[fitsbits] Interpretation of repeat count in binary tables

[William Pence]

Paddy,

In the example you cite below, the binary table contains 12288 rows of 
data, and each row contains 3 vectors, containing 1024 single precision 
floating point numbers leash.  There is no explicit relationship between 
the vectors in different rows of the table.  Structurally, the table 
begins with the 1024 element vector in the first column and first row, 
followed by the vectors in the 2nd and 3rd columns in the first row. 
These are followed by the 3 vectors in the 2nd row, then the 3rd row, 
and finally ending with the 3 vectors in the 12288th row.

The TDIMn keyword, if present in this case, would specify the 
dimensionality of each individual 1024 element vector in that column. 
For example, TDIM1 = '(16,64)', would mean that each vector in column 1 
should be interpreted as a 16 x 64 2D array.  If there is no TDIMn 
keyword, then the vector would be interpreted as a 1024 element 1-D array.

Bill Pence

Paddy Leahy wrote:
> Is the repeat count in TFORM descriptors provided purely for efficiency 
> reasons, or does it have some implications for the logical structure of 
> the data? Specifically, suppose we have
> 
> NAXIS1  =                12288 / width of table in bytes
> NAXIS2  =                12288 / number of rows in table
> ...
> TFIELDS = 3
> TFORM1 = '1024E'
> TFORM2 = '1024E'
> TFORM3 = '1024E'
> 
> Should the three columns each be interpreted as a 1024 x 12288 element 
> 2-D array, or as a 12582912-element 1-D array? The first implies that if 
> TFORMn = 'rTa', the default value of TDIMn = '(r)'. The second implies 
> that if TDIMn is not explicitly specified then the repeat count is just 
> provided for (rather spurious) efficiency reasons. Some FITS writers 
> certainly use it as such.
> 
> This question arises out of pure ignorance, but I have failed to find an 
> answer in either the original binary table paper (Cotton et al 1995) or
> the current (2.0) or draft (3.0) FITS standards. In fact, none of these 
> documents give any hint as to what the repeat count is for (unless TDIMn
> is explicitly present, or it is a character field).
> 
> regards,
>  		Paddy
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