    return "s3a://XXXXX/summerinterns2020/yfinance/"

ScaDaMaLe Course site and book

Utilities Needed for Mass Media Data

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

Here, certain delta.io tables are loaded. These tables have been prepared already.

You will not be able to load them directly but libraries used in the process are all open-sourced.

object GdeltUtils {
  private val gdeltV1Path = "s3a://XXXXXX/GDELT/delta/bronze/v1/"
  private val eoiCheckpointPath = "s3a://XXXXXX/.../texata/"
  private val poiCheckpointPath = "s3a://XXXXXX/.../person_graph/"

  
  def getGdeltV1Path = gdeltV1Path
  def getEOICheckpointPath = eoiCheckpointPath
  def getPOICheckpointPath = poiCheckpointPath
}

defined object GdeltUtils

class GdeltUtils:
  
  def getEOICheckpointPath():
    return "s3a://XXXXXX/.../texata/"

ScaDaMaLe Course site and book

Trends in Financial Stocks and News Events

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

According to Merriam-Webster Dictionary the definitionof trend is as follows:

a prevailing tendency or inclination : drift. How to use trend in a sentence. Synonym Discussion of trend.

Since people invest in financial stocks of publicly traded companies and make these decisions based on their understanding of current events reported in mass media, a natural question is:

How can one try to represent and understand this interplay?

The following material, first goes through the ETL process to ingest:

financial data and then
mass-media data

in a structured manner so that one can begin scalable data science processes upon them.

In the sequel two libraries are used to take advantage of SparkSQL and delta.io tables ("Spark on ACID"):

for encoding and interpreting trends (so-called trend calculus) in any time-series, say financial stock prices, for instance.
for structured representaiton of the worl'd largest open-sourced mass media data:
- The GDELT Project: https://www.gdeltproject.org/.

The last few notebooks show some simple data analytics to help extract and identify events that may be related to trends of interest.

We note that the sequel here is mainly focused on the data engineering science of ETL and basic ML Pipelines. We hope it will inspire others to do more sophisticated research, including scalable causal inference and various forms of distributed deep/reinforcement learning for more sophisticated decision problems.

ScaDaMaLe Course site and book

Historical FX-1-M Financial Data

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

Resources

This notebook builds on the following repository in order to obtain SparkSQL DatSets and DataFrames of freely available FX-1-M Data so that they can be ingested into delta.io Tables:

https://github.com/philipperemy/FX-1-Minute-Data

"./000a_finance_utils"

The Trend Calculus library is needed for case classes and parsers for the data.

import org.lamastex.spark.trendcalculus._

import org.lamastex.spark.trendcalculus._

defined object TrendUtils

val filePathRoot = TrendUtils.getFx1mPath

There are many pairs of currencies and/or commodities available.

dbutils.fs.ls(filePathRoot).foreach(fi => println("exchange pair: " + fi.name))

exchange pair: audcad/
exchange pair: audchf/
exchange pair: audjpy/
exchange pair: audnzd/
exchange pair: audusd/
exchange pair: auxaud/
exchange pair: bcousd/
exchange pair: cadchf/
exchange pair: cadjpy/
exchange pair: chfjpy/
exchange pair: etxeur/
exchange pair: euraud/
exchange pair: eurcad/
exchange pair: eurchf/
exchange pair: eurczk/
exchange pair: eurdkk/
exchange pair: eurgbp/
exchange pair: eurhuf/
exchange pair: eurjpy/
exchange pair: eurnok/
exchange pair: eurnzd/
exchange pair: eurpln/
exchange pair: eursek/
exchange pair: eurtry/
exchange pair: eurusd/
exchange pair: frxeur/
exchange pair: gbpaud/
exchange pair: gbpcad/
exchange pair: gbpchf/
exchange pair: gbpjpy/
exchange pair: gbpnzd/
exchange pair: gbpusd/
exchange pair: grxeur/
exchange pair: hkxhkd/
exchange pair: jpxjpy/
exchange pair: nsxusd/
exchange pair: nzdcad/
exchange pair: nzdchf/
exchange pair: nzdjpy/
exchange pair: nzdusd/
exchange pair: sgdjpy/
exchange pair: spxusd/
exchange pair: udxusd/
exchange pair: ukxgbp/
exchange pair: usdcad/
exchange pair: usdchf/
exchange pair: usdczk/
exchange pair: usddkk/
exchange pair: usdhkd/
exchange pair: usdhuf/
exchange pair: usdjpy/
exchange pair: usdmxn/
exchange pair: usdnok/
exchange pair: usdpln/
exchange pair: usdsek/
exchange pair: usdsgd/
exchange pair: usdtry/
exchange pair: usdzar/
exchange pair: wtiusd/
exchange pair: xagusd/
exchange pair: xauaud/
exchange pair: xauchf/
exchange pair: xaueur/
exchange pair: xaugbp/
exchange pair: xauusd/
exchange pair: zarjpy/

Let's look at Brent Oil price in USD.

dbutils.fs.ls(filePathRoot + "bcousd/").foreach(fi => println("name: " + fi.name + ", size: " + fi.size))

name: DAT_ASCII_BCOUSD_M1_2010.csv.gz, size: 284384
name: DAT_ASCII_BCOUSD_M1_2010.txt.gz, size: 41157
name: DAT_ASCII_BCOUSD_M1_2011.csv.gz, size: 2479115
name: DAT_ASCII_BCOUSD_M1_2011.txt.gz, size: 216327
name: DAT_ASCII_BCOUSD_M1_2012.csv.gz, size: 2327511
name: DAT_ASCII_BCOUSD_M1_2012.txt.gz, size: 321867
name: DAT_ASCII_BCOUSD_M1_2013.csv.gz, size: 2109500
name: DAT_ASCII_BCOUSD_M1_2013.txt.gz, size: 417973
name: DAT_ASCII_BCOUSD_M1_2014.csv.gz, size: 1961172
name: DAT_ASCII_BCOUSD_M1_2014.txt.gz, size: 431591
name: DAT_ASCII_BCOUSD_M1_2015.csv.gz, size: 2205678
name: DAT_ASCII_BCOUSD_M1_2015.txt.gz, size: 333277
name: DAT_ASCII_BCOUSD_M1_2016.csv.gz, size: 2131659
name: DAT_ASCII_BCOUSD_M1_2016.txt.gz, size: 342616
name: DAT_ASCII_BCOUSD_M1_2017.csv.gz, size: 1854793
name: DAT_ASCII_BCOUSD_M1_2017.txt.gz, size: 434781
name: DAT_ASCII_BCOUSD_M1_2018.csv.gz, size: 2251250
name: DAT_ASCII_BCOUSD_M1_2018.txt.gz, size: 306810
name: DAT_ASCII_BCOUSD_M1_2019.csv.gz, size: 2701059
name: DAT_ASCII_BCOUSD_M1_2019.txt.gz, size: 102290
name: DAT_ASCII_BCOUSD_M1_202001.csv.gz, size: 233757
name: DAT_ASCII_BCOUSD_M1_202001.txt.gz, size: 8391
name: DAT_ASCII_BCOUSD_M1_202002.csv.gz, size: 222628
name: DAT_ASCII_BCOUSD_M1_202002.txt.gz, size: 4379
name: DAT_ASCII_BCOUSD_M1_202003.csv.gz, size: 265471
name: DAT_ASCII_BCOUSD_M1_202003.txt.gz, size: 834
name: DAT_ASCII_BCOUSD_M1_202004.csv.gz, size: 245819
name: DAT_ASCII_BCOUSD_M1_202004.txt.gz, size: 953
name: DAT_ASCII_BCOUSD_M1_202005.csv.gz, size: 233828
name: DAT_ASCII_BCOUSD_M1_202005.txt.gz, size: 850
name: DAT_ASCII_BCOUSD_M1_202006.csv.gz, size: 244557
name: DAT_ASCII_BCOUSD_M1_202006.txt.gz, size: 1394
name: DAT_ASCII_BCOUSD_M1_202007.csv.gz, size: 74976
name: DAT_ASCII_BCOUSD_M1_202007.txt.gz, size: 1637

We use the parser available from Trend Calculus to read the csv files into a Spark Dataset.

val oilPath = filePathRoot + "bcousd/*.csv.gz"
val oilDS = spark.read.fx1m(oilPath).orderBy($"time")

oilDS.show(20, false)

+-------------------+-----+-----+-----+-----+------+
|time               |open |high |low  |close|volume|
+-------------------+-----+-----+-----+-----+------+
|2010-11-14 20:15:00|86.73|86.74|86.73|86.74|0     |
|2010-11-14 20:17:00|86.75|86.75|86.75|86.75|0     |
|2010-11-14 20:18:00|86.76|86.78|86.76|86.76|0     |
|2010-11-14 20:19:00|86.74|86.74|86.74|86.74|0     |
|2010-11-14 20:21:00|86.75|86.75|86.74|86.74|0     |
|2010-11-14 20:24:00|86.75|86.75|86.75|86.75|0     |
|2010-11-14 20:26:00|86.76|86.77|86.74|86.77|0     |
|2010-11-14 20:27:00|86.79|86.79|86.75|86.75|0     |
|2010-11-14 20:28:00|86.77|86.79|86.75|86.79|0     |
|2010-11-14 20:32:00|86.8 |86.81|86.79|86.81|0     |
|2010-11-14 20:33:00|86.81|86.81|86.81|86.81|0     |
|2010-11-14 20:34:00|86.81|86.81|86.81|86.81|0     |
|2010-11-14 20:35:00|86.81|86.81|86.79|86.79|0     |
|2010-11-14 20:36:00|86.79|86.8 |86.78|86.8 |0     |
|2010-11-14 20:37:00|86.78|86.8 |86.78|86.79|0     |
|2010-11-14 20:38:00|86.79|86.79|86.79|86.79|0     |
|2010-11-14 20:39:00|86.79|86.8 |86.79|86.79|0     |
|2010-11-14 20:40:00|86.79|86.8 |86.79|86.8 |0     |
|2010-11-14 20:41:00|86.8 |86.8 |86.8 |86.8 |0     |
|2010-11-14 20:42:00|86.8 |86.8 |86.8 |86.8 |0     |
+-------------------+-----+-----+-----+-----+------+
only showing top 20 rows

ScaDaMaLe Course site and book

yfinance Stock Data

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

This notebook builds on the following repositories in order to obtain SparkSQL DataSets and DataFrames of freely available Yahoo! Finance Data so that they can be ingested into delta.io Tables for trend analysis and more:

Resources:

Yfinance is a python library that makes it easy to download various financial data from Yahoo Finance.

pip install yfinance

"./000a_finance_utils"

To illustrate the library, we use two stocks of the Swedish bank SEB. The (default) data resolution is one day so we use 20 years of data to get a lot of observations.

import yfinance as yf
dataSEBAST = yf.download("SEB-A.ST", start="2001-07-01", end="2020-07-12")
dataSEBCST = yf.download("SEB-C.ST", start="2001-07-01", end="2020-07-12")

dataSEBAST.size

dataSEBAST

We can also download several tickers at once.

Note that the result is in a pandas dataframe so we are not doing any distributed computing.

This means that some care has to be taken to not overwhelm the local machine.

defined object TrendUtils

dataSEBAandCSTBST = yf.download("SEB-A.ST SEB-C.ST", start="2020-07-01", end="2020-07-12", group_by="ticker")
dataSEBAandCSTBST

type(dataSEBAST)

Loading the data into a Spark DataFrame.

dataSEBAST_sp = spark.createDataFrame(dataSEBAandCSTBST)

dataSEBAST_sp.printSchema()

The conversion to Spark DataFrame works but is quite messy. Just imagine if there were more tickers!

dataSEBAST_sp.show(20, False)

When selecting a column with a dot in the name (as in ('SEB-A.ST', 'High')) using PySpark, we have to enclose the column name in backticks `.

dataSEBAST_sp.select("`('SEB-A.ST', 'High')`")

We can also get information about individual tickers.

msft = yf.Ticker("MSFT")
print(msft)

msft.info

We write a function to transform data downloaded by yfinance and write a better formatted Spark DataFrame.

import pandas as pd
import yfinance as yf
import sys, getopt

# example:
# python3 yfin_to_csv.py -i "60m" "SEB-A.ST INVE-A.ST" "2019-07-01" "2019-07-06" "/root/GIT/yfin_test.csv"
def ingest(interval, tickers, start, end, csv_path):
  df = yf.download(tickers, start=start, end=end, interval=interval, group_by='ticker')
  findf = df.unstack().unstack(1).sort_index(level=1)
  findf.reset_index(level=0, inplace=True)
  findf = findf.loc[start:end]
  findf.rename(columns={'level_0':'Ticker'}, inplace=True)
  findf.index.name='Time'
  findf['Volume'] = pd.to_numeric(findf['Volume'], downcast='integer')
  findf = findf.reset_index(drop=False)
  findf['Time'] = findf['Time'].map(lambda x: str(x))
  spark.createDataFrame(findf).write.mode('overwrite').save(csv_path, format='csv')
  return(findf)

Let's look at some top value companies in the world as well as an assortment of Swedish Companies.

The number of tickers is now much larger, using the previous method would result in over 100 columns.

This would make it quite difficult to see what's going on, not to mention trying to analyze the data!

The data resolution is now one minute, meaning that 7 days gives a lot of observations.

Yfinance only allows downloading 1-minute data one week at a time and only for dates within the last 30 days.

topValueCompanies = 'MSFT AAPL AMZN GOOG BABA FB BRK-B BRK-A TSLA'
swedishCompanies = 'ASSA-B.ST ATCO-A.ST ALIV-SDB.ST ELUX-A.ST ELUX-B.ST EPI-A.ST EPI-B.ST ERIC-A.ST ERIC-B.ST FORTUM.HE HUSQ-A.ST HUSQ-B.ST INVE-A.ST INVE-B.ST KESKOA.HE KESKOB.HE KNEBV.HE KCR.HE MTRS.ST SAAB-B.ST SAS.ST SEB-A.ST SEB-C.ST SKF-A.ST SKF-B.ST STE-R.ST STERV.HE WRT1V.HE'
tickers = topValueCompanies + ' ' + swedishCompanies
interval = '1m'
start = '2021-01-01'
end = '2021-01-07'
csv_path = TrendUtils.getYfinancePath() + 'stocks_' + interval + '_' + start + '_' + end + '.csv'

dbutils.fs.rm(csv_path, recurse=True)

df = ingest(interval, tickers, start, end, csv_path)

Having written the result to a csv file, we can use the parser in the Trend Calculus library https://github.com/lamastex/spark-trend-calculus to read the data into a Dataset in Scala Spark.

import org.lamastex.spark.trendcalculus._

import org.lamastex.spark.trendcalculus._

val rootPath = TrendUtils.getYfinancePath
val csv_path = rootPath + "stocks_1m_2021-01-01_2021-01-07.csv"
val yfinDF = spark.read.yfin(csv_path)

yfinDF.count

res1: Long = 71965

yfinDF.show(20, false)

+-------------------+---------+------------------+------------------+------------------+------------------+------------------+------+
|time               |ticker   |open              |high              |low               |close             |adjClose          |volume|
+-------------------+---------+------------------+------------------+------------------+------------------+------------------+------+
|2021-01-04 14:45:00|BRK-B    |230.7899932861328 |230.99000549316406|230.72999572753906|230.97000122070312|230.97000122070312|13367 |
|2021-01-04 14:45:00|ELUX-A.ST|null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|ELUX-B.ST|190.14999389648438|190.14999389648438|190.14999389648438|190.14999389648438|190.14999389648438|2770  |
|2021-01-04 14:45:00|EPI-A.ST |null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|EPI-B.ST |null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|ERIC-A.ST|null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|ERIC-B.ST|null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|FB       |271.30499267578125|271.42498779296875|271.30499267578125|271.42498779296875|271.42498779296875|28330 |
|2021-01-04 14:45:00|FORTUM.HE|20.31999969482422 |20.31999969482422 |20.31999969482422 |20.31999969482422 |20.31999969482422 |49824 |
|2021-01-04 14:45:00|GOOG     |1749.4150390625   |1751.260009765625 |1749.4150390625   |1750.18994140625  |1750.18994140625  |4109  |
|2021-01-04 14:45:00|HUSQ-A.ST|null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|HUSQ-B.ST|108.9000015258789 |108.9000015258789 |108.9000015258789 |108.9000015258789 |108.9000015258789 |7170  |
|2021-01-04 14:45:00|INVE-A.ST|null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|INVE-B.ST|612.5999755859375 |612.5999755859375 |612.4000244140625 |612.4000244140625 |612.4000244140625 |1628  |
|2021-01-04 14:45:00|KCR.HE   |29.040000915527344|29.040000915527344|29.040000915527344|29.040000915527344|29.040000915527344|0     |
|2021-01-04 14:45:00|KESKOA.HE|null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|KESKOB.HE|null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|KNEBV.HE |null              |null              |null              |null              |null              |null  |
|2021-01-04 14:45:00|MSFT     |220.25            |220.32000732421875|220.1699981689453 |220.1699981689453 |220.1699981689453 |96255 |
|2021-01-04 14:45:00|MTRS.ST  |null              |null              |null              |null              |null              |null  |
+-------------------+---------+------------------+------------------+------------------+------------------+------------------+------+
only showing top 20 rows

ScaDaMaLe Course site and book

Finding trends in oil price data.

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

Resources

This builds on the following library and its antecedents therein to find trends in historical oil prices:

https://github.com/lamastex/spark-trend-calculus

This work was inspired by:

Antoine Aamennd's texata-2017
Andrew Morgan's Trend Calculus Library

"./000a_finance_utils"

When dealing with time series, it can be difficult to find a good way to find and analyze trends in the data.

One approach is by using the Trend Calculus algorithm invented by Andrew Morgan. More information about Trend Calculus can be found at https://lamastex.github.io/spark-trend-calculus-examples/.

defined object TrendUtils

import org.lamastex.spark.trendcalculus._
import spark.implicits._
import org.apache.spark.sql._
import org.apache.spark.sql.functions._
import java.sql.Timestamp

import org.lamastex.spark.trendcalculus._
import spark.implicits._
import org.apache.spark.sql._
import org.apache.spark.sql.functions._
import java.sql.Timestamp

The input to the algorithm is data in the format (ticker, time, value). In this example, ticker is "BCOUSD" (Brent Crude Oil), time is given in minutes and value is the closing price for Brent Crude Oil during that minute.

This data is historical data from 2010 to 2019 taken from https://www.histdata.com/ using methods from FX-1-Minute-Data by Philippe Remy. In this notebook, everything is done on static dataframes. We will soon see examples on streaming dataframes.

There are gaps in the data, notably during the weekends when no trading takes place, but this does not affect the algorithm as it is does not place any assumptions on the data other than that time is monotonically increasing.

The window size is set to 2, which is minimal, because we want to retain as much information as possible.

val windowSize = 2
val dataRootPath = TrendUtils.getFx1mPath
val oilDS = spark.read.fx1m(dataRootPath + "bcousd/*.csv.gz").toDF.withColumn("ticker", lit("BCOUSD")).select($"ticker", $"time" as "x", $"close" as "y").as[TickerPoint].orderBy("x")

If we want to look at long term trends, we can use the output time series as input for another iteration. The output contains the points of the input where the trend changes (reversals). This can be repeated several times, resulting in longer term trends.

Here, we look at (up to) 15 iterations of the algorithm. It is no problem if the output of some iteration is too small to find a reversal in the next iteration, since the output will just be an empty dataframe in that case.

val numReversals = 15
val dfWithReversals = new TrendCalculus2(oilDS, windowSize, spark).nReversalsJoinedWithMaxRev(numReversals)

numReversals: Int = 15
dfWithReversals: org.apache.spark.sql.DataFrame = [ticker: string, x: timestamp ... 17 more fields]

dfWithReversals.show(20, false)

+------+-------------------+-----+---------+---------+---------+---------+---------+---------+---------+---------+---------+----------+----------+----------+----------+----------+----------+------+
|ticker|x                  |y    |reversal1|reversal2|reversal3|reversal4|reversal5|reversal6|reversal7|reversal8|reversal9|reversal10|reversal11|reversal12|reversal13|reversal14|reversal15|maxRev|
+------+-------------------+-----+---------+---------+---------+---------+---------+---------+---------+---------+---------+----------+----------+----------+----------+----------+----------+------+
|BCOUSD|2010-11-14 20:15:00|86.74|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:17:00|86.75|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:18:00|86.76|-1       |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |1     |
|BCOUSD|2010-11-14 20:19:00|86.74|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:21:00|86.74|1        |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |1     |
|BCOUSD|2010-11-14 20:24:00|86.75|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:26:00|86.77|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:27:00|86.75|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:28:00|86.79|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:32:00|86.81|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:33:00|86.81|-1       |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |1     |
|BCOUSD|2010-11-14 20:34:00|86.81|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:35:00|86.79|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:36:00|86.8 |null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:37:00|86.79|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:38:00|86.79|1        |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |1     |
|BCOUSD|2010-11-14 20:39:00|86.79|null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:40:00|86.8 |null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:41:00|86.8 |null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
|BCOUSD|2010-11-14 20:42:00|86.8 |null     |null     |null     |null     |null     |null     |null     |null     |null     |null      |null      |null      |null      |null      |null      |0     |
+------+-------------------+-----+---------+---------+---------+---------+---------+---------+---------+---------+---------+----------+----------+----------+----------+----------+----------+------+
only showing top 20 rows

The number of reversals decrease rapidly as more iterations are done.

dfWithReversals.cache.count

res3: Long = 2859310

(1 to numReversals).foreach( i => println(dfWithReversals.filter(s"reversal$i is not null").count))

We write the resulting dataframe to parquet in order to produce visualizations using Python.

val checkPointPath = TrendUtils.getTrendCalculusCheckpointPath
dfWithReversals.write.mode(SaveMode.Overwrite).parquet(checkPointPath + "joinedDSWithMaxRev_new")
dfWithReversals.unpersist

Visualization

The Python library plotly is used to make interactive visualizations.

from plotly.offline import plot
from plotly.graph_objs import *
from datetime import *
checkPointPath = TrendUtils.getTrendCalculusCheckpointPath()
joinedDS = spark.read.parquet(checkPointPath + "joinedDSWithMaxRev_new").orderBy("x")

We check the size of the dataframe to see if it possible to handle locally since plotly is not available for distributed data.

joinedDS.count()

Almost 3 million rows might be too much for the driver! The timeseries has to be thinned out in order to display locally.

No information about higher order trend reversals is lost since every higher order reversal is also a lower order reversal and the lowest orders of reversal are on the scale of minutes (maybe hours) and that is probably not very interesting considering that the data stretches over roughly 10 years!

joinedDS.filter("maxRev > 2").count()

Just shy of 100k rows is no problem for the driver.

We select the relevant information in the dataframe for visualization.

fullTS = joinedDS.filter("maxRev > 2").select("x","y","maxRev").collect()

Picking an interval to focus on.

Start and end dates as (year, month, day, hour, minute, second). Only year, month and day are required. The interval from years 1800 to 2200 ensures all data is selected.

startDate = datetime(1800,1,1)
endDate= datetime(2200,12,31)
TS = [row for row in fullTS if startDate <= row['x'] and row['x'] <= endDate]

Setting up the visualization.

numReversals = 15
startReversal = 7

allData = {'x': [row['x'] for row in TS], 'y': [row['y'] for row in TS], 'maxRev': [row['maxRev'] for row in TS]}
revTS = [row for row in TS if row[2] >= startReversal]
colorList = ['rgba(' + str(tmp) + ',' + str(255-tmp) + ',' + str(255-tmp) + ',1)' for tmp in [int(i*255/(numReversals-startReversal+1)) for i in range(1,numReversals-startReversal+2)]]

def getRevTS(tsWithRevMax, revMax):
  x = [row[0] for row in tsWithRevMax if row[2] >= revMax]
  y = [row[1] for row in tsWithRevMax if row[2] >= revMax]
  return x,y,revMax

reducedData = [getRevTS(revTS, i) for i in range(startReversal, numReversals+1)]

markerPlots = [Scattergl(x=x, y=y, mode='markers', marker=dict(color=colorList[i-startReversal], size=i), name='Reversal ' + str(i)) for (x,y,i) in [getRevTS(revTS, i) for i in range(startReversal, numReversals+1)]]

Plotting result as plotly graph

The graph is interactive, one can drag to zoom in on an area (double-click to get back) and click on the legend to hide or show different series.

Note that we have left out many of the lower order reversals in order to not make the graph too cluttered. The seventh order reversal (the lowest order shown) is still on the scale of hours to a few days.

p = plot(
  [Scattergl(x=allData['x'], y=allData['y'], mode='lines', name='Oil Price')] + markerPlots
  ,
  output_type='div'
)

displayHTML(p)

trendcalculusoil

ScaDaMaLe Course site and book

Streaming Trend Calculus with Maximum Necessary Reversals

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

Resources

This builds on the following library and its antecedents therein:

https://github.com/lamastex/spark-trend-calculus

This work was inspired by:

Antoine Aamennd's texata-2017
Andrew Morgan's Trend Calculus Library

"./000a_finance_utils"

We use the spark-trend-calculus library and Spark structured streams over delta.io files to obtain a representation of the complete time series of trends with their k-th order reversal.

This representation is a sufficient statistic for a Markov model of trends that we show in the next notebook.

defined object TrendUtils

import java.sql.Timestamp
import io.delta.tables._
import org.apache.spark.sql._
import org.apache.spark.sql.functions._
import org.apache.spark.sql.streaming.{GroupState, GroupStateTimeout, OutputMode, Trigger}
import org.apache.spark.sql.types._
import org.apache.spark.sql.expressions.{Window, WindowSpec}
import org.lamastex.spark.trendcalculus._

import java.sql.Timestamp
import io.delta.tables._
import org.apache.spark.sql._
import org.apache.spark.sql.functions._
import org.apache.spark.sql.streaming.{GroupState, GroupStateTimeout, OutputMode, Trigger}
import org.apache.spark.sql.types._
import org.apache.spark.sql.expressions.{Window, WindowSpec}
import org.lamastex.spark.trendcalculus._

Input data in s3. The data contains oil price data from 2010 to last month and gold price data from 2009 to last month.

val rootPath = "s3a://XXXXX/summerinterns2020/johannes/streamable-trend-calculus/"
val oilGoldPath = rootPath + "oilGoldDelta"

spark.read.format("delta").load(oilGoldPath).orderBy("x").show(20,false)

+------+-------------------+------+
|ticker|x                  |y     |
+------+-------------------+------+
|XAUUSD|2009-03-15 17:00:00|929.6 |
|XAUUSD|2009-03-15 18:00:00|926.05|
|XAUUSD|2009-03-15 18:01:00|925.9 |
|XAUUSD|2009-03-15 18:02:00|925.9 |
|XAUUSD|2009-03-15 18:03:00|926.95|
|XAUUSD|2009-03-15 18:04:00|925.8 |
|XAUUSD|2009-03-15 18:05:00|926.35|
|XAUUSD|2009-03-15 18:06:00|925.8 |
|XAUUSD|2009-03-15 18:07:00|925.6 |
|XAUUSD|2009-03-15 18:08:00|925.7 |
|XAUUSD|2009-03-15 18:09:00|925.4 |
|XAUUSD|2009-03-15 18:10:00|925.75|
|XAUUSD|2009-03-15 18:11:00|925.7 |
|XAUUSD|2009-03-15 18:12:00|925.65|
|XAUUSD|2009-03-15 18:13:00|925.65|
|XAUUSD|2009-03-15 18:14:00|925.75|
|XAUUSD|2009-03-15 18:15:00|925.75|
|XAUUSD|2009-03-15 18:16:00|925.65|
|XAUUSD|2009-03-15 18:17:00|925.6 |
|XAUUSD|2009-03-15 18:18:00|925.85|
+------+-------------------+------+
only showing top 20 rows

Reading the data from s3 as a Structured Stream to simulate streaming.

val input = spark
  .readStream
  .format("delta")
  .load(oilGoldPath)
  .as[TickerPoint]

input: org.apache.spark.sql.Dataset[org.lamastex.spark.trendcalculus.TickerPoint] = [ticker: string, x: timestamp ... 1 more field]

Using the trendcalculus library to 1. Apply Trend Calculus to the streaming dataset. - Save the result as a delta table. - Read the result as a stream. - Repeat from 1. using the latest result as input. Stop when result is empty.

val windowSize = 2

// Initializing variables for while loop.
var i = 1
var prevSinkPath = ""
var sinkPath = rootPath + "multiSinks/reversal" + (i)
var chkptPath = rootPath + "multiSinks/checkpoint/" + (i)

// The first order reversal.
var stream = new TrendCalculus2(input, windowSize, spark)
  .reversals
  .select("tickerPoint.ticker", "tickerPoint.x", "tickerPoint.y", "reversal")
  .as[FlatReversal]
  .writeStream
  .format("delta")
  .option("path", sinkPath)
  .option("checkpointLocation", chkptPath)
  .trigger(Trigger.Once())
  .start

stream.processAllAvailable

i += 1

var lastReversalSeries = spark.emptyDataset[TickerPoint]
while (!spark.read.format("delta").load(sinkPath).isEmpty) {
  
  prevSinkPath = rootPath + "multiSinks/reversal" + (i-1)
  sinkPath = rootPath + "multiSinks/reversal" + (i)
  chkptPath = rootPath + "multiSinks/checkpoint/" + (i)
  
  // Reading last result as stream
  lastReversalSeries = spark
    .readStream
    .format("delta")
    .load(prevSinkPath)
    .drop("reversal")
    .as[TickerPoint]

  // Writing next result
  stream = new TrendCalculus2(lastReversalSeries, windowSize, spark)
    .reversals
    .select("tickerPoint.ticker", "tickerPoint.x", "tickerPoint.y", "reversal")
    .as[FlatReversal]
    .map( rev => rev.copy(reversal=i*rev.reversal))
    .writeStream
    .format("delta")
    .option("path", sinkPath)
    .option("checkpointLocation", chkptPath)
    .partitionBy("ticker")
    .trigger(Trigger.Once())
    .start
  
  stream.processAllAvailable()
  
  i += 1
}

Checking the total number of reversals written. The last sink is empty so the highest order reversal is \[\text{number of sinks} - 1\].

val i = dbutils.fs.ls(rootPath + "multiSinks").length - 1

i: Int = 18

The written delta tables can be read as streams but for now we read them as static datasets to be able to join them together.

val sinkPaths = (1 to i-1).map(rootPath + "multiSinks/reversal" + _)
val maxRevPath = rootPath + "maxRev"
val revTables = sinkPaths.map(DeltaTable.forPath(_).toDF.as[FlatReversal])
val oilGoldTable = DeltaTable.forPath(oilGoldPath).toDF.as[TickerPoint]

The number of reversals decrease rapidly as the reversal order increases.

revTables.map(_.cache.count)

res6: scala.collection.immutable.IndexedSeq[Long] = Vector(1954849, 677939, 262799, 108202, 46992, 21154, 9703, 4427, 1992, 890, 404, 183, 83, 35, 15, 7, 2)

Joining all results to get a dataset with all reversals in a single column.

def maxByAbs(a: Int, b: Int): Int = {
  Seq(a,b).maxBy(math.abs)
}

val maxByAbsUDF = udf((a: Int, b: Int) => maxByAbs(a,b))

val maxRevDS = revTables.foldLeft(oilGoldTable.toDF.withColumn("reversal", lit(0)).as[FlatReversal]){ (acc: Dataset[FlatReversal], ds: Dataset[FlatReversal]) => 
  acc
    .toDF
    .withColumnRenamed("reversal", "oldMaxRev")
    .join(ds.select($"ticker" as "tmpt", $"x" as "tmpx", $"reversal" as "newRev"), $"ticker" === $"tmpt" && $"x" === $"tmpx", "left")
    .drop("tmpt", "tmpx")
    .na.fill(0,Seq("newRev"))
    .withColumn("reversal", maxByAbsUDF($"oldMaxRev", $"newRev"))
    .select("ticker", "x", "y", "reversal")
    .as[FlatReversal]    
}

maxByAbs: (a: Int, b: Int)Int
maxByAbsUDF: org.apache.spark.sql.expressions.UserDefinedFunction = SparkUserDefinedFunction($Lambda$9089/155868360@d163ce5,IntegerType,List(Some(class[value[0]: int]), Some(class[value[0]: int])),None,false,true)
maxRevDS: org.apache.spark.sql.Dataset[org.lamastex.spark.trendcalculus.FlatReversal] = [ticker: string, x: timestamp ... 2 more fields]

Writing result as delta table.

maxRevDS.write.format("delta").partitionBy("ticker").save(maxRevPath)

The reversal column in the joined dataset contains the information of all orders of reversals.

0 indicates that no reversal happens while a non-zero value indicates that this is a reversal point for that order and every lower order.

For example, row 33 contains the value -4, meaning that this point is trend reversal downwards for orders 1, 2, 3, and 4.

DeltaTable.forPath(maxRevPath).toDF.as[FlatReversal].filter("ticker == 'BCOUSD'").orderBy("x").show(35, false)

+------+-------------------+-----+--------+
|ticker|x                  |y    |reversal|
+------+-------------------+-----+--------+
|BCOUSD|2010-11-14 20:15:00|86.74|0       |
|BCOUSD|2010-11-14 20:17:00|86.75|0       |
|BCOUSD|2010-11-14 20:18:00|86.76|-1      |
|BCOUSD|2010-11-14 20:19:00|86.74|0       |
|BCOUSD|2010-11-14 20:21:00|86.74|1       |
|BCOUSD|2010-11-14 20:24:00|86.75|0       |
|BCOUSD|2010-11-14 20:26:00|86.77|0       |
|BCOUSD|2010-11-14 20:27:00|86.75|0       |
|BCOUSD|2010-11-14 20:28:00|86.79|0       |
|BCOUSD|2010-11-14 20:32:00|86.81|0       |
|BCOUSD|2010-11-14 20:33:00|86.81|-1      |
|BCOUSD|2010-11-14 20:34:00|86.81|0       |
|BCOUSD|2010-11-14 20:35:00|86.79|0       |
|BCOUSD|2010-11-14 20:36:00|86.8 |0       |
|BCOUSD|2010-11-14 20:37:00|86.79|0       |
|BCOUSD|2010-11-14 20:38:00|86.79|1       |
|BCOUSD|2010-11-14 20:39:00|86.79|0       |
|BCOUSD|2010-11-14 20:40:00|86.8 |0       |
|BCOUSD|2010-11-14 20:41:00|86.8 |0       |
|BCOUSD|2010-11-14 20:42:00|86.8 |0       |
|BCOUSD|2010-11-14 20:43:00|86.82|0       |
|BCOUSD|2010-11-14 20:44:00|86.81|0       |
|BCOUSD|2010-11-14 20:47:00|86.84|0       |
|BCOUSD|2010-11-14 20:48:00|86.82|0       |
|BCOUSD|2010-11-14 20:49:00|86.84|-1      |
|BCOUSD|2010-11-14 20:50:00|86.82|0       |
|BCOUSD|2010-11-14 20:51:00|86.83|0       |
|BCOUSD|2010-11-14 20:52:00|86.82|1       |
|BCOUSD|2010-11-14 20:53:00|86.83|0       |
|BCOUSD|2010-11-14 20:54:00|86.84|0       |
|BCOUSD|2010-11-14 20:58:00|86.88|0       |
|BCOUSD|2010-11-14 20:59:00|86.89|0       |
|BCOUSD|2010-11-14 21:00:00|86.9 |-4      |
|BCOUSD|2010-11-14 21:03:00|86.87|0       |
|BCOUSD|2010-11-14 21:04:00|86.87|0       |
+------+-------------------+-----+--------+
only showing top 35 rows

ScaDaMaLe Course site and book

Detecting Events of Interest to OIL/GAS Price Trends

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

Here we will build a pipeline to investigate possible events related to oil and gas that are reported in mass media around the world and their possible co-occurrence with certain trends and trend-reversals in oil price.

Steps:

Step 0. Setting up and loading GDELT delta.io tables
Step 1. Extracting coverage around gas and oil from each country
Step 2. Extracting the news around dates with high coverage (big events)
Step 3. Enrich oil price with trend calculus and comparing it to the coverage

Resources:

This builds on the following libraries and its antecedents therein:

This work was inspired by:

Antoine Aamennd's texata-2017
Andrew Morgan's Trend Calculus Library

Step 0. Setting up and loading GDELT delta.io tables

import spark.implicits._
import io.delta.tables._
import com.aamend.spark.gdelt._
import org.apache.spark.sql.{Dataset,DataFrame,SaveMode}
import org.apache.spark.sql.functions._
import org.apache.spark.sql.expressions._
import org.lamastex.spark.trendcalculus._
import java.sql.{Date,Timestamp}
import java.text.SimpleDateFormat

import spark.implicits._
import io.delta.tables._
import com.aamend.spark.gdelt._
import org.apache.spark.sql.{Dataset, DataFrame, SaveMode}
import org.apache.spark.sql.functions._
import org.apache.spark.sql.expressions._
import org.lamastex.spark.trendcalculus._
import java.sql.{Date, Timestamp}
import java.text.SimpleDateFormat

Loading in the data from our live-updating delta.io tables

"./000a_finance_utils"

defined object TrendUtils

"./000b_gdelt_utils"

defined object GdeltUtils

val rootPath = GdeltUtils.getGdeltV1Path
val rootCheckpointPath = GdeltUtils.getEOICheckpointPath
val gkgPath = rootPath+"gkg"
val eventPath = rootPath+"events"

val gkg_v1 = spark.read.format("delta").load(gkgPath).as[GKGEventV1]
val eve_v1 = spark.read.format("delta").load(eventPath).as[EventV1]

Extracting coverage around gas and oil from each country

Limits the data and extracts the events related to oil and gas theme

val gkg_v1_filt = gkg_v1.filter($"publishDate">"2013-04-01 00:00:00" && $"publishDate"<"2019-12-31 00:00:00")
val oil_gas_themeGKG = gkg_v1_filt.filter(c =>c.themes.contains("ENV_GAS") || c.themes.contains("ENV_OIL"))
                              .select(explode($"eventIds"))
                              .toDF("eventId")
                              .groupBy($"eventId")
                              .agg(count($"eventId"))
                              .toDF("eventId","count") 
val oil_gas_eventDF = eve_v1.toDF()
                            .join( oil_gas_themeGKG, "eventId")

Checkpoint

oil_gas_eventDF.write.parquet(rootCheckpointPath + "oil_gas_event_v1")

val  oil_gas_eventDF = spark.read.parquet(rootCheckpointPath + "oil_gas_event_v1")

Extracting coverage for each country

// Counting number of articles for each country, each day and applying a moving average on each country's coverage
def movingAverage(df:DataFrame,size:Int,avgOn:String):DataFrame = {
  val windowSpec = Window.partitionBy($"country").orderBy($"date").rowsBetween(-size/2, size/2)
  return df.withColumn("coverage",avg(avgOn).over(windowSpec))
}
val (mean_articles, std_articles) = oilEventTemp.select(mean("articles"), stddev("articles"))
  .as[(Double, Double)]
  .first() 
val oilEventTemp = oil_gas_eventDF
  .filter(length(col("eventGeo.countryCode")) > 0)
  .groupBy(
    col("eventGeo.countryCode").as("country"),
    col("eventDay").as("date")
  )
  .agg(
    sum(col("numArticles")).as("articles"),
  )
                                        
//Applying moving averge over weeks and of normalized number of articles.
val oilEventWeeklyCoverage = movingAverage(oilEventTemp.withColumn("normArticles",
                                                                   ($"articles"-mean_articles) / std_articles),
                                                                    7,
                                                                    "normArticles")
  .drop("normArticles")

movingAverage: (df: org.apache.spark.sql.DataFrame, size: Int, avgOn: String)org.apache.spark.sql.DataFrame
oilEventTemp: org.apache.spark.sql.DataFrame = [country: string, date: date ... 1 more field]
mean_articles: Double = 1593.3213115310818
std_articles: Double = 10276.10388376719
oilEventWeeklyCoverage: org.apache.spark.sql.DataFrame = [country: string, date: date ... 2 more fields]

Checkpoint

oilEventWeeklyCoverage.write.parquet(rootCheckpointPath +"oil_gas_cov_norm")

val oil_gas_cov_norm = spark.read.parquet(rootCheckpointPath +"oil_gas_cov_norm")

Enrich the event data with the extracted coverage

val oilEventWeeklyCoverageC = oil_gas_cov_norm.drop($"articles").toDF("country","tempDate","coverage")
val oilEventCoverageDF = oilEventWeeklyCoverageC.join(oil_gas_eventDF,oil_gas_eventDF("eventDay") === oilEventWeeklyCoverageC("tempDate") && oil_gas_eventDF("eventGeo.countryCode")
                       === oilEventWeeklyCoverageC("country"))

Checkpoint

oilEventCoverageDF.write.parquet(rootCheckpointPath+"oil_gas_eve_cov")

val oilEventCoverageDF = spark.read.parquet(rootCheckpointPath+"oil_gas_eve_cov")

Let us look at 2018

val tot_cov_2018 = oil_gas_cov_norm.filter($"date" >"2018-01-01" && $"date"<"2018-12-31").groupBy($"date").agg(sum($"coverage").as("coverage")).orderBy(desc("coverage"))

Total Coverage

display(tot_cov_2018)

date	coverage
2018-05-11	27.486972103755587
2018-05-12	23.96793050873498
2018-05-10	22.996724752589337
2018-05-09	22.386286223280464
2018-05-08	20.1775002337218
2018-05-13	18.849262389568942
2018-05-07	18.356561615113378
2018-10-20	15.61132729731101
2018-04-16	15.462361791574757
2018-12-02	15.35916815092816
2018-04-15	15.283319413257985
2018-05-06	15.074567688377858
2018-10-14	14.456182009909384
2018-12-03	14.029036688423556
2018-04-21	13.984623515510002
2018-10-15	13.913223469927237
2018-10-17	13.899999502069956
2018-03-10	13.596583766909582
2018-03-11	13.328385180680641
2018-04-22	13.313579680574394
2018-04-17	13.06945600192825
2018-10-21	13.05918925998796
2018-10-19	13.042145921984297
2018-12-01	12.686288838799623
2018-10-18	12.395778148350379
2018-12-04	12.259894218727634
2018-04-18	12.19829841568054
2018-10-16	11.886229012014399
2018-04-20	11.528415547014669
2018-03-08	11.404094561394555
2018-04-14	11.330716620584942
2018-03-09	11.287064996907633
2018-04-19	11.254357433090025
2018-04-28	10.78023000863521
2018-04-29	10.393243293127174
2018-10-13	10.336221435744559
2018-09-22	10.000035737769323
2018-06-17	9.89640767482373
2018-09-23	9.743320330587773
2018-08-05	9.629453375016213
2018-12-05	9.51893722763343
2018-10-27	9.478760481207281
2018-03-04	9.062493219829184
2018-08-19	8.696936272089726
2018-06-23	8.508148813945867
2018-05-14	8.433635112149537
2018-10-23	8.378055403769487
2018-11-04	8.361164257492085
2018-03-12	8.332151356942868
2018-06-20	8.288965286725801
2018-05-27	8.195992626048099
2018-10-28	8.172456609861717
2018-11-30	8.076037057921956
2018-04-27	7.992062718099141
2018-06-19	7.982720769955921
2018-09-24	7.928409505440399
2018-10-22	7.7411860313545
2018-04-23	7.671714791621996
2018-12-08	7.477213251581839
2018-04-24	7.470870941142693
2018-11-10	7.411391505403686
2018-03-03	7.325979536642015
2018-04-08	7.268136025226444
2018-09-25	7.248527813504637
2018-10-25	7.192913236533858
2018-05-15	7.168859614571561
2018-01-13	7.126823571685313
2018-05-05	6.906878404112484
2018-08-21	6.841289525780963
2018-11-18	6.796834601675052
2018-06-21	6.764683340770092
2018-06-24	6.596574538956665
2018-11-03	6.522762585872373
2018-05-16	6.48615923713745
2018-01-07	6.420844453924965
2018-11-05	6.417688909844269
2018-03-06	6.349945149300961
2018-08-18	6.187501294449016
2018-03-07	6.172352349287472
2018-08-20	6.13211999534919
2018-06-16	6.118537632718658
2018-11-29	6.065241569765681
2018-03-17	6.006603083752083
2018-12-06	5.996538534079764
2018-03-18	5.910026828166202
2018-11-17	5.808400635657502
2018-09-26	5.801206664345313
2018-10-26	5.779325153878007
2018-06-18	5.734887914637875
2018-05-26	5.602190842490095
2018-04-13	5.596783148609628
2018-11-06	5.576395930577082
2018-01-08	5.517962782003598
2018-06-22	5.497506327930426
2018-05-19	5.490496043971789
2018-04-25	5.466491283594766
2018-08-06	5.445391605702541
2018-09-08	5.4006446510414
2018-04-07	5.382023244868721
2018-06-09	5.3258559201817555
2018-08-04	5.245437247626126
2018-11-11	5.241172880707882
2018-08-26	5.204499498662823
2018-03-13	5.185461263940412
2018-08-07	5.135946238463144
2018-10-24	5.134761205866823
2018-01-06	5.128352030068818
2018-04-12	5.125693671750433
2018-11-09	5.1252556486967205
2018-10-06	5.09820222957644
2018-05-20	5.095244730309911
2018-07-14	5.0886378741637985
2018-01-09	5.049410466223003
2018-08-25	4.980661941915239
2018-04-05	4.9786741555894025
2018-04-30	4.819035426044705
2018-01-10	4.76593736234763
2018-05-28	4.68026580074614
2018-12-09	4.625354233483328
2018-11-08	4.6069033872765415
2018-09-02	4.595944833281466
2018-07-22	4.593393861441349
2018-10-12	4.524520721372113
2018-02-18	4.255421749359614
2018-04-11	4.15326769550994
2018-05-01	4.148203765592582
2018-09-06	4.074638491116442
2018-01-21	4.040933228369039
2018-03-05	4.028081329371769
2018-01-20	3.983184963690456
2018-02-17	3.9592179437267587
2018-12-07	3.928415210549354
2018-05-17	3.900997379661076
2018-11-07	3.781090171979379
2018-08-22	3.7540960066842066
2018-07-08	3.691214257139836
2018-11-19	3.6381439060823175
2018-07-09	3.587919930383572
2018-08-08	3.582098553125515
2018-09-09	3.5759640874830154
2018-09-27	3.569020349975437
2018-01-14	3.4918510250085406
2018-04-26	3.4455823158435064
2018-01-12	3.4339601863531612
2018-04-10	3.4318089048960854
2018-01-11	3.4028826063454725
2018-06-30	3.355114219075089
2018-10-31	3.3540417080572116
2018-03-25	3.3523733004600995
2018-05-22	3.3116791760493247
2018-04-09	3.284132718620538
2018-11-28	3.2337105614328596
2018-02-11	3.1992058723611114
2018-06-14	3.1851964256157874
2018-06-10	3.161260627929845
2018-04-06	3.110227198132983
2018-08-09	3.0843001500412646
2018-05-25	3.0016326095327823
2018-09-01	2.9837093513174255
2018-09-15	2.9179880634576563
2018-07-21	2.8933506992926987
2018-07-15	2.8759383920429187
2018-05-18	2.8735511886835856
2018-04-01	2.8681500129386905
2018-03-21	2.859885597017876
2018-08-24	2.8589575441530255
2018-05-24	2.83382654942222
2018-07-13	2.787470623222106
2018-11-16	2.7626001178609734
2018-06-03	2.75461670243995
2018-11-02	2.74905636125065
2018-11-01	2.712890648324257
2018-03-24	2.705494621418867
2018-01-19	2.6930317927735197
2018-06-15	2.6915907378300803
2018-10-29	2.686991403988603
2018-11-20	2.668421959015086
2018-03-14	2.6656798705206937
2018-07-01	2.639377107255994
2018-03-16	2.567052974029147
2018-03-31	2.4768260481588094
2018-07-12	2.4322463716166536
2018-10-30	2.4248784673751347
2018-11-23	2.4229459696536297
2018-08-23	2.40527330970895
2018-02-13	2.3758812754650664
2018-05-29	2.316169222449841
2018-10-07	2.3156859613446947
2018-08-29	2.1799793376147036
2018-11-12	2.1693098056774884
2018-09-07	2.1595089361052366
2018-04-02	2.1315521682622944
2018-11-14	2.1134659160565357
2018-11-13	2.0047810335864957
2018-03-19	1.9628808187501918
2018-02-14	1.9227148290299392
2018-11-24	1.906880362157891
2018-06-02	1.8526803126666398
2018-02-10	1.8259332815621994
2018-03-22	1.8111175258908978
2018-09-20	1.8086046133719123
2018-01-18	1.7316578551283315
2018-02-24	1.679820897111581
2018-05-21	1.666972371077739
2018-06-25	1.648684473303101
2018-11-21	1.6143364878774755
2018-08-11	1.6057134493921184
2018-09-05	1.6002086245984404
2018-01-15	1.5938763419330733
2018-03-15	1.5571475346089114
2018-02-12	1.5543185252081144
2018-02-15	1.4696386764646396
2018-01-05	1.456344971425907
2018-06-08	1.4293196749694965
2018-09-21	1.382626912966169
2018-07-10	1.3382347067653138
2018-05-23	1.306861677680712
2018-08-03	1.2780186081652762
2018-07-11	1.2738690114677595
2018-10-11	1.2464405605483622
2018-11-25	1.2250799832621464
2018-11-22	1.214306483368349
2018-08-31	1.0760382222088678
2018-05-03	1.0552549601062509
2018-03-20	1.0422082525834733
2018-01-17	1.0252444061854975
2018-07-24	1.0143208574559224
2018-10-09	1.0071266127941847
2018-09-04	1.0005788282401595
2018-11-15	0.9223148101050318
2018-02-16	0.9074606306465425
2018-08-10	0.9036341501072411
2018-02-25	0.8639406420071154
2018-01-16	0.826683836667204
2018-08-12	0.7744852475885409
2018-05-30	0.7712897297484758
2018-07-20	0.7028110841076054
2018-05-02	0.6991097660288634
2018-09-03	0.683775948999076
2018-07-29	0.6335306876798337
2018-07-23	0.6152813959254133
2018-09-16	0.6123061206765863
2018-09-28	0.4523549405630516
2018-09-30	0.4515656786872553
2018-02-27	0.41566505849738844
2018-06-29	0.3820426144303619
2018-04-03	0.370570192088862
2018-07-25	0.3567793924043352
2018-01-02	0.3212670677455316
2018-03-02	0.25908410397409654
2018-03-30	0.17316334177262105
2018-02-04	0.16616025932341172
2018-08-17	0.1629558992156963
2018-03-26	6.727633754213702e-2
2018-04-04	6.601144887406996e-2
2018-03-23	3.179181663940911e-2
2018-05-31	3.136427694204036e-2
2018-06-01	-4.39999461099605e-2
2018-03-27	-4.958289477016642e-2
2018-09-19	-5.8010942496990126e-2
2018-07-28	-0.11868598530518337
2018-02-28	-0.1254175938875366
2018-08-30	-0.13668850733493443
2018-06-12	-0.2045192799011617
2018-08-27	-0.23392175194313714
2018-10-08	-0.2850772445866747
2018-08-28	-0.47637045929834043
2018-10-05	-0.4849237606022401
2018-10-10	-0.4941231461582305
2018-02-26	-0.5065333868479032
2018-07-07	-0.5303029545852589
2018-07-03	-0.6413684311625434
2018-02-09	-0.6442009502015447
2018-01-04	-0.7244459631773861
2018-01-23	-0.8192604176824385
2018-01-03	-0.8225724376179675
2018-07-26	-0.9098762772299227
2018-12-15	-0.9122642095213793
2018-09-14	-0.9531946203004753
2018-09-10	-0.9810538927641539
2018-03-01	-1.0602110951733992
2018-01-28	-1.0608057763149794
2018-09-11	-1.0616430797274217
2018-02-03	-1.0717219413020924
2018-01-22	-1.0789334608052936
2018-06-27	-1.0891339752023268
2018-06-28	-1.130141051322766
2018-06-26	-1.137654948062775
2018-11-27	-1.1812408908959169
2018-07-02	-1.3086446749179
2018-12-16	-1.309809287500618
2018-09-29	-1.3248856236581052
2018-03-28	-1.3552367963698195
2018-10-01	-1.3870131165921822
2018-02-02	-1.3895744806721257
2018-02-08	-1.4776949758916373
2018-02-22	-1.5599837016132585
2018-12-10	-1.6813019271362846
2018-07-17	-1.74591448327502
2018-07-19	-1.7573347621843314
2018-10-02	-1.8101306308776306
2018-02-23	-1.8113157090322092
2018-02-05	-1.8461329397893045
2018-07-06	-1.8676357265862635
2018-07-04	-1.9752014850954325
2018-12-14	-1.9804298977904016
2018-07-18	-2.090632333608432
2018-06-07	-2.142892866101778
2018-06-04	-2.1431848510987486
2018-06-13	-2.1665641636390136
2018-12-19	-2.1964153243240783
2018-10-03	-2.200248596348493
2018-08-16	-2.2183974753427886
2018-05-04	-2.2567422734823293
2018-02-19	-2.260530603583992
2018-08-15	-2.504414714014903
2018-02-20	-2.5476634565787677
2018-08-14	-2.582734658569964
2018-07-27	-2.748020923559909
2018-12-18	-2.8451915413795694
2018-12-11	-2.8570741374604642
2018-07-16	-2.930993932605596
2018-12-12	-2.9849609775754398
2018-02-07	-2.9921828893184763
2018-12-13	-3.035720198357624
2018-01-31	-3.0422540354753624
2018-06-11	-3.0482803401492116
2018-06-06	-3.1153431364601376
2018-12-22	-3.128129764637562
2018-09-13	-3.14691361777108
2018-09-18	-3.1473488148909317
2018-10-04	-3.1826525202627054
2018-11-26	-3.206987780540401
2018-03-29	-3.2177095470263226
2018-09-12	-3.3188840423945587
2018-02-21	-3.3415718617878376
2018-08-01	-3.374807833645513
2018-07-05	-3.401297748343711
2018-02-06	-3.41801131537882
2018-09-17	-3.5595776490375344
2018-01-29	-3.75670988031478
2018-08-02	-3.766465397939953
2018-02-01	-3.8767280752294666
2018-01-24	-4.0353868362684135
2018-01-25	-4.099231233918816
2018-01-30	-4.132258540931211
2018-06-05	-4.204603868662037
2018-01-27	-4.225338770320211
2018-07-30	-4.340032591506121
2018-12-23	-4.496748804270663
2018-12-20	-4.530356321068381
2018-12-17	-4.685629860910394
2018-08-13	-5.158738574164472
2018-01-26	-5.786964396963983
2018-12-21	-5.938428867782927
2018-07-31	-6.001366042606405
2018-12-30	-6.048890091027438
2018-12-24	-6.303273492337473
2018-12-29	-7.5290821169025826
2018-12-25	-7.942541335592582
2018-12-26	-8.732956905335165
2018-12-28	-10.492764195593848
2018-12-27	-11.056655636490078

trendcalculusmcmodelperformance

Coverage Grouped by Country

display(oil_gas_cov_norm.filter($"date" >"2018-01-01" && $"date"<"2018-12-31").orderBy(desc("coverage")).limit(1000))

country	date	articles	coverage
US	2018-04-19	293978.0	17.06571958044547
US	2018-03-10	121473.0	16.997419653664288
US	2018-04-20	128613.0	16.8411625445618
US	2018-04-16	121972.0	16.804795231624784
US	2018-04-18	325093.0	16.69630497544722
US	2018-04-21	94415.0	16.66300997755572
US	2018-03-11	192305.0	16.321746675576378
US	2018-04-17	198695.0	16.118084162377855
US	2018-03-12	121061.0	16.02109075933443
US	2018-03-08	167306.0	16.003087827280364
US	2018-05-10	239649.0	15.9504831207996
US	2018-03-09	172436.0	15.937985332447004
US	2018-05-11	156365.0	15.620396928759616
US	2018-01-08	125330.0	15.618951133444076
US	2018-05-09	250456.0	15.48443656158681
US	2018-01-07	75339.0	15.46596096567959
US	2018-04-15	49398.0	15.288016926844017
US	2018-01-09	135528.0	15.24454575423161
US	2018-04-22	75971.0	15.150165904258586
US	2018-03-13	254054.0	15.04659691290507
US	2018-05-08	249174.0	15.008311140799353
US	2018-01-10	269866.0	14.808527251572325
US	2018-03-14	156586.0	14.661737321411012
US	2018-12-04	143569.0	14.583942411932586
US	2018-08-19	39816.0	14.553163653965246
US	2018-08-20	147857.0	14.451221182341712
US	2018-06-20	191796.0	14.431702945581934
US	2018-05-07	122164.0	14.423876188248778
US	2018-08-21	249440.0	14.406957602681363
US	2018-11-05	120204.0	14.290807411707052
US	2018-06-21	184814.0	14.249073973848898
US	2018-03-07	205189.0	14.224467649728664
US	2018-01-11	200361.0	14.220547320123071
US	2018-12-03	152099.0	14.201279317167904
US	2018-11-07	309670.0	14.157238167556102
US	2018-11-06	122098.0	14.120787443350878
US	2018-04-24	185880.0	14.027617056766815
US	2018-11-08	194910.0	13.999187716187226
US	2018-03-04	64364.0	13.985730698250288
US	2018-04-25	216270.0	13.917486378981236
US	2018-04-27	156431.0	13.857416363996196
US	2018-08-23	137032.0	13.819353021939026
US	2018-06-23	120879.0	13.788852301532364
US	2018-12-02	91072.0	13.773893880767753
US	2018-03-03	47130.0	13.73437084151701
US	2018-06-22	218166.0	13.678457488064144
US	2018-01-12	203985.0	13.651376629653857
US	2018-04-23	105819.0	13.640894613616197
US	2018-01-13	65962.0	13.617164107812112
US	2018-11-10	64706.0	13.606612582384283
US	2018-09-25	270785.0	13.592029512326587
US	2018-08-22	224768.0	13.588415024037738
US	2018-04-26	185412.0	13.5723444530304
US	2018-05-12	74624.0	13.565184985842878
US	2018-01-19	188615.0	13.551477734101324
US	2018-03-05	125744.0	13.548697358494518
US	2018-06-19	137218.0	13.493937860918477
US	2018-11-09	144998.0	13.474364016646565
US	2018-09-24	184067.0	13.394525531097136
US	2018-06-24	51756.0	13.392064898685112
US	2018-08-24	143121.0	13.323584247489487
US	2018-01-06	97326.0	13.23302741397582
US	2018-01-20	182911.0	13.232971806463684
US	2018-03-16	102338.0	13.232457436976429
US	2018-04-28	86493.0	13.21701245048062
US	2018-03-06	177846.0	13.19096033104485
US	2018-05-06	32559.0	13.183856471369461
US	2018-09-26	159017.0	13.145681914288017
US	2018-11-04	72936.0	13.084555356572393
US	2018-01-18	160609.0	13.077229066848458
US	2018-03-20	145334.0	13.059212232916357
US	2018-09-23	65296.0	13.002534276171621
US	2018-03-22	148019.0	12.917079431896443
US	2018-01-17	157335.0	12.912283283974704
US	2018-09-27	122838.0	12.795479704732795
US	2018-06-25	90453.0	12.78376042155011
US	2018-03-21	177917.0	12.748171613782992
SA	2018-10-18	101417.0	12.684765148069788
SA	2018-10-17	194570.0	12.679829981367707
US	2018-04-14	52822.0	12.663425765287553
US	2018-12-05	175971.0	12.61896755933473
US	2018-08-18	105451.0	12.58164101681336
US	2018-03-15	145679.0	12.549889127383638
US	2018-01-05	230917.0	12.53889274185872
US	2018-12-01	198620.0	12.532331055426658
US	2018-03-02	198169.0	12.500885007313688
US	2018-02-27	89118.0	12.491028575787562
US	2018-01-04	189356.0	12.48233990201629
US	2018-01-21	44909.0	12.383150002243495
SA	2018-10-19	73494.0	12.331977189200233
US	2018-09-22	85630.0	12.31143021346594
US	2018-11-11	61567.0	12.179709919093515
US	2018-06-18	131499.0	12.142897746059406
US	2018-01-14	33044.0	12.052771870764795
US	2018-03-19	170160.0	12.050116612060297
US	2018-05-13	66083.0	12.02158995833447
US	2018-03-18	40394.0	12.01758621746067
US	2018-10-10	176220.0	12.002155132842898
US	2018-08-25	46571.0	11.99847113516388
US	2018-04-29	51144.0	11.917756831298309
US	2018-04-13	178010.0	11.870893600445594
US	2018-02-28	187108.0	11.82981355085504
US	2018-03-01	198743.0	11.80548526429549
US	2018-01-22	118502.0	11.7943359581122
US	2018-11-30	131668.0	11.764530331607242
US	2018-04-05	151628.0	11.763904747095708
US	2018-10-09	187842.0	11.761305095903344
US	2018-12-06	139691.0	11.756884298688522
US	2018-03-23	174925.0	11.754715605715216
US	2018-01-03	109245.0	11.73426594312716
US	2018-03-17	93789.0	11.721045257116797
US	2018-06-26	145159.0	11.720266751946893
US	2018-02-26	75722.0	11.688403647492896
US	2018-05-26	77976.0	11.6531901904327
US	2018-10-11	140387.0	11.62099344090589
US	2018-04-04	176372.0	11.548161501885613
US	2018-04-10	141686.0	11.541516404185346
US	2018-02-14	127538.0	11.518022230307839
US	2018-09-28	101232.0	11.507498508636077
US	2018-02-13	133936.0	11.506761709100273
US	2018-01-15	84388.0	11.500144415156077
US	2018-04-12	184872.0	11.498267661621483
US	2018-05-27	99428.0	11.497072100110556
US	2018-08-27	112195.0	11.488355622583217
US	2018-08-29	184301.0	11.448095783796672
US	2018-06-27	163254.0	11.447164357968393
US	2018-08-26	56428.0	11.435903836760827
US	2018-04-30	126325.0	11.431733273350618
US	2018-01-02	85597.0	11.41303524739485
US	2018-05-05	40375.0	11.409351249715835
US	2018-10-07	62963.0	11.407961061912431
US	2018-04-11	136299.0	11.38833161012838
US	2018-03-24	71415.0	11.37479118092324
US	2018-10-08	92961.0	11.371663258365583
US	2018-04-06	123941.0	11.30307139214568
US	2018-01-16	133067.0	11.28647254977305
US	2018-05-28	69840.0	11.266676275452593
US	2018-10-12	148567.0	11.254359211514444
US	2018-08-28	154121.0	11.245170070133952
US	2018-02-12	95901.0	11.223844589229751
US	2018-10-31	150322.0	11.222843654011301
US	2018-04-02	128317.0	11.218923324405706
US	2018-02-15	211996.0	11.193886042066419
US	2018-04-03	171774.0	11.180095379056663
US	2018-11-01	108141.0	11.171921074772655
US	2018-11-12	82452.0	11.163816279878814
US	2018-11-02	157228.0	11.159993263419455
US	2018-10-28	76599.0	11.156031228179758
US	2018-11-17	67482.0	11.151429706550493
SA	2018-10-16	232742.0	11.147328652530456
US	2018-06-28	141057.0	11.13551205620153
US	2018-06-29	141666.0	11.115076295491507
US	2018-05-24	146696.0	11.10189731511525
US	2018-10-30	143007.0	11.096322662023605
US	2018-08-30	140805.0	11.092749879368858
US	2018-10-27	52983.0	11.036808722159924
US	2018-10-29	121062.0	11.020446211713873
US	2018-06-17	64893.0	11.008448890970508
US	2018-11-16	112630.0	10.980547821756213
US	2018-08-06	129756.0	10.961307622557113
US	2018-02-25	66114.0	10.947350137010949
US	2018-09-07	95556.0	10.937368588582514
US	2018-04-01	25971.0	10.898387722575098
US	2018-04-07	63841.0	10.88479168585782
US	2018-11-03	62084.0	10.869318895605945
US	2018-05-25	177910.0	10.849327994993013
US	2018-05-01	139814.0	10.846380796849797
US	2018-02-01	140101.0	10.839874717929872
US	2018-02-16	139981.0	10.837261164859473
US	2018-08-07	158735.0	10.81875776519618
US	2018-02-03	80910.0	10.807830889061433
US	2018-12-07	159194.0	10.804369321430963
US	2018-09-03	41958.0	10.80388275569977
US	2018-04-09	95168.0	10.789855760763434
US	2018-11-14	207029.0	10.752431905095829
US	2018-10-06	48236.0	10.747343817735375
US	2018-09-02	30867.0	10.738543928939833
US	2018-01-31	173319.0	10.726921958903386
US	2018-06-30	101234.0	10.718636439595103
US	2018-11-13	131611.0	10.713840291673364
SA	2018-10-20	128817.0	10.709919962067769
US	2018-08-05	31112.0	10.692181165696349
US	2018-10-26	151770.0	10.69042952906406
SA	2018-10-15	141823.0	10.667699958478423
US	2018-03-25	52544.0	10.650322610935886
US	2018-02-18	26847.0	10.644177980844844
US	2018-09-06	145505.0	10.623491986330208
US	2018-02-17	80161.0	10.621587429039549
US	2018-08-09	137140.0	10.604668843472135
US	2018-02-02	177181.0	10.596633557968469
US	2018-05-14	98420.0	10.596522342944194
US	2018-01-23	110156.0	10.596007973456935
US	2018-12-08	57274.0	10.56952489580211
US	2018-02-23	140434.0	10.549186448238325
US	2018-08-17	146305.0	10.511957218863193
US	2018-05-29	157439.0	10.508398338086483
US	2018-09-08	67881.0	10.495636414051246
US	2018-11-29	108948.0	10.482360120528751
US	2018-09-05	214833.0	10.479148786702885
US	2018-02-22	145437.0	10.473087567880048
US	2018-10-25	117894.0	10.464134758426136
US	2018-08-08	174538.0	10.464093052792034
US	2018-11-18	33272.0	10.4360946704315
US	2018-10-23	118091.0	10.407623624217809
US	2018-09-04	168347.0	10.38582547946045
US	2018-03-26	86548.0	10.379958886930089
US	2018-05-15	101337.0	10.376942179396707
US	2018-05-23	120110.0	10.36708574787058
US	2018-11-15	121834.0	10.35907826612298
US	2018-08-10	94133.0	10.342326503091973
US	2018-04-08	41490.0	10.327701727400177
US	2018-09-01	61168.0	10.31409178880486
US	2018-05-16	139421.0	10.262515821298615
US	2018-02-04	40178.0	10.239786250712976
US	2018-05-30	108880.0	10.23472596710859
US	2018-05-22	99615.0	10.206060294602423
US	2018-05-02	122811.0	10.205253985676448
US	2018-01-30	104797.0	10.204836929335428
US	2018-02-10	79351.0	10.195953629271683
US	2018-03-31	37365.0	10.195397554150322
US	2018-10-13	65561.0	10.157973698482717
US	2018-02-05	56912.0	10.142973572084
US	2018-02-24	94693.0	10.14180581432914
US	2018-02-11	50163.0	10.12755638934426
US	2018-08-31	125628.0	10.116323671892767
US	2018-09-21	87025.0	10.073464181913854
US	2018-08-15	82951.0	10.017550828460989
US	2018-02-09	119630.0	10.00206413633108
US	2018-08-16	144365.0	9.997976984189078
US	2018-05-17	137140.0	9.99126237709864
US	2018-10-14	35545.0	9.96765698819686
US	2018-05-03	150451.0	9.94688758241402
US	2018-02-21	129163.0	9.927202523117833
US	2018-05-04	114325.0	9.889041867914427
US	2018-05-18	140570.0	9.84651602300833
US	2018-09-14	123342.0	9.836381553921525
US	2018-05-19	66393.0	9.822576989033735
US	2018-10-24	141746.0	9.798165291205978
SA	2018-10-21	50740.0	9.754541197935195
US	2018-11-19	127156.0	9.733215717030996
US	2018-10-20	96823.0	9.728767116060103
US	2018-02-20	118422.0	9.725180431527326
US	2018-02-19	70248.0	9.71888288077791
US	2018-06-16	53423.0	9.718146081242109
US	2018-03-27	118005.0	9.7100134825922
US	2018-10-05	120539.0	9.6986556482384
US	2018-05-21	88008.0	9.68696416881178
US	2018-10-04	142998.0	9.677218952309927
US	2018-10-22	104784.0	9.618970083347346
US	2018-10-19	95040.0	9.60205149777993
US	2018-12-09	29060.0	9.587315507063863
US	2018-11-28	86662.0	9.577403468025599
SA	2018-10-14	50385.0	9.574067017297429
US	2018-12-13	109585.0	9.55767670309531
US	2018-05-20	46571.0	9.554117822318602
US	2018-08-04	63962.0	9.5381445644575
US	2018-08-11	38450.0	9.53361255221841
US	2018-10-15	66588.0	9.47582244523095
US	2018-09-15	48527.0	9.46422827895057
US	2018-02-08	133137.0	9.460043813662326
US	2018-03-30	126734.0	9.447907474138619
US	2018-06-01	123365.0	9.444543219654383
US	2018-10-21	28694.0	9.439830483000849
US	2018-10-02	112407.0	9.432949053374003
US	2018-09-09	41250.0	9.423885028895816
US	2018-07-01	29338.0	9.423551383822998
US	2018-07-02	88983.0	9.381150655819212
US	2018-10-03	128700.0	9.359449824208093
US	2018-02-06	119989.0	9.342906589347596
US	2018-12-14	105697.0	9.339903783692248
US	2018-02-07	132458.0	9.321233561492546
US	2018-05-31	130123.0	9.318536597153946
US	2018-09-29	53523.0	9.305746869362638
US	2018-06-04	78904.0	9.298045228931786
US	2018-07-03	116642.0	9.256464711732006
US	2018-03-28	125804.0	9.236654535533516
US	2018-07-23	107114.0	9.206348441419332
US	2018-06-03	33524.0	9.203484654544322
US	2018-12-18	63736.0	9.169313838336679
US	2018-12-10	83582.0	9.168785566971385
US	2018-10-17	162530.0	9.166297130803295
US	2018-01-29	74409.0	9.165463018121253
US	2018-10-01	91419.0	9.164545494171007
US	2018-09-11	136572.0	9.15999958005388
US	2018-09-13	98737.0	9.135031807104763
US	2018-09-20	94641.0	9.1131085454451
US	2018-08-14	100562.0	9.086111098303014
US	2018-12-12	105318.0	9.07701927006876
US	2018-10-18	105008.0	9.07105536439216
US	2018-09-16	58808.0	9.068928377052954
US	2018-07-22	53621.0	9.03136550260501
US	2018-09-19	109304.0	9.02291316076032
US	2018-09-17	114986.0	9.011986284625573
US	2018-11-21	155573.0	8.964136020432443
US	2018-07-24	120368.0	8.961021999752822
US	2018-11-20	143903.0	8.948148860693312
US	2018-07-25	96753.0	8.903259696521433
US	2018-09-12	137739.0	8.89094263258328
US	2018-09-30	40105.0	8.884283633004982
SA	2018-10-22	116446.0	8.871146358262825
US	2018-03-29	128571.0	8.867239930535263
US	2018-11-22	71274.0	8.862707918296168
US	2018-01-28	32053.0	8.861748688711822
US	2018-07-21	47326.0	8.843829167925959
US	2018-06-15	120982.0	8.803902974212228
US	2018-07-26	108648.0	8.789778666129655
US	2018-09-10	64536.0	8.773721997000349
US	2018-06-02	58290.0	8.771469892758835
US	2018-10-16	108976.0	8.73169661970348
US	2018-08-03	104387.0	8.658030568001163
US	2018-01-24	96205.0	8.655917482539987
US	2018-06-05	109023.0	8.612918973780738
US	2018-12-17	67917.0	8.544869280804166
US	2018-09-18	109802.0	8.507111780063742
US	2018-01-25	118254.0	8.477194938534513
US	2018-12-15	104170.0	8.464919580230465
US	2018-12-11	126676.0	8.425076797784937
SA	2018-10-23	116063.0	8.419627261595597
US	2018-06-08	74082.0	8.414149921650191
US	2018-06-07	136925.0	8.39927491215378
US	2018-06-06	139956.0	8.382578756634912
US	2018-12-19	95718.0	8.377184827957707
US	2018-08-13	110885.0	8.360822317511655
US	2018-07-27	121914.0	8.333560734686925
US	2018-12-16	63635.0	8.331461551103787
US	2018-07-04	70095.0	8.32111855384647
US	2018-07-08	21576.0	8.270515717802605
US	2018-08-12	41224.0	8.260381248715797
US	2018-07-05	138007.0	8.213212176546335
US	2018-07-20	139561.0	8.141047527671692
US	2018-06-14	103210.0	8.087608708508885
US	2018-08-01	91525.0	8.086482656388128
US	2018-07-30	74297.0	8.041106926485059
US	2018-07-28	43171.0	7.986820092762175
US	2018-07-09	49654.0	7.96962346963408
US	2018-11-23	56158.0	7.927292251020463
US	2018-07-29	45458.0	7.914141074400271
US	2018-06-09	41721.0	7.891870265789757
US	2018-08-02	117781.0	7.887046314111948
US	2018-01-26	102416.0	7.864219430380073
US	2018-07-31	95426.0	7.797448710182633
US	2018-01-27	43355.0	7.7897192659957115
US	2018-11-27	88339.0	7.770326146138241
US	2018-12-20	124936.0	7.756841324445233
US	2018-06-13	98981.0	7.668216851978299
US	2018-07-06	132697.0	7.66646521534601
IR	2018-05-10	98317.0	7.607938308822747
IR	2018-05-11	42017.0	7.539958125236347
IR	2018-05-09	196921.0	7.532895971195059
US	2018-06-12	71454.0	7.505537075224091
IR	2018-05-08	170920.0	7.434123127763284
US	2018-07-07	33952.0	7.421361203728045
US	2018-07-10	99011.0	7.3869679574718585
US	2018-07-19	96061.0	7.366003925396543
US	2018-07-11	131177.0	7.326383572999561
US	2018-06-10	34725.0	7.322240813345419
SA	2018-10-13	18580.0	7.281967072680836
US	2018-07-13	90785.0	7.214014692850504
US	2018-07-12	116363.0	7.190256383290348
US	2018-11-24	68632.0	7.154848299937678
US	2018-12-21	150615.0	7.150024348259869
IR	2018-05-07	20107.0	7.117785893098955
US	2018-06-11	79974.0	6.853538995428132
US	2018-07-14	29594.0	6.808135461768994
US	2018-07-18	83263.0	6.784391054086874
SA	2018-10-24	125847.0	6.782917455015266
US	2018-11-26	59869.0	6.7205953357887145
US	2018-12-22	47190.0	6.635710468512932
US	2018-07-17	69815.0	6.537882952787471
IR	2018-09-25	74769.0	6.407858687535197
IR	2018-09-24	49741.0	6.326894149865013
SA	2018-10-25	37872.0	6.225048991387717
US	2018-11-25	25976.0	6.196855982734706
US	2018-07-15	11784.0	6.14204087764653
IR	2018-09-23	109693.0	6.0511921046941515
IR	2018-05-06	8554.0	5.899091657123839
US	2018-07-16	51363.0	5.859804949799675
US	2018-12-23	19012.0	5.682639416134008
IR	2018-05-12	16179.0	5.45491275205858
IR	2018-09-22	126435.0	5.316311028059311
IR	2018-09-26	62879.0	4.890885756461957
SA	2018-10-26	41015.0	4.7543693141677945
US	2018-12-24	24267.0	4.737603649258753
SY	2018-04-14	77719.0	4.541837402783558
TU	2018-10-19	32942.0	4.493472769103172
TU	2018-10-17	87405.0	4.406919676463308
SA	2018-10-12	38993.0	4.402749113053098
IR	2018-09-21	6514.0	4.39340705101423
TU	2018-10-18	31166.0	4.386261485704741
US	2018-12-30	23279.0	4.318462026532781
SY	2018-04-15	92616.0	4.209123755795143
TU	2018-10-20	32608.0	4.161412510382355
SY	2018-04-16	51381.0	4.067310697970013
TU	2018-10-16	72217.0	4.017722699022632
IS	2018-05-12	2255.0	3.939816574519934
SY	2018-04-13	12182.0	3.928722875848778
SY	2018-04-17	51599.0	3.9177820978359974
IS	2018-05-13	1307.0	3.8505943212975358
IR	2018-09-20	16401.0	3.830172462465547
KN	2018-05-11	9007.0	3.8239305192282673
KN	2018-05-10	151876.0	3.7756910024501873
KN	2018-05-09	99867.0	3.7698522136758945
TU	2018-10-15	49492.0	3.7396851383420526
SY	2018-04-12	21443.0	3.725936180966398
KN	2018-05-08	12105.0	3.6731924557052915
KN	2018-05-12	7621.0	3.6677012138818506
US	2018-12-29	31458.0	3.6640728237149687
US	2018-12-28	50325.0	3.6340725709175348
IR	2018-08-06	61148.0	3.6273301600710304
KN	2018-05-07	329.0	3.6256341309508784
IR	2018-08-07	100863.0	3.560489930483419
RS	2018-07-19	40550.0	3.538052299336496
IR	2018-08-05	15094.0	3.51967401657551
RS	2018-07-18	28985.0	3.5130011151191765
RS	2018-07-17	68773.0	3.509470038098533
IR	2018-08-08	53752.0	3.5018379070578507
IR	2018-09-27	36233.0	3.4635243311960666
TU	2018-10-21	20839.0	3.4264063168452097
TU	2018-10-14	22325.0	3.426142181162563
IR	2018-08-09	21172.0	3.357981273161719
US	2018-12-25	26740.0	3.3433843012259885
IR	2018-05-05	9074.0	3.317318279912184
SA	2018-10-27	11084.0	3.3093803075547537
IR	2018-11-05	75534.0	3.2770028336135
IR	2018-11-04	32874.0	3.276127015297356
RS	2018-07-14	8640.0	3.1989020828183254
TU	2018-10-22	57204.0	3.1911865405094395
US	2018-12-27	56957.0	3.1839992695658466
IR	2018-11-03	29708.0	3.1837768395173023
IR	2018-09-28	12338.0	3.1835822132248253
TU	2018-10-23	48331.0	3.1767702929881514
IS	2018-05-11	8186.0	3.168234539875258
IR	2018-05-13	13952.0	3.149286280114876
US	2018-12-26	27161.0	3.1246799559946448
RS	2018-07-16	58266.0	3.084837173549118
RS	2018-07-15	6153.0	3.0744802744137663
RS	2018-03-16	25299.0	3.044549531006502
IR	2018-08-04	10215.0	3.038460508427597
IR	2018-07-24	34917.0	2.9866204052387033
RS	2018-07-20	52232.0	2.978765844149476
IR	2018-07-25	13467.0	2.9717175919862244
IS	2018-05-14	132441.0	2.9480426936942727
IR	2018-07-23	121138.0	2.9291222376899593
SA	2018-11-20	41960.0	2.915665219753019
KN	2018-03-08	8525.0	2.8903916054871543
RS	2018-03-18	66413.0	2.8767816668918407
SY	2018-04-18	6987.0	2.8668140203414416
RS	2018-03-19	61502.0	2.8591540855446915
SA	2018-11-21	61467.0	2.8581670522042755
IS	2018-05-15	62384.0	2.8523004596739154
FR	2018-12-03	26729.0	2.848922303311646
FR	2018-12-04	22382.0	2.8355904022770124
IS	2018-05-16	8920.0	2.828778482040338
KN	2018-03-07	10783.0	2.8284587388455553
IS	2018-05-17	7721.0	2.8191861861968586
IR	2018-07-22	21615.0	2.8127913223012047
RS	2018-04-13	28932.0	2.7998486738515243
IR	2018-11-06	37292.0	2.79624808744071
TU	2018-10-24	34534.0	2.786405557792618
RS	2018-03-17	11413.0	2.745992798347696
IR	2018-07-26	14868.0	2.7445887086662597
IR	2018-11-02	42823.0	2.7344820433355195
RS	2018-04-14	31685.0	2.733786949433818
IR	2018-07-21	8979.0	2.726933323563042
SA	2018-10-11	22749.0	2.7074845961934355
SA	2018-11-19	16766.0	2.6906077162601245
SA	2018-11-22	40463.0	2.679694742003412
RS	2018-03-20	14935.0	2.664319264897776
SY	2018-04-11	30920.0	2.6611079310719146
KN	2018-03-09	101156.0	2.646177314063368
IR	2018-08-10	5025.0	2.6344302271246134
RS	2018-04-15	15941.0	2.5899720211717887
TU	2018-10-25	14246.0	2.56675588485496
CH	2018-03-26	15479.0	2.5665056510503477
SA	2018-11-23	26002.0	2.553187651893748
RS	2018-03-21	24279.0	2.545305287048454
KN	2018-05-13	1944.0	2.491560626568898
IR	2018-11-07	15431.0	2.4846513931859855
CH	2018-03-25	19450.0	2.466189699156795
CH	2018-03-27	25021.0	2.458418549335772
IR	2018-07-20	6869.0	2.4519958816840512
FR	2018-12-02	23278.0	2.4396093083557315
CH	2018-03-28	101895.0	2.4361755444813262
KN	2018-03-06	36844.0	2.4332005425820435
CH	2018-03-30	6122.0	2.425054042054103
KN	2018-03-10	32100.0	2.4148778673331934
IR	2018-09-19	10017.0	2.4123060198968984
RS	2018-04-12	38212.0	2.39581839254854
RS	2018-02-14	15800.0	2.390118622554588
TU	2018-10-13	4612.0	2.379900742199577
UK	2018-04-18	56380.0	2.3646364801182136
RS	2018-03-15	14247.0	2.361161010609706
AR	2018-11-30	48495.0	2.3373887991715168
SA	2018-11-18	20211.0	2.333454567687886
RS	2018-07-13	21687.0	2.3163135520719282
UK	2018-04-21	13971.0	2.308097542153817
KN	2018-03-11	4607.0	2.3030650623054987
KN	2018-06-12	53681.0	2.284380938227764
RS	2018-04-16	35940.0	2.2754976381640195
UK	2018-04-20	21037.0	2.274454997311467
IR	2018-09-29	17315.0	2.26625288927139
KN	2018-06-13	21236.0	2.264765388321749
AR	2018-12-01	36929.0	2.2638756681275716
KN	2018-06-11	71286.0	2.2607894512040168
CH	2018-03-31	2621.0	2.2375594130091545
UK	2018-04-17	16163.0	2.2356965613525945
RS	2018-04-11	30356.0	2.2337781021838987
KN	2018-06-10	16032.0	2.2238104556334997
UK	2018-04-19	32276.0	2.2161783245928177
CH	2018-03-29	15806.0	2.2137454959368625
KN	2018-03-12	7485.0	2.2016091564131552
AR	2018-12-02	48505.0	2.183091854871829
SA	2018-11-24	9880.0	2.1829111304573865
IR	2018-08-03	9833.0	2.166298386206722
AR	2018-11-29	13730.0	2.154745925560444
RS	2018-07-21	8894.0	2.146557719398401
RS	2018-04-17	26736.0	2.131696611780024
IR	2018-11-08	13215.0	2.1220070027903057
UK	2018-07-11	27825.0	2.107090287659793
SA	2018-10-10	29693.0	2.1045184402234973
UK	2018-04-16	23182.0	2.103823346321796
RS	2018-04-09	6877.0	2.098401613888524
RS	2018-12-02	5691.0	2.0927574514067087
UK	2018-07-12	38075.0	2.088545182362398
UK	2018-07-10	24389.0	2.060449486855625
KN	2018-06-14	5682.0	2.0519276356207654
RS	2018-02-15	22046.0	2.0507181722318046
IR	2018-05-14	15217.0	2.042947022410783
FR	2018-12-01	70292.0	2.0375252899775114
UK	2018-05-14	13079.0	2.0163666316097197
AR	2018-12-03	15700.0	2.007302607131533
UK	2018-05-11	42485.0	1.9899391614670308
FR	2018-12-05	34985.0	1.9873534121527012
RS	2018-02-13	15796.0	1.9761484984572735
UK	2018-05-16	26616.0	1.9717416031204864
IR	2018-01-02	25965.0	1.9606618063273653
UK	2018-05-15	13218.0	1.9470379658540171
UK	2018-05-17	44767.0	1.944243688369177
KN	2018-06-09	2175.0	1.9374873756446391
UK	2018-07-13	41539.0	1.9361388934753383
RS	2018-04-10	31488.0	1.9333307141124645
UK	2018-05-18	37498.0	1.9209580426621784
RS	2018-02-16	43709.0	1.9187476440547682
UK	2018-04-15	18239.0	1.9088773106506076
UK	2018-06-19	33154.0	1.9045677284600584
UK	2018-05-19	9638.0	1.8946973950558978
SA	2018-10-09	25632.0	1.8912080236693567
FR	2018-12-06	33466.0	1.8872737921857266
UK	2018-05-10	32097.0	1.8818103541183535
IR	2018-05-18	12730.0	1.8800448156080312
IR	2018-09-09	17329.0	1.8762217991486734
RS	2018-12-03	7632.0	1.8636266976498435
CA	2018-08-08	20157.0	1.8594700361176686
IR	2018-09-10	6322.0	1.8592615079471582
TU	2018-10-26	31905.0	1.8554245896097663
RS	2018-12-01	21909.0	1.8538953830260227
CA	2018-08-09	20022.0	1.8528805459295388
UK	2018-06-17	15941.0	1.8499194459082908
SA	2018-10-28	10611.0	1.8495162914453036
UK	2018-05-13	8170.0	1.8402298369185723
FR	2018-11-30	4952.0	1.8362399979228063
IR	2018-09-11	28622.0	1.8351695533141859
CA	2018-08-07	16160.0	1.8335291317061704
IR	2018-01-04	14518.0	1.8334457204379664
UK	2018-06-20	20877.0	1.8305124241727861
RS	2018-11-30	54768.0	1.8242148734233707
RS	2018-07-22	7955.0	1.8189460616484745
RS	2018-02-17	36154.0	1.8171388175040502
IR	2018-09-30	7019.0	1.8123982770944465
IR	2018-11-01	13152.0	1.8119951226314597
UK	2018-05-09	19946.0	1.80440469722488
RS	2018-11-29	30313.0	1.8014296953255975
CA	2018-12-05	19699.0	1.7984963990604175
IR	2018-01-03	39705.0	1.7984963990604173
FR	2018-11-12	15471.0	1.7952016539663525
UK	2018-06-18	23572.0	1.7947706957472975
IR	2018-05-19	12641.0	1.7812858740542894
IR	2018-09-08	58230.0	1.7794647280318316
CA	2018-12-06	32143.0	1.7773238388145916
SA	2018-08-20	17978.0	1.7772126237903192
CA	2018-06-09	16115.0	1.7692468476768202
RS	2018-04-18	20011.0	1.7652292049249863
RS	2018-03-14	14871.0	1.754135506253831
FR	2018-11-11	49234.0	1.7502568822823368
RS	2018-03-22	12979.0	1.7489779095032063
CH	2018-04-05	15074.0	1.74785185738245
RS	2018-02-18	6168.0	1.7476294273339055
UK	2018-05-12	7861.0	1.7475043104315995
ID	2018-10-31	25051.0	1.7457665756773455
UK	2018-06-16	18227.0	1.7452522061900866
UK	2018-05-20	6192.0	1.7444180935080447
ID	2018-11-01	3857.0	1.7443346822398405
SA	2018-08-16	1506.0	1.7423328118029404
RS	2018-11-28	9878.0	1.7415126009989326
UK	2018-05-08	30657.0	1.739163183611182
SA	2018-08-21	5519.0	1.7389685573187055
UK	2018-07-14	6163.0	1.7280555830619928
RS	2018-04-01	7520.0	1.72587298821065
ID	2018-10-30	21182.0	1.7245662116754514
CA	2018-12-07	37891.0	1.7241908609685326
CH	2018-04-04	55902.0	1.72014541446063
CH	2018-04-03	11534.0	1.71907496985201
CA	2018-06-10	20236.0	1.7165726318058847
UK	2018-04-22	7560.0	1.709218538325883
CH	2018-04-07	2698.0	1.708926598887169
CA	2018-04-24	31092.0	1.7049645636474706
CA	2018-12-04	16089.0	1.7045475073064495
BE	2018-07-12	45304.0	1.6975965682894352
BE	2018-07-11	63508.0	1.6848207423761625
CA	2018-08-30	32008.0	1.6814981935260296
RS	2018-04-08	4285.0	1.6806084733318514
ID	2018-10-29	81121.0	1.6759235404343842
UK	2018-06-21	9841.0	1.6759235404343842
FR	2018-11-10	31170.0	1.6752145446546487
RS	2018-03-31	8229.0	1.670571317391283
RS	2018-03-13	36411.0	1.669208933343948
CA	2018-12-08	11951.0	1.6688752882711313
BE	2018-07-10	12444.0	1.6625638356436823
CA	2018-08-06	61635.0	1.6617297229616403
FR	2018-11-28	6062.0	1.656683341235288
RS	2018-04-04	19788.0	1.6560577567237567
IZ	2018-05-10	1888.0	1.6546397651642857
RS	2018-05-08	15439.0	1.652290347776535
FR	2018-12-07	3993.0	1.6509696693633023
RS	2018-04-06	40806.0	1.6503440848517705
FR	2018-11-13	18592.0	1.6492736402431507
IZ	2018-05-11	12134.0	1.647980765585986
CH	2018-12-03	15953.0	1.644602609223717
RS	2018-05-09	45093.0	1.6387360166933564
IR	2018-05-15	20937.0	1.6358027204281762
BE	2018-07-09	7253.0	1.635121528404509
SA	2018-08-17	6684.0	1.6334811067964934
RS	2018-02-26	14538.0	1.630923161238232
RS	2018-04-03	39879.0	1.6304226936290074
CH	2018-11-30	15171.0	1.6300473429220883
RS	2018-04-02	4053.0	1.6294634640446592
IZ	2018-05-12	88160.0	1.6277535330464736
ID	2018-10-28	186.0	1.627405986095623
CA	2018-08-29	11360.0	1.6258072701217097
RS	2018-05-10	30477.0	1.6227210531981553
CA	2018-12-09	4267.0	1.6219703517843178
CH	2018-12-02	35823.0	1.616910068179931
CA	2018-04-25	17322.0	1.6163122874244678
RS	2018-05-07	16782.0	1.6134067949153559
CH	2018-04-06	15551.0	1.6119609995998165
TU	2018-10-12	12942.0	1.6118219808194765
RS	2018-04-05	8159.0	1.6110851812836728
BE	2018-07-13	2186.0	1.6104456948941075
RS	2018-07-12	39805.0	1.6099313254068484
RS	2018-02-19	9501.0	1.6077070249214038
IR	2018-08-02	13428.0	1.6048293361683599
CA	2018-06-08	25083.0	1.6033001295846165
SY	2018-04-19	11242.0	1.602090666195656
IR	2018-01-05	12007.0	1.5995049168813267
CH	2018-04-01	3450.0	1.5981703365900601
CH	2018-12-04	7477.0	1.5969052656889633
SY	2018-04-10	7496.0	1.5960294473728194
SA	2018-08-19	37751.0	1.5951119234225735
SA	2018-08-18	53071.0	1.5941109882041236
CA	2018-06-11	17851.0	1.5905104017933098
UK	2018-07-09	21538.0	1.5881748862835932
CH	2018-04-02	30679.0	1.5879941618691509
IZ	2018-05-13	12415.0	1.5872573623333472
IR	2018-05-16	31071.0	1.5866178759437817
CA	2018-09-02	7408.0	1.5862564271148971
IZ	2018-09-07	13050.0	1.585658646359434
CA	2018-04-26	18877.0	1.5770116782222678
IZ	2018-05-14	7622.0	1.5745788495663129
RS	2018-04-19	15591.0	1.5735501105917948
RS	2018-02-24	10084.0	1.5718401795936092
CA	2018-08-31	42147.0	1.5701997579855937
FR	2018-11-29	4023.0	1.5689485889625314
RS	2018-03-09	15082.0	1.5658345682829087
UK	2018-04-25	13301.0	1.5613025560438152
IR	2018-05-22	13833.0	1.553600915612963
IR	2018-05-20	11321.0	1.5513210076153825
RS	2018-05-11	11097.0	1.550125446104456
IR	2018-05-17	18735.0	1.5500420348362514
RS	2018-07-11	37935.0	1.5493886465686526
SA	2018-11-17	14016.0	1.5488186695692572
IZ	2018-09-08	48602.0	1.5475814024242285
FR	2018-11-14	7486.0	1.5465248596936425
CH	2018-12-01	23734.0	1.544773223061355
IR	2018-08-29	21165.0	1.5437305822088025
RS	2018-03-28	15810.0	1.5413811648210516
IR	2018-08-30	10478.0	1.5351253197057386
CH	2018-05-20	18729.0	1.5346804596086496
KN	2018-05-06	1524.0	1.5345553427063436
IR	2018-09-06	10386.0	1.5345553427063436
RS	2018-04-07	10073.0	1.5336934262682338
SA	2018-10-29	10656.0	1.5321920234405586
CH	2018-11-29	14561.0	1.529564568492127
RS	2018-02-23	25545.0	1.5293421384435828
RS	2018-02-25	39728.0	1.5282438900788942
RS	2018-03-12	12344.0	1.5271734454702741
CA	2018-04-23	15267.0	1.521821222427173
RS	2018-03-29	15094.0	1.5189852393082308
CA	2018-08-28	16504.0	1.5153290453852815
CA	2018-04-27	32303.0	1.5119230852669443
CA	2018-04-21	11152.0	1.5117979683646379
IR	2018-09-07	10204.0	1.5110472669508004
UK	2018-04-13	11551.0	1.5107692293901198
SY	2018-04-09	36794.0	1.5062233152729922
CA	2018-09-01	11791.0	1.506167707760856
UK	2018-06-15	18644.0	1.5053892025909505
IR	2018-08-28	26057.0	1.504054622299684
RS	2018-03-10	5304.0	1.5039156035193437
SY	2018-12-22	10096.0	1.5002733114744282
UK	2018-04-26	15228.0	1.4996477269628967
IR	2018-10-01	29604.0	1.497479033989588
IR	2018-05-03	10653.0	1.4965337062832742
CA	2018-06-13	8809.0	1.494948892187395
CA	2018-04-22	7783.0	1.4947681677729523
IR	2018-05-21	38955.0	1.4941286813833872
CH	2018-05-19	6233.0	1.4908339362893224
FR	2018-11-09	12853.0	1.4904724874604376
RS	2018-03-11	22748.0	1.4887903602183201
SA	2018-11-25	7373.0	1.488387205755333
UK	2018-07-15	1859.0	1.4880535606825167
IZ	2018-09-06	14122.0	1.485440007612119
IZ	2018-05-09	4305.0	1.485203675685541
FR	2018-12-08	9276.0	1.4834798428093212
AR	2018-11-28	8399.0	1.4811026216655023
CH	2018-05-11	4308.0	1.4802963127395283
RS	2018-07-10	5286.0	1.4784890685951046
CH	2018-05-17	33464.0	1.4749301878183931
RS	2018-03-08	11486.0	1.47333147184448
IR	2018-07-29	5277.0	1.4725807704306422
UK	2018-04-23	27374.0	1.4722193216017576
UK	2018-06-22	26542.0	1.4708847413104909
IR	2018-08-01	19137.0	1.4683545995082972
CA	2018-08-05	3423.0	1.4673953699239495
SY	2018-12-21	51717.0	1.467020019217031
RS	2018-03-27	21497.0	1.466630766632078
RS	2018-02-12	18994.0	1.4644064661466332
IR	2018-01-10	18383.0	1.461473169881453
RS	2018-11-27	12183.0	1.4595825144688253
RS	2018-02-22	11981.0	1.4593183787861788
IR	2018-01-11	12379.0	1.4535490994020566
IR	2018-05-23	14529.0	1.4533127674754784
SY	2018-12-23	2846.0	1.4528679073783894
IR	2018-07-30	20760.0	1.4525620660616405
FR	2018-11-27	7903.0	1.449809494210903
IR	2018-05-02	11207.0	1.4486278345780104
CA	2018-06-07	27936.0	1.4457362439469321
UK	2018-04-12	18253.0	1.4456389308006943
RS	2018-07-24	8910.0	1.4452774819718093
BE	2018-07-14	1617.0	1.4449716406550608
CH	2018-05-18	17601.0	1.440314511513661
RS	2018-07-23	18035.0	1.4389521274663264
IR	2018-07-31	38126.0	1.4362690650057586
IZ	2018-05-15	1718.0	1.4274691762102183
UK	2018-01-14	3048.0	1.425314385114944
RS	2018-02-27	11544.0	1.4217416024601985
CA	2018-10-15	15977.0	1.421588681801824
UK	2018-06-14	13808.0	1.4206433540955101
IR	2018-08-27	41619.0	1.4179602916349427
IR	2018-07-04	19242.0	1.4178768803667385
FR	2018-11-26	7502.0	1.4166257113436758
RS	2018-03-30	40737.0	1.4150269953697623
SA	2018-12-03	8704.0	1.4106757075451113
RS	2018-05-12	3757.0	1.4094940479122189
SN	2018-06-11	38071.0	1.407214139914638
IR	2018-10-31	8788.0	1.4044059605517643
IR	2018-08-26	5418.0	1.4041418248691178
SA	2018-10-08	19878.0	1.4039889042107434
FR	2018-11-22	2050.0	1.4029740671142592
SN	2018-06-10	22899.0	1.3943966083672632
CA	2018-06-12	18601.0	1.3943827064892294
IR	2018-07-28	7907.0	1.3937571219776983
FR	2018-11-23	2565.0	1.3933539675147113
IR	2018-08-25	4286.0	1.3908238257125178
FR	2018-11-24	55411.0	1.3900592224206465
FR	2018-11-25	29589.0	1.3891973059825367
SA	2018-12-04	21457.0	1.3871815336676023
IR	2018-10-02	8783.0	1.3833168115741423
UK	2018-01-15	13569.0	1.3828858533550874
UK	2018-04-14	4696.0	1.3786874861888108
CA	2018-10-16	24171.0	1.3774224152877141
RS	2018-07-25	5419.0	1.3735993988283561
CH	2018-05-07	10919.0	1.3719728790983745
UK	2018-04-24	18583.0	1.3671489274205662
IR	2018-07-05	17456.0	1.3656614264709255
IR	2018-06-07	9686.0	1.3656197208368235
RS	2018-07-09	7454.0	1.363478831619583
IS	2018-05-09	15338.0	1.362922756498222
CA	2018-06-14	18868.0	1.3608930823052536
IR	2018-09-05	8062.0	1.3603648109399606
IS	2018-05-10	72644.0	1.3594333851116807
UK	2018-01-13	12563.0	1.3590997400388638
CA	2018-09-03	2884.0	1.3566530095048748
RS	2018-02-20	8487.0	1.3551933123113018
SA	2018-12-02	12480.0	1.3533304606547418
IS	2018-05-08	6882.0	1.3532470493865376
CA	2018-12-10	13139.0	1.3519124690952709
CA	2018-10-17	33541.0	1.3517178428027943
CA	2018-10-14	10781.0	1.3498688930242686
IR	2018-05-01	28455.0	1.3492989160248734
IR	2018-07-27	11005.0	1.349145995366499
CH	2018-05-06	2251.0	1.3471302230515647
AR	2018-12-04	2242.0	1.3466019516862722
SY	2018-04-08	16020.0	1.342459192032131
IR	2018-05-24	14621.0	1.3422089582275187
CA	2018-12-03	16961.0	1.3412775323992387
CA	2018-01-18	13738.0	1.3391088394259298
CH	2018-07-08	2205.0	1.3379688854271399
IR	2018-05-04	19262.0	1.3367872257942472
UK	2018-04-10	25664.0	1.3359392112341717
IR	2018-01-06	6834.0	1.3340485558215438
CA	2018-06-17	10593.0	1.3338400276510332
IR	2018-06-08	6583.0	1.3332144431395019
IR	2018-07-03	21279.0	1.33217180228695
UK	2018-05-07	5301.0	1.330003109313641
VE	2018-05-25	1774.0	1.3277788088281965
FR	2018-05-11	12034.0	1.326569345439236
SN	2018-06-12	31123.0	1.3251374520017312
FR	2018-11-08	2248.0	1.3230799740526948
CH	2018-05-21	22177.0	1.32178709939553
CA	2018-04-20	19129.0	1.3207583604210118
TU	2018-10-27	4528.0	1.3195349951540176
IR	2018-07-06	15913.0	1.3192152519592348
IR	2018-08-11	5996.0	1.3185618636916352
UK	2018-04-09	18497.0	1.3161985444258504
IZ	2018-09-09	15579.0	1.3148361603785157
CH	2018-05-16	8081.0	1.3134876782092146
RS	2018-12-07	14087.0	1.312625761771105
IR	2018-01-12	19851.0	1.311833354723165
CA	2018-01-19	18253.0	1.3110548495532597
IR	2018-06-05	31939.0	1.3101234237249797
IS	2018-05-07	2329.0	1.3096090542377208
UK	2018-04-11	18242.0	1.3050214344864912
CH	2018-12-05	14743.0	1.3037146579512924
RS	2018-12-08	19621.0	1.302046432587209
VE	2018-05-26	14188.0	1.3010315954907252
IZ	2018-09-05	18357.0	1.301017693612691
RS	2018-02-28	7664.0	1.3009898898566228
UK	2018-05-21	11404.0	1.2999750527601388
SN	2018-06-09	2957.0	1.2989602156636546
CA	2018-08-04	3257.0	1.2985570612006678
RS	2018-12-04	14318.0	1.2980843973475107
CH	2018-07-09	6810.0	1.2980009860793065
SY	2018-12-20	30894.0	1.2926487630362058
RS	2018-07-26	13216.0	1.2913975940131428
SN	2018-06-13	7445.0	1.2907442057455434
CH	2018-05-10	19231.0	1.2891732935276983
ID	2018-10-27	53.0	1.2841130099233116
IR	2018-06-06	42002.0	1.2839878930210051
CH	2018-05-15	8474.0	1.2837932667285288
UK	2018-04-27	13479.0	1.2823474714129899
CA	2018-04-19	16931.0	1.281388241828642
SA	2018-12-01	18669.0	1.277050855882025
UK	2018-04-08	8124.0	1.2756606680786218
UK	2018-06-13	13348.0	1.2738534239341983
RS	2018-02-11	30582.0	1.273797816422062
RS	2018-12-06	13831.0	1.2664576248200947
RS	2018-12-05	27060.0	1.2662769004056522
IR	2018-06-04	8450.0	1.266054470357108
VE	2018-05-24	2234.0	1.265595708381985
IR	2018-01-13	31617.0	1.2649284182363516
CA	2018-01-17	22089.0	1.2645113618953305
UK	2018-07-08	3193.0	1.2640525999202077
CA	2018-04-18	18547.0	1.258450143072494
CA	2018-05-31	17206.0	1.257351894707806
UK	2018-03-19	10345.0	1.2568931327326829
CA	2018-05-30	16372.0	1.2558504918801305
CH	2018-06-18	11364.0	1.2555446505633818
CA	2018-06-18	8726.0	1.2549190660518508
SY	2018-12-19	7622.0	1.2543768928085235
SA	2018-08-15	3313.0	1.2514714002994116
UK	2018-04-28	27937.0	1.2506233857393358
CA	2018-10-18	13234.0	1.2487744359608102
CA	2018-04-17	17350.0	1.245396279598541
RS	2018-05-06	6387.0	1.2431580772350623
CA	2018-06-01	18011.0	1.2414203424808083
CH	2018-05-22	12108.0	1.2403498978721885
UK	2018-04-29	3125.0	1.2380421861185393
CA	2018-07-25	18416.0	1.237277582826668
UK	2018-03-04	5144.0	1.236777115217443
CA	2018-07-24	18424.0	1.2365407832908646
CH	2018-08-05	3110.0	1.235915198779333
FR	2018-05-10	3506.0	1.2357205724868567
IR	2018-11-09	8241.0	1.2352062029995976
KN	2018-06-08	3686.0	1.2351227917313936
CA	2018-04-28	4775.0	1.2350810860972914
KN	2018-05-27	4184.0	1.2345806184880666
CH	2018-05-08	34641.0	1.2341496602690116
CA	2018-06-15	10975.0	1.2340384452447393
UK	2018-04-30	11743.0	1.2263090010578193
CA	2018-01-16	25882.0	1.226281197301751
CA	2018-05-29	33358.0	1.225669514668254
UK	2018-02-07	18936.0	1.2238205648897278
CH	2018-05-09	23575.0	1.2215406568921474
UK	2018-05-01	16301.0	1.2203868010153227
IR	2018-07-02	16038.0	1.219052220724056
CA	2018-07-26	6261.0	1.2161050225808423
CH	2018-05-23	11235.0	1.2149650685820517
UK	2018-11-22	11056.0	1.2136721939248871
UK	2018-03-18	11517.0	1.212365417389688
UK	2018-04-07	6920.0	1.2121290854631095
UK	2018-03-09	14277.0	1.211920557292599
IR	2018-06-03	2185.0	1.2110586408544894
CA	2018-06-06	12598.0	1.2098352755874946
IR	2018-08-24	4128.0	1.2078751107846968
VE	2018-05-27	59244.0	1.2072078206390633
UK	2018-06-23	12900.0	1.2061234741524092
IR	2018-07-07	14391.0	1.2040520943253388
UK	2018-03-08	16241.0	1.201480246889043
SA	2018-10-07	7012.0	1.2006461342070016
UK	2018-02-04	14635.0	1.1999510403053004
CH	2018-03-24	4221.0	1.199408867061973
UK	2018-02-06	15372.0	1.1989362032088162
VE	2018-05-28	9163.0	1.1985608525018974
IR	2018-10-03	30232.0	1.1971845665765284
UK	2018-03-21	22001.0	1.193597882043749
KN	2018-05-28	18718.0	1.1935005688975107
KN	2018-07-05	10469.0	1.1933198444830684
UK	2018-03-20	23703.0	1.1931947275807622
CH	2018-06-17	3934.0	1.192054773581972
SA	2018-11-30	14191.0	1.1918045397773593
CA	2018-06-19	13254.0	1.1911650533877938
RS	2018-07-29	2042.0	1.191095543997624
CA	2018-07-22	2925.0	1.190692389534637
KN	2018-04-21	24575.0	1.1871057050018574
CA	2018-10-19	8756.0	1.1822539495679811
CH	2018-03-08	8583.0	1.180655233594068
VE	2018-05-29	9601.0	1.1801547659848433
RS	2018-03-07	15959.0	1.1797377096438222
SA	2018-11-29	16006.0	1.1773743903780372
CA	2018-07-23	41474.0	1.172925789407148
RS	2018-03-04	1629.0	1.1712714659210985
UK	2018-02-05	19498.0	1.170048100654104
UK	2018-03-05	10324.0	1.1689359504113814
UK	2018-03-10	6580.0	1.167740388900455
SY	2018-12-24	13111.0	1.1651546395861259
CA	2018-08-03	6032.0	1.1647653870011732
SA	2018-12-05	16995.0	1.1642510175139138
UK	2018-07-16	10575.0	1.1642232137578457
IR	2018-12-04	11543.0	1.1634725123440082
IR	2018-10-30	4973.0	1.1627079090521366
CH	2018-03-09	22473.0	1.1626383996619665
SA	2018-08-07	12130.0	1.1618459926140268
CA	2018-06-16	23349.0	1.1597051033967862
RS	2018-07-30	3423.0	1.1596633977626845
UK	2018-06-12	15900.0	1.157522508545444
UK	2018-11-21	20627.0	1.1571749615945932
RS	2018-07-08	1798.0	1.1559376944495647
CA	2018-04-15	6133.0	1.1524483230630231
CA	2018-04-16	12435.0	1.152378813672853
CA	2018-05-27	3159.0	1.150891312723212
SY	2018-04-07	1105.0	1.150488158260225
IR	2018-10-04	13580.0	1.1499459850168983
SA	2018-11-15	14772.0	1.1488199328961417
SA	2018-11-26	7666.0	1.1483889746770866
FR	2018-11-21	6124.0	1.146998786873684
UK	2018-03-07	20636.0	1.1469431793615477
RS	2018-03-24	2852.0	1.1455112859240426
IR	2018-07-08	5070.0	1.1437040417796192
IR	2018-04-30	31598.0	1.142703106561169
UK	2018-05-22	11329.0	1.1408958624167451
UK	2018-03-23	8327.0	1.138935697613947
UK	2018-11-24	9398.0	1.1382684074683136
UK	2018-01-12	31543.0	1.1382684074683136
IR	2018-07-01	8826.0	1.137517706054476
FR	2018-12-09	16079.0	1.1353768168372356
SA	2018-11-16	9813.0	1.1333888482783696
SA	2018-08-09	11301.0	1.133124712595723
UK	2018-03-06	20454.0	1.132165483011375
UK	2018-02-03	4853.0	1.1320542679871026
CA	2018-12-02	5790.0	1.1320125623530006
IZ	2018-09-10	8923.0	1.131748426670354
RS	2018-04-20	18588.0	1.1270217881387843
SA	2018-12-06	20131.0	1.1267020449440017
RS	2018-03-06	40865.0	1.125436974042905
SY	2018-12-18	394.0	1.1228234209725076
RS	2018-05-23	12048.0	1.1220171120465339
CA	2018-03-08	13220.0	1.1185277406599927
IR	2018-01-09	6870.0	1.116942926564113
CH	2018-05-12	4097.0	1.1165258702230925
CH	2018-06-19	20359.0	1.1149688598832812
UK	2018-03-22	13776.0	1.1141486490792734
CH	2018-08-04	6976.0	1.113940120908763
RS	2018-05-22	5681.0	1.1139262190307289
IR	2018-09-12	15022.0	1.113523064567742
SA	2018-08-08	11386.0	1.1131477138608235
CA	2018-04-12	16936.0	1.1124387180810877
KN	2018-07-04	1450.0	1.1116185072770801
CA	2018-04-14	10213.0	1.1106453758146981
RS	2018-02-10	6376.0	1.1104646514002556
CA	2018-01-15	7031.0	1.1093107955234314
UK	2018-03-17	7314.0	1.108170841524641
UK	2018-11-03	6218.0	1.1078232945737903
SA	2018-12-07	12501.0	1.10675284996517
SA	2018-11-28	11508.0	1.1063774992582514
CH	2018-05-05	5004.0	1.1054738771860393
CA	2018-04-29	4956.0	1.1048343907964742
SY	2018-04-06	5722.0	1.1040280818705004
UK	2018-11-05	18989.0	1.1017203701168514
IR	2018-04-28	1929.0	1.100497004849857
CA	2018-03-09	19018.0	1.1002189672891765
CA	2018-08-10	18390.0	1.10009385038687

coveragebycountry

Coverage without USA

display(oil_gas_cov_norm.filter($"date" >"2018-01-01" && $"date"<"2018-12-31" && $"country" =!="US").orderBy(desc("coverage")).limit(1000))

country	date	articles	coverage
SA	2018-10-18	101417.0	12.684765148069788
SA	2018-10-17	194570.0	12.679829981367707
SA	2018-10-19	73494.0	12.331977189200233
SA	2018-10-16	232742.0	11.147328652530456
SA	2018-10-20	128817.0	10.709919962067769
SA	2018-10-15	141823.0	10.667699958478423
SA	2018-10-21	50740.0	9.754541197935195
SA	2018-10-14	50385.0	9.574067017297429
SA	2018-10-22	116446.0	8.871146358262825
SA	2018-10-23	116063.0	8.419627261595597
IR	2018-05-10	98317.0	7.607938308822747
IR	2018-05-11	42017.0	7.539958125236347
IR	2018-05-09	196921.0	7.532895971195059
IR	2018-05-08	170920.0	7.434123127763284
SA	2018-10-13	18580.0	7.281967072680836
IR	2018-05-07	20107.0	7.117785893098955
SA	2018-10-24	125847.0	6.782917455015266
IR	2018-09-25	74769.0	6.407858687535197
IR	2018-09-24	49741.0	6.326894149865013
SA	2018-10-25	37872.0	6.225048991387717
IR	2018-09-23	109693.0	6.0511921046941515
IR	2018-05-06	8554.0	5.899091657123839
IR	2018-05-12	16179.0	5.45491275205858
IR	2018-09-22	126435.0	5.316311028059311
IR	2018-09-26	62879.0	4.890885756461957
SA	2018-10-26	41015.0	4.7543693141677945
SY	2018-04-14	77719.0	4.541837402783558
TU	2018-10-19	32942.0	4.493472769103172
TU	2018-10-17	87405.0	4.406919676463308
SA	2018-10-12	38993.0	4.402749113053098
IR	2018-09-21	6514.0	4.39340705101423
TU	2018-10-18	31166.0	4.386261485704741
SY	2018-04-15	92616.0	4.209123755795143
TU	2018-10-20	32608.0	4.161412510382355
SY	2018-04-16	51381.0	4.067310697970013
TU	2018-10-16	72217.0	4.017722699022632
IS	2018-05-12	2255.0	3.939816574519934
SY	2018-04-13	12182.0	3.928722875848778
SY	2018-04-17	51599.0	3.9177820978359974
IS	2018-05-13	1307.0	3.8505943212975358
IR	2018-09-20	16401.0	3.830172462465547
KN	2018-05-11	9007.0	3.8239305192282673
KN	2018-05-10	151876.0	3.7756910024501873
KN	2018-05-09	99867.0	3.7698522136758945
TU	2018-10-15	49492.0	3.7396851383420526
SY	2018-04-12	21443.0	3.725936180966398
KN	2018-05-08	12105.0	3.6731924557052915
KN	2018-05-12	7621.0	3.6677012138818506
IR	2018-08-06	61148.0	3.6273301600710304
KN	2018-05-07	329.0	3.6256341309508784
IR	2018-08-07	100863.0	3.560489930483419
RS	2018-07-19	40550.0	3.538052299336496
IR	2018-08-05	15094.0	3.51967401657551
RS	2018-07-18	28985.0	3.5130011151191765
RS	2018-07-17	68773.0	3.509470038098533
IR	2018-08-08	53752.0	3.5018379070578507
IR	2018-09-27	36233.0	3.4635243311960666
TU	2018-10-21	20839.0	3.4264063168452097
TU	2018-10-14	22325.0	3.426142181162563
IR	2018-08-09	21172.0	3.357981273161719
IR	2018-05-05	9074.0	3.317318279912184
SA	2018-10-27	11084.0	3.3093803075547537
IR	2018-11-05	75534.0	3.2770028336135
IR	2018-11-04	32874.0	3.276127015297356
RS	2018-07-14	8640.0	3.1989020828183254
TU	2018-10-22	57204.0	3.1911865405094395
IR	2018-11-03	29708.0	3.1837768395173023
IR	2018-09-28	12338.0	3.1835822132248253
TU	2018-10-23	48331.0	3.1767702929881514
IS	2018-05-11	8186.0	3.168234539875258
IR	2018-05-13	13952.0	3.149286280114876
RS	2018-07-16	58266.0	3.084837173549118
RS	2018-07-15	6153.0	3.0744802744137663
RS	2018-03-16	25299.0	3.044549531006502
IR	2018-08-04	10215.0	3.038460508427597
IR	2018-07-24	34917.0	2.9866204052387033
RS	2018-07-20	52232.0	2.978765844149476
IR	2018-07-25	13467.0	2.9717175919862244
IS	2018-05-14	132441.0	2.9480426936942727
IR	2018-07-23	121138.0	2.9291222376899593
SA	2018-11-20	41960.0	2.915665219753019
KN	2018-03-08	8525.0	2.8903916054871543
RS	2018-03-18	66413.0	2.8767816668918407
SY	2018-04-18	6987.0	2.8668140203414416
RS	2018-03-19	61502.0	2.8591540855446915
SA	2018-11-21	61467.0	2.8581670522042755
IS	2018-05-15	62384.0	2.8523004596739154
FR	2018-12-03	26729.0	2.848922303311646
FR	2018-12-04	22382.0	2.8355904022770124
IS	2018-05-16	8920.0	2.828778482040338
KN	2018-03-07	10783.0	2.8284587388455553
IS	2018-05-17	7721.0	2.8191861861968586
IR	2018-07-22	21615.0	2.8127913223012047
RS	2018-04-13	28932.0	2.7998486738515243
IR	2018-11-06	37292.0	2.79624808744071
TU	2018-10-24	34534.0	2.786405557792618
RS	2018-03-17	11413.0	2.745992798347696
IR	2018-07-26	14868.0	2.7445887086662597
IR	2018-11-02	42823.0	2.7344820433355195
RS	2018-04-14	31685.0	2.733786949433818
IR	2018-07-21	8979.0	2.726933323563042
SA	2018-10-11	22749.0	2.7074845961934355
SA	2018-11-19	16766.0	2.6906077162601245
SA	2018-11-22	40463.0	2.679694742003412
RS	2018-03-20	14935.0	2.664319264897776
SY	2018-04-11	30920.0	2.6611079310719146
KN	2018-03-09	101156.0	2.646177314063368
IR	2018-08-10	5025.0	2.6344302271246134
RS	2018-04-15	15941.0	2.5899720211717887
TU	2018-10-25	14246.0	2.56675588485496
CH	2018-03-26	15479.0	2.5665056510503477
SA	2018-11-23	26002.0	2.553187651893748
RS	2018-03-21	24279.0	2.545305287048454
KN	2018-05-13	1944.0	2.491560626568898
IR	2018-11-07	15431.0	2.4846513931859855
CH	2018-03-25	19450.0	2.466189699156795
CH	2018-03-27	25021.0	2.458418549335772
IR	2018-07-20	6869.0	2.4519958816840512
FR	2018-12-02	23278.0	2.4396093083557315
CH	2018-03-28	101895.0	2.4361755444813262
KN	2018-03-06	36844.0	2.4332005425820435
CH	2018-03-30	6122.0	2.425054042054103
KN	2018-03-10	32100.0	2.4148778673331934
IR	2018-09-19	10017.0	2.4123060198968984
RS	2018-04-12	38212.0	2.39581839254854
RS	2018-02-14	15800.0	2.390118622554588
TU	2018-10-13	4612.0	2.379900742199577
UK	2018-04-18	56380.0	2.3646364801182136
RS	2018-03-15	14247.0	2.361161010609706
AR	2018-11-30	48495.0	2.3373887991715168
SA	2018-11-18	20211.0	2.333454567687886
RS	2018-07-13	21687.0	2.3163135520719282
UK	2018-04-21	13971.0	2.308097542153817
KN	2018-03-11	4607.0	2.3030650623054987
KN	2018-06-12	53681.0	2.284380938227764
RS	2018-04-16	35940.0	2.2754976381640195
UK	2018-04-20	21037.0	2.274454997311467
IR	2018-09-29	17315.0	2.26625288927139
KN	2018-06-13	21236.0	2.264765388321749
AR	2018-12-01	36929.0	2.2638756681275716
KN	2018-06-11	71286.0	2.2607894512040168
CH	2018-03-31	2621.0	2.2375594130091545
UK	2018-04-17	16163.0	2.2356965613525945
RS	2018-04-11	30356.0	2.2337781021838987
KN	2018-06-10	16032.0	2.2238104556334997
UK	2018-04-19	32276.0	2.2161783245928177
CH	2018-03-29	15806.0	2.2137454959368625
KN	2018-03-12	7485.0	2.2016091564131552
AR	2018-12-02	48505.0	2.183091854871829
SA	2018-11-24	9880.0	2.1829111304573865
IR	2018-08-03	9833.0	2.166298386206722
AR	2018-11-29	13730.0	2.154745925560444
RS	2018-07-21	8894.0	2.146557719398401
RS	2018-04-17	26736.0	2.131696611780024
IR	2018-11-08	13215.0	2.1220070027903057
UK	2018-07-11	27825.0	2.107090287659793
SA	2018-10-10	29693.0	2.1045184402234973
UK	2018-04-16	23182.0	2.103823346321796
RS	2018-04-09	6877.0	2.098401613888524
RS	2018-12-02	5691.0	2.0927574514067087
UK	2018-07-12	38075.0	2.088545182362398
UK	2018-07-10	24389.0	2.060449486855625
KN	2018-06-14	5682.0	2.0519276356207654
RS	2018-02-15	22046.0	2.0507181722318046
IR	2018-05-14	15217.0	2.042947022410783
FR	2018-12-01	70292.0	2.0375252899775114
UK	2018-05-14	13079.0	2.0163666316097197
AR	2018-12-03	15700.0	2.007302607131533
UK	2018-05-11	42485.0	1.9899391614670308
FR	2018-12-05	34985.0	1.9873534121527012
RS	2018-02-13	15796.0	1.9761484984572735
UK	2018-05-16	26616.0	1.9717416031204864
IR	2018-01-02	25965.0	1.9606618063273653
UK	2018-05-15	13218.0	1.9470379658540171
UK	2018-05-17	44767.0	1.944243688369177
KN	2018-06-09	2175.0	1.9374873756446391
UK	2018-07-13	41539.0	1.9361388934753383
RS	2018-04-10	31488.0	1.9333307141124645
UK	2018-05-18	37498.0	1.9209580426621784
RS	2018-02-16	43709.0	1.9187476440547682
UK	2018-04-15	18239.0	1.9088773106506076
UK	2018-06-19	33154.0	1.9045677284600584
UK	2018-05-19	9638.0	1.8946973950558978
SA	2018-10-09	25632.0	1.8912080236693567
FR	2018-12-06	33466.0	1.8872737921857266
UK	2018-05-10	32097.0	1.8818103541183535
IR	2018-05-18	12730.0	1.8800448156080312
IR	2018-09-09	17329.0	1.8762217991486734
RS	2018-12-03	7632.0	1.8636266976498435
CA	2018-08-08	20157.0	1.8594700361176686
IR	2018-09-10	6322.0	1.8592615079471582
TU	2018-10-26	31905.0	1.8554245896097663
RS	2018-12-01	21909.0	1.8538953830260227
CA	2018-08-09	20022.0	1.8528805459295388
UK	2018-06-17	15941.0	1.8499194459082908
SA	2018-10-28	10611.0	1.8495162914453036
UK	2018-05-13	8170.0	1.8402298369185723
FR	2018-11-30	4952.0	1.8362399979228063
IR	2018-09-11	28622.0	1.8351695533141859
CA	2018-08-07	16160.0	1.8335291317061704
IR	2018-01-04	14518.0	1.8334457204379664
UK	2018-06-20	20877.0	1.8305124241727861
RS	2018-11-30	54768.0	1.8242148734233707
RS	2018-07-22	7955.0	1.8189460616484745
RS	2018-02-17	36154.0	1.8171388175040502
IR	2018-09-30	7019.0	1.8123982770944465
IR	2018-11-01	13152.0	1.8119951226314597
UK	2018-05-09	19946.0	1.80440469722488
RS	2018-11-29	30313.0	1.8014296953255975
CA	2018-12-05	19699.0	1.7984963990604175
IR	2018-01-03	39705.0	1.7984963990604173
FR	2018-11-12	15471.0	1.7952016539663525
UK	2018-06-18	23572.0	1.7947706957472975
IR	2018-05-19	12641.0	1.7812858740542894
IR	2018-09-08	58230.0	1.7794647280318316
CA	2018-12-06	32143.0	1.7773238388145916
SA	2018-08-20	17978.0	1.7772126237903192
CA	2018-06-09	16115.0	1.7692468476768202
RS	2018-04-18	20011.0	1.7652292049249863
RS	2018-03-14	14871.0	1.754135506253831
FR	2018-11-11	49234.0	1.7502568822823368
RS	2018-03-22	12979.0	1.7489779095032063
CH	2018-04-05	15074.0	1.74785185738245
RS	2018-02-18	6168.0	1.7476294273339055
UK	2018-05-12	7861.0	1.7475043104315995
ID	2018-10-31	25051.0	1.7457665756773455
UK	2018-06-16	18227.0	1.7452522061900866
UK	2018-05-20	6192.0	1.7444180935080447
ID	2018-11-01	3857.0	1.7443346822398405
SA	2018-08-16	1506.0	1.7423328118029404
RS	2018-11-28	9878.0	1.7415126009989326
UK	2018-05-08	30657.0	1.739163183611182
SA	2018-08-21	5519.0	1.7389685573187055
UK	2018-07-14	6163.0	1.7280555830619928
RS	2018-04-01	7520.0	1.72587298821065
ID	2018-10-30	21182.0	1.7245662116754514
CA	2018-12-07	37891.0	1.7241908609685326
CH	2018-04-04	55902.0	1.72014541446063
CH	2018-04-03	11534.0	1.71907496985201
CA	2018-06-10	20236.0	1.7165726318058847
UK	2018-04-22	7560.0	1.709218538325883
CH	2018-04-07	2698.0	1.708926598887169
CA	2018-04-24	31092.0	1.7049645636474706
CA	2018-12-04	16089.0	1.7045475073064495
BE	2018-07-12	45304.0	1.6975965682894352
BE	2018-07-11	63508.0	1.6848207423761625
CA	2018-08-30	32008.0	1.6814981935260296
RS	2018-04-08	4285.0	1.6806084733318514
ID	2018-10-29	81121.0	1.6759235404343842
UK	2018-06-21	9841.0	1.6759235404343842
FR	2018-11-10	31170.0	1.6752145446546487
RS	2018-03-31	8229.0	1.670571317391283
RS	2018-03-13	36411.0	1.669208933343948
CA	2018-12-08	11951.0	1.6688752882711313
BE	2018-07-10	12444.0	1.6625638356436823
CA	2018-08-06	61635.0	1.6617297229616403
FR	2018-11-28	6062.0	1.656683341235288
RS	2018-04-04	19788.0	1.6560577567237567
IZ	2018-05-10	1888.0	1.6546397651642857
RS	2018-05-08	15439.0	1.652290347776535
FR	2018-12-07	3993.0	1.6509696693633023
RS	2018-04-06	40806.0	1.6503440848517705
FR	2018-11-13	18592.0	1.6492736402431507
IZ	2018-05-11	12134.0	1.647980765585986
CH	2018-12-03	15953.0	1.644602609223717
RS	2018-05-09	45093.0	1.6387360166933564
IR	2018-05-15	20937.0	1.6358027204281762
BE	2018-07-09	7253.0	1.635121528404509
SA	2018-08-17	6684.0	1.6334811067964934
RS	2018-02-26	14538.0	1.630923161238232
RS	2018-04-03	39879.0	1.6304226936290074
CH	2018-11-30	15171.0	1.6300473429220883
RS	2018-04-02	4053.0	1.6294634640446592
IZ	2018-05-12	88160.0	1.6277535330464736
ID	2018-10-28	186.0	1.627405986095623
CA	2018-08-29	11360.0	1.6258072701217097
RS	2018-05-10	30477.0	1.6227210531981553
CA	2018-12-09	4267.0	1.6219703517843178
CH	2018-12-02	35823.0	1.616910068179931
CA	2018-04-25	17322.0	1.6163122874244678
RS	2018-05-07	16782.0	1.6134067949153559
CH	2018-04-06	15551.0	1.6119609995998165
TU	2018-10-12	12942.0	1.6118219808194765
RS	2018-04-05	8159.0	1.6110851812836728
BE	2018-07-13	2186.0	1.6104456948941075
RS	2018-07-12	39805.0	1.6099313254068484
RS	2018-02-19	9501.0	1.6077070249214038
IR	2018-08-02	13428.0	1.6048293361683599
CA	2018-06-08	25083.0	1.6033001295846165
SY	2018-04-19	11242.0	1.602090666195656
IR	2018-01-05	12007.0	1.5995049168813267
CH	2018-04-01	3450.0	1.5981703365900601
CH	2018-12-04	7477.0	1.5969052656889633
SY	2018-04-10	7496.0	1.5960294473728194
SA	2018-08-19	37751.0	1.5951119234225735
SA	2018-08-18	53071.0	1.5941109882041236
CA	2018-06-11	17851.0	1.5905104017933098
UK	2018-07-09	21538.0	1.5881748862835932
CH	2018-04-02	30679.0	1.5879941618691509
IZ	2018-05-13	12415.0	1.5872573623333472
IR	2018-05-16	31071.0	1.5866178759437817
CA	2018-09-02	7408.0	1.5862564271148971
IZ	2018-09-07	13050.0	1.585658646359434
CA	2018-04-26	18877.0	1.5770116782222678
IZ	2018-05-14	7622.0	1.5745788495663129
RS	2018-04-19	15591.0	1.5735501105917948
RS	2018-02-24	10084.0	1.5718401795936092
CA	2018-08-31	42147.0	1.5701997579855937
FR	2018-11-29	4023.0	1.5689485889625314
RS	2018-03-09	15082.0	1.5658345682829087
UK	2018-04-25	13301.0	1.5613025560438152
IR	2018-05-22	13833.0	1.553600915612963
IR	2018-05-20	11321.0	1.5513210076153825
RS	2018-05-11	11097.0	1.550125446104456
IR	2018-05-17	18735.0	1.5500420348362514
RS	2018-07-11	37935.0	1.5493886465686526
SA	2018-11-17	14016.0	1.5488186695692572
IZ	2018-09-08	48602.0	1.5475814024242285
FR	2018-11-14	7486.0	1.5465248596936425
CH	2018-12-01	23734.0	1.544773223061355
IR	2018-08-29	21165.0	1.5437305822088025
RS	2018-03-28	15810.0	1.5413811648210516
IR	2018-08-30	10478.0	1.5351253197057386
CH	2018-05-20	18729.0	1.5346804596086496
IR	2018-09-06	10386.0	1.5345553427063436
KN	2018-05-06	1524.0	1.5345553427063436
RS	2018-04-07	10073.0	1.5336934262682338
SA	2018-10-29	10656.0	1.5321920234405586
CH	2018-11-29	14561.0	1.529564568492127
RS	2018-02-23	25545.0	1.5293421384435828
RS	2018-02-25	39728.0	1.5282438900788942
RS	2018-03-12	12344.0	1.5271734454702741
CA	2018-04-23	15267.0	1.521821222427173
RS	2018-03-29	15094.0	1.5189852393082308
CA	2018-08-28	16504.0	1.5153290453852815
CA	2018-04-27	32303.0	1.5119230852669443
CA	2018-04-21	11152.0	1.5117979683646379
IR	2018-09-07	10204.0	1.5110472669508004
UK	2018-04-13	11551.0	1.5107692293901198
SY	2018-04-09	36794.0	1.5062233152729922
CA	2018-09-01	11791.0	1.506167707760856
UK	2018-06-15	18644.0	1.5053892025909505
IR	2018-08-28	26057.0	1.504054622299684
RS	2018-03-10	5304.0	1.5039156035193437
SY	2018-12-22	10096.0	1.5002733114744282
UK	2018-04-26	15228.0	1.4996477269628967
IR	2018-10-01	29604.0	1.497479033989588
IR	2018-05-03	10653.0	1.4965337062832742
CA	2018-06-13	8809.0	1.494948892187395
CA	2018-04-22	7783.0	1.4947681677729523
IR	2018-05-21	38955.0	1.4941286813833872
CH	2018-05-19	6233.0	1.4908339362893224
FR	2018-11-09	12853.0	1.4904724874604376
RS	2018-03-11	22748.0	1.4887903602183201
SA	2018-11-25	7373.0	1.488387205755333
UK	2018-07-15	1859.0	1.4880535606825167
IZ	2018-09-06	14122.0	1.485440007612119
IZ	2018-05-09	4305.0	1.485203675685541
FR	2018-12-08	9276.0	1.4834798428093212
AR	2018-11-28	8399.0	1.4811026216655023
CH	2018-05-11	4308.0	1.4802963127395283
RS	2018-07-10	5286.0	1.4784890685951046
CH	2018-05-17	33464.0	1.4749301878183931
RS	2018-03-08	11486.0	1.47333147184448
IR	2018-07-29	5277.0	1.4725807704306422
UK	2018-04-23	27374.0	1.4722193216017576
UK	2018-06-22	26542.0	1.4708847413104909
IR	2018-08-01	19137.0	1.4683545995082972
CA	2018-08-05	3423.0	1.4673953699239495
SY	2018-12-21	51717.0	1.467020019217031
RS	2018-03-27	21497.0	1.466630766632078
RS	2018-02-12	18994.0	1.4644064661466332
IR	2018-01-10	18383.0	1.461473169881453
RS	2018-11-27	12183.0	1.4595825144688253
RS	2018-02-22	11981.0	1.4593183787861788
IR	2018-01-11	12379.0	1.4535490994020566
IR	2018-05-23	14529.0	1.4533127674754784
SY	2018-12-23	2846.0	1.4528679073783894
IR	2018-07-30	20760.0	1.4525620660616405
FR	2018-11-27	7903.0	1.449809494210903
IR	2018-05-02	11207.0	1.4486278345780104
CA	2018-06-07	27936.0	1.4457362439469321
UK	2018-04-12	18253.0	1.4456389308006943
RS	2018-07-24	8910.0	1.4452774819718093
BE	2018-07-14	1617.0	1.4449716406550608
CH	2018-05-18	17601.0	1.440314511513661
RS	2018-07-23	18035.0	1.4389521274663264
IR	2018-07-31	38126.0	1.4362690650057586
IZ	2018-05-15	1718.0	1.4274691762102183
UK	2018-01-14	3048.0	1.425314385114944
RS	2018-02-27	11544.0	1.4217416024601985
CA	2018-10-15	15977.0	1.421588681801824
UK	2018-06-14	13808.0	1.4206433540955101
IR	2018-08-27	41619.0	1.4179602916349427
IR	2018-07-04	19242.0	1.4178768803667385
FR	2018-11-26	7502.0	1.4166257113436758
RS	2018-03-30	40737.0	1.4150269953697623
SA	2018-12-03	8704.0	1.4106757075451113
RS	2018-05-12	3757.0	1.4094940479122189
SN	2018-06-11	38071.0	1.407214139914638
IR	2018-10-31	8788.0	1.4044059605517643
IR	2018-08-26	5418.0	1.4041418248691178
SA	2018-10-08	19878.0	1.4039889042107434
FR	2018-11-22	2050.0	1.4029740671142592
SN	2018-06-10	22899.0	1.3943966083672632
CA	2018-06-12	18601.0	1.3943827064892294
IR	2018-07-28	7907.0	1.3937571219776983
FR	2018-11-23	2565.0	1.3933539675147113
IR	2018-08-25	4286.0	1.3908238257125178
FR	2018-11-24	55411.0	1.3900592224206465
FR	2018-11-25	29589.0	1.3891973059825367
SA	2018-12-04	21457.0	1.3871815336676023
IR	2018-10-02	8783.0	1.3833168115741423
UK	2018-01-15	13569.0	1.3828858533550874
UK	2018-04-14	4696.0	1.3786874861888108
CA	2018-10-16	24171.0	1.3774224152877141
RS	2018-07-25	5419.0	1.3735993988283561
CH	2018-05-07	10919.0	1.3719728790983745
UK	2018-04-24	18583.0	1.3671489274205662
IR	2018-07-05	17456.0	1.3656614264709255
IR	2018-06-07	9686.0	1.3656197208368235
RS	2018-07-09	7454.0	1.363478831619583
IS	2018-05-09	15338.0	1.362922756498222
CA	2018-06-14	18868.0	1.3608930823052536
IR	2018-09-05	8062.0	1.3603648109399606
IS	2018-05-10	72644.0	1.3594333851116807
UK	2018-01-13	12563.0	1.3590997400388638
CA	2018-09-03	2884.0	1.3566530095048748
RS	2018-02-20	8487.0	1.3551933123113018
SA	2018-12-02	12480.0	1.3533304606547418
IS	2018-05-08	6882.0	1.3532470493865376
CA	2018-12-10	13139.0	1.3519124690952709
CA	2018-10-17	33541.0	1.3517178428027943
CA	2018-10-14	10781.0	1.3498688930242686
IR	2018-05-01	28455.0	1.3492989160248734
IR	2018-07-27	11005.0	1.349145995366499
CH	2018-05-06	2251.0	1.3471302230515647
AR	2018-12-04	2242.0	1.3466019516862722
SY	2018-04-08	16020.0	1.342459192032131
IR	2018-05-24	14621.0	1.3422089582275187
CA	2018-12-03	16961.0	1.3412775323992387
CA	2018-01-18	13738.0	1.3391088394259298
CH	2018-07-08	2205.0	1.3379688854271399
IR	2018-05-04	19262.0	1.3367872257942472
UK	2018-04-10	25664.0	1.3359392112341717
IR	2018-01-06	6834.0	1.3340485558215438
CA	2018-06-17	10593.0	1.3338400276510332
IR	2018-06-08	6583.0	1.3332144431395019
IR	2018-07-03	21279.0	1.33217180228695
UK	2018-05-07	5301.0	1.330003109313641
VE	2018-05-25	1774.0	1.3277788088281965
FR	2018-05-11	12034.0	1.326569345439236
SN	2018-06-12	31123.0	1.3251374520017312
FR	2018-11-08	2248.0	1.3230799740526948
CH	2018-05-21	22177.0	1.32178709939553
CA	2018-04-20	19129.0	1.3207583604210118
TU	2018-10-27	4528.0	1.3195349951540176
IR	2018-07-06	15913.0	1.3192152519592348
IR	2018-08-11	5996.0	1.3185618636916352
UK	2018-04-09	18497.0	1.3161985444258504
IZ	2018-09-09	15579.0	1.3148361603785157
CH	2018-05-16	8081.0	1.3134876782092146
RS	2018-12-07	14087.0	1.312625761771105
IR	2018-01-12	19851.0	1.311833354723165
CA	2018-01-19	18253.0	1.3110548495532597
IR	2018-06-05	31939.0	1.3101234237249797
IS	2018-05-07	2329.0	1.3096090542377208
UK	2018-04-11	18242.0	1.3050214344864912
CH	2018-12-05	14743.0	1.3037146579512924
RS	2018-12-08	19621.0	1.302046432587209
VE	2018-05-26	14188.0	1.3010315954907252
IZ	2018-09-05	18357.0	1.301017693612691
RS	2018-02-28	7664.0	1.3009898898566228
UK	2018-05-21	11404.0	1.2999750527601388
SN	2018-06-09	2957.0	1.2989602156636546
CA	2018-08-04	3257.0	1.2985570612006678
RS	2018-12-04	14318.0	1.2980843973475107
CH	2018-07-09	6810.0	1.2980009860793065
SY	2018-12-20	30894.0	1.2926487630362058
RS	2018-07-26	13216.0	1.2913975940131428
SN	2018-06-13	7445.0	1.2907442057455434
CH	2018-05-10	19231.0	1.2891732935276983
ID	2018-10-27	53.0	1.2841130099233116
IR	2018-06-06	42002.0	1.2839878930210051
CH	2018-05-15	8474.0	1.2837932667285288
UK	2018-04-27	13479.0	1.2823474714129899
CA	2018-04-19	16931.0	1.281388241828642
SA	2018-12-01	18669.0	1.277050855882025
UK	2018-04-08	8124.0	1.2756606680786218
UK	2018-06-13	13348.0	1.2738534239341983
RS	2018-02-11	30582.0	1.273797816422062
RS	2018-12-06	13831.0	1.2664576248200947
RS	2018-12-05	27060.0	1.2662769004056522
IR	2018-06-04	8450.0	1.266054470357108
VE	2018-05-24	2234.0	1.265595708381985
IR	2018-01-13	31617.0	1.2649284182363516
CA	2018-01-17	22089.0	1.2645113618953305
UK	2018-07-08	3193.0	1.2640525999202077
CA	2018-04-18	18547.0	1.258450143072494
CA	2018-05-31	17206.0	1.257351894707806
UK	2018-03-19	10345.0	1.2568931327326829
CA	2018-05-30	16372.0	1.2558504918801305
CH	2018-06-18	11364.0	1.2555446505633818
CA	2018-06-18	8726.0	1.2549190660518508
SY	2018-12-19	7622.0	1.2543768928085235
SA	2018-08-15	3313.0	1.2514714002994116
UK	2018-04-28	27937.0	1.2506233857393358
CA	2018-10-18	13234.0	1.2487744359608102
CA	2018-04-17	17350.0	1.245396279598541
RS	2018-05-06	6387.0	1.2431580772350623
CA	2018-06-01	18011.0	1.2414203424808083
CH	2018-05-22	12108.0	1.2403498978721885
UK	2018-04-29	3125.0	1.2380421861185393
CA	2018-07-25	18416.0	1.237277582826668
UK	2018-03-04	5144.0	1.236777115217443
CA	2018-07-24	18424.0	1.2365407832908646
CH	2018-08-05	3110.0	1.235915198779333
FR	2018-05-10	3506.0	1.2357205724868567
IR	2018-11-09	8241.0	1.2352062029995976
KN	2018-06-08	3686.0	1.2351227917313936
CA	2018-04-28	4775.0	1.2350810860972914
KN	2018-05-27	4184.0	1.2345806184880666
CH	2018-05-08	34641.0	1.2341496602690116
CA	2018-06-15	10975.0	1.2340384452447393
UK	2018-04-30	11743.0	1.2263090010578193
CA	2018-01-16	25882.0	1.226281197301751
CA	2018-05-29	33358.0	1.225669514668254
UK	2018-02-07	18936.0	1.2238205648897278
CH	2018-05-09	23575.0	1.2215406568921474
UK	2018-05-01	16301.0	1.2203868010153227
IR	2018-07-02	16038.0	1.219052220724056
CA	2018-07-26	6261.0	1.2161050225808423
CH	2018-05-23	11235.0	1.2149650685820517
UK	2018-11-22	11056.0	1.2136721939248871
UK	2018-03-18	11517.0	1.212365417389688
UK	2018-04-07	6920.0	1.2121290854631095
UK	2018-03-09	14277.0	1.211920557292599
IR	2018-06-03	2185.0	1.2110586408544894
CA	2018-06-06	12598.0	1.2098352755874946
IR	2018-08-24	4128.0	1.2078751107846968
VE	2018-05-27	59244.0	1.2072078206390633
UK	2018-06-23	12900.0	1.2061234741524092
IR	2018-07-07	14391.0	1.2040520943253388
UK	2018-03-08	16241.0	1.201480246889043
SA	2018-10-07	7012.0	1.2006461342070016
UK	2018-02-04	14635.0	1.1999510403053004
CH	2018-03-24	4221.0	1.199408867061973
UK	2018-02-06	15372.0	1.1989362032088162
VE	2018-05-28	9163.0	1.1985608525018974
IR	2018-10-03	30232.0	1.1971845665765284
UK	2018-03-21	22001.0	1.193597882043749
KN	2018-05-28	18718.0	1.1935005688975107
KN	2018-07-05	10469.0	1.1933198444830684
UK	2018-03-20	23703.0	1.1931947275807622
CH	2018-06-17	3934.0	1.192054773581972
SA	2018-11-30	14191.0	1.1918045397773593
CA	2018-06-19	13254.0	1.1911650533877938
RS	2018-07-29	2042.0	1.191095543997624
CA	2018-07-22	2925.0	1.190692389534637
KN	2018-04-21	24575.0	1.1871057050018574
CA	2018-10-19	8756.0	1.1822539495679811
CH	2018-03-08	8583.0	1.180655233594068
VE	2018-05-29	9601.0	1.1801547659848433
RS	2018-03-07	15959.0	1.1797377096438222
SA	2018-11-29	16006.0	1.1773743903780372
CA	2018-07-23	41474.0	1.172925789407148
RS	2018-03-04	1629.0	1.1712714659210985
UK	2018-02-05	19498.0	1.170048100654104
UK	2018-03-05	10324.0	1.1689359504113814
UK	2018-03-10	6580.0	1.167740388900455
SY	2018-12-24	13111.0	1.1651546395861259
CA	2018-08-03	6032.0	1.1647653870011732
SA	2018-12-05	16995.0	1.1642510175139138
UK	2018-07-16	10575.0	1.1642232137578457
IR	2018-12-04	11543.0	1.1634725123440082
IR	2018-10-30	4973.0	1.1627079090521366
CH	2018-03-09	22473.0	1.1626383996619665
SA	2018-08-07	12130.0	1.1618459926140268
CA	2018-06-16	23349.0	1.1597051033967862
RS	2018-07-30	3423.0	1.1596633977626845
UK	2018-06-12	15900.0	1.157522508545444
UK	2018-11-21	20627.0	1.1571749615945932
RS	2018-07-08	1798.0	1.1559376944495647
CA	2018-04-15	6133.0	1.1524483230630231
CA	2018-04-16	12435.0	1.152378813672853
CA	2018-05-27	3159.0	1.150891312723212
SY	2018-04-07	1105.0	1.150488158260225
IR	2018-10-04	13580.0	1.1499459850168983
SA	2018-11-15	14772.0	1.1488199328961417
SA	2018-11-26	7666.0	1.1483889746770866
FR	2018-11-21	6124.0	1.146998786873684
UK	2018-03-07	20636.0	1.1469431793615477
RS	2018-03-24	2852.0	1.1455112859240426
IR	2018-07-08	5070.0	1.1437040417796192
IR	2018-04-30	31598.0	1.142703106561169
UK	2018-05-22	11329.0	1.1408958624167451
UK	2018-03-23	8327.0	1.138935697613947
UK	2018-11-24	9398.0	1.1382684074683136
UK	2018-01-12	31543.0	1.1382684074683136
IR	2018-07-01	8826.0	1.137517706054476
FR	2018-12-09	16079.0	1.1353768168372356
SA	2018-11-16	9813.0	1.1333888482783696
SA	2018-08-09	11301.0	1.133124712595723
UK	2018-03-06	20454.0	1.132165483011375
UK	2018-02-03	4853.0	1.1320542679871026
CA	2018-12-02	5790.0	1.1320125623530006
IZ	2018-09-10	8923.0	1.131748426670354
RS	2018-04-20	18588.0	1.1270217881387843
SA	2018-12-06	20131.0	1.1267020449440017
RS	2018-03-06	40865.0	1.125436974042905
SY	2018-12-18	394.0	1.1228234209725076
RS	2018-05-23	12048.0	1.1220171120465339
CA	2018-03-08	13220.0	1.1185277406599927
IR	2018-01-09	6870.0	1.116942926564113
CH	2018-05-12	4097.0	1.1165258702230925
CH	2018-06-19	20359.0	1.1149688598832812
UK	2018-03-22	13776.0	1.1141486490792734
CH	2018-08-04	6976.0	1.113940120908763
RS	2018-05-22	5681.0	1.1139262190307289
IR	2018-09-12	15022.0	1.113523064567742
SA	2018-08-08	11386.0	1.1131477138608235
CA	2018-04-12	16936.0	1.1124387180810877
KN	2018-07-04	1450.0	1.1116185072770801
CA	2018-04-14	10213.0	1.1106453758146981
RS	2018-02-10	6376.0	1.1104646514002556
CA	2018-01-15	7031.0	1.1093107955234314
UK	2018-03-17	7314.0	1.108170841524641
UK	2018-11-03	6218.0	1.1078232945737903
SA	2018-12-07	12501.0	1.10675284996517
SA	2018-11-28	11508.0	1.1063774992582514
CH	2018-05-05	5004.0	1.1054738771860393
CA	2018-04-29	4956.0	1.1048343907964742
SY	2018-04-06	5722.0	1.1040280818705004
UK	2018-11-05	18989.0	1.1017203701168514
IR	2018-04-28	1929.0	1.100497004849857
CA	2018-03-09	19018.0	1.1002189672891765
CA	2018-08-10	18390.0	1.10009385038687
IS	2018-04-28	5808.0	1.0996628921678153
CA	2018-04-13	12438.0	1.0992597377048283
CH	2018-05-14	24667.0	1.0989956020221818
IR	2018-08-20	24475.0	1.0989260926320117
TU	2018-10-28	5039.0	1.0980641761939018
CH	2018-08-06	8152.0	1.0949084498801773
UK	2018-11-02	20256.0	1.0912661578352618
CA	2018-05-26	3550.0	1.089931577543995
IR	2018-04-29	5108.0	1.088555291618626
RS	2018-07-27	52687.0	1.0882633521799117
UK	2018-03-03	5517.0	1.088013118375299
CH	2018-03-10	17365.0	1.0858861310360923
UK	2018-05-06	2602.0	1.083759143696886
CH	2018-11-28	9554.0	1.083689634306716
CA	2018-05-28	7663.0	1.0833698911119334
CH	2018-03-11	12040.0	1.0828972272587762
UK	2018-03-11	9067.0	1.0825218765518576
SA	2018-08-06	45949.0	1.0818128807721221
RS	2018-05-24	15901.0	1.0814514319432373
CA	2018-10-01	18141.0	1.0810621793582844
IR	2018-12-03	4767.0	1.079894421603426
UK	2018-11-23	20375.0	1.0787683694826697
UK	2018-11-20	13630.0	1.0787127619705337
CH	2018-03-07	8085.0	1.078448626287887
UK	2018-01-11	14748.0	1.077461592947471
KN	2018-04-20	2020.0	1.0753346056082647
KN	2018-06-15	5383.0	1.074556100438359
UK	2018-01-16	22671.0	1.0738749084146915
UK	2018-05-24	12797.0	1.072582033757527
UK	2018-01-10	10775.0	1.0692594849073938
KN	2018-05-30	17110.0	1.0689397417126112
CA	2018-12-01	5193.0	1.0684670778594543
IR	2018-08-31	10321.0	1.067938806494161
UK	2018-05-23	15806.0	1.067883198982025
SA	2018-10-30	12121.0	1.0674939463970723
IR	2018-08-19	8024.0	1.0664791093005879
UK	2018-02-28	9935.0	1.0662010717399075
CA	2018-06-05	6664.0	1.0653391553017977
RS	2018-12-09	5704.0	1.0636014205475441
UK	2018-02-08	11861.0	1.0634624017672039
IS	2018-04-29	7653.0	1.0631843642065235
UK	2018-11-04	8334.0	1.0628090134996044
UK	2018-06-24	4821.0	1.062127821475937
RS	2018-03-05	5690.0	1.0617107651349165
UK	2018-06-09	9859.0	1.0594169552593014
RS	2018-03-26	11531.0	1.0571787528958227
KN	2018-05-31	17935.0	1.0562612289455768
RS	2018-03-03	1398.0	1.0559553876288281
IR	2018-01-14	9977.0	1.0552185880930245
RS	2018-07-28	3738.0	1.0551629805808886
RS	2018-03-23	11284.0	1.0542871622647445
CA	2018-03-07	11165.0	1.0538423021676557
CA	2018-04-11	15540.0	1.0521462730475042
CH	2018-07-07	4860.0	1.05106192656085
IR	2018-07-09	12697.0	1.0509368096585436
IS	2018-05-18	1299.0	1.0502000101227402
UK	2018-07-07	2808.0	1.0479340040031935
IR	2018-08-21	12897.0	1.0477949852228532
UK	2018-06-10	5382.0	1.047252811979526
UK	2018-06-25	8823.0	1.0470998913211518
UK	2018-02-02	10163.0	1.0469191669067093
CA	2018-01-14	3228.0	1.043791244349053
IR	2018-12-09	7075.0	1.0416642570098464
TU	2018-10-11	8612.0	1.039439956524402
IR	2018-01-07	10547.0	1.0376327123799778
CH	2018-04-08	5443.0	1.0370071278684467
RS	2018-05-27	2486.0	1.0346299067246276
CA	2018-09-30	11807.0	1.0340738316032667
KN	2018-03-05	25052.0	1.032919975726442
CA	2018-10-03	15137.0	1.0325585268975574
CA	2018-11-24	4068.0	1.031404671020733
UK	2018-11-18	793.0	1.0312239466062907
UK	2018-02-27	9407.0	1.0306261658508273
SA	2018-08-22	3385.0	1.0302786188999769
UK	2018-12-07	12547.0	1.0296113287543434
CA	2018-12-20	13876.0	1.029569623120241
UK	2018-03-15	10573.0	1.0289718423647778
IS	2018-04-27	13252.0	1.0287633141942676
UK	2018-06-11	17476.0	1.028513080389655
RS	2018-03-25	9131.0	1.0277762808538515
IR	2018-12-06	39453.0	1.0272480094885583
UK	2018-03-24	7343.0	1.026580719342925
UK	2018-12-04	21935.0	1.0248707883447394
KN	2018-05-26	586.0	1.0245371432719228
CA	2018-10-02	13771.0	1.023272072370826
UK	2018-04-06	10131.0	1.0230079366881795
CH	2018-06-20	27492.0	1.0222989409084442
CH	2018-08-07	26144.0	1.0216872582749468
IR	2018-09-14	8471.0	1.0200607385449654
UK	2018-03-16	12909.0	1.0188234713999367
CA	2018-07-21	2059.0	1.0183647094248138
IR	2018-06-30	8226.0	1.0180032605959293
CA	2018-01-20	11892.0	1.0175305967427721
FR	2018-11-15	5481.0	1.017447185474568
UK	2018-03-01	21121.0	1.0170162272555132
SA	2018-12-14	28075.0	1.0167242878167986
CH	2018-03-12	13670.0	1.0157928619885186
UK	2018-12-06	17595.0	1.013638070893244
KN	2018-05-29	23746.0	1.012706645064964
CH	2018-05-24	18150.0	1.0121922755777049
CA	2018-11-30	11760.0	1.0115944948222417
UK	2018-12-05	15555.0	1.0114137704077992
IR	2018-12-07	9526.0	1.0110940272130167
ID	2018-10-26	257.0	1.010273816409009
IR	2018-12-05	5942.0	1.0101208957506347
BE	2018-07-08	35.0	1.0099123675801243
CA	2018-08-27	10890.0	1.0091894699223547
IR	2018-01-08	16634.0	1.00789659526519
RS	2018-12-10	10953.0	1.0059781360964941
IR	2018-08-22	20207.0	1.0057696079259837
CA	2018-09-07	15692.0	1.0054359628531668
CA	2018-10-13	3775.0	1.0042264994642063
UK	2018-03-12	11075.0	1.0037260318549814
UK	2018-11-25	4857.0	1.0018631801984212
CA	2018-10-20	1926.0	0.99837380881188
IZ	2018-09-11	3842.0	0.998332103177778
CA	2018-11-23	12671.0	0.9979428505928253
RS	2018-08-04	19353.0	0.9974701867396681
FR	2018-05-12	2803.0	0.9967055834477968
RS	2018-08-06	10523.0	0.9958297651316528
RS	2018-08-07	12989.0	0.9950234562056791
UK	2018-03-14	14506.0	0.9949122411814069
RS	2018-02-21	10800.0	0.9927713519641665
UK	2018-11-06	14804.0	0.9917009073555462
RS	2018-02-09	6898.0	0.9908111871613686
CH	2018-05-27	4143.0	0.9893375880897615
UK	2018-05-25	26055.0	0.9891012561631829
CA	2018-09-04	11898.0	0.9888788261146384
RS	2018-05-26	8213.0	0.9878083815060181
YM	2018-06-16	3404.0	0.9865711143609895
UK	2018-03-13	17276.0	0.9847082627044296
SA	2018-11-27	15325.0	0.9841938932171707
VE	2018-05-30	1787.0	0.9838880519004221
CA	2018-03-10	22253.0	0.9825117659750531
UK	2018-05-26	4386.0	0.9822615321704407
KN	2018-04-24	8835.0	0.9822476302924067
CA	2018-11-21	26536.0	0.9821364152681343
IS	2018-02-12	4864.0	0.9818166720733518
CH	2018-06-21	9251.0	0.9806350124404594
IR	2018-09-13	9166.0	0.9796896847341452
UK	2018-02-26	16264.0	0.9794116471734647
CA	2018-11-22	15732.0	0.9789945908324437
UK	2018-05-05	3168.0	0.9787999645399674
CA	2018-04-10	16531.0	0.9784246138330486
SZ	2018-01-24	3483.0	0.9778268330775853
KN	2018-08-05	9905.0	0.9768258978591353
UK	2018-11-26	8809.0	0.9760334908111956
SZ	2018-01-25	20766.0	0.9751298687389837
KN	2018-08-04	39472.0	0.974768419910099
SA	2018-08-05	1005.0	0.9745181861054866
CA	2018-04-09	13383.0	0.9741150316424995
SN	2018-06-14	2214.0	0.9735172508870363
CA	2018-11-20	9591.0	0.9733921339847299
AR	2018-11-27	7530.0	0.9733643302286622
SA	2018-10-31	20835.0	0.9703754264513458
GM	2018-07-09	4080.0	0.969944468232291
IR	2018-08-23	9484.0	0.9695413137693042
UK	2018-11-01	12158.0	0.969026944282045
CH	2018-06-22	10153.0	0.9681094203317991
SA	2018-12-15	1776.0	0.9679147940393228
SA	2018-10-06	3236.0	0.9679008921612888
CA	2018-06-04	6517.0	0.9670250738451449
CA	2018-12-18	16498.0	0.9667192325283961
UK	2018-10-17	12923.0	0.9658990217243885
RS	2018-05-25	31239.0	0.9650510071643127
CH	2018-08-08	18205.0	0.9646478527013258
CA	2018-08-11	5123.0	0.9641334832140667
CH	2018-05-26	4407.0	0.962785001044766
UK	2018-11-07	6845.0	0.9625208653621194
UK	2018-06-08	9364.0	0.960894345632138
CA	2018-12-19	15228.0	0.9603660742668448
CH	2018-04-09	20904.0	0.9601158404622324
SA	2018-12-11	6143.0	0.9600602329500963
UK	2018-12-03	10186.0	0.9597126859992456
UK	2018-10-16	11278.0	0.9595319615848033
TU	2018-10-29	6036.0	0.9578776380987538
CA	2018-12-11	12110.0	0.9578359324646516
CH	2018-08-09	8107.0	0.9572659554652565
UK	2018-05-27	6530.0	0.9572103479531204
KN	2018-08-03	8845.0	0.956974016026542
IR	2018-06-09	2669.0	0.9562650202468067
FR	2018-05-07	1171.0	0.9559035714179218
CA	2018-09-08	6725.0	0.9543465610781103
UK	2018-11-19	18513.0	0.9509684047158414
UK	2018-10-15	18420.0	0.9499396657413233
CH	2018-05-02	6192.0	0.9497589413268809
CA	2018-09-29	4279.0	0.9495643150344044
CA	2018-04-30	10585.0	0.9494391981320983
UK	2018-01-17	15538.0	0.9484660666697161
SA	2018-12-12	8236.0	0.9481463234749336
UK	2018-10-23	11972.0	0.9480768140847634
IS	2018-04-30	39359.0	0.9476041502316066
CH	2018-07-05	14510.0	0.9466171168911907
SA	2018-11-02	7588.0	0.9461305511599993
RS	2018-08-05	3183.0	0.9449488915271068
IR	2018-04-27	4401.0	0.9437533300161804
CH	2018-08-10	13952.0	0.9435448018456699
FR	2018-05-09	26697.0	0.9433501755531933
IR	2018-07-19	6500.0	0.9420016933838927
CH	2018-07-04	5185.0	0.9418904783596206
UK	2018-01-18	11696.0	0.9405002905562176
CH	2018-04-21	2238.0	0.9389710839724744
FR	2018-05-06	5113.0	0.9386235370216236
UK	2018-02-23	13238.0	0.9378311299736841
CH	2018-03-23	13897.0	0.9373306623644589
SZ	2018-01-23	7784.0	0.9368162928771999
CH	2018-06-23	2137.0	0.9366355684627576
UK	2018-10-22	17641.0	0.9349812449767081
UK	2018-03-02	16922.0	0.9344390717333811
SA	2018-08-04	5427.0	0.9341749360507345
IR	2018-12-08	6740.0	0.9341332304166324
UK	2018-10-25	19331.0	0.9331879027103184
RS	2018-05-28	5004.0	0.9309079947127376
SA	2018-11-14	5026.0	0.9275993477406388
CH	2018-05-03	17444.0	0.9274881327163664
UK	2018-01-09	6786.0	0.9263898843516782
CH	2018-05-01	8212.0	0.925305537865024
IR	2018-05-25	17008.0	0.9251804209627178
CA	2018-03-11	6414.0	0.9250553040604114
CA	2018-10-04	12889.0	0.9237207237691446
UK	2018-10-18	14860.0	0.9212461894790874
CH	2018-07-06	37715.0	0.9211627782108834
IR	2018-07-10	12995.0	0.9211210725767813
FR	2018-05-08	27687.0	0.920995955674475
UK	2018-10-20	6742.0	0.920064529846195
UK	2018-02-09	12241.0	0.9199950204560251
UK	2018-11-08	14957.0	0.9196613753832082
CA	2018-11-19	7151.0	0.9192860246762893
RS	2018-12-11	13557.0	0.919077496505779
IR	2018-01-15	6440.0	0.9189940852375748
IS	2018-02-13	22920.0	0.9187438514329623
CA	2018-09-05	17121.0	0.9184519119942476
KN	2018-03-04	152.0	0.9181877763116011
GM	2018-07-10	5768.0	0.9180070518971587
CA	2018-06-20	21335.0	0.9177568180925463
FR	2018-11-16	2356.0	0.9162832190209391
CA	2018-05-14	9529.0	0.9159495739481225
IS	2018-02-11	14216.0	0.9158105551677822
UK	2018-10-24	9525.0	0.9137252734626777
RS	2018-08-21	22844.0	0.9120292443425262
UK	2018-10-31	10083.0	0.9107780753194635
UK	2018-10-19	10454.0	0.910416626490579
CA	2018-09-06	15492.0	0.9079003865664196
RS	2018-08-03	10704.0	0.907664054639841
UK	2018-02-25	8682.0	0.9066631194213911
IS	2018-02-10	12914.0	0.9064406893728467
SA	2018-12-16	1953.0	0.9035073931076667
CH	2018-06-16	8803.0	0.9031320424007477
UK	2018-05-28	5399.0	0.9026871823036586
SA	2018-11-03	4098.0	0.9024647522551144
CH	2018-05-13	7116.0	0.9011301719638475
UK	2018-12-08	3237.0	0.900866036281201
CH	2018-04-10	18509.0	0.9007548212569289
IZ	2018-07-16	11945.0	0.9002404517696698
SY	2018-04-20	1426.0	0.8996287691361725
UK	2018-02-24	2958.0	0.899475848477798
KN	2018-07-06	23753.0	0.8987112451859265
CH	2018-07-03	6130.0	0.8980439550402932
CH	2018-03-06	12569.0	0.8966398653588562
CA	2018-11-28	15128.0	0.894665798678024
CA	2018-11-29	17090.0	0.894165331068799
SA	2018-12-08	2633.0	0.8938594897520504
CH	2018-04-11	7569.0	0.8935675503133359
CA	2018-09-28	12893.0	0.8933451202647913
CA	2018-11-26	8514.0	0.891690796778742
RS	2018-05-21	13377.0	0.8901337864389307
CA	2018-11-18	6052.0	0.8896611225857737
CA	2018-01-13	9142.0	0.8895360056834675
IR	2018-05-26	5427.0	0.8894386925372293
IR	2018-11-19	18393.0	0.8889660286840723
GM	2018-07-11	47291.0	0.8847259558836935
CH	2018-11-11	8793.0	0.884044763860026
UK	2018-10-30	13613.0	0.8837111187872092
KN	2018-08-02	10142.0	0.8836416093970392
CA	2018-03-12	3857.0	0.8829882211294399
CH	2018-07-10	15474.0	0.8818621690086835
CA	2018-12-21	17800.0	0.8804997849613485
CH	2018-04-12	9543.0	0.8804441774492126
CA	2018-05-17	24157.0	0.8800132192301576
CA	2018-11-27	11998.0	0.8790261858897415
CA	2018-05-16	18050.0	0.8784701107683803
UK	2018-08-31	12558.0	0.8784145032562442
GM	2018-07-12	14380.0	0.8774552736718962
KN	2018-04-23	16828.0	0.8772328436233519
SN	2018-06-08	7669.0	0.8772189417453179
IR	2018-08-18	7309.0	0.8770104135748072
UK	2018-05-02	12396.0	0.8760511839904593
UK	2018-10-14	5956.0	0.8753977957228598
SA	2018-11-01	15046.0	0.8730483783351091
UK	2018-10-21	2744.0	0.8728259482865646
CA	2018-11-25	5826.0	0.8728120464085306
RS	2018-02-01	16355.0	0.8723393825553735
RS	2018-08-20	7343.0	0.871588681141536
CH	2018-11-07	6557.0	0.871546975507434
RS	2018-08-22	20034.0	0.8708935872398345
GM	2018-07-13	2052.0	0.8704765308988138
CA	2018-06-02	5721.0	0.8703236102404394
CA	2018-02-02	17797.0	0.8699065538994184
CH	2018-09-15	3144.0	0.8698648482653165
UK	2018-02-01	14012.0	0.8693782825341254
RS	2018-05-13	5235.0	0.8691419506075467
UK	2018-05-03	14384.0	0.8687805017786622
CH	2018-09-21	4692.0	0.8683356416815732
UK	2018-09-03	13948.0	0.8679046834625181
CA	2018-05-15	5417.0	0.8673903139752592
CA	2018-06-21	13191.0	0.867320804585089
CH	2018-09-25	15812.0	0.8671678839267148
RS	2018-02-02	21319.0	0.8667925332197959
UK	2018-03-26	12128.0	0.8654301491724612
IZ	2018-07-15	15445.0	0.8652633266360529
CA	2018-02-03	4060.0	0.8645960364904194
CH	2018-05-25	11743.0	0.8637341200523094
UK	2018-12-09	3012.0	0.8630390261506082
CH	2018-11-08	12463.0	0.8622327172246346
UK	2018-10-28	4144.0	0.8602586505438025
KN	2018-08-06	5699.0	0.860022318617224
KN	2018-07-03	13087.0	0.8595635566421009
RS	2018-01-31	5469.0	0.8593967341056926
CA	2018-07-20	5966.0	0.8573809617907584
IR	2018-10-05	4126.0	0.8560602833775256
CH	2018-11-12	8098.0	0.8540862166966935
CH	2018-01-14	6669.0	0.8539610997943873
RS	2018-04-21	5324.0	0.8534606321851623
UK	2018-02-10	6643.0	0.8534328284290942
SA	2018-08-10	7530.0	0.8531269871123455
IS	2018-04-23	1538.0	0.8527238326493587
IR	2018-11-18	4890.0	0.8525014026008143
UK	2018-10-27	4271.0	0.8525014026008141
CA	2018-10-12	11933.0	0.8521677575279974
CA	2018-12-17	11961.0	0.851945327479453
UK	2018-09-24	12292.0	0.8518758180892829
CH	2018-11-06	12781.0	0.8512919392118538
IR	2018-11-20	8532.0	0.8512224298216837
CA	2018-12-15	2845.0	0.8510834110413432
KN	2018-04-19	7284.0	0.8501797889691315
UK	2018-09-23	3256.0	0.8496515176038383
UK	2018-03-25	5802.0	0.849053736848375
CH	2018-12-06	16553.0	0.8489981293362391
UK	2018-11-12	13789.0	0.8487756992876945
CH	2018-09-26	11491.0	0.8485532692391501
CA	2018-09-09	6649.0	0.8482057222882992
UK	2018-11-09	12342.0	0.8473716096062576
CH	2018-03-05	14966.0	0.8472881983380534
AR	2018-12-05	2588.0	0.8468850438750665
KN	2018-05-25	14726.0	0.8468433382409645
UK	2018-01-19	9315.0	0.846106538705161
IZ	2018-07-17	21518.0	0.8458145992664464
CA	2018-09-18	16734.0	0.844716350901758
CH	2018-11-09	16631.0	0.844716350901758
SY	2018-02-23	5520.0	0.8444383133410774
UK	2018-10-13	6284.0	0.844257588926635
UK	2018-02-22	15888.0	0.8436598081711718
UK	2018-12-02	2852.0	0.8429786161475044
UK	2018-02-20	12166.0	0.8428395973671641
UK	2018-03-27	15621.0	0.8426171673186197
CH	2018-11-18	6278.0	0.8422696203677689
CH	2018-08-03	19219.0	0.8422418166117007
UK	2018-10-12	9764.0	0.8417830546365778
RS	2018-08-23	11478.0	0.8413381945394889
UK	2018-09-01	2609.0	0.8406152968817194
CA	2018-09-19	12751.0	0.8402260442967666
UK	2018-06-07	15156.0	0.8394753428829291
SA	2018-12-13	18078.0	0.839350225980623

coveragewithoutusa

Step 2. Extracting the news around dates with high coverage (big events)

Investigating a seemingly inflentiual (2018-10-18) in Saudi Arabia (SA) using the scalable web scraper library goose

//Initializing the web scraper.
val urlContentFetcher = {new ContentFetcher()
    .setInputCol("sourceUrl")
    .setOutputTitleCol("title")
    .setOutputContentCol("content")
    .setOutputKeywordsCol("keywords")
    .setOutputPublishDateCol("publishDateCollected")
    .setOutputDescriptionCol("description")
    .setUserAgent("Mozilla/5.0 (X11; U; Linux x86_64; de; rv:1.9.2.8) Gecko/20100723 Ubuntu/10.04 Firefox/")
    .setConnectionTimeout(1000)
    .setSocketTimeout(1000)
                        }

val big_event_SA = oilEventCoverageDF.filter($"country" ==="SA" && $"eventDay" === "2018-10-18").orderBy(desc("coverage")).limit(100)
val SAEventURLS = urlContentFetcher.transform(big_event_SA.select($"country",$"coverage",$"date",$"sourceUrl",$"eventId")).filter(col("description") =!= "").orderBy(desc("coverage"))

SAEventURLS.printSchema

root
 |-- sourceUrl: string (nullable = true)
 |-- description: string (nullable = false)
 |-- content: string (nullable = false)
 |-- keywords: array (nullable = false)
 |    |-- element: string (containsNull = true)
 |-- title: string (nullable = false)
 |-- publishDateCollected: date (nullable = true)
 |-- country: string (nullable = true)
 |-- coverage: double (nullable = true)
 |-- date: date (nullable = true)
 |-- eventId: integer (nullable = true)

SAEventURLS.select($"description").show(6,false)

+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|description                                                                                                                                                                                           |
+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|The old Saudi Arabia was a place the United States often turned to in times of turbulence — when world oil prices were spiking or political tensions in the                                           |
|APPS-KHASHOGGI/ (COLUMN):COLUMN-Khashoggi case shows America's collapsing Mideast clout                                                                                                               |
|The disappearance of Jamal Khashoggi reveals the true nature of the Saudi crown prince, says author Dilip Hiro                                                                                        |
|Everything you wanted to know about U.S.-Saudi arms sales and the politics around them, but were afraid to ask.                                                                                       |
|The money transfer curiously coincided with the visit of US Secretary of State Mike Pompeo to Riyadh to sort out frictions between the allies over the Khashoggi killing in Turkey earlier this month.|
|If you had to pick a year in the past decade when the contradictions of the American-Saudi relationship seemed likeliest to explode into crisis, 2018 would not be the obvious choice.                |
+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
only showing top 6 rows

Investigating seemingly inflentiual events in Iran (IR) using goose on:

2018-05-10
2018-09-25

Events on 2018-05-10

val big_event_IR1 = oilEventCoverageDF.filter($"country" ==="IR" && $"eventDay" === "2018-05-10").orderBy(desc("coverage")).limit(100)
val IR1EventURLS = urlContentFetcher.transform(big_event_IR1.select($"country",$"coverage",$"date",$"sourceUrl",$"eventId")).filter(col("description") =!= "").orderBy(desc("coverage"))

IR1EventURLS.select($"description").show(10,false)

+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|description                                                                                                                                                                                                                                               |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|See related links to what you are looking for.                                                                                                                                                                                                            |
|See related links to what you are looking for.                                                                                                                                                                                                            |
|See related links to what you are looking for.                                                                                                                                                                                                            |
|Iran's Supreme Leader Ayatollah Ali Khamenei said Wednesday that US President Donald Trump's anti-Iran remarks, upon announcement of his withdrawal for the nuclear deal on Tuesday, was                                                                  |
|Before the May 12 deadline, President Donald Trump has withdrawn the US from the multilateral Iran nuclear deal, with the objective to find a different method of dealing with the purported Iranian...                                                   |
|Before the May 12 deadline, President Donald Trump has withdrawn the US from the multilateral Iran nuclear deal, with the objective to find a different method of dealing with the purported Iranian...                                                   |
|It is dangerous that neither Trump nor Netanyahu appears to fully grasp the dire regional and international implications of the unilateral decertification of the deal by the US.                                                                         |
|So, Bibi helps Trump decide on Iran, he threatens to strike Syria if the Russians sell them S-400 and now hes a guest of honor at the Victory Day parade in Moscow. How much weirder can Middle Eastern politics get, I wonder.                           |
|Canadian stocks may continue to rise Thursday, stoked by higher oil prices and a diplomatic breakthrough with North Korea.  Three Americans Americans ere freed Wednesday ahead of President Trump's upcoming summit with North Korean leader Kim Jong Un.|
|For Iran, Iraq is the most important Arab state, even more than Syria and Lebanon                                                                                                                                                                         |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
only showing top 10 rows

Events on 2018-09-25

val big_event_IR2 = oilEventCoverageDF.filter($"country" ==="IR" && $"eventDay" === "2018-09-25").orderBy(desc("coverage")).limit(100)
val IR2EventURLS = urlContentFetcher.transform(big_event_IR2.select($"country",$"coverage",$"date",$"sourceUrl",$"eventId")).filter(col("description") =!= "").orderBy(desc("coverage"))

IR2EventURLS.select($"description").show(6,false)

+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|description                                                                                                                                                                                                                                                                                                                                    |
+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|Following the deadly attack in the Iranian city of Ahvaz on Saturday morning, which killed 25 and wounded 53 during a parade commemorating the 38th anniversary of the...                                                                                                                                                                      |
|Following the deadly attack in the Iranian city of Ahvaz on Saturday morning, which killed 25 and wounded 53 during a parade commemorating the 38th anniversary of the...                                                                                                                                                                      |
|Trump said his administration has accomplished more in less than two years 'than almost any administration in the history of our country'                                                                                                                                                                                                      |
|A crowd largely comprised of Iranian-Americans gathered to protest the Iranian regime and President Hassan Rouhani.                                                                                                                                                                                                                            |
|With European companies abandoning Iran in the face of growing U.S. pressure, European politicians backing Iran are counting on oil demand from China, India and Turkey to keep the 2015 nuclear deal alive. Since the U.S. withdrawal from the nuclear deal in May, Iran has threatened to resume its nuclear program if it loses economic ...|
|President Trump won't meet with Iranian President Hassan Rouhani during his time at the United Nations General Assembly meeting and blasted the country in his speech to delegates.                                                                                                                                                            |
+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
only showing top 6 rows

Enrich Data with Trend Calculus

For more information about Trend Calculus, see https://lamastex.github.io/spark-trend-calculus-examples/

val rootTrendPath = TrendUtils.getStreamableTrendCalculusPath
val oilGoldPath = rootTrendPath +"oilGoldDelta"

Gather trend reversals of all oil price data

val oil_data_all = spark.read.format("delta").load(oilGoldPath).as[TickerPoint].filter($"ticker" === "BCOUSD")
val trend_oil_all = new TrendCalculus2(oil_data_all,2,spark).nReversalsJoinedWithMaxRev(15)

trend_oil_all.write.parquet(rootCheckpointPath+"trend_oil_all")

Step 3. Comparing the coverage with oil price

Code needed for the interactive plot below

from plotly.offline import plot
from plotly.graph_objs import *
from datetime import *
from pyspark.sql import functions as F
import pyspark.sql.functions
from pyspark.sql.functions import col, avg

rootCheckpointPath = GdeltUtils.getEOICheckpointPath()

trend_oil_all = spark.read.parquet(rootCheckpointPath+"trend_oil_all")

oil_gas_cov_us_2015_2018 = spark.read.parquet(rootCheckpointPath+"oil_gas_cov_norm").select(F.col('date'),F.col('country'),F.col('coverage')).filter(F.col('country') == 'US').drop('country').filter(F.col('date')>'2015-01-01').filter(F.col('date')<'2018-12-31')

trend_oil_2015_2018 = trend_oil_all.filter(F.col('x')>'2015-01-01').filter(F.col('x')<'2018-12-31').orderBy(F.col('x'))

max_price = trend_oil_2015_2018.agg({'y': 'max'}).first()[0]
min_price = trend_oil_2015_2018.agg({'y': 'min'}).first()[0]
trend_oil_2015_2018_2 =trend_oil_2015_2018.withColumn('sy', (F.col('y')-min_price)/(max_price-min_price))

fullTS = trend_oil_2015_2018_2.filter("maxRev > 2").select("x","sy","maxRev").collect()
coverage =oil_gas_cov_us_2015_2018.collect()

TS = [row for row in fullTS]

numReversals = 15
startReversal = 7

allData = {'x': [row['x'] for row in TS], 'y': [row['sy'] for row in TS], 'maxRev': [row['maxRev'] for row in TS]}
allDataCov = {'x': [row['date'] for row in coverage], 'y': [row['coverage'] for row in coverage]}

temp2 = max(allDataCov['y'])-min(allDataCov['y'])
standardCoverage = list(map(lambda x: (x-min(allDataCov['y']))/temp2,allDataCov['y']))

revTS = [row for row in TS if row[2] >= startReversal]
colorList = ['rgba(' + str(tmp) + ',' + str(255-tmp) + ',' + str(255-tmp) + ',1)' for tmp in [int(i*255/(numReversals-startReversal+1)) for i in range(1,numReversals-startReversal+2)]]

def getRevTS(tsWithRevMax, revMax):
  x = [row[0] for row in tsWithRevMax if row[2] >= revMax]
  y = [row[1] for row in tsWithRevMax if row[2] >= revMax]
  return x,y,revMax

reducedData = [getRevTS(revTS, i) for i in range(startReversal, numReversals+1)]

markerPlots = [Scattergl(x=x, y=y, mode='markers', marker=dict(color=colorList[i-startReversal], size=i), name='Reversal ' + str(i)) for (x,y,i) in [getRevTS(revTS, i) for i in range(startReversal, numReversals+1)]]

Plot of oil price together with oil and gas coverage for USA

p = plot(
  [Scattergl(x=allData['x'], y=allData['y'], mode='lines', name='Oil Price'),Scattergl(x=allDataCov['x'], y=standardCoverage, mode='lines', name='Oil and gas coverage usa ')] + markerPlots 
  ,
  output_type='div'
)
displayHTML(p)

oiltrendevents

ScaDaMaLe Course site and book

Detecting Persons of Interest to OIL/GAS Price Trends

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

Here we will build a pipeline to investigate possible persons, organisations and other entities related to oil and gas that are reported in mass media around the world and their possible co-occurrence with certain trends and trend-reversals in oil price.

Steps:

Step 0. Setting up and loading GDELT delta.io tables
Step 1. Create a graph of persons related to gas and oil
Step 2. Extract communties
Step 3. Find key Influencers
Step 4. Visualisation

Resources:

This builds on the following libraries and its antecedents therein:

This work was inspired by:

Antoine Aamennd's texata-2017
Andrew Morgan's Trend Calculus Library

Step 0. Setting up and loading GDELT delta.io tables

import spark.implicits._
import io.delta.tables._
import com.aamend.spark.gdelt._
import org.apache.spark.sql.{Dataset,DataFrame,SaveMode}
import org.apache.spark.sql.functions._
import org.apache.spark.sql.expressions._
import org.graphframes.GraphFrame 
import org.apache.spark.sql.SparkSession

"./000b_gdelt_utils"

val rootPath = GdeltUtils.getGdeltV1Path
val rootCheckpointPath = GdeltUtils.getPOICheckpointPath
val gkgPath = rootPath+"gkg"

defined object GdeltUtils

val gkg_v1 = spark.read.format("delta").load(gkgPath).as[GKGEventV1]

val gkg_v1_filt = gkg_v1.filter($"publishDate">"2013-04-01 00:00:00" && $"publishDate"<"2019-12-31 00:00:00")

val oil_gas_themeGKG = gkg_v1_filt.filter(c =>c.themes.contains("ENV_GAS") || c.themes.contains("ENV_OIL"))

The first step is to create a graph between people releated to gas and oil where the edges are number of articles that they are mentioned in together.

Create the GraphFrame of Interest

val edges = oil_gas_themeGKG.select($"persons",$"numArticles")
                          .withColumn("src",explode($"persons"))
                          .withColumn("dst",explode($"persons"))
                          .filter($"src".notEqual($"dst") && $"src" =!= "" && $"dst" =!= "")
                          .groupBy($"src",$"dst")
                          .agg(sum("numArticles").as("count"))
                          .toDF()

val vertices = oil_gas_themeGKG.select($"persons",$"numArticles")
                          .withColumn("id",explode($"persons"))
                          .filter($"id" =!= "")
                          .drop($"persons")
                          .groupBy($"id")
                          .agg(sum("numArticles").as("numArticles"))
                          .toDF()
val pers_graph = GraphFrame(vertices,edges)

Count how many vertices and edges there is in our graph

println("vertex count: " +pers_graph.vertices.count())
println("edge count: " + pers_graph.edges.count())

vertex count: 3422103
edge count: 133703116

val fil_pers_graph = pers_graph.filterEdges($"count" >10).dropIsolatedVertices()

Count how many vertices and edges are in our graph after being filtered

println("filtered vertex count: " +fil_pers_graph.vertices.count())
println("filtered edge count: " + fil_pers_graph.edges.count())

filtered vertex count: 214514
filtered edge count: 4525828

sc.setCheckpointDir(rootCheckpointPath)

Compute the connected components

val comp_vertices = fil_pers_graph.connectedComponents.run()

Checkpoint

comp_vertices.write.parquet(rootCheckpointPath+"comp_vertices")

val comp_vertices = spark.read.parquet(rootCheckpointPath+"comp_vertices")
val comp_graph = GraphFrame(comp_vertices,fil_pers_graph.edges)

Note that almost all edges and vertices are in the connected component labelled 0, our giant component.

comp_graph.vertices.groupBy($"component").agg(count("component").as("count")).orderBy(desc("count")).show()

+------------+------+
|   component| count|
+------------+------+
|           0|195316|
|  8589935254|    97|
| 34359738385|    23|
|        1084|    22|
|         150|    21|
| 94489280677|    20|
| 94489280553|    19|
| 60129543033|    19|
|395136991484|    19|
|180388626903|    17|
|146028888838|    17|
| 25769804801|    16|
| 17179869819|    16|
|231928234487|    16|
|146028888649|    15|
| 51539608679|    15|
| 51539607916|    15|
| 60129543026|    15|
| 42949673514|    15|
|  8589935379|    15|
+------------+------+
only showing top 20 rows

Filter out the graph to only focus on the giant component

val big_comp_graph = comp_graph.filterVertices($"component" === 0)

big_comp_graph: org.graphframes.GraphFrame = GraphFrame(v:[id: string, numArticles: bigint ... 1 more field], e:[src: string, dst: string ... 1 more field])

Step 2. Extract communities

Next, let us extract communities within the giant component.

There are many algorithms for community structure detection:

https://en.wikipedia.org/wiki/Community_structure

We use a simple scalable one via label propagation here.

Apply label propagation to find interesting community structures

val label_vertices = big_comp_graph.labelPropagation.maxIter(10).run()

label_vertices: org.apache.spark.sql.DataFrame = [id: string, numArticles: bigint ... 2 more fields]

Checkpoint

label_vertices.write.parquet(rootCheckpointPath+"label_vertices")
big_comp_graph.edges.write.parquet(rootCheckpointPath+"label_edges")

val label_vertices = spark.read.parquet(rootCheckpointPath+"label_vertices")
val label_edges = spark.read.parquet(rootCheckpointPath+"label_edges")

val label_graph = GraphFrame(label_vertices,label_edges)

Step 3. Find key Influencers

Apply page rank to find the key influencers

val com_rank_graph =label_graph.pageRank.resetProbability(0.15).tol(0.015).run()

com_rank_graph: org.graphframes.GraphFrame = GraphFrame(v:[id: string, numArticles: bigint ... 3 more fields], e:[src: string, dst: string ... 2 more fields])

Checkpoint

com_rank_graph.vertices.write.parquet(rootCheckpointPath+"com_rank_vertices")
com_rank_graph.edges.write.parquet(rootCheckpointPath+"com_rank_edges")

val com_rank_vertices = spark.read.parquet(rootCheckpointPath+"com_rank_vertices")
val com_rank_edges =spark.read.parquet(rootCheckpointPath+"com_rank_edges")
val com_rank_graph = GraphFrame(com_rank_vertices,com_rank_edges)

com_rank_graph.vertices.groupBy($"label").agg(count($"label").as("count")).orderBy(desc("count")).show()

Step 4. Visualisation

Look at the top three communities

val toplabel1 = com_rank_graph.filterVertices($"label" === 1520418423783L)
val toplabel2 = com_rank_graph.filterVertices($"label" === 8589934959L)
val toplabel3 =com_rank_graph.filterVertices($"label" === 1580547965452L)

Filter out the top 100 according to pagerank score

val toplabel1Filt =  toplabel1.filterVertices($"pagerank" >=55.47527731815801)

Filter out edges to make the graph more comprehensive

val toplabel1FiltE = toplabel1Filt.filterEdges($"count">2000).dropIsolatedVertices()

In the interactive d3 graph below, the size of circle correlates with pagerank score.

case class Edge(src: String, dst: String, count: Long)

case class Node(name: String,importance: Double)
case class Link(source: Int, target: Int, value: Long)
case class Graph(nodes: Seq[Node], links: Seq[Link])

object graphs {

val sqlContext = SparkSession.builder().getOrCreate().sqlContext
import sqlContext.implicits._
  
def force(vertices: Dataset[Node],clicks: Dataset[Edge], height: Int = 100, width: Int = 960): Unit = {
  val data = clicks.collect()
  val nodes = vertices.collect()
  val links = data.map { t =>
    Link(nodes.indexWhere(_.name == t.src.replaceAll("_", " ")), nodes.indexWhere(_.name == t.dst.replaceAll("_", " ")), t.count / 20 + 1)
  }
  showGraph(height, width, Seq(Graph(nodes, links)).toDF().toJSON.first())
}

/**
 * Displays a force directed graph using d3
 * input: {"nodes": [{"name": "..."}], "links": [{"source": 1, "target": 2, "value": 0}]}
 */
def showGraph(height: Int, width: Int, graph: String): Unit = {

displayHTML(s"""
<style>

.node_circle {
  stroke: #777;
  stroke-width: 1.3px;
}

.node_label {
  pointer-events: none;
}

.link {
  stroke: #777;
  stroke-opacity: .2;
}

.node_count {
  stroke: #777;
  stroke-width: 1.0px;
  fill: #999;
}

text.legend {
  font-family: Verdana;
  font-size: 13px;
  fill: #000;
}

.node text {
  font-family: "Helvetica Neue","Helvetica","Arial",sans-serif;
  font-size: function(d) {return (d.importance)+ "px"};
  font-weight: 200;
}

</style>

<div id="clicks-graph">
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var graph = $graph;

var width = $width,
    height = $height;

var color = d3.scale.category20();

var force = d3.layout.force()
    .charge(-200)
    .linkDistance(350)
    .size([width, height]);

var svg = d3.select("#clicks-graph").append("svg")
    .attr("width", width)
    .attr("height", height);
    
force
    .nodes(graph.nodes)
    .links(graph.links)
    .start();

var link = svg.selectAll(".link")
    .data(graph.links)
    .enter().append("line")
    .attr("class", "link")
    .style("stroke-width", function(d) { return Math.sqrt(d.value)/10; });

var node = svg.selectAll(".node")
    .data(graph.nodes)
    .enter().append("g")
    .attr("class", "node")
    .call(force.drag);

node.append("circle")
    .attr("r", function(d) { return Math.sqrt(d.importance); })
    .style("fill", function (d) {
    if (d.name.startsWith("other")) { return color(1); } else { return color(2); };
})

node.append("text")
      .attr("dx", function(d) { return (Math.sqrt(d.importance)*30)/Math.sqrt(1661.1815574713858); })
      .attr("dy", ".35em")
      .text(function(d) { return d.name });
      
//Now we are giving the SVGs co-ordinates - the force layout is generating the co-ordinates which this code is using to update the attributes of the SVG elements
force.on("tick", function () {
    link.attr("x1", function (d) {
        return d.source.x;
    })
        .attr("y1", function (d) {
        return d.source.y;
    })
        .attr("x2", function (d) {
        return d.target.x;
    })
        .attr("y2", function (d) {
        return d.target.y;
    });
    d3.selectAll("circle").attr("cx", function (d) {
        return d.x;
    })
        .attr("cy", function (d) {
        return d.y;
    });
    d3.selectAll("text").attr("x", function (d) {
        return d.x;
    })
        .attr("y", function (d) {
        return d.y;
    });
});
</script>
</div>
""")
}
  
  def help() = {
displayHTML("""
<p>
Produces a force-directed graph given a collection of edges of the following form:</br>
<tt><font color="#a71d5d">case class</font> <font color="#795da3">Edge</font>(<font color="#ed6a43">src</font>: <font color="#a71d5d">String</font>, <font color="#ed6a43">dest</font>: <font color="#a71d5d">String</font>, <font color="#ed6a43">count</font>: <font color="#a71d5d">Long</font>)</tt>
</p>
<p>Usage:<br/>
<tt><font color="#a71d5d">import</font> <font color="#ed6a43">d3._</font></tt><br/>
<tt><font color="#795da3">graphs.force</font>(</br>
&nbsp;&nbsp;<font color="#ed6a43">height</font> = <font color="#795da3">500</font>,<br/>
&nbsp;&nbsp;<font color="#ed6a43">width</font> = <font color="#795da3">500</font>,<br/>
&nbsp;&nbsp;<font color="#ed6a43">clicks</font>: <font color="#795da3">Dataset</font>[<font color="#795da3">Edge</font>])</tt>
</p>""")
  }
}
graphs.force(
  height = 800,
  width = 1200,
  clicks = toplabel1FiltE.edges.as[Edge],
  vertices = toplabel1FiltE.vertices.select($"id".as("name"),$"pagerank".as("importance")).as[Node]
  )

usa_cluster

Filter out the top 100 according to pagerank score

val toplabel2Filt =  toplabel2.filterVertices($"pagerank" >=7.410990956624706)

Filter out edges to and vertices with small amount of edges to make the graph more comprehensive

val toplabel2FiltE = toplabel2Filt.filterEdges($"count">136).dropIsolatedVertices()

Nigerian cluster

case class Edge(src: String, dst: String, count: Long)

case class Node(name: String,importance: Double)
case class Link(source: Int, target: Int, value: Long)
case class Graph(nodes: Seq[Node], links: Seq[Link])

object graphs {
// val sqlContext = SQLContext.getOrCreate(org.apache.spark.SparkContext.getOrCreate())  /// fix
val sqlContext = SparkSession.builder().getOrCreate().sqlContext
import sqlContext.implicits._
  
def force(vertices: Dataset[Node],clicks: Dataset[Edge], height: Int = 100, width: Int = 960): Unit = {
  val data = clicks.collect()
  val nodes = vertices.collect()
  val links = data.map { t =>
    Link(nodes.indexWhere(_.name == t.src.replaceAll("_", " ")), nodes.indexWhere(_.name == t.dst.replaceAll("_", " ")), t.count / 20 + 1)
  }
  showGraph(height, width, Seq(Graph(nodes, links)).toDF().toJSON.first())
}

/**
 * Displays a force directed graph using d3
 * input: {"nodes": [{"name": "..."}], "links": [{"source": 1, "target": 2, "value": 0}]}
 */
def showGraph(height: Int, width: Int, graph: String): Unit = {

displayHTML(s"""
<style>

.node_circle {
  stroke: #777;
  stroke-width: 1.3px;
}

.node_label {
  pointer-events: none;
}

.link {
  stroke: #777;
  stroke-opacity: .2;
}

.node_count {
  stroke: #777;
  stroke-width: 1.0px;
  fill: #999;
}

text.legend {
  font-family: Verdana;
  font-size: 13px;
  fill: #000;
}

.node text {
  font-family: "Helvetica Neue","Helvetica","Arial",sans-serif;
  font-size: function(d) {return (d.importance)+ "px"};
  font-weight: 200;
}

</style>

<div id="clicks-graph">
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var graph = $graph;

var width = $width,
    height = $height;

var color = d3.scale.category20();

var force = d3.layout.force()
    .charge(-200)
    .linkDistance(350)
    .size([width, height]);

var svg = d3.select("#clicks-graph").append("svg")
    .attr("width", width)
    .attr("height", height);
    
force
    .nodes(graph.nodes)
    .links(graph.links)
    .start();

var link = svg.selectAll(".link")
    .data(graph.links)
    .enter().append("line")
    .attr("class", "link")
    .style("stroke-width", function(d) { return Math.sqrt(d.value)/10; });

var node = svg.selectAll(".node")
    .data(graph.nodes)
    .enter().append("g")
    .attr("class", "node")
    .call(force.drag);

node.append("circle")
    .attr("r", function(d) { return Math.sqrt(d.importance); })
    .style("fill", function (d) {
    if (d.name.startsWith("other")) { return color(1); } else { return color(2); };
})

node.append("text")
      .attr("dx", function(d) { return (Math.sqrt(d.importance)*30)/Math.sqrt(453.6031403843406); })
      .attr("dy", ".35em")
      .text(function(d) { return d.name });
      
//Now we are giving the SVGs co-ordinates - the force layout is generating the co-ordinates which this code is using to update the attributes of the SVG elements
force.on("tick", function () {
    link.attr("x1", function (d) {
        return d.source.x;
    })
        .attr("y1", function (d) {
        return d.source.y;
    })
        .attr("x2", function (d) {
        return d.target.x;
    })
        .attr("y2", function (d) {
        return d.target.y;
    });
    d3.selectAll("circle").attr("cx", function (d) {
        return d.x;
    })
        .attr("cy", function (d) {
        return d.y;
    });
    d3.selectAll("text").attr("x", function (d) {
        return d.x;
    })
        .attr("y", function (d) {
        return d.y;
    });
});
</script>
</div>
""")
}
  
  def help() = {
displayHTML("""
<p>
Produces a force-directed graph given a collection of edges of the following form:</br>
<tt><font color="#a71d5d">case class</font> <font color="#795da3">Edge</font>(<font color="#ed6a43">src</font>: <font color="#a71d5d">String</font>, <font color="#ed6a43">dest</font>: <font color="#a71d5d">String</font>, <font color="#ed6a43">count</font>: <font color="#a71d5d">Long</font>)</tt>
</p>
<p>Usage:<br/>
<tt><font color="#a71d5d">import</font> <font color="#ed6a43">d3._</font></tt><br/>
<tt><font color="#795da3">graphs.force</font>(</br>
&nbsp;&nbsp;<font color="#ed6a43">height</font> = <font color="#795da3">500</font>,<br/>
&nbsp;&nbsp;<font color="#ed6a43">width</font> = <font color="#795da3">500</font>,<br/>
&nbsp;&nbsp;<font color="#ed6a43">clicks</font>: <font color="#795da3">Dataset</font>[<font color="#795da3">Edge</font>])</tt>
</p>""")
  }
}
graphs.force(
  height = 800,
  width = 1200,
  clicks = toplabel2FiltE.edges.as[Edge],
  vertices = toplabel2FiltE.vertices.select($"id".as("name"),$"pagerank".as("importance")).as[Node]
  )

nigerian_cluster

Filter out the top 100 according to pagerank score

val toplabel3Filt =  toplabel3.filterVertices($"pagerank" >=3.160183413696083).filterEdges($"count">4*18).dropIsolatedVertices()

Filter out edges to and vertices with small amount of edges to make the graph more comprehensive

val toplabel3FiltE = toplabel3Filt.filterEdges($"count">50).dropIsolatedVertices()

Malaysian cluster

case class Edge(src: String, dst: String, count: Long)

case class Node(name: String,importance: Double)
case class Link(source: Int, target: Int, value: Long)
case class Graph(nodes: Seq[Node], links: Seq[Link])

object graphs {
// val sqlContext = SQLContext.getOrCreate(org.apache.spark.SparkContext.getOrCreate())  /// fix
val sqlContext = SparkSession.builder().getOrCreate().sqlContext
import sqlContext.implicits._
  
def force(vertices: Dataset[Node],clicks: Dataset[Edge], height: Int = 100, width: Int = 960): Unit = {
  val data = clicks.collect()
  val nodes = vertices.collect()
  val links = data.map { t =>
    Link(nodes.indexWhere(_.name == t.src.replaceAll("_", " ")), nodes.indexWhere(_.name == t.dst.replaceAll("_", " ")), t.count / 20 + 1)
  }
  showGraph(height, width, Seq(Graph(nodes, links)).toDF().toJSON.first())
}

/**
 * Displays a force directed graph using d3
 * input: {"nodes": [{"name": "..."}], "links": [{"source": 1, "target": 2, "value": 0}]}
 */
def showGraph(height: Int, width: Int, graph: String): Unit = {

displayHTML(s"""
<style>

.node_circle {
  stroke: #777;
  stroke-width: 1.3px;
}

.node_label {
  pointer-events: none;
}

.link {
  stroke: #777;
  stroke-opacity: .2;
}

.node_count {
  stroke: #777;
  stroke-width: 1.0px;
  fill: #999;
}

text.legend {
  font-family: Verdana;
  font-size: 13px;
  fill: #000;
}

.node text {
  font-family: "Helvetica Neue","Helvetica","Arial",sans-serif;
  font-size: function(d) {return (d.importance)+ "px"};
  font-weight: 200;
}

</style>

<div id="clicks-graph">
<script src="//d3js.org/d3.v3.min.js"></script>
<script>

var graph = $graph;

var width = $width,
    height = $height;

var color = d3.scale.category20();

var force = d3.layout.force()
    .charge(-200)
    .linkDistance(300)
    .size([width, height]);

var svg = d3.select("#clicks-graph").append("svg")
    .attr("width", width)
    .attr("height", height);
    
force
    .nodes(graph.nodes)
    .links(graph.links)
    .start();

var link = svg.selectAll(".link")
    .data(graph.links)
    .enter().append("line")
    .attr("class", "link")
    .style("stroke-width", function(d) { return Math.sqrt(d.value)/3; });

var node = svg.selectAll(".node")
    .data(graph.nodes)
    .enter().append("g")
    .attr("class", "node")
    .call(force.drag);

node.append("circle")
    .attr("r", function(d) { return (Math.sqrt(d.importance)*30)/Math.sqrt(98.7695771886648); })
    .style("fill", function (d) {
    if (d.name.startsWith("other")) { return color(1); } else { return color(2); };
})

node.append("text")
      .attr("dx", function(d) { return (Math.sqrt(d.importance)*30)/Math.sqrt(26.343032735543023); })
      .attr("dy", ".35em")
      .text(function(d) { return d.name });
      
//Now we are giving the SVGs co-ordinates - the force layout is generating the co-ordinates which this code is using to update the attributes of the SVG elements
force.on("tick", function () {
    link.attr("x1", function (d) {
        return d.source.x;
    })
        .attr("y1", function (d) {
        return d.source.y;
    })
        .attr("x2", function (d) {
        return d.target.x;
    })
        .attr("y2", function (d) {
        return d.target.y;
    });
    d3.selectAll("circle").attr("cx", function (d) {
        return d.x;
    })
        .attr("cy", function (d) {
        return d.y;
    });
    d3.selectAll("text").attr("x", function (d) {
        return d.x;
    })
        .attr("y", function (d) {
        return d.y;
    });
});
</script>
</div>
""")
}
  
  def help() = {
displayHTML("""
<p>
Produces a force-directed graph given a collection of edges of the following form:</br>
<tt><font color="#a71d5d">case class</font> <font color="#795da3">Edge</font>(<font color="#ed6a43">src</font>: <font color="#a71d5d">String</font>, <font color="#ed6a43">dest</font>: <font color="#a71d5d">String</font>, <font color="#ed6a43">count</font>: <font color="#a71d5d">Long</font>)</tt>
</p>
<p>Usage:<br/>
<tt><font color="#a71d5d">import</font> <font color="#ed6a43">d3._</font></tt><br/>
<tt><font color="#795da3">graphs.force</font>(</br>
&nbsp;&nbsp;<font color="#ed6a43">height</font> = <font color="#795da3">500</font>,<br/>
&nbsp;&nbsp;<font color="#ed6a43">width</font> = <font color="#795da3">500</font>,<br/>
&nbsp;&nbsp;<font color="#ed6a43">clicks</font>: <font color="#795da3">Dataset</font>[<font color="#795da3">Edge</font>])</tt>
</p>""")
  }
}
graphs.force(
  height = 800,
  width = 1200,
  clicks = toplabel3FiltE.edges.as[Edge],
  vertices = toplabel3FiltE.vertices.select($"id".as("name"),$"pagerank".as("importance")).as[Node]
  )

malaysian_cluster

ScaDaMaLe Course site and book

Plugging into GDELT Mass Media Streams

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

This is just a brief teaser into the world of the GDELT-project: * https://www.gdeltproject.org/

This exposition was originally from Mastering Spark for Data Science which we will try to dive into in the geospatial modules.

We will use a spark-gdelt library for Spark 3.0.1:

https://github.com/aamend/spark-gdelt

Also see the following that this work build on:

https://github.com/lamastex/spark-gdelt-examples

What is The GDELT-Project?

From https://www.gdeltproject.org/

Watching our World Unfold

A Global Database of Society

Supported by Google Jigsaw, the GDELT Project monitors the world's broadcast, print, and web news from nearly every corner of every country in over 100 languages and identifies the people, locations, organizations, themes, sources, emotions, counts, quotes, images and events driving our global society every second of every day, creating a free open platform for computing on the entire world.

spinningglobe gdelt project

import com.aamend.spark.gdelt._
import org.apache.spark.sql.Dataset
import spark.implicits._

import com.aamend.spark.gdelt._
import org.apache.spark.sql.Dataset
import spark.implicits._

ls dbfs:/datasets/ScaDaMaLe/GDELT/

path	name	size
dbfs:/datasets/ScaDaMaLe/GDELT/EventV1/	EventV1/	0.0
dbfs:/datasets/ScaDaMaLe/GDELT/EventV2/	EventV2/	0.0
dbfs:/datasets/ScaDaMaLe/GDELT/GKGV1/	GKGV1/	0.0
dbfs:/datasets/ScaDaMaLe/GDELT/GKGV2/	GKGV2/	0.0

Download from gdelt-project

Just a pinky toe dip in this ocean of information!

Here we just show briefly how you can download the zipped CSV files from the GDELT-project and turn them into DataSets using the libraries we have contributed to.

In order to scalably analyze this data one needs delta.io tables (just a couple more steps to turn these SparkSQL datasets actually). We use such delta.io tables we have built in another project to present more interesting detection of events and entities of interest in the sequel.

Note first that there are several types of GDELT datasets. There is indeed a large set of code-books and manuals one should first familiarise oneself with before trying to understand what all the structured data means - it is fairly detailed. These are available from manual searches through the gdelt project pages.

Here is a collection of them that will be immediately and minimally necessary to make cohesive sense of a large fraction of the datasets available to anyone:

https://github.com/lamastex/spark-gdelt-examples/tree/master/gdelt-docs

ls dbfs:///datasets/ScaDaMaLe/GDELT/

path	name	size
dbfs:/datasets/ScaDaMaLe/GDELT/20180416121500.gkg.csv	20180416121500.gkg.csv	3.4277858e7
dbfs:/datasets/ScaDaMaLe/GDELT/20190517121500.gkg.csv	20190517121500.gkg.csv	2.5728991e7
dbfs:/datasets/ScaDaMaLe/GDELT/20190523121500.gkg.csv	20190523121500.gkg.csv	2.9695688e7
dbfs:/datasets/ScaDaMaLe/GDELT/EventV1/	EventV1/	0.0
dbfs:/datasets/ScaDaMaLe/GDELT/EventV2/	EventV2/	0.0
dbfs:/datasets/ScaDaMaLe/GDELT/GKGV1/	GKGV1/	0.0
dbfs:/datasets/ScaDaMaLe/GDELT/GKGV2/	GKGV2/	0.0

Download Event v2 data from Gdelt.

curl -O http://data.gdeltproject.org/gdeltv2/20190517121500.gkg.csv.zip
curl -O http://data.gdeltproject.org/gdeltv2/20190523121500.gkg.csv.zip
curl -O http://data.gdeltproject.org/gdeltv2/20180416121500.gkg.csv.zip

unzip 20190517121500.gkg.csv.zip
unzip 20190523121500.gkg.csv.zip
unzip 20180416121500.gkg.csv.zip

cp "file:///databricks/driver/20180416121500.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/EventV2/20180416121500.gkg.csv"

res2: Boolean = true

cp "file:///databricks/driver/20190523121500.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/EventV2/20190523121500.gkg.csv"

res3: Boolean = true

cp "file:///databricks/driver/20190517121500.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/EventV2/20190517121500.gkg.csv"

res4: Boolean = true

val gdeltEventV2DS: Dataset[GKGEventV2] = spark.read.gdeltGkgV2("dbfs:/datasets/ScaDaMaLe/GDELT/EventV2/20190523121500.gkg.csv")

gdeltEventV2DS: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.GKGEventV2] = [gkgRecordId: struct<publishDate: timestamp, translingual: boolean ... 1 more field>, publishDate: timestamp ... 27 more fields]

display(gdeltEventV2DS)

Download GKG v2 data from Gdelt.

curl -O http://data.gdeltproject.org/gdeltv2/20180417121500.gkg.csv.zip
curl -O http://data.gdeltproject.org/gdeltv2/20190523121500.gkg.csv.zip
curl -O http://data.gdeltproject.org/gdeltv2/20190517121500.gkg.csv.zip

ls dbfs:///datasets/ScaDaMaLe/GDELT/

unzip 20180417121500.gkg.csv.zip
unzip 20190523121500.gkg.csv.zip
unzip 20190517121500.gkg.csv.zip

cp "file:///databricks/driver/20180417121500.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/GKGV2/20180417121500.gkg.csv"

res8: Boolean = true

cp "file:///databricks/driver/20190523121500.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/GKGV2/20190523121500.gkg.csv"

res9: Boolean = true

cp "file:///databricks/driver/20190517121500.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/GKGV2/20190517121500.gkg.csv"

res10: Boolean = true

val gdeltGkgV2DS: Dataset[GKGEventV2] = spark.read.gdeltGkgV2("dbfs:///datasets/ScaDaMaLe/GDELT/GKGV2/20190517121500.gkg.csv")

gdeltGkgV2DS: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.GKGEventV2] = [gkgRecordId: struct<publishDate: timestamp, translingual: boolean ... 1 more field>, publishDate: timestamp ... 27 more fields]

display(gdeltGkgV2DS)

Dowload Gkg V1 Data from Gdelt

curl -O http://data.gdeltproject.org/gkg/20190517.gkg.csv.zip
curl -O http://data.gdeltproject.org/gkg/20190523.gkg.csv.zip
curl -O http://data.gdeltproject.org/gkg/20180417.gkg.csv.zip

unzip 20190517.gkg.csv.zip
unzip 20190523.gkg.csv.zip
unzip 20180417.gkg.csv.zip

cp "file:///databricks/driver/20180417.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/GKGV1/20180417.gkg.csv"

res32: Boolean = true

cp "file:///databricks/driver//20190523.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/GKGV1/20190523.gkg.csv"

cp "file:///databricks/driver/20190517.gkg.csv" "dbfs:///datasets/ScaDaMaLe/GDELT/GKGV1/20190517.gkg.csv"

val gdeltGkgV1DS: Dataset[GKGEventV1] = spark.read.gdeltGkgV1("dbfs:///datasets/ScaDaMaLe/GDELT/GKGV1/20190517.gkg.csv")

gdeltGkgV1DS: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.GKGEventV1] = [publishDate: timestamp, numArticles: int ... 11 more fields]

display(gdeltGkgV1DS)

Download Event v1 data from Gdelt

curl -O http://data.gdeltproject.org/events/20190517.export.CSV.zip
curl -O http://data.gdeltproject.org/events/20190523.export.CSV.zip
curl -O http://data.gdeltproject.org/events/20180416.export.CSV.zip

unzip 20190517.export.CSV.zip
unzip 20190523.export.CSV.zip
unzip 20180416.export.CSV.zip

cp "file:///databricks/driver/20190517.export.CSV" "dbfs:///datasets/ScaDaMaLe/GDELT/EventV1/20190517.export.CSV"

res34: Boolean = true

cp "file:///databricks/driver/20190523.export.CSV" "dbfs:///datasets/ScaDaMaLe/GDELT/EventV1/20190523.export.CSV"

cp "file:///databricks/driver/20180416.export.CSV" "dbfs:///datasets/ScaDaMaLe/GDELT/EventV1/20180416.export.CSV"

We have now downloaded and ingested the data in our distributed file store. It is time for some structured data processing using Datasets in Spark!

GDELT SparkSQL Datasets

Let us turn these ingested CSV files into Spark Datasets next.

val gdeltEventV1DS: Dataset[EventV1] = spark.read.gdeltEventV1("dbfs:///datasets/ScaDaMaLe/GDELT/EventV1/20180416.export.CSV")

gdeltEventV1DS: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.EventV1] = [eventId: int, eventDay: date ... 19 more fields]

display(gdeltEventV1DS)

Let's look a the locations field.

We want to be able to filter by a country.

val gdeltGkgDS: Dataset[GKGEventV2] = spark.read.gdeltGkgV2("dbfs:///datasets/ScaDaMaLe/GDELT/GKGV2/20190517121500.gkg.csv")

gdeltGkgDS: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.GKGEventV2] = [gkgRecordId: struct<publishDate: timestamp, translingual: boolean ... 1 more field>, publishDate: timestamp ... 27 more fields]

display(gdeltGkgDS.select($"locations"))

val USgdeltGkgDS = gdeltGkgDS.withColumn("loc",$"locations"(0))
          .filter($"loc.countryCode" contains "US").drop("loc")

USgdeltGkgDS: org.apache.spark.sql.DataFrame = [gkgRecordId: struct<publishDate: timestamp, translingual: boolean ... 1 more field>, publishDate: timestamp ... 27 more fields]

val IEgdeltGkgDS = gdeltGkgDS.withColumn("loc",$"locations"(0))
          .filter($"loc.countryCode" contains "IE").drop("loc")

IEgdeltGkgDS: org.apache.spark.sql.DataFrame = [gkgRecordId: struct<publishDate: timestamp, translingual: boolean ... 1 more field>, publishDate: timestamp ... 27 more fields]

IEgdeltGkgDS.count

res17: Long = 0

USgdeltGkgDS.count

res18: Long = 549

display(USgdeltGkgDS)

GDELT Reference data

Here are various code-books used in the GDELT project. They are nicely available for you through the spark-gdelt library we have already loaded.

val countryCodes: Dataset[CountryCode] = spark.loadCountryCodes
val gcam: Dataset[GcamCode] = spark.loadGcams
val cameoEvent: Dataset[CameoCode] = spark.loadCameoEventCodes
val cameoType: Dataset[CameoCode] = spark.loadCameoTypeCodes
val cameoGroup: Dataset[CameoCode] = spark.loadCameoGroupCodes
val cameoEthnic: Dataset[CameoCode] = spark.loadCameoEthnicCodes
val cameoReligion: Dataset[CameoCode] = spark.loadCameoReligionCodes
val cameoCountry: Dataset[CameoCode] = spark.loadCameoCountryCodes

countryCodes: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.CountryCode] = [iso: string, iso3: string ... 3 more fields]
gcam: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.GcamCode] = [gcamCode: string, dictionaryId: string ... 6 more fields]
cameoEvent: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.CameoCode] = [cameoCode: string, cameoValue: string]
cameoType: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.CameoCode] = [cameoCode: string, cameoValue: string]
cameoGroup: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.CameoCode] = [cameoCode: string, cameoValue: string]
cameoEthnic: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.CameoCode] = [cameoCode: string, cameoValue: string]
cameoReligion: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.CameoCode] = [cameoCode: string, cameoValue: string]
cameoCountry: org.apache.spark.sql.Dataset[com.aamend.spark.gdelt.CameoCode] = [cameoCode: string, cameoValue: string]

display(countryCodes)

iso	iso3	isoNumeric	fips	country
AD	AND	020	AN	andorra
AE	ARE	784	AE	united arab emirates
AF	AFG	004	AF	afghanistan
AG	ATG	028	AC	antigua and barbuda
AI	AIA	660	AV	anguilla
AL	ALB	008	AL	albania
AM	ARM	051	AM	armenia
AO	AGO	024	AO	angola
AQ	ATA	010	AY	antarctica
AR	ARG	032	AR	argentina
AS	ASM	016	AQ	american samoa
AT	AUT	040	AU	austria
AU	AUS	036	AS	australia
AW	ABW	533	AA	aruba
AX	ALA	248		aland islands
AZ	AZE	031	AJ	azerbaijan
BA	BIH	070	BK	bosnia and herzegovina
BB	BRB	052	BB	barbados
BD	BGD	050	BG	bangladesh
BE	BEL	056	BE	belgium
BF	BFA	854	UV	burkina faso
BG	BGR	100	BU	bulgaria
BH	BHR	048	BA	bahrain
BI	BDI	108	BY	burundi
BJ	BEN	204	BN	benin
BL	BLM	652	TB	saint barthelemy
BM	BMU	060	BD	bermuda
BN	BRN	096	BX	brunei
BO	BOL	068	BL	bolivia
BQ	BES	535		bonaire, saint eustatius and saba
BR	BRA	076	BR	brazil
BS	BHS	044	BF	bahamas
BT	BTN	064	BT	bhutan
BV	BVT	074	BV	bouvet island
BW	BWA	072	BC	botswana
BY	BLR	112	BO	belarus
BZ	BLZ	084	BH	belize
CA	CAN	124	CA	canada
CC	CCK	166	CK	cocos islands
CD	COD	180	CG	democratic republic of the congo
CF	CAF	140	CT	central african republic
CG	COG	178	CF	republic of the congo
CH	CHE	756	SZ	switzerland
CI	CIV	384	IV	ivory coast
CK	COK	184	CW	cook islands
CL	CHL	152	CI	chile
CM	CMR	120	CM	cameroon
CN	CHN	156	CH	china
CO	COL	170	CO	colombia
CR	CRI	188	CS	costa rica
CU	CUB	192	CU	cuba
CV	CPV	132	CV	cape verde
CW	CUW	531	UC	curacao
CX	CXR	162	KT	christmas island
CY	CYP	196	CY	cyprus
CZ	CZE	203	EZ	czechia
DE	DEU	276	GM	germany
DJ	DJI	262	DJ	djibouti
DK	DNK	208	DA	denmark
DM	DMA	212	DO	dominica
DO	DOM	214	DR	dominican republic
DZ	DZA	012	AG	algeria
EC	ECU	218	EC	ecuador
EE	EST	233	EN	estonia
EG	EGY	818	EG	egypt
EH	ESH	732	WI	western sahara
ER	ERI	232	ER	eritrea
ES	ESP	724	SP	spain
ET	ETH	231	ET	ethiopia
FI	FIN	246	FI	finland
FJ	FJI	242	FJ	fiji
FK	FLK	238	FK	falkland islands
FM	FSM	583	FM	micronesia
FO	FRO	234	FO	faroe islands
FR	FRA	250	FR	france
GA	GAB	266	GB	gabon
GB	GBR	826	UK	united kingdom
GD	GRD	308	GJ	grenada
GE	GEO	268	GG	georgia
GF	GUF	254	FG	french guiana
GG	GGY	831	GK	guernsey
GH	GHA	288	GH	ghana
GI	GIB	292	GI	gibraltar
GL	GRL	304	GL	greenland
GM	GMB	270	GA	gambia
GN	GIN	324	GV	guinea
GP	GLP	312	GP	guadeloupe
GQ	GNQ	226	EK	equatorial guinea
GR	GRC	300	GR	greece
GS	SGS	239	SX	south georgia and the south sandwich islands
GT	GTM	320	GT	guatemala
GU	GUM	316	GQ	guam
GW	GNB	624	PU	guinea-bissau
GY	GUY	328	GY	guyana
HK	HKG	344	HK	hong kong
HM	HMD	334	HM	heard island and mcdonald islands
HN	HND	340	HO	honduras
HR	HRV	191	HR	croatia
HT	HTI	332	HA	haiti
HU	HUN	348	HU	hungary
ID	IDN	360	ID	indonesia
IE	IRL	372	EI	ireland
IL	ISR	376	IS	israel
IM	IMN	833	IM	isle of man
IN	IND	356	IN	india
IO	IOT	086	IO	british indian ocean territory
IQ	IRQ	368	IZ	iraq
IR	IRN	364	IR	iran
IS	ISL	352	IC	iceland
IT	ITA	380	IT	italy
JE	JEY	832	JE	jersey
JM	JAM	388	JM	jamaica
JO	JOR	400	JO	jordan
JP	JPN	392	JA	japan
KE	KEN	404	KE	kenya
KG	KGZ	417	KG	kyrgyzstan
KH	KHM	116	CB	cambodia
KI	KIR	296	KR	kiribati
KM	COM	174	CN	comoros
KN	KNA	659	SC	saint kitts and nevis
KP	PRK	408	KN	north korea
KR	KOR	410	KS	south korea
XK	XKX	0	KV	kosovo
KW	KWT	414	KU	kuwait
KY	CYM	136	CJ	cayman islands
KZ	KAZ	398	KZ	kazakhstan
LA	LAO	418	LA	laos
LB	LBN	422	LE	lebanon
LC	LCA	662	ST	saint lucia
LI	LIE	438	LS	liechtenstein
LK	LKA	144	CE	sri lanka
LR	LBR	430	LI	liberia
LS	LSO	426	LT	lesotho
LT	LTU	440	LH	lithuania
LU	LUX	442	LU	luxembourg
LV	LVA	428	LG	latvia
LY	LBY	434	LY	libya
MA	MAR	504	MO	morocco
MC	MCO	492	MN	monaco
MD	MDA	498	MD	moldova
ME	MNE	499	MJ	montenegro
MF	MAF	663	RN	saint martin
MG	MDG	450	MA	madagascar
MH	MHL	584	RM	marshall islands
MK	MKD	807	MK	macedonia
ML	MLI	466	ML	mali
MM	MMR	104	BM	myanmar
MN	MNG	496	MG	mongolia
MO	MAC	446	MC	macao
MP	MNP	580	CQ	northern mariana islands
MQ	MTQ	474	MB	martinique
MR	MRT	478	MR	mauritania
MS	MSR	500	MH	montserrat
MT	MLT	470	MT	malta
MU	MUS	480	MP	mauritius
MV	MDV	462	MV	maldives
MW	MWI	454	MI	malawi
MX	MEX	484	MX	mexico
MY	MYS	458	MY	malaysia
MZ	MOZ	508	MZ	mozambique
NA	NAM	516	WA	namibia
NC	NCL	540	NC	new caledonia
NE	NER	562	NG	niger
NF	NFK	574	NF	norfolk island
NG	NGA	566	NI	nigeria
NI	NIC	558	NU	nicaragua
NL	NLD	528	NL	netherlands
NO	NOR	578	NO	norway
NP	NPL	524	NP	nepal
NR	NRU	520	NR	nauru
NU	NIU	570	NE	niue
NZ	NZL	554	NZ	new zealand
OM	OMN	512	MU	oman
PA	PAN	591	PM	panama
PE	PER	604	PE	peru
PF	PYF	258	FP	french polynesia
PG	PNG	598	PP	papua new guinea
PH	PHL	608	RP	philippines
PK	PAK	586	PK	pakistan
PL	POL	616	PL	poland
PM	SPM	666	SB	saint pierre and miquelon
PN	PCN	612	PC	pitcairn
PR	PRI	630	RQ	puerto rico
PS	PSE	275	WE	palestinian territory
PT	PRT	620	PO	portugal
PW	PLW	585	PS	palau
PY	PRY	600	PA	paraguay
QA	QAT	634	QA	qatar
RE	REU	638	RE	reunion
RO	ROU	642	RO	romania
RS	SRB	688	RI	serbia
RU	RUS	643	RS	russia
RW	RWA	646	RW	rwanda
SA	SAU	682	SA	saudi arabia
SB	SLB	090	BP	solomon islands
SC	SYC	690	SE	seychelles
SD	SDN	729	SU	sudan
SS	SSD	728	OD	south sudan
SE	SWE	752	SW	sweden
SG	SGP	702	SN	singapore
SH	SHN	654	SH	saint helena
SI	SVN	705	SI	slovenia
SJ	SJM	744	SV	svalbard and jan mayen
SK	SVK	703	LO	slovakia
SL	SLE	694	SL	sierra leone
SM	SMR	674	SM	san marino
SN	SEN	686	SG	senegal
SO	SOM	706	SO	somalia
SR	SUR	740	NS	suriname
ST	STP	678	TP	sao tome and principe
SV	SLV	222	ES	el salvador
SX	SXM	534	NN	sint maarten
SY	SYR	760	SY	syria
SZ	SWZ	748	WZ	swaziland
TC	TCA	796	TK	turks and caicos islands
TD	TCD	148	CD	chad
TF	ATF	260	FS	french southern territories
TG	TGO	768	TO	togo
TH	THA	764	TH	thailand
TJ	TJK	762	TI	tajikistan
TK	TKL	772	TL	tokelau
TL	TLS	626	TT	east timor
TM	TKM	795	TX	turkmenistan
TN	TUN	788	TS	tunisia
TO	TON	776	TN	tonga
TR	TUR	792	TU	turkey
TT	TTO	780	TD	trinidad and tobago
TV	TUV	798	TV	tuvalu
TW	TWN	158	TW	taiwan
TZ	TZA	834	TZ	tanzania
UA	UKR	804	UP	ukraine
UG	UGA	800	UG	uganda
UM	UMI	581		united states minor outlying islands
US	USA	840	US	united states
UY	URY	858	UY	uruguay
UZ	UZB	860	UZ	uzbekistan
VA	VAT	336	VT	vatican
VC	VCT	670	VC	saint vincent and the grenadines
VE	VEN	862	VE	venezuela
VG	VGB	092	VI	british virgin islands
VI	VIR	850	VQ	u.s. virgin islands
VN	VNM	704	VM	vietnam
VU	VUT	548	NH	vanuatu
WF	WLF	876	WF	wallis and futuna
WS	WSM	882	WS	samoa
YE	YEM	887	YM	yemen
YT	MYT	175	MF	mayotte
ZA	ZAF	710	SF	south africa
ZM	ZMB	894	ZA	zambia
ZW	ZWE	716	ZI	zimbabwe
CS	SCG	891	YI	serbia and montenegro
AN	ANT	530	NT	netherlands antilles

display(cameoEvent)

cameoCode	cameoValue
01	make public statement
010	make statement, not specified below
011	decline comment
012	make pessimistic comment
013	make optimistic comment
014	consider policy option
015	acknowledge or claim responsibility
016	deny responsibility
017	engage in symbolic act
018	make empathetic comment
019	express accord
02	appeal
020	appeal, not specified below
021	appeal for material cooperation, not specified below
0211	appeal for economic cooperation
0212	appeal for military cooperation
0213	appeal for judicial cooperation
0214	appeal for intelligence
022	appeal for diplomatic cooperation, such as policy support
023	appeal for aid, not specified below
0231	appeal for economic aid
0232	appeal for military aid
0233	appeal for humanitarian aid
0234	appeal for military protection or peacekeeping
024	appeal for political reform, not specified below
0241	appeal for change in leadership
0242	appeal for policy change
0243	appeal for rights
0244	appeal for change in institutions, regime
025	appeal to yield
0251	appeal for easing of administrative sanctions
0252	appeal for easing of popular dissent
0253	appeal for release of persons or property
0254	appeal for easing of economic sanctions, boycott, or embargo
0255	appeal for target to allow international involvement (non-mediation)
0256	appeal for de-escalation of military engagement
026	appeal to others to meet or negotiate
027	appeal to others to settle dispute
028	appeal to others to engage in or accept mediation
03	express intent to cooperate
030	express intent to cooperate, not specified below
031	express intent to engage in material cooperation, not specified below
0311	express intent to cooperate economically
0312	express intent to cooperate militarily
0313	express intent to cooperate on judicial matters
0314	express intent to cooperate on intelligence
032	express intent to provide diplomatic cooperation such as policy support
033	express intent to provide matyerial aid, not specified below
0331	express intent to provide economic aid
0332	express intent to provide military aid
0333	express intent to provide humanitarian aid
0334	express intent to provide military protection or peacekeeping
034	express intent to institute political reform, not specified below
0341	express intent to change leadership
0342	express intent to change policy
0343	express intent to provide rights
0344	express intent to change institutions, regime
035	express intent to yield, not specified below
0351	express intent to ease administrative sanctions
0352	express intent to ease popular dissent
0353	express intent to release persons or property
0354	express intent to ease economic sanctions, boycott, or embargo
0355	express intent allow international involvement (not mediation)
0356	express intent to de-escalate military engagement
036	express intent to meet or negotiate
037	express intent to settle dispute
038	express intent to accept mediation
039	express intent to mediate
04	consult
040	consult, not specified below
041	discuss by telephone
042	make a visit
043	host a visit
044	meet at a ã’hirdã“location
045	mediate
046	engage in negotiation
05	engage in diplomatic cooperation
050	engage in diplomatic cooperation, not specified below
051	praise or endorse
052	defend verbally
053	rally support on behalf of
054	grant diplomatic recognition
055	apologize
056	forgive
057	sign formal agreement
06	engage in material cooperation
060	engage in material cooperation, not specified below
061	cooperate economically
062	cooperate militarily
063	engage in judicial cooperation
064	share intelligence or information
07	provide aid
070	provide aid, not specified below
071	provide economic aid
072	provide military aid
073	provide humanitarian aid
074	provide military protection or peacekeeping
075	grant asylum
08	yield
080	yield, not specified below
081	ease administrative sanctions, not specified below
0811	ease restrictions on political freedoms
0812	ease ban on political parties or politicians
0813	ease curfew
0814	ease state of emergency or martial law
082	ease political dissent
083	accede to requests or demands for political reform not specified below
0831	accede to demands for change in leadership
0832	accede to demands for change in policy
0833	accede to demands for rights
0834	accede to demands for change in institutions, regime
084	return, release, not specified below
0841	return, release person(s)
0842	return, release property
085	ease economic sanctions, boycott, embargo
086	allow international involvement not specified below
0861	receive deployment of peacekeepers
0862	receive inspectors
0863	allow delivery of humanitarian aid
087	de-escalate military engagement
0871	declare truce, ceasefire
0872	ease military blockade
0873	demobilize armed forces
0874	retreat or surrender militarily
09	investigate
090	investigate, not specified below
091	investigate crime, corruption
092	investigate human rights abuses
093	investigate military action
094	investigate war crimes
10	demand
100	demand, not specified below
101	demand information, investigation
1011	demand economic cooperation
1012	demand military cooperation
1013	demand judicial cooperation
1014	demand intelligence cooperation
102	demand policy support
103	demand aid, protection, or peacekeeping
1031	demand economic aid
1032	demand military aid
1033	demand humanitarian aid
1034	demand military protection or peacekeeping
104	demand political reform, not specified below
1041	demand change in leadership
1042	demand policy change
1043	demand rights
1044	demand change in institutions, regime
105	demand mediation
1051	demand easing of administrative sanctions
1052	demand easing of political dissent
1053	demand release of persons or property
1054	demand easing of economic sanctions, boycott, or embargo
1055	demand that target allows international involvement (non-mediation)
1056	demand de-escalation of military engagement106:[-5.0] demand withdrawal
107	demand ceasefire
108	demand meeting, negotiation
11	disapprove
110	disapprove, not specified below
111	criticize or denounce
112	accuse, not specified below
1121	accuse of crime, corruption
1122	accuse of human rights abuses
1123	accuse of aggression
1124	accuse of war crimes
1125	accuse of espionage, treason
113	rally opposition against
114	complain officially
115	bring lawsuit against
116	find guilty or liable (legally)
12	reject
120	reject, not specified below
121	reject material cooperation
1211	reject economic cooperation
1212	reject military cooperation
122	reject request or demand for material aid, not specified below
1221	reject request for economic aid
1222	reject request for military aid
1223	reject request for humanitarian aid
1224	reject request for military protection or peacekeeping
123	reject request or demand for political reform, not specified below
1231	reject request for change in leadership
1232	reject request for policy change
1233	reject request for rights
1234	reject request for change in institutions, regime
124	refuse to yield, not specified below
1241	refuse to ease administrative sanctions
1242	refuse to ease popular dissent
1243	refuse to release persons or property
1244	refuse to ease economic sanctions, boycott, or embargo
1245	refuse to allow international involvement (non mediation)
1246	refuse to de-escalate military engagement
125	reject proposal to meet, discuss, or negotiate
126	reject mediation
127	reject plan, agreement to settle dispute
128	defy norms, law
129	veto
13	threaten
130	threaten, not specified below
131	threaten non-force, not specified below
1311	threaten to reduce or stop aid
1312	threaten to boycott, embargo, or sanction
1313	threaten to reduce or break relations
132	threaten with administrative sanctions, not specified below
1321	threaten to impose restrictions on political freedoms
1322	threaten to ban political parties or politicians
1323	threaten to impose curfew
1324	threaten to impose state of emergency or martial law
133	threaten political dissent, protest
134	threaten to halt negotiations
135	threaten to halt mediation
136	threaten to halt international involvement (non-mediation)
137	threaten with violent repression
138	threaten to use military force, not specified below
1381	threaten blockade
1382	threaten occupation
1383	threaten unconventional violence
1384	threaten conventional attack
1385	threaten attack with wmd
139	give ultimatum
14	protest
140	engage in political dissent, not specified below
141	demonstrate or rally
1411	demonstrate for leadership change
1412	demonstrate for policy change
1413	demonstrate for rights
1414	demonstrate for change in institutions, regime
142	conduct hunger strike, not specified below
1421	conduct hunger strike for leadership change
1422	conduct hunger strike for policy change
1423	conduct hunger strike for rights
1424	conduct hunger strike for change in institutions, regime
143	conduct strike or boycott, not specified below
1431	conduct strike or boycott for leadership change
1432	conduct strike or boycott for policy change
1433	conduct strike or boycott for rights
1434	conduct strike or boycott for change in institutions, regime
144	obstruct passage, block
1441	obstruct passage to demand leadership change
1442	obstruct passage to demand policy change
1443	obstruct passage to demand rights
1444	obstruct passage to demand change in institutions, regime
145	protest violently, riot
1451	engage in violent protest for leadership change
1452	engage in violent protest for policy change
1453	engage in violent protest for rights
1454	engage in violent protest for change in institutions, regime
15	exhibit force posture
150	demonstrate military or police power, not specified below
151	increase police alert status
152	increase military alert status
153	mobilize or increase police power
154	mobilize or increase armed forces
16	reduce relations
160	reduce relations, not specified below
161	reduce or break diplomatic relations
162	reduce or stop aid, not specified below
1621	reduce or stop economic assistance
1622	reduce or stop military assistance
1623	reduce or stop humanitarian assistance
163	impose embargo, boycott, or sanctions
164	halt negotiations
165	halt mediation
166	expel or withdraw, not specified below
1661	expel or withdraw peacekeepers
1662	expel or withdraw inspectors, observers
1663	expel or withdraw aid agencies
17	coerce
170	coerce, not specified below
171	seize or damage property, not specified below
1711	confiscate property
1712	destroy property
172	impose administrative sanctions, not specified below
1721	impose restrictions on political freedoms
1722	ban political parties or politicians
1723	impose curfew
1724	impose state of emergency or martial law
173	arrest, detain, or charge with legal action
174	expel or deport individuals
175	use tactics of violent repression
18	assault
180	use unconventional violence, not specified below
181	abduct, hijack, or take hostage
182	physically assault, not specified below
1821	sexually assault
1822	torture
1823	kill by physical assault
183	conduct suicide, car, or other non-military bombing, not spec below
1831	carry out suicide bombing
1832	carry out car bombing
1833	carry out roadside bombing
184	use as human shield
185	attempt to assassinate
186	assassinate
19	fight
190	use conventional military force, not specified below
191	impose blockade, restrict movement
192	occupy territory
193	fight with small arms and light weapons
194	fight with artillery and tanks
195	employ aerial weapons
196	violate ceasefire
20	use unconventional mass violence
200	use unconventional mass violence, not specified below
201	engage in mass expulsion
202	engage in mass killings
203	engage in ethnic cleansing
204	use weapons of mass destruction, not specified below
2041	use chemical, biological, or radiologicalweapons
2042	detonate nuclear weapons

ls dbfs:/datasets/ScaDaMaLe/GDELT/

path	name	size
dbfs:/datasets/ScaDaMaLe/GDELT/20180416121500.gkg.csv	20180416121500.gkg.csv	3.4277858e7
dbfs:/datasets/ScaDaMaLe/GDELT/20190517121500.gkg.csv	20190517121500.gkg.csv	2.5728991e7
dbfs:/datasets/ScaDaMaLe/GDELT/20190523121500.gkg.csv	20190523121500.gkg.csv	2.9695688e7

ScaDaMaLe Course site and book

Markov Model for Trend Calculus

Johannes Graner (LinkedIn), Albert Nilsson (LinkedIn) and Raazesh Sainudiin (LinkedIn)

2020, Uppsala, Sweden

This project was supported by Combient Mix AB through summer internships at:

Combient Competence Centre for Data Engineering Sciences, Department of Mathematics, Uppsala University, Uppsala, Sweden

We use the dataset generated in the last notebook to build a simple, proof of concept Markov model for predicting trends.

This is merely to verify using a simple model if there is indeed any predictive value in the trends and their reversals that many real-worl traders bet on every instant in the market.

Resources

This builds on the following library and its antecedents therein:

https://github.com/lamastex/spark-trend-calculus

This work was inspired by:

Antoine Aamennd's texata-2017
Andrew Morgan's Trend Calculus Library

"./000a_finance_utils"

import java.sql.Timestamp
import io.delta.tables._
import org.apache.spark.sql._
import org.apache.spark.sql.functions._
import org.apache.spark.sql.streaming.{GroupState, GroupStateTimeout, OutputMode, Trigger}
import org.apache.spark.sql.types._
import org.apache.spark.sql.expressions.{Window, WindowSpec}
import org.lamastex.spark.trendcalculus._
import scala.util.Random

import java.sql.Timestamp
import io.delta.tables._
import org.apache.spark.sql._
import org.apache.spark.sql.functions._
import org.apache.spark.sql.streaming.{GroupState, GroupStateTimeout, OutputMode, Trigger}
import org.apache.spark.sql.types._
import org.apache.spark.sql.expressions.{Window, WindowSpec}
import org.lamastex.spark.trendcalculus._
import scala.util.Random

defined object TrendUtils

Reading the joined dataset from the last notebook.

We train the model using both oil and gold data and predict trends in oil data. We show that this yields better results than just training on the oil data.

val rootPath = TrendUtils.getStreamableTrendCalculusPath
val maxRevPath = rootPath + "maxRev"
val maxRevDS = spark.read.format("delta").load(maxRevPath).as[FlatReversal]

We want to predict what the trend of the next data point will be given the trend reversals we have observed.

For this, we use an m-th order Markov model. We look at the reversal state of the last m points and use this to predict the trends in the next n points. k is the maximum order of reversal that is considered when training the model.

trainingRatio is the ratio of the data used for training the model, the rest is used for testing.

val modelPath = rootPath + "estimators/"
val maxRevDSWithLagCountPath = modelPath + "maxRevDSWithLag"

val numPartitions = 10
val partialModelPaths = (1 to numPartitions).map( i => modelPath + s"partialModel${i}" )
val fullModelPath = modelPath + "fullModel"

val m = 10
val n = 1
val k = 18
val trainingRatio = 0.7
type FinalModel = Map[Seq[Int], Map[Seq[Int], Double]]

def truncRev(k: Int)(rev: Int): Int = {
  if (math.abs(rev) > k) k*rev.signum else rev
}
val truncRevUDF = udf{ rev: Int => rev.signum }
def truncRevsUDF(k: Int) = udf{ revs: Seq[Int] => revs.map(truncRev(k)) }

def lagColumn(df: DataFrame, orderColumnName: String, lagKeyName: String, lagValueName: String, m: Int, n: Int): DataFrame = {
  val windowSpec = Window.partitionBy("ticker").orderBy(orderColumnName)
  val laggedKeyColNames = (1 to m).map( i => s"lagKey$i" ).toSeq
  val laggedValueColNames = (1 to n).map( i => s"lagValue$i" ).toSeq
  val dfWithLaggedKeyColumns = (n+1 to m+n)
    .foldLeft(df)( (df: DataFrame, i: Int) => df.withColumn(laggedKeyColNames(i-n-1), lag(lagKeyName, i-1, Int.MaxValue).over(windowSpec)) )
  val dfWithLaggedKeyValueColumns = (1 to n)
    .foldLeft(dfWithLaggedKeyColumns)( (df: DataFrame, i: Int) => df.withColumn(laggedValueColNames(i-1), lag(lagValueName, i-1, Int.MaxValue).over(windowSpec)) )
  
  dfWithLaggedKeyValueColumns
    .withColumn("lagKey", array(laggedKeyColNames.reverse.take(m).map(col(_)):_*))
    .withColumn("lagValue", array(laggedValueColNames.reverse.takeRight(n).map(col(_)):_*))
    .withColumn("lagKeyFirst", col(laggedKeyColNames.last))
    .filter($"lagKeyFirst" =!= Int.MaxValue)
    .drop("lagKeyFirst")
    .drop(laggedKeyColNames:_*)
    .drop(laggedValueColNames:_*)
}

truncRev: (k: Int)(rev: Int)Int
truncRevUDF: org.apache.spark.sql.expressions.UserDefinedFunction = SparkUserDefinedFunction($Lambda$9209/1126103335@6b64702c,IntegerType,List(Some(class[value[0]: int])),None,false,true)
truncRevsUDF: (k: Int)org.apache.spark.sql.expressions.UserDefinedFunction
lagColumn: (df: org.apache.spark.sql.DataFrame, orderColumnName: String, lagKeyName: String, lagValueName: String, m: Int, n: Int)org.apache.spark.sql.DataFrame

The trend at each point can be extracted from the trend reversals by taking the sum of all previous 1-st order trend reversals. This sum will always be either 0 (up trend) or -1 (down trend) and 0 is therefore mapped to 1 to get (1, -1) as (up, down).

val maxRevDSWithLag = lagColumn(
  maxRevDS
    .orderBy("x")
    .toDF
    .withColumn("truncRev", truncRevUDF($"reversal"))
    .withColumn(
      "tmpTrend",
      sum("truncRev").over(
        Window
          .partitionBy("ticker")
          .orderBy("x")
          .rowsBetween(Window.unboundedPreceding, Window.currentRow)
      )
    )
    .withColumn("trend", when($"tmpTrend" === 0, 1).otherwise(-1))
    .drop("truncRev", "tmpTrend"),
  "x", 
  "reversal",
  "trend",
  m, 
  n
)

maxRevDSWithLag: org.apache.spark.sql.DataFrame = [ticker: string, x: timestamp ... 5 more fields]

We now want to predict lagValue from lagKey.

maxRevDSWithLag.show(20, false)

+------+-------------------+------+--------+-----+--------------------------------+--------+
|ticker|x                  |y     |reversal|trend|lagKey                          |lagValue|
+------+-------------------+------+--------+-----+--------------------------------+--------+
|XAUUSD|2009-03-15 18:09:00|925.4 |4       |1    |[-6, 0, 0, 1, -1, 0, 0, 0, 0, 0]|[1]     |
|XAUUSD|2009-03-15 18:10:00|925.75|-2      |-1   |[0, 0, 1, -1, 0, 0, 0, 0, 0, 4] |[-1]    |
|XAUUSD|2009-03-15 18:11:00|925.7 |0       |-1   |[0, 1, -1, 0, 0, 0, 0, 0, 4, -2]|[-1]    |
|XAUUSD|2009-03-15 18:12:00|925.65|1       |1    |[1, -1, 0, 0, 0, 0, 0, 4, -2, 0]|[1]     |
|XAUUSD|2009-03-15 18:13:00|925.65|0       |1    |[-1, 0, 0, 0, 0, 0, 4, -2, 0, 1]|[1]     |
|XAUUSD|2009-03-15 18:14:00|925.75|0       |1    |[0, 0, 0, 0, 0, 4, -2, 0, 1, 0] |[1]     |
|XAUUSD|2009-03-15 18:15:00|925.75|-1      |-1   |[0, 0, 0, 0, 4, -2, 0, 1, 0, 0] |[-1]    |
|XAUUSD|2009-03-15 18:16:00|925.65|0       |-1   |[0, 0, 0, 4, -2, 0, 1, 0, 0, -1]|[-1]    |
|XAUUSD|2009-03-15 18:17:00|925.6 |2       |1    |[0, 0, 4, -2, 0, 1, 0, 0, -1, 0]|[1]     |
|XAUUSD|2009-03-15 18:18:00|925.85|0       |1    |[0, 4, -2, 0, 1, 0, 0, -1, 0, 2]|[1]     |
|XAUUSD|2009-03-15 18:19:00|926.05|0       |1    |[4, -2, 0, 1, 0, 0, -1, 0, 2, 0]|[1]     |
|XAUUSD|2009-03-15 18:20:00|925.95|0       |1    |[-2, 0, 1, 0, 0, -1, 0, 2, 0, 0]|[1]     |
|XAUUSD|2009-03-15 18:21:00|926.55|0       |1    |[0, 1, 0, 0, -1, 0, 2, 0, 0, 0] |[1]     |
|XAUUSD|2009-03-15 18:22:00|926.95|0       |1    |[1, 0, 0, -1, 0, 2, 0, 0, 0, 0] |[1]     |
|XAUUSD|2009-03-15 18:23:00|927.25|0       |1    |[0, 0, -1, 0, 2, 0, 0, 0, 0, 0] |[1]     |
|XAUUSD|2009-03-15 18:24:00|927.45|-4      |-1   |[0, -1, 0, 2, 0, 0, 0, 0, 0, 0] |[-1]    |
|XAUUSD|2009-03-15 18:25:00|927.2 |0       |-1   |[-1, 0, 2, 0, 0, 0, 0, 0, 0, -4]|[-1]    |
|XAUUSD|2009-03-15 18:26:00|926.85|0       |-1   |[0, 2, 0, 0, 0, 0, 0, 0, -4, 0] |[-1]    |
|XAUUSD|2009-03-15 18:27:00|926.7 |0       |-1   |[2, 0, 0, 0, 0, 0, 0, -4, 0, 0] |[-1]    |
|XAUUSD|2009-03-15 18:28:00|926.5 |0       |-1   |[0, 0, 0, 0, 0, 0, -4, 0, 0, 0] |[-1]    |
+------+-------------------+------+--------+-----+--------------------------------+--------+
only showing top 20 rows

Cleaning up last run and writing model training input to delta tables.

dbutils.fs.rm(maxRevDSWithLagCountPath, recurse=true)

maxRevDSWithLag
  .withColumn("count", lit(1L))
  .write
  .format("delta")
  .mode("overwrite")
  .save(maxRevDSWithLagCountPath)

val divUDF = udf{ (a: Long, b: Long) => a.toDouble/b }
val maxRevDSWithLagCount = spark.read.format("delta").load(maxRevDSWithLagCountPath)
val numberOfRows = maxRevDSWithLagCount.count

divUDF: org.apache.spark.sql.expressions.UserDefinedFunction = SparkUserDefinedFunction($Lambda$9266/71459450@6a0e8651,DoubleType,List(Some(class[value[0]: bigint]), Some(class[value[0]: bigint])),None,false,true)
maxRevDSWithLagCount: org.apache.spark.sql.DataFrame = [ticker: string, x: timestamp ... 6 more fields]
numberOfRows: Long = 6845798

The data is split into training and testing data. This is not done randomly as there is a dependence on previous data points. We don't want to train on data that is dependent on the testing data and therefore the training data consists of the first (for example) 70% of the data and the last 30% is saved for testing. This also reflects how the model would be used since we can only train on data points that have already been observed.

val tickers = maxRevDSWithLagCount.select("ticker").distinct.as[String].collect.toSeq
val tickerDFs = tickers.map( ticker => maxRevDSWithLagCount.filter($"ticker" === ticker))
val trainingDF = tickerDFs.map( df => df.limit((df.count*trainingRatio).toInt) ).reduce( _.union(_) ).orderBy("x")
val trainingRows = trainingDF.count

val testingDF = maxRevDSWithLagCount.except(trainingDF)

tickers: Seq[String] = WrappedArray(XAUUSD, BCOUSD)
tickerDFs: Seq[org.apache.spark.sql.Dataset[org.apache.spark.sql.Row]] = ArrayBuffer([ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields])
trainingDF: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [ticker: string, x: timestamp ... 6 more fields]
trainingRows: Long = 4792058
testingDF: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [ticker: string, x: timestamp ... 6 more fields]

Create numTrainingSets training set of increasing size to get snapshots of how a partially trained model looks like. The sizes are spaced logarithmically since the improvement in the model is fastest in the beginning.

val rowsInPartitions = (1 to numPartitions).map{ i: Int => (math.exp(math.log(trainingRows)*i/numPartitions)).toInt }//.scanLeft(0.0)(_-_)

rowsInPartitions: scala.collection.immutable.IndexedSeq[Int] = Vector(4, 21, 100, 470, 2189, 10193, 47464, 221012, 1029129, 4792058)

Model is trained by counting how many times each (lagKey, lagValue) pair is observed and dividing by how many times lagKey is observed to get an estimation of the transition probabilities.

val keyValueCountPartialDFs = rowsInPartitions.map(
  trainingDF
    .limit(_)
    .withColumn("keyValueObs", sum("count").over(Window.partitionBy($"lagKey", $"lagValue")))
    .withColumn("totalKeyObs", sum("count").over(Window.partitionBy($"lagKey")))
    .drop("count")
)

keyValueCountPartialDFs: scala.collection.immutable.IndexedSeq[org.apache.spark.sql.DataFrame] = Vector([ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields], [ticker: string, x: timestamp ... 7 more fields])

keyValueCountPartialDFs.last.orderBy($"keyValueObs".desc).show(20,false)

+------+-------------------+------+--------+-----+------------------------------+--------+-----------+-----------+
|ticker|x                  |y     |reversal|trend|lagKey                        |lagValue|keyValueObs|totalKeyObs|
+------+-------------------+------+--------+-----+------------------------------+--------+-----------+-----------+
|XAUUSD|2009-03-15 19:41:00|926.55|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-17 05:27:00|921.73|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 04:51:00|928.75|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 04:52:00|928.7 |0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 04:53:00|928.68|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 06:24:00|925.1 |-5      |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 09:19:00|917.73|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 09:20:00|917.83|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 09:21:00|917.0 |0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 14:47:00|922.9 |0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 14:48:00|922.88|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 14:49:00|922.93|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 14:50:00|922.83|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 22:49:00|922.28|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 22:50:00|922.25|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 22:51:00|922.13|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-16 22:52:00|922.08|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-17 05:11:00|923.8 |-1      |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-17 05:24:00|922.23|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
|XAUUSD|2009-03-17 05:25:00|922.03|0       |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]|[-1]    |53544      |106773     |
+------+-------------------+------+--------+-----+------------------------------+--------+-----------+-----------+
only showing top 20 rows

keyValueCountPartialDFs
  .map( df =>
    df
      .withColumn("probability", divUDF($"keyValueObs", $"totalKeyObs"))
      .drop("keyValueObs", "totalKeyObs")
  )
  .zip(partialModelPaths).map{ case (df: DataFrame, path: String) =>
    df.write.mode("overwrite").format("delta").save(path)  
  }

val probDFs = partialModelPaths.map(spark.read.format("delta").load(_))

probDFs: scala.collection.immutable.IndexedSeq[org.apache.spark.sql.DataFrame] = Vector([ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields], [ticker: string, x: timestamp ... 6 more fields])

probDFs.last.orderBy("probability").show(20,false)

+------+-------------------+-------+--------+-----+---------------------------------+--------+--------------------+
|ticker|x                  |y      |reversal|trend|lagKey                           |lagValue|probability         |
+------+-------------------+-------+--------+-----+---------------------------------+--------+--------------------+
|BCOUSD|2011-04-29 11:59:00|125.61 |2       |1    |[0, -4, 0, 0, 0, 1, 0, 0, 0, -1] |[1]     |0.007142857142857143|
|XAUUSD|2015-07-31 00:05:00|1084.69|-1      |-1   |[-2, 0, 0, 0, 1, -1, 0, 0, 0, 3] |[-1]    |0.013513513513513514|
|XAUUSD|2016-09-07 11:09:00|1344.18|-2      |-1   |[0, 0, 0, 0, 6, 0, 0, 0, -1, 1]  |[-1]    |0.014492753623188406|
|XAUUSD|2015-11-06 00:05:00|1108.14|-1      |-1   |[0, 4, 0, 0, -1, 0, 0, 0, 0, 1]  |[-1]    |0.014705882352941176|
|XAUUSD|2010-05-13 01:54:00|1237.83|2       |1    |[-3, 0, 0, 1, 0, 0, 0, 0, 0, -1] |[1]     |0.01639344262295082 |
|BCOUSD|2011-04-05 16:30:00|121.63 |-3      |-1   |[-2, 0, 0, 0, 0, 1, 0, -1, 0, 3] |[-1]    |0.016666666666666666|
|XAUUSD|2009-09-30 22:16:00|1006.65|1       |1    |[0, 0, 0, 0, 1, 0, 0, -1, 1, -1] |[1]     |0.016666666666666666|
|XAUUSD|2010-11-05 04:43:00|1386.98|1       |1    |[0, 0, 0, 0, 1, 0, 0, -1, 1, -1] |[1]     |0.016666666666666666|
|XAUUSD|2010-11-19 15:13:00|1351.4 |-1      |-1   |[0, 0, 0, 0, 0, 1, -1, 0, 0, 5]  |[-1]    |0.017094017094017096|
|BCOUSD|2012-10-10 14:23:00|114.27 |-1      |-1   |[0, 0, 0, 0, 0, 1, -1, 0, 0, 5]  |[-1]    |0.017094017094017096|
|XAUUSD|2015-06-28 19:18:00|1185.37|2       |1    |[-4, 0, 0, 0, 1, 0, 0, 0, 0, -1] |[1]     |0.017241379310344827|
|BCOUSD|2015-10-15 01:18:00|49.75  |2       |1    |[0, -3, 0, 1, 0, -1, 0, 0, 1, -1]|[1]     |0.017543859649122806|
|XAUUSD|2012-02-27 20:23:00|1767.83|1       |1    |[0, -5, 0, 0, 0, 1, 0, 0, 0, -1] |[1]     |0.01818181818181818 |
|BCOUSD|2015-04-27 23:58:00|63.96  |-1      |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 8]   |[-1]    |0.0196078431372549  |
|XAUUSD|2009-04-08 15:54:00|880.88 |-1      |-1   |[0, 0, 0, 0, 0, 0, 0, 0, 0, 8]   |[-1]    |0.0196078431372549  |
|BCOUSD|2015-09-11 11:06:00|47.27  |-1      |-1   |[0, 0, 0, 0, 1, -1, 0, 0, 0, 6]  |[-1]    |0.0196078431372549  |
|XAUUSD|2012-01-24 23:36:00|1666.11|1       |1    |[0, 1, 0, 0, 0, -1, 0, 1, 0, -4] |[1]     |0.02040816326530612 |
|XAUUSD|2009-12-28 23:56:00|1104.68|-1      |-1   |[0, -2, 2, 0, 0, 0, 0, -1, 0, 1] |[-1]    |0.020833333333333332|
|BCOUSD|2014-03-12 09:33:00|107.74 |-3      |-1   |[0, 0, 7, 0, 0, 0, 0, -1, 0, 1]  |[-1]    |0.020833333333333332|
|XAUUSD|2016-04-06 09:50:00|1221.57|2       |1    |[0, -1, 0, 1, -3, 0, 0, 0, 1, -1]|[1]     |0.02127659574468085 |
+------+-------------------+-------+--------+-----+---------------------------------+--------+--------------------+
only showing top 20 rows

The prediction is given by taking

\[ V \in argmax(P_K(V)) \]

where *P_K(V)* is the probability that V is the next trend when the last m points have had reversals K. If there are more than one elements in argmax, an element is chosen uniformly at random.

val aggWindow = Window.partitionBy("lagKey").orderBy('probability desc)
val testedDFs = probDFs
  .map { df =>
     val predictionDF = df
      .select("lagKey", "lagValue", "probability")
      .distinct
      .withColumn("rank", rank().over(aggWindow))
      .filter("rank == 1")
      .groupBy("lagKey")
      .agg(collect_list("lagValue"))
    
    testingDF
      .filter($"ticker" === "BCOUSD")
      .join(predictionDF, Seq("lagKey"), "left")
      .withColumnRenamed("collect_list(lagValue)", "test")
  }

warning: there was one feature warning; for details, enable `:setting -feature' or `:replay -feature'
aggWindow: org.apache.spark.sql.expressions.WindowSpec = org.apache.spark.sql.expressions.WindowSpec@2dbd5c17
testedDFs: scala.collection.immutable.IndexedSeq[org.apache.spark.sql.DataFrame] = Vector([lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields], [lagKey: array<int>, ticker: string ... 7 more fields])

We use a binary loss function that indicates if the prediction was correct or not.

getRandomUDF is used to choose an element at random in argmax(P_K(V)). safeArr is used since we might see patterns in the test data that were not present in the training data.

val getRandomUDF = udf( (arr: Seq[Seq[Int]]) => {
  val safeArr = Option(arr).getOrElse(Seq[Seq[Int]]())
  if (safeArr.isEmpty) Seq[Int]() else safeArr(Random.nextInt(safeArr.size))
} )

val lossUDF = udf{ (value: Seq[Int], pred: Seq[Int]) =>
  if (value == pred) 0 else 1
}

getRandomUDF: org.apache.spark.sql.expressions.UserDefinedFunction = SparkUserDefinedFunction($Lambda$9416/1051216045@79bf6d73,ArrayType(IntegerType,false),List(Some(class[value[0]: array<array<int>>])),None,true,true)
lossUDF: org.apache.spark.sql.expressions.UserDefinedFunction = SparkUserDefinedFunction($Lambda$9417/777777096@6e1c4ce7,IntegerType,List(Some(class[value[0]: array<int>]), Some(class[value[0]: array<int>])),None,false,true)

val lossDFs = testedDFs.map(_.withColumn("prediction", getRandomUDF($"test")).withColumn("loss", lossUDF($"lagValue", $"prediction")))

lossDFs: scala.collection.immutable.IndexedSeq[org.apache.spark.sql.DataFrame] = Vector([lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields], [lagKey: array<int>, ticker: string ... 9 more fields])

Already on line 2 we see a case where lagKey was previously not observed (indicated by null in test column).

lossDFs.last.show(20,false)

+---------------------------------+------+-------------------+-----+--------+-----+--------+-----+------+----------+----+
|lagKey                           |ticker|x                  |y    |reversal|trend|lagValue|count|test  |prediction|loss|
+---------------------------------+------+-------------------+-----+--------+-----+--------+-----+------+----------+----+
|[0, 0, 0, 0, 0, 0, -2, 0, 0, 0]  |BCOUSD|2017-10-02 02:03:00|56.56|0       |-1   |[-1]    |1    |[[-1]]|[-1]      |0   |
|[-4, 0, 1, 0, 0, 0, -1, 0, 0, 0] |BCOUSD|2017-10-03 07:07:00|56.0 |1       |1    |[1]     |1    |[[-1]]|[-1]      |1   |
|[0, 1, 0, -1, 3, -1, 0, 1, 0, 0] |BCOUSD|2017-10-03 13:23:00|55.92|-2      |-1   |[-1]    |1    |[[1]] |[1]       |1   |
|[0, 2, 0, 0, -2, 0, 0, 0, 0, 1]  |BCOUSD|2017-10-13 06:59:00|57.43|0       |1    |[1]     |1    |[[1]] |[1]       |0   |
|[0, 0, 0, 0, 1, -1, 2, 0, 0, -2] |BCOUSD|2017-10-18 07:21:00|58.21|0       |-1   |[-1]    |1    |[[-1]]|[-1]      |0   |
|[0, 0, 0, -1, 0, 0, 0, 2, 0, 0]  |BCOUSD|2017-10-25 06:08:00|58.21|0       |1    |[1]     |1    |[[1]] |[1]       |0   |
|[0, -4, 1, 0, -1, 1, 0, -1, 0, 0]|BCOUSD|2017-10-31 08:44:00|60.52|0       |-1   |[-1]    |1    |[[-1]]|[-1]      |0   |
|[0, 0, -1, 0, 1, 0, -1, 0, 1, 0] |BCOUSD|2017-11-15 12:35:00|61.96|0       |1    |[1]     |1    |[[1]] |[1]       |0   |
|[0, 0, 0, 0, 0, 0, 0, 0, -4, 0]  |BCOUSD|2017-11-15 13:28:00|62.02|0       |-1   |[-1]    |1    |[[-1]]|[-1]      |0   |
|[1, 0, -1, 0, 2, -2, 0, 0, 0, 0] |BCOUSD|2017-11-16 11:37:00|61.7 |0       |-1   |[-1]    |1    |[[-1]]|[-1]      |0   |
|[0, 0, 0, -2, 0, 0, 0, 2, 0, 0]  |BCOUSD|2017-12-08 09:10:00|63.37|0       |1    |[1]     |1    |[[1]] |[1]       |0   |
|[0, 0, 0, -1, 0, 0, 2, 0, 0, 0]  |BCOUSD|2017-12-15 06:19:00|63.45|0       |1    |[1]     |1    |[[1]] |[1]       |0   |
|[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]   |BCOUSD|2017-12-19 01:46:00|63.56|0       |1    |[1]     |1    |[[-1]]|[-1]      |1   |
|[1, 0, -1, 0, 0, 0, 0, 0, 3, 0]  |BCOUSD|2017-12-21 07:09:00|64.39|0       |1    |[1]     |1    |[[1]] |[1]       |0   |
|[-1, 0, 0, 0, 0, 0, 0, 1, 0, -1] |BCOUSD|2017-12-22 13:50:00|65.18|0       |-1   |[-1]    |1    |[[-1]]|[-1]      |0   |
|[0, 1, 0, -1, 0, 0, 0, 0, 0, 1]  |BCOUSD|2017-12-27 14:51:00|65.92|-1      |-1   |[-1]    |1    |[[1]] |[1]       |1   |
|[0, 0, 0, 0, 1, 0, 0, -2, 1, -1] |BCOUSD|2018-01-03 22:15:00|67.91|0       |-1   |[-1]    |1    |[[-1]]|[-1]      |0   |
|[0, 0, 0, -3, 0, 0, 1, 0, -1, 0] |BCOUSD|2018-01-08 10:17:00|67.72|0       |-1   |[-1]    |1    |[[-1]]|[-1]      |0   |
|[-1, 0, 1, 0, 0, 0, -1, 0, 1, 0] |BCOUSD|2018-01-23 16:24:00|70.15|0       |1    |[1]     |1    |[[1]] |[1]       |0   |
|[0, 0, 1, 0, -1, 0, 0, 2, 0, 0]  |BCOUSD|2018-01-30 07:53:00|69.02|0       |1    |[1]     |1    |[[1]] |[1]       |0   |
+---------------------------------+------+-------------------+-----+--------+-----+--------+-----+------+----------+----+
only showing top 20 rows

val testLength = testingDF.count
val oilTestDF = testingDF.filter($"ticker" === "BCOUSD")
val oilTestLength = oilTestDF.count

testLength: Long = 2053732
oilTestDF: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [ticker: string, x: timestamp ... 6 more fields]
oilTestLength: Long = 857750

Out of roughly 2 million observations, about 860k were oil price.

We find the mean loss for each training dataset of increasing size. As one can see, the loss decreases as more data is supplied.

Further, training on both oil and gold data yields a better result than just oil, suggesting that trends behave similarly in the two commodities.

val losses = lossDFs.map( _.agg(sum("loss")).select($"sum(loss)".as("totalLoss")).collect.head.getLong(0).toDouble/oilTestLength )
// Data up to 2019
// k=max, m=2 ,n=1: (0.5489615950080244, 0.4014721726541194, 0.3660973816818738, 0.36497087640146797, 0.36485163238050344)
// k=max, m=10,n=1: (0.9812730246821787, 0.8523390131056561, 0.5819573469954631, 0.3552177121357085, 0.2807503135425113)
// k=max,m=100,n=1: (1.0, 1.0, 1.0, 1.0, 1.0)
// k=5  , m=10,n=1: (0.9812730246821787, 0.8522267831239777, 0.5820597568537447, 0.3550507700379618, 0.2806352778112909)
// k=1  , m=10,n=1: (0.9812730246821787, 0.852200128503329, 0.5821242890932098, 0.3553383593660128, 0.2806549180580846)

// k=max, m=10,n=2: (0.9879380657977248, 0.9049354606556204, 0.7243136776273427, 0.5472986906951395, 0.4783823708897465)

// k=max(17), m=10,n=1, 10 training sets: (0.9977203284971564, 0.9812730246821787, 0.9455375956409875, 0.8523810993487855, 0.7183644724769999, 0.5819320952495854, 0.44607349380350214, 0.35513915114853356, 0.3029480010437388, 0.280629666312207)

// Data up to last month
// k=max(18), m=10,n=1, 10 training sets: (0.9973104051296998, 0.9843882250072865, 0.9510789857184494, 0.8574351501020111, 0.7515744680851064, 0.6360547945205479, 0.5099656076945497, 0.4249921305741766, 0.3735668901194987, 0.34609501603031184)
// Could the difference be due to Corona?

// Trained on both oil and gold. testing on oil as previously.
// k=max(18), m=10,n=1, 10 training sets: (0.9999778490236083, 0.9980728650539201, 0.9527158262897114, 0.8921317400174876, 0.7559988341591373, 0.5820915185077237, 0.46675488195861264, 0.3923101136694841, 0.3574876129408336, 0.3355837948120082)

losses: scala.collection.immutable.IndexedSeq[Double] = Vector(0.9999778490236083, 0.9980728650539201, 0.9528044301952784, 0.8921084232002332, 0.7558216263480035, 0.5819551151267852, 0.4666686097347712, 0.3920524628388225, 0.35745380355581463, 0.3355488195861265)

Visualizing the improvement of the model as the size of training data increases.

val trainingSizes = probDFs.map(_.count)
val lossesDS = sc
  .parallelize(losses.zip(trainingSizes))
  .toDF("loss", "size")
  .withColumn("training", lit("Oil and Gold"))
  .union(
    sc
      .parallelize(Seq(0.9973104051296998, 0.9843882250072865, 0.9510789857184494, 0.8574351501020111, 0.7515744680851064, 0.6360547945205479, 0.5099656076945497, 0.4249921305741766, 0.3735668901194987, 0.34609501603031184).zip(Seq(4, 18, 77, 331, 1414, 6036, 25759, 109918, 469036, 2001430)))
      .toDF("loss", "size")
      .withColumn("training", lit("Oil"))
  )
  .as[(Double,Long,String)]

trainingSizes: scala.collection.immutable.IndexedSeq[Long] = Vector(4, 21, 100, 470, 2189, 10193, 47464, 221012, 1029129, 4792058)
lossesDS: org.apache.spark.sql.Dataset[(Double, Long, String)] = [loss: double, size: bigint ... 1 more field]

display(lossesDS)

loss	size	training
0.9999778490236083	4.0	Oil and Gold
0.9980728650539201	21.0	Oil and Gold
0.9528044301952784	100.0	Oil and Gold
0.8921084232002332	470.0	Oil and Gold
0.7558216263480035	2189.0	Oil and Gold
0.5819551151267852	10193.0	Oil and Gold
0.4666686097347712	47464.0	Oil and Gold
0.3920524628388225	221012.0	Oil and Gold
0.35745380355581463	1029129.0	Oil and Gold
0.3355488195861265	4792058.0	Oil and Gold
0.9973104051296998	4.0	Oil
0.9843882250072865	18.0	Oil
0.9510789857184494	77.0	Oil
0.8574351501020111	331.0	Oil
0.7515744680851064	1414.0	Oil
0.6360547945205479	6036.0	Oil
0.5099656076945497	25759.0	Oil
0.4249921305741766	109918.0	Oil
0.3735668901194987	469036.0	Oil
0.34609501603031184	2001430.0	Oil

trendcalculusmcmodelperformance

The series using only oil data is very similar to the one with both oil and gold data. The final data point has a loss of about 0.35, meaning that the model accuracy is around 65% for predicting the the trend of the next point in the time series.

To better understand the difference between the different (partially trained) models, we want to calculate the total variation distance between them.

The first step is to collect the models and work with them locally.

val partialModels = probDFs.map{df => 
  val tmpMap = df
    .select("lagKey", "lagValue", "probability")
    .distinct
    .collect
    .map{ r => 
      (r.getAs[Seq[Int]](0), r.getAs[Seq[Int]](1), r.getDouble(2))
    }
    .groupBy(_._1) // Grouping by lagKey
    .mapValues(_.map(tup => Map(tup._2 -> tup._3)).flatten.toMap)
  
  tmpMap: FinalModel
}

If a lagKey sequence only belongs to one of the models we are comparing, the variation distance is maximal, i.e. 1. Otherwise, we compute the total variation distance between the probabilities of observing a sequence of n trends, following the sequence of trends lagKey.

def totalVarDist(m1: FinalModel, m2: FinalModel): Map[Seq[Int], Double] = {
  val allKeys = m1.keys.toSet.union(m2.keys.toSet)
  val sharedKeys = m1.keys.toSet.intersect(m2.keys.toSet)
  val totalVarDists = allKeys.toSeq.map{ key =>
    if (!sharedKeys.contains(key)) {
      1.0
    } else {
      val val1 = m1.getOrElse(key, Map())
      val val2 = m2.getOrElse(key, Map())
      val allValKeys = val1.keys.toSet.union(val2.keys.toSet)
      allValKeys.map( valKey => 0.5*math.abs(val1.getOrElse(valKey, 0.0) - val2.getOrElse(valKey, 0.0)) ).sum
    }
  }
  allKeys.zip(totalVarDists).toMap
}

totalVarDist: (m1: FinalModel, m2: FinalModel)Map[Seq[Int],Double]

Computing the variation distance for all possible pairs of partially trained models.

val totalVariationDistances = partialModels.map( m1 => partialModels.map( m2 => totalVarDist(m1,m2) ) )

totalVariationDistances: scala.collection.immutable.IndexedSeq[scala.collection.immutable.IndexedSeq[Map[Seq[Int],Double]]] = Vector(Vector(Map(WrappedArray(0, 1, -1, 0, 0, 0, 0, 0, 4, -2) -> 0.0, WrappedArray(-6, 0, 0, 1, -1, 0, 0, 0, 0, 0) -> 0.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 0, 4) -> 0.0, WrappedArray(1, -1, 0, 0, 0, 0, 0, 4, -2, 0) -> 0.0), Map(WrappedArray(-6, 0, 0, 1, -1, 0, 0, 0, 0, 0) -> 0.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, 0, -4, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 0, 4, -2) -> 0.0, WrappedArray(-1, 0, 2, 0, 0, 0, 0, 0, 0, -4) -> 1.0, WrappedArray(0, 4, -2, 0, 1, 0, 0, -1, 0, 2) -> 1.0, WrappedArray(0, 0, 0, 4, -2, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(-2, 0, 1, 0, 0, -1, 0, 2, 0, 0) -> 1.0, WrappedArray(4, -2, 0, 1, 0, 0, -1, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 0, 4) -> 0.0, WrappedArray(1, -1, 0, 0, 0, 0, 0, 4, -2, 0) -> 0.0, WrappedArray(0, 1, 0, 0, -1, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, 0, 0, -4, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -4, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -4, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 4, -2, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 4, -2, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 4, -2, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 4, -2, 0, 1, 0, 0) -> 1.0), Map(WrappedArray(0, 0, 0, 0, 0, -2, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-6, 0, 0, 1, -1, 0, 0, 0, 0, 0) -> 0.0, WrappedArray(0, 0, 0, 0, 0, 0, 1, -1, 3, 0) -> 1.0, WrappedArray(0, 1, -1, 3, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, 0, -4, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 0, 4, -2) -> 0.0, WrappedArray(1, 0, -3, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -4, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 2, 0, 0, 0, 0, 0, 0, -4) -> 1.0, WrappedArray(0, 4, -2, 0, 1, 0, 0, -1, 0, 2) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(0, 0, 0, 4, -2, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(-1, 3, 0, 0, 0, 0, 0, 0, -2, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 1, -1, 0, 2, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, 0, 0, 0, -2, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 1, 0, -3, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -2, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(-2, 0, 1, 0, 0, -1, 0, 2, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, -3, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -4, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 3, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, 0, 0, -1, 0, 1, 0, -3) -> 1.0, WrappedArray(0, 1, 0, 0, -1, 0, 1, 0, -3, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 3, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 1, -1, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 1, -1, 0, 2) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(4, -2, 0, 1, 0, 0, -1, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 0, 4) -> 0.0, WrappedArray(0, 0, -1, 0, 0, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 0, 4, -2, 0) -> 0.0, WrappedArray(2, 0, 0, 0, -1, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 3, 0, 0, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 1, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 2, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 1, 0, 0, -1, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 1, 0, -3, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 2, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(-3, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, 0, 0, -4, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -2, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 1, -1, 0, 2, 0) -> 1.0, WrappedArray(1, -1, 3, 0, 0, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(0, 0, 0, 0, 2, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, -1, 0, 2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -2, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -4, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -4, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, -3, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 0, 0, 1, -1, 3) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -4, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 2, 0, 0, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 4, -2, 0, 1, 0) -> 1.0, WrappedArray(0, -3, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, -2, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 4, -2, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(-4, 0, 0, 0, 0, 0, 0, 0, 0, 2) -> 1.0, WrappedArray(0, 2, 0, 0, 0, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 3, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 2, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 2, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, -3, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 4, -2, 0, 1) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 0, -4, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 0, 2) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, 0, -2, 0, 0) -> 1.0, WrappedArray(3, 0, 0, 0, 0, 0, 0, -2, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 4, -2, 0, 1, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 0, 0, 0, 0, 1, -1) -> 1.0), Map(WrappedArray(0, 0, 0, 0, 0, -2, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 2, 0, -1, 0, 1, 0, -3) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 0, 6, -2) -> 1.0, WrappedArray(0, 0, -3, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 1, -1, 1, -1, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 2, 0, -1, 0) -> 1.0, WrappedArray(1, -1, 0, 1, -1, 0, 0, 3, -1, 0) -> 1.0, WrappedArray(0, 0, 4, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, -2, 1, 0, -1, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, 0, 0, -2, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 1, 0, 0, 0, 0) -> 1.0, WrappedArray(-6, 0, 0, 1, -1, 0, 0, 0, 0, 0) -> 0.0, WrappedArray(0, 0, -4, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 5, 0, 0, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 0, 0, 0, 1, 0, -1) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 5, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -4, 0, 1, 0, -1, 0, 1) -> 1.0, WrappedArray(0, -1, 0, 1, 0, -3, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(-1, 0, 1, -1, 0, 0, 3, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 1, -1, 0, 0) -> 1.0, WrappedArray(6, -2, 0, 0, 0, 2, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 1, -1, 3, 0) -> 1.0, WrappedArray(0, 0, 2, 0, -1, 0, 1, -1, 0, 1) -> 1.0, WrappedArray(0, -2, 0, 0, 1, -1, 0, 1, -1, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(-5, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, 0, 0, -5, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 3, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, -1, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 2, -2, 3, -1, 1) -> 1.0, WrappedArray(1, 0, -1, 0, 1, 0, 0, -1, 0, 2) -> 1.0, WrappedArray(0, 0, 0, 2, 0, 0, 0, 0, -1, 1) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, 0, -4, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 1, 0, -2, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 5, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, 0, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(-3, 0, 1, 0, -1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 3, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 0, 4, -2) -> 0.0, WrappedArray(-1, 1, -2, 0, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 1, 0, -2, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 4, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, -1, 0, 2, -2, 3) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, -2, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 1, 0, -2, 0, 2, 0, -1) -> 1.0, WrappedArray(-2, 3, -1, 1, 0, 0, -3, 0, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 0, 2, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(1, 0, -3, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(2, 0, -1, 0, 1, 0, -2, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, -1, 1, -2) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 0, 0, 2, -2) -> 1.0, WrappedArray(3, -1, 1, 0, 0, -3, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -4, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 2, 0, 0, 0, 0, 0, 0, -4) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 1, -1, 0, 0, 3) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, -4, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, -1, 1, -2, 0, 0) -> 1.0, WrappedArray(0, 4, -2, 0, 1, 0, 0, -1, 0, 2) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -4, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 1, -1, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(0, 0, 0, 4, -2, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(1, 0, -2, 0, 2, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 1, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(3, 0, -1, 1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 0, 1, 0, -2) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 3, 0, -1, 1) -> 1.0, WrappedArray(0, 0, -4, 0, 1, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 0, 4) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 1, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 3, -1, 0, 1, 0, 0, -3, 1) -> 1.0, WrappedArray(0, -3, 0, 1, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 3, 0, 0, 0, 0, 0, 0, -2, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 4, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 1, -1, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 6, -2, 0, 0, 0, 2) -> 1.0, WrappedArray(-1, 0, 1, 0, -2, 0, 2, 0, -1, 0) -> 1.0, WrappedArray(0, 6, -2, 0, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 0, 0, 3, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, 0, 0, 0, -4) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, -2, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -2, 0, 0, 0) -> 1.0, WrappedArray(0, 2, -2, 0, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -5, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, -1, 0, 1, 0, -1) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, -4, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 3, 0, -1, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, -1, 0, 1, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 0, 1, 0, -2) -> 1.0, WrappedArray(0, -2, 0, 0, 1, -1, 0, 2, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 1, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, 0, 0, 0, -2, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 1, 0, -3, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 6, -2, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, -4, 0, 1, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(1, 0, 0, -3, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 6, -2, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 2, 0, -1, 0, 1, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 1, 0, -1, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, -2, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(1, 0, 0, -3, 1, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 3, 0, -1) -> 1.0, WrappedArray(-2, 0, 2, 0, -1, 0, 1, 0, -3, 1) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 1, 0, -3, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, -3, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 0, -4) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -2, 0, 0, 1) -> 1.0, WrappedArray(0, -1, 1, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(-2, 0, 1, 0, 0, -1, 0, 2, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, -3, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 1, 0, -2, 1, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 2, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, -1, 1, -2, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(-1, 0, 0, 0, 1, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -4, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, -2, 0, 0, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, 0, 0, -5, 0) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 3, 0, 0, 0, 0) -> 1.0, WrappedArray(-4, 0, 0, 0, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, -1, 0, 2, -2) -> 1.0, WrappedArray(-4, 0, 1, 0, -1, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 2, 0, -1, 0, 1, 0, -3, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -4, 0, 1, 0, -1) -> 1.0, WrappedArray(-2, 0, 0, 1, -1, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, -2, 1, 0, -1, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, -3, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 2, -2, 0, 1, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, -2, 1, 0, -1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -5, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 2, 0, -1, 0, 1, 0, -2) -> 1.0, WrappedArray(0, 1, 0, -2, 0, 2, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 1, 0, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(2, -2, 0, 1, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 1, 0, 0, -1, 0, 1, 0, -3) -> 1.0, WrappedArray(0, 0, 2, -2, 0, 1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 1, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 1, 0, 0, -1, 0, 1, 0, -3, 0) -> 1.0, WrappedArray(3, -1, 0, 1, 0, 0, -3, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 3, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 1, -1, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 0, 0, 3) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 5, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 0, 2, 0, -1) -> 1.0, WrappedArray(0, 4, 0, 0, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 3, -1, 0, 1, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, -3, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 4, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, 0, 0, 0, 0, -4, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, -4, 0, 0, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(-2, 0, 2, 0, -1, 0, 1, 0, -2, 0) -> 1.0, WrappedArray(-1, 0, 0, 1, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, 0, 0, -4, 0) -> 1.0, WrappedArray(0, 0, 0, 2, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(-1, 0, 0, 3, -1, 0, 1, 0, 0, -3) -> 1.0, WrappedArray(0, 0, 0, 4, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(4, 0, 0, 0, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 2, -2, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 1, -1, 0, 2) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 0, 0, 2) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(-1, 0, 0, 2, 0, -1, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(4, -2, 0, 1, 0, 0, -1, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 0, 4) -> 0.0, WrappedArray(0, 3, 0, -1, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, -1, 1, -2, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 1, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(2, -2, 3, -1, 1, 0, 0, -3, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 5, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(-1, 0, 2, -2, 3, -1, 1, 0, 0, -3) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 3, 0, -1, 1, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -1, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 0, 4, -2, 0) -> 0.0, WrappedArray(-1, 0, 0, 0, 1, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 0, 0, 1, 0) -> 1.0, WrappedArray(2, 0, 0, 0, -1, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, -1, 0, 0, 2) -> 1.0, WrappedArray(0, -1, 0, 0, 2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 3, 0, 0, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(-2, 1, 0, -1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 1, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 1, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 1, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 5, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 2, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 6, -2, 0, 0) -> 1.0, WrappedArray(1, 0, -2, 1, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -5, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 0, 0, 0, 0, 6) -> 1.0, WrappedArray(0, 1, 0, 0, -1, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, -3, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 0, 2) -> 1.0, WrappedArray(-1, 1, -1, 0, 0, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 1, 0, -3, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 2, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, -1, 1, -2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-3, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 0, 2, -2, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -5, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 1, -2, 0, 0, 0, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, 0, 0, -4, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, -5, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 1, -1, 0, 1, -1) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 1, 0, -2, 0, 2) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 5, 0) -> 1.0, WrappedArray(0, 0, 6, -2, 0, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 4, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(-3, 1, 0, 0, -1, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -2, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 2, 0, -1, 0, 1, 0, -2, 0, 2) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 1, -1, 0, 2, 0) -> 1.0, WrappedArray(1, -1, 3, 0, 0, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(0, -3, 1, 0, 0, -1, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 3, -1, 0, 1, 0, 0, -3, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 2, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(-1, 1, 0, 0, -3, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(-1, 1, 0, 0, 0, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(0, -1, 0, 1, 0, -3, 0, 1, 0, -1) -> 1.0, WrappedArray(2, 0, 0, 0, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 4, 0) -> 1.0, WrappedArray(0, -3, 0, 0, 0, 0, 0, 0, 0, 2) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -5, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 4, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, -4, 0, 1) -> 1.0, WrappedArray(0, 0, -1, 0, 2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 2, 0, -1, 0, 1, -1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 2, -2, 3, -1, 1, 0, 0, -3, 0) -> 1.0, WrappedArray(-2, 0, 0, 1, -1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, 0, 0, 0, -5) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 1, 0, -2, 1) -> 1.0, WrappedArray(0, 0, -3, 1, 0, 0, -1, 0, 0, 2) -> 1.0, WrappedArray(1, 0, 0, 0, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 2, -2, 3, -1, 1, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -4, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, -1, 0, 2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, -1, 0, 0, 1) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 1, 0, -1, 0, 0) -> 1.0, WrappedArray(-3, 0, 0, 0, 0, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -4, 0, 1, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 0, 1, -1, 1) -> 1.0, WrappedArray(0, 0, 0, 0, -4, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, -3, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 0, 0, 1, -1, 3) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -4, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 2, 0, 0, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 4, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, -1, 0, 2, -2, 3, -1) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 0, 0, 0, 5) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, -4, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 5, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 2, -2, 0, 1) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 4, -2, 0, 1, 0) -> 1.0, WrappedArray(0, -3, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, -2, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 1, 0, -2, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 1, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 4, -2, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 1, -1, 0, 0, 3, -1) -> 1.0, WrappedArray(0, -1, 0, 1, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 1, -1, 1, -1) -> 1.0, WrappedArray(0, 0, 1, 0, -1, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, 0, 0, 0, 0) -> 1.0, WrappedArray(-4, 0, 0, 0, 0, 0, 0, 0, 0, 2) -> 1.0, WrappedArray(0, 2, 0, 0, 0, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 1, -1, 0, 1) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(-2, 0, 1, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 3, 0, -1, 1, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -2, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 3, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 2, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(1, 0, -3, 0, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 1, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, -1, 0, 2, -2, 3, -1, 1, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 2, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, 0, -2, 0, 2, 0, -1, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, -3, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, -1, 0, 1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 4, -2, 0, 1) -> 1.0, WrappedArray(2, 0, -1, 0, 1, 0, -3, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 1, -2, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 0, 6, -2, 0) -> 1.0, WrappedArray(0, 0, -4, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 4, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 2, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, -2, 1, 0, -1) -> 1.0, WrappedArray(0, -1, 0, 1, 0, -2, 0, 2, 0, -1) -> 1.0, WrappedArray(0, 2, 0, 0, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 0, 2) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, 0, -2, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 3, 0, -1, 1, 0, 0, 0) -> 1.0, WrappedArray(3, 0, 0, 0, 0, 0, 0, -2, 0, 0) -> 1.0, WrappedArray(2, 0, -1, 0, 1, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, 0, -3, 0, 1, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 2, -2, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(5, 0, 0, 0, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(4, 0, 0, 0, 0, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 4, -2, 0, 1, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 0, 0, 0, 0, 1, -1) -> 1.0), Map(WrappedArray(-1, 0, 2, -1, 0, 0, 0, 1, -3, 3) -> 1.0, WrappedArray(-3, 0, 0, 0, 1, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 1, 0, 0, 0, -3) -> 1.0, WrappedArray(2, 0, 0, 0, -1, 0, 1, 0, 0, -4) -> 1.0, WrappedArray(-1, 0, 0, 0, 1, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 2, -2, 0, 1, -1, 0, 0, 1) -> 1.0, WrappedArray(-1, 1, 0, -2, 0, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 3, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -2, 0, 0, 1, -1) -> 1.0, WrappedArray(1, 0, 0, 0, -1, 1, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 5, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(0, -2, 0, 1, 0, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 0, 1, 0, -2) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 3, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 2, 0, -1, 0, 1, 0, -3) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 0, 6, -2) -> 1.0, WrappedArray(0, 0, -3, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 1, 0, -1, 0) -> 1.0, WrappedArray(2, -2, 0, 6, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(1, 0, -2, 0, 1, 0, -1, 0, 0, 2) -> 1.0, WrappedArray(0, 0, 1, 0, 0, 0, 0, 0, 0, -6) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 0, 0, 0, 0, 3) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 1, -1, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 2, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 3, 0, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(-4, 0, 0, 0, 0, 2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 1, 0, -1, 0, 0, 2, 0) -> 1.0, WrappedArray(0, -1, 2, 0, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, -3, 0, 0, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 1, -1, 0, 0, 3, -1, 0) -> 1.0, WrappedArray(0, 0, 4, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -3, 0, 1, 0, -1, 0, 2, -2) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 3, -1, 0, 1, -1, 0, 1, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, -2, 1, 0, -1, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, 0, 0, -2, 0) -> 1.0, WrappedArray(-2, 0, 1, -1, 0, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(2, 0, 0, 0, -1, 0, 1, 0, 0, -2) -> 1.0, WrappedArray(1, 0, -2, 0, 0, 0, 0, 0, 3, -1) -> 1.0, WrappedArray(0, 0, 0, 2, 0, -1, 1, 0, 0, -2) -> 1.0, WrappedArray(0, 0, 0, -2, 2, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, -2, 1, 0, -1, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, 2, 0, -1, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 0, 0, 2, -2) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 1, 0, 0, -1, 1) -> 1.0, WrappedArray(0, -3, 0, 0, 2, -2, 0, 1, 0, -1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -2, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 1, 0, -1, 1) -> 1.0, WrappedArray(1, -1, 0, 0, 2, -2, 1, 0, -1, 0) -> 1.0, WrappedArray(-1, 0, 0, 1, 0, -2, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, -4, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 0, 0, 0, 3) -> 1.0, WrappedArray(0, 0, 3, -1, 1, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(-1, 0, 0, 2, 0, 0, 0, -2, 0, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, 0, -1, 1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -1, 1, -2, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 1, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, -3, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(-5, 0, 0, 0, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 6, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, -1, 0, 5, -1, 0) -> 1.0, WrappedArray(0, -1, 1, 0, -1, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(4, 0, 0, 0, 0, 0, 0, 0, -1, 1) -> 1.0, WrappedArray(0, 0, -1, 2, 0, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(-6, 0, 0, 1, -1, 0, 0, 0, 0, 0) -> 0.0, WrappedArray(0, 0, 0, 0, 0, 0, -2, 2, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, -4, 0, 1, 0, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 1, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, -4, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 2, 0, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(-1, 1, 0, 0, 0, 0, -2, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 5, 0, 0, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(-1, 1, 0, 0, -1, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, -1, 5, -1, 1) -> 1.0, WrappedArray(1, 0, -3, 0, 4, -2, 2, -1, 0, 0) -> 1.0, WrappedArray(0, 6, 0, 0, 0, -1, 0, 0, 1, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 1, -2, 0, 1) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 1, 0, 0, 0, -1) -> 1.0, WrappedArray(-1, 0, 2, 0, 0, 0, -3, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 5, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 0, 0, 0, 1, 0, -1) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 0, 5, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 0, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 5, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, -1, 0, 1, -3, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 1, 0, -1, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -4, 0, 1, 0, -1, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, 0, 0, 0, -5) -> 1.0, WrappedArray(0, -1, 0, 1, 0, -3, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, -1, 1) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 1, 0, -1, 1, 0) -> 1.0, WrappedArray(0, 6, 0, 0, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 3, 0, -2, 2, 0, -1, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 0, 0, 0, 2) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(-3, 1, 0, 0, -1, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(-1, 0, 1, -1, 0, 0, 3, -1, 0, 1) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 2, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, -1, 1, -1, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 0, 3, -1, 0, 1) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(6, -2, 0, 0, 0, 2, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 2, 0, 0, -3, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 1, -1, 3, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 3, 0, 0, -3, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -4, 0, 1, 0, 0) -> 1.0, WrappedArray(-1, 1, 0, 0, -2, 0, 2, 0, -1, 0) -> 1.0, WrappedArray(-1, 0, 0, 1, -1, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(0, 0, 2, 0, -1, 0, 1, -1, 0, 1) -> 1.0, WrappedArray(-1, 0, 1, 0, -2, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 1, -1, 0, 1, -1, 0) -> 1.0, WrappedArray(-4, 0, 1, 0, 0, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 2, 0, -2, 1, 0) -> 1.0, WrappedArray(2, 0, -1, 0, 0, 1, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, -4, 0, 0, 4, 0, -2) -> 1.0, WrappedArray(0, 1, -1, 0, 1, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 2, 0, 0, 0, -2) -> 1.0, WrappedArray(-5, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 1, -1, 0, 1, -1, 0) -> 1.0, WrappedArray(-5, 0, 0, 0, 0, 1, -1, 0, 0, 4) -> 1.0, WrappedArray(-1, 2, 0, 0, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(-3, 0, 0, 2, -2, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(-3, 0, 0, 2, -2, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(0, 1, -3, 0, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, 0, 0, -5, 0, 0) -> 1.0, WrappedArray(0, 1, 0, -4, 0, 2, -1, 1, 0, -2) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -2, 0, 1, -1, 2, 0, -1) -> 1.0, WrappedArray(0, 1, -1, 3, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, -1, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, -5, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -5, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 3, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 4, 0, 0, -3) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -4, 0, 0, 4, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 5, 0) -> 1.0, WrappedArray(1, 0, 0, -1, 0, 2, -2, 3, -1, 1) -> 1.0, WrappedArray(0, -1, 0, 1, -1, 0, 1, -3, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 2, 0, 0, -4, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 1, 0, -3, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 6, 0, 0, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 1, 0, 0, -1, 0, 2) -> 1.0, WrappedArray(0, -2, 0, 0, 1, -1, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 2, 0, 0, 0, 0, -1, 1) -> 1.0, WrappedArray(0, 0, 1, 0, 0, -1, 0, 2, 0, 0) -> 1.0, WrappedArray(0, 2, -1, 0, 0, 0, 1, -3, 3, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 2, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, 0, -4, 0) -> 1.0, WrappedArray(-2, 2, 0, -1, 0, 1, -1, 0, 1, -3) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 1, 0, -2, 0) -> 1.0, WrappedArray(0, 0, 1, 0, 0, -1, 0, 4, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 5, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 1, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 2, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 2, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 1, -2, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, -2, 0, 1, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, -1, 0, 1, -2) -> 1.0, WrappedArray(0, 0, 0, 4, 0, 0, -3, 1, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(5, -1, 1, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -6, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, -2, 0, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 7, 0, 0, -1, 1, 0) -> 1.0, WrappedArray(3, 0, 0, -2, 0, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 1, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 1, 0, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(-3, 0, 1, 0, -1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, -1, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(-1, 1, 0, -1, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 2, 0, -1, 0, 1) -> 1.0, WrappedArray(1, -1, 0, 0, 3, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 0, 4, -2) -> 0.0, WrappedArray(0, 0, 0, 0, 1, 0, -1, 0, 2, 0) -> 1.0, WrappedArray(-1, 1, -2, 0, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 4, 0, 0, -2, 0, 0, 2, -1, 0) -> 1.0, WrappedArray(1, 0, -2, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 1, 0, -1, 0, 0, 2, 0) -> 1.0, WrappedArray(0, 1, 0, -2, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 7, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 0, 4, 0, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, -1, 0, 2, -2, 3) -> 1.0, WrappedArray(0, -1, 1, -2, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, 0, 0, 0, -1) -> 1.0, WrappedArray(-1, 0, 0, 0, 3, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, -3, 0, 3, 0, -2) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, -2, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 1, 0, -2, 0, 2, 0, -1) -> 1.0, WrappedArray(0, 0, -1, 1, -2, 1, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 2, 0, 0, -4, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, -1, 0, 2, 0) -> 1.0, WrappedArray(0, 2, 0, -1, 1, 0, 0, -2, 0, 2) -> 1.0, WrappedArray(-2, 3, -1, 1, 0, 0, -3, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 1, -1, 0, 0, 2, 0) -> 1.0, WrappedArray(-2, 1, 0, 0, -1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -5, 0, 0, 0, 0, 0, 2) -> 1.0, WrappedArray(1, 0, -2, 0, 0, 1, -1, 2, 0, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 0, 2, -1, 1, 0, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 5, -1, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -2, 0, 0, 1, 0, -1) -> 1.0, WrappedArray(-1, 0, 1, 0, -2, 0, 0, 3, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 0, 0, 1) -> 1.0, WrappedArray(-2, 0, 0, 0, 2, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(1, 0, -3, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 0, 0, 3, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -2, 2, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(2, 0, -1, 0, 1, 0, -2, 0, 2, 0) -> 1.0, WrappedArray(-5, 0, 0, 0, 0, 0, 2, 0, -2, 1) -> 1.0, WrappedArray(1, 0, 0, -1, 2, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(2, -1, 0, 0, 0, 1, 0, -2, 0, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, -1, 1, -2) -> 1.0, WrappedArray(0, 0, 2, -2, 0, 1, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 3, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -3, 1, 0, 0, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 1, 0, -1, 0, 1, -1, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 0, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(-1, 0, 2, 0, 0, -3, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 1, 0, 0, 0, -1, 0, 2) -> 1.0, WrappedArray(1, 0, -2, 1, 0, -1, 0, 0, 0, 3) -> 1.0, WrappedArray(2, -1, 0, 1, 0, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -1, 0, 0, 0, 1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 0, 0, 2, -2) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, -4, 0, 1, -1, 0) -> 1.0, WrappedArray(-1, 0, 0, 1, 0, -1, 0, 0, 0, 2) -> 1.0, WrappedArray(3, -1, 1, 0, 0, -3, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 4, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -1, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 1, 0, 0, -4, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 4, 0, 0, -2, 1, -1, 0, 2, -1) -> 1.0, WrappedArray(0, 0, -3, 0, 0, 2, -2, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 3, 0, 0, 0, 0, -1) -> 1.0, WrappedArray(-1, 0, 3, 0, 0, 0, -2, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, -4, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 2, 0, 0, 0, 0, 0, 0, -4) -> 1.0, WrappedArray(2, 0, -1, 0, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 1, -6, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 1, -1, 0, 0, 3) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -2, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 3, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 1, -1, 0, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 2, -2, 1, 0, -1, 0, 0, 3, -1) -> 1.0, WrappedArray(0, 1, -3, 0, 0, 0, 0, 0, 3, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 0, 1, 0, 0, -4) -> 1.0, WrappedArray(0, 2, -2, 0, 1, -1, 0, 0, 1, 0) -> 1.0, WrappedArray(1, 0, -2, 0, 1, 0, -1, 1, 0, -1) -> 1.0, WrappedArray(-1, 0, 3, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 2, 0, -1, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 1, 0, -2, 0, 0, 1, -1, 2) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, -4, 0) -> 1.0, WrappedArray(0, 0, 0, 2, 0, -1, 0, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 1, 0, 0, -2) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 2, 0, 0, -3, 0) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, -1, 1, -2, 0, 0) -> 1.0, WrappedArray(2, 0, -1, 0, 1, -1, 0, 1, 0, -2) -> 1.0, WrappedArray(0, 0, 1, 0, -1, 0, 3, 0, 0, 0) -> 1.0, WrappedArray(0, 4, -2, 0, 1, 0, 0, -1, 0, 2) -> 1.0, WrappedArray(0, 1, 0, -2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(2, 0, 0, 0, 0, -2, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 2, -2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 2, 0, -2, 1, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 1, -2, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 0, 4, 0, 0) -> 1.0, WrappedArray(6, 0, 0, 0, -1, 0, 0, 1, 0, -2) -> 1.0, WrappedArray(0, 0, 0, -5, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 4, 0, 0, -2, 0) -> 1.0, WrappedArray(-1, 0, 1, -1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, -2, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(-3, 0, 0, 0, 0, 0, 0, 1, 0, -1) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -4, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 0, 2, 0) -> 1.0, WrappedArray(0, 0, -1, 0, 0, 2, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 1, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 3, 0, 0, -2, 2, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, -4, 0, 0, 4) -> 1.0, WrappedArray(-1, 1, 0, 0, 0, -1, 1, 0, -1, 0) -> 1.0, WrappedArray(0, 0, -2, 0, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, -3, 0, 0, 2) -> 1.0, WrappedArray(0, -1, 0, 1, 0, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, -2, 0, 0, 2) -> 1.0, WrappedArray(-2, 0, 0, 1, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 0, 0, 0, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 0, 4, -2, 0, 1, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 2, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 1, -1, 2, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(1, 0, 0, 0, 0, -2, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, -1, 0, 0, 2, -1) -> 1.0, WrappedArray(0, -2, 0, 0, 0, 0, 0, 1, 0, -1) -> 1.0, WrappedArray(1, 0, -2, 0, 2, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, 0, -2, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 0, 3, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 2, -2, 0, 6, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 0, 0, 2, 0, 0) -> 1.0, WrappedArray(-2, 1, 0, -1, 0, 0, 0, 3, 0, -1) -> 1.0, WrappedArray(0, 1, -1, 0, 0, 0, 3, 0, 0, -2) -> 1.0, WrappedArray(-1, 1, 0, 0, 0, 0, -1, 1, -2, 1) -> 1.0, WrappedArray(0, 0, 1, 0, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 5, 0, -1, 1, -2, 0, 0, 2) -> 1.0, WrappedArray(0, 0, 0, -2, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 7, 0, 0) -> 1.0, WrappedArray(3, 0, -1, 1, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, 0, 0, 0, -5, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, 0, -1, 1, 0, 0) -> 1.0, WrappedArray(0, 0, -2, 2, 0, 0, -1, 1, 0, 0) -> 1.0, WrappedArray(-2, 0, 0, 0, 0, 0, 0, 0, 0, 3) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -6, 0, 0, 0, 0, 0, 4) -> 1.0, WrappedArray(1, 0, -1, 0, 1, 0, -1, 0, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 0, 1, -1, 0, 2, 0) -> 1.0, WrappedArray(0, -2, 0, 1, -1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(1, 0, -1, 0, 0, 1, 0, 0, -4, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 0, 1, -1, 0, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, -1, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 3, -1, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 0, 1, 0, -2) -> 1.0, WrappedArray(0, 1, -1, 0, 1, 0, -2, 1, 0, -1) -> 1.0, WrappedArray(0, 0, 1, 0, 0, 0, 0, -1, 0, 1) -> 1.0, WrappedArray(0, -1, 1, 0, -2, 0, 1, 0, -1, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 1, 0, -1, 0, 0, 2) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 1, 0, -2, 0, 1) -> 1.0, WrappedArray(0, -4, 0, 0, 0, 0, 2, 0, 0, 0) -> 1.0, WrappedArray(0, 2, 0, 0, 0, 0, -2, 1, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 3, 0, 0, -2, 0, 0, 1) -> 1.0, WrappedArray(0, 0, 2, 0, -1, 1, 0, 0, -2, 0) -> 1.0, WrappedArray(-1, 0, 1, 0, 0, -2, 0, 0, 0, 1) -> 1.0, WrappedArray(0, -1, 1, -6, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, -3, 0, 0, 0, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 3, 0, -1, 1) -> 1.0, WrappedArray(0, 0, 0, 1, -2, 0, 1, -1, 2, 0) -> 1.0, WrappedArray(0, 0, -4, 0, 1, 0, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 1, 0, 0, 0, -1, 0, 1, 0, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 1, -1, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(0, 0, 0, 1, -1, 0, 0, 0, 0, 4) -> 1.0, WrappedArray(1, 0, -1, 0, 1, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(-1, 0, 0, 0, 1, -1, 0, 2, -2, 0) -> 1.0, WrappedArray(-1, 0, 0, 2, -1, 0, 0, 0, 1, 0) -> 1.0, WrappedArray(1, 0, -1, 0, 0, 0, 2, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 1, 0, -2, 0, 1, 0) -> 1.0, WrappedArray(0, -1, 0, 0, 0, 1, 0, 0, 0, -1) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 1, -2, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, -1, 0, 0, 2, -1) -> 1.0, WrappedArray(0, 0, 0, 0, 2, 0, 0, 0, 0, -2) -> 1.0, WrappedArray(-1, 4, 0, -1, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 2, 0, -1, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 3, 0, 0, -2, 0) -> 1.0, WrappedArray(0, 1, 0, -1, 0, 0, 1, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 1, 0, -1, 0, 3, 0) -> 1.0, WrappedArray(2, 0, -1, 1, 0, 0, 0, -1, 0, 0) -> 1.0, WrappedArray(0, -2, 0, 0, 0, 0, 0, 3, -1, 0) -> 1.0, WrappedArray(0, 0, 1, 0, -1, 0, 0, 0, 1, -1) -> 1.0, WrappedArray(-1, 0, 1, -1, 0, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -2, 2, -1, 0, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, -1, 0, 0, 1, 0, 0) -> 1.0, WrappedArray(-4, 0, 0, 1, 0, 0, 0, 0, -1, 0) -> 1.0, WrappedArray(0, 0, 0, 1, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 3, -1, 0, 1, 0, 0, -3, 1) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 1, -1, 4) -> 1.0, WrappedArray(0, -6, 0, 0, 0, 0, 0, 4, 0, 0) -> 1.0, WrappedArray(0, -3, 0, 1, 0, -1, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, -1, 0, 0, 2, -1, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 0, 0, -5) -> 1.0, WrappedArray(-1, 3, 0, 0, 0, 0, 0, 0, -2, 0) -> 1.0, WrappedArray(0, 0, 1, -1, 0, 2, 0, 0, 0, -3) -> 1.0, WrappedArray(0, 0, 0, 1, 0, -1, 0, 0, 1, 0) -> 1.0, WrappedArray(-1, 0, 0, 4, 0, 0, -2, 1, -1, 0) -> 1.0, WrappedArray(0, 0, 2, 0, 0, 0, 0, -2, 1, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, -5, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 3, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 0, 0, 0, 0, 4, 0, 0, 0) -> 1.0, WrappedArray(1, -1, 1, -1, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(0, 5, 0, -1, 1, -2, 0, 0, 2, 0) -> 1.0, WrappedArray(0, -1, 0, 1, -2, 0, 0, 0, 0, 0) -> 1.0, WrappedArray(0, 0, 0, 0, 0, 0, 0, 1, -1, 0) -> 1.0, WrappedArray(-8, 0, 0, 0, 0, 0, 0, 0, 0, 0) -> ...

def aggToMatrix(totalVarDists: Seq[Seq[Map[Seq[Int],Double]]], aggFunc: Seq[Double] => Double): Seq[Seq[Double]] = {
  totalVariationDistances.map(_.map( t => aggFunc(t.values.toSeq)))
}

def printMatrix(mat: Seq[Seq[Double]]): Unit = {
  mat.map( s => { s.map( a => print(f"$a%2.3f ") ); println() } )
}

aggToMatrix: (totalVarDists: Seq[Seq[Map[Seq[Int],Double]]], aggFunc: Seq[Double] => Double)Seq[Seq[Double]]
printMatrix: (mat: Seq[Seq[Double]])Unit

We compute three different metrics of the total variation distances.

maxDists is the maximal total variation distance over the different lagKeys.
minDists is the minimal total variation distance over the different lagKeys.
meanDists is an estimate of the average total variation distance over the different lagKeys.

val maxDists = aggToMatrix(totalVariationDistances, s => s.max)
val minDists = aggToMatrix(totalVariationDistances, s => s.min)
val meanDists = aggToMatrix(totalVariationDistances, s => s.sum/s.size)

maxDists: Seq[Seq[Double]] = Vector(Vector(0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0), Vector(1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0), Vector(1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0), Vector(1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0), Vector(1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 1.0), Vector(1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0), Vector(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0), Vector(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0), Vector(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0), Vector(1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0))
minDists: Seq[Seq[Double]] = Vector(Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.1111111111111111), Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Vector(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0), Vector(0.1111111111111111, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0))
meanDists: Seq[Seq[Double]] = Vector(Vector(0.0, 0.8095238095238095, 0.9595959595959596, 0.9902676399026764, 0.9975932611311673, 0.9992509363295881, 0.999785112600997, 0.9999212988949179, 0.9999637822897781, 0.9999828303297199), Vector(0.8095238095238095, 0.0, 0.7878787878787878, 0.948905109489051, 0.9879412354592861, 0.9962818797931157, 0.9988235824354509, 0.9995277161089322, 0.9997797200520187, 0.9999006682605777), Vector(0.9595959595959596, 0.7878787878787878, 0.0, 0.7675182481751823, 0.9456465498353374, 0.9839165434703036, 0.9949339063117071, 0.9979342365055828, 0.9990263999070653, 0.9995453963182023), Vector(0.9902676399026764, 0.948905109489051, 0.7675182481751823, 0.0, 0.76569626045364, 0.9313390461281573, 0.9778513135067101, 0.9912980359273889, 0.9959874223204074, 0.998122961240012), Vector(0.9975932611311673, 0.9879412354592861, 0.9456465498353374, 0.76569626045364, 0.0, 0.709855350171288, 0.9069532060773262, 0.9635540738278638, 0.9834585383266629, 0.992240400344003), Vector(0.9992509363295881, 0.9962818797931157, 0.9839165434703036, 0.9313390461281573, 0.709855350171288, 0.0, 0.6846310864524279, 0.8780374739844375, 0.9450969813814848, 0.9743411917827652), Vector(0.999785112600997, 0.9988235824354509, 0.9949339063117071, 0.9778513135067101, 0.9069532060773262, 0.6846310864524279, 0.0, 0.6217124078957903, 0.8326361431674983, 0.9226862715145945), Vector(0.9999212988949179, 0.9995277161089322, 0.9979342365055828, 0.9912980359273889, 0.9635540738278638, 0.8780374739844375, 0.6217124078957903, 0.0, 0.57277338181383, 0.8064805024139434), Vector(0.9999637822897781, 0.9997797200520187, 0.9990263999070653, 0.9959874223204074, 0.9834585383266629, 0.9450969813814848, 0.8326361431674983, 0.57277338181383, 0.0, 0.5653338124646969), Vector(0.9999828303297199, 0.9999006682605777, 0.9995453963182023, 0.998122961240012, 0.992240400344003, 0.9743411917827652, 0.9226862715145945, 0.8064805024139434, 0.5653338124646969, 0.0))

Each model is a mapping {key: {value: probability}} where key (lagKey) is a sequence of reversals and non-reversals of length m, value is a sequence of trends of length n and probability is the estimated probability that value is observed immediately following key.

Hence, for any two models A and B, we can calculate the total variation distance between the mappings {value: probability} for a given key in the union of the keys for A and B. If a key is not present in one of the models, the total variation distance is 1 for that key.

In the matrix below, the (i,j)-th position is the arithmetic mean of the total variation distances for all keys in the union of the keysets. The matrix is symmetric with the smallest model in the top row and leftmost column and the largest model in the bottom row and rightmost column. All diagonal elements are 0 since the total variation distance from one model to itself is always 0.

If there are three models labeled M1, M2, M3 and Vi_j is the arithmetic mean described above, the matrix is

\[ \begin{matrix} V_{1,1} & V_{1,2} & V_{1,3} \end{matrix} \] \[ \begin{matrix} V_{2,1} & V_{2,2} & V_{2,3} \end{matrix} \] \[ \begin{matrix} V_{3,1} & V_{3,2} & V_{3,3} \end{matrix} \]

As one can see, the models differ a lot from each other, suggesting that the estimate can still be improved given more data.

printMatrix(meanDists)

0.000 0.810 0.960 0.990 0.998 0.999 1.000 1.000 1.000 1.000 
0.810 0.000 0.788 0.949 0.988 0.996 0.999 1.000 1.000 1.000 
0.960 0.788 0.000 0.768 0.946 0.984 0.995 0.998 0.999 1.000 
0.990 0.949 0.768 0.000 0.766 0.931 0.978 0.991 0.996 0.998 
0.998 0.988 0.946 0.766 0.000 0.710 0.907 0.964 0.983 0.992 
0.999 0.996 0.984 0.931 0.710 0.000 0.685 0.878 0.945 0.974 
1.000 0.999 0.995 0.978 0.907 0.685 0.000 0.622 0.833 0.923 
1.000 1.000 0.998 0.991 0.964 0.878 0.622 0.000 0.573 0.806 
1.000 1.000 0.999 0.996 0.983 0.945 0.833 0.573 0.000 0.565 
1.000 1.000 1.000 0.998 0.992 0.974 0.923 0.806 0.565 0.000

To reference dbfs from markdown, use /files instead of /FileStore

Trend Calculus on oil prices

trendcalculusoil

Performance of Trend Calculus Markov Chain model

ls dbfs:/FileStore/shared_uploads/

path	name	size
dbfs:/FileStore/shared_uploads/adlindhe@kth.se/	adlindhe@kth.se/	0.0
dbfs:/FileStore/shared_uploads/ahlsen@math.su.se/	ahlsen@math.su.se/	0.0
dbfs:/FileStore/shared_uploads/alek@kth.se/	alek@kth.se/	0.0
dbfs:/FileStore/shared_uploads/amanda.olmin@liu.se/	amanda.olmin@liu.se/	0.0
dbfs:/FileStore/shared_uploads/amirhossein.ahmadian@liu.se/	amirhossein.ahmadian@liu.se/	0.0
dbfs:/FileStore/shared_uploads/axel.berg@arm.com/	axel.berg@arm.com/	0.0
dbfs:/FileStore/shared_uploads/caylak@kth.se/	caylak@kth.se/	0.0
dbfs:/FileStore/shared_uploads/ciwan@kth.se/	ciwan@kth.se/	0.0
dbfs:/FileStore/shared_uploads/dali@cs.umu.se/	dali@cs.umu.se/	0.0
dbfs:/FileStore/shared_uploads/emilio.jorge@chalmers.se/	emilio.jorge@chalmers.se/	0.0
dbfs:/FileStore/shared_uploads/fabiansi@kth.se/	fabiansi@kth.se/	0.0
dbfs:/FileStore/shared_uploads/hugower@kth.se/	hugower@kth.se/	0.0
dbfs:/FileStore/shared_uploads/johan.oxenstierna@cs.lth.se/	johan.oxenstierna@cs.lth.se/	0.0
dbfs:/FileStore/shared_uploads/johannes.graner@gmail.com/	johannes.graner@gmail.com/	0.0
dbfs:/FileStore/shared_uploads/ka_barber@live.co.uk/	ka_barber@live.co.uk/	0.0
dbfs:/FileStore/shared_uploads/karl.bengtsson_bernander@it.uu.se/	karl.bengtsson_bernander@it.uu.se/	0.0
dbfs:/FileStore/shared_uploads/linn.ostrom@math.lth.se/	linn.ostrom@math.lth.se/	0.0
dbfs:/FileStore/shared_uploads/martin.andersson@math.uu.se/	martin.andersson@math.uu.se/	0.0
dbfs:/FileStore/shared_uploads/niklas.gunnarsson@it.uu.se/	niklas.gunnarsson@it.uu.se/	0.0
dbfs:/FileStore/shared_uploads/pavlo.melnyk@liu.se/	pavlo.melnyk@liu.se/	0.0
dbfs:/FileStore/shared_uploads/petterre@kth.se/	petterre@kth.se/	0.0
dbfs:/FileStore/shared_uploads/robert.gieselmann@gmail.com/	robert.gieselmann@gmail.com/	0.0
dbfs:/FileStore/shared_uploads/scenegraph_motifs/	scenegraph_motifs/	0.0
dbfs:/FileStore/shared_uploads/vpol@kth.se/	vpol@kth.se/	0.0

displayHTML("<img src='/files/shared_uploads/johannes.graner@gmail.com/trend_calculus_oil.png'>")

displayHTML("<img src='/files/shared_uploads/johannes.graner@gmail.com/trend_calculus_mc_model_performance.png'>")

displayHTML("<img src='/files/shared_uploads/johannes.graner@gmail.com/trend_calculus_mc_model_performance.png'>")

sds-3.x/ScaDaMaLe