mostly convert to retraction_t

ext/ManifoldsTestExt/tests_general.jl

@@ -330,7 +330,7 @@ function test_manifold(
                 Test.@test isapprox(
                     M,
                     p,
-                    retract(M, p, X, 0, retr_method);
+                    retract_t(M, p, X, 0, retr_method);
                     atol=epsx * retraction_atol_multiplier,
                     rtol=retraction_atol_multiplier == 0 ?
                          sqrt(epsx) * retraction_rtol_multiplier : 0,

src/Manifolds.jl

@@ -147,6 +147,8 @@ import ManifoldsBase:
     retract_qr!,
     retract_sasaki!,
     retract_softmax!,
+    retract_t,
+    retract_t!,
     riemann_tensor,
     riemann_tensor!,
     sectional_curvature,
@@ -920,6 +922,8 @@ export ×,
     representation_size,
     retract,
     retract!,
+    retract_t,
+    retract_t!,
     riemannian_gradient,
     riemannian_gradient!,
     riemannian_Hessian,

src/manifolds/Elliptope.jl

@@ -162,7 +162,7 @@ compute a projection based retraction by projecting ``q+Y`` back onto the manifo
 """
 retract(::Elliptope, ::Any, ::Any, ::ProjectionRetraction)
 
-function retract_project!(M::Elliptope, r, q, Y, t::Number)
+function ManifoldsBase.retract_project_t!(M::Elliptope, r, q, Y, t::Number)
     r .= q .+ t .* Y
     project!(M, r, r)
     return r

src/manifolds/FixedRankMatrices.jl

@@ -164,7 +164,7 @@ Compute the in-place variant of the [`OrthographicInverseRetraction`](@ref).
 inverse_retract_orthographic!(M::AbstractManifold, X, p, q)
 
 ## Layer II
-function _retract!(
+function ManifoldsBase._retract_t!(
     M::AbstractManifold,
     q,
     p,
@@ -173,16 +173,16 @@ function _retract!(
     ::OrthographicRetraction;
     kwargs...,
 )
-    return retract_orthographic!(M, q, p, X, t; kwargs...)
+    return retract_orthographic_t!(M, q, p, X, t; kwargs...)
 end
 
 ## Layer III
 """
-    retract_orthographic!(M::AbstractManifold, q, p, X, t::Number)
+    retract_orthographic!(M::AbstractManifold, q, p, X)
 
 Compute the in-place variant of the [`OrthographicRetraction`](@ref).
 """
-retract_orthographic!(M::AbstractManifold, q, p, X, t::Number)
+retract_orthographic!(M::AbstractManifold, q, p, X)
 
 # \|---
 
@@ -655,7 +655,7 @@ For more details, see [AbsilOseledets:2014](@cite).
 """
 retract(::FixedRankMatrices, ::Any, ::Any, ::OrthographicRetraction)
 
-function retract_orthographic!(
+function retract_orthographic_t!(
     M::FixedRankMatrices,
     q::SVDMPoint,
     p::SVDMPoint,
@@ -689,7 +689,7 @@ singular values and ``U`` and ``V`` are shortened accordingly.
 """
 retract(::FixedRankMatrices, ::Any, ::Any, ::PolarRetraction)
 
-function retract_polar!(
+function ManifoldsBase.retract_polar_t!(
     M::FixedRankMatrices,
     q::SVDMPoint,
     p::SVDMPoint,

src/manifolds/FlagOrthogonal.jl

@@ -168,7 +168,7 @@ as the first order approximation to the exponential map. Similar to QR retractio
 """
 retract(M::Flag, p::OrthogonalPoint, X::OrthogonalTangentVector, ::QRRetraction)
 
-function retract_qr!(
+function ManifoldsBase.retract_qr_t!(
     ::Flag,
     q::OrthogonalPoint{<:AbstractMatrix{T}},
     p::OrthogonalPoint,

src/manifolds/FlagStiefel.jl

@@ -182,7 +182,7 @@ where $\cdot^{\mathrm{H}}$ denotes the complex conjugate transposed or Hermitian
 """
 retract(::Flag, ::Any, ::Any, ::PolarRetraction)
 
-function retract_polar!(::Flag, q, p, X, t::Number)
+function ManifoldsBase.retract_polar_t!(::Flag, q, p, X, t::Number)
     s = svd(p .+ t .* X)
     return mul!(q, s.U, s.Vt)
 end

src/manifolds/GeneralUnitaryMatrices.jl

@@ -1029,7 +1029,7 @@ This is also the default retraction on these manifolds.
 """
 retract(::GeneralUnitaryMatrices, ::Any, ::Any, ::QRRetraction)
 
-function retract_qr!(
+function ManifoldsBase.retract_qr_t!(
     ::GeneralUnitaryMatrices,
     q::AbstractArray{T},
     p,
@@ -1042,7 +1042,7 @@ function retract_qr!(
     D = Diagonal(sign.(d .+ convert(T, 0.5)))
     return copyto!(q, qr_decomp.Q * D)
 end
-function retract_polar!(M::GeneralUnitaryMatrices, q, p, X, t::Number)
+function ManifoldsBase.retract_polar_t!(M::GeneralUnitaryMatrices, q, p, X, t::Number)
     A = p + p * (t * X)
     return project!(M, q, A; check_det=false)
 end

src/manifolds/GeneralizedGrassmann.jl

@@ -373,12 +373,12 @@ Compute the SVD-based retraction [`PolarRetraction`](@extref `ManifoldsBase.Pola
 """
 retract(::GeneralizedGrassmann, ::Any, ::Any, ::PolarRetraction)
 
-function retract_polar!(M::GeneralizedGrassmann, q, p, X, t::Number)
+function ManifoldsBase.retract_polar_t!(M::GeneralizedGrassmann, q, p, X, t::Number)
     q .= p .+ t .* X
     project!(M, q, q)
     return q
 end
-function retract_project!(M::GeneralizedGrassmann, q, p, X, t::Number)
+function ManifoldsBase.retract_project_t!(M::GeneralizedGrassmann, q, p, X, t::Number)
     q .= p .+ t .* X
     project!(M, q, q)
     return q

src/manifolds/GeneralizedStiefel.jl

@@ -243,12 +243,12 @@ retract(::GeneralizedStiefel, ::Any...)
 
 default_retraction_method(::GeneralizedStiefel) = ProjectionRetraction()
 
-function retract_polar!(M::GeneralizedStiefel, q, p, X, t::Number)
+function ManifoldsBase.retract_polar_t!(M::GeneralizedStiefel, q, p, X, t::Number)
     q .= p .+ t .* X
     project!(M, q, q)
     return q
 end
-function retract_project!(M::GeneralizedStiefel, q, p, X, t::Number)
+function ManifoldsBase.retract_project_t!(M::GeneralizedStiefel, q, p, X, t::Number)
     q .= p .+ t .* X
     project!(M, q, q)
     return q

src/manifolds/GrassmannStiefel.jl

@@ -319,7 +319,7 @@ where ``⋅^{\mathrm{H}}`` denotes the complex conjugate transposed or Hermitian
 """
 retract(::Grassmann, ::Any, ::Any, ::PolarRetraction)
 
-function retract_polar!(M::Grassmann, q, p, X, t::Number)
+function ManifoldsBase.retract_polar_t!(M::Grassmann, q, p, X, t::Number)
     q .= p .+ t .* X
     project!(M, q, q)
     return q
@@ -340,7 +340,7 @@ D = \operatorname{diag}\left( \operatorname{sgn}\left(R_{ii}+\frac{1}{2}\right)_
 """
 retract(::Grassmann, ::Any, ::Any, ::QRRetraction)
 
-function retract_qr!(::Grassmann, q, p, X, t::Number)
+function ManifoldsBase.retract_qr_t!(::Grassmann, q, p, X, t::Number)
     q .= p .+ t .* X
     qrfac = qr(q)
     d = diag(qrfac.R)

src/manifolds/Hyperrectangle.jl

@@ -395,7 +395,7 @@ Return the array dimensions required to represent an element on the
 """
 representation_size(M::Hyperrectangle) = size(M.lb)
 
-function retract_project!(M::Hyperrectangle, r, q, Y, t::Number)
+function ManifoldsBase.retract_project_t!(M::Hyperrectangle, r, q, Y, t::Number)
     r .= q .+ t .* Y
     project!(M, r, r)
     return r

src/manifolds/MultinomialDoublyStochastic.jl

@@ -269,7 +269,13 @@ refers to the elementwise exponentiation.
 """
 retract(::MultinomialDoubleStochastic, ::Any, ::Any, ::ProjectionRetraction)
 
-function retract_project!(M::MultinomialDoubleStochastic, q, p, X, t::Number)
+function ManifoldsBase.retract_project_t!(
+    M::MultinomialDoubleStochastic,
+    q,
+    p,
+    X,
+    t::Number,
+)
     return project!(M, q, p .* exp.(t .* X ./ p))
 end
 

src/manifolds/MultinomialSymmetric.jl

@@ -181,7 +181,7 @@ refers to the elementwise exponentiation.
 """
 retract(::MultinomialSymmetric, ::Any, ::Any, ::ProjectionRetraction)
 
-function retract_project!(M::MultinomialSymmetric, q, p, X, t::Number)
+function ManifoldsBase.retract_project_t!(M::MultinomialSymmetric, q, p, X, t::Number)
     return project!(M, q, p .* exp.(t .* X ./ p))
 end
 

src/manifolds/ProbabilitySimplex.jl

@@ -462,7 +462,7 @@ where multiplication, exponentiation and division are meant elementwise.
 """
 retract(::ProbabilitySimplex, ::Any, ::Any, ::SoftmaxRetraction)
 
-function retract_softmax!(::ProbabilitySimplex, q, p, X, t::Number)
+function ManifoldsBase.retract_softmax_t!(::ProbabilitySimplex, q, p, X, t::Number)
     s = zero(eltype(q))
     @inbounds for i in eachindex(q, p, X)
         q[i] = p[i] * exp(t * X[i])

src/manifolds/ProjectiveSpace.jl

@@ -506,15 +506,15 @@ retract(
     ::Union{ProjectionRetraction,PolarRetraction,QRRetraction},
 )
 
-function retract_polar!(M::AbstractProjectiveSpace, q, p, X, t::Number)
+function ManifoldsBase.retract_polar_t!(M::AbstractProjectiveSpace, q, p, X, t::Number)
     q .= p .+ t .* X
     return project!(M, q, q)
 end
-function retract_project!(M::AbstractProjectiveSpace, q, p, X, t::Number)
+function ManifoldsBase.retract_project_t!(M::AbstractProjectiveSpace, q, p, X, t::Number)
     q .= p .+ t .* X
     return project!(M, q, q)
 end
-function retract_qr!(M::AbstractProjectiveSpace, q, p, X, t::Number)
+function ManifoldsBase.retract_qr_t!(M::AbstractProjectiveSpace, q, p, X, t::Number)
     q .= p .+ t .* X
     return project!(M, q, q)
 end

src/manifolds/Spectrahedron.jl

@@ -162,7 +162,9 @@ compute a projection based retraction by projecting ``q+Y`` back onto the manifo
 """
 retract(::Spectrahedron, ::Any, ::Any, ::ProjectionRetraction)
 
-retract_project!(M::Spectrahedron, r, q, Y, t::Number) = project!(M, r, q .+ t .* Y)
+function ManifoldsBase.retract_project_t!(M::Spectrahedron, r, q, Y, t::Number)
+    return project!(M, r, q .+ t .* Y)
+end
 
 @doc raw"""
     representation_size(M::Spectrahedron)

src/manifolds/Sphere.jl

@@ -498,7 +498,7 @@ Compute the retraction that is based on projection, i.e.
 """
 retract(::AbstractSphere, ::Any, ::Any, ::ProjectionRetraction)
 
-function retract_project!(M::AbstractSphere, q, p, X, t::Number)
+function ManifoldsBase.retract_project_t!(M::AbstractSphere, q, p, X, t::Number)
     q .= p .+ t .* X
     return project!(M, q, q)
 end

src/manifolds/Stiefel.jl

@@ -471,7 +471,14 @@ retract(::Stiefel, ::Any, ::Any, ::QRRetraction)
 _qrfac_to_q(qrfac) = Matrix(qrfac.Q)
 _qrfac_to_q(qrfac::StaticArrays.QR) = qrfac.Q
 
-function retract_pade!(::Stiefel, q, p, X, t::Number, ::PadeRetraction{m}) where {m}
+function ManifoldsBase.retract_pade_t!(
+    ::Stiefel,
+    q,
+    p,
+    X,
+    t::Number,
+    ::PadeRetraction{m},
+) where {m}
     tX = t * X
     Pp = I - 1 // 2 * p * p'
     WpX = Pp * tX * p' - p * tX' * Pp
@@ -493,12 +500,12 @@ function retract_pade!(::Stiefel, q, p, X, t::Number, ::PadeRetraction{m}) where
     end
     return copyto!(q, (qm \ pm) * p)
 end
-function retract_polar!(::Stiefel, q, p, X, t::Number)
+function ManifoldsBase.retract_polar_t!(::Stiefel, q, p, X, t::Number)
     q .= p .+ t .* X
     s = svd(q)
     return mul!(q, s.U, s.Vt)
 end
-function retract_qr!(::Stiefel, q, p, X, t::Number)
+function ManifoldsBase.retract_qr_t!(::Stiefel, q, p, X, t::Number)
     q .= p .+ t .* X
     qrfac = qr(q)
     d = diag(qrfac.R)

src/manifolds/StiefelEuclideanMetric.jl

@@ -179,7 +179,7 @@ The retraction is computed by projecting the exponential map in the embedding to
 """
 retract(::Stiefel, ::Any, ::Any, ::ProjectionRetraction)
 
-function retract_project!(M::Stiefel, q, p, X, t::Number)
+function ManifoldsBase.retract_project_t!(M::Stiefel, q, p, X, t::Number)
     q .= p .+ t .* X
     project!(M, q, q)
     return q

src/manifolds/SymplecticStiefel.jl

@@ -557,7 +557,7 @@ This expression is computed inplace of `q`.
 """
 retract(::SymplecticStiefel, p, X, ::CayleyRetraction)
 
-function retract_cayley!(M::SymplecticStiefel, q, p, X, t::Number)
+function ManifoldsBase.retract_cayley_t!(M::SymplecticStiefel, q, p, X, t::Number)
     tX = t * X
     # Define intermediate matrices for later use:
     A = symplectic_inverse_times(M, p, tX)

src/manifolds/Tucker.jl

@@ -697,7 +697,7 @@ retraction produces a boundary point, which is outside the manifold.
 """
 retract(::Tucker, ::Any, ::Any, ::PolarRetraction)
 
-function retract_polar!(
+function ManifoldsBase.retract_polar_t!(
     ::Tucker,
     q::TuckerPoint,
     p::TuckerPoint{T,D},

src/manifolds/VectorBundle.jl

@@ -237,7 +237,7 @@ function project!(B::VectorBundle, Y, p, X)
     return Y
 end
 
-function _retract!(M::VectorBundle, q, p, X, t::Number, ::FiberBundleProductRetraction)
+function _retract_t!(M::VectorBundle, q, p, X, t::Number, ::FiberBundleProductRetraction)
     return retract_product!(M, q, p, X, t)
 end
 
@@ -249,16 +249,22 @@ which by default allocates and calls `retract_product!`.
 """
 retract(::VectorBundle, p, q, t::Number, ::FiberBundleProductRetraction)
 
-function _retract(M::VectorBundle, p, X, t::Number, ::FiberBundleProductRetraction)
+function ManifoldsBase._retract_t(
+    M::VectorBundle,
+    p,
+    X,
+    t::Number,
+    ::FiberBundleProductRetraction,
+)
     return retract_product(M, p, X, t)
 end
 
-function retract_product(M::VectorBundle, p, X, t::Number)
+function retract_product_t(M::VectorBundle, p, X, t::Number)
     q = allocate_result(M, retract, p, X)
     return retract_product!(M, q, p, X, t)
 end
 
-function retract_product!(B::VectorBundle, q, p, X, t::Number)
+function retract_product_t!(B::VectorBundle, q, p, X, t::Number)
     tX = t * X
     xp, Xp = submanifold_components(B.manifold, p)
     xq, Xq = submanifold_components(B.manifold, q)
@@ -277,7 +283,14 @@ function retract_product!(B::VectorBundle, q, p, X, t::Number)
     return q
 end
 
-function retract_sasaki!(B::TangentBundle, q, p, X, t::Number, m::SasakiRetraction)
+function ManifoldsBase.retract_sasaki_t!(
+    B::TangentBundle,
+    q,
+    p,
+    X,
+    t::Number,
+    m::SasakiRetraction,
+)
     tX = t * X
     xp, Xp = submanifold_components(B.manifold, p)
     xq, Xq = submanifold_components(B.manifold, q)

src/statistics.jl

@@ -217,7 +217,7 @@ function Statistics.mean!(
             inverse_retract!(M, vtmp, yold, x[j], inverse_retraction)
             v .+= α[j] .* (vtmp .- v)
         end
-        retract!(M, y, yold, v, 0.5, retraction)
+        retract_t!(M, y, yold, v, 0.5, retraction)
         isapprox(M, y, yold; kwargs...) && break
     end
     return y
@@ -283,7 +283,7 @@ function Statistics.mean!(
         s += w[j]
         t = w[j] / s
         inverse_retract!(M, v, q, x[j], inverse_retraction)
-        retract!(M, ytmp, q, v, t, retraction)
+        retract_t!(M, ytmp, q, v, t, retraction)
         copyto!(q, ytmp)
     end
     return q