nifty8.domains.lm_space module#

class LMSpace(lmax, mmax=None)[source]#

Bases: StructuredDomain

Represents a set of spherical harmonic coefficients.

Its harmonic partner spaces are HPSpace and GLSpace.

Parameters:

lmax (int) – The maximum $l$ value of any spherical harmonic coefficient $a_{lm}$ that is represented by this object. Must be $\ge 0$ .
mmax (int, optional) – The maximum $m$ value of any spherical harmonic coefficient $a_{lm}$ that is represented by this object. If not supplied, it is set to lmax. Must be $\ge 0$ and $\le$ lmax.

__init__(lmax, mmax=None)[source]#

__repr__()[source]#: Return repr(self).

check_codomain(codomain)[source]#: Raises TypeError if codomain is not a matching partner domain for self.

Notes

This function only checks whether codomain is of type GLSpace or HPSpace.

get_conv_kernel_from_func(func)[source]#

Creates a convolution kernel defined by a function.

Assumes the function to be radially symmetric, e.g. only dependant on theta in radians.

Parameters:: func (function) – This function needs to take exactly one argument, which is colatitude in radians, and return the kernel amplitude at that colatitude.

get_default_codomain()[source]#

Returns a GLSpace object, which is capable of storing an accurate representation of data residing on self.

Returns:: The partner domain
Return type:: GLSpace

get_fft_smoothing_kernel_function(sigma)[source]#

Helper for Gaussian smoothing.

This method, which is only implemented for harmonic domains, helps to smoothe fields that are defined on a domain that has this domain as its harmonic partner. The returned function does a pointwise evaluation of a zero-centered Gaussian on the field values, which corresponds to a convolution with a Gaussian kernel with sigma standard deviation in position space.

Parameters:: sigma (float) – A real number representing a physical scale on which the smoothing takes place. Mathematically sigma is the standard deviation of a convolution with a normalized, zero-centered Gaussian that takes place in position space.
Returns:: A smoothing operation that multiplies values with a Gaussian kernel.
Return type:: function (array-like -> array-like)

get_k_length_array()[source]#

k vector lengths, if applicable.

Returns the length of the k vector for every pixel. This method is only implemented for harmonic domains.

Returns:: An array containing the k vector lengths
Return type:: nifty8.field.Field

get_unique_k_lengths()[source]#

Sorted unique k-vector lengths, if applicable.

Returns an array of floats containing the unique k vector lengths for this domain. This method is only implemented for harmonic domains.

property harmonic#

True iff this domain is a harmonic domain.

Type:: bool

property lmax#

maximum allowed $l$

The maximum $l$ value of any spherical harmonic coefficient $a_{lm}$ that is represented in this domain.

Type:: int

property mmax#

maximum allowed $m$

The maximum $m$ value of any spherical harmonic coefficient $a_{lm}$ that is represented in this domain.

Type:: int

property scalar_dvol#

uniform pixel volume, if applicable

Returns the volume factors of this domain as a floating point scalar, if the volume factors are all identical, otherwise returns None.

Type:: float or None

property shape#

number of pixels along each axis

The shape of the array-like object required to store information defined on the domain.

Type:: tuple of int

property size#

total number of pixels.

Equivalent to the products over all entries in the domain’s shape.

Type:: int