Suggestion for main interface

[willwerscheid]

It would be nice if we had something like a method option with useful combinations of ebnm_fn, ebnm_param, and init_fn. For example, "fast" could be the usual ebnm_pn. "Nonnegative" could give a nonnegative MF, and we could also have "nonneg_loadings" and "nonneg_factors" (which I've been using quite a bit). As we find new uses for flash, we could add to this list. I am thinking of the method parameter in ashr which has a similar purpose.

[willwerscheid]

As a long-term goal, it would be nice to have a single flash function. flash_greedy and flash_backfit are already redundant. We can return a sampler function with the flash object and eliminate flash_sampler. We can add S as a parameter to flash and eliminate flash_set_data. We could add parameters FF_init and LL_init with some way to indicate which elements are fixed, and get rid of flash_add_fixed_factors, flash_add_fixed_loadings, and flash_add_factors_from_data. To do this, we need to decide whether it's better to add greedy before fixed or fixed before greedy (this is not an easy problem). flash_fill is a trivial function and does not need to be exported. Finally, flash_zero_out_factor is sort of useful as a utility but is probably best filed alongside other utilities for experienced flash users (that is, not exported).

[willwerscheid]

My ideal interface would be something like
flash(Y, S = NULL, var_type = c(...), method = c(...), flash_init = NULL, LL_init = NULL, FF_init = NULL, greedy_Kmax = 100, greedy_maxiter = 500, backfit_maxiter = 0, nullcheck = TRUE, verbose = TRUE, custom_params = list())
where LL_init is either a matrix or a list with one matrix specifying LL and one specifying fixl, and custom_params is a list that can include init_fn, ebnm_fn, ebnm_param, stopping_rule, tol, and verbose_output (which override the method-specific defaults)