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- Table Data

# Table Data

In this chapter, we will discuss the data component in a table HDU. A table will always be in an extension HDU, never in a primary HDU.

There are two kinds of tables in the FITS standard: binary tables and ASCII tables. Binary tables are more economical in storage and faster in data access and manipulation. ASCII tables store the data in a “human readable” form and therefore take up more storage space as well as more processing time since the ASCII text needs to be parsed into numerical values.

Note

If you want to read or write a single table in FITS format then the most convenient method is often via the high-level Unified File Read/Write Interface. In particular see the Unified I/O FITS section.

## Table Data as a Record Array

### What is a Record Array?

A record array is an array which contains records (i.e., rows) of heterogeneous data types. Record arrays are available through the records module in the NumPy library.

Here is a sample record array:

    >>> import numpy as np
    >>> bright = np.rec.array([(1,'Sirius', -1.45, 'A1V'),
    ...                        (2,'Canopus', -0.73, 'F0Ib'),
    ...                        (3,'Rigil Kent', -0.1, 'G2V')],
    ...                       formats='int16,a20,float32,a10',
    ...                       names='order,name,mag,Sp')

In this example, there are three records (rows) and four fields (columns). The first field is a short integer, the second a character string (of length 20), the third a floating point number, and the fourth a character string (of length 10). Each record has the same (heterogeneous) data structure.

The underlying data structure used for FITS tables is a class called `FITS_rec` which is a specialized subclass of `numpy.recarray`. A `FITS_rec` can be instantiated directly using the same initialization format presented for plain recarrays as in the example above. You may also instantiate a new `FITS_rec` from a list of `astropy.io.fits.Column` objects using the `FITS_rec.from_columns()` class method. This has the exact same semantics as `BinTableHDU.from_columns()` and `TableHDU.from_columns()`, except that it only returns an actual FITS_rec array and not a whole HDU object.

### Metadata of a Table

The data in a FITS table HDU is basically a record array with added attributes. The metadata (i.e., information about the table data) are stored in the header. For example, the keyword TFORM1 contains the format of the first field, TTYPE2 the name of the second field, etc. NAXIS2 gives the number of records (rows) and TFIELDS gives the number of fields (columns). For FITS tables, the maximum number of fields is 999. The data type specified in TFORM is represented by letter codes for binary tables and a Fortran-like format string for ASCII tables. Note that this is different from the format specifications when constructing a record array.

### Reading a FITS Table

Like images, the `.data` attribute of a table HDU contains the data of the table.

#### Example

To read a FITS Table:

    >>> from astropy.io import fits
    >>> fits_table_filename = fits.util.get_testdata_filepath('btable.fits')

    >>> hdul = fits.open(fits_table_filename)  # open a FITS file
    >>> data = hdul[1].data  # assume the first extension is a table
    >>> # show the first two rows
    >>> first_two_rows = data[:2]
    >>> first_two_rows
    [(1, 'Sirius', -1.45000005, 'A1V') (2, 'Canopus', -0.73000002, 'F0Ib')]
    >>> # show the values in field "mag"
    >>> magnitudes = data['mag']
    >>> magnitudes
    array([-1.45000005, -0.73000002, -0.1       ], dtype=float32)
    >>> # columns can be referenced by index too
    >>> names = data.field(1)
    >>> names.tolist()
    ['Sirius', 'Canopus', 'Rigil Kent']
    >>> hdul.close()

Note that in `astropy`, when using the `field()` method, it is 0-indexed while the suffixes in header keywords such as TFORM is 1-indexed. So, `data.field(0)` is the data in the column with the name specified in TTYPE1 and format in TFORM1.

Warning

The FITS format allows table columns with a zero-width data format, such as `'0D'`. This is probably intended as a space-saving measure on files in which that column contains no data. In such files, the zero-width columns are omitted when accessing the table data, so the indexes of fields might change when using the `field()` method. For this reason, if you expect to encounter files containing zero-width columns it is recommended to access fields by name rather than by index.

## Table Operations

### Selecting Records in a Table

Like image data, we can use the same “mask array” idea to pick out desired records from a table and make a new table out of it.

#### Examples

Assuming the table’s second field as having the name ‘magnitude’, an output table containing all the records of magnitude > -0.5 from the input table is generated:

    >>> with fits.open(fits_table_filename) as hdul:
    ...     data = hdul[1].data
    ...     mask = data['mag'] > -0.5
    ...     newdata = data[mask]
    ...     hdu = fits.BinTableHDU(data=newdata)
    ...     hdu.writeto('newtable.fits')

It is also possible to update the data from the HDU object in-place:

    >>> with fits.open(fits_table_filename) as hdul:
    ...     hdu = hdul[1]
    ...     mask = hdu.data['mag'] > -0.5
    ...     hdu.data = hdu.data[mask]
    ...     hdu.writeto('newtable2.fits')

### Merging Tables

Merging different tables is very convenient in `astropy`.

#### Examples

To merge the column definitions of the input tables:

    >>> fits_other_table_filename = fits.util.get_testdata_filepath('table.fits')

    >>> with fits.open(fits_table_filename) as hdul1:
    ...     with fits.open(fits_other_table_filename) as hdul2:
    ...         new_columns = hdul1[1].columns + hdul2[1].columns
    ...         new_hdu = fits.BinTableHDU.from_columns(new_columns)
    >>> new_columns
    ColDefs(
            name = 'order'; format = 'I'
            name = 'name'; format = '20A'
            name = 'mag'; format = 'E'
            name = 'Sp'; format = '10A'
            name = 'target'; format = '20A'
            name = 'V_mag'; format = 'E'
        )

The number of fields in the output table will be the sum of numbers of fields of the input tables. Users have to make sure the input tables do not share any common field names. The number of records in the output table will be the largest number of records of all input tables. The expanded slots for the originally shorter table(s) will be zero (or blank) filled.

Another version of this example can be used to append a new column to a table. Updating an existing table with a new column is generally more difficult than it is worth, but you can “append” a column to a table by creating a new table with columns from the existing table plus the new column(s):

    >>> with fits.open(fits_table_filename) as hdul:
    ...     orig_table = hdul[1].data
    ...     orig_cols = orig_table.columns
    >>> new_cols = fits.ColDefs([
    ...     fits.Column(name='NEWCOL1', format='D',
    ...                 array=np.zeros(len(orig_table))),
    ...     fits.Column(name='NEWCOL2', format='D',
    ...                 array=np.zeros(len(orig_table)))])
    >>> hdu = fits.BinTableHDU.from_columns(orig_cols + new_cols)

Now `newtable.fits` contains a new table with the original table, plus the two new columns filled with zeros.

### Appending Tables

Appending one table after another is slightly trickier, since the two tables may have different field attributes.

#### Examples

Here, the first example is to append by field indices, and the second one is to append by field names. In both cases, the output table will inherit the column attributes (name, format, etc.) of the first table:

    >>> with fits.open(fits_table_filename) as hdul1:
    ...     with fits.open(fits_table_filename) as hdul2:
    ...         nrows1 = hdul1[1].data.shape[0]
    ...         nrows2 = hdul2[1].data.shape[0]
    ...         nrows = nrows1 + nrows2
    ...         hdu = fits.BinTableHDU.from_columns(hdul1[1].columns, nrows=nrows)
    ...         for colname in hdul1[1].columns.names:
    ...             hdu.data[colname][nrows1:] = hdul2[1].data[colname]

## Scaled Data in Tables

A table field’s data, like an image, can also be scaled. Scaling in a table has a more generalized meaning than in images. In images, the physical data is a simple linear transformation from the storage data. The table fields do have such a construct too, where BSCALE and BZERO are stored in the header as TSCALn and TZEROn. In addition, boolean columns and ASCII tables’ numeric fields are also generalized “scaled” fields, but without TSCAL and TZERO.

All scaled fields, like the image case, will take extra memory space as well as processing. So, if high performance is desired, try to minimize the use of scaled fields.

All of the scalings are done for the user, so the user only sees the physical data. Thus, there is no need to worry about scaling back and forth between the physical and storage column values.

## Creating a FITS Table

### Column Creation

To create a table from scratch, it is necessary to create individual columns first. A `Column` constructor needs the minimal information of column name and format. Here is a summary of all allowed formats for a binary table:

    FITS format code         Description                     8-bit bytes

    L                        logical (Boolean)               1
    X                        bit                             *
    B                        Unsigned byte                   1
    I                        16-bit integer                  2
    J                        32-bit integer                  4
    K                        64-bit integer                  8
    A                        character                       1
    E                        single precision float (32-bit) 4
    D                        double precision float (64-bit) 8
    C                        single precision complex        8
    M                        double precision complex        16
    P                        array descriptor                8
    Q                        array descriptor                16

We will concentrate on binary tables in this chapter. ASCII tables will be discussed in a later chapter. The less frequently used X format (bit array) and P format (used in variable length tables) will also be discussed in a later chapter.

Besides the required name and format arguments in constructing a `Column`, there are many optional arguments which can be used in creating a column. Here is a list of these arguments and their corresponding header keywords and descriptions:

    Argument        Corresponding         Description
    in Column()     header keyword

    name            TTYPE                 column name
    format          TFORM                 column format
    unit            TUNIT                 unit
    null            TNULL                 null value (only for B, I, and J)
    bscale          TSCAL                 scaling factor for data
    bzero           TZERO                 zero point for data scaling
    disp            TDISP                 display format
    dim             TDIM                  multi-dimensional array spec
    start           TBCOL                 starting position for ASCII table
    coord_type      TCTYP                 coordinate/axis type
    coord_unit      TCUNI                 coordinate/axis unit
    coord_ref_point TCRPX                 pixel coordinate of the reference point
    coord_ref_value TCRVL                 coordinate value at reference point
    coord_inc       TCDLT                 coordinate increment at reference point
    time_ref_pos    TRPOS                 reference position for a time coordinate column
    ascii                                 specifies a column for an ASCII table
    array                                 the data of the column

#### Examples

Here are a few Columns using various combinations of the optional arguments:

    >>> counts = np.array([312, 334, 308, 317])
    >>> names = np.array(['NGC1', 'NGC2', 'NGC3', 'NGC4'])
    >>> values = np.arange(2*2*4).reshape(4, 2, 2)
    >>> col1 = fits.Column(name='target', format='10A', array=names)
    >>> col2 = fits.Column(name='counts', format='J', unit='count', array=counts)
    >>> col3 = fits.Column(name='notes', format='A10')
    >>> col4 = fits.Column(name='spectrum', format='10E')
    >>> col5 = fits.Column(name='flag', format='L', array=[True, False, True, True])
    >>> col6 = fits.Column(name='intarray', format='4I', dim='(2, 2)', array=values)

In this example, formats are specified with the FITS letter codes. When there is a number (>1) preceding a (numeric type) letter code, it means each cell in that field is a one-dimensional array. In the case of column “col4”, each cell is an array (a NumPy array) of 10 elements. And in the case of column “col6”, with the use of the “dim” argument, each cell is a multi-dimensional array of 2x2 elements.

For character string fields, the number should be to the left of the letter ‘A’ when creating binary tables, and should be to the right when creating ASCII tables. However, as this is a common confusion, both formats are understood when creating binary tables (note, however, that upon writing to a file the correct format will be written in the header). So, for columns “col1” and “col3”, they both have 10 characters in each of their cells. For numeric data type, the dimension number must be before the letter code, not after.

After the columns are constructed, the `BinTableHDU.from_columns()` class method can be used to construct a table HDU. We can either go through the column definition object:

    >>> coldefs = fits.ColDefs([col1, col2, col3, col4, col5, col6])
    >>> hdu = fits.BinTableHDU.from_columns(coldefs)
    >>> coldefs
    ColDefs(
        name = 'target'; format = '10A'
        name = 'counts'; format = 'J'; unit = 'count'
        name = 'notes'; format = '10A'
        name = 'spectrum'; format = '10E'
        name = 'flag'; format = 'L'
        name = 'intarray'; format = '4I'; dim = '(2, 2)'
    )

or directly use the `BinTableHDU.from_columns()` method:

    >>> hdu = fits.BinTableHDU.from_columns([col1, col2, col3, col4, col5, col6])
    >>> hdu.columns
    ColDefs(
        name = 'target'; format = '10A'
        name = 'counts'; format = 'J'; unit = 'count'
        name = 'notes'; format = '10A'
        name = 'spectrum'; format = '10E'
        name = 'flag'; format = 'L'
        name = 'intarray'; format = '4I'; dim = '(2, 2)'
    )

Note

Users familiar with older versions of `astropy` will wonder what happened to `astropy.io.fits.new_table`. `BinTableHDU.from_columns()` and its companion for ASCII tables `TableHDU.from_columns()` are the same in the arguments they accept and their behavior, but make it more explicit as to what type of table HDU they create.

A look at the newly created HDU’s header will show that relevant keywords are properly populated:

    >>> hdu.header
    XTENSION= 'BINTABLE'           / binary table extension
    BITPIX  =                    8 / array data type
    NAXIS   =                    2 / number of array dimensions
    NAXIS1  =                   73 / length of dimension 1
    NAXIS2  =                    4 / length of dimension 2
    PCOUNT  =                    0 / number of group parameters
    GCOUNT  =                    1 / number of groups
    TFIELDS =                    6 / number of table fields
    TTYPE1  = 'target  '
    TFORM1  = '10A     '
    TTYPE2  = 'counts  '
    TFORM2  = 'J       '
    TUNIT2  = 'count   '
    TTYPE3  = 'notes   '
    TFORM3  = '10A     '
    TTYPE4  = 'spectrum'
    TFORM4  = '10E     '
    TTYPE5  = 'flag    '
    TFORM5  = 'L       '
    TTYPE6  = 'intarray'
    TFORM6  = '4I      '
    TDIM6   = '(2, 2)  '

Warning

It should be noted that when creating a new table with `BinTableHDU.from_columns()`, an in-memory copy of all of the input column arrays is created. This is because it is not guaranteed that the columns are arranged contiguously in memory in row-major order (in fact, they are most likely not), so they have to be combined into a new array.

However, if the array data is already contiguous in memory, such as in an existing record array, a kludge can be used to create a new table HDU without any copying. First, create the Columns as before, but without using the `array=` argument:

    >>> col1 = fits.Column(name='target', format='10A')

Then call `BinTableHDU.from_columns()`:

    >>> hdu = fits.BinTableHDU.from_columns([col1, col2, col3, col4, col5])

This will create a new table HDU as before, with the correct column definitions, but an empty data section. Now you can assign your array directly to the HDU’s data attribute:

    >>> hdu.data = mydata

In a future version of `astropy`, table creation will be simplified and this process will not be necessary.

## FITS Tables with Time Columns

The FITS Time standard paper defines the formats and keywords used to represent timing information in FITS files. The `astropy` FITS package provides support for reading and writing native `Time` columns and objects using this format. This is done within the FITS unified I/O interface and examples of usage can be found in the TDISPn Keyword section. The support is not complete and only a subset of the full standard is implemented.

### Example

The following is an example of a Header extract of a binary table (event list) with a time column:

    COMMENT      ---------- Globally valid key words ----------------
    TIMESYS = ’TT      ’          / Time system
    MJDREF  = 50814.000000000000  / MJD zero point for (native) TT (= 1998-01-01)
    MJD-OBS = 53516.257939301￼￼     / MJD for observation in (native) TT

    COMMENT      ---------- Time Column -----------------------
    TTYPE1  = ’Time    ’          / S/C TT corresponding to mid-exposure
    TFORM1  = ’2D      ’          / format of field
    TUNIT1  = ’s       ’
    TCTYP1  = ’TT      ’
    TCNAM1  = ’Terrestrial Time’  / This is TT
    TCUNI1  = ’s       ’

However, the FITS standard and the `astropy` Time object are not perfectly mapped and some compromises must be made. To help the user understand how the `astropy` code deals with these situations, the following text describes the approach that `astropy` takes in some detail.

To create FITS columns which adhere to the FITS Time standard, we have taken into account the following important points stated in the FITS Time paper.

The strategy used to store `Time` columns in FITS tables is to create a `Header` with the appropriate time coordinate global reference keywords and the column-specific override keywords. The module `astropy.io.fits.fitstime` deals with the reading and writing of Time columns.

The following keywords set the Time Coordinate Frame:

- TIME SCALE

  The most important of all of the metadata is the time scale which is a specification for measuring time.

      TIMESYS (string-valued)
      Time scale; default UTC

      TCTYPn (string-valued)
      Column-specific override keyword

  The global time scale may be overridden by a time scale recorded in the table equivalent keyword `TCTYPn` for time coordinates in FITS table columns. `TCTYna` is used for alternate coordinates.

- TIME REFERENCE

  The reference point in time to which all times in the HDU are relative. Since there are no context-specific reference times in case there are multiple time columns in the same table, we need to adjust the reference times for the columns using some other keywords.

  The reference point in time shall be specified through one of the three following keywords, which are listed in decreasing order of preference:

      MJDREF (floating-valued)
      Reference time in MJD

      JDREF (floating-valued)
      Reference time in JD

      DATEREF (datetime-valued)
      Reference time in ISO-8601

  The time reference keywords (MJDREF, JDREF, DATEREF) are interpreted using the time scale specified in `TIMESYS`.

  Note

  If none of the three keywords are present, there is no problem as long as all times in the HDU are expressed in ISO-8601 `Datetime Strings` format: `CCYY-MM-DD[Thh:mm:ss[.s...]]` (e.g., `"2015-04-05T12:22:33.8"`); otherwise MJDREF = 0.0 must be assumed.

  The value of the reference time has global validity for all time values, but it does not have a particular time scale associated with it. Thus we need to use `TCRVLn` (time coordinate reference value) keyword to compensate for the time scale differences.

- TIME REFERENCE POSITION

  The reference position, specified by the keyword `TREFPOS`, specifies the spatial location at which the time is valid, either where the observation was made or the point in space for which light-time corrections have been applied. This may be a standard location (such as `GEOCENTER` or `TOPOCENTER`) or a point in space defined by specific coordinates.

      TREFPOS (string-valued)
      Time reference position; default TOPOCENTER

      TRPOSn (string-valued)
      Column-specific override keyword

  Note

  For TOPOCENTER, we need to specify the observatory location (ITRS Cartesian coordinates or geodetic latitude/longitude/height) in the `OBSGEO-*` keywords.

- TIME REFERENCE DIRECTION

  If any pathlength corrections have been applied to the time stamps (i.e., if the reference position is not `TOPOCENTER` for observational data), the reference direction that is used in calculating the pathlength delay should be provided in order to maintain a proper analysis trail of the data. However, this is useful only if there is also information available on the location from where the observation was made (the observatory location).

  The reference direction is indicated through a reference to specific keywords. These keywords may explicitly hold the direction or indicate columns holding the coordinates.

      TREFDIR (string-valued)
      Pointer to time reference direction

      TRDIRn (string-valued)
      Column-specific override keyword

- TIME UNIT

  The FITS standard recommends the time unit to be one of the allowed ones in the specification.

      TIMEUNIT (string-valued)
      Time unit; default s

      TCUNIn (string-valued)
      Column-specific override

- TIME OFFSET

  It is sometimes convenient to be able to apply a uniform clock correction in bulk by putting that number in a single keyword. A second use for a time offset is to set a zero offset to a relative time series, allowing zero-relative times, or higher precision, in the time stamps. Its default value is zero.

      TIMEOFFS (floating-valued)
      This has global validity

- The absolute, relative errors and time resolution, time binning can be used when needed.

The following keywords define the global time informational keywords:

- DATE and DATE-* keywords

  These define the date of HDU creation and observation in ISO-8601. `DATE` is in UTC if the file is constructed on the Earth’s surface and others are in the time scale given by `TIMESYS`.

- MJD-* keywords

  These define the same as above, but in `MJD` (Modified Julian Date).

The implementation writes a subset of the above FITS keywords, which map to the Time metadata. Time is intrinsically a coordinate and hence shares keywords with the `World Coordinate System` specification for spatial coordinates. Therefore, while reading FITS tables with time columns, the verification that a coordinate column is indeed time is done using the FITS WCS standard rules and suggestions.