message: improved doc readability
diff: @@ -33,35 +33,37 @@ def _mean(x, m):
  def lagrangian_barycenter(pdiagset, init=None, verbose=False):
  '''
  - :param pdiagset: a list of size m containing numpy.array of shape (n x 2)
  - (n can variate), encoding a set of
  + :param pdiagset: a list of ``numpy.array`` of shape `(n x 2)`
  + (`n` can variate), encoding a set of
  persistence diagrams with only finite coordinates.
  :param init: The initial value for barycenter estimate.
  - If None, init is made on a random diagram from the dataset.
  - Otherwise, it must be an int
  - (then we init with diagset[init])
  - or a (n x 2) numpy.array enconding
  - a persistence diagram with n points.
  - :param verbose: if True, returns additional information about the
  + If ``None``, init is made on a random diagram from the dataset.
  + Otherwise, it can be an ``int``
  + (then initialization is made on ``pdiagset[init]``)
  + or a `(n x 2)` ``numpy.array`` enconding
  + a persistence diagram with `n` points.
  + :type init: int, (n x 2) np.array
  + :param verbose: if ``True``, returns additional information about the
  barycenter.
  - :returns: If not verbose (default), a numpy.array encoding
  + :type verbose: boolean
  + :returns: If not verbose (default), a ``numpy.array`` encoding
  the barycenter estimate of pdiagset
  - (local minima of the energy function).
  - If pdiagset is empty, returns None.
  - If verbose, returns a couple (Y, log)
  - where Y is the barycenter estimate,
  - and log is a dict that contains additional informations:
  - - groupings, a list of list of pairs (i,j),
  - That is, G[k] = [(i, j) ...], where (i,j) indicates
  - that X[i] is matched to Y[j]
  - if i = -1 or j = -1, it means they
  + (local minimum of the energy function).
  + If ``pdiagset`` is empty, returns ``None``.
  + If verbose, returns a couple ``(Y, log)``
  + where ``Y`` is the barycenter estimate,
  + and ``log`` is a ``dict`` that contains additional informations:
  +
  + - `"groupings"`, a list of list of pairs ``(i,j)``.
  + Namely, ``G[k] = [...(i, j)...]``, where ``(i,j)`` indicates
  + that ``pdiagset[k][i]`` is matched to ``Y[j]``
  + if ``i = -1`` or ``j = -1``, it means they
  represent the diagonal.
  - - energy, a float representing the Frechet
  - energy value obtained,
  - that is the mean of squared distances
  - of observations to the output.
  - - nb_iter, integer representing the number of iterations
  - performed before convergence of the algorithm.
  +
  + - `"energy"`, ``float`` representing the Frechet energy value obtained.
  + It is the mean of squared distances of observations to the output.
  +
  + - `"nb_iter"`, ``int`` number of iterations performed before convergence of the algorithm.
  '''
  X = pdiagset # to shorten notations, not a copy
  m = len(X) # number of diagrams we are averaging
  