# Source code for ot.bregman._utils

```# -*- coding: utf-8 -*-
"""
Common tools of Bregman projections solvers for entropic regularized OT
"""

# Author: Remi Flamary <remi.flamary@unice.fr>
#         Nicolas Courty <ncourty@irisa.fr>
#

from ..utils import list_to_array
from ..backend import get_backend

[docs]
def geometricBar(weights, alldistribT):
"""return the weighted geometric mean of distributions"""
weights, alldistribT = list_to_array(weights, alldistribT)
nx = get_backend(weights, alldistribT)
assert (len(weights) == alldistribT.shape[1])
return nx.exp(nx.dot(nx.log(alldistribT), weights.T))

[docs]
def geometricMean(alldistribT):
"""return the  geometric mean of distributions"""
alldistribT = list_to_array(alldistribT)
nx = get_backend(alldistribT)
return nx.exp(nx.mean(nx.log(alldistribT), axis=1))

[docs]
def projR(gamma, p):
"""return the KL projection on the row constraints """
gamma, p = list_to_array(gamma, p)
nx = get_backend(gamma, p)
return (gamma.T * p / nx.maximum(nx.sum(gamma, axis=1), 1e-10)).T

[docs]
def projC(gamma, q):
"""return the KL projection on the column constraints """
gamma, q = list_to_array(gamma, q)
nx = get_backend(gamma, q)
return gamma * q / nx.maximum(nx.sum(gamma, axis=0), 1e-10)

```