Replace Val-types by singleton types in lu and qr (JuliaLang#40623)

Co-authored-by: Andreas Noack <andreas@noack.dk>

NEWS.md

@@ -115,6 +115,10 @@ Standard library changes
 * The shape of an `UpperHessenberg` matrix is preserved under certain arithmetic operations, e.g. when multiplying or dividing by an `UpperTriangular` matrix. ([#40039])
 * `cis(A)` now supports matrix arguments ([#40194]).
 * `dot` now supports `UniformScaling` with `AbstractMatrix` ([#40250]).
+* `qr[!]` and `lu[!]` now support `LinearAlgebra.PivotingStrategy` (singleton type) values
+  as their optional `pivot` argument: defaults are `qr(A, NoPivot())` (vs.
+  `qr(A, ColumnNorm())` for pivoting) and `lu(A, RowMaximum())` (vs. `lu(A, NoPivot())`
+  without pivoting); the former `Val{true/false}`-based calls are deprecated. ([#40623])
 * `det(M::AbstractMatrix{BigInt})` now calls `det_bareiss(M)`, which uses the [Bareiss](https://en.wikipedia.org/wiki/Bareiss_algorithm) algorithm to calculate precise values.([#40868]).
 
 #### Markdown

stdlib/LinearAlgebra/src/LinearAlgebra.jl

@@ -35,19 +35,22 @@ export
     BunchKaufman,
     Cholesky,
     CholeskyPivoted,
+    ColumnNorm,
     Eigen,
     GeneralizedEigen,
     GeneralizedSVD,
     GeneralizedSchur,
     Hessenberg,
     LU,
     LDLt,
+    NoPivot,
     QR,
     QRPivoted,
     LQ,
     Schur,
     SVD,
     Hermitian,
+    RowMaximum,
     Symmetric,
     LowerTriangular,
     UpperTriangular,
@@ -164,6 +167,10 @@ abstract type Algorithm end
 struct DivideAndConquer <: Algorithm end
 struct QRIteration <: Algorithm end
 
+abstract type PivotingStrategy end
+struct NoPivot <: PivotingStrategy end
+struct RowMaximum <: PivotingStrategy end
+struct ColumnNorm <: PivotingStrategy end
 
 # Check that stride of matrix/vector is 1
 # Writing like this to avoid splatting penalty when called with multiple arguments,

stdlib/LinearAlgebra/src/dense.jl

@@ -1371,7 +1371,7 @@ function factorize(A::StridedMatrix{T}) where T
         end
         return lu(A)
     end
-    qr(A, Val(true))
+    qr(A, ColumnNorm())
 end
 factorize(A::Adjoint)   =   adjoint(factorize(parent(A)))
 factorize(A::Transpose) = transpose(factorize(parent(A)))

stdlib/LinearAlgebra/src/factorization.jl

@@ -16,9 +16,9 @@ size(F::Adjoint{<:Any,<:Factorization}) = reverse(size(parent(F)))
 size(F::Transpose{<:Any,<:Factorization}) = reverse(size(parent(F)))
 
 checkpositivedefinite(info) = info == 0 || throw(PosDefException(info))
-checknonsingular(info, pivoted::Val{true}) = info == 0 || throw(SingularException(info))
-checknonsingular(info, pivoted::Val{false}) = info == 0 || throw(ZeroPivotException(info))
-checknonsingular(info) = checknonsingular(info, Val{true}())
+checknonsingular(info, ::RowMaximum) = info == 0 || throw(SingularException(info))
+checknonsingular(info, ::NoPivot) = info == 0 || throw(ZeroPivotException(info))
+checknonsingular(info) = checknonsingular(info, RowMaximum())
 
 """
     issuccess(F::Factorization)

stdlib/LinearAlgebra/src/generic.jl

@@ -1141,7 +1141,7 @@ function (\)(A::AbstractMatrix, B::AbstractVecOrMat)
         end
         return lu(A) \ B
     end
-    return qr(A,Val(true)) \ B
+    return qr(A, ColumnNorm()) \ B
 end
 
 (\)(a::AbstractVector, b::AbstractArray) = pinv(a) * b

stdlib/LinearAlgebra/src/lu.jl

@@ -76,22 +76,26 @@ adjoint(F::LU) = Adjoint(F)
 transpose(F::LU) = Transpose(F)
 
 # StridedMatrix
-function lu!(A::StridedMatrix{T}, pivot::Union{Val{false}, Val{true}} = Val(true);
-             check::Bool = true) where T<:BlasFloat
-    if pivot === Val(false)
-        return generic_lufact!(A, pivot; check = check)
-    end
+lu!(A::StridedMatrix{<:BlasFloat}; check::Bool = true) = lu!(A, RowMaximum(); check=check)
+function lu!(A::StridedMatrix{T}, ::RowMaximum; check::Bool = true) where {T<:BlasFloat}
     lpt = LAPACK.getrf!(A)
     check && checknonsingular(lpt[3])
     return LU{T,typeof(A)}(lpt[1], lpt[2], lpt[3])
 end
-function lu!(A::HermOrSym, pivot::Union{Val{false}, Val{true}} = Val(true); check::Bool = true)
+function lu!(A::StridedMatrix{<:BlasFloat}, pivot::NoPivot; check::Bool = true)
+    return generic_lufact!(A, pivot; check = check)
+end
+function lu!(A::HermOrSym, pivot::Union{RowMaximum,NoPivot} = RowMaximum(); check::Bool = true)
     copytri!(A.data, A.uplo, isa(A, Hermitian))
     lu!(A.data, pivot; check = check)
 end
+# for backward compatibility
+# TODO: remove towards Julia v2
+@deprecate lu!(A::Union{StridedMatrix,HermOrSym,Tridiagonal}, ::Val{true}; check::Bool = true) lu!(A, RowMaximum(); check=check)
+@deprecate lu!(A::Union{StridedMatrix,HermOrSym,Tridiagonal}, ::Val{false}; check::Bool = true) lu!(A, NoPivot(); check=check)
 
 """
-    lu!(A, pivot=Val(true); check = true) -> LU
+    lu!(A, pivot = RowMaximum(); check = true) -> LU
 
 `lu!` is the same as [`lu`](@ref), but saves space by overwriting the
 input `A`, instead of creating a copy. An [`InexactError`](@ref)
@@ -127,19 +131,22 @@ Stacktrace:
 [...]
 ```
 """
-lu!(A::StridedMatrix, pivot::Union{Val{false}, Val{true}} = Val(true); check::Bool = true) =
+lu!(A::StridedMatrix, pivot::Union{RowMaximum,NoPivot} = RowMaximum(); check::Bool = true) =
     generic_lufact!(A, pivot; check = check)
-function generic_lufact!(A::StridedMatrix{T}, ::Val{Pivot} = Val(true);
-                         check::Bool = true) where {T,Pivot}
+function generic_lufact!(A::StridedMatrix{T}, pivot::Union{RowMaximum,NoPivot} = RowMaximum();
+                         check::Bool = true) where {T}
+    # Extract values
     m, n = size(A)
     minmn = min(m,n)
+
+    # Initialize variables
     info = 0
     ipiv = Vector{BlasInt}(undef, minmn)
     @inbounds begin
         for k = 1:minmn
             # find index max
             kp = k
-            if Pivot && k < m
+            if pivot === RowMaximum() && k < m
                 amax = abs(A[k, k])
                 for i = k+1:m
                     absi = abs(A[i,k])
@@ -175,7 +182,7 @@ function generic_lufact!(A::StridedMatrix{T}, ::Val{Pivot} = Val(true);
             end
         end
     end
-    check && checknonsingular(info, Val{Pivot}())
+    check && checknonsingular(info, pivot)
     return LU{T,typeof(A)}(A, ipiv, convert(BlasInt, info))
 end
 
@@ -200,7 +207,7 @@ end
 
 # for all other types we must promote to a type which is stable under division
 """
-    lu(A, pivot=Val(true); check = true) -> F::LU
+    lu(A, pivot = RowMaximum(); check = true) -> F::LU
 
 Compute the LU factorization of `A`.
 
@@ -211,7 +218,7 @@ validity (via [`issuccess`](@ref)) lies with the user.
 In most cases, if `A` is a subtype `S` of `AbstractMatrix{T}` with an element
 type `T` supporting `+`, `-`, `*` and `/`, the return type is `LU{T,S{T}}`. If
 pivoting is chosen (default) the element type should also support [`abs`](@ref) and
-[`<`](@ref).
+[`<`](@ref). Pivoting can be turned off by passing `pivot = NoPivot()`.
 
 The individual components of the factorization `F` can be accessed via [`getproperty`](@ref):
 
@@ -267,11 +274,14 @@ julia> l == F.L && u == F.U && p == F.p
 true
 ```
 """
-function lu(A::AbstractMatrix{T}, pivot::Union{Val{false}, Val{true}}=Val(true);
-            check::Bool = true) where T
+function lu(A::AbstractMatrix{T}, pivot::Union{RowMaximum,NoPivot} = RowMaximum(); check::Bool = true) where {T}
     S = lutype(T)
     lu!(copy_oftype(A, S), pivot; check = check)
 end
+# TODO: remove for Julia v2.0
+@deprecate lu(A::AbstractMatrix, ::Val{true}; check::Bool = true) lu(A, RowMaximum(); check=check)
+@deprecate lu(A::AbstractMatrix, ::Val{false}; check::Bool = true) lu(A, NoPivot(); check=check)
+
 
 lu(S::LU) = S
 function lu(x::Number; check::Bool=true)
@@ -481,9 +491,11 @@ inv(A::LU{<:BlasFloat,<:StridedMatrix}) = inv!(copy(A))
 # Tridiagonal
 
 # See dgttrf.f
-function lu!(A::Tridiagonal{T,V}, pivot::Union{Val{false}, Val{true}} = Val(true);
-             check::Bool = true) where {T,V}
+function lu!(A::Tridiagonal{T,V}, pivot::Union{RowMaximum,NoPivot} = RowMaximum(); check::Bool = true) where {T,V}
+    # Extract values
     n = size(A, 1)
+
+    # Initialize variables
     info = 0
     ipiv = Vector{BlasInt}(undef, n)
     dl = A.dl
@@ -500,7 +512,7 @@ function lu!(A::Tridiagonal{T,V}, pivot::Union{Val{false}, Val{true}} = Val(true
         end
         for i = 1:n-2
             # pivot or not?
-            if pivot === Val(false) || abs(d[i]) >= abs(dl[i])
+            if pivot === NoPivot() || abs(d[i]) >= abs(dl[i])
                 # No interchange
                 if d[i] != 0
                     fact = dl[i]/d[i]
@@ -523,7 +535,7 @@ function lu!(A::Tridiagonal{T,V}, pivot::Union{Val{false}, Val{true}} = Val(true
         end
         if n > 1
             i = n-1
-            if pivot === Val(false) || abs(d[i]) >= abs(dl[i])
+            if pivot === NoPivot() || abs(d[i]) >= abs(dl[i])
                 if d[i] != 0
                     fact = dl[i]/d[i]
                     dl[i] = fact

stdlib/LinearAlgebra/src/qr.jl

@@ -246,17 +246,17 @@ function qrfactPivotedUnblocked!(A::AbstractMatrix)
 end
 
 # LAPACK version
-qr!(A::StridedMatrix{<:BlasFloat}, ::Val{false} = Val(false); blocksize=36) =
+qr!(A::StridedMatrix{<:BlasFloat}, ::NoPivot; blocksize=36) =
     QRCompactWY(LAPACK.geqrt!(A, min(min(size(A)...), blocksize))...)
-qr!(A::StridedMatrix{<:BlasFloat}, ::Val{true}) = QRPivoted(LAPACK.geqp3!(A)...)
+qr!(A::StridedMatrix{<:BlasFloat}, ::ColumnNorm) = QRPivoted(LAPACK.geqp3!(A)...)
 
 # Generic fallbacks
 
 """
-    qr!(A, pivot=Val(false); blocksize)
+    qr!(A, pivot = NoPivot(); blocksize)
 
-`qr!` is the same as [`qr`](@ref) when `A` is a subtype of
-[`StridedMatrix`](@ref), but saves space by overwriting the input `A`, instead of creating a copy.
+`qr!` is the same as [`qr`](@ref) when `A` is a subtype of [`StridedMatrix`](@ref),
+but saves space by overwriting the input `A`, instead of creating a copy.
 An [`InexactError`](@ref) exception is thrown if the factorization produces a number not
 representable by the element type of `A`, e.g. for integer types.
 
@@ -292,14 +292,17 @@ Stacktrace:
 [...]
 ```
 """
-qr!(A::AbstractMatrix, ::Val{false}) = qrfactUnblocked!(A)
-qr!(A::AbstractMatrix, ::Val{true}) = qrfactPivotedUnblocked!(A)
-qr!(A::AbstractMatrix) = qr!(A, Val(false))
+qr!(A::AbstractMatrix, ::NoPivot) = qrfactUnblocked!(A)
+qr!(A::AbstractMatrix, ::ColumnNorm) = qrfactPivotedUnblocked!(A)
+qr!(A::AbstractMatrix) = qr!(A, NoPivot())
+# TODO: Remove in Julia v2.0
+@deprecate qr!(A::AbstractMatrix, ::Val{true})  qr!(A, ColumnNorm())
+@deprecate qr!(A::AbstractMatrix, ::Val{false}) qr!(A, NoPivot())
 
 _qreltype(::Type{T}) where T = typeof(zero(T)/sqrt(abs2(one(T))))
 
 """
-    qr(A, pivot=Val(false); blocksize) -> F
+    qr(A, pivot = NoPivot(); blocksize) -> F
 
 Compute the QR factorization of the matrix `A`: an orthogonal (or unitary if `A` is
 complex-valued) matrix `Q`, and an upper triangular matrix `R` such that
@@ -310,7 +313,7 @@ A = Q R
 
 The returned object `F` stores the factorization in a packed format:
 
- - if `pivot == Val(true)` then `F` is a [`QRPivoted`](@ref) object,
+ - if `pivot == ColumnNorm()` then `F` is a [`QRPivoted`](@ref) object,
 
  - otherwise if the element type of `A` is a BLAS type ([`Float32`](@ref), [`Float64`](@ref),
    `ComplexF32` or `ComplexF64`), then `F` is a [`QRCompactWY`](@ref) object,
@@ -340,7 +343,7 @@ and `F.Q*A` are supported. A `Q` matrix can be converted into a regular matrix w
 orthogonal matrix.
 
 The block size for QR decomposition can be specified by keyword argument
-`blocksize :: Integer` when `pivot == Val(false)` and `A isa StridedMatrix{<:BlasFloat}`.
+`blocksize :: Integer` when `pivot == NoPivot()` and `A isa StridedMatrix{<:BlasFloat}`.
 It is ignored when `blocksize > minimum(size(A))`.  See [`QRCompactWY`](@ref).
 
 !!! compat "Julia 1.4"
@@ -382,6 +385,10 @@ function qr(A::AbstractMatrix{T}, arg...; kwargs...) where T
     copyto!(AA, A)
     return qr!(AA, arg...; kwargs...)
 end
+# TODO: remove in Julia v2.0
+@deprecate qr(A::AbstractMatrix, ::Val{false}; kwargs...) qr(A, NoPivot(); kwargs...)
+@deprecate qr(A::AbstractMatrix, ::Val{true}; kwargs...)  qr(A, ColumnNorm(); kwargs...)
+
 qr(x::Number) = qr(fill(x,1,1))
 function qr(v::AbstractVector)
     require_one_based_indexing(v)

stdlib/LinearAlgebra/test/diagonal.jl

@@ -565,7 +565,7 @@ end
     D = Diagonal(randn(5))
     Q = qr(randn(5, 5)).Q
     @test D * Q' == Array(D) * Q'
-    Q = qr(randn(5, 5), Val(true)).Q
+    Q = qr(randn(5, 5), ColumnNorm()).Q
     @test_throws ArgumentError lmul!(Q, D)
 end
 

stdlib/LinearAlgebra/test/generic.jl

@@ -387,13 +387,13 @@ LinearAlgebra.Transpose(a::ModInt{n}) where {n} = transpose(a)
     A = [ModInt{2}(1) ModInt{2}(0); ModInt{2}(1) ModInt{2}(1)]
     b = [ModInt{2}(1), ModInt{2}(0)]
 
-    @test A*(lu(A, Val(false))\b) == b
+    @test A*(lu(A, NoPivot())\b) == b
 
     # Needed for pivoting:
     Base.abs(a::ModInt{n}) where {n} = a
     Base.:<(a::ModInt{n}, b::ModInt{n}) where {n} = a.k < b.k
 
-    @test A*(lu(A, Val(true))\b) == b
+    @test A*(lu(A, RowMaximum())\b) == b
 end
 
 @testset "Issue 18742" begin

stdlib/LinearAlgebra/test/lq.jl

@@ -40,7 +40,7 @@ rectangularQ(Q::LinearAlgebra.LQPackedQ) = convert(Array, Q)
                 lqa   = lq(a)
                 x = lqa\b
                 l,q   = lqa.L, lqa.Q
-                qra   = qr(a, Val(true))
+                qra   = qr(a, ColumnNorm())
                 @testset "Basic ops" begin
                     @test size(lqa,1) == size(a,1)
                     @test size(lqa,3) == 1

stdlib/LinearAlgebra/test/lu.jl

@@ -61,7 +61,7 @@ dimg  = randn(n)/2
         lua   = factorize(a)
         @test_throws ErrorException lua.Z
         l,u,p = lua.L, lua.U, lua.p
-        ll,ul,pl = lu(a)
+        ll,ul,pl = @inferred lu(a)
         @test ll * ul ≈ a[pl,:]
         @test l*u ≈ a[p,:]
         @test (l*u)[invperm(p),:] ≈ a
@@ -85,9 +85,9 @@ dimg  = randn(n)/2
     end
     κd    = cond(Array(d),1)
     @testset "Tridiagonal LU" begin
-        lud   = lu(d)
+        lud = @inferred lu(d)
         @test LinearAlgebra.issuccess(lud)
-        @test lu(lud) == lud
+        @test @inferred(lu(lud)) == lud
         @test_throws ErrorException lud.Z
         @test lud.L*lud.U ≈ lud.P*Array(d)
         @test lud.L*lud.U ≈ Array(d)[lud.p,:]
@@ -199,14 +199,14 @@ dimg  = randn(n)/2
             @test lua.L*lua.U ≈ lua.P*a[:,1:n1]
         end
         @testset "Fat LU" begin
-            lua   = lu(a[1:n1,:])
+            lua   = @inferred lu(a[1:n1,:])
             @test lua.L*lua.U ≈ lua.P*a[1:n1,:]
         end
     end
 
     @testset "LU of Symmetric/Hermitian" begin
         for HS in (Hermitian(a'a), Symmetric(a'a))
-            luhs = lu(HS)
+            luhs = @inferred lu(HS)
             @test luhs.L*luhs.U ≈ luhs.P*Matrix(HS)
         end
     end
@@ -229,12 +229,12 @@ end
     @test_throws SingularException lu!(copy(A); check = true)
     @test !issuccess(lu(A; check = false))
     @test !issuccess(lu!(copy(A); check = false))
-    @test_throws ZeroPivotException lu(A, Val(false))
-    @test_throws ZeroPivotException lu!(copy(A), Val(false))
-    @test_throws ZeroPivotException lu(A, Val(false); check = true)
-    @test_throws ZeroPivotException lu!(copy(A), Val(false); check = true)
-    @test !issuccess(lu(A, Val(false); check = false))
-    @test !issuccess(lu!(copy(A), Val(false); check = false))
+    @test_throws ZeroPivotException lu(A, NoPivot())
+    @test_throws ZeroPivotException lu!(copy(A), NoPivot())
+    @test_throws ZeroPivotException lu(A, NoPivot(); check = true)
+    @test_throws ZeroPivotException lu!(copy(A), NoPivot(); check = true)
+    @test !issuccess(lu(A, NoPivot(); check = false))
+    @test !issuccess(lu!(copy(A), NoPivot(); check = false))
     F = lu(A; check = false)
     @test sprint((io, x) -> show(io, "text/plain", x), F) ==
         "Failed factorization of type $(typeof(F))"
@@ -320,7 +320,7 @@ include("trickyarithmetic.jl")
 @testset "lu with type whose sum is another type" begin
     A = TrickyArithmetic.A[1 2; 3 4]
     ElT = TrickyArithmetic.D{TrickyArithmetic.C,TrickyArithmetic.C}
-    B = lu(A, Val(false))
+    B = lu(A, NoPivot())
     @test B isa LinearAlgebra.LU{ElT,Matrix{ElT}}
 end