Manellic products are now multiscale (also for unbalanced trees) (#282)

* refactor prods w label_sets

* use BT labels toward multiscale sampling

* multiscale functional, untested, suspect permute issue

* refac manellic util fncs toward multiscale tests

* refac manellic left right index

* manellic multiscale prod cov_cont functional, but not yet

* manellic multiscale product working and few tests

src/ApproxManifoldProducts.jl

@@ -29,7 +29,7 @@ using Distributions
 
 import Random: rand
 
-import Base: *, isapprox, convert, show, eltype
+import Base: *, isapprox, convert, show, eltype, length
 import LinearAlgebra: rotate!, det
 import Statistics: mean, std, cov, var, entropy
 import KernelDensityEstimate: getPoints, getBW, evalAvgLogL, entropy, evaluate

src/CommonUtils.jl

@@ -116,6 +116,10 @@ Notes
 - calc lambdas first and use to calculate mean product second.
 - https://ccrma.stanford.edu/~jos/sasp/Product_Two_Gaussian_PDFs.html
 - Pennec, X. Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements, HAL Archive, 2011, Inria, France.
+
+DevNotes:
+- FIXME is parallel transport needed as products involve covariances from different tangent spaces?
+- TODO avoid recomputing covariance matrix inverses all the time
 """
 function calcProductGaussians(
   M::AbstractManifold, 
@@ -166,7 +170,14 @@ calcProductGaussians(
 ) where {N,P} = calcProductGaussians(M, μ_, nothing; dim, Λ_=Λ_ )
 
 
+"""
+    $SIGNATURES
+
+EXPERIMENTAL: On-manifold product of Gaussians.
 
+DevNotes
+- FIXME is parallel transport needed when multiplying with covariances from difffent tangent spaces?
+"""
 function calcProductGaussians(
   M::AbstractManifold,
   comps::AbstractVector{<:MvNormalKernel},
@@ -175,23 +186,11 @@ function calcProductGaussians(
   μ_ = mean.(comps)
   Σ_ = cov.(comps)
 
+  # FIXME is parallel transport needed here for covariances from different tangent spaces?
+
   _μ, _Σ = calcProductGaussians(M, μ_, Σ_)
 
   return MvNormalKernel(_μ, _Σ)
-  # d = manifold_dimension(M)
-  # # TODO avoid recomputing covariance matrix inverses all the time
-  # _Sigma2 = zeros(d,d)
-  # _Sig2mu = zeros(d)
-  # for c in comps
-  #   concentration = inv(cov(c))
-  #   _Sigma2 += concentration
-  #   _Sig2mu += concentration * mean(c)
-  # end
-
-  # Sigma2 = inv(_Sigma2)
-  # mu = Sigma2 * _Sig2mu  
-
-  # return MvNormalKernel(mu, Sigma2)
 end
 
 

src/entities/ManellicTree.jl

@@ -31,5 +31,6 @@ struct ManellicTree{M,D<:AbstractVector,N,HL,HT}
 
   # workaround to overcome bug for StaticArrays `isdefined() != false` issue
   _workaround_isdef_treekernel::Set{Int}
+  _workaround_isdef_leafkernel::Set{Int}
 end
 

src/services/KernelEval.jl

@@ -7,7 +7,7 @@ function projectSymPosDef(c::AbstractMatrix)
   issymmetric(_c) ? _c : project(SymmetricPositiveDefinite(s[1]),_c,_c)
 end
 
-# FIXME, REMOVE TYPE DISPLACEMENT
+# FIXME ON FIRE, REMOVE TYPE DISPLACEMENT
 Base.eltype(mt::MvNormalKernel) = eltype(mt.p)
 
 function MvNormalKernel(