small commit

src/manifolds/Segre.jl

@@ -74,7 +74,7 @@ end
 ````math
     \mathcal{P} = ℝ^{+} \times \mathbb{S}^{n_1 - 1} \times \dots \times \mathbb{S}^{n_d - 1}
 ````
-with the metric [`inner`](@ref inner(::Segre, ::Any, ::Any, ::Any)).
+with a warped product metric.
 Every equivalence class ``q \in \mathcal{S}`` has ``2^d`` representatives in ``\mathcal{P}``.
 `closest_representative!(M, q, p)` changes representative of `q` to the one that is closest to `p` in ``\mathcal{P}``.
 """

src/manifolds/SegreWarpedMetric.jl

@@ -228,9 +228,9 @@ and assume ``(μ, y_1,…, y_d)`` is the representative of ``q`` that minimizes
     \operatorname{log}_p(q) =
     \left(
         \mu \cos{m} - \lambda,
-        (y_1 - ⟨x_1, y_1⟩ x_1) \frac{\mu \sphericalangle(x_1, y_1) \sin{A m}}{\lambda A m \sin{\sphericalangle(x_1, y_1)}},
+        (y_1 - ⟨x_1, y_1⟩ x_1) \frac{\mu \sphericalangle(x_1, y_1) \sin(A m)}{\lambda A m \sin{\sphericalangle(x_1, y_1)}},
         \dots,
-        (y_d - ⟨x_d, y_d⟩ x_d) \frac{\mu \sphericalangle(x_d, y_d) \sin{A m}}{\lambda A m \sin{\sphericalangle(x_d, y_d)}}
+        (y_d - ⟨x_d, y_d⟩ x_d) \frac{\mu \sphericalangle(x_d, y_d) \sin(A m)}{\lambda A m \sin{\sphericalangle(x_d, y_d)}}
     \right).
 ````
 

test/manifolds/segre.jl

@@ -7,10 +7,10 @@ using Manifolds, Test, Random, LinearAlgebra, FiniteDifferences
         Segre(7, 2),
         Segre(7, 9, 9),
         Segre(9, 3, 6, 6),
-        MetricManifold(Segre(10), WarpedMetric(1.2025837056880606)),
-        MetricManifold(Segre(2, 9), WarpedMetric(1.1302422072971439)),
-        MetricManifold(Segre(9, 6, 10), WarpedMetric(1.4545138169484464)),
-        MetricManifold(Segre(9, 3, 8, 10), WarpedMetric(1.396673190458706)),
+        MetricManifold(Segre(10), WarpedMetric(1.20)),
+        MetricManifold(Segre(2, 9), WarpedMetric(1.13)),
+        MetricManifold(Segre(9, 6, 10), WarpedMetric(0.87)),
+        MetricManifold(Segre(9, 3, 8, 10), WarpedMetric(1.40)),
     ]
 
     # Vs[i] is the valence of Ms[i]
@@ -115,6 +115,11 @@ using Manifolds, Test, Random, LinearAlgebra, FiniteDifferences
                     [[1.0, 0.0], p[2:end]...];
                     error=:error,
                 )
+                @test_throws DomainError is_point(
+                    M,
+                    [p[1], [1.0], p[3:end]...];
+                    error=:error,
+                )
                 @test_throws DomainError is_point(M, [[-1.0], p[2:end]...]; error=:error)
                 @test_throws DomainError is_point(M, [p[1], 2 * p[2:end]...]; error=:error)
             end
@@ -139,6 +144,10 @@ using Manifolds, Test, Random, LinearAlgebra, FiniteDifferences
                 @test_throws DomainError is_vector(M, p, p, false, true)
             end
 
+            @testset "connected_by_geodesic" begin
+                @test connected_by_geodesic(M, p, q)
+            end
+
             Random.seed!(1)
             @testset "rand" begin
                 @test is_point(M, rand(M))
@@ -319,4 +328,22 @@ using Manifolds, Test, Random, LinearAlgebra, FiniteDifferences
         q_ = [q[1], q[2], q[3], q[4], -q[5]]
         @test is_vector(M, p, log(M, p, q_))
     end
+
+    # Test the formulas for sectional curvature stated in the docs
+    @testset "sectional_curvature" begin
+        M = Segre(3, 3)
+        p = [[1.3], [1.0, 0.0, 0.0], [1.0, 0.0, 0.0]]
+        X = [[0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 0.0]]
+        Y = [[0.0], [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]]
+        Z = [[0.0], [0.0, 0.0, 0.0], [0.0, 1.0, 0.0]]
+        V = [[1.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]
+        @test isapprox(0.0, sectional_curvature(M, p, X, Y))
+        @test isapprox(-1 / p[1][1]^2, sectional_curvature(M, p, X, Z))
+        @test isapprox(0.0, sectional_curvature(M, p, X, V))
+
+        M = MetricManifold(Segre(3, 3, 3), WarpedMetric(1.23))
+        @test isapprox((1.23^(-2) - 1) / p[1][1]^2, sectional_curvature(M, p, X, Y))
+        @test isapprox(-1 / p[1][1]^2, sectional_curvature(M, p, X, Z))
+        @test isapprox(0.0, sectional_curvature(M, p, X, V))
+    end
 end