Introduce has_components for Euclidean (#759)

* Adapt Euclidean to ManifoldsBase 0.15.18 to the r-norms feature.
* Improve docs, start Test suite.
* Move this to 0.10.4

NEWS.md

@@ -9,6 +9,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Added
 
+* `uniform_distribution` now has an error hint explaining what has to be done to make it work.
+* `Euclidean` now follows the new `has_components` function from `ManifoldsBase.jl` (0.15.18)
+  and can handle also the `r`-norms now.
 - Union type `MatrixGroup`
 - Columnwise group action with arbitrary matrix groups
 - `uniform_distribution` now has an error hint explaining what has to be done to make it work.
@@ -22,7 +25,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Fixed
 
 * Fixed `solve_exp_ode` only returning the starting position ([#744](https://github.com/JuliaManifolds/Manifolds.jl/issues/744))
-* Fixed documentation of `solve_exp_ode` function signature ([#740](https://github.com/JuliaManifolds/Manifolds.jl/issues/740))  
+* Fixed documentation of `solve_exp_ode` function signature ([#740](https://github.com/JuliaManifolds/Manifolds.jl/issues/740))
 
 ## [0.10.2] - 2024-09-24
 

Project.toml

@@ -55,7 +55,7 @@ HybridArrays = "0.4"
 Kronecker = "0.4, 0.5"
 LinearAlgebra = "1.6"
 ManifoldDiff = "0.3.7"
-ManifoldsBase = "0.15.17"
+ManifoldsBase = "0.15.18"
 Markdown = "1.6"
 MatrixEquations = "2.2"
 NLsolve = "4"

src/Manifolds.jl

@@ -89,6 +89,7 @@ import ManifoldsBase:
     get_vector_orthonormal!,
     get_vectors,
     gram_schmidt,
+    has_components,
     hat,
     hat!,
     injectivity_radius,
@@ -870,6 +871,7 @@ export ×,
     get_embedding,
     get_orbit_action,
     get_total_space,
+    has_components,
     hat,
     hat!,
     horizontal_component,

src/manifolds/Euclidean.jl

@@ -132,11 +132,12 @@ function diagonalizing_projectors(::Euclidean, p, X)
 end
 
 """
-    distance(M::Euclidean, p, q)
+    distance(M::Euclidean, p, q, r::Real=2)
 
 Compute the Euclidean distance between two points on the [`Euclidean`](@ref)
 manifold `M`, i.e. for vectors it's just the norm of the difference, for matrices
 and higher order arrays, the matrix and tensor Frobenius norm, respectively.
+Specifying further an `r≠2`, other norms, like the 1-norm or the ∞-norm can also be computed.
 """
 Base.@propagate_inbounds function distance(M::Euclidean, p, q)
     # Inspired by euclidean distance calculation in Distances.jl
@@ -154,6 +155,7 @@ Base.@propagate_inbounds function distance(M::Euclidean, p, q)
     end
     return sqrt(s)
 end
+distance(M::Euclidean, p, q, r::Real) = norm(p - q, r)
 distance(::Euclidean{TypeParameter{Tuple{1}}}, p::Number, q::Number) = abs(p - q)
 distance(::Euclidean{TypeParameter{Tuple{}}}, p::Number, q::Number) = abs(p - q)
 distance(::Euclidean{Tuple{Int}}, p::Number, q::Number) = abs(p - q) # for 1-dimensional Euclidean
@@ -390,6 +392,9 @@ function get_vector_diagonalizing!(
     copyto!(Y, reshape(c[1:N] + im * c[(N + 1):end], S))
     return Y
 end
+
+has_components(::Euclidean) = true
+
 @doc raw"""
     injectivity_radius(M::Euclidean)
 
@@ -631,14 +636,21 @@ function mid_point!(::Euclidean, q, p1, p2)
 end
 
 @doc raw"""
-    norm(M::Euclidean, p, X)
+    norm(M::Euclidean, p, X, r::Real=2)
 
 Compute the norm of a tangent vector `X` at `p` on the [`Euclidean`](@ref)
 `M`, i.e. since every tangent space can be identified with `M` itself
-in this case, just the (Frobenius) norm of `X`.
+in this case, just the (Frobenius) norm of `X`. Specifying `r`, other norms are available as well
 """
-LinearAlgebra.norm(::Euclidean, ::Any, X) = norm(X)
-LinearAlgebra.norm(::MetricManifold{ℝ,<:AbstractManifold,EuclideanMetric}, p, X) = norm(X)
+LinearAlgebra.norm(::Euclidean, ::Any, X, r::Real=2) = norm(X, r)
+function LinearAlgebra.norm(
+    ::MetricManifold{ℝ,<:AbstractManifold,EuclideanMetric},
+    p,
+    X,
+    r::Real=2,
+)
+    return norm(X, r)
+end
 
 function project!(
     ::EmbeddedManifold{𝔽,Euclidean{nL,𝔽},Euclidean{mL,𝔽2}},

test/ManifoldsTestSuite.jl/ManifoldsTestSuite.jl

@@ -0,0 +1,18 @@
+"""
+    ManifoldsTestSuite.jl
+
+An internal small module to encapsulate
+
+* dummy types
+* test functions
+* a test suite
+
+This is a slow work-in-progress to replace the `test_manifold` function,
+and encapsulate and collect common tools for testing a manifold.
+
+The current plan is to slowly move parts to this test suite whenever revising some tests or¨
+time permits.
+"""
+module ManifoldsTestSuite
+
+end

test/manifolds/euclidean.jl

@@ -26,6 +26,16 @@ using FiniteDifferences
         A = Manifolds.RetractionAtlas()
         B = induced_basis(EM, A, p, TangentSpaceType())
         @test det_local_metric(EM, p, B) == one(eltype(p))
+        for M in [E, Ec, EH]
+            @test has_components(M)
+            p = [1.0, 2.0, 3.0]
+            q = [1.0, 2.0, 3.0]
+            X = [4.0, 5.0, 6.0]
+            for r in [1, 2, Inf]
+                @test norm(M, p, X, r) ≈ norm(X, r)
+                @test distance(M, p, q, r) ≈ norm(p - q, r)
+            end
+        end
         @test log_local_metric_density(EM, p, B) == zero(eltype(p))
         @test project!(E, p, p) == p
         @test embed!(E, p, p) == p