New manifold kernel eval bug

[dehann]

• 80d35d1#r141478899

[dehann]

Consolidated Malahanobis Usage

Working towards consolidation with Malahanobis operations in IIF parametric:
https://github.com/JuliaRobotics/IncrementalInference.jl/blob/d470e902f1d774904ce383f7003e690fce6b81af/src/parametric/services/ParametricUtils.jl#L364-L374

as well as consolidation with RKHS work here:

ApproxManifoldProducts.jl/src/KernelHilbertEmbeddings.jl

Line 14 in 9250da2

ret = ker(MF, a[i], b[j], bw)

ker eval is:

ApproxManifoldProducts.jl/src/services/KernelEval.jl

Line 128 in 9250da2

ker(M::AbstractManifold, p, q, sigma::Real=0.001, distFnc=(_M,_p,_q)->distance(_M,_p,_q)^2) = exp( -sigma*distFnc(M, p, q) ) # _distance(M,p,q) #

Current code

and also have efficient code, the current (unrolled) compute steps for evaluate in code are:

ApproxManifoldProducts.jl/src/services/KernelEval.jl

Lines 36 to 38 in 9250da2

	dim = manifold_dimension(M)
	nscl = 1/sqrt((2*pi)^dim * det(cov(ekr)))
	return nscl * ker(M, ekr, p, 0.5, distanceMalahanobisSq)

which uses Malahanobis definition:

ApproxManifoldProducts.jl/src/services/KernelEval.jl

Lines 101 to 105 in 9250da2

	δc = distanceMalahanobisCoordinates(M,K,q,basis)
	p = mean(K)
	ϵ = identity_element(M, q)
	X = get_vector(M, ϵ, δc, basis)
	return inner(M, p, X, X)

which does the coordinate conversion via:

ApproxManifoldProducts.jl/src/services/KernelEval.jl

Lines 86 to 92 in 9250da2

	p = mean(K)
	i_p = inv(M,p)
	pq = Manifolds.compose(M, i_p, q)
	ϵ = identity_element(M,q)
	X = log(M, ϵ, pq)
	Xc = get_coordinates(M, ϵ, X, basis)
	return K.sqrt_iΣ*Xc

Would like

I would like to keep the unrolled structure and suggest we confirm that each of the unrolled steps in computing a MvNormal density are coming out right.

[dehann]

Should be in "local" coordinates,

ApproxManifoldProducts.jl/src/services/KernelEval.jl

Line 88 in 9250da2

pq = Manifolds.compose(M, i_p, q)