Minimal refactor of #439 for merging RHMC implementation into main

docs/src/api.md

@@ -9,7 +9,16 @@ This modularity means that different HMC variants can be easily constructed by c
   - Diagonal metric: `DiagEuclideanMetric(dim)`
   - Dense metric: `DenseEuclideanMetric(dim)`
 
-where `dim` is the dimensionality of the sampling space.
+where `dim` is the dimension of the sampling space.
+
+Furthermore, there is now an experimental dense Riemannian metric implementation, specifiable as `DenseRiemannianMetric(dim, premetric, premetric_sensitivities, metric_map=IdentityMap())`, with
+
+  - `dim`: again the dimension of the sampling space,
+  - `premetric`: a function which, for a given posterior position `pos`, computes either 
+     a) a symmetric, **positive definite** matrix acting as the position dependent Riemannian metric (if `metric_map = IdentityMap()`), or
+     b) a symmetric, **not necessarily positive definite** matrix acting as the position dependent Riemannian metric after being passed through the `metric_map` argument, which will have to ensure that its return value *is* positive definite (like `metric_map = SoftAbsMap(alpha)`),
+  - `premetric_sensitivities`: a function which, again for a given posterior position `pos`, computes the sensitivities with respect to this position of the **`premetric`** function,
+  - `metric_map=IdentityMap()`: a function which takes in `premetric(pos)` and returns a symmetric positive definite matrix. Provided options are `IdentityMap()` or `SoftAbsMap(alpha)`, with the `SoftAbsMap` type allowing to work directly with the `premetric` returning the Hessian of the log density function, which generally is not guaranteed to be positive definite..
 
 ### [Integrator (`integrator`)](@id integrator)
 

src/AdvancedHMC.jl

@@ -2,7 +2,19 @@ module AdvancedHMC
 
 using Statistics: mean, var, middle
 using LinearAlgebra:
-    Symmetric, UpperTriangular, mul!, ldiv!, dot, I, diag, cholesky, UniformScaling
+    Symmetric,
+    UpperTriangular,
+    mul!,
+    ldiv!,
+    dot,
+    I,
+    diag,
+    cholesky,
+    UniformScaling,
+    logdet,
+    tr,
+    eigen,
+    diagm
 using StatsFuns: logaddexp, logsumexp, loghalf
 using Random: Random, AbstractRNG
 using ProgressMeter: ProgressMeter
@@ -40,7 +52,7 @@ struct GaussianKinetic <: AbstractKinetic end
 export GaussianKinetic
 
 include("metric.jl")
-export UnitEuclideanMetric, DiagEuclideanMetric, DenseEuclideanMetric
+export UnitEuclideanMetric, DiagEuclideanMetric, DenseEuclideanMetric, DenseRiemannianMetric
 
 include("hamiltonian.jl")
 export Hamiltonian
@@ -50,6 +62,11 @@ export Leapfrog, JitteredLeapfrog, TemperedLeapfrog
 include("riemannian/integrator.jl")
 export GeneralizedLeapfrog
 
+include("riemannian/metric.jl")
+export IdentityMap, SoftAbsMap, DenseRiemannianMetric
+
+include("riemannian/hamiltonian.jl")
+
 include("trajectory.jl")
 export Trajectory,
     HMCKernel,