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Table of Contents
Purpose
The idea is to write all image parameters for data and Monte Carlo files into a database, so that the access to the data becomes more easy. To some extend (also not necessarily very efficient) the database server can already do the analysis. Everybody is free to use the programming language or tool of their choice to do the analysis. Writing the data to be analysed into a root file has the advantage that no additional software installation other than root itself is required. However, be aware that the files can easily become large.
The original proposal can be found here: https://www.fact-project.org/logbook/showthread.php?tid=5604&pid=27027#pid27027
Status
Most of the data is in the database. Due to some technical reasons still about 1/5th of the data is missing. Most of it from 2016 (seems 2016 the data was more noisy). No automatic process is currently updating the tables and no process is replicating the existing data from La Palma.
Basics
Although this page will give some basic examples how to implement an analysis, this is neither an analysis tutorial nor a reference guide to SQL or the required tools. For this, please refer to their manuals. Here are a few examples:
- MySQL Manual: https://dev.mysql.com/doc/refman/5.7/en/
- MAN page of the mysql client:
man mysql rootifysql --helpand https://www.fact-project.org/logbook/showthread.php?tid=4192- PHP MySQL API: http://php.net/manual/en/book.mysql.php
- MySQL++: https://tangentsoft.com/mysqlpp/home
Installing FACT++
If you want to install rootifysql, you find a description here: InstallingFACT++
Connecting to the Database
Find some basic instructions here how to access the database: DatabaseBasedAnalysis/Connection
Tools to access the database
mysql
The mysql-client is the classical way to connect to the database and get data. Data is retrieved from a MySQl database always as pure ascii. mysql can print the ascii table to the console either as a nicely formatted text or as a machine readable ascii table.
rootifysql
A convenient way to retrieve data is the rootifysql tool which is part of the FACT++ package. As the name suggests, it writes the data into root files (but can also write the data into ascii files as the mysql-client). More details can be found either calling it with the --help option or at https://www.fact-project.org/logbook/showthread.php?tid=4192.
To build only the FACT++ tools (fitsdump, root2sql, fits2sql, rootifysql) you can use cmake -DTOOLS_ONLY=1. You can create a debian and package and a tar file then with make package. You will certainly need the development packages of curses, libnova, libmysql-client, libmysql++ and libopenssl. In addition, you need help2man and groff.
Some more detailed instructions can be found at DatabaseBasedAnalysis/rootifysql.
Other alternatives
Many possibilities exist to access a mysql database as a C API, MySQL++, Python (MySQL.Connector), PHP and others. You are free to use whatever tool you like. In the following, an analysis will be outlined using the rootifysql client and because it is most convenient.
PhpMyAdmin
To get a fast glimpse on the accessible databases and the contents of the tables, you can log-in to PhpMyAdmin at http://iph-pc45.ethz.ch/phpmyadmin
The Analysis
Generally speaking, it makes sens to get familiar with the available columns in the table and their meaning. Right now, the best is to guess from the column name (see !PhPMyAdmin). More details will follow soon.
Data Selection
For data selection only run-wise information should be relevant which are stored in the table RunInfo. The reason is that if you select data on a more fine grained level (e.g. event-wise zenith angle), right now there is no easy method to determine the corresponding observation time. So whenever data is selected event-wise make sure that you do not cut the data in a variable which cuts out events systematically and not randomly. For example, an event-wise cut in zenith angel usually keeps or discards two consecutive events because their zenith angle is correlated. For a cut in any image parameter (Width, Length, Size, ...), the result on two consecutive events is random because their image parameters are not correlated.
As an example we analyse the Crab data from our public sample (01/11/2013 - 06/11/2013).
Let's first have a look at the total observation time of all Crab data in this period:
SELECT COUNT(*), SUM(TIME_TO_SEC(TIMEDIFF(fRunStop,fRunStart))*fEffectiveOn/3600) AS EffOnTime, MIN(fZenithDistanceMin) AS MinZd, MAX(fZenithDistanceMax) AS MaxZd, MIN(fR750Cor/fR750Ref) AS MinQ, MAX(fR750Cor/fR750Ref) AS MaxQ FROM RunInfo WHERE fSourceKey=5 AND fRunTypeKey=1 AND FileId BETWEEN 131101000 AND 131107000
The result using mysql is
+----------+-------------+-------+-------+---------+---------+ | COUNT(*) | EffOnTime | MinZd | MaxZd | MinQ | MaxQ | +----------+-------------+-------+-------+---------+---------+ | 435 | 32.53992354 | 6.36 | 67.89 | 0.01477 | 1.10584 | +----------+-------------+-------+-------+---------+---------+ 1 row in set (0.01 sec)
So we have 435 data runs from Crab with a total effective observation time of 32.5 hours in a zenith angle range between 6° and 68° and a bad weather factor between 0.01 (really bad) to 1.1 (extremely good).
Taking only good data by adding "AND fR750Cor/fR750Ref>0.9" to the WHERE-clause gives us
+----------+-------------+-------+-------+---------+---------+ | COUNT(*) | EffOnTime | ZdMin | ZdMax | MinQ | MaxQ | +----------+-------------+-------+-------+---------+---------+ | 328 | 24.58955887 | 6.36 | 67.86 | 0.90084 | 1.10584 | +----------+-------------+-------+-------+---------+---------+ 1 row in set (0.00 sec)
But we also want to restrict ourselves to "good" zenith angles (zenith angles at which there is no significant efficiency loss). So we add "AND fZenithDistanceMax<35" to the WHERE-clause which yields
+----------+-------------+-------+-------+---------+---------+ | COUNT(*) | EffOnTime | ZdMin | ZdMax | MinQ | MaxQ | +----------+-------------+-------+-------+---------+---------+ | 244 | 19.06608557 | 6.36 | 34.90 | 0.90084 | 1.10584 | +----------+-------------+-------+-------+---------+---------+ 1 row in set (0.00 sec)
Now we need to get a list of these runs with
SELECT FileId FROM RunInfo WHERE fSourceKey=5 AND fRunTypeKey=1 AND FileId BETWEEN 131101000 AND 131107000 AND fR750Ref/fR750Cor>0.9 AND fZenithDistanceMax<35
This can later be JOINed with the following queries.
Let's write the list of runs into a file. There are plenty of options. Here are a few (assuming the query is in a file query.sql)
mysql -N [...] < query.sql > Crab.txt cat query.sql | mysql -N [...] > Crab.txt rootifysql [...] -n -v0 -d query.sql > Crab.txt rootifysql [...] -n -w Crab.txt query.sql
The [...] is placeholder for additional options, in particular the login credentials (ideally they are kept in a file which can not be read by everyone).
An alternative is to put
#!/path/to/rootifysql --config=/path/to/resources.rc
in the first line of your query.sql. Make it executable "chmod u+x query.sql" and put your credentials (uri=) into resources.rc. Now you can call it directly
./query.sql -n -w Crab.txt
Data statistics
Now we want to get some statistics about the Crab data between 01/11/2013 and 06/11/2013 and see if we can do simple plots. For this we write the table into a root file.
rootifysql [...] --query " \
SELECT \
* \
FROM \
RunInfo \
WHERE \
fSourceKey=5 \
AND \
fRunTypeKey=1 \
AND \
FileId BETWEEN 131101000 AND 131107000 \
AND \
fR750Ref/fR750Cor>0.9 \
AND \
fZenithDistanceMax<35 \
"
If the file already exists, either give it a different name (see --help for details) or overwrite it with --force.
The output should look similar to this
------------------------ Rootify SQL ------------------------- Connecting to database... Client Version: 5.7.23 Server Version: 5.7.23-0ubuntu0.18.04.1 Requesting data... Opening file 'rootify.root' [compression=1]... Trying to setup 120 branches... Configured 115 branches. Filling branches... 317 rows fetched. 317 rows skipped due to NULL field. 0 rows filled into tree. 10 kB written to disk. File closed. Execution time: 0.0537751s (169.6 us/row) --------------------------------------------------------------
Per default rows which contain any NULL are not written to the file because all values are converted to a DOUBLE and there is no representation for a NULL-value in double. So, we need to force the output with --ignore-null and will get something like:
------------------------ Rootify SQL ------------------------- Connecting to database... Client Version: 5.7.23 Server Version: 5.7.23-0ubuntu0.18.04.1 Requesting data... Opening file 'rootify.root' [compression=1]... Trying to setup 120 branches... Configured 115 branches. Filling branches... 317 rows fetched. 317 rows filled into tree. 86 kB written to disk. File closed. Execution time: 0.072247s (227.9 us/row) --------------------------------------------------------------
Now we can open the file in root and do plots. The easiest ist to use the tree viewer:
root rootify.root
root [0]
Attaching file rootify.root as _file0...
root [1] TTree *T = (TTree*)_file0->Get("Result");
root [2] T->StartViewer();
root [3]
Or plot the zenith angle distribution directly:
root rootify.root
root [0]
Attaching file rootify.root as _file0...
root [1] TTree *T = (TTree*)_file0->Get("Result");
root [2] T->Draw("fZenithDistanceMean");
root [3]
or zenith angle versus time (Hint: DATETIME columns are converted to Unix-time in seconds):
root rootify.root
root [0]
Attaching file rootify.root as _file0...
root [1] TTree *T = (TTree*)_file0->Get("Result");
root [2] T->Draw("fZenithDistanceMean:fRunStart");
root [3]
Data retrieval
The events themselves are stored in a table named Events. The position of the source in camera coordinates is stored in Position. To get them, you can run the following query
SELECT Events.*, Position.X, Position.Y FROM RunInfo LEFT JOIN Events USING (FileId) LEFT JOIN Position USING (FileId, EvtNumber) WHERE fSourceKey=5 AND fRunTypeKey=1 AND FileId BETWEEN 131101000 AND 131107000 AND fZenithDistanceMax<35 AND fR750Ref/fR750Cor>0.9
or with the list you wrote before
SELECT Events.*, Position.X, Position.Y LEFT JOIN Events USING (FileId) LEFT JOIN Position USING (FileId, EvtNumber) WHERE FileId IN ($MyList)
using --list.MyList=Crab.txt as command-line option to rootifysql. Both queries are similar in execution time.
Let's assume the output file is crab-data-only.root (rootifysql --out=crab-data-only.root). Requesting the data and writing the file took me about 60s.
To run an analysis on the data you can use the following root macro "analysis.C". It produces a theta-square plot. Its execution took about five seconds (root analysis.C++). The ++ behind the macro name forces root to compile the macro before execution (might not be necessary anymore with root 6) to increase performance.
#include <iostream> #include <TMath.h> #include <TH1.h> #include <TChain.h> #include <TStopwatch.h> void analysis() { // Create chain for the tree Result // This is just easier than using TFile/TTree TChain c("Result"); // Add the input file to the c.AddFile("crab-data-only.root"); // Define variables for all leaves to be accessed // By definition rootifysql writes only doubles double X, Y, MeanX, MeanY, Width, Length, CosDelta, SinDelta, M3Long, SlopeLong, Leakage1, SlopeSpreadWeighted, Size, ConcCore, ConcCOG, NumIslands, NumUsedPixels; // Connect the variables to the cordesponding leaves c.SetBranchAddress("X", &X); c.SetBranchAddress("Y", &Y); c.SetBranchAddress("MeanX", &MeanX); c.SetBranchAddress("MeanY", &MeanY); c.SetBranchAddress("Width", &Width); c.SetBranchAddress("Length", &Length); c.SetBranchAddress("CosDelta", &CosDelta); c.SetBranchAddress("SinDelta", &SinDelta); c.SetBranchAddress("M3Long", &M3Long); c.SetBranchAddress("SlopeLong", &SlopeLong); c.SetBranchAddress("Leakage1", &Leakage1); c.SetBranchAddress("NumIslands", &NumIslands); c.SetBranchAddress("NumUsedPixels", &NumUsedPixels); c.SetBranchAddress("SlopeSpreadWeighted", &SlopeSpreadWeighted); c.SetBranchAddress("Size", &Size); c.SetBranchAddress("ConcCOG", &ConcCOG); c.SetBranchAddress("ConcCore", &ConcCore); // Set some constants (they could be included in the database // in the future) double mm2deg = +0.0117193246260285378; double abberation = 1.02; // -------------------- Source dependent parameter calculation ------------------- // Create a histogram for on- and off-data TH1F hon("on", "", 55, 0, 1); TH1F hoff("off", "", 55, 0, 1); // Loop over all events TStopwatch clock; for (int i=0; i<c.GetEntries(); i++) { // read the i-th event from the file c.GetEntry(i); // First calculate all cuts to speedup the analysis double area = TMath::Pi()*Width*Length; bool cutq = NumIslands<3.5 && NumUsedPixels>5.5 && Leakage1<0.1; bool cut0 = log10(area)<log10(Size)*898-1535; if (!cutq || !cut0) continue; // Loop over all wobble positions in the camera for (int angle=0; angle<360; angle+=60) { // -------------------- Source dependent parameter calculation ------------------- double cr = cos(angle*TMath::DegToRad()); double sr = sin(angle*TMath::DegToRad()); double px = cr*X-sr*Y; double py = cr*Y+sr*X; double dx = MeanX - px/abberation; double dy = MeanY - py/abberation; double dist = sqrt(dx*dx + dy*dy); double alpha = asin((CosDelta*dy - SinDelta*dx)/dist); double sgn = TMath::Sign(1., (CosDelta*dx + SinDelta*dy)/dist); // ------------------------------- Application ---------------------------------- double m3l = M3Long*sgn*mm2deg; double slope = SlopeLong*sgn/mm2deg; // --------------------------------- Analysis ----------------------------------- double xi = 1.39252 + 0.154247*slope + 1.67972 *(1-1/(1+4.86232*Leakage1)); double sign1 = m3l+0.07; double sign2 = (dist*mm2deg-0.5)*7.2-slope; double disp = (sign1<0 || sign2<0 ? -xi : xi)*(1-Width/Length)/mm2deg; double thetasq = (disp*disp + dist*dist - 2*disp*dist*cos(alpha))*mm2deg*mm2deg; // Fill the on- and off-histograms if (angle==0) hon.Fill(thetasq); else hoff.Fill(thetasq, 1./5); } } clock.Print(); // Plot the result hon.SetMinimum(0); hon.DrawCopy(); hoff.DrawCopy("same"); }
You can of course include all the calculations into your query already
SELECT Events.*, Angle, weight, @PX := cosa*X - sina*Y, @PY := cosa*Y + sina*X, @DX := MeanX-@PX/1.02, @DY := MeanY-@PY/1.02, @Norm := SQRT(@DX*@DX + @DY*@DY), @Dist := @Norm*0.0117193246260285378 AS Dist, PI()*Width*Length*0.0117193246260285378*0.0117193246260285378 AS Area, @LX := TRUNCATE((CosDelta*@DY - SinDelta*@DX)/@Norm, 6), @LY := TRUNCATE((CosDelta*@DX + SinDelta*@DY)/@Norm, 6), @Alpha := ASIN(@LX) AS Alpha, @Sign := SIGN(@LY) AS Sign, @M3L := M3Long*@Sign*0.0117193246260285378, @Slope := SlopeLong*@Sign/0.0117193246260285378 AS Slope, @Xi := 1.39 + 0.154*@Slope + 1.679*(1-1/(1+4.86*Leakage1)), @Sign1 := @M3L+0.07, @Sign2 := (@Dist-0.5)*7.2-@Slope, @Disp := IF (SIGN(@Sign1)<0 || SIGN(@Sign2)<0, -@Xi, @Xi) * (1-Width/Length), @ThetaSq := (@Disp*@Disp + @Dist*@Dist - 2*@Disp*@Dist*SQRT(1-@LX*@LX)) AS ThetaSq FROM RunInfo LEFT JOIN Events USING (FileId) LEFT JOIN Position USING (FileId, EvtNumber) CROSS JOIN ( SELECT 0 AS Angle UNION ALL SELECT 60 AS Angle UNION ALL SELECT 120 AS Angle UNION ALL SELECT 180 AS Angle UNION ALL SELECT 240 AS Angle UNION ALL SELECT 300 AS Angle ) Wobble60deg WHERE fSourceKey=5 AND fRunTypeKey=1 AND FileId BETWEEN 131101000 AND 131107000 AND fZenithDistanceMax<35 AND fR750Ref/fR750Cor>0.9
Or you use the existing table for the standard 60° Wobble positions and do just CROSS JOIN Wobble.
This will give you all you need in crab.root (rootifysql --out=crab.root), but significantly increases computing time and the output file will be about six times larger.
A simple macro just applying all the cuts would then be enough to do a theta-square plot
void analysis() { // Create chain for the tree Result // This is just easier than using TFile/TTree TChain c("Result"); // Add the input file to the c.AddFile("crab.root"); // Set some constants (they could be included in the database // in the future) c.SetAlias("mm2deg", "+0.0117193246260285378"); // Define the cuts c.SetAlias("CutQ", "NumIslands<3.5 && NumUsedPixels>5.5 && Leakage1<0.1"); c.SetAlias("Cut0", "log10(Area)<log10(Size)*898-1535"); // Do one plot for each wobble position c.Draw("ThetaSq", "(ThetaSq<1 && CutQ && Cut0 && Angle==0)*( weight)"); c.Draw("ThetaSq", "(ThetaSq<1 && CutQ && Cut0 && Angle!=0)*(-weight)", "same"); }
Combining everything into a single query is a bit tricky but works:
SELECT Counter.*, `Signal` - `Background`/5 AS `Excess`, LiMa(`Signal`, `Background`/5) AS `Significance` FROM ( SELECT COUNT(IF(Weight>0, 1, NULL)) AS `Signal`, COUNT(IF(Weight<0, 1, NULL)) AS `Background` FROM ( SELECT Size, NumUsedPixels, NumIslands, Leakage1, Weight, PI()*Width*Length AS Area, @PX := cosa*X - sina*Y, @PY := cosa*Y + sina*X, @DX := MeanX-@PX/1.02, @DY := MeanY-@PY/1.02, @Norm := SQRT(@DX*@DX + @DY*@DY), @Dist := @Norm*0.0117193246260285378 AS Dist, @LX := TRUNCATE((CosDelta*@DY - SinDelta*@DX)/@Norm, 6), @LY := TRUNCATE((CosDelta*@DX + SinDelta*@DY)/@Norm, 6), @Alpha := ASIN(@LX) AS Alpha, @Sign := SIGN(@LY) AS Sign, @M3L := M3Long*@Sign*0.0117193246260285378, @Slope := SlopeLong*@Sign/0.0117193246260285378 AS Slope, @Xi := 1.39252 + 0.154247*@Slope + 1.67972*(1-1/(1+4.86232*Leakage1)), @Sign1 := @M3L+0.07, @Sign2 := (@Dist-0.5)*7.2-@Slope, @Disp := IF (SIGN(@Sign1)<0 || SIGN(@Sign2)<0, -@Xi, @Xi) * (1-Width/Length), @ThetaSq := (@Disp*@Disp + @Dist*@Dist - 2*@Disp*@Dist*SQRT(1-@LX*@LX)) AS ThetaSq FROM RunInfo LEFT JOIN Events USING (FileId) LEFT JOIN Position USING (FileId, EvtNumber) CROSS JOIN Wobble WHERE fSourceKey=5 AND fRunTypeKey=1 AND FileId BETWEEN 131101000 AND 131107000 AND fZenithDistanceMax<35 AND fR750Cor>0.9*fR750Ref ) TableAlias WHERE ThetaSq<0.024 AND Area < LOG10(Size)*898-1535 AND NumUsedPixels>5.5 AND NumIslands<3.5 AND Leakage1<0.1 ) Counter
The output in mysql looks something like:
+--------+------------+----------+-------------------+ | Signal | Background | Excess | Significance | +--------+------------+----------+-------------------+ | 984 | 2205 | 543.0000 | 19.72239008502298 | +--------+------------+----------+-------------------+ 1 row in set (2 min 5.48 sec)
Or like this if you finish the query with "\G" instead of a semicolon:
*************************** 1. row ***************************
Signal: 984
Background: 2205
Excess: 543.0000
Significance: 19.72239008502298
1 row in set (2 min 0.02 sec)
I am sure there is also a query which in addition prints the effective on-time.
WARNING: SQL User Variables
The MySQL Reference manual warns explicitly
As a general rule, other than in SET statements, you should never assign a value to a user variable and read the value within the same statement.
This is explain in the manual in more details here: https://dev.mysql.com/doc/refman/8.0/en/user-variables.html
So generally speaking, the above example is supposed to FAIL! (...and works only by chance...)
I have kept that here for convenience (and with the current server, it works, simply because the optimizer does not shuffle the columns.
Now let's have a look at how the query should look correctly ( Don't panic! ):
SELECT Counter.*, `Signal` - `Background`/5 AS `Excess`, LiMa(`Signal`, `Background`/5) AS `Significance` FROM ( /* Counter */ SELECT COUNT(IF(Weight>0, 1, NULL)) AS `Signal`, COUNT(IF(Weight<0, 1, NULL)) AS `Background` FROM ( /* Table9 */ SELECT Weight, (Disp*Disp + Dist*Dist - 2*Disp*Dist*SQRT(1-LX*LX)) AS ThetaSq FROM ( /* Table8 */ SELECT Weight, Dist, LX, IF (SIGN(Sign1)<0 || SIGN(Sign2)<0, -Xi, Xi) * (1-WL) AS Disp FROM ( /* Table7 */ SELECT Weight, WL, Dist, LX, 1.39252 + 0.154247*Slope + 1.67972*(1-1/(1+4.86232*Leakage1)) AS Xi, M3L+0.07 AS Sign1, (Dist-0.5)*7.2-Slope AS Sign2 FROM ( /* Table6 */ SELECT Weight, Leakage1, WL, LX, Norm *0.0117193246260285378 AS Dist, M3Long *Sign*0.0117193246260285378 AS M3L, SlopeLong*Sign/0.0117193246260285378 AS Slope FROM ( /* Table5 */ SELECT Weight, M3Long, SlopeLong, Leakage1, Norm, WL, LX, ASIN(LX) AS Alpha, SIGN(LY) AS Sign FROM ( /* Table4 */ SELECT Weight, M3Long, SlopeLong, Leakage1, Norm, WL, TRUNCATE((CosDelta*DY - SinDelta*DX)/Norm, 6) AS LX, TRUNCATE((CosDelta*DX + SinDelta*DY)/Norm, 6) AS LY FROM ( /* Table3 */ SELECT Weight, CosDelta, SinDelta, DX, DY, M3Long, SlopeLong, Leakage1, WL, SQRT(DX*DX + DY*DY) AS Norm FROM ( /* Table2 */ SELECT Weight, CosDelta, SinDelta, M3Long, SlopeLong, Leakage1, WL, MeanX - PX/1.02 AS DX, MeanY - PY/1.02 AS DY FROM ( /* Table1 */ SELECT Weight, MeanX, MeanY, CosDelta, SinDelta, M3Long, SlopeLong, Leakage1, WL, cosa*X - sina*Y AS PX, cosa*Y + sina*X AS PY FROM ( /* Table0 */ SELECT Weight, Size, NumUsedPixels, NumIslands, Leakage1, MeanX, MeanY, CosDelta, SinDelta, M3Long, SlopeLong, Width/Length AS WL, PI()*Width*Length AS Area, cosa, sina, X, Y FROM RunInfo LEFT JOIN Events USING (FileId) LEFT JOIN Position USING (FileId, EvtNumber) CROSS JOIN Wobble WHERE fSourceKey=5 AND fRunTypeKey=1 AND FileId BETWEEN 131101000 AND 131107000 AND fZenithDistanceMax<35 AND fR750Cor>0.9*fR750Ref AND NumUsedPixels>5.5 AND NumIslands<3.5 AND Leakage1<0.1 ) Table0 WHERE Area < LOG10(Size)*898-1535 ) Table1 ) Table2 ) Table3 ) Table4 ) Table5 ) Table6 ) Table7 ) Table8 HAVING ThetaSq<0.024 ) Table9 ) Counter
Now what makes the difference... first, execution time shows the power of MySQL. The old query leads:
Execution time: 122.145s
This new query results in
Execution time: 14.7086s
Note that this is the result of the analysis of a dataset which, as a whole, is more than 100GB and even reduced to Crab after quality cuts still is of the order of GB! As a comparison. The source code which does all the calculations in compiled C++ code takes about 4.5s on the same machine.
Why is this query so much faster? I guess it has two reasons:
1) Only variables which are really needed in the next step are kept (reduces memory consumption) 2) Cuts are evaluated by the optimizer as soon as possible (e.g. the Area cuts might be evaluated even before the other values are loaded from disk)
Another example (apart from the obvious difficulty to read the query) is that it is very well structured. For each step it is very well defined what values are available from the previous step (the fields which are requested in each SELECT statement) and it is very well defined in which order the algorithm is executed.
If somebody find a way to write that query in an easier readable way, I would be glad to know.
Generally, it is not recommended to run the full analysis on the server - as long as you want to optimize or change things. Running it on the server only makes sense if you have finished optimizing your analysis and want to process a lot of data (as in an automatic process).
Optimization and precision maths
A very interesting read is https://dev.mysql.com/doc/refman/5.7/en/precision-math.html (and its sub-sections! Click on NEXT).
In short: A value like 1.234 is an exact value and exact math calculation are performed. If a value is given as an approximate floating-point value (which all DOUBLE columns are), for example 1.234e0, the calculation is not exact. Not exact means that it using (faster) floating-point arithmetic rather than (slower) exact arithmetic.
Now, any mathematical operation which at least contains one floating-point number is evaluated as a floating-point approximation. This sounds very simple and as if it has nothing to do with our analysis, but it has:
All the numbers in the previous SQL queries were given as exact numbers and thus stored by the engine as exact numbers. Whenever they take place in one of our calculations, they have to be converted to a floating-point value first (it seems this does not happen in advance but during run-time), which is an operation which is obviously not for free.
So as a test, let's append a e0 to all fractional values in the query, e.g. instead of 0.5, let's write 0.5e0 (or 5e-1). This essentially tells the SQL engine to store the value as an approximate floating-point value and not as an exact value. Now, let's run the query again...
And voila!
Execution time: 10.0701s
This is again much faster!
Conclusion: Wherever you use floating-point values in your query and you are not interested in a 100% machine independent result, write them as floating-point values by appending e0 instead of exact values. For integer values (numbers without fractional parts) this is not needed. They mix well with floating-point values and thus no internal conversion is required.
