# N-Dimensional Datasets (`astropy.nddata`

)#

## Introduction#

The `nddata`

package provides classes to represent images and other
gridded data, some essential functions for manipulating images, and the
infrastructure for package developers who wish to include support for the
image classes. This subpackage was developed based on APE 7.

## Getting Started#

### NDData#

The primary purpose of `NDData`

is to act as a *container* for
data, metadata, and other related information like a mask.

An `NDData`

object can be instantiated by passing it an
n-dimensional `numpy`

array:

```
>>> import numpy as np
>>> from astropy.nddata import NDData
>>> array = np.zeros((12, 12, 12)) # a 3-dimensional array with all zeros
>>> ndd1 = NDData(array)
```

Or something that can be converted to a `numpy.ndarray`

:

```
>>> ndd2 = NDData([1, 2, 3, 4])
>>> ndd2
NDData([1, 2, 3, 4])
```

And can be accessed again via the `data`

attribute:

```
>>> ndd2.data
array([1, 2, 3, 4])
```

It also supports additional properties like a `unit`

or `mask`

for the
data, a `wcs`

(World Coordinate System) and `uncertainty`

of the data and
additional `meta`

attributes:

```
>>> data = np.array([1,2,3,4])
>>> mask = data > 2
>>> unit = 'erg / s'
>>> from astropy.nddata import StdDevUncertainty
>>> uncertainty = StdDevUncertainty(np.sqrt(data)) # representing standard deviation
>>> meta = {'object': 'fictional data.'}
>>> ndd = NDData(data, mask=mask, unit=unit, uncertainty=uncertainty,
... meta=meta)
>>> ndd
NDData([1, 2, —, —], unit='erg / s')
```

The representation only displays the `data`

; the other attributes need to be
accessed directly, for example, `ndd.mask`

to access the mask.

### NDDataRef#

Building upon this pure container, `NDDataRef`

implements:

A

`read`

and`write`

method to access`astropy`

’s unified file I/O interface.Simple arithmetic like addition, subtraction, division, and multiplication.

Slicing.

Instances are created in the same way:

```
>>> from astropy.nddata import NDDataRef
>>> ndd = NDDataRef(ndd)
>>> ndd
NDDataRef([1, 2, —, —], unit='erg / s')
```

But also support arithmetic (NDData Arithmetic) like addition:

```
>>> import astropy.units as u
>>> ndd2 = ndd.add([4, -3.5, 3, 2.5] * u.erg / u.s)
>>> ndd2
NDDataRef([ 5. , -1.5, ———, ———], unit='erg / s')
```

Because these operations have a wide range of options, these are not available
using arithmetic operators like `+`

.

Slicing or indexing (Slicing and Indexing NDData) is possible (with warnings issued if some attribute cannot be sliced):

```
>>> ndd2[2:] # discard the first two elements
NDDataRef([———, ———], unit='erg / s')
>>> ndd2[1] # get the second element
NDDataRef(-1.5, unit='erg / s')
```

### Working with Two-Dimensional Data Like Images#

Though the `nddata`

package supports any kind of gridded data, this
introduction will focus on the use of `nddata`

for two-dimensional
images. To get started, we will construct a two-dimensional image with a few
sources, some Gaussian noise, and a “cosmic ray” which we will later mask out.

#### Examples#

First, construct a two-dimensional image with a few sources, some Gaussian noise, and a “cosmic ray”:

```
>>> import numpy as np
>>> from astropy.modeling.models import Gaussian2D
>>> rng = np.random.default_rng()
>>> y, x = np.mgrid[0:500, 0:600]
>>> data = (Gaussian2D(1, 150, 100, 20, 10, theta=0.5)(x, y) +
... Gaussian2D(0.5, 400, 300, 8, 12, theta=1.2)(x,y) +
... Gaussian2D(0.75, 250, 400, 5, 7, theta=0.23)(x,y) +
... Gaussian2D(0.9, 525, 150, 3, 3)(x,y) +
... Gaussian2D(0.6, 200, 225, 3, 3)(x,y))
>>> data += 0.01 * rng.standard_normal((500, 600))
>>> cosmic_ray_value = 0.997
>>> data[100, 300:310] = cosmic_ray_value
```

This image has a large “galaxy” in the lower left and the “cosmic ray” is the horizontal line in the lower middle of the image:

```
>>> import matplotlib.pyplot as plt
>>> plt.imshow(data, origin='lower')
```

The “cosmic ray” can be masked out in this test image, like this:

```
>>> mask = (data == cosmic_ray_value)
```

`CCDData`

Class for Images#

The `CCDData`

object, like the other objects in this package,
can store the data, a mask, and metadata. The `CCDData`

object
requires that a unit be specified:

```
>>> from astropy.nddata import CCDData
>>> ccd = CCDData(data, mask=mask,
... meta={'object': 'fake galaxy', 'filter': 'R'},
... unit='adu')
```

### Slicing#

Slicing works the way you would expect with the mask and, if present, WCS, sliced appropriately:

```
>>> ccd2 = ccd[:200, :]
>>> ccd2.data.shape
(200, 600)
>>> ccd2.mask.shape
(200, 600)
>>> # Show the mask in a region around the cosmic ray:
>>> ccd2.mask[99:102, 299:311]
array([[False, False, False, False, False, False, False, False, False,
False, False, False],
[False, True, True, True, True, True, True, True, True,
True, True, False],
[False, False, False, False, False, False, False, False, False,
False, False, False]]...)
```

For many applications it may be more convenient to use
`Cutout2D`

, described in image_utilities.

### Image Arithmetic, Including Uncertainty#

Methods are provided for basic arithmetic operations between images, including
propagation of uncertainties. Three uncertainty types are supported: variance
(`VarianceUncertainty`

), standard deviation
(`StdDevUncertainty`

), and inverse variance
(`InverseVariance`

).

#### Examples#

This example creates an uncertainty that is Poisson error, stored as a variance:

```
>>> from astropy.nddata import VarianceUncertainty
>>> poisson_noise = np.ma.sqrt(np.ma.abs(ccd.data))
>>> ccd.uncertainty = VarianceUncertainty(poisson_noise ** 2)
```

As a convenience, the uncertainty can also be set with a `numpy`

array. In
that case, the uncertainty is assumed to be the standard deviation:

```
>>> ccd.uncertainty = poisson_noise
INFO: array provided for uncertainty; assuming it is a StdDevUncertainty. [astropy.nddata.ccddata]
```

If we make a copy of the image and add that to the original, the uncertainty changes as expected:

```
>>> ccd2 = ccd.copy()
>>> added_ccds = ccd.add(ccd2, handle_meta='first_found')
>>> added_ccds.uncertainty.array[0, 0] / ccd.uncertainty.array[0, 0] / np.sqrt(2)
0.99999999999999989
```

### Reading and Writing#

A `CCDData`

can be saved to a FITS file:

```
>>> ccd.write('test_file.fits')
```

And can also be read in from a FITS file:

```
>>> ccd2 = CCDData.read('test_file.fits')
```

Note the unit is stored in the `BUNIT`

keyword in the header on saving, and is
read from the header if it is present.

Detailed help on the available keyword arguments for reading and writing
can be obtained via the `help()`

method as follows:

```
>>> CCDData.read.help('fits') # Get help on the CCDData FITS reader
>>> CCDData.writer.help('fits') # Get help on the CCDData FITS writer
```

### Image Utilities#

#### Cutouts#

Though slicing directly is one way to extract a subframe,
`Cutout2D`

provides more convenient access to cutouts from the
data.

##### Examples#

This example pulls out the large “galaxy” in the lower left of the image, with
the center of the cutout at `position`

:

```
>>> from astropy.nddata import Cutout2D
>>> position = (149.7, 100.1)
>>> size = (81, 101) # pixels
>>> cutout = Cutout2D(ccd, position, size)
>>> plt.imshow(cutout.data, origin='lower')
```

This cutout can also plot itself on the original image:

```
>>> plt.imshow(ccd, origin='lower')
>>> cutout.plot_on_original(color='white')
```

The cutout also provides methods for finding pixel coordinates in the original
or in the cutout; recall that `position`

is the center of the cutout in the
original image:

```
>>> position
(149.7, 100.1)
>>> cutout.to_cutout_position(position)
(49.7, 40.099999999999994)
>>> cutout.to_original_position((49.7, 40.099999999999994))
(149.7, 100.1)
```

For more details, including constructing a cutout from World Coordinates and the options for handling cutouts that go beyond the bounds of the original image, see 2D Cutout Images.

#### Image Resizing#

The functions `block_reduce`

and
`block_replicate`

resize images.

##### Example#

This example reduces the size of the image by a factor of 4. Note that the
result is a `numpy.ndarray`

; the mask, metadata, etc. are discarded:

```
>>> from astropy.nddata import block_reduce, block_replicate
>>> smaller = block_reduce(ccd, 4)
>>> smaller
array(...)
>>> plt.imshow(smaller, origin='lower')
```

By default, both `block_reduce`

and
`block_replicate`

conserve flux.

### Other Image Classes#

There are two less restrictive classes, `NDDataArray`

and
`NDDataRef`

, that can be used to hold image data. They are
primarily of interest to those who may want to create their own image class by
subclassing from one of the classes in the `nddata`

package. The main
differences between them are:

`NDDataRef`

can be sliced and has methods for basic arithmetic operations, but the user needs to use one of the uncertainty classes to define an uncertainty. See NDDataRef for more detail. Most of its properties must be set when the object is created because they are not mutable.`NDDataArray`

extends`NDDataRef`

by adding the methods necessary for it to behave like a`numpy`

array in expressions and adds setters for several properties. It lacks the ability to automatically recognize and read data from FITS files and does not attempt to automatically set the WCS property.`CCDData`

extends`NDDataArray`

by setting up a default uncertainty class, setting up straightforward read/write to FITS files, and automatically setting up a WCS property.

### More General Gridded Data Classes#

There are two generic classes in the `nddata`

package that are of
interest primarily to users who either need a custom image class that goes
beyond the classes discussed so far, or who are working with gridded data that
is not an image.

`NDData`

is a container class for holding general gridded data. It includes a handful of basic attributes, but no slicing or arithmetic. More information about this class is in NDData.`NDDataBase`

is an abstract base class that developers of new gridded data classes can subclass to declare that the new class follows the`NDData`

interface. More details are in Subclassing.

## Additional Examples#

The list of packages below that use the `nddata`

framework is intended to be
useful to either users writing their own image classes or those looking
for an image class that goes beyond what `CCDData`

does.

The SunPy project uses

`NDData`

as the foundation for its Map classes.The class

`NDDataRef`

is used in specutils as the basis for Spectrum1D, which adds several methods useful for spectra.The package ndmapper, which makes it easy to build reduction pipelines for optical data, uses

`NDDataArray`

as its image object.The package ccdproc uses the

`CCDData`

class throughout for implementing optical/IR image reduction.

## Using `nddata`

#

## Performance Tips#

Using the uncertainty class

`VarianceUncertainty`

will be somewhat more efficient than the other two uncertainty classes,`InverseVariance`

and`StdDevUncertainty`

. The latter two are converted to variance for the purposes of error propagation and then converted from variance back to the original uncertainty type. The performance difference should be small.When possible, mask values by setting them to

`np.nan`

and use the`numpy`

functions and methods that automatically exclude`np.nan`

, like`np.nanmedian`

and`np.nanstd`

. This will typically be much faster than using`numpy.ma.MaskedArray`

.