ref fix

Author: eloitanguy

README.md

@@ -54,8 +54,8 @@ POT provides the following generic OT solvers (links to examples):
 * [Co-Optimal Transport](https://pythonot.github.io/auto_examples/others/plot_COOT.html) [49] and
 [unbalanced Co-Optimal Transport](https://pythonot.github.io/auto_examples/others/plot_learning_weights_with_COOT.html) [71].
 * Fused unbalanced Gromov-Wasserstein [70].
-* [Optimal Transport Barycenters for Generic Costs](https://pythonot.github.io/auto_examples/barycenters/plot_free_support_barycenter_generic_cost.html) [74]
-* [Barycenters between Gaussian Mixture Models](https://pythonot.github.io/auto_examples/barycenters/plot_gmm_barycenter.html) [69, 74]
+* [Optimal Transport Barycenters for Generic Costs](https://pythonot.github.io/auto_examples/barycenters/plot_free_support_barycenter_generic_cost.html) [76]
+* [Barycenters between Gaussian Mixture Models](https://pythonot.github.io/auto_examples/barycenters/plot_gmm_barycenter.html) [69, 76]
 
 POT provides the following Machine Learning related solvers:
 

examples/barycenters/plot_free_support_barycenter_generic_cost.py

@@ -8,13 +8,13 @@
 a ground cost that is not a power of a norm. We take the example of ground costs
 :math:`c_k(x, y) = \|P_k(x)-y\|_2^2`, where :math:`P_k` is the (non-linear)
 projection onto a circle k. This is an example of the fixed-point barycenter
-solver introduced in [74] which generalises [20] and [43].
+solver introduced in [76] which generalises [20] and [43].
 
 The ground barycenter function :math:`B(y_1, ..., y_K) = \mathrm{argmin}_{x \in
 \mathbb{R}^2} \sum_k \lambda_k c_k(x, y_k)` is computed by gradient descent over
 :math:`x` with Pytorch.
 
-[74] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing
+[76] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing
 Barycentres of Measures for Generic Transport Costs. arXiv preprint 2501.04016
 (2024)
 

examples/barycenters/plot_gmm_barycenter.py

@@ -6,7 +6,7 @@
 
 This example illustrates the computation of a barycenter between Gaussian
 Mixtures in the sense of GMM-OT [69]. This computation is done using the
-fixed-point method for OT barycenters with generic costs [74], for which POT
+fixed-point method for OT barycenters with generic costs [76], for which POT
 provides a general solver, and a specific GMM solver. Note that this is a
 'free-support' method, implying that the number of components of the barycenter
 GMM and their weights are fixed.
@@ -22,7 +22,7 @@
 [69] Delon, J., & Desolneux, A. (2020). A Wasserstein-type distance in the space
 of Gaussian mixture models. SIAM Journal on Imaging Sciences, 13(2), 936-970.
 
-[74] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing
+[76] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing
 Barycentres of Measures for Generic Transport Costs. arXiv preprint 2501.04016
 (2024)
 
@@ -140,5 +140,3 @@ def draw_gmm(ms, Cs, ws, color=None, nstd=0.5, alpha=1, label=None, ax=None):
 draw_gmm(means_bar, covs_bar, ot.unif(n), color="C1", ax=ax)
 ax.axis(axis)
 ax.axis("off")
-
-# %%

ot/gmm.py

@@ -456,7 +456,7 @@ def gmm_barycenter_fixed_point(
 ):
     r"""
     Solves the Gaussian Mixture Model OT barycenter problem (defined in [69])
-    using the fixed point algorithm (proposed in [74]). The
+    using the fixed point algorithm (proposed in [76]). The
     weights of the barycenter are not optimized, and stay the same as the input
     `w_list` or are initialized to uniform.
 
@@ -504,7 +504,7 @@ def gmm_barycenter_fixed_point(
     ----------
     .. [69] Delon, J., & Desolneux, A. (2020). A Wasserstein-type distance in the space of Gaussian mixture models. SIAM Journal on Imaging Sciences, 13(2), 936-970.
 
-    .. [74] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing barycenters of Measures for Generic Transport Costs. arXiv preprint 2501.04016 (2024)
+    .. [76] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing barycenters of Measures for Generic Transport Costs. arXiv preprint 2501.04016 (2024)
 
     See Also
     --------

ot/lp/_barycenter_solvers.py

@@ -495,7 +495,7 @@ def free_support_barycenter_generic_costs(
     function B takes a list of K arrays of shape (n, d_k) and returns an array
     of shape (n, d).
 
-    This function implements [74] Algorithm 2, which generalises [20] and [43]
+    This function implements [76] Algorithm 2, which generalises [20] and [43]
     to general costs and includes convergence guarantees, including for discrete
     measures.
 
@@ -535,7 +535,7 @@ def free_support_barycenter_generic_costs(
 
     References
     ----------
-    .. [74] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing
+    .. [76] Tanguy, Eloi and Delon, Julie and Gozlan, Nathaël (2024). Computing
         barycenters of Measures for Generic Transport Costs. arXiv preprint
         2501.04016 (2024)