new optimizeManifold_FD convenience function

Author: dehann

Project.toml

@@ -17,13 +17,15 @@ DistributedFactorGraphs = "b5cc3c7e-6572-11e9-2517-99fb8daf2f04"
 Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
+FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 FunctionalStateMachine = "3e9e306e-7e3c-11e9-12d2-8f8f67a2f951"
 JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
 KernelDensityEstimate = "2472808a-b354-52ea-a80e-1658a3c6056d"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
 Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
 ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
+ManifoldDiff = "af67fdf4-a580-4b9f-bbec-742ef357defd"
 MetaGraphs = "626554b9-1ddb-594c-aa3c-2596fe9399a5"
 NLSolversBase = "d41bc354-129a-5804-8e4c-c37616107c6c"
 NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
@@ -78,12 +80,10 @@ julia = "1.8"
 
 [extras]
 DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
-FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
-ManifoldDiff = "af67fdf4-a580-4b9f-bbec-742ef357defd"
 Manopt = "0fc0a36d-df90-57f3-8f93-d78a9fc72bb5"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Rotations = "6038ab10-8711-5258-84ad-4b1120ba62dc"

src/IncrementalInference.jl

@@ -15,6 +15,7 @@ using Reexport
 using Manifolds
 using RecursiveArrayTools: ArrayPartition
 export ArrayPartition
+using ManifoldDiff
 
 using OrderedCollections: OrderedDict
 

src/ManifoldsExtentions.jl

@@ -1,3 +1,50 @@
+
+## ================================================================================================
+## Manifold and ManifoldDiff use with Optim
+## ================================================================================================
+
+# Modified from: https://gist.github.com/mateuszbaran/0354c0edfb9cdf25e084a2b915816a09
+"""
+    ManifoldWrapper{TM<:AbstractManifold} <: Optim.Manifold
+    
+Adapts Manifolds.jl manifolds for use in Optim.jl
+"""
+struct ManifoldWrapper{TM<:AbstractManifold} <: Optim.Manifold
+    M::TM
+end
+
+function Optim.retract!(M::ManifoldWrapper, x)
+    ManifoldsBase.embed_project!(M.M, x, x)
+    return x
+end
+
+function Optim.project_tangent!(M::ManifoldWrapper, g, x)
+    ManifoldsBase.embed_project!(M.M, g, x, g)
+    return g
+end
+
+# experimental
+function optimizeManifold_FD(
+  M::AbstractManifold, 
+  cost::Function,
+  x0::AbstractArray;
+  algorithm = Optim.ConjugateGradient(; manifold=ManifoldWrapper(M))
+)
+  # finitediff setup
+  r_backend = ManifoldDiff.TangentDiffBackend(
+    ManifoldDiff.FiniteDifferencesBackend()
+  )
+  
+  ## finitediff gradient (non-manual)
+  function costgrad_FD!(X,p)
+    X .= ManifoldDiff.gradient(M, cost, p, r_backend)
+    X
+  end
+
+  Optim.optimize(cost, costgrad_FD!, x0, algorithm)
+end
+
+
 ## ================================================================================================
 ## AbstractPowerManifold with N as field to avoid excessive compiling time.
 ## ================================================================================================

test/manifolds/manifolddiff.jl

@@ -22,7 +22,7 @@ r_backend = ManifoldDiff.TangentDiffBackend(
 # problem setup
 n = 100
 σ = π / 8
-M = Sphere(2)
+M = Manifolds.Sphere(2)
 p = 1 / sqrt(2) * [1.0, 0.0, 1.0]
 data = [exp(M, p,  σ * rand(M; vector_at=p)) for i in 1:n];