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- Less Familiar Objects

# Less Familiar Objects

In this chapter, we’ll discuss less frequently used FITS data structures. They include ASCII tables, variable length tables, and random access group FITS files.

## ASCII Tables

FITS standard supports both binary and ASCII tables. In ASCII tables, all the data are stored in a human readable text form, so it takes up more space and extra processing to parse the text for numeric data. Depending on how the columns are formatted, floating point data may also lose precision.

In Astropy, the interface for ASCII tables and binary tables is basically the same, i.e. the data is in the `.data` attribute and the `field()` method is used to refer to the columns and returns a numpy array. When reading the table, Astropy will automatically detect what kind of table it is.

    >>> from astropy.io import fits
    >>> hdus = fits.open('ascii_table.fits')
    >>> hdus[1].data[:1]
    FITS_rec(
    ... [(10.123000144958496, 37)],
    ... dtype=[('a', '>f4'),('b','>i4')])
    >>> hdus[1].data['a']
    array([ 10.12300014, 5.19999981, 15.60999966, 0. ,
    345. ], dtype=float32)
    >>> hdus[1].data.formats
    ['E10.4', 'I5']

Note that the formats in the record array refer to the raw data which are ASCII strings (therefore ‘a11’ and ‘a5’), but the `.formats` attribute of data retains the original format specifications (‘E10.4’ and ‘I5’).

### Creating an ASCII Table

Creating an ASCII table from scratch is similar to creating a binary table. The difference is in the Column definitions. The columns/fields in an ASCII table are more limited than in a binary table. It does not allow more than one numerical value in a cell. Also, it only supports a subset of what allowed in a binary table, namely character strings, integer, and (single and double precision) floating point numbers. Boolean and complex numbers are not allowed.

The format syntax (the values of the TFORM keywords) is different from that of a binary table, they are:

    Aw         Character string
    Iw         (Decimal) Integer
    Fw.d       Single precision real
    Ew.d       Single precision real, in exponential notation
    Dw.d       Double precision real, in exponential notation

where, w is the width, and d the number of digits after the decimal point. The syntax difference between ASCII and binary tables can be confusing. For example, a field of 3-character string is specified ‘3A’ in a binary table and as ‘A3’ in an ASCII table.

The other difference is the need to specify the table type when using the `TableHDU.from_columns()` method, and that `Column` should be provided the `ascii=True` argument in order to be unambiguous.

Note

Although binary tables are more common in most FITS files, earlier versions of the FITS format only supported ASCII tables. That is why the class `TableHDU` is used for representing ASCII tables specifically, whereas `BinTableHDU` is more explicit that it represents a binary table. These names come from the value `XTENSION` keyword in the tables’ headers, which is `TABLE` for ASCII tables and `BINTABLE` for binary tables.

`TableHDU.from_columns()` can be used like so:

    >>> import numpy as np
    >>> from astropy.io import fits
    >>> a1 = np.array(['abcd', 'def'])
    >>> r1 = np.array([11., 12.])
    >>> c1 = fits.Column(name='abc', format='A3', array=a1, ascii=True)
    >>> c2 = fits.Column(name='def', format='E', array=r1, bscale=2.3,
    ...                    bzero=0.6, ascii=True)
    >>> c3 = fits.Column(name='t1', format='I', array=[91, 92, 93],
    ...                    ascii=True)
    >>> hdu = fits.TableHDU.from_columns([c1, c2, c3])
    >>> hdu.writeto('ascii.fits')
    >>> hdu.data
    FITS_rec([('abcd', 11.0, 91), ('def', 12.0, 92), ('', 0.0, 93)],
             dtype=[('abc', '|S3'), ('def', '|S14'), ('t1', '|S10')])

It should be noted that when the formats of the columns are unambiguously specific to ASCII tables it is not necessary to specify `ascii=True` in the `ColDefs` constructor. In this case there is ambiguity because the format code `'I'` represents a 16-bit integer in binary tables, while in ASCII tables it is not technically a valid format. ASCII table format codes technically require a character width for each column, such as `'I10'` to create a column that can hold integers up to 10 characters wide.

However, PyFITS allows the width specification to be omitted in some cases. When it is ommitted from `'I'` format columns the minimum width needed to accurately represent all integers in the column is used. The only problem with using this shortcut is its ambiguity with the binary table `'I'` format, so specifying `ascii=True` is a good practice (though PyFITS will still figure out what you meant in most cases).

## Variable Length Array Tables

The FITS standard also supports variable length array tables. The basic idea is that sometimes it is desirable to have tables with cells in the same field (column) that have the same data type but have different lengths/dimensions. Compared with the standard table data structure, the variable length table can save storage space if there is a large dynamic range of data lengths in different cells.

A variable length array table can have one or more fields (columns) which are variable length. The rest of the fields (columns) in the same table can still be regular, fixed-length ones. Astropy will automatically detect what kind of field it is during reading; no special action is needed from the user. The data type specification (i.e. the value of the TFORM keyword) uses an extra letter ‘P’ and the format is

    rPt(max)

where `r` may be 0 or 1 (typically omitted, as it is not applicable to variable length arrays), `t` is one of the letter codes for basic data types (L, B, I, J, etc.; currently, the X format is not supported for variable length array field in Astropy), and `max` is the maximum number of elements of any array in the column. So, for a variable length field of int16, the corresponding format spec is, e.g. ‘PJ(100)’:

    >>> f = fits.open('variable_length_table.fits')
    >>> print f[1].header['tform5']
    1PI(20)
    >>> print f[1].data.field(4)[:3]
    [array([1], dtype=int16) array([88, 2], dtype=int16)
    array([ 1, 88, 3], dtype=int16)]

The above example shows a variable length array field of data type int16. Its first row has one element, second row has 2 elements etc. Accessing variable length fields is almost identical to regular fields, except that operations on the whole field simultaneously are usually not possible. A user has to process the field row by row as though they are independent arrays.

### Creating a Variable Length Array Table

Creating a variable length table is almost identical to creating a regular table. The only difference is in the creation of field definitions which are variable length arrays. First, the data type specification will need the ‘P’ letter, and secondly, the field data must be an objects array (as included in the numpy module). Here is an example of creating a table with two fields, one is regular and the other variable length array:

    >>> from astropy.io import fits
    >>> import numpy as np
    >>> c1 = fits.Column(name='var', format='PJ()',
    ...                  array=np.array([[45., 56]
    ...                                  [11, 12, 13]],
    ...                                 dtype=np.object))
    >>> c2 = fits.Column(name='xyz', format='2I', array=[[11, 3], [12, 4]])
    >>> tbhdu = fits.BinTableHDU.from_columns([c1, c2])
    >>> print tbhdu.data
    FITS_rec([(array([45, 56]), array([11,  3], dtype=int16)),
           (array([11, 12, 13]), array([12,  4], dtype=int16))],
          dtype=[('var', '<i4', 2), ('xyz', '<i2', 2)])
    >>> tbhdu.writeto('var_table.fits')
    >>> hdu = fits.open('var_table.fits')
    >>> hdu[1].header
    XTENSION= 'BINTABLE'       / binary table extension
    BITPIX  =                8 / array data type
    NAXIS   =                2 / number of array dimensions
    NAXIS1  =               12 / length of dimension 1
    NAXIS2  =                2 / length of dimension 2
    PCOUNT  =               20 / number of group parameters
    GCOUNT  =                1 / number of groups
    TFIELDS =                2 / number of table fields
    TTYPE1  = 'var '
    TFORM1  = 'PJ(3) '
    TTYPE2  = 'xyz '
    TFORM2  = '2I '

## Random Access Groups

Another less familiar data structure supported by the FITS standard is the random access group. This convention was established before the binary table extension was introduced. In most cases its use can now be superseded by the binary table. It is mostly used in radio interferometry.

Like Primary HDUs, a Random Access Group HDU is always the first HDU of a FITS file. Its data has one or more groups. Each group may have any number (including 0) of parameters, together with an image. The parameters and the image have the same data type.

All groups in the same HDU have the same data structure, i.e. same data type (specified by the keyword BITPIX, as in image HDU), same number of parameters (specified by PCOUNT), and the same size and shape (specified by NAXISn keywords) of the image data. The number of groups is specified by GCOUNT and the keyword NAXIS1 is always 0. Thus the total data size for a Random Access Group HDU is

    |BITPIX| * GCOUNT * (PCOUNT + NAXIS2 * NAXIS3 * ... * NAXISn)

### Header and Summary

Accessing the header of a Random Access Group HDU is no different from any other HDU. Just use the .header attribute.

The content of the HDU can similarly be summarized by using the `HDUList.info()` method:

    >>> f = fits.open('random_group.fits')
    >>> print f[0].header['groups']
    True
    >>> print f[0].header['gcount']
    7956
    >>> print f[0].header['pcount']
    6
    >>> f.info()
    Filename: random_group.fits
    No. Name Type Cards Dimensions Format
    0 AN GroupsHDU 158 (3, 4, 1, 1, 1) Float32 7956 Groups
    6 Parameters

### Data: Group Parameters

The data part of a random access group HDU is, like other HDUs, in the `.data` attribute. It includes both parameter(s) and image array(s).

Show the data in 100th group, including parameters and data:

    >>> print f[0].data[99]
    (-8.1987486677035799e-06, 1.2010923615889215e-05,
    -1.011189139244005e-05, 258.0, 2445728., 0.10, array([[[[[ 12.4308672 ,
    0.56860745, 3.99993873],
    [ 12.74043655, 0.31398511, 3.99993873],
    [ 0. , 0. , 3.99993873],
    [ 0. , 0. , 3.99993873]]]]], dtype=float32))

The data first lists all the parameters, then the image array, for the specified group(s). As a reminder, the image data in this file has the shape of (1,1,1,4,3) in Python or C convention, or (3,4,1,1,1) in IRAF or FORTRAN convention.

To access the parameters, first find out what the parameter names are, with the .parnames attribute:

    >>> f[0].data.parnames # get the parameter names
    ['uu--', 'vv--', 'ww--', 'baseline', 'date', 'date']

The group parameter can be accessed by the `par()` method. Like the table `field()` method, the argument can be either index or name:

    >>> print f[0].data.par(0)[99] # Access group parameter by name or by index
    -8.1987486677035799e-06
    >>> print f[0].data.par('uu--')[99]
    -8.1987486677035799e-06

Note that the parameter name ‘date’ appears twice. This is a feature in the random access group, and it means to add the values together. Thus:

    >>> f[0].data.parnames  # get the parameter names
    ['uu--', 'vv--', 'ww--', 'baseline', 'date', 'date']
    >>> print f[0].data.par(4)[99]  # Duplicate parameter name 'date'
    2445728.0
    >>> print f[0].data.par(5)[99]
    0.10
    >>> # When accessed by name, it adds the values together if the name is
    >>> # shared by more than one parameter
    >>> print f[0].data.par('date')[99]
    2445728.10

The `par()` is a method for either the entire data object or one data item (a group). So there are two possible ways to get a group parameter for a certain group, this is similar to the situation in table data (with its `field()` method):

    >>> print f[0].data.par(0)[99]
    -8.1987486677035799e-06
    >>> print f[0].data[99].par(0)
    -8.1987486677035799e-06

On the other hand, to modify a group parameter, we can either assign the new value directly (if accessing the row/group number last) or use the `setpar()` method (if accessing the row/group number first). The method `setpar()` is also needed for updating by name if the parameter is shared by more than one parameters:

    >>> # Update group parameter when selecting the row (group) number last
    >>> f[0].data.par(0)[99] = 99.
    >>> # Update group parameter when selecting the row (group) number first
    >>> f[0].data[99].setpar(0, 99.) # or setpar('uu--', 99.)
    >>>
    >>> # Update group parameter by name when the name is shared by more than
    >>> # one parameters, the new value must be a tuple of constants or
    >>> # sequences
    >>> f[0].data[99].setpar('date', (2445729., 0.3))
    >>> f[0].data[:3].setpar('date', (2445729., [0.11, 0.22, 0.33]))
    >>> f[0].data[:3].par('date')
    array([ 2445729.11 , 2445729.22 , 2445729.33000001])

### Data: Image Data

The image array of the data portion is accessible by the `data` attribute of the data object. A numpy array is returned:

    >>> print f[0].data.data[99]
    array([[[[[ 12.4308672 , 0.56860745, 3.99993873],
    [ 12.74043655, 0.31398511, 3.99993873],
    [ 0. , 0. , 3.99993873],
    [ 0. , 0. , 3.99993873]]]]], type=float32)

### Creating a Random Access Group HDU

To create a random access group HDU from scratch, use `GroupData` to encapsulate the data into the group data structure, and use `GroupsHDU` to create the HDU itself:

    >>> # Create the image arrays. The first dimension is the number of groups.
    >>> imdata = numpy.arange(100.0, shape=(10, 1, 1, 2, 5))
    >>> # Next, create the group parameter data, we'll have two parameters.
    >>> # Note that the size of each parameter's data is also the number of
    >>> # groups.
    >>> # A parameter's data can also be a numeric constant.
    >>> pdata1 = numpy.arange(10) + 0.1
    >>> pdata2 = 42
    >>> # Create the group data object, put parameter names and parameter data
    >>> # in lists assigned to their corresponding arguments.
    >>> # If the data type (bitpix) is not specified, the data type of the
    >>> # image will be used.
    >>> x = fits.GroupData(imdata, parnames=['abc', 'xyz'],
    ...                    pardata=[pdata1, pdata2], bitpix=-32)
    >>> # Now, create the GroupsHDU and write to a FITS file.
    >>> hdu = fits.GroupsHDU(x)
    >>> hdu.writeto('test_group.fits')
    >>> hdu.header
    SIMPLE =            T / conforms to FITS standard
    BITPIX =          -32 / array data type
    NAXIS  =            5 / number of array dimensions
    NAXIS1 =            0
    NAXIS2 =            5
    NAXIS3 =            2
    NAXIS4 =            1
    NAXIS5 =            1
    EXTEND =            T
    GROUPS =            T / has groups
    PCOUNT =            2 / number of parameters
    GCOUNT =           10 / number of groups
    PTYPE1 = 'abc '
    PTYPE2 = 'xyz '
    >>> print hdu.data[:2]
    FITS_rec[
    (0.10000000149011612, 42.0, array([[[[ 0., 1., 2., 3., 4.],
    [ 5., 6., 7., 8., 9.]]]], dtype=float32)),
    (1.1000000238418579, 42.0, array([[[[ 10., 11., 12., 13., 14.],
    [ 15., 16., 17., 18., 19.]]]], dtype=float32))
    ]

## Compressed Image Data

A general technique has been developed for storing compressed image data in FITS binary tables. The principle used in this convention is to first divide the n-dimensional image into a rectangular grid of sub images or ‘tiles’. Each tile is then compressed as a continuous block of data, and the resulting compressed byte stream is stored in a row of a variable length column in a FITS binary table. Several commonly used algorithms for compressing image tiles are supported. These include, Gzip, Rice, IRAF Pixel List (PLIO), and Hcompress.

For more details, reference “A FITS Image Compression Proposal” from:

> http://www.adass.org/adass/proceedings/adass99/P2-42/

and “Registered FITS Convention, Tiled Image Compression Convention”:

> http://fits.gsfc.nasa.gov/registry/tilecompression.html

Compressed image data is accessed, in Astropy, using the optional “astropy.io.fits.compression” module contained in a C shared library (compression.so). If an attempt is made to access an HDU containing compressed image data when the compression module is not available, the user is notified of the problem and the HDU is treated like a standard binary table HDU. This notification will only be made the first time compressed image data is encountered. In this way, the compression module is not required in order for Astropy to work.

### Header and Summary

In Astropy, the header of a compressed image HDU appears to the user like any image header. The actual header stored in the FITS file is that of a binary table HDU with a set of special keywords, defined by the convention, to describe the structure of the compressed image. The conversion between binary table HDU header and image HDU header is all performed behind the scenes. Since the HDU is actually a binary table, it may not appear as a primary HDU in a FITS file.

The content of the HDU header may be accessed using the `.header` attribute:

    >>> f = fits.open('compressed_image.fits')
    >>> print f[1].header
    XTENSION= 'IMAGE   '           / extension type
    BITPIX  =                   16 / array data type
    NAXIS   =                    2 / number of array dimensions
    NAXIS1  =                  512 / length of data axis
    NAXIS2  =                  512 / length of data axis
    PCOUNT  =                    0 / number of parameters
    GCOUNT  =                    1 / one data group (required keyword)
    EXTNAME = 'COMPRESSED'         / name of this binary table extension

The contents of the corresponding binary table HDU may be accessed using the hidden `._header` attribute. However, all user interface with the HDU header should be accomplished through the image header (the `.header` attribute):

    >>> f = fits.open('compressed_image.fits')
    >>> print f[1]._header
    XTENSION= 'BINTABLE'           / binary table extension
    BITPIX  =                    8 / 8-bit bytes
    NAXIS   =                    2 / 2-dimensional binary table
    NAXIS1  =                    8 / width of table in bytes
    NAXIS2  =                  512 / number of rows in table
    PCOUNT  =               157260 / size of special data area
    GCOUNT  =                    1 / one data group (required keyword)
    TFIELDS =                    1 / number of fields in each row
    TTYPE1  = 'COMPRESSED_DATA'    / label for field   1
    TFORM1  = '1PB(384)'           / data format of field: variable length array
    ZIMAGE  =                    T / extension contains compressed image
    ZBITPIX =                   16 / data type of original image
    ZNAXIS  =                    2 / dimension of original image
    ZNAXIS1 =                  512 / length of original image axis
    ZNAXIS2 =                  512 / length of original image axis
    ZTILE1  =                  512 / size of tiles to be compressed
    ZTILE2  =                    1 / size of tiles to be compressed
    ZCMPTYPE= 'RICE_1  '           / compression algorithm
    ZNAME1  = 'BLOCKSIZE'          / compression block size
    ZVAL1   =                   32 / pixels per block
    EXTNAME = 'COMPRESSED'         / name of this binary table extension

The contents of the HDU can be summarized by using either the `info()` convenience function or method:

    >>> fits.info('compressed_image.fits')
    Filename: compressed_image.fits
    No.    Name         Type      Cards   Dimensions   Format
    0    PRIMARY     PrimaryHDU       6  ()            int16
    1    COMPRESSED  CompImageHDU    52  (512, 512)    int16
    >>>
    >>> f = fits.open('compressed_image.fits')
    >>> f.info()
    Filename: compressed_image.fits
    No.    Name         Type      Cards   Dimensions   Format
    0    PRIMARY     PrimaryHDU       6  ()            int16
    1    COMPRESSED  CompImageHDU    52  (512, 512)    int16
    >>>

### Data

As with the header, the data of a compressed image HDU appears to the user as standard uncompressed image data. The actual data is stored in the fits file as Binary Table data containing at least one column (COMPRESSED_DATA). Each row of this variable-length column contains the byte stream that was generated as a result of compressing the corresponding image tile. Several optional columns may also appear. These include, UNCOMPRESSED_DATA to hold the uncompressed pixel values for tiles that cannot be compressed, ZSCALE and ZZERO to hold the linear scale factor and zero point offset which may be needed to transform the raw uncompressed values back to the original image pixel values, and ZBLANK to hold the integer value used to represent undefined pixels (if any) in the image.

The contents of the uncompressed HDU data may be accessed using the `.data` attribute:

    >>> f = fits.open('compressed_image.fits')
    >>> f[1].data
    array([[38, 43, 35, ..., 45, 43, 41],
           [36, 41, 37, ..., 42, 41, 39],
           [38, 45, 37, ..., 42, 35, 43],
           ...,
           [49, 52, 49, ..., 41, 35, 39],
           [57, 52, 49, ..., 40, 41, 43],
           [53, 57, 57, ..., 39, 35, 45]], dtype=int16)

The compressed data can be accessed via the `.compressed_data` attribute, but this rarely need be accessed directly. It may be useful for performing direct copies of the compressed data without needing to decompress it first.

### Creating a Compressed Image HDU

To create a compressed image HDU from scratch, simply construct a `CompImageHDU` object from an uncompressed image data array and its associated image header. From there, the HDU can be treated just like any other image HDU:

    >>> hdu = fits.CompImageHDU(imageData, imageHeader)
    >>> hdu.writeto('compressed_image.fits')

The API documentation for the `CompImageHDU` initializer method describes the possible options for constructing a `CompImageHDU` object.