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-rw-r--r--ot/weak.py6
1 files changed, 4 insertions, 2 deletions
diff --git a/ot/weak.py b/ot/weak.py
index f7d5b23..7364e68 100644
--- a/ot/weak.py
+++ b/ot/weak.py
@@ -18,7 +18,7 @@ def weak_optimal_transport(Xa, Xb, a=None, b=None, verbose=False, log=False, G0=
.. math::
- \gamma = \mathop{\arg \min}_\gamma \quad \|X_a-diag(1/a)\gammaX_b\|_F^2
+ \gamma = \mathop{\arg \min}_\gamma \quad \sum_i \mathbf{a}_i \left(\mathbf{X^a}_i - \frac{1}{\mathbf{a}_i} \sum_j \gamma_{ij} \mathbf{X^b}_j \right)^2
s.t. \ \gamma \mathbf{1} = \mathbf{a}
@@ -28,7 +28,7 @@ def weak_optimal_transport(Xa, Xb, a=None, b=None, verbose=False, log=False, G0=
where :
- - :math:`X_a` :math:`X_b` are the sample matrices.
+ - :math:`X^a` and :math:`X^b` are the sample matrices.
- :math:`\mathbf{a}` and :math:`\mathbf{b}` are the sample weights
@@ -49,6 +49,8 @@ def weak_optimal_transport(Xa, Xb, a=None, b=None, verbose=False, log=False, G0=
Source histogram (uniform weight if empty list)
b : (nt,) array-like, float
Target histogram (uniform weight if empty list))
+ G0 : (ns,nt) array-like, float
+ initial guess (default is indep joint density)
numItermax : int, optional
Max number of iterations
numItermaxEmd : int, optional