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- Masking and missing values

# Masking and missing values

The `astropy.table` package provides support for masking and missing values in a table by wrapping the `numpy.ma` masked array package. This allows handling tables with missing or invalid entries in much the same manner as for standard (unmasked) tables. It is useful to be familiar with the masked array documentation when using masked tables within `astropy.table`.

In a nutshell, the concept is to define a boolean mask that mirrors the structure of the table data array. Wherever a mask value is `True`, the corresponding entry is considered to be missing or invalid. Operations involving column or row access and slicing are unchanged. The key difference is that arithmetic or reduction operations involving columns or column slices follow the rules for operations on masked arrays.

Note

Reduction operations like `numpy.sum` or `numpy.mean` follow the convention of ignoring masked (invalid) values. This differs from the behavior of the floating point `NaN`, for which the sum of an array including one or more `NaN's` will result in `NaN`. See http://numpy.scipy.org/NA-overview.html for a very interesting discussion of different strategies for handling missing data in the context of `numpy`.

## Table creation

A masked table can be created in several ways:

Create a new table object and specify masked=True

    >>> from astropy.table import Table, Column, MaskedColumn
    >>> Table([(1, 2), (3, 4)], names=('a', 'b'), masked=True, dtype=('i4', 'i8'))
    <Table masked=True length=2>
      a     b
    int32 int64
    ----- -----
        1     3
        2     4

Notice the table attributes `mask` and `fill_value` that are available for a masked table.

Create a table with one or more columns as a MaskedColumn object

    >>> a = MaskedColumn([1, 2], name='a', mask=[False, True], dtype='i4')
    >>> b = Column([3, 4], name='b', dtype='i8')
    >>> Table([a, b])
    <Table masked=True length=2>
      a     b
    int32 int64
    ----- -----
        1     3
       --     4

The `MaskedColumn` is the masked analog of the `Column` class and provides the interface for creating and manipulating a column of masked data. The `MaskedColumn` class inherits from `numpy.ma.MaskedArray`, in contrast to `Column` which inherits from `numpy.ndarray`. This distinction is the main reason there are different classes for these two cases.

Notice that masked entries in the table output are shown as `--`.

Create a table with one or more columns as a numpy MaskedArray

    >>> from numpy import ma  # masked array package
    >>> a = ma.array([1, 2])
    >>> b = [3, 4]
    >>> t = Table([a, b], names=('a', 'b'))

Add a MaskedColumn object to an existing table

    >>> t = Table([[1, 2]], names=['a'])
    >>> b = MaskedColumn([3, 4], mask=[True, False])
    >>> t['b'] = b
    INFO: Upgrading Table to masked Table. Use Table.filled() to convert to unmasked table. [astropy.table.table]

Note the INFO message because the underlying type of the table is modified in this operation.

Add a new row to an existing table and specify a mask argument

    >>> a = Column([1, 2], name='a')
    >>> b = Column([3, 4], name='b')
    >>> t = Table([a, b])
    >>> t.add_row([3, 6], mask=[True, False])
    INFO: Upgrading Table to masked Table. Use Table.filled() to convert to unmasked table. [astropy.table.table]

Convert an existing table to a masked table

    >>> t = Table([[1, 2], ['x', 'y']])  # standard (unmasked) table
    >>> t = Table(t, masked=True)  # convert to masked table

## Table access

Nearly all the of standard methods for accessing and modifying data columns, rows, and individual elements also apply to masked tables.

There are two minor differences for the `Row` object that is obtained by indexing a single row of a table:

- For standard tables, two such rows can be compared for equality, but in masked tables this comparison will produce an exception.

Both of these differences are due to issues in the underlying `numpy.ma.MaskedArray` implementation.

## Masking and filling

Both the `Table` and `MaskedColumn` classes provide attributes and methods to support manipulating tables with missing or invalid data.

### Mask

The actual mask for the table as a whole or a single column can be viewed and modified via the `mask` attribute:

    >>> t = Table([(1, 2), (3, 4)], names=('a', 'b'), masked=True)
    >>> t['a'].mask = [False, True]  # Modify column mask (boolean array)
    >>> t['b'].mask = [True, False]  # Modify column mask (boolean array)
    >>> print(t)
     a   b
    --- ---
      1  --
     --   4

Masked entries are shown as `--` when the table is printed. You can view the mask directly, either at the column or table level:

    >>> t['a'].mask
    array([False,  True], dtype=bool)

    >>> t.mask
    <Table length=2>
      a     b
     bool  bool
    ----- -----
    False  True
     True False

To get the indices of masked elements use an expression like:

    >>> t['a'].mask.nonzero()[0]
    array([1])

### Filling

The entries which are masked (i.e. missing or invalid) can be replaced with specified fill values. In this case the `MaskedColumn` or masked `Table` will be converted to a standard `Column` or table. Each column in a masked table has a `fill_value` attribute that specifies the default fill value for that column. To perform the actual replacement operation the `filled()` method is called. This takes an optional argument which can override the default column `fill_value` attribute.

    >>> t['a'].fill_value = -99
    >>> t['b'].fill_value = 33

    >>> print(t.filled())
     a   b
    --- ---
      1  33
    -99   4

    >>> print(t['a'].filled())
     a
    ---
      1
    -99

    >>> print(t['a'].filled(999))
     a
    ---
      1
    999

    >>> print(t.filled(1000))
     a    b
    ---- ----
       1 1000
    1000    4