Minor changes (name changing mainly)

nn_fac/update_rules/min_vol_mu.py

 import warnings
 import numpy as np
 
-from nn_fac.utils.normalize_wh import normalize_WH
+import nn_fac.utils.normalize_wh as normalize_wh
 from nn_fac.utils.beta_divergence import beta_divergence
 
 eps = 1e-12
@@ -27,7 +27,7 @@ def KL_mu_min_vol(data, W, H, delta, lambda_, gamma = None, tol_update_lagrangia
 
     else:
         lagragian_multipliers_0 = np.zeros((k, 1)) #(D[:,0] - C[:,0] * W[:,0]).T
-        lagragian_multipliers = update_lagragian_multipliers(C, S, D, W, lagragian_multipliers_0, tol_update_lagrangian)
+        lagragian_multipliers = update_lagragian_multipliers_Wminvol(C, S, D, W, lagragian_multipliers_0, tol_update_lagrangian)
 
         W = W * ((((C + Jm1 @ lagragian_multipliers.T) ** 2 + S) ** 0.5 - (C + Jm1 @ lagragian_multipliers.T)) / (D + eps))
         
@@ -44,15 +44,15 @@ def gamma_line_search(data, W_update, W_gamma_init, H_gamma_init, beta, delta, g
     while cur_err > prev_error and gamma > 1e-16:
         gamma *= 0.8
         W_gamma = (1 - gamma) * W_prev + gamma * W_update
-        W_gamma, H_gamma = normalize_WH(W_gamma, H_gamma, "W")
+        W_gamma, H_gamma = normalize_wh.normalize_WH(W_gamma, H_gamma, "W")
         cur_log_det = compute_log_det(W_gamma, delta)
         cur_err = beta_divergence(data, W_gamma @ H_gamma, beta) + lambda_tilde * cur_log_det
     
     gamma = min(gamma * 1.2, 1)
     return W_gamma, H_gamma, gamma
 
-def update_lagragian_multipliers(C, S, D, W, lagrangian_multipliers_0, tol = 1e-6, n_iter_max = 1000):
-    # Comes from 
+def update_lagragian_multipliers_Wminvol(C, S, D, W, lagrangian_multipliers_0, tol = 1e-6, n_iter_max = 100):
+    # Comes from Multiplicative Updates for NMF with β-Divergences under Disjoint Equality Constraints, https://arxiv.org/pdf/2010.16223.pdf
     m, k = W.shape
     Jm1 = np.ones((m,1))
     Jk1 = np.ones(k)
@@ -74,7 +74,7 @@ def update_lagragian_multipliers(C, S, D, W, lagrangian_multipliers_0, tol = 1e-
             break
 
         if iter == n_iter_max - 1:
-            warnings.warn('Maximum of iterations reached in the update of mu.')
+            warnings.warn('Maximum of iterations reached in the update of the Lagrangian multipliers.')
 
     return lagrangian_multipliers