Adapt to TensorKit v0.15

Project.toml

@@ -1,14 +1,16 @@
 name = "TensorKitManifolds"
 uuid = "11fa318c-39cb-4a83-b1ed-cdc7ba1e3684"
 authors = ["Jutho Haegeman <jutho.haegeman@ugent.be>", "Markus Hauru <markus@mhauru.org>"]
-version = "0.7.2"
+version = "0.7.3"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+MatrixAlgebraKit = "6c742aac-3347-4629-af66-fc926824e5e4"
 TensorKit = "07d1fe3e-3e46-537d-9eac-e9e13d0d4cec"
 
 [compat]
-TensorKit = "0.13,0.14"
+MatrixAlgebraKit = "0.5.0"
+TensorKit = "0.15"
 julia = "1.10"
 
 [extras]

src/TensorKitManifolds.jl

@@ -7,6 +7,9 @@ export Grassmann, Stiefel, Unitary
 export inner, retract, transport, transport!
 
 using TensorKit
+using MatrixAlgebraKit: MatrixAlgebraKit, AbstractAlgorithm, Algorithm, PolarViaSVD,
+                        LAPACK_DivideAndConquer, diagview
+import MatrixAlgebraKit as MAK
 
 # Every submodule -- Grassmann, Stiefel, and Unitary -- implements their own methods for
 # these. The signatures should be
@@ -28,23 +31,8 @@ checkbase(x, y, z, args...) = checkbase(checkbase(x, y), z, args...)
 # the machine epsilon for the elements of an object X, name inspired from eltype
 scalareps(X) = eps(real(scalartype(X)))
 
-# default SVD algorithm used in the algorithms
-default_svd_alg(::AbstractTensorMap) = TensorKit.SVD()
-
-function isisometry(W::AbstractTensorMap; tol=10 * scalareps(W))
-    WdW = W' * W
-    s = zero(float(real(scalartype(W))))
-    for (c, b) in blocks(WdW)
-        _subtractone!(b)
-        s += dim(c) * length(b)
-    end
-    return norm(WdW) <= tol * sqrt(s)
-end
-
-function isunitary(W::AbstractTensorMap; tol=10 * scalareps(W))
-    return isisometry(W; tol=tol) && isisometry(W'; tol=tol)
-end
-
+# TODO: these functions should be replaced by MAK functions
+projecthermitian(W::AbstractTensorMap) = projecthermitian!(copy(W))
 function projecthermitian!(W::AbstractTensorMap)
     codomain(W) == domain(W) ||
         throw(DomainError("Tensor with distinct domain and codomain cannot be hermitian."))
@@ -53,6 +41,8 @@ function projecthermitian!(W::AbstractTensorMap)
     end
     return W
 end
+
+projectantihermitian(W::AbstractTensorMap) = projectantihermitian!(copy(W))
 function projectantihermitian!(W::AbstractTensorMap)
     codomain(W) == domain(W) ||
         throw(DomainError("Tensor with distinct domain and codomain cannot be anithermitian."))
@@ -62,27 +52,18 @@ function projectantihermitian!(W::AbstractTensorMap)
     return W
 end
 
-struct PolarNewton <: TensorKit.OrthogonalFactorizationAlgorithm
-end
-function projectisometric!(W::AbstractTensorMap; alg=default_svd_alg(W))
-    if alg isa TensorKit.Polar || alg isa TensorKit.SDD
-        foreach(blocks(W)) do (c, b)
-            return _polarsdd!(b)
-        end
-    elseif alg isa TensorKit.SVD
-        foreach(blocks(W)) do (c, b)
-            return _polarsvd!(b)
-        end
-    elseif alg isa PolarNewton
-        foreach(blocks(W)) do (c, b)
-            return _polarnewton!(b)
-        end
-    else
-        throw(ArgumentError("unkown algorithm for projectisometric!: alg = $alg"))
+projectisometric(W::AbstractTensorMap; kwargs...) = projectisometric!(copy(W); kwargs...)
+function projectisometric!(W::AbstractTensorMap;
+                           alg::AbstractAlgorithm=MAK.select_algorithm(left_polar!, W))
+    TensorKit.foreachblock(W) do c, (b,)
+        return _left_polar!(b, alg)
     end
     return W
 end
 
+function projectcomplement(X::AbstractTensorMap, W::AbstractTensorMap, kwargs...)
+    return projectcomplement!(copy(X), W; kwargs...)
+end
 function projectcomplement!(X::AbstractTensorMap, W::AbstractTensorMap;
                             tol=10 * scalareps(X))
     P = W' * X
@@ -97,18 +78,6 @@ function projectcomplement!(X::AbstractTensorMap, W::AbstractTensorMap;
     return X
 end
 
-projecthermitian(W::AbstractTensorMap) = projecthermitian!(copy(W))
-projectantihermitian(W::AbstractTensorMap) = projectantihermitian!(copy(W))
-
-function projectisometric(W::AbstractTensorMap;
-                          alg=default_svd_alg(W))
-    return projectisometric!(copy(W); alg=alg)
-end
-function projectcomplement(X::AbstractTensorMap, W::AbstractTensorMap,
-                           tol=10 * scalareps(X))
-    return projectcomplement!(copy(X), W; tol=tol)
-end
-
 include("auxiliary.jl")
 include("grassmann.jl")
 include("stiefel.jl")

src/auxiliary.jl

@@ -70,37 +70,43 @@ function _subtractone!(a::AbstractMatrix)
     view(a, diagind(a)) .= view(a, diagind(a)) .- 1
     return a
 end
-function _polarsdd!(A::StridedMatrix)
-    U, S, V = svd!(A; alg=LinearAlgebra.DivideAndConquer())
-    return mul!(A, U, V')
-end
-function _polarsvd!(A::StridedMatrix)
-    U, S, V = svd!(A; alg=LinearAlgebra.QRIteration())
-    return mul!(A, U, V')
+
+# TODO: _left_polar! is more or less the same as MAK.left_polar! but doesn't compute the P
+# which is not needed here. Can we unify this?
+function _left_polar!(A::StridedMatrix,
+                      alg::PolarViaSVD=PolarViaSVD(LAPACK_DivideAndConquer()))
+    U, _, Vᴴ = svd_compact!(A, alg.svdalg)
+    return mul!(A, U, Vᴴ)
 end
+
+# TODO: can we move this to a dedicated MAK algorithm?
+MatrixAlgebraKit.@algdef PolarNewton
+
+_left_polar!(A::StridedMatrix, alg::PolarNewton) = _polarnewton!(A; alg.kwargs...)
 function _polarnewton!(A::StridedMatrix; tol=10 * scalareps(A), maxiter=5)
     m, n = size(A)
     @assert m >= n
     A2 = copy(A)
-    Q, R = qr!(A2)
-    Ri = ldiv!(UpperTriangular(R)', TensorKit.MatrixAlgebra.one!(similar(R)))
+    Q, R = LinearAlgebra.qr!(A2)
+    Ri = ldiv!(UpperTriangular(R)', MatrixAlgebraKit.one!(similar(R)))
     R, Ri = _avgdiff!(R, Ri)
     i = 1
     R2 = view(A, 1:n, 1:n)
     fill!(view(A, (n + 1):m, 1:n), zero(eltype(A)))
     copyto!(R2, R)
     while maximum(abs, Ri) > tol
         if i == maxiter # if not converged by now, fall back to sdd
-            _polarsdd!(Ri)
+            _left_polar!(Ri)
             break
         end
-        Ri = ldiv!(lu!(R2)', TensorKit.MatrixAlgebra.one!(Ri))
+        Ri = ldiv!(lu!(R2)', MatrixAlgebraKit.one!(Ri))
         R, Ri = _avgdiff!(R, Ri)
         copyto!(R2, R)
         i += 1
     end
     return lmul!(Q, A)
 end
+
 # in place computation of the average and difference of two arrays
 function _avgdiff!(A::AbstractArray, B::AbstractArray)
     axes(A) == axes(B) || throw(DimensionMismatch())
@@ -124,7 +130,7 @@ end
 function _stiefelexp(W::StridedMatrix, A::StridedMatrix, Z::StridedMatrix, α)
     n, p = size(W)
     r = min(2 * p, n)
-    QQ, _ = qr!([W Z])
+    QQ, _ = LinearAlgebra.qr!([W Z])
     Q = similar(W, n, r - p)
     @inbounds for j in Base.OneTo(r - p)
         for i in Base.OneTo(n)
@@ -139,7 +145,7 @@ function _stiefelexp(W::StridedMatrix, A::StridedMatrix, Z::StridedMatrix, α)
     A2[1:p, (p + 1):end] .= (-α) .* (R')
     A2[(p + 1):end, (p + 1):end] .= 0
     U = [W Q] * exp(A2)
-    U = _polarnewton!(U)
+    U = _left_polar!(U, PolarNewton())
     W′ = U[:, 1:p]
     Q′ = U[:, (p + 1):end]
     R′ = R
@@ -152,7 +158,7 @@ function _stiefellog(Wold::StridedMatrix, Wnew::StridedMatrix;
     r = min(2 * p, n)
     P = Wold' * Wnew
     dW = Wnew - Wold * P
-    QQ, _ = qr!([Wold dW])
+    QQ, _ = LinearAlgebra.qr!([Wold dW])
     Q = similar(Wold, n, r - p)
     @inbounds for j in Base.OneTo(r - p)
         for i in Base.OneTo(n)
@@ -161,23 +167,17 @@ function _stiefellog(Wold::StridedMatrix, Wnew::StridedMatrix;
     end
     Q = lmul!(QQ, Q)
     R = Q' * dW
-    Wext = [Wold Q]
-    F = qr!([P; R])
-    U = lmul!(F.Q, TensorKit.MatrixAlgebra.one!(similar(P, r, r)))
+    F = LinearAlgebra.qr!([P; R])
+    U = lmul!(F.Q, MatrixAlgebraKit.one!(similar(P, r, r)))
     U[1:p, 1:p] .= P
     U[(p + 1):r, 1:p] .= R
     X = view(U, 1:p, (p + 1):r)
     Y = view(U, (p + 1):r, (p + 1):r)
     if p < n
-        YSVD = svd!(Y)
-        mul!(X, X * (YSVD.V), (YSVD.U)')
-        UsqrtS = YSVD.U
-        @inbounds for j in 1:size(UsqrtS, 2)
-            s = sqrt(YSVD.S[j])
-            @simd for i in 1:size(UsqrtS, 1)
-                UsqrtS[i, j] *= s
-            end
-        end
+        USVᴴ = svd_compact!(Y)
+        mul!(X, X * USVᴴ[3]', USVᴴ[1]')
+        diagview(USVᴴ[2]) .= sqrt.(diagview(USVᴴ[2]))
+        UsqrtS = rmul!(USVᴴ[1], USVᴴ[2])
         mul!(Y, UsqrtS, UsqrtS')
     end
     logU = _projectantihermitian!(log(U))

src/grassmann.jl

@@ -7,8 +7,7 @@ module Grassmann
 using TensorKit
 using TensorKit: similarstoragetype, SectorDict
 using ..TensorKitManifolds: projecthermitian!, projectantihermitian!,
-                            projectisometric!, projectcomplement!, PolarNewton,
-                            default_svd_alg
+                            projectisometric!, projectcomplement!, PolarNewton
 import ..TensorKitManifolds: base, checkbase, inner, retract, transport, transport!
 
 # special type to store tangent vectors using Z
@@ -32,8 +31,8 @@ end
 
 # output type of U, S, V in tsvd
 function _tsvd_types(Z::AbstractTensorMap)
-    TUSV = Core.Compiler.return_type(tsvd, Tuple{typeof(Z)})
-    TU, TS, TV, = TUSV.types
+    TUSV = Core.Compiler.return_type(svd_compact, Tuple{typeof(Z)})
+    TU, TS, TV = TUSV.types
     return TU, TS, TV
 end
 
@@ -60,7 +59,7 @@ function Base.getproperty(Δ::GrassmannTangent, sym::Symbol)
     elseif sym ∈ (:U, :S, :V)
         v = Base.getfield(Δ, sym)
         v !== nothing && return v
-        U, S, V, = tsvd(Δ.Z; alg=default_svd_alg(Δ.Z))
+        U, S, V = svd_compact(Δ.Z)
         Base.setfield!(Δ, :U, U)
         Base.setfield!(Δ, :S, S)
         Base.setfield!(Δ, :V, V)
@@ -198,7 +197,7 @@ function invretract(Wold::AbstractTensorMap, Wnew::AbstractTensorMap; alg=nothin
     space(Wold) == space(Wnew) || throw(SpaceMismatch())
     WodWn = Wold' * Wnew # V' * cos(S) * V * Y
     Wneworth = Wnew - Wold * WodWn
-    Vd, cS, VY = tsvd!(WodWn; alg=default_svd_alg(WodWn))
+    Vd, cS, VY = svd_compact!(WodWn)
     Scmplx = acos(cS)
     # acos always returns a complex TensorMap. We cast back to real if possible.
     S = scalartype(WodWn) <: Real && isreal(sectortype(Scmplx)) ? real(Scmplx) : Scmplx

src/unitary.jl

@@ -7,6 +7,7 @@ using TensorKit
 import TensorKit: similarstoragetype, SectorDict
 using ..TensorKitManifolds: projectantihermitian!, projectisometric!, PolarNewton
 import ..TensorKitManifolds: base, checkbase, inner, retract, transport, transport!
+import MatrixAlgebraKit as MAK
 
 struct UnitaryTangent{T<:AbstractTensorMap,TA<:AbstractTensorMap}
     W::T
@@ -82,10 +83,11 @@ end
 project(X, W; metric=:euclidean) = project!(copy(X), W; metric=:euclidean)
 
 # geodesic retraction, coincides with Stiefel retraction (which is not geodesic for p < n)
-function retract(W::AbstractTensorMap, Δ::UnitaryTangent, α; alg=nothing)
+function retract(W::AbstractTensorMap, Δ::UnitaryTangent, α;
+                 alg=MAK.select_algorithm(left_polar!, W))
     W == base(Δ) || throw(ArgumentError("not a valid tangent vector at base point"))
     E = exp(α * Δ.A)
-    W′ = projectisometric!(W * E; alg=SDD())
+    W′ = projectisometric!(W * E; alg)
     A′ = Δ.A
     return W′, UnitaryTangent(W′, A′)
 end
@@ -104,7 +106,7 @@ function transport!(Θ::UnitaryTangent, W::AbstractTensorMap, Δ::UnitaryTangent
 end
 function transport(Θ::UnitaryTangent, W::AbstractTensorMap, Δ::UnitaryTangent, α::Real, W′;
                    alg=:stiefel)
-    return transport!(copy(Θ), W, Δ, α, W′; alg=alg)
+    return transport!(copy(Θ), W, Δ, α, W′; alg)
 end
 
 # transport_parallel correspondings to the torsion-free Levi-Civita connection

test/runtests.jl

@@ -8,7 +8,7 @@ const α = 0.75
 
 @testset "Grassmann with space $V" for V in spaces
     for T in (Float64,)
-        W, = leftorth(randn(T, V * V * V, V * V); alg=Polar())
+        W, = left_polar(randn(T, V * V * V, V * V))
         X = randn(T, space(W))
         Y = randn(T, space(W))
         Δ = @inferred Grassmann.project(X, W)
@@ -124,7 +124,7 @@ end
 
 @testset "Unitary with space $V" for V in spaces
     for T in (Float64, ComplexF64)
-        W, = leftorth(randn(T, V * V * V, V * V); alg=Polar())
+        W, = left_polar(randn(T, V * V * V, V * V))
         X = randn(T, space(W))
         Y = randn(T, space(W))
         Δ = @inferred Unitary.project(X, W)