ave_rdc_tensor(dj,
vect,
N,
A,
weights=None)
 source code

Calculate the ensemble average RDC, using the 3D tensor.
This function calculates the average RDC for a set of XH bond vectors
from a structural ensemble, using the 3D tensorial form of the alignment
tensor. The formula for this ensemble average RDC value is:
_N_
\ T
Dij(theta) = dj > pc . mu_jc . Ai . mu_jc,
/__
c=1
where:

i is the alignment tensor index,

j is the index over spins,

c is the index over the states or multiple structures,

theta is the parameter vector,

dj is the dipolar constant for spin j,

N is the total number of states or structures,

pc is the population probability or weight associated with state c
(equally weighted to 1/N if weights are not provided),

mu_jc is the unit vector corresponding to spin j and state c,

Ai is the alignment tensor.
The dipolar constant is defined as:
dj = 3 / (2pi) d',
where the factor of 2pi is to convert from units of rad.s^1 to Hertz,
the factor of 3 is associated with the alignment tensor and the pure
dipolar constant in SI units is:
mu0 gI.gS.h_bar
d' =    ,
4pi r**3
where:

mu0 is the permeability of free space,

gI and gS are the gyromagnetic ratios of the I and S spins,

h_bar is Dirac's constant which is equal to Planck's constant divided
by 2pi,

r is the distance between the two spins.
 Parameters:
dj (float)  The dipolar constant for spin j.
vect (numpy matrix)  The unit XH bond vector matrix. The first dimension corresponds
to the structural index, the second dimension is the coordinates
of the unit vector.
N (int)  The total number of structures.
A (numpy rank2 3D tensor)  The alignment tensor.
weights (numpy rank1 array)  The weights for each member of the ensemble (the last member need
not be supplied).
 Returns: float
 The average RDC value.
