inverse participation ratio

[eminamitani]

construct module to calculate inverse participation ratio

[Sctdhy]

nmodes=len(eigenvector)
iprdat=np.zeros(nmodes)
for i in range(nmodes):
vec=eigenvector[:,i]
inner=vecvec
ipr=innerinner
print(ipr.sum())
iprdat[i]=ipr.sum()
In the original paper, it seems that we should first calculate the sum of squares for the three directions of an atom within a particular pattern before squaring it again.

[eminamitani]

I made get_IPR_rev module to evaluate the following equation directly. The eigenvector of vibrational mode is normalized, thus, the denomintor is 1. Thus, I evaluate IPR by using np.power(eigenvector_for_mode,4).

[eminamitani]

And, this method and the previous version return the same results, since both evaluate the sum of respective elements to the 4th power, 1x^4+1y^4+1z^4 ..... Nx^4+Ny^4+Nz^4

[Sctdhy]

Thank you,Prof. Minamitani. I've sorted this problem.

[eminamitani]

I checked your point and implemented the original definition version as follows:

def get_IPR_original_definition(eigenvector):
    '''
    Inversion perticipation ratio
    $$
    IPR=N_{atom} \sum_{l=1}^{nmodes} (\sum_{\alpha}(u^l_\alpha^2)})^2 
    $$
    '''
    #eigenvector: np.array(3*natom, nmodes), eigenvector of the mode
    nmodes=len(eigenvector[1])
    natoms=len(eigenvector[0])//3

    eigen_3D = np.reshape(eigenvector.T, (nmodes, natoms, 3))

    vec2sum = np.sum(eigen_3D**2, axis=2) 
    ipr = np.sum(vec2sum**2, axis=1) * natoms

    return ipr