HEALPix for MySQL

MySQL wrapper of some of the functions provided by the HEALPix library. For a more detailed description of what these function do please see the documentation here.

Installation

• Make sure you have MySQL (>=5.5) sources. Also, make sure that mysql_config and mysqlbug are available.
• Edit CMakeList.txt and point it to the directory where mysql and its sources are installed.
• Compile:

mkdir build
cd build
cmake ..
make
make install

• Log into mysql server as root and run:

source install_healpix.sql

• If you feel like you don't like it for some reason, uninstall it with

source uninstall_healpix.sql

Usage

Currently, only functions for computing the HEALPix index from a pair or coordinates and 3D vectors, and their inverses are supported. Both work for the RING ordering (default) as well as the NESTED ordering. In addition, given a pixel number and ordering scheme, all 8 neighbours can be computed.

To get a HEALPix value for a set of two coordinates:

SELECT ang2pix(64, 0.23, 1.3);
SELECT ang2pix(64, 0.23, 1.3, 'nest');

If the polar angle is out of bounds ([0, PI]), the function returns -1.

As a more real-world example we might want to compute the HEALPix indices using nside=128 for the stars inside the tycho2 catalog:

SELECT RA. DE, ang2pix(128, RADIANS(DE + 90), RADIANS(RA)) AS healpix FROM tycho2;

Note that the first argument to ang2pix() is the polar angle and runs between 0 and PI, therefore we need to add 90 degrees to the declination column.

To add them permanently to the tycho2 table, we can create a new column and update it with computed HEALPix values.

ALTER TABLE tycho2 ADD COLUMN healpix INT(11) AFTER ...;
UPDATE tycho2 SET healpix=ang2pix(128, RADIANS(DE + 90), RADIANS(RA));

Going the other direction is more annoying because MySQL doesn't allow returning multiple values so multiple function calls are necessary. To get coordinates of a pixel:

SELECT pix2ang(128, 3312, 1), pix2ang(128, 3312, 2);
SELECT pix2ang(128, 3312, 1, 'nest'), pix2ang(128, 3312, 2, 'nest');

We can also get the i-th neighbour ([1, 8]) of any pixel by issuing

SELECT neighbours(128, 3312, i);
SELECT neighbours(128, 3312, i, 'nest');

Note that not all pixels always have 8 neighbours. In those cases -1 is returned as the neighbour pixel value.

For a few more supported functions see the test.sql.

Credits & License

Written by Gal Matijevic // E-Science group // AIP

Based on the mysql_sphere plugin by Adrian M. Partl.

Original HEALPix library by Krzysztof M. Gorski, Eric Hivon, Martin Reinecke, Benjamin D. Wandelt, Anthony J. Banday, Matthias Bartelmann, Reza Ansari & Kenneth M. Ganga

C++ HEALPix port by Martin Reinecke, Max-Planck-Society

Licensed under the GPL License.