switch from === to == for checking base point.

Author: Jutho

src/grassmann.jl

@@ -56,7 +56,7 @@ end
 
 Base.getindex(Δ::GrassmannTangent) = Δ.Z
 base(Δ::GrassmannTangent) = Δ.W
-checkbase(Δ₁::GrassmannTangent, Δ₂::GrassmannTangent) = Δ₁.W === Δ₂.W ? Δ₁.W :
+checkbase(Δ₁::GrassmannTangent, Δ₂::GrassmannTangent) = Δ₁.W == Δ₂.W ? Δ₁.W :
     throw(ArgumentError("tangent vectors with different base points"))
 
 function Base.getproperty(Δ::GrassmannTangent, sym::Symbol)
@@ -142,7 +142,7 @@ function inner(W::AbstractTensorMap, Δ₁::GrassmannTangent, Δ₂::GrassmannTa
 end
 
 function retract(W::AbstractTensorMap, Δ::GrassmannTangent, α)
-    W === base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
     U, S, V = Δ.U, Δ.S, Δ.V
     WVd = W*V'
     cS = cos(α*S)
@@ -158,7 +158,7 @@ function retract(W::AbstractTensorMap, Δ::GrassmannTangent, α)
 end
 
 function transport!(Θ::GrassmannTangent, W::AbstractTensorMap, Δ::GrassmannTangent, α, W′)
-    W === checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
     U, S, V = Δ.U, Δ.S, Δ.V
     WVd = W*V'
     cS = cos(α*S)

src/stiefel.jl

@@ -65,7 +65,7 @@ end
 
 Base.getindex(Δ::StiefelTangent) = Δ.W * Δ.A + Δ.Z
 base(Δ::StiefelTangent) = Δ.W
-checkbase(Δ₁::StiefelTangent, Δ₂::StiefelTangent) = Δ₁.W === Δ₂.W ? Δ₁.W :
+checkbase(Δ₁::StiefelTangent, Δ₂::StiefelTangent) = Δ₁.W == Δ₂.W ? Δ₁.W :
     throw(ArgumentError("tangent vectors with different base points"))
 
 function Base.getproperty(Δ::StiefelTangent, sym::Symbol)
@@ -228,7 +228,7 @@ project_canonical(X, W) = project_canonical!(copy(X), W)
 # geodesic retraction for canonical metric using exponential
 # can be computed efficiently: O(np^2) + O(p^3)
 function retract_exp(W::AbstractTensorMap, Δ::StiefelTangent, α::Real)
-    W === base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
     A, Z, U, S, V, A2 = Δ.A, Δ.Z, Δ.U, Δ.S, Δ.V, Δ.A2
     UU = catdomain(W*V', U)
     VV = catcodomain(V, zero(V))
@@ -248,7 +248,7 @@ end
 # can be computed efficiently: O(np^2) + O(p^3)
 function transport_exp!(Θ::StiefelTangent, W::AbstractTensorMap,
                         Δ::StiefelTangent, α::Real, W′)
-    W === checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
     U, S, V, A2 = Δ.U, Δ.S, Δ.V, Δ.A2
     UU = catdomain(W*V', U)
     P = catcodomain(zero(S), one(S))
@@ -264,7 +264,7 @@ transport_exp(Θ::StiefelTangent, W::AbstractTensorMap, Δ::StiefelTangent, α::
 # Cayley retraction, slightly more efficient than above?
 # can be computed efficiently: O(np^2) + O(p^3)
 function retract_cayley(W::AbstractTensorMap, Δ::StiefelTangent, α::Real)
-    W === base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
     A, Z = Δ.A, Δ.Z
     ZdZ = Z'*Z
     X = axpy!(α^2/4, ZdZ, axpy!(-α/2, A, one(A)))
@@ -281,7 +281,7 @@ end
 # can be computed efficiently: O(np^2) + O(p^3)
 function transport_cayley!(Θ::StiefelTangent, W::AbstractTensorMap, Δ::StiefelTangent,
                             α::Real, W′)
-    W === checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
     A, Z = Δ.A, Δ.Z
     X = axpy!(α^2/4, Z'*Z, axpy!(-α/2, A, one(A)))
     A′ = Θ.A

src/unitary.jl

@@ -20,7 +20,7 @@ end
 Base.copy(Δ::UnitaryTangent) = UnitaryTangent(Δ.W, copy(Δ.A))
 Base.getindex(Δ::UnitaryTangent) = Δ.W * Δ.A
 base(Δ::UnitaryTangent) = Δ.W
-checkbase(Δ₁::UnitaryTangent, Δ₂::UnitaryTangent) = Δ₁.W === Δ₂.W ? Δ₁.W :
+checkbase(Δ₁::UnitaryTangent, Δ₂::UnitaryTangent) = Δ₁.W == Δ₂.W ? Δ₁.W :
     throw(ArgumentError("tangent vectors with different base points"))
 
 function Base.getproperty(Δ::UnitaryTangent, sym::Symbol)
@@ -84,7 +84,7 @@ project(X, W) = project!(copy(X), W)
 
 # geodesic retraction, coincides with Stiefel retraction (which is not geodesic for p < n)
 function retract(W::AbstractTensorMap, Δ::UnitaryTangent, α)
-    W === base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
     E = exp(α*Δ.A)
     # W′, = leftorth!(W*E; alg = QRpos()) # additional QRpos for stability
     W′ = W*E # no additional QRpos as this changes space
@@ -114,7 +114,7 @@ end
 function transport_parallel!(Θ::UnitaryTangent,
                                 W::AbstractTensorMap,
                                 Δ::UnitaryTangent, α, W′)
-    W === checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
     E = exp((α/2)*Δ.A)
     A′ = projectantihermitian!(E'*Θ.A*E) # exra projection for stability
     return UnitaryTangent(W′, A′)
@@ -125,7 +125,7 @@ transport_parallel(Θ::UnitaryTangent, W::AbstractTensorMap, Δ::UnitaryTangent,
 function transport_stiefel!(Θ::UnitaryTangent,
                                 W::AbstractTensorMap,
                                 Δ::UnitaryTangent, α, W′)
-    W === checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
+    W == checkbase(Δ,Θ) || throw(ArgumentError("not a valid tangent vector at base point"))
     A′ = Θ.A
     return UnitaryTangent(W′, A′)
 end