Change design for dispatch

[dahong67]

Currently we define two methods for gcp:

1. GCPDecompositions.jl/src/gcp-opt.jl

   Lines 18 to 25 in 6c3c18d

   	gcp(X::Array, r, loss::AbstractLoss = LeastSquaresLoss()) = _gcp(
   	X,
   	r,
   	(x, m) -> value(loss, x, m),
   	(x, m) -> deriv(loss, x, m),
   	_factor_matrix_lower_bound(loss),
   	(;),
   	)

2. GCPDecompositions.jl/ext/LossFunctionsExt.jl

   Lines 8 to 15 in 6c3c18d

   	GCPDecompositions.gcp(X::Array, r, loss::SupportedLosses) = GCPDecompositions._gcp(
   	X,
   	r,
   	(x, m) -> loss(m, x),
   	(x, m) -> LossFunctions.deriv(loss, m, x),
   	_factor_matrix_lower_bound(loss),
   	(;),
   	)

These call the following _gcp method:

GCPDecompositions.jl/src/gcp-opt.jl

Line 55 in 6c3c18d

function _gcp(X::Array{TX,N}, r, func, grad, lower, lbfgsopts) where {TX,N}

Idea: unify the two gcp methods and pass the inputs directly to _gcp so we just have gcp(X, r, loss = LeastSquaresLoss()) = _gcp(X, r, loss). Handle LossFunctions.jl losses by adding methods for value, deriv and domain.

With this design:

• gcp provides the user-friendly interface and handles defaults
• _gcp does not handle defaults - it only implements the algorithms

Separating concerns this way has some potential benefits:

• reduces duplication in LossFunctionsExt - don't need to duplicate code for defaults, etc.
• prepares for adding specialized _gcp methods, e.g., ALS for least-squares (ALS doesn't apply to other loss functions), etc.

[codecov]

Codecov Report

All modified lines are covered by tests ✅

Comparison is base (6c3c18d) 100.00% compared to head (4b5431a) 100.00%.

Additional details and impacted files

@@            Coverage Diff            @@
##            master       #22   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files            5         5           
  Lines          107       106    -1     
=========================================
- Hits           107       106    -1     

Files	Coverage Δ
ext/LossFunctionsExt.jl	100.00% <100.00%> (ø)
src/gcp-opt.jl	100.00% <100.00%> (ø)

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[dahong67]

One more TODO remaining:

GCPDecompositions.jl/src/gcp-opt.jl

Lines 48 to 55 in 4b5431a

	# TODO: remove this `func, grad, lower` signature
	# will require reworking how we do testing
	_gcp(X::Array{TX,N}, r, func, grad, lower, lbfgsopts) where {TX,N} = _gcp(
	X,
	r,
	UserDefinedLoss(func; deriv = grad, domain = Interval(lower, +Inf)),
	lbfgsopts,
	)

Will require reworking how we do the testing since we currently use that signature. For example:

GCPDecompositions.jl/test/items/gcp-opt.jl

Lines 51 to 58 in 4b5431a

	Mr = GCPDecompositions._gcp(
	X,
	r,
	(x, m) -> m - x * log(m + 1e-10),
	(x, m) -> 1 - x / (m + 1e-10),
	0.0,
	(;),
	)

Since this would affect ongoing work in #20, can address this in a separate PR after #20 is merged. Should probably rethink how we do this testing anyway.

[UPDATE 10/12/2023: now tracking this TODO in #23]