def from_dataframe(cls, dataframe):
        """Convert a pandas.DataFrame into an xarray.Dataset

        Each column will be converted into an independent variable in the
        Dataset. If the dataframe's index is a MultiIndex, it will be expanded
        into a tensor product of one-dimensional indices (filling in missing
        values with NaN). This method will produce a Dataset very similar to
        that on which the 'to_dataframe' method was called, except with
        possibly redundant dimensions (since all dataset variables will have
        the same dimensionality).
        """
        # TODO: Add an option to remove dimensions along which the variables
        # are constant, to enable consistent serialization to/from a dataframe,
        # even if some variables have different dimensionality.

        if not dataframe.columns.is_unique:
            raise ValueError(
                'cannot convert DataFrame with non-unique columns')

        idx = dataframe.index
        obj = cls()

        if isinstance(idx, pd.MultiIndex):
            # it's a multi-index
            # expand the DataFrame to include the product of all levels
            full_idx = pd.MultiIndex.from_product(idx.levels, names=idx.names)
            dataframe = dataframe.reindex(full_idx)
            dims = [name if name is not None else 'level_%i' % n
                    for n, name in enumerate(idx.names)]
            for dim, lev in zip(dims, idx.levels):
                obj[dim] = (dim, lev)
            shape = [lev.size for lev in idx.levels]
        else:
            dims = (idx.name if idx.name is not None else 'index',)
            obj[dims[0]] = (dims, idx)
            shape = -1

        for name, series in dataframe.items():
            data = np.asarray(series).reshape(shape)
            obj[name] = (dims, data)
        return obj