3.2 Random Groups

  The random groups structure (Greisen and Harten 1981) was originally designed for applications in radio astronomy but was intended for other applications as well. It never gained acceptance outside the radio interferometry community, and some FITS readers designed for other communities cannot read it. In addition, the random groups records are a structural anomaly in FITS, as they are the only records that do not conform to the primary HDU - extensions - special records sequence. All of the original objectives originally intended for random groups can now be achieved through the use of the now standard binary table format described in section 3.6. Even the interferometry community, for whom random groups was originally intended, is developing new conventions based upon binary tables. Do not create FITS files using random groups; use binary tables instead. The description of random groups presented here is intended as a reference for those who may have to read old random groups FITS files, not as an encouragement to write them. A number of keywords have been reserved for the random groups structure, and may not be used for any other purpose, unless specifically stated in the FITS rules. Also, the random groups structure is the original source of the PCOUNT and GCOUNT keywords that were incorporated into the Generalized Extensions rules discussed in section 3.3.

While the basic array structure of FITS can handle a data matrix when the data are distributed evenly along all axes, sometimes the data may not be distributed uniformly along one or more axes. The random groups structure was created to handle such situations. Instead of being followed by a data array, the primary header is followed by a special set of records, of standard FITS 23040-bit size, called random groups records. These records contain a series of groups, each consisting of a sequence of parameters followed by an array. The parameters carry the data whose spacing is not uniform and which are not ordered, i.e., random, hence the name. The number of random parameters and the dimensions of the array must be the same in all groups.

On application is for uv interferometric visibility data; in fact, random groups are sometimes referred to as UV FITS. Consider a set of weighted complex fringe visibilities for the four Stokes polarizations at a sequence of evenly spaced frequencies. The axes are u, v, w, hour angle, baseline, fringe visibility information (real part, complex part, and weight), Stokes parameter, and frequency. The points along the frequency axis are evenly spaced, and the fringe visibility and Stokes axes can both be handled by using ``evenly spaced'' integer index points to represent the separate components - real, complex, and weight - for the visibility and the four Stokes parameters. Thus, an individual observation can easily be structured as a matrix with axes of visibility components, Stokes parameter, and frequency. However, the individual matrices are at nonuniformly distributed values of baseline, hour angle, and (u, v, w).

Using the random groups structure, the values of baseline, hour angle, and (u, v, w) would be specified as parameters before each (visibility, polarization, frequency) matrix. The combination of parameters and array constitutes a group. The structure of the group would be given by the form

 

$$\vert r_{1}, r_{2}, r_{3}, r_{4}, \ldots , r_{N}\vert p_{111}, p_{112}, \ldots , p_{lmn}\vert$$ (3.6)

corresponding, in this example, to

|u, v, w, time, baseline|(visibility component, Stokes parameter, frequency)|

where $r_{1}, \ldots ,r_{N}$are random parameters 1 through N and $p_{111}, \ldots , p_{lmn}$are pixel values in the order defined for a data matrix. The value of p could, in principle, be as large as 998 for each axis, as opposed to the 999 maximum for Basic FITS. The data array p_ijk starts immediately after the last parameter, r_N. The storage order and internal representation of a random groups data array are the same as for a Basic FITS simple array. It is interesting to note that the Basic FITS data structure is actually a subset of this more general structure, with no parameters.