The GLSpace
class – GaussLegendre pixelization of the sphere¶

class
nifty.
GLSpace
[source]¶ Bases:
nifty.spaces.space.space.Space
NIFTY subclass for GaussLegendre pixelizations [1] of the twosphere.
Parameters: nlat : int
Number of latitudinal bins (or rings) that are used for this pixelization.
nlon : int, optional
Number of longditudinal bins that are used for this pixelization.
Raises: ValueError
If input nlat or nlon is invalid.
ImportError
If the pyHealpix module is not available
See also
hp_space
 A class for the HEALPix discretization of the sphere [2].
lm_space
 A class for spherical harmonic components.
References
[1] M. Reinecke and D. Sverre Seljebotn, 2013, “Libsharp  spherical harmonic transforms revisited”; arXiv:1303.4945 [2] K.M. Gorski et al., 2005, “HEALPix: A Framework for HighResolution Discretization and Fast Analysis of Data Distributed on the Sphere”, ApJ 622..759G. Attributes
dim
Returns the number of pixeldimensions the object has. harmonic
Returns True if this space is a harmonic space. nlat
Number of latitudinal bins (or rings) that are used for this pixelization. nlon
Number of longditudinal bins that are used for this pixelization. total_volume
Returns the total volume of the space. shape
The domainobject’s shape contribution to the underlying array. Methods
copy
()Returns a copy of this Space instance. get_distance_array
(distribution_strategy)The distances of the pixel to zero. get_fft_smoothing_kernel_function
(sigma)This method returns a smoothing kernel function. weight
(x[, power, axes, inplace])Weights the field on this domain with the space’s volumeweights. 
get_distance_array
(distribution_strategy)[source]¶ The distances of the pixel to zero.
This returns an array that gives for each pixel its distance to the center of the manifolds grid.
Parameters: distribution_strategy : str
The distribution_strategy which shall be used the returned distributed_data_object.
Returns: distributed_data_object
A d2o containing the distances
Raises: NotImplementedError
If called for this abstract class.

get_fft_smoothing_kernel_function
(sigma)[source]¶ This method returns a smoothing kernel function.
This method, which is only implemented for harmonic spaces, helps smoothing fields that live in a position space that has this space as its harmonic space. The returned function multiplies field values of a field with a zero centered Gaussian which corresponds to a convolution with a Gaussian kernel and sigma standard deviation in position space.
Parameters: sigma : float
A real number representing a physical scale on which the smoothing takes place. The smoothing is defined with respect to the real physical field and points that are closer together than one sigma are blurred together. Mathematically sigma is the standard deviation of a convolution with a normalized, zerocentered Gaussian that takes place in position space.
Returns: function (arraylike > arraylike)
A smoothing operation that multiplies values with a Gaussian kernel.
Raises: NotImplementedError :
If called for this abstract class.

weight
(x, power=1, axes=None, inplace=False)[source]¶ Weights the field on this domain with the space’s volumeweights.
Weights hereby refer to integration weights, as they appear in discretized integrals. Per default, this function mutliplies each bin of the field x by its volume, which lets it behave like a density (top form). However, different powers of the volume can be applied with the power parameter. The axes parameter specifies which of the field array’s indices correspond to this domain.
Parameters: x : distributed_data_object
The fields data array.
power : int, optional
The power to which the volumeweight is raised (default: 1).
axes : {int, tuple}, optional
Specifies the axes of x which represent this domain (default: None). If axes==None:
weighting is applied with respect to all axes
inplace : bool, optional
If this is True, the weighting is done on the values of x, if it is False, x is not modified and this method returns a weighted copy of x (default: False).
Returns: distributed_data_object
A weighted version of x, with volumeweights raised to the given power.
Raises: NotImplementedError
If called for this abstract class.

dim
¶ Returns the number of pixeldimensions the object has.
Returns: int
An Integer representing the number of pixels the discretized manifold has.
Raises: NotImplementedError
If called for this abstract class.

harmonic
¶ Returns True if this space is a harmonic space.
Raises: NotImplementedError
If called for this abstract class.

nlat
¶ Number of latitudinal bins (or rings) that are used for this pixelization.

nlon
¶ Number of longditudinal bins that are used for this pixelization.

shape
¶ The domainobject’s shape contribution to the underlying array.
Returns: tuple of ints
The shape of the underlying arraylike object.
Raises: NotImplementedError
If called for this abstract class.

total_volume
¶ Returns the total volume of the space.
Returns: float
A real number representing the sum of all pixel volumes.
Raises: NotImplementedError
If called for this abstract class.