Normalization in dd_models._multigaussfun

[sergeqzin]

Dear all,

The function dd_models._multigaussfun has a misleading normalization step, in my opinion

if not np.all(P==0):
        # Normalization
        P = np.squeeze(P)/np.sum([np.trapz(c,r) for c in P.T])

In K-Gaussian models, P is a matrix N \times K, where N is the size of the input r-axis. The columns are individual Gaussians normalized to the unit area. After the current normalization step, the integral of each Gaussian is 1/K. This is at least inconsistent with the model description in the documentation. E.g. from https://jeschkelab.github.io/DeerLab/_autosummary/deerlab.dd_gauss2.html#deerlab.dd_gauss2 I conclude that the condition (a1 + a2 = 1) yields a normalized distribution which is not true in reality.

The code below tests the normalization

import deerlab as dl
import numpy as np

r = np.linspace(1, 5, 200)

mean = 3
std = 0.5

P1 = dl.dd_gauss(r, 
                 mean, std
                 ) # expected: area = 1
P2 = dl.dd_gauss2(r, 
                  mean, std, 
                  mean, std, 
                  1/2, 1/2) # expected: area = 1
P3 = dl.dd_gauss3(r, 
                  mean, std, 
                  mean, std, 
                  mean, std, 
                  1/3, 1/3, 1/3) # expected: area = 1

print(np.trapz(P1, r)) # output: 1
print(np.trapz(P2, r)) # output: 0.5
print(np.trapz(P3, r)) # output: 0.3333

Thanks!

[sergeqzin]

Issue 2:

in dd_model.py, in the Section dd_gauss3, the variable notes is misspelled as ntoes. Because of this, the documentation on dd_gauss3 displays a LaTeX formula of dd_gauss2 (as it precedes dd_gauss3 in dd_models.py).

Please, fix this as well. Thank you!