Update _gw.py (#637)

doc typos Co-authored-by: Cédric Vincent-Cuaz <cedvincentcuaz@gmail.com>

Author: simon-forb

ot/gromov/_gw.py

@@ -43,11 +43,11 @@ def gromov_wasserstein(C1, C2, p=None, q=None, loss_fun='square_loss', symmetric
 
  Where :
 
- - :math:`\mathbf{C_1}`: Metric cost matrix in the source space
- - :math:`\mathbf{C_2}`: Metric cost matrix in the target space
- - :math:`\mathbf{p}`: distribution in the source space
- - :math:`\mathbf{q}`: distribution in the target space
- - `L`: loss function to account for the misfit between the similarity matrices
+ - :math:`\mathbf{C_1}`: Metric cost matrix in the source space.
+ - :math:`\mathbf{C_2}`: Metric cost matrix in the target space.
+ - :math:`\mathbf{p}`: Distribution in the source space.
+ - :math:`\mathbf{q}`: Distribution in the target space.
+ - `L`: Loss function to account for the misfit between the similarity matrices.
 
  .. note:: This function is backend-compatible and will work on arrays
  from all compatible backends. But the algorithm uses the C++ CPU backend
@@ -62,39 +62,39 @@ def gromov_wasserstein(C1, C2, p=None, q=None, loss_fun='square_loss', symmetric
  Parameters
  ----------
  C1 : array-like, shape (ns, ns)
- Metric cost matrix in the source space
+ Metric cost matrix in the source space.
  C2 : array-like, shape (nt, nt)
- Metric cost matrix in the target space
+ Metric cost matrix in the target space.
  p : array-like, shape (ns,), optional
  Distribution in the source space.
  If let to its default value None, uniform distribution is taken.
  q : array-like, shape (nt,), optional
  Distribution in the target space.
  If let to its default value None, uniform distribution is taken.
  loss_fun : str, optional
- loss function used for the solver either 'square_loss' or 'kl_loss'
+ Loss function used for the solver either 'square_loss' or 'kl_loss'.
  symmetric : bool, optional
  Either C1 and C2 are to be assumed symmetric or not.
  If let to its default None value, a symmetry test will be conducted.
  Else if set to True (resp. False), C1 and C2 will be assumed symmetric (resp. asymmetric).
  verbose : bool, optional
- Print information along iterations
+ Print information along iterations.
  log : bool, optional
- record log if True
+ Record log if True.
  armijo : bool, optional
- If True the step of the line-search is found via an armijo research. Else closed form is used.
- If there are convergence issues use False.
+ If True, the step of the line-search is found via an armijo search. Else closed form is used.
+ If there are convergence issues, use False.
  G0: array-like, shape (ns,nt), optional
- If None the initial transport plan of the solver is pq^T.
+ If None, the initial transport plan of the solver is pq^T.
  Otherwise G0 must satisfy marginal constraints and will be used as initial transport of the solver.
  max_iter : int, optional
- Max number of iterations
+ Max number of iterations.
  tol_rel : float, optional
- Stop threshold on relative error (>0)
+ Stop threshold on relative error (>0).
  tol_abs : float, optional
- Stop threshold on absolute error (>0)
+ Stop threshold on absolute error (>0).
  **kwargs : dict
- parameters can be directly passed to the ot.optim.cg solver
+ Parameters can be directly passed to the ot.optim.cg solver.
 
  Returns
  -------
@@ -175,7 +175,7 @@ def line_search(cost, G, deltaG, Mi, cost_G, **kwargs):
 
  if not nx.is_floating_point(C10):
  warnings.warn(
- "Input structure matrix consists of integer. The transport plan will be "
+ "Input structure matrix consists of integers. The transport plan will be "
  "casted accordingly, possibly resulting in a loss of precision. "
  "If this behaviour is unwanted, please make sure your input "
  "structure matrix consists of floating point elements.",