Masked Values (astropy.utils.masked)

Often, data sets are incomplete or corrupted and it would be handy to be able to mask certain values. Astropy provides a Masked class to help represent such data sets.

Warning

Masked is experimental! While we hope basic usage will remain similar, we are not yet sure whether it will not be necessary to change it to make things work throughout Astropy. This also means that comments and suggestions for improvements are especially welcome!

Note

Masked is similar to Numpy’s MaskedArray, but it supports subclasses much better and also has some important differences in behaviour.

Usage

Astropy Masked instances behave like ndarray or subclasses such as Quantity but with a mask associated, which is propagated in operations such as addition, etc.:

>>> import numpy as np
>>> from astropy import units as u
>>> from astropy.utils.masked import Masked
>>> ma = Masked([1., 2., 3.], mask=[False, False, True])
>>> ma
MaskedNDArray([1., 2., ——])
>>> mq = ma * u.m
>>> mq + 25 * u.cm
<MaskedQuantity [1.25, 2.25,  ———] m>

You can get the values without the mask using unmasked, or, if you need to control what should be substituted for any masked values, with filled():

>>> mq.unmasked
<Quantity [1., 2., 3.] m>
>>> mq.filled(fill_value=-75*u.cm)
<Quantity [ 1.  ,  2.  , -0.75] m>

For reductions such as sums, the mask propagates as if the sum was done directly:

>>> ma = Masked([[0., 1.], [2., 3.]], mask=[[False, True], [False, False]])
>>> ma.sum(axis=-1)
MaskedNDArray([——, 5.])
>>> ma.sum()
MaskedNDArray(——)

You might wonder why masked elements are propagated, instead of just being skipped (as is done in MaskedArray; see below). The rationale is that this leaves a sum which is generally not useful unless one knows the number of masked elements. In contrast, for sample properties such as the mean, for which the number of elements are counted, it seems natural to simply omit the masked elements from the calculation:

>> ma.mean(-1)
MaskedNDArray([0.0, 2.5])

Differences from numpy.ma.MaskedArray

Masked differs from MaskedArray in a number of ways. In usage, a major difference is that most operations act on the masked values, i.e., no effort is made to preserve values. For instance, compare:

>>> np_ma = np.ma.MaskedArray([1., 2., 3.], mask=[False, True, False])
>>> (np_ma + 1).data
array([2., 2., 4.])
>>> (Masked(np_ma) + 1).unmasked
array([2., 3., 4.])

The main reason for this decision is that for some masked subclasses, like masked Quantity, keeping the original value makes no sense (e.g., consider dividing a length by a time: if the unit of a masked quantity is changing, why should its value not change?). But it also helps to keep the implementation considerably simpler, as the Masked class now primarily has to deal with propagating the mask rather than deciding what to do with values.

A second difference is that for reductions, the mask propagates as it would have if the operations were done on the individual elements:

>>> np_ma.prod()
3.0
>>> np_ma[0] * np_ma[1] * np_ma[2]
masked
>>> Masked(np_ma).prod()
MaskedNDArray(——)

The rationale for this becomes clear again by thinking about subclasses like a masked Quantity. For instance, consider an array s of lengths with shape (N, 3), in which the last axis represents width, height, and depth. With this, you could compute corresponding volumes by taking the product of the values in the last axis, s.prod(axis=-1). But if masked elements were skipped, the physical dimension of entries in the result would depend how many elements were masked, which is something Quantity could not represent (and would be rather surprising!). As noted above, however, masked elements are skipped for operations for which this is well defined, such as for getting the mean and other sample properties such as the variance and standard deviation.

A third difference is more conceptual. For MaskedArray, the instance that is created is a masked version of the unmasked instance, i.e., MaskedArray remembers that is has wrapped a subclass like Quantity, but does not share any of its methods. Hence, even though the resulting class looks reasonable at first glance, it does not work as expected:

>>> q = [1., 2.] * u.m
>>> np_mq = np.ma.MaskedArray(q, mask=[False, True])
>>> np_mq
masked_Quantity(data=[1.0, --],
                mask=[False,  True],
          fill_value=1e+20)
>>> np_mq.unit
Traceback (most recent call last):
...
AttributeError: 'MaskedArray' object has no attribute 'unit'
>>> np_mq / u.s
<Quantity [1., 2.] 1 / s>

In contrast, Masked is always wrapped around the data properly, i.e., a MaskedQuantity is a quantity which has masked values, but with a unit that is never masked. Indeed, one can see this from the class hierarchy:

>>> mq.__class__.__mro__
(<class 'astropy.utils.masked.core.MaskedQuantity'>,
 <class 'astropy.units.quantity.Quantity'>,
 <class 'astropy.utils.masked.core.MaskedNDArray'>,
 <class 'astropy.utils.masked.core.Masked'>,
 <class 'astropy.utils.shapes.NDArrayShapeMethods'>,
 <class 'numpy.ndarray'>,
 <class 'object'>)

This choice has made the implementation much simpler: Masked only has to worry about how to deal with masked values, while Quantity can worry just about unit propagation, etc. Indeed, an experiment showed that applying Masked to Column (which is a subclass of ndarray), the result is a new MaskedColumn that “just works”, with no need for the overrides and special-casing that were needed to make MaskedArray work with Column. (Because the behaviour does change somewhat, however, we chose not to replace the existing implementation.)

In some respects, rather than think of Masked as similar to MaskedArray, it may be more useful to think of Masked as similar to marking bad elements in arrays with NaN (not-a-number). Like those NaN, the mask just propagates, except that for some operations like taking the mean the equivalence of nanmean is used.

Reference/API

astropy.utils.masked Package

Built-in mask mixin class.

The design uses Masked as a factory class which automatically generates new subclasses for any data class that is itself a subclass of a predefined masked class, with MaskedNDArray providing such a predefined class for ndarray.

Classes

Masked(*args, **kwargs)

A scalar value or array of values with associated mask.

MaskedNDArray(*args[, mask])

Masked version of ndarray.

Class Inheritance Diagram

Inheritance diagram of astropy.utils.masked.core.Masked, astropy.utils.masked.core.MaskedNDArray

astropy.utils.masked.function_helpers Module

Helpers for letting numpy functions interact with Masked arrays.

The module supplies helper routines for numpy functions that propagate masks appropriately., for use in the __array_function__ implementation of MaskedNDArray. They are not very useful on their own, but the ones with docstrings are included in the documentation so that there is a place to find out how the mask is interpreted.

Functions

bincount(x[, weights, minlength])

Count number of occurrences of each value in array of non-negative ints.

broadcast_arrays(*args[, subok])

Broadcast arrays to a common shape.

broadcast_to(array, shape[, subok])

Broadcast array to the given shape.

choose(a, choices[, out, mode])

Construct an array from an index array and a set of arrays to choose from.

copyto(dst, src[, casting, where])

Copies values from one array to another, broadcasting as necessary.

count_nonzero(a[, axis, keepdims])

Counts the number of non-zero values in the array a.

empty_like(prototype[, dtype, order, subok, …])

Return a new array with the same shape and type as a given array.

full_like(a, fill_value[, dtype, order, …])

Return a full array with the same shape and type as a given array.

insert(arr, obj, values[, axis])

Insert values along the given axis before the given indices.

interp(x, xp, fp, *args, **kwargs)

One-dimensional linear interpolation.

lexsort(keys[, axis])

Perform an indirect stable sort using a sequence of keys.

ones_like(a[, dtype, order, subok, shape])

Return an array of ones with the same shape and type as a given array.

piecewise(x, condlist, funclist, *args, **kw)

Evaluate a piecewise-defined function.

place(arr, mask, vals)

Change elements of an array based on conditional and input values.

put(a, ind, v[, mode])

Replaces specified elements of an array with given values.

putmask(a, mask, values)

Changes elements of an array based on conditional and input values.

select(condlist, choicelist[, default])

Return an array drawn from elements in choicelist, depending on conditions.

zeros_like(a[, dtype, order, subok, shape])

Return an array of zeros with the same shape and type as a given array.