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# Masked Values and Quantities (`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.

## 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>

You can mask or unmask individual elements by setting them to `masked` or `nomask`:

    >>> mq.mask
    array([False, False,  True])
    >>> mq[:] = np.ma.nomask
    >>> mq[2] = np.ma.masked
    >>> mq.mask
    array([False, False,  True])
    >>> mq
    <MaskedQuantity [1., 2., ——] m>

These same procedures also work for higher-level classes like |Time| and |SkyCoord|, which use |Masked| under the hood.

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])

Numpy functions work as expected on |Masked| instances, with non-obvious choices documented in `astropy.utils.masked.function_helpers` (please report numpy functions that do not work properly with |Masked| values!). For example, `nansum()` does not propagate masked elements, but instead replaces them with zero, and returns an unmasked instance:

    >> np.nansum(ma, axis=-1)
    array([0., 5.])

## Differences from `MaskedArray`

|Masked| differs from `MaskedArray` in a number of ways, which we detail below. Overall, it may be helpful to think of |Masked| not as a replacement of `MaskedArray`, but just as a way of marking bad elements, as one might do without needing a different class by setting them to NaN (not-a-number). Like those NaN, the mask just propagates, except that for some operations like taking the mean the equivalent of `nanmean` is used.

### Values under masked are operated on

A difference in usage 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.

### Masked values are not skipped in reductions

In reductions, the mask propagates as it would have if the operations were done on the individual elements:

    >>> np_ma.prod()
    np.float64(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.

### Setting the mask attribute replaces it

If one sets the mask attribute of a `MaskedArray`, it will attempt to change the mask inplace:

    >>> np_ma = np.ma.MaskedArray([1., 2., 3.], mask=[False, True, False])
    >>> np_ma_mask_ref = np_ma.mask
    >>> np_ma.mask = False
    >>> np_ma_mask_ref
    array([False, False, False])

In contrast, if one sets the mask on a |Masked| class, it just sets it:

    >>> ma = Masked([1., 2., 3.], mask=[False, True, False])
    >>> ma_mask_ref = ma.mask
    >>> ma.mask = False
    >>> ma.mask
    array([False, False, False])
    >>> ma_mask_ref
    array([False,  True, False])

This has a consequence for setting the mask on a slice: for `MaskedArray` it propagates back, but for |Masked| it does not:

    >>> np_ma = np.ma.MaskedArray([1., 2., 3.], mask=[False, True, False])
    >>> np_ma_view = np_ma[2:3]
    >>> np_ma_view.mask = True
    >>> np_ma_view
    masked_array(data=[--],
                 mask=[ True],
           fill_value=1e+20,
                dtype=float64)
    >>> np_ma
    masked_array(data=[1.0, --, --],
                 mask=[False,  True,  True],
           fill_value=1e+20)

    >>> ma = Masked([1., 2., 3.], mask=[False, True, False])
    >>> ma_view = ma[2:3]
    >>> ma_view.mask = True
    >>> ma_view
    MaskedNDArray([——])
    >>> ma
    MaskedNDArray([1., ——, 3.])

In order for the mask to be set in-place, one should do it explicitly:

    >>> ma[1:2].mask[...] = True
    >>> ma.mask
    array([False,  True, False])

The reason for not attempting to propagate is partially just that assignment should be just that, assignment. But also that it is tricky to get right. Indeed, also for `MaskedArray` it does not always work:

    >>> np_ma[0].mask = True
    Traceback (most recent call last):
    ...
    AttributeError: 'numpy.float64' object has no attribute 'mask'...

Note

We recommend not dealing with the mask directly but setting the instance to `masked` or `nomask`, as described above. This is also the only way to mask values for the higher-level classes such as |Time| and |SkyCoord|.

### Numpy functions work as expected

For `MaskedArray`, a number of regular numpy functions do not work properly, and instead one has to use variants from the `np.ma` namespace. For |Masked|, numpy functions do work as expected (but those under the `np.ma` namespace typically do not).

### Masked subclasses behave like the subclass

A more conceptual difference is that 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 proper, 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.)

## 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`.

#### Functions

`combine_masks`(masks, *[, out, where, copy]) | Combine masks, possibly storing it in some output.
`get_data_and_mask`(array) | Split possibly masked array into unmasked and mask.

#### Classes

`MaskableShapedLikeNDArray`() | Like ShapedLikeNDArray, but for classes that can work with masked data.
`Masked`(*args, **kwargs) | A scalar value or array of values with associated mask.
`MaskedNDArray`(*args[, mask]) | Masked version of ndarray.

#### Class Inheritance Diagram

### 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`.
`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.
`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.