# 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.

Note

`Masked` is similar to Numpy’s `MaskedArray`, but it supports subclasses much better and also has some important differences in behaviour. As a result, the behaviour of functions inside `numpy.ma` is poorly defined, and one should instead use regular `numpy` functions, which are overridden to work properly with masks (with non-obvious choices documented in `astropy.utils.masked.function_helpers`; please report numpy functions that do not work properly with `Masked` values!).

## 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
>>> ma
>>> mq = ma * u.m
>>> mq + 25 * u.cm
```

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)
>>> ma.sum()
```

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)
```

## 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.])
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 * np_ma * np_ma
```

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
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.units.quantity.Quantity'>,
<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#

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#

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.
 `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. `nanargmax`(a, *args, **kwargs) Like `numpy.nanargmax`, skipping masked values as well. `nanargmin`(a, *args, **kwargs) Like `numpy.nanargmin`, skipping masked values as well. `nancumprod`(a, *args, **kwargs) Like `numpy.nancumprod`, skipping masked values as well. `nancumsum`(a, *args, **kwargs) Like `numpy.nancumsum`, skipping masked values as well. `nanmax`(a, *args, **kwargs) Like `numpy.nanmax`, skipping masked values as well. `nanmean`(a, *args, **kwargs) Like `numpy.nanmean`, skipping masked values as well. `nanmedian`(a, *args, **kwargs) Like `numpy.nanmedian`, skipping masked values as well. `nanmin`(a, *args, **kwargs) Like `numpy.nanmin`, skipping masked values as well. `nanpercentile`(a, *args, **kwargs) Like `numpy.nanpercentile`, skipping masked values as well. `nanprod`(a, *args, **kwargs) Like `numpy.nanprod`, skipping masked values as well. `nanquantile`(a, *args, **kwargs) Like `numpy.nanquantile`, skipping masked values as well. `nanstd`(a, *args, **kwargs) Like `numpy.nanstd`, skipping masked values as well. `nansum`(a, *args, **kwargs) Like `numpy.nansum`, skipping masked values as well. `nanvar`(a, *args, **kwargs) Like `numpy.nanvar`, skipping masked values as well. `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.