Classes

HealpixBase

class mhealpy.HealpixBase(uniq=None, order=None, nside=None, npix=None, scheme='ring', coordsys=None, base=None)

Bases: object

Basic operations related to HEALPix pixelization, for which the map contents information is not needed. This class is conceptually very similar the the Healpix_Base class of Healpix_cxx.

Single resolution maps are fully defined by specifying their order (or NSIDE) and ordering scheme (“RING” or “NESTED”).

Multi-resolution maps follow an explicit “NUNIQ” scheme, with each pixel identfied by a _uniq_ number. No specific is needed nor guaranteed.

Warning

The initialization input is not validated by default. Consider calling is_mesh_valid() after initialization, otherwise results might be unexpected.

Parameters:

• uniq (array) – Explicit numbering of each pixel in an “NUNIQ” scheme.

• Order (int) – Order of HEALPix map.

• nside (int) – Alternatively, you can specify the NSIDE parameter.

• npix (int) – Alternatively, you can specify the total number of pixels.

• scheme (str) – Healpix scheme. Either ‘RING’, ‘NESTED’ or ‘NUNIQ’

• coordsys (BaseFrameRepresentation or str) – Instrinsic coordinates of the map. Either ‘G’ (Galactic), ‘E’ (Ecliptic) , ‘C’ (Celestial = Equatorial) or any other coordinate frame recognized by astropy.

• base (HealpixBase) – Alternatively, you can copy the properties of another HealpixBase object

classmethod adaptive_moc_mesh(max_nside, split_fun, coordsys=None)

Return a MOC mesh with an adaptive resolution determined by an arbitrary function.

Parameters:

• max_nside (int) – Maximum HEALPix nside to consider

• split_fun (function) – This method should return True if a pixel

• order (should be split into pixel of a higher) –

• otherwise. (and False) –

• integers (It takes two) –

• start (inclusive) and stop (exclusive) –

• a (which correspond to a single pixel in nested rangeset format for) –

• max_nside. (map of nside) –

• coordsys (BaseFrameRepresentation or str) – Assigns a coordinate system to the map

Returns:

HealpixBase

classmethod moc_from_pixels(nside, pixels, nest=False, coordsys=None)

Return a MOC mesh where a list of pixels are kept at a given nside, and every other pixel is appropiately downsampled.

Also see the more generic adaptive_moc() and adaptive_moc_mesh().

Parameters:

• nside (int) – Maximum healpix NSIDE (that is, the NSIDE for the pixel list)

• pixels (array) – Pixels that must be kept at the finest pixelation

• nest (bool) – Whether the pixels are a ‘NESTED’ or ‘RING’ scheme

• coordsys (BaseFrameRepresentation or str) – Assigns a coordinate system to the map

conformable(other)

For single-resolution maps, return True if both maps have the same nside, scheme and coordinate system.

For MOC maps, return True if both maps have the same list of UNIQ pixels (including the ordering)

property npix

Get number of pixels.

For multi-resolutions maps, this corresponds to the number of utilized UNIQ pixels.

Returns:

int

property order

Get map order

Returns:

int

property nside

Get map NSIDE

Returns:

int

property scheme

Return HEALPix scheme

Returns:

Either ‘NESTED’, ‘RING’ or ‘NUNIQ’

Return type:

str

property is_nested

Return true if scheme is NESTED or NUNIQ

Return

bool

property is_ring

Return true if scheme is RING

Return

bool

property is_moc

Return true if this is a Multi-Dimensional Coverage (MOC) map (multi-resolution)

Returns:

bool

pix_rangesets(nside=None, argsort=False)

Get the equivalent range of child pixels in nested scheme for a map of equal or higher nside

Parameters:

• nside (int or None) – Nside of output range sets. If None, the map nside will be used. nside = mhealpy.MAX_NSIDE returns the cached result

• argsort (bool) – Also return also the indices that would sort the array.

Returns:

With columns named ‘start’ (inclusive) and

’stop’ (exclusive)

Return type:

recarray

pix_order_list()

Get a list of lists containing all pixels sorted by order

Returns:

(pix_per_order, nest_pix_per_order)

Each list has a size equal to the map order. Each element is a list of all pixels whose order matches the index of the list position. The first output contains the index of the pixels, while the second contains their coresponding pixel number in a nested scheme.

Return type:

(list, list)

pix2range(nside, pix)

Get the equivalent range of child pixels in nested scheme for a map of equal or higher nside

Parameters:

• nside (int) – Nside of output range sets

• pix (int or array) – Pixel numbers

Returns:

Start pixel (inclusive) and

stop pixel (exclusive)

Return type:

(int or array, int or array)

pixarea(pix=None)

Return area of a pixel

Parameters:

pix (int or array) – Pixel number. Only relevant for MOC maps. Default: All pixels for MOC, a single value for single resolution

Returns:

Quantity

pix2ang(pix, lonlat=False)

Return the coordinates of the center of a pixel

Parameters:

pix (int or array) –

Returns:

(float or array, float or array)

pix2vec(pix)

Return a vector corresponding to the center of a pixel

Parameters:

pix (int or array) –

Returns:

Size (3,N)

Return type:

array

pix2skycoord(pix)

Return the sky coordinate for the center of a given pixel

Parameters:

pix (int or array) – Pixel number

Returns:

SkyCoord

ang2pix(theta, phi=None, lonlat=False)

Get the pixel (as used in []) that contains a given coordinate

Parameters:

• theta (float, array or SkyCoord) – Zenith angle

• phi (float or arrray) – Azimuth angle

Returns:

int or array

vec2pix(x, y, z)

Get the pixel (as used in []) that contains a given coordinate

Parameters:

• x (float or array) – x coordinate

• y (float or array) – y coordinate

• z (float or array) – z coordinate

Returns:

int or array

pix2uniq(pix)

Get the UNIQ representation of a given pixel index.

Parameters:

pix (int) – Pixel number in the current scheme (as used for [])

property uniq

Get an array with the NUNIQ numbers for all pixels

nest2pix(pix)

Get the corresponding pixel in the current grid for a pixel in NESTED scheme. For MOC map, return the pixel that contains it.

Parameters:

pix (int or array) – Pixel number in NESTED scheme. Must correspond to a map of the same order as the current.

Returns:

int or array

get_interp_weights(theta, phi=None, lonlat=False)

Return the 4 closest pixels on the two rings above and below the location and corresponding weights. Weights are provided for bilinear interpolation along latitude and longitude

Parameters:

• theta (float or array) – Zenith angle (rad)

• phi (float or array) – Azimuth angle (rad)

Returns:

(pixels, weights), each with of (4,) if the input is scalar,

if (4,N) where N is size of theta and phi. For MOC maps, these pixel numbers might repeate.

Return type:

tuple

get_all_neighbours(theta, phi=None, lonlat=False)

Return the 8 nearest pixels. For MOC maps, these might repeat, as this is equivalent to raterizing the maps to the highest order, getting the neighbohrs, and then finding the pixels tha contain them.

Parameters:

• theta (float or int or array) – Zenith angle (rad). If phi is None, these are assummed to be pixels numbers.

• phi (float or array or None) – Azimuth angle (rad)

Returns:

pixel number of the SW, W, NW, N, NE, E, SE and S neighbours,

shape is (8,) if input is scalar, otherwise shape is (8, N) if input is of length N. If a neighbor does not exist (it can be the case for W, N, E and S) the corresponding pixel number will be -1.

Return type:

array

is_mesh_valid()

Return True if the map pixelization is valid. For single resolution this simply checks that the size is a valid NSIDE value. For MOC maps, it checks that every point in the sphere is covered by one and only one pixel.

Returns:

True

query_polygon(vertices, inclusive=False, fact=4)

Returns the pixels whose centers lie within the convex polygon defined by the vertices array (if inclusive is False), or which overlap with this polygon (if inclusive is True).

Parameters:

• vertices (float) – Vertex array containing the vertices of the polygon, shape (N, 3).

• inclusive (bool) – f False, return the exact set of pixels whose pixels centers lie within the region; if True, return all pixels that overlap with the region.

• fact (int) – Only used when inclusive=True. The overlapping test will be done at the resolution fact*nside. For NESTED ordering, fact must be a power of 2, less than 2**30, else it can be any positive integer. Default: 4.

Returns:

The pixels which lie within the given polygon.

Return type:

int array

query_disc(vec, radius, inclusive=False, fact=4)

Parameters:

• vec (float, sequence of 3 elements, SkyCoord) – The coordinates of unit vector defining the disk center.

• radius (float) – The radius (in radians) of the disk

• inclusive (bool) – f False, return the exact set of pixels whose pixels centers lie within the region; if True, return all pixels that overlap with the region.

• fact (int) – Only used when inclusive=True. The overlapping test will be done at the resolution fact*nside. For NESTED ordering, fact must be a power of 2, less than 2**30, else it can be any positive integer. Default: 4.

Returns:

The pixels which lie within the given disc.

Return type:

int array

query_strip(theta1, theta2, inclusive=False)

Returns pixels whose centers lie within the colatitude range defined by theta1 and theta2 (if inclusive is False), or which overlap with this region (if inclusive is True). If theta1<theta2, the region between both angles is considered, otherwise the regions 0<theta<theta2 and theta1<theta<pi.

Parameters:

• theta (float) – First colatitude (radians)

• phi (float) – Second colatitude (radians)

• inclusive (bool) – f False, return the exact set of pixels whose pixels centers lie within the region; if True, return all pixels that overlap with the region.

Returns:

The pixels which lie within the given strip.

Return type:

int array

boundaries(pix, step=1)

Returns an array containing vectors to the boundary of the nominated pixel.

The returned array has shape (3, 4*step), the elements of which are the x,y,z positions on the unit sphere of the pixel boundary. In order to get vector positions for just the corners, specify step=1.

plot_grid(ax='mollview', ax_kw={}, step=32, coord=None, **kwargs)

Plot the pixel boundaries of a Healpix grid

Parameters:

• ax (WCSAxes or str) – Astropy’s WCSAxes to plot the map. Either an existing instance or the name of a registered projection.

• ax_kw (dict) – Extra arguments if a new axes needs to be created.

• step (int) – How many points per pixel side

• coord (str) – Instrinsic coordinates of the map. Either ‘G’ (Galactic), ‘E’ (Ecliptic) , ‘C’ (Celestial = Equatorial) or any other coordinate frame recognized by astropy. The default is ‘C’ unless coordsys is defined. This option overrides coordsys

• **kwargs – Passed to matplotlib.pyplot.plot()

Returns:

The first return value

corresponds to the output pyplot.plot() for one of the pixels. The second is the astropy WCSAxes object used.

Return type:

matplotlib.lines.Line2D list, WCSAxes

moc_sort()

Sort the uniq pixels composing a MOC map based on its rangeset representation

HealpixMap

class mhealpy.HealpixMap(data=None, uniq=None, order=None, nside=None, scheme='ring', base=None, density=False, dtype=None, coordsys=None, unit=None)

Bases: HealpixBase

Object-oriented healpy wrapper with support for multi-resolutions maps (known as multi-order coverage map, or MOC).

You can instantiate a map by providing either:

• Size (through order or nside), and a scheme (‘RING’ or ‘NESTED’). This will initialize an empty map.

• A list of UNIQ pixels. This will initialize a MOC map. Providing the values for each pixel is optional, zero-initialized by default.

• An array (in data) and an a scheme (‘RING’ or ‘NESTED’). This will initialize the contents of the single-resolution map.

• A HealpixBase object. The data will be zero-initialized.

Warning

The initialization input is not validated by default. Consider calling is_mesh_valid() after initialization, otherwise results might be unexpected.

Regardless of the underlaying grid, you can operate on maps using *, /, +, -, **, == and abs. For binary operations the result always corresponds to the finest grid, so there is no loss of information. If any of the operands is a MOC, the result is a MOC with an appropiate updated grid.. If both operands have the same NSIDE, the scheme of the result corresponds to the left operand. If you want to preserve the grid for a specific operand, use *=, /=, etc.

The result of most binary operations have the same density parameter as the left-most operand, except the following cases: 1) the product of a density-like maps with a histogram-like results in histogram-like map. 2) the ratio between two histogram-like maps is a density-like map. Operations with scalars leave the map type unchanged.

Warning

Information might degrade if you use in-place operators (e.g. *=, /=)

The maps are array-like, that is, the can be casted into a regular numpy array (as used by healpy), are iterable (over the pixel values) and can be used with built-in function such as sum and max.

You can also access the value of pixels using regular numpy indexing with []. For MOC maps, no specific pixel ordering is guaranted. For a given pixel number ipix in the current grid, you can get the corresponding UNIQ pixel number using m.pix2uniq(ipix).

Parameters:

• data (array) – Values to initialize map. Zero-initialized it not provided. The map NSIDE is deduced from the array size, unless uniq is specified in which case this is considered a multi-resolution map.

• uniq (array or HealpixBase) – List of NUNIQ pixel number to initialize a MOC map.

• order (int) – Order of HEALPix map.

• nside (int) – Alternatively, you can specify the NSIDE parameter.

• scheme (str) – Healpix scheme. Either ‘RING’, ‘NESTED’ or ‘NUNIQ’

• base (HealpixBase) – Specify the grid using a HealpixBase object

• density (bool) – Whether the value of each pixel should be treated as counts in a histogram (False) or as the value of a [density] function evaluated at the center of the pixel (True). This affect operations involving the splitting of a pixel.

• dtype (array) – Numpy data type. Will be ignored if data is provided.

• coordsys (BaseFrameRepresentation or str) – Instrinsic coordinates of the map. Either ‘G’ (Galactic), ‘E’ (Ecliptic) , ‘C’ (Celestial = Equatorial) or any other coordinate frame recognized by astropy.

to(unit, equivalencies=[], update=True, copy=True)

Return a map with converted units

Parameters:

• unit (unit-like) – Unit to convert to.

• equivalencies (list or tuple) – A list of equivalence pairs to try if the units are not directly convertible.

• update (bool) – If update is False, only the units will be changed without updating the contents accordingly

• copy (bool) – If True (default), then the value is copied. Otherwise, a copy will only be made if necessary.

classmethod read_map(filename, field=None, uniq_field=0, hdu=1, density=False)

Read a HEALPix map from a FITS file.

Parameters:

• filename (Path) – Path to file

• field (int) – Column where the map contents are. Default: 0 for single-resolution maps, 1 for MOC maps.

• uniq_field (int) – Column where the UNIQ pixel numbers are. For MOC maps only.

• hdu (int) – The header number to look at. Starts at 0.

• density (bool) – Whether this is a histogram-like or a density-like map.

Returns:

HealpixMap

get_fits_hdu(extra_maps=None, column_names=None)

Build HDU needed to store map in a FITS file

Parameters:

• extra_maps (HealpixMap or array) – Save more maps in the same file as extra columns. Must be conformable.

• column_names (str or array) – Name of colums. Must have the same length as the number for maps. Defaults to ‘CONTENTSn’, where n is the map number (ommited for a single map). For MOC maps, the pixel information is always stored in the first column, called ‘UNIQ’.

Returns:

astropy.io.fits.BinTableHDU

write_map(filename, extra_maps=None, column_names=None, extra_header=None, overwrite=False)

Write map to disc.

Parameters:

• filename (Path) – Path to output file

• extra_maps (HealpixMap or array) – Save more maps in the same file as extra columns. Must be conformable.

• column_names (str or array) – Name of colums. Must have the same length as the number for maps. Defaults to ‘CONTENTSn’, where n is the map number (ommited for a single map). For MOC maps, the pixel information is always stored in the first column, called ‘UNIQ’.

• extra_header (iterable) – Iterable of (keyword, value, [comment]) tuples

• overwrite (bool) – If True, overwrite the output file if it exists. Raises an OSError if False and the output file exists.

classmethod adaptive_moc_mesh(max_nside, split_fun, density=False, dtype=None, coordsys=None, unit=None)

Return a zero-initialized MOC map, with an adaptive resolution determined by an arbitrary function.

Parameters:

• max_nside (int) – Maximum HEALPix nside to consider

• split_fun (function) – This method should return True if a pixel

• order (should be split into pixel of a higher) –

• otherwise. (and False) –

• integers (It takes two) –

• start (inclusive) and stop (exclusive) –

• a (which correspond to a single pixel in nested rangeset format for) –

• max_nside. (map of nside) –

• density (bool) – Will be pass to HealpixMap initialization.

• dtype (dtype) – Data type

• coordsys (BaseFrameRepresentation or str) – Assigns a coordinate system to the map

Returns:

HealpixMap

classmethod moc_from_pixels(nside, pixels, nest=False, density=False, dtype=None, coordsys=None, unit=None)

Return a zero-initialize MOC map where a list of pixels are kept at a given nside, and every other pixel is appropiately downsampled.

Also see the more generic adaptive_moc_mesh().

Parameters:

• nside (int) – Maximum healpix NSIDE (that is, the NSIDE for the pixel order list)

• pixels (array) – Pixels that must be kept at the finest pixelation

• nest (bool) – Whether the pixels are a ‘NESTED’ or ‘RING’ scheme

• density (bool) – Wheather the map is density-like or histogram-like

• dtype – Daty type

• coordsys (BaseFrameRepresentation or str) – Assigns a coordinate system to the map

classmethod moc_histogram(nside, samples, max_value, nest=False, weights=None, coordsys=None, unit=None)

Generate an adaptive MOC map by histogramming samples.

If the number of samples is greater than the number of pixels in a map of the input nside, consider generating a single-resolution map and then use to_moc().

Also see the more generic adaptive_moc_mesh().

Parameters:

• nside (int) – Healpix NSIDE of the samples and maximum NSIDE of the output map

• samples (int array) – List of pixels representing the samples. e.g. the output of healpy.ang2pix().

• max_value – maximum number of samples (or sum of weights) per pixel. Note that due to limitations of the input nside, the output could contain pixels with a value largen than this

• nest (bool) – Whether the samples are in NESTED or RING scheme

• weights (array) – Optionally weight the samples. Both must have the same size.

• coordsys (BaseFrameRepresentation or str) – Assigns a coordinate system to the map

Returns:

HealpixMap

to_moc(max_value)

Convert a single-resolution map into a MOC based on the maximum value a given pixel the latter should have.

Note

The maximum nside of the MOC map is the same as the nside of the single-resolution map, so the output map could contain pixels with a value greater than this.

If the map is already a MOC map, it will recompute the grid accordingly by combining uniq pixels. Uniq pixels are never split.

Also see the more generic adaptive_moc_mesh().

Parameters:

max_value – Maximum value per pixel of the MOC. Whether the map is histogram-like or density-like is taken into account.

Returns:

HealpixMap

density(density=None, update=True)

Switch between a density-like map and a histogram-like map.

Parameters:

• density (bool or None) – Whether the value of each pixel should be treated as counts in a histogram (False) or as the value of a [density] function evaluated at the center of the pixel (True). This affect operations involving the splitting of a pixel. None will leave this paramter unchanged.

• update (bool) – If True, the values of the map will be updated accordingly. Otherwise only the density parameter is changed.

Note

The updat=True the pixels values are divided/multiplied by their effective number of pixels rather than their solid angle area. In order to achieve this scale the map by 1/m.pixarea()

Returns:

The current density

Return type:

bool

property data

Get the raw data in the form of an array.

rasterize(nside=None, scheme='ring', uniq=None, order=None, npix=None, base=None)

Convert to map of a given NSIDE and scheme, or any arbitrary MOC mesh.

Parameters:

• uniq (array) – Explicit numbering of each pixel in an “NUNIQ” scheme.

• Order (int) – Order of HEALPix map.

• nside (int) – Alternatively, you can specify the NSIDE parameter.

• npix (int) – Alternatively, you can specify the total number of pixels.

• scheme (str) – Healpix scheme. Either ‘RING’, ‘NESTED’ or ‘NUNIQ’

• base (HealpixBase) – Alternatively, you can copy the properties of another HealpixBase object

Returns:

HealpixMap

get_wcs_img(wcs, coord=None, rasterize=True)

Rasterize map into a set of WCS axes.

Parameters:

• wcs (WCS or WCSAxes) – Astropy’s WCSAxes to plot the map. Either an existing instance or the name of a registered projection.

• coord (str) – Instrinsic coordinates of the map. Either ‘G’ (Galactic), ‘E’ (Ecliptic) , ‘C’ (Celestial = Equatorial) or any other coordinate frame recognized by astropy. The default is ‘C’ unless coordsys is defined. This option overrides coordsys

• rasterize (bool) – If True, the resulting image is equivalent to having called rasterize() before plotting. This only affects multi-resolution histogram-like maps.

Returns:

array

plot(ax='mollview', ax_kw={}, rasterize=True, coord=None, cbar=True, **kwargs)

Plot map. This is a wrapper for matplotlib.pyplot.imshow

Parameters:

• ax (WCSAxes or str) – Astropy’s WCSAxes to plot the map. Either an existing instance or the name of a registered projection.

• ax_kw (dict) – Extra arguments if a new axes needs to be created.

• rasterize (bool) – If True, the resulting image is equivalent to having called rasterize() before plotting. This only affects multi-resolution histogram-like maps.

• coord (str) – Instrinsic coordinates of the map. Either ‘G’ (Galactic), ‘E’ (Ecliptic) , ‘C’ (Celestial = Equatorial) or any other coordinate frame recognized by astropy. The default is ‘C’ unless coordsys is defined. This option overrides coordsys

• cbar (bool) – Whether to plot the colorbar.

• **kwargs – Passed to matplotlib.pyplot.imshow

Returns:

The first return value

corresponds to the output imgshow. The second is the astropy WCSAxes object used.

Return type:

AxesImage, WCSAxes

ang2pix(theta, phi=None, lonlat=False)

Get the pixel (as used in []) that contains a given coordinate

Parameters:

• theta (float, array or SkyCoord) – Zenith angle

• phi (float or arrray) – Azimuth angle

Returns:

int or array

boundaries(pix, step=1)

Returns an array containing vectors to the boundary of the nominated pixel.

The returned array has shape (3, 4*step), the elements of which are the x,y,z positions on the unit sphere of the pixel boundary. In order to get vector positions for just the corners, specify step=1.

conformable(other)

For single-resolution maps, return True if both maps have the same nside, scheme and coordinate system.

For MOC maps, return True if both maps have the same list of UNIQ pixels (including the ordering)

get_all_neighbours(theta, phi=None, lonlat=False)

Return the 8 nearest pixels. For MOC maps, these might repeat, as this is equivalent to raterizing the maps to the highest order, getting the neighbohrs, and then finding the pixels tha contain them.

Parameters:

• theta (float or int or array) – Zenith angle (rad). If phi is None, these are assummed to be pixels numbers.

• phi (float or array or None) – Azimuth angle (rad)

Returns:

pixel number of the SW, W, NW, N, NE, E, SE and S neighbours,

shape is (8,) if input is scalar, otherwise shape is (8, N) if input is of length N. If a neighbor does not exist (it can be the case for W, N, E and S) the corresponding pixel number will be -1.

Return type:

array

get_interp_val(theta, phi=None, lonlat=False)

Return the bi-linear interpolation value of a map using 4 nearest neighbours.

For MOC maps, this is equivalent to raterizing the map first to the highest order.

Parameters:

• theta (float, array or SkyCoord) – Zenith angle (rad)

• phi (float or array) – Azimuth angle (rad)

Returns:

scalar or array

get_interp_weights(theta, phi=None, lonlat=False)

Return the 4 closest pixels on the two rings above and below the location and corresponding weights. Weights are provided for bilinear interpolation along latitude and longitude

Parameters:

• theta (float or array) – Zenith angle (rad)

• phi (float or array) – Azimuth angle (rad)

Returns:

(pixels, weights), each with of (4,) if the input is scalar,

if (4,N) where N is size of theta and phi. For MOC maps, these pixel numbers might repeate.

Return type:

tuple

is_mesh_valid()

Return True if the map pixelization is valid. For single resolution this simply checks that the size is a valid NSIDE value. For MOC maps, it checks that every point in the sphere is covered by one and only one pixel.

Returns:

True

property is_moc

Return true if this is a Multi-Dimensional Coverage (MOC) map (multi-resolution)

Returns:

bool

property is_nested

Return true if scheme is NESTED or NUNIQ

Return

bool

property is_ring

Return true if scheme is RING

Return

bool

nest2pix(pix)

Get the corresponding pixel in the current grid for a pixel in NESTED scheme. For MOC map, return the pixel that contains it.

Parameters:

pix (int or array) – Pixel number in NESTED scheme. Must correspond to a map of the same order as the current.

Returns:

int or array

property npix

Get number of pixels.

For multi-resolutions maps, this corresponds to the number of utilized UNIQ pixels.

Returns:

int

property nside

Get map NSIDE

Returns:

int

property order

Get map order

Returns:

int

pix2ang(pix, lonlat=False)

Return the coordinates of the center of a pixel

Parameters:

pix (int or array) –

Returns:

(float or array, float or array)

pix2range(nside, pix)

Get the equivalent range of child pixels in nested scheme for a map of equal or higher nside

Parameters:

• nside (int) – Nside of output range sets

• pix (int or array) – Pixel numbers

Returns:

Start pixel (inclusive) and

stop pixel (exclusive)

Return type:

(int or array, int or array)

pix2skycoord(pix)

Return the sky coordinate for the center of a given pixel

Parameters:

pix (int or array) – Pixel number

Returns:

SkyCoord

pix2uniq(pix)

Get the UNIQ representation of a given pixel index.

Parameters:

pix (int) – Pixel number in the current scheme (as used for [])

pix2vec(pix)

Return a vector corresponding to the center of a pixel

Parameters:

pix (int or array) –

Returns:

Size (3,N)

Return type:

array

pix_order_list()

Get a list of lists containing all pixels sorted by order

Returns:

(pix_per_order, nest_pix_per_order)

Each list has a size equal to the map order. Each element is a list of all pixels whose order matches the index of the list position. The first output contains the index of the pixels, while the second contains their coresponding pixel number in a nested scheme.

Return type:

(list, list)

pix_rangesets(nside=None, argsort=False)

Get the equivalent range of child pixels in nested scheme for a map of equal or higher nside

Parameters:

• nside (int or None) – Nside of output range sets. If None, the map nside will be used. nside = mhealpy.MAX_NSIDE returns the cached result

• argsort (bool) – Also return also the indices that would sort the array.

Returns:

With columns named ‘start’ (inclusive) and

’stop’ (exclusive)

Return type:

recarray

pixarea(pix=None)

Return area of a pixel

Parameters:

pix (int or array) – Pixel number. Only relevant for MOC maps. Default: All pixels for MOC, a single value for single resolution

Returns:

Quantity

plot_grid(ax='mollview', ax_kw={}, step=32, coord=None, **kwargs)

Plot the pixel boundaries of a Healpix grid

Parameters:

• ax (WCSAxes or str) – Astropy’s WCSAxes to plot the map. Either an existing instance or the name of a registered projection.

• ax_kw (dict) – Extra arguments if a new axes needs to be created.

• step (int) – How many points per pixel side

• coord (str) – Instrinsic coordinates of the map. Either ‘G’ (Galactic), ‘E’ (Ecliptic) , ‘C’ (Celestial = Equatorial) or any other coordinate frame recognized by astropy. The default is ‘C’ unless coordsys is defined. This option overrides coordsys

• **kwargs – Passed to matplotlib.pyplot.plot()

Returns:

The first return value

corresponds to the output pyplot.plot() for one of the pixels. The second is the astropy WCSAxes object used.

Return type:

matplotlib.lines.Line2D list, WCSAxes

query_disc(vec, radius, inclusive=False, fact=4)

Parameters:

• vec (float, sequence of 3 elements, SkyCoord) – The coordinates of unit vector defining the disk center.

• radius (float) – The radius (in radians) of the disk

• inclusive (bool) – f False, return the exact set of pixels whose pixels centers lie within the region; if True, return all pixels that overlap with the region.

• fact (int) – Only used when inclusive=True. The overlapping test will be done at the resolution fact*nside. For NESTED ordering, fact must be a power of 2, less than 2**30, else it can be any positive integer. Default: 4.

Returns:

The pixels which lie within the given disc.

Return type:

int array

query_polygon(vertices, inclusive=False, fact=4)

Returns the pixels whose centers lie within the convex polygon defined by the vertices array (if inclusive is False), or which overlap with this polygon (if inclusive is True).

Parameters:

• vertices (float) – Vertex array containing the vertices of the polygon, shape (N, 3).

• inclusive (bool) – f False, return the exact set of pixels whose pixels centers lie within the region; if True, return all pixels that overlap with the region.

• fact (int) – Only used when inclusive=True. The overlapping test will be done at the resolution fact*nside. For NESTED ordering, fact must be a power of 2, less than 2**30, else it can be any positive integer. Default: 4.

Returns:

The pixels which lie within the given polygon.

Return type:

int array

query_strip(theta1, theta2, inclusive=False)

Returns pixels whose centers lie within the colatitude range defined by theta1 and theta2 (if inclusive is False), or which overlap with this region (if inclusive is True). If theta1<theta2, the region between both angles is considered, otherwise the regions 0<theta<theta2 and theta1<theta<pi.

Parameters:

• theta (float) – First colatitude (radians)

• phi (float) – Second colatitude (radians)

• inclusive (bool) – f False, return the exact set of pixels whose pixels centers lie within the region; if True, return all pixels that overlap with the region.

Returns:

The pixels which lie within the given strip.

Return type:

int array

property scheme

Return HEALPix scheme

Returns:

Either ‘NESTED’, ‘RING’ or ‘NUNIQ’

Return type:

str

property uniq

Get an array with the NUNIQ numbers for all pixels

vec2pix(x, y, z)

Get the pixel (as used in []) that contains a given coordinate

Parameters:

• x (float or array) – x coordinate

• y (float or array) – y coordinate

• z (float or array) – z coordinate

Returns:

int or array

moc_sort()

Sort the uniq pixels composing a MOC map based on its rangeset representation