Author: Sergey Koposov, Institute of Astronomy, Cambridge, UK

Copyright (c) 2004-2016 Sergey Koposov

Email: [email protected]

Idea and implementation by Sergey Koposov with help from Oleg Bartunov.

Fresh versions of the software could be obtained here: https://github.com/segasai/q3c

To read more about the Q3C indexing, please read the Q3C paper published in ADASS conference proceedings http://adsabs.harvard.edu/abs/2006ASPC..351..735K The citation is "Koposov, S., & Bartunov, O. 2006, Astronomical Society of the Pacific Conference Series, 351, 735" If you use Q3C you are kindly asked to cite this paper. I would be also happy to hear about any usage of Q3C.

To work with Q3C you will only need to have a PostgreSQL database installed (version 9.1 or later). If you have PostgreSQL version lower than 9.1 your will need an older version of Q3C (1.4.x).

• make
• make install
• Execute "create extension q3c" in PostgreSQL client

Note: To successfully compile Q3C have to have pg_config in your PATH

After the installation you will have several new functions in PostgreSQL. All names of these functions start with the "q3c_" prefix.

To begin use Q3C for searches and cross-matches you should create the indexes on the tables.

In this demonstration we'll assume that you have the table called "mytable" with "ra" and "dec" columns (right ascension and declination in degrees).

First, you will need to create the spatial index, using the following command:

my_db# CREATE INDEX ON mytable (q3c_ang2ipix(ra, dec));

The next procedure is optional but strongly recommended: cluster the table using newly created index. The clustering procedure is the procedure of ordering the data on the disk according to the Q3C spatial index values, which will ensure faster queries. If the data have been ingested in the database while ordered by some spherical zones, the clustering step can be ommited (although still recommended). The clustering step may take a while if your dataset is large.

my_db# CLUSTER q3c_mytable_idx ON mytable;

Now the last step is analyzing your table:

my_db# ANALYZE mytable;

Now you should be able to use q3c queries.

IMPORTANT Throughout q3c it is assumed that all the angles are in degrees.

The functions installed by Q3C are:

• q3c_ang2ipix(ra, dec) -- returns the ipix value at ra and dec

• q3c_dist(ra1, dec1, ra2, dec2) -- returns the distance in degrees between (ra1,dec1) and (ra2,dec2)

• q3c_join(ra1, dec1, ra2, dec2, radius) -- returns true if (ra1, dec1) is within radius spherical distance of (ra2, dec2). It should be used when the index on q3c_ang2ipix(ra2, dec2) is created. See below for examples.

• q3c_ellipse_join(ra1, dec1, ra2, dec2, major, ratio, pa) -- like q3c_join, except (ra1, dec1) have to be within an ellipse with major axis major, the axis ratio ratio and the position angle pa (from north through east)

• q3c_radial_query(ra, dec, center_ra, center_dec, radius) -- returns true if ra, dec is within radius degrees of center_ra, center_dec. This is the main function for cone searches. This function should be used when the index on q3c_ang2ipix(ra,dec) is created.

• q3c_ellipse_query(ra, dec, center_ra, center_dec, maj_ax, axis_ratio, PA ) -- returns true if ra, dec is within the ellipse from center_ra, center_dec. The ellipse is specified by major axis, axis ratio and positional angle. This function should be used if when the index on q3c_ang2ipix(ra,dec) is created.

• q3c_poly_query(ra, dec, poly) -- returns true if ra, dec is within the postgresql polygon poly specified as an array of right ascensions and declinations.

• q3c_ipix2ang(ipix) -- returns a 2-array of (ra,dec) corresponding to ipix.

• q3c_pixarea(ipix, bits) -- returns the area corresponding to ipix at level bits (1 is smallest, 30 is the cube face) in steradians.

• q3c_ipixcenter(ra, dec, bits) -- the function returning the ipix value of the pixel center of certain depth covering the specified (ra,dec)

• q3c_version() -- returns the version of Q3C that is installed

• The cone search (the query of all objects within the circular region of the sky): For example to query all objects within radius of 0.1 deg from (ra,dec) = (11,12)deg in the table mytable you should do:

my_db# SELECT * FROM mytable WHERE q3c_radial_query(ra, dec, 11, 12, 0.1);

  The order of arguments is important, so that the column names of the table should come first, and the 
  location where you search after, otherwise the index won't be used.

  There is also another way of doing cone searches which may be appropriate if the
  table that you are working with is small. In that case q3c_radial_query may 
  be too CPU heavy. So you may want to query the table:

my_db# SELECT * FROM mytable WHERE q3c_join(11, 12, ra, dec, 0.1);

- The ellipse search: search for objects within the ellipse from a given point:

my_db=# select * from mytable WHERE q3c_ellipse_query(ra, dec, 10, 20, 1, 0.5 ,10);

  returns the objects which are within the ellipse with the center at (ra,dec)=(10,20)
  major axis of 1 degree, axis ratio of 0.5 and positional angle of 10 degrees.

- The polygonal query, i.e. the query of the objects which lie inside the region
  bounded by the polygon on the sphere. 
  
  To query the objects in the polygon ((0,0),(2,0),(2,1),(0,1)) )
  (this is the spherical polygon with following vertices:
  (ra=0, dec=0) ; (ra=2, dec=0); (ra=2, dec=1); (ra=0, dec=1)):

my_db# SELECT * FROM mytable WHERE q3c_poly_query(ra, dec, '{0, 0, 2, 0, 2, 1, 0, 1}');

- The positional cross-match of the tables:
  In this example we will assume that we have a huge table "table2" with ra and dec columns and
  an already created Q3C index on them and a smaller table "table1" with ra and dec columns.
  
  Now, if we want to cross-match the tables "table1" and "table2" by position 
  with the crossmatch radius of say 0.001 degrees, we would do it with the following query:
  

my_db# SELECT * FROM table1 AS a, table2 AS b WHERE q3c_join(a.ra, a.dec, b.ra, b.dec, 0.001);

  
  The order of arguments is important again, because it determines whether an
  index is going to be used or not. The ra,dec columns from the table with the 
  index should go after the ra,dec columns from the table without the index.

  It is important that the query will return *ALL* the pairs within the matching distance, rather than 
  say nearest neighbors. For nearest neighbors see below.
  
  If every object in the table1 have his own error circle, here we'll assume 
  that the radius of that circle in degrees is stored in the column "err",
  then you should run the query:
  

my_db# SELECT * FROM table1 AS a, table2 AS b WHERE q3c_join(a.ra, a.dec, b.ra, b.dec, a.err);

- The positional cross-match of the tables with the ellipse error-area:
  (for example if you want to find all the objects from one catalogue which lies
  inside the elliptical bodies of the galaxies from the second catalogue)
  
  It is possible to do the join when the error area of each record of the 
  catalogue is an ellipse. Then you can do the query like this

my_db# SELECT * FROM table1 AS a, table2 AS b WHERE q3c_ellipse_join(a.ra, a.dec, b.ra, b.dec, a.maj_ax a.axis_ratio, a.PA);

  where axis_ratio is the column with axis ratio of the ellipses and PA is the 
  column with the positional angles of them, and maj_ax is the column with major
  axises of those ellipses.
  
- The density estimation of your objects using pixelation depth of 25:

my_db# SELECT (q3c_ipix2ang(i))[1] as ra ,(q3c_ipix2ang(i))[2] as dec ,c, q3c_pixarea(i,25) as area from (select q3c_ipixcenter(ra,dec, 25) as i, count(*) as c from mytable group by i) as x;

  returns the list of ra,dec of the Q3C pixel center, number of objects
  within a given pixel, and pixel area. If you use that query you should
  keep in mind that Q3C doesn't have the property of uniform pixel areas (as 
  opposed to HEALPIX).

- Nearest neighbor queries: 

  This query selects the only nearest neighbor for each row in your table. If there is no neighbor, 
  the columns are filled with nulls.

my_db# SELECT t., ss. FROM mytable AS t, LEFT JOIN LATERAL ( SELECT s.* FROM sdssdr9.phototag AS s WHERE q3c_join(t.ra, t.dec, s.ra, s.dec, 1./3600) ORDER BY q3c_dist(t.ra,t.dec,s.ra,s.dec) ASC LIMIT 1 ) as ss ON true;

  The idea is very simple for every row of your table mytable LATERAL() executes the "subquery" orders them by distance and limit by 1.
  
  If you want only the objects which do have the neighbors then the query will look like that
  

my_db# SELECT t., ss. FROM mytable AS t, LATERAL ( SELECT s.* FROM sdssdr9.phototag AS s WHERE q3c_join(t.ra, t.dec, s.ra, s.dec, 1./3600) ORDER BY q3c_dist(t.ra,t.dec,s.ra,s.dec) ASC LIMIT 1 ) as ss ;

-  Nearest neighbor 2 

  This query selects the only nearest neighbor for each row in your table. If there are no neighbor, the columns are filled with nulls. This query requires presence of some object id column with the index on the table.

my_db# WITH x AS ( SELECT *, ( SELECT objid FROM sdssdr9.phototag AS p WHERE q3c_join(m.ra, m.dec, p.ra, p.dec, 1./3600) ORDER BY q3c_dist(m.ra, m.dec, p.ra, p.dec) ASC LIMIT 1) AS match_objid FROM mytable AS m ) SELECT * FROM x, sdssdr9.phototag AS s WHERE x.match_objid=s.objid;