# Data Structures for Images and Cubes (gammapy.maps)¶

Warning

The code in gammapy.maps is currently in an experimental/development state. Method and class names may change in the future.

## Introduction¶

gammapy.maps contains classes for representing pixelized data structures with at least two spatial dimensions representing coordinates on a sphere (e.g. an image in celestial coordinates). These classes support an arbitrary number of non-spatial dimensions and can represent images (2D), cubes (3D), or hypercubes (4+D). Two pixelization schemes are supported:

• WCS : Projection onto a 2D cartesian grid following the conventions of the World Coordinate System (WCS). Pixels are square in projected coordinates and as such are not equal area in spherical coordinates.
• HEALPix : Hierarchical Equal Area Iso Latitude pixelation of the sphere. Pixels are equal area but have irregular shapes.

gammapy.maps is organized around two data structures: geometry classes inheriting from MapGeom and map classes inheriting from MapBase. A geometry defines the map boundaries, pixelization scheme, and provides methods for converting to/from map and pixel coordinates. A map owns a MapGeom instance as well as a data structure containing map values. Where possible it is recommended to use the abstract MapBase interface for accessing or updating the contents of a map as this allows algorithms to be used interchangeably with different map representations. The following reviews methods of the abstract map interface. Documentation specific to WCS- and HEALPix-based maps is provided in HEALPix-based Maps and WCS-based Maps.

## Getting Started¶

All map objects have an abstract inteface provided through the methods of the MapBase. These methods can be used for accessing and manipulating the contents of a map without reference to the underlying data representation (e.g. whether a map uses WCS or HEALPix pixelization). For applications which do depend on the specific representation one can also work directly with the classes derived from MapBase. In the following we review some of the basic methods for working with map objects.

### Constructing with Factory Methods¶

The MapBase class provides a create factory method to facilitate creating an empty map object from scratch. The map_type argument can be used to control the pixelization scheme (WCS or HPX) and whether the map internally uses a sparse representation of the data.

from gammapy.maps import MapBase
from astropy.coordinates import SkyCoord
position = SkyCoord(0.0, 5.0, frame='galactic', unit='deg')

# Create a WCS Map
m_wcs = MapBase.create(binsz=0.1, map_type='wcs', skydir=position, width=10.0)

# Create a HPX Map
m_hpx = MapBase.create(binsz=0.1, map_type='hpx', skydir=position, width=10.0)


Higher dimensional map objects (cubes and hypercubes) can be constructed by passing a list of MapAxis objects for non-spatial dimensions with the axes parameter:

from gammapy.maps import MapBase, MapAxis
from astropy.coordinates import SkyCoord
position = SkyCoord(0.0, 5.0, frame='galactic', unit='deg')
energy_axis = MapAxis.from_bounds(100., 1E5, 12, interp='log')

# Create a WCS Map
m_wcs = MapBase.create(binsz=0.1, map_type='wcs', skydir=position, width=10.0,
axes=[energy_axis])

# Create a HPX Map
m_hpx = MapBase.create(binsz=0.1, map_type='hpx', skydir=position, width=10.0,
axes=[energy_axis])


Multi-resolution maps (maps with a different pixel size or geometry in each image plane) can be constructed by passing a vector argument for any of the geometry parameters. This vector must have the same shape as the non-spatial dimensions of the map. The following example demonstrates creating an energy cube with a pixel size proportional to the Fermi-LAT PSF:

import numpy as np
from gammapy.maps import MapBase, MapAxis
from astropy.coordinates import SkyCoord
position = SkyCoord(0.0, 5.0, frame='galactic', unit='deg')
energy_axis = MapAxis.from_bounds(100., 1E5, 12, interp='log')

binsz = np.sqrt((3.0*(energy_axis.center/100.)**-0.8)**2 + 0.1**2)

# Create a WCS Map
m_wcs = MapBase.create(binsz=binsz, map_type='wcs', skydir=position, width=10.0,
axes=[energy_axis])

# Create a HPX Map
m_hpx = MapBase.create(binsz=binsz, map_type='hpx', skydir=position, width=10.0,
axes=[energy_axis])


### Get, Set, and Fill Methods¶

All map objects have a set of accessor methods provided through the abstract MapBase class. These methods can be used to access or update the contents of the map irrespective of its underlying representation. Three types of accessor methods are provided:

All accessor methods accept as their first argument a coordinate tuple containing scalars, lists, or numpy arrays with one tuple element for each dimension of the map. By convention the first two elements in the coordinate tuple correspond to longitude and latitude followed by one element for each non-spatial dimension. Map coordinates can be expressed in one of three coordinate systems:

• idx : Pixel indices. These are explicit (integer) pixel indices into the map.
• pix : Coordinates in pixel space. Pixel coordinates are continuous defined on the interval [0,N-1] where N is the number of pixels along a given map dimension with pixel centers at integer values. For methods that reference a discrete pixel, pixel coordinates wil be rounded to the nearest pixel index and passed to the corresponding idx method.
• coord : Sky (spherical) coordinates. The tuple should contain longitude and latitude in degrees followed by one coordinate array for each non-spatial dimension.

The coordinate system accepted by a given accessor method can be inferred from the suffix of the method name (e.g. get_by_idx). The following demonstrates how one can access the same pixels of a WCS map using each of the three coordinate systems:

from gammapy.maps import MapBase
m = MapBase.create(binsz=0.1, map_type='wcs', width=10.0)

vals = m.get_by_idx( ([49,50],[49,50]) )
vals = m.get_by_pix( ([49.0,50.0],[49.0,50.0]) )
vals = m.get_by_coords( ([-0.05,-0.05],[0.05,0.05]) )


Coordinate arguments obey normal numpy broadcasting rules. The coordinate tuple may contain any combination of scalars, lists or numpy arrays as long as they have compatible shapes. For instance a combination of scalar and vector arguments can be used to perform an operation along a slice of the map at a fixed value along that dimension. Multi-dimensional arguments can be use to broadcast a given operation across a grid of coordinate values.

from gammapy.maps import MapBase
m = MapBase.create(binsz=0.1, map_type='wcs', width=10.0)
coords = np.linspace(-4.0,4.0,9)

# Equivalent calls for accessing value at pixel (49,49)
vals = m.get_by_idx( (49,49) )
vals = m.get_by_idx( ([49],[49]) )
vals = m.get_by_idx( (np.array([49]),np.array([49])) )

# Retrieve map values along latitude at fixed longitude=0.0
vals = m.get_by_coords( (0.0, coords) )
# Retrieve map values on a 2D grid of latitude/longitude points
vals = m.get_by_coords( (coords[None,:], coords[:,None]) )
# Set map values along slice at longitude=0.0 to twice their existing value
m.set_by_coords((0.0, coords), 2.0*m.get_by_coords((0.0, coords)))


The set and fill methods can both be used to set pixel values. The following demonstrates how one can set pixel values:

from gammapy.maps import MapBase
m = MapBase.create(binsz=0.1, map_type='wcs', width=10.0)

m.set_by_coords( ([-0.05,-0.05],[0.05,0.05]), [0.5, 1.5] )
m.fill_by_coords( ([-0.05,-0.05],[0.05,0.05]), weights=[0.5, 1.5] )


### Interpolation¶

Maps support interpolation via the get_by_coords and get_by_pix methods. Currently the following interpolation methods are supported:

• nearest : Return value of nearest pixel (no interpolation).
• linear : Interpolation with first order polynomial. This is the only interpolation method that is supported for all map types.
• quadratic : Interpolation with second order polynomial.
• cubic : Interpolation with third order polynomial.

Note that quadratic and cubic interpolation are currently only supported for WCS-based maps with regular geometry (e.g. 2D or ND with the same geometry in every image plane). linear and higher order interpolation by pixel coordinates is only supported for WCS-based maps.

from gammapy.maps import MapBase
m = MapBase.create(binsz=0.1, map_type='wcs', width=10.0)

m.get_by_coords( ([-0.05,-0.05],[0.05,0.05]), interp='linear' )
m.get_by_coords( ([-0.05,-0.05],[0.05,0.05]), interp='cubic' )


### Projection¶

The reproject method can be used to project a map onto a different geometry. This can be used to convert between different WCS projections, extract a cut-out of a map, or to convert between WCS and HPX map types. If the projection geometry lacks non-spatial dimensions then the non-spatial dimensions of the original map will be copied over to the projected map.

from gammapy.maps import WcsMapND, HpxGeom
geom = HpxGeom.create(nside=8, coordsys='GAL')
# Convert LAT standard IEM to HPX (nside=8)
m_proj = m.project(geom)
m_proj.write('gll_iem_v06_hpx_nside8.fits')


### Iterating on a Map¶

Iterating over a map can be performed with the iter_by_coords and iter_by_pix methods. These return an iterator that traverses the map returning (value, coordinate) pairs with map and pixel coordinates, respectively. The optional buffersize argument can be used to split the iteration into chunks of a given size. The following example illustrates how one can use this method to fill a map with a 2D Gaussian:

import numpy as np
from astropy.coordinates import SkyCoord
from gammapy.maps import MapBase
m = MapBase.create(binsz=0.05, map_type='wcs', width=10.0)
for val, coords in m.iter_by_coords(buffersize=10000):
skydir = SkyCoord(coords[0],coords[1], unit='deg')
sep = skydir.separation(m.geom.center_skydir).deg
new_val = np.exp(-sep**2/2.0)
m.set_by_coords(coords, new_val)


For maps with non-spatial dimensions the iter_by_image method can be used to loop over image slices:

from astropy.coordinates import SkyCoord
from astropy.convolution import Gaussian2DKernel, convolve
from gammapy.maps import MapBase
m = MapBase.create(binsz=0.05, map_type='wcs', width=10.0)
for img, idx in m.iter_by_image():
img = convolve(img, Gaussian2DKernel(stddev=2.0) )


### FITS I/O¶

Maps can be written to and read from a FITS file with the write and read methods:

from gammapy.maps import MapBase, WcsMapND
m = MapBase.create(binsz=0.1, map_type='wcs', width=10.0)
m.write('file.fits', extname='IMAGE')


Maps can be serialized to a sparse data format by calling write with sparse=True. This will write all non-zero pixels in the map to a data table appropriate to the pixelization scheme.

from gammapy.maps import MapBase, WcsMapND
m = MapBase.create(binsz=0.1, map_type='wcs', width=10.0)
m.write('file.fits', extname='IMAGE', sparse=True)


Sparse maps have the same read and write methods with the exception that they will be written to a sparse format by default:

from gammapy.maps import MapBase, HpxMapSparse
m = MapBase.create(binsz=0.1, map_type='hpx-sparse', width=10.0)
m.write('file.fits', extname='IMAGE')


By default files will be written to the gamma-astro-data-format specification for sky maps (see here). The GADF format offers a number of enhancements over existing map formats such as support for writing multi-resolution maps, sparse maps, and cubes with different geometries to the same file. For backward compatibility with software using other formats, the conv keyword option is provided to write a file using a format other than the GADF format:

from gammapy.maps import MapBase, MapAxis
energy_axis = MapAxis.from_bounds(100., 1E5, 12, interp='log')
m = MapBase.create(binsz=0.1, map_type='wcs', width=10.0,
axes=[energy_axis])
# Write a counts cube in a format compatible with the Fermi Science Tools
m.write('ccube.fits', conv='fgst-ccube')


### Visualization¶

All map objects provide a plot method for generating a visualization of a map. This method returns figure, axes, and image objects that can be used to further tweak/customize the image.

import matplotlib.pyplot as plt
from gammapy.maps import MapBase
from gammapy.maps.utils import fill_poisson
m = MapBase.create(binsz=0.1, map_type='wcs', width=10.0)
fill_poisson(m, mu=1.0, random_state=0)
fig, ax, im = m.plot(cmap='magma')
plt.colorbar(im)


## Examples¶

### Creating a Counts Cube from an FT1 File¶

This example shows how to fill a counts cube from an FT1 file:

from astropy.io import fits
from gammapy.maps import WcsGeom, WcsMapND, MapAxis

h = fits.open('ft1.fits')
energy_axis = MapAxis.from_bounds(100., 1E5, 12, interp='log')
m = WcsMapND.create(binsz=0.1, width=10.0, skydir=(45.0,30.0),
coordsys='CEL', axes=[energy_axis])
m.fill_by_coords((h['EVENTS'].data.field('RA'),
h['EVENTS'].data.field('DEC'),
h['EVENTS'].data.field('ENERGY')))
m.write('ccube.fits', conv='fgst-ccube')


### Generating a Cutout of a Model Cube¶

This example shows how to extract a cut-out of LAT galactic diffuse model cube using the reproject method:

from gammapy.maps import WcsGeom, WcsMapND
geom = WcsGeom(binsz=0.125, skydir=(45.0,30.0), coordsys='GAL', proj='AIT')
m_proj = m.reproject(geom)
m_proj.write('cutout.fits', conv='fgst-template')


## Using gammapy.maps¶

Gammapy tutorial notebooks that show examples using gammapy.maps:

More detailed documentation on the WCS and HPX classes in gammapy.maps can be found in the following sub-pages:

## Reference/API¶

### gammapy.maps Package¶

Maps (2D and 3D).

This is work in progress, we’re prototyping.

• Names and API might change.
• Not mentioned to users in the HTML docs at this point
• Contributions and feedback welcome!

#### Classes¶

 HpxGeom(nside[, nest, coordsys, region, …]) Geometry class for HEALPIX maps. HpxMap(geom, data) Base class for HEALPIX map classes. HpxMapND(geom[, data, dtype]) Representation of a N+2D map using HEALPix with two spatial dimensions and N non-spatial dimensions. HpxMapSparse(geom[, data, dtype]) Representation of a N+2D map using HEALPIX with two spatial dimensions and N non-spatial dimensions. MapAxis(nodes[, interp, name, node_type, unit]) Class representing an axis of a map. MapBase(geom, data) Abstract map class. MapCoords(data[, coordsys]) Represents a sequence of n-dimensional map coordinates. MapGeom Base class for WCS and HEALPix geometries. SparseArray(shape[, idx, data, dtype, …]) Sparse N-dimensional array object. WcsGeom(wcs, npix[, cdelt, axes, conv]) Geometry class for WCS maps. WcsMap(geom, data) Base class for WCS map classes. WcsMapND(geom[, data, dtype]) Representation of a N+2D map using WCS with two spatial dimensions and N non-spatial dimensions.