Deprecate svdfact to svd.

NEWS.md

@@ -246,6 +246,9 @@ This section lists changes that do not have deprecation warnings.
     `CholeskyPivoted`, and `SuiteSparse.CHOLMOD.Factor` rather than
     tuples of arrays or tuples of numbers or numbers ([#27159]).
 
+  * `svd` methods now return decomposition objects such as `SVD` and
+    `GeneralizedSVD` rather than tuples of arrays or tuples of numbers ([#27159]).
+
   * `countlines` now always counts the last non-empty line even if it does not
     end with EOL, matching the behavior of `eachline` and `readlines` ([#25845]).
 
@@ -695,8 +698,8 @@ Deprecated or removed
     `type` is fully deprecated to `mutable struct` ([#19157], [#20418]).
 
   * `lufact`, `eigfact`, `schurfact`, `lqfact`, `qrfact`, `bkfact`, `cholfact`,
-    `ldltfact`, and `hessfact` have respectively been deprecated to `lu`, `eig`,
-    `schur`, `lq`, `qr`, `bk`, `chol`, `ldlt`, and `hess` ([#27159]).
+    `ldltfact`, `hessfact`, and `svdfact` have respectively been deprecated to
+    `lu`, `eig`, `schur`, `lq`, `qr`, `bk`, `chol`, `ldlt`, `hess`, and `svd` ([#27159]).
 
   * `lufact!`, `eigfact!`, `schurfact!`, `lqfact!`, `qrfact!`, `cholfact!`,
     `bkfact!`, `ldltfact!`, `hessfact!`, and `svdfact!` have respectively been

doc/src/manual/parallel-computing.md

@@ -457,7 +457,7 @@ we could compute the singular values of several large random matrices in paralle
 ```julia-repl
 julia> M = Matrix{Float64}[rand(1000,1000) for i = 1:10];
 
-julia> pmap(svd, M);
+julia> pmap(svdvals, M);
 ```
 
 Julia's [`pmap`](@ref) is designed for the case where each function call does a large amount
@@ -486,7 +486,7 @@ As an example, consider computing the singular values of matrices of different s
 ```julia-repl
 julia> M = Matrix{Float64}[rand(800,800), rand(600,600), rand(800,800), rand(600,600)];
 
-julia> pmap(svd, M);
+julia> pmap(svdvals, M);
 ```
 
 If one process handles both 800×800 matrices and another handles both 600×600 matrices, we will

doc/src/manual/performance-tips.md

@@ -544,7 +544,7 @@ function norm(A)
     if isa(A, Vector)
         return sqrt(real(dot(A,A)))
     elseif isa(A, Matrix)
-        return maximum(svd(A)[2])
+        return maximum(svdvals(A))
     else
         error("norm: invalid argument")
     end
@@ -555,7 +555,7 @@ This can be written more concisely and efficiently as:
 
 ```julia
 norm(x::Vector) = sqrt(real(dot(x,x)))
-norm(A::Matrix) = maximum(svd(A)[2])
+norm(A::Matrix) = maximum(svdvals(A))
 ```
 
 ## Write "type-stable" functions

stdlib/Distributed/test/distributed_exec.jl

@@ -576,8 +576,8 @@ end
 n = 10
 as = [rand(4,4) for i in 1:n]
 bs = deepcopy(as)
-cs = collect(Distributed.pgenerate(x->(sleep(rand()*0.1); svdfact(x)), bs))
-svdas = map(svdfact, as)
+cs = collect(Distributed.pgenerate(x->(sleep(rand()*0.1); svd(x)), bs))
+svdas = map(svd, as)
 for i in 1:n
     @test cs[i].U ≈ svdas[i].U
     @test cs[i].S ≈ svdas[i].S

stdlib/IterativeEigensolvers/test/runtests.jl

@@ -189,16 +189,16 @@ end
     S2 = svd(Array(A))
 
     ## singular values match:
-    @test S1[1].S ≈ S2[2][1:2]
+    @test S1[1].S ≈ S2.S[1:2]
     @testset "singular vectors" begin
         ## 1st left singular vector
         s1_left = sign(S1[1].U[3,1]) * S1[1].U[:,1]
-        s2_left = sign(S2[1][3,1]) * S2[1][:,1]
+        s2_left = sign(S2.U[3,1]) * S2.U[:,1]
         @test s1_left ≈ s2_left
 
         ## 1st right singular vector
         s1_right = sign(S1[1].V[3,1]) * S1[1].V[:,1]
-        s2_right = sign(S2[3][3,1]) * S2[3][:,1]
+        s2_right = sign(S2.V[3,1]) * S2.V[:,1]
         @test s1_right ≈ s2_right
     end
     # Issue number 10329
@@ -213,7 +213,7 @@ end
     end
     @testset "passing guess for Krylov vectors" begin
         S1 = svds(A, nsv = 2, v0=rand(eltype(A),size(A,2)))
-        @test S1[1].S ≈ S2[2][1:2]
+        @test S1[1].S ≈ S2.S[1:2]
     end
 
     @test_throws ArgumentError svds(A,nsv=0)
@@ -251,21 +251,21 @@ end
     S2 = svd(Array(A))
 
     ## singular values match:
-    @test S1[1].S ≈ S2[2][1:2]
+    @test S1[1].S ≈ S2.S[1:2]
     @testset "singular vectors" begin
         ## left singular vectors
         s1_left = abs.(S1[1].U[:,1:2])
-        s2_left = abs.(S2[1][:,1:2])
+        s2_left = abs.(S2.U[:,1:2])
         @test s1_left ≈ s2_left
 
         ## right singular vectors
         s1_right = abs.(S1[1].V[:,1:2])
-        s2_right = abs.(S2[3][:,1:2])
+        s2_right = abs.(S2.V[:,1:2])
         @test s1_right ≈ s2_right
     end
     @testset "passing guess for Krylov vectors" begin
         S1 = svds(A, nsv = 2, v0=rand(eltype(A),size(A,2)))
-        @test S1[1].S ≈ S2[2][1:2]
+        @test S1[1].S ≈ S2.S[1:2]
     end
 
     @test_throws ArgumentError svds(A,nsv=0)

stdlib/LinearAlgebra/docs/src/index.md

@@ -343,9 +343,8 @@ LinearAlgebra.schur!
 LinearAlgebra.schur
 LinearAlgebra.ordschur
 LinearAlgebra.ordschur!
-LinearAlgebra.svdfact
-LinearAlgebra.svd!
 LinearAlgebra.svd
+LinearAlgebra.svd!
 LinearAlgebra.svdvals
 LinearAlgebra.svdvals!
 LinearAlgebra.Givens

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -132,7 +132,6 @@ export
     schur!,
     svd,
     svd!,
-    svdfact,
     svdvals!,
     svdvals,
     sylvester,

stdlib/LinearAlgebra/src/bidiag.jl

@@ -199,12 +199,12 @@ function svd!(M::Bidiagonal{<:BlasReal}; full::Bool = false, thin::Union{Bool,No
     d, e, U, Vt, Q, iQ = LAPACK.bdsdc!(M.uplo, 'I', M.dv, M.ev)
     SVD(U, d, Vt)
 end
-function svdfact(M::Bidiagonal; full::Bool = false, thin::Union{Bool,Nothing} = nothing)
+function svd(M::Bidiagonal; full::Bool = false, thin::Union{Bool,Nothing} = nothing)
     # DEPRECATION TODO: remove deprecated thin argument and associated logic after 0.7
     if thin != nothing
-        Base.depwarn(string("the `thin` keyword argument in `svdfact(A; thin = $(thin))` has ",
+        Base.depwarn(string("the `thin` keyword argument in `svd(A; thin = $(thin))` has ",
             "been deprecated in favor of `full`, which has the opposite meaning, ",
-            "e.g. `svdfact(A; full = $(!thin))`."), :svdfact)
+            "e.g. `svd(A; full = $(!thin))`."), :svd)
         full::Bool = !thin
     end
     return svd!(copy(M), full = full)

stdlib/LinearAlgebra/src/dense.jl

@@ -1292,7 +1292,7 @@ function pinv(A::StridedMatrix{T}, tol::Real) where T
             return B
         end
     end
-    SVD         = svdfact(A, full = false)
+    SVD         = svd(A, full = false)
     Stype       = eltype(SVD.S)
     Sinv        = zeros(Stype, length(SVD.S))
     index       = SVD.S .> tol*maximum(SVD.S)
@@ -1344,7 +1344,7 @@ julia> nullspace(M, 2)
 function nullspace(A::StridedMatrix, tol::Real = min(size(A)...)*eps(real(float(one(eltype(A))))))
     m, n = size(A)
     (m == 0 || n == 0) && return Matrix{T}(I, n, n)
-    SVD = svdfact(A, full=true)
+    SVD = svd(A, full=true)
     indstart = sum(SVD.S .> SVD.S[1]*tol) + 1
     return copy(SVD.Vt[indstart:end,:]')
 end

stdlib/LinearAlgebra/src/deprecated.jl

@@ -1397,3 +1397,15 @@ export svdfact!
 @deprecate(svdfact!(A::StridedMatrix{T}; full::Bool = false, thin::Union{Bool,Nothing} = nothing) where T<:BlasFloat, svd!(A; full=full, thin=thin))
 @deprecate(svdfact!(A::StridedMatrix{T}, B::StridedMatrix{T}) where T<:BlasFloat, svd!(A, B))
 @deprecate(svdfact!(A::AbstractTriangular), svd!(A))
+
+# deprecate svdfact to svd
+export svdfact
+@deprecate(svdfact(D::Diagonal), svd(D))
+@deprecate(svdfact(A::StridedVecOrMat{T}; full::Bool = false, thin::Union{Bool,Nothing} = nothing) where T, svd(A; full=full, thin=thin))
+@deprecate(svdfact(x::Number; full::Bool = false, thin::Union{Bool,Nothing} = nothing), svd(x; full=full, thin=thin))
+@deprecate(svdfact(x::Integer; full::Bool = false, thin::Union{Bool,Nothing} = nothing), svd(x; full=full, thin=thin))
+@deprecate(svdfact(A::StridedMatrix{T}, B::StridedMatrix{T}) where {T<:BlasFloat}, svd(A, B))
+@deprecate(svdfact(A::StridedMatrix{TA}, B::StridedMatrix{TB}) where {TA,TB}, svd(A, B))
+@deprecate(svdfact(x::Number, y::Number), svd(x, y))
+@deprecate(svdfact(M::Bidiagonal; full::Bool = false, thin::Union{Bool,Nothing} = nothing), svd(M; full=full, thin=thin))
+@deprecate(svdfact(A::AbstractTriangular), svd(A))

stdlib/LinearAlgebra/src/diagonal.jl

@@ -462,11 +462,7 @@ function svd(D::Diagonal{<:Number})
     Up  = hcat([U[:,i] for i = 1:length(D.diag)][piv]...)
     V   = Diagonal(fill!(similar(D.diag), one(eltype(D.diag))))
     Vp  = hcat([V[:,i] for i = 1:length(D.diag)][piv]...)
-    return (Up, S[piv], Vp)
-end
-function svdfact(D::Diagonal)
-    U, s, V = svd(D)
-    SVD(U, s, copy(V'))
+    return SVD(Up, S[piv], copy(Vp'))
 end
 
 # dismabiguation methods: * of Diagonal and Adj/Trans AbsVec