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pysofft.stats

pysofft.stats

Classes:

Name Description
CharView

Helper class that allows to acces a characteristic function \(M_{l,n,k}\) by its indices l,n,k.

CharFuncSO3

A class to represent Charactersitic functions \(M_{lnk}\) of distributions \(\rho(\alpha,\beta,\gamma)\) on SO(3).

CharFuncFactory

Factory that can create various characteristic functions of probability distribitions on SO(3)

CharView [source]

Helper class that allows to acces a characteristic function \(M_{l,n,k}\) by its indices l,n,k. i.e. charview[l,n,k] returns \(M_{l,n,k}\). It is also possible to use slice notation i.e. charview[:,0,:] returns a view into \(M_{l,n,k}\) corresponding to all values with n=0.

Attributes:

Name Type Description
bw int
Bandwidth
array (ndarray, ((4 * bw ** 4 - bw) / 3,), complex)
characteristic function array
ls (ndarray, (bw,), int64)
l indices 0,...,bw
ns (ndarray, 2 * bw + 1, int64)
n indices 0,...,bw,-bw+1,...,-1
ks (ndarray, 2 * bw + 1, int64)
k indices 0,...,bw,-bw+1,...,-1
_lnks (ndarray, (3, (4 * bw ** 4 - bw) / 3), int64)
l,n,k value grid
_lookups (ndarray, ((4 * bw ** 4 - bw) / 3,), int64)
array ids associated to each entry of _lnks

CharFuncSO3 [source]

Bases: ndarray

A class to represent Charactersitic functions \(M_{lnk}\) of distributions \(\rho(\alpha,\beta,\gamma)\) on SO(3). $\(M_{lnk} = \int_{SO(3)} \rho(\alpha,\beta,\gamma) D^l_{nk}(\alpha,\beta,\gamma) sin(\beta)\,d\alpha d\beta d\gamma\)$ where \(D^l_{nk}(\alpha,\beta,\gamma)\) are Wigner-D matrices.

Acts as a normal numpy array with additional attributes

Attributes:

Name Type Description
bw int
Bandwidth of the distribution.
soft Soft
Fourier transform instance on SO(3)
Methods
lnk CharView
allows to acces $M_{lnk}$ by its indices l,n,k
distrib (ndarray, (2 * bw,) * 3, complex)
property that calculates the SO3 distribution by inverse fourier transform of the current characteristic function.

Methods:

Name Description
mean

Computes the average of a scalar/ndarray valued function on SO3 using the current probability distribution.

mean_density

Expects the density to be of shape (…,Nr,Ntheta,Nphi) where the last three dimensions correspond to the spherical coordinates and … can be any shape

mean_spherical_coeff

Expects input coeff to be stored in a 1d array with the l,m's coefficient beeing at location $ l(l+1)+m $.

mean(so3_function) [source]

Computes the average of a scalar/ndarray valued function on SO3 using the current probability distribution. Expects the function values to be given in the shape shape (M1,…,Mn,2bw,2bw,2bw) and (2bw,2bw,2bw) for scalar functions. Where bw is the bandwidth of the this probability distribution i.e. self._soft.bw and M1,…,Mn are the value array dimensions)

mean_density(density) [source]

Expects the density to be of shape (…,Nr,Ntheta,Nphi) where the last three dimensions correspond to the spherical coordinates and … can be any shape

mean_spherical_coeff(spherical_harmonic_coeff) [source]

Expects input coeff to be stored in a 1d array with the l,m's coefficient beeing at location $ l(l+1)+m $.

CharFuncFactory [source]

Factory that can create various characteristic functions of probability distribitions on SO(3) All of the distributions here use orthonormalized versions of the Wigner D matrices …

Methods:

Name Description
uniform

creates char function of uniform distribution

uniform(bw=16) [source] staticmethod

Creates uniform characteristif function $$ M_{lnk} = delta_{l,0}delta_{n,0}delta_{k,0} $$

delta(bw=16, angles=None) [source] staticmethod

Creates characteristic function for the deltadistribution $$ M_{lnk} = D^l_{nk}(alpha,beta,gamma) $$