  The canonical and grand-canonical ensembles are two usual marginal cases for
ultracold Bose gases, but real collections of experimental runs commonly have
intermediate properties. Here we study the continuum of intermediate cases, and
look into the appearance of ensemble equivalence as interaction rises for
mesoscopic 1d systems. We demonstrate how at sufficient interaction strength
the distributions of condensate and excited atoms become practically identical
regardless of the ensemble used. Importantly, we find that features that are
fragile in the ideal gas and appear only in a strict canonical ensemble can
become robust in all ensembles when interactions become strong. As evidence,
the steep cliff in the distribution of the number of excited atoms is
preserved. To make this study, a straightforward approach for generating
canonical and intermediate classical field ensembles using a modified
stochastic Gross-Pitaevskii equation (SGPE) is developed.
