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Merge pull request #272 from JuliaRobotics/master
release v0.8.4-rc1
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| @@ -0,0 +1,31 @@ | ||
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| # """ | ||
| # $TYPEDEF | ||
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| # Elliptical structure for use in a (Manellic) Ball Tree. | ||
| # """ | ||
| # struct HyperEllipse{P <:AbstractArray,D,DD} | ||
| # """ manifold point at which this ellipse is based """ | ||
| # point::P | ||
| # """ Covariance of coords at either TBD this point or some other reference point? """ | ||
| # coord_cov::SMatrix{D,D,Float64,DD} | ||
| # end | ||
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| # ManellicTree | ||
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| # Short for Manifold Ellipse Metric Tree | ||
| # starting as a balanced tree, relax to unbalanced in future. | ||
| struct ManellicTree{M,D<:AbstractVector,N,HL,HT} | ||
| manifold::M | ||
| data::D | ||
| weights::MVector{N,<:Real} | ||
| permute::MVector{N,Int} | ||
| # kernels::ArrayPartition{<:Number,KT} | ||
| leaf_kernels::SizedVector{N,HL} | ||
| tree_kernels::SizedVector{N,HT} | ||
| left_idx::MVector{N,Int} | ||
| right_idx::MVector{N,Int} | ||
| end | ||
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| # also makes static | ||
| function projectSymPosDef(c::AbstractMatrix) | ||
| s = size(c) | ||
| # pretty fast to make or remake isbitstype form matrix | ||
| _c = SMatrix{s...}(c) | ||
| issymmetric(_c) ? _c : project(SymmetricPositiveDefinite(s[1]),_c,_c) | ||
| end | ||
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| abstract type AbstractKernel end | ||
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| @kwdef struct MvNormalKernel{T,M} <: AbstractKernel | ||
| @kwdef struct MvNormalKernel{T,M,iM} <: AbstractKernel | ||
| p::MvNormal{T,M} | ||
| sqrt_iΣ::M = sqrt(inv(p.Σ)) | ||
| # TDB might already be covered in p.Σ.chol but having issues with SymPD (not particular to this AMP repo) | ||
| sqrt_iΣ::iM = sqrt(inv(p.Σ)) | ||
| end | ||
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| Base.eltype(mt::MvNormalKernel) = eltype(mt.p) | ||
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| function MvNormalKernel(m::AbstractVector,c::AbstractArray) | ||
| _c = projectSymPosDef(c) | ||
| p=MvNormal(m,_c) | ||
| # NOTE, TBD, why not sqrt(inv(p.Σ)), this had an issue seemingly internal to PDMat.chol which breaks an already forced SymPD matrix to again be not SymPD??? | ||
| sqrt_iΣ = sqrt(inv(_c)) | ||
| MvNormalKernel(;p, sqrt_iΣ) | ||
| end | ||
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| Statistics.mean(m::MvNormalKernel) = m.p.μ | ||
| Statistics.cov(m::MvNormalKernel) = m.p.Σ # note also about m.sqrt_iΣ | ||
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| function distanceMalahanobisCoordinates( | ||
| M::AbstractManifold, | ||
| K::AbstractKernel, | ||
| q, | ||
| basis=DefaultOrthonormalBasis() | ||
| basis=DefaultOrthogonalBasis() | ||
| ) | ||
| p = mean(K) | ||
| i_p = inv(M,p) | ||
| pq = Manifolds.compose(M, i_p, q) | ||
| X = log(M, p, pq) | ||
| Xc = get_coordinates(M, p, X, basis) | ||
| ϵ = identity_element(M,q) | ||
| X = log(M, ϵ, pq) | ||
| Xc = get_coordinates(M, ϵ, X, basis) | ||
| return K.sqrt_iΣ*Xc | ||
| end | ||
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| function distanceMalahanobisSq( | ||
| M::AbstractManifold, | ||
| K::AbstractKernel, | ||
| q, | ||
| basis=DefaultOrthonormalBasis() | ||
| basis=DefaultOrthogonalBasis() | ||
| ) | ||
| δc = distanceMalahanobisCoordinates(M,K,q,basis) | ||
| p = mean(K) | ||
| # ϵ = identity_element(M, q) | ||
| X = get_vector(M, p, δc, basis) | ||
| ϵ = identity_element(M, q) | ||
| X = get_vector(M, ϵ, δc, basis) | ||
| return inner(M, p, X, X) | ||
| end | ||
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| # function distance( | ||
| # M::AbstractManifold, | ||
| # p::AbstractVector, | ||
| # q::AbstractVector, | ||
| # kernel=(_p) -> MvNormalKernel( | ||
| # p=MvNormal(_p,SVector(ones(manifold_dimension(M))...)) | ||
| # ), | ||
| # distFnc::Function=distanceMalahanobisSq | ||
| # ) | ||
| # distFnc(M, kernel(p), q) | ||
| # end | ||
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| function _distance( | ||
| M::AbstractManifold, | ||
| p::AbstractVector, | ||
| q::AbstractVector, | ||
| kernel = (_p) -> MvNormalKernel( | ||
| p=MvNormal(_p,SVector(ntuple((s)->1,manifold_dimension(M))...)) | ||
| ), | ||
| distFnc::Function=distanceMalahanobisSq, | ||
| # distFnc::Function=distanceMalahanobisSq, | ||
| ) | ||
| distFnc(M, kernel(p), q) | ||
| end | ||
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| """ | ||
| $SIGNATURES | ||
| $SIGNATURES | ||
| Normal kernel used for Hilbert space embeddings. | ||
| """ | ||
| ker(M::AbstractManifold, p, q, sigma::Real=0.001) = exp( -sigma*(distance(M, p, q)^2) ) | ||
| 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) # | ||
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