fix equation

Author: tgnassou

ot/da.py

@@ -680,12 +680,7 @@ def df(G):
  return G, L
 
 
-@deprecated()
-def OT_mapping_linear(xs, xt, reg=1e-6, ws=None,
- wt=None, bias=True, log=False):
- """ Deprecated see ot.gaussian.empirical_bures_wasserstein_mapping"""
- return empirical_bures_wasserstein_mapping(xs, xt, reg=1e-6, ws=None,
- wt=None, bias=True, log=False)
+OT_mapping_linear = deprecated(empirical_bures_wasserstein_mapping)
 
 
 def emd_laplace(a, b, xs, xt, M, sim='knn', sim_param=None, reg='pos', eta=1, alpha=.5,

ot/gaussian.py

@@ -84,8 +84,6 @@ def bures_wasserstein_mapping(ms, mt, Cs, Ct, log=False):
 
  if log:
  log = {}
- log['Cs'] = Cs
- log['Ct'] = Ct
  log['Cs12'] = Cs12
  log['Cs12inv'] = Cs12inv
  return A, b, log
@@ -179,23 +177,13 @@ def empirical_bures_wasserstein_mapping(xs, xt, reg=1e-6, ws=None,
  Cs = nx.dot((xs * ws).T, xs) / nx.sum(ws) + reg * nx.eye(d, type_as=xs)
  Ct = nx.dot((xt * wt).T, xt) / nx.sum(wt) + reg * nx.eye(d, type_as=xt)
 
- Cs12 = nx.sqrtm(Cs)
- Cs12inv = nx.inv(Cs12)
-
- M0 = nx.sqrtm(dots(Cs12, Ct, Cs12))
-
- A = dots(Cs12inv, M0, Cs12inv)
-
- b = mxt - nx.dot(mxs, A)
-
  if log:
- log = {}
+ A, b, log = bures_wasserstein_mapping(mxs, mxt, Cs, Ct, log=log)
  log['Cs'] = Cs
  log['Ct'] = Ct
- log['Cs12'] = Cs12
- log['Cs12inv'] = Cs12inv
  return A, b, log
  else:
+ A, b = bures_wasserstein_mapping(mxs, mxt, Cs, Ct)
  return A, b
 
 
@@ -251,7 +239,7 @@ def bures_wasserstein_distance(ms, mt, Cs, Ct, log=False):
  Cs12 = nx.sqrtm(Cs)
 
  B = nx.trace(Cs + Ct - 2 * nx.sqrtm(dots(Cs12, Ct, Cs12)))
- W = nx.norm(ms - mt) + B
+ W = nx.sqrt(nx.norm(ms - mt)**2 + B)
  if log:
  log = {}
  log['Cs12'] = Cs12
@@ -334,15 +322,12 @@ def empirical_bures_wasserstein_distance(xs, xt, reg=1e-6, ws=None,
 
  Cs = nx.dot((xs * ws).T, xs) / nx.sum(ws) + reg * nx.eye(d, type_as=xs)
  Ct = nx.dot((xt * wt).T, xt) / nx.sum(wt) + reg * nx.eye(d, type_as=xt)
- Cs12 = nx.sqrtm(Cs)
 
- B = nx.trace(Cs + Ct - 2 * nx.sqrtm(dots(Cs12, Ct, Cs12)))
- W = nx.norm(mxs - mxt) + B
  if log:
- log = {}
+ W, log = bures_wasserstein_distance(mxs, mxt, Cs, Ct, log=log)
  log['Cs'] = Cs
  log['Ct'] = Ct
- log['Cs12'] = Cs12
  return W, log
  else:
+ W = bures_wasserstein_distance(mxs, mxt, Cs, Ct)
  return W

test/test_gaussian.py

@@ -83,10 +83,10 @@ def test_bures_wasserstein_distance(nx):
 
 @pytest.mark.parametrize("bias", [True, False])
 def test_empirical_bures_wasserstein_distance(nx, bias):
- ns = 200
- nt = 200
+ ns = 400
+ nt = 400
 
- rng = np.random.RandomState(2)
+ rng = np.random.RandomState(10)
  Xs = rng.normal(0, 1, ns)[:, np.newaxis]
  Xt = rng.normal(10 * bias, 1, nt)[:, np.newaxis]