Replace Val-types in cholesky[!] (JuliaLang#41640)

NEWS.md

@@ -92,6 +92,10 @@ Standard library changes
 #### LinearAlgebra
 * The BLAS submodule now supports the level-2 BLAS subroutine `spr!` ([#42830]).
 
+* `cholesky[!]` now supports `LinearAlgebra.PivotingStrategy` (singleton type) values
+  as its optional `pivot` argument: the default is `cholesky(A, NoPivot())` (vs.
+  `cholesky(A, RowMaximum())`); the former `Val{true/false}`-based calls are deprecated. ([#41640])
+
 #### Markdown
 
 #### Printf

stdlib/LinearAlgebra/src/cholesky.jl

@@ -10,10 +10,10 @@
 # In the methods below, LAPACK is called when possible, i.e. StridedMatrices with Float32,
 # Float64, ComplexF32, and ComplexF64 element types. For other element or
 # matrix types, the unblocked Julia implementation in _chol! is used. For cholesky
-# and cholesky! pivoting is supported through a Val(Bool) argument. A type argument is
+# and cholesky! pivoting is supported through a RowMaximum() argument. A type argument is
 # necessary for type stability since the output of cholesky and cholesky! is either
 # Cholesky or CholeskyPivoted. The latter is only
-# supported for the four LAPACK element types. For other types, e.g. BigFloats Val(true) will
+# supported for the four LAPACK element types. For other types, e.g. BigFloats RowMaximum() will
 # give an error. It is required that the input is Hermitian (including real symmetric) either
 # through the Hermitian and Symmetric views or exact symmetric or Hermitian elements which
 # is checked for and an error is thrown if the check fails.
@@ -106,7 +106,7 @@ Base.iterate(C::Cholesky, ::Val{:done}) = nothing
     CholeskyPivoted
 
 Matrix factorization type of the pivoted Cholesky factorization of a dense symmetric/Hermitian
-positive semi-definite matrix `A`. This is the return type of [`cholesky(_, Val(true))`](@ref),
+positive semi-definite matrix `A`. This is the return type of [`cholesky(_, ::RowMaximum)`](@ref),
 the corresponding matrix factorization function.
 
 The triangular Cholesky factor can be obtained from the factorization `F::CholeskyPivoted`
@@ -126,7 +126,7 @@ julia> X = [1.0, 2.0, 3.0, 4.0];
 
 julia> A = X * X';
 
-julia> C = cholesky(A, Val(true), check = false)
+julia> C = cholesky(A, RowMaximum(), check = false)
 CholeskyPivoted{Float64, Matrix{Float64}}
 U factor with rank 1:
 4×4 UpperTriangular{Float64, Matrix{Float64}}:
@@ -261,15 +261,15 @@ end
 # cholesky!. Destructive methods for computing Cholesky factorization of real symmetric
 # or Hermitian matrix
 ## No pivoting (default)
-function cholesky!(A::RealHermSymComplexHerm, ::Val{false}=Val(false); check::Bool = true)
+function cholesky!(A::RealHermSymComplexHerm, ::NoPivot = NoPivot(); check::Bool = true)
     C, info = _chol!(A.data, A.uplo == 'U' ? UpperTriangular : LowerTriangular)
     check && checkpositivedefinite(info)
     return Cholesky(C.data, A.uplo, info)
 end
 
 ### for StridedMatrices, check that matrix is symmetric/Hermitian
 """
-    cholesky!(A::StridedMatrix, Val(false); check = true) -> Cholesky
+    cholesky!(A::StridedMatrix, NoPivot(); check = true) -> Cholesky
 
 The same as [`cholesky`](@ref), but saves space by overwriting the input `A`,
 instead of creating a copy. An [`InexactError`](@ref) exception is thrown if
@@ -289,57 +289,62 @@ Stacktrace:
 [...]
 ```
 """
-function cholesky!(A::StridedMatrix, ::Val{false}=Val(false); check::Bool = true)
+function cholesky!(A::StridedMatrix, ::NoPivot = NoPivot(); check::Bool = true)
     checksquare(A)
     if !ishermitian(A) # return with info = -1 if not Hermitian
         check && checkpositivedefinite(-1)
         return Cholesky(A, 'U', convert(BlasInt, -1))
     else
-        return cholesky!(Hermitian(A), Val(false); check = check)
+        return cholesky!(Hermitian(A), NoPivot(); check = check)
     end
 end
+@deprecate cholesky!(A::StridedMatrix, ::Val{false}; check::Bool = true) cholesky!(A, NoPivot(); check) false
+@deprecate cholesky!(A::RealHermSymComplexHerm, ::Val{false}; check::Bool = true) cholesky!(A, NoPivot(); check) false
 
 ## With pivoting
 ### BLAS/LAPACK element types
 function cholesky!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix},
-                   ::Val{true}; tol = 0.0, check::Bool = true)
+                   ::RowMaximum; tol = 0.0, check::Bool = true)
     AA, piv, rank, info = LAPACK.pstrf!(A.uplo, A.data, tol)
     C = CholeskyPivoted{eltype(AA),typeof(AA)}(AA, A.uplo, piv, rank, tol, info)
     check && chkfullrank(C)
     return C
 end
+@deprecate cholesky!(A::RealHermSymComplexHerm{<:BlasReal,<:StridedMatrix}, ::Val{true}; kwargs...) cholesky!(A, RowMaximum(); kwargs...) false
 
 ### Non BLAS/LAPACK element types (generic). Since generic fallback for pivoted Cholesky
 ### is not implemented yet we throw an error
-cholesky!(A::RealHermSymComplexHerm{<:Real}, ::Val{true}; tol = 0.0, check::Bool = true) =
+cholesky!(A::RealHermSymComplexHerm{<:Real}, ::RowMaximum; tol = 0.0, check::Bool = true) =
     throw(ArgumentError("generic pivoted Cholesky factorization is not implemented yet"))
+@deprecate cholesky!(A::RealHermSymComplexHerm{<:Real}, ::Val{true}; kwargs...) cholesky!(A, RowMaximum(); kwargs...) false
 
 ### for StridedMatrices, check that matrix is symmetric/Hermitian
 """
-    cholesky!(A::StridedMatrix, Val(true); tol = 0.0, check = true) -> CholeskyPivoted
+    cholesky!(A::StridedMatrix, RowMaximum(); tol = 0.0, check = true) -> CholeskyPivoted
 
 The same as [`cholesky`](@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.
 """
-function cholesky!(A::StridedMatrix, ::Val{true}; tol = 0.0, check::Bool = true)
+function cholesky!(A::StridedMatrix, ::RowMaximum; tol = 0.0, check::Bool = true)
     checksquare(A)
     if !ishermitian(A)
         C = CholeskyPivoted(A, 'U', Vector{BlasInt}(),convert(BlasInt, 1),
                             tol, convert(BlasInt, -1))
         check && chkfullrank(C)
         return C
     else
-        return cholesky!(Hermitian(A), Val(true); tol = tol, check = check)
+        return cholesky!(Hermitian(A), RowMaximum(); tol = tol, check = check)
     end
 end
+@deprecate cholesky!(A::StridedMatrix, ::Val{true}; kwargs...) cholesky!(A, RowMaximum(); kwargs...) false
 
 # cholesky. Non-destructive methods for computing Cholesky factorization of real symmetric
 # or Hermitian matrix
 ## No pivoting (default)
 """
-    cholesky(A, Val(false); check = true) -> Cholesky
+    cholesky(A, NoPivot(); check = true) -> Cholesky
 
 Compute the Cholesky factorization of a dense symmetric positive definite matrix `A`
 and return a [`Cholesky`](@ref) factorization. The matrix `A` can either be a [`Symmetric`](@ref) or [`Hermitian`](@ref)
@@ -391,17 +396,18 @@ true
 ```
 """
 cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}},
-    ::Val{false}=Val(false); check::Bool = true) = cholesky!(cholcopy(A); check = check)
+    ::NoPivot=NoPivot(); check::Bool = true) = cholesky!(cholcopy(A); check = check)
+@deprecate cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}}, ::Val{false}; check::Bool = true) cholesky(A, NoPivot(); check) false
 
-function cholesky(A::Union{StridedMatrix{Float16},RealHermSymComplexHerm{Float16,<:StridedMatrix}}, ::Val{false}=Val(false); check::Bool = true)
+function cholesky(A::Union{StridedMatrix{Float16},RealHermSymComplexHerm{Float16,<:StridedMatrix}}, ::NoPivot=NoPivot(); check::Bool = true)
     X = cholesky!(cholcopy(A); check = check)
     return Cholesky{Float16}(X)
 end
-
+@deprecate cholesky(A::Union{StridedMatrix{Float16},RealHermSymComplexHerm{Float16,<:StridedMatrix}}, ::Val{false}; check::Bool = true) cholesky(A, NoPivot(); check) false
 
 ## With pivoting
 """
-    cholesky(A, Val(true); tol = 0.0, check = true) -> CholeskyPivoted
+    cholesky(A, RowMaximum(); tol = 0.0, check = true) -> CholeskyPivoted
 
 Compute the pivoted Cholesky factorization of a dense symmetric positive semi-definite matrix `A`
 and return a [`CholeskyPivoted`](@ref) factorization. The matrix `A` can either be a [`Symmetric`](@ref)
@@ -431,7 +437,7 @@ julia> X = [1.0, 2.0, 3.0, 4.0];
 
 julia> A = X * X';
 
-julia> C = cholesky(A, Val(true), check = false)
+julia> C = cholesky(A, RowMaximum(), check = false)
 CholeskyPivoted{Float64, Matrix{Float64}}
 U factor with rank 1:
 4×4 UpperTriangular{Float64, Matrix{Float64}}:
@@ -456,8 +462,9 @@ true
 ```
 """
 cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}},
-    ::Val{true}; tol = 0.0, check::Bool = true) =
-    cholesky!(cholcopy(A), Val(true); tol = tol, check = check)
+    ::RowMaximum; tol = 0.0, check::Bool = true) =
+    cholesky!(cholcopy(A), RowMaximum(); tol = tol, check = check)
+@deprecate cholesky(A::Union{StridedMatrix,RealHermSymComplexHerm{<:Real,<:StridedMatrix}}, ::Val{true}; tol = 0.0, check::Bool = true) cholesky(A, RowMaximum(); tol, check) false
 
 ## Number
 function cholesky(x::Number, uplo::Symbol=:U)

stdlib/LinearAlgebra/src/diagonal.jl

@@ -715,7 +715,7 @@ function _mapreduce_prod(f, x, D::Diagonal, y)
     end
 end
 
-function cholesky!(A::Diagonal, ::Val{false} = Val(false); check::Bool = true)
+function cholesky!(A::Diagonal, ::NoPivot = NoPivot(); check::Bool = true)
     info = 0
     for (i, di) in enumerate(A.diag)
         if isreal(di) && real(di) > 0
@@ -729,9 +729,11 @@ function cholesky!(A::Diagonal, ::Val{false} = Val(false); check::Bool = true)
     end
     Cholesky(A, 'U', convert(BlasInt, info))
 end
+@deprecate cholesky!(A::Diagonal, ::Val{false}; check::Bool = true) cholesky!(A::Diagonal, NoPivot(); check) false
 
-cholesky(A::Diagonal, ::Val{false} = Val(false); check::Bool = true) =
-    cholesky!(cholcopy(A), Val(false); check = check)
+cholesky(A::Diagonal, ::NoPivot = NoPivot(); check::Bool = true) =
+    cholesky!(cholcopy(A), NoPivot(); check = check)
+@deprecate cholesky(A::Diagonal, ::Val{false}; check::Bool = true) cholesky(A::Diagonal, NoPivot(); check) false
 
 function getproperty(C::Cholesky{<:Any,<:Diagonal}, d::Symbol)
     Cfactors = getfield(C, :factors)

stdlib/LinearAlgebra/test/cholesky.jl

@@ -136,7 +136,7 @@ end
 
         #pivoted upper Cholesky
         if eltya != BigFloat
-            cpapd = cholesky(apdh, Val(true))
+            cpapd = cholesky(apdh, RowMaximum())
             unary_ops_tests(apdh, cpapd, ε*κ*n)
             @test rank(cpapd) == n
             @test all(diff(diag(real(cpapd.factors))).<=0.) # diagonal should be non-increasing
@@ -167,11 +167,11 @@ end
 
                 if eltya != BigFloat && eltyb != BigFloat # Note! Need to implement pivoted Cholesky decomposition in julia
 
-                    cpapd = cholesky(apdh, Val(true))
+                    cpapd = cholesky(apdh, RowMaximum())
                     @test norm(apd * (cpapd\b) - b)/norm(b) <= ε*κ*n # Ad hoc, revisit
                     @test norm(apd * (cpapd\b[1:n]) - b[1:n])/norm(b[1:n]) <= ε*κ*n
 
-                    lpapd = cholesky(apdhL, Val(true))
+                    lpapd = cholesky(apdhL, RowMaximum())
                     @test norm(apd * (lpapd\b) - b)/norm(b) <= ε*κ*n # Ad hoc, revisit
                     @test norm(apd * (lpapd\b[1:n]) - b[1:n])/norm(b[1:n]) <= ε*κ*n
                 end
@@ -194,7 +194,7 @@ end
                 @test norm(apd \ B - BB, 1) / norm(BB, 1) <= (3n^2 + n + n^3*ε)*ε/(1-(n+1)*ε)*κ
                 @test norm(apd * BB - B, 1) / norm(B, 1) <= (3n^2 + n + n^3*ε)*ε/(1-(n+1)*ε)*κ
                 if eltya != BigFloat
-                    cpapd = cholesky(apdh, Val(true))
+                    cpapd = cholesky(apdh, RowMaximum())
                     BB = copy(B)
                     ldiv!(cpapd, BB)
                     @test norm(apd \ B - BB, 1) / norm(BB, 1) <= (3n^2 + n + n^3*ε)*ε/(1-(n+1)*ε)*κ
@@ -225,12 +225,12 @@ end
                 @test norm(B / apd - BB, 1) / norm(BB, 1) <= (3n^2 + n + n^3*ε)*ε/(1-(n+1)*ε)*κ
                 @test norm(BB * apd - B, 1) / norm(B, 1) <= (3n^2 + n + n^3*ε)*ε/(1-(n+1)*ε)*κ
                 if eltya != BigFloat
-                    cpapd = cholesky(eltya <: Complex ? apdh : apds, Val(true))
+                    cpapd = cholesky(eltya <: Complex ? apdh : apds, RowMaximum())
                     BB = copy(B)
                     rdiv!(BB, cpapd)
                     @test norm(B / apd - BB, 1) / norm(BB, 1) <= (3n^2 + n + n^3*ε)*ε/(1-(n+1)*ε)*κ
                     @test norm(BB * apd - B, 1) / norm(B, 1) <= (3n^2 + n + n^3*ε)*ε/(1-(n+1)*ε)*κ
-                    cpapd = cholesky(eltya <: Complex ? apdhL : apdsL, Val(true))
+                    cpapd = cholesky(eltya <: Complex ? apdhL : apdsL, RowMaximum())
                     BB = copy(B)
                     rdiv!(BB, cpapd)
                     @test norm(B / apd - BB, 1) / norm(BB, 1) <= (3n^2 + n + n^3*ε)*ε/(1-(n+1)*ε)*κ
@@ -266,15 +266,15 @@ end
         @test !LinearAlgebra.issuccess(cholesky!(copy(M); check = false))
     end
     for M in (A, Hermitian(A), B)
-        @test_throws RankDeficientException cholesky(M, Val(true))
-        @test_throws RankDeficientException cholesky!(copy(M), Val(true))
-        @test_throws RankDeficientException cholesky(M, Val(true); check = true)
-        @test_throws RankDeficientException cholesky!(copy(M), Val(true); check = true)
-        @test !LinearAlgebra.issuccess(cholesky(M, Val(true); check = false))
-        @test !LinearAlgebra.issuccess(cholesky!(copy(M), Val(true); check = false))
-        C = cholesky(M, Val(true); check = false)
+        @test_throws RankDeficientException cholesky(M, RowMaximum())
+        @test_throws RankDeficientException cholesky!(copy(M), RowMaximum())
+        @test_throws RankDeficientException cholesky(M, RowMaximum(); check = true)
+        @test_throws RankDeficientException cholesky!(copy(M), RowMaximum(); check = true)
+        @test !LinearAlgebra.issuccess(cholesky(M, RowMaximum(); check = false))
+        @test !LinearAlgebra.issuccess(cholesky!(copy(M), RowMaximum(); check = false))
+        C = cholesky(M, RowMaximum(); check = false)
         @test_throws RankDeficientException chkfullrank(C)
-        C = cholesky!(copy(M), Val(true); check = false)
+        C = cholesky!(copy(M), RowMaximum(); check = false)
         @test_throws RankDeficientException chkfullrank(C)
     end
     @test !isposdef(A)
@@ -339,7 +339,7 @@ end
         0.25336108035924787 + 0.975317836492159im 0.0628393808469436 - 0.1253397353973715im
         0.11192755545114 - 0.1603741874112385im 0.8439562576196216 + 1.0850814110398734im
         -1.0568488936791578 - 0.06025820467086475im 0.12696236014017806 - 0.09853584666755086im]
-    cholesky(Hermitian(apd, :L), Val(true)) \ b
+    cholesky(Hermitian(apd, :L), RowMaximum()) \ b
     r = factorize(apd).U
     E = abs.(apd - r'*r)
     ε = eps(abs(float(one(ComplexF32))))
@@ -350,7 +350,7 @@ end
 end
 
 @testset "fail for non-BLAS element types" begin
-    @test_throws ArgumentError cholesky!(Hermitian(rand(Float16, 5,5)), Val(true))
+    @test_throws ArgumentError cholesky!(Hermitian(rand(Float16, 5,5)), RowMaximum())
 end
 
 @testset "cholesky Diagonal" begin
@@ -398,7 +398,7 @@ end
     @test Cholesky(factors, uplo, Int32(info)) == chol
     @test Cholesky(factors, uplo, Int64(info)) == chol
 
-    cholp = cholesky(x'x, Val(true))
+    cholp = cholesky(x'x, RowMaximum())
 
     factors, uplo, piv, rank, tol, info =
         cholp.factors, cholp.uplo, cholp.piv, cholp.rank, cholp.tol, cholp.info
@@ -417,25 +417,25 @@ end
 @testset "issue #33704, casting low-rank CholeskyPivoted to Matrix" begin
     A = randn(1,8)
     B = A'A
-    C = cholesky(B, Val(true), check=false)
+    C = cholesky(B, RowMaximum(), check=false)
     @test B ≈ Matrix(C)
 end
 
 @testset "CholeskyPivoted and Factorization" begin
     A = randn(8,8)
     B = A'A
-    C = cholesky(B, Val(true), check=false)
+    C = cholesky(B, RowMaximum(), check=false)
     @test CholeskyPivoted{eltype(C)}(C) === C
     @test Factorization{eltype(C)}(C) === C
-    @test Array(CholeskyPivoted{complex(eltype(C))}(C)) ≈ Array(cholesky(complex(B), Val(true), check=false))
-    @test Array(Factorization{complex(eltype(C))}(C)) ≈ Array(cholesky(complex(B), Val(true), check=false))
+    @test Array(CholeskyPivoted{complex(eltype(C))}(C)) ≈ Array(cholesky(complex(B), RowMaximum(), check=false))
+    @test Array(Factorization{complex(eltype(C))}(C)) ≈ Array(cholesky(complex(B), RowMaximum(), check=false))
     @test eltype(Factorization{complex(eltype(C))}(C)) == complex(eltype(C))
 end
 
 @testset "REPL printing of CholeskyPivoted" begin
     A = randn(8,8)
     B = A'A
-    C = cholesky(B, Val(true), check=false)
+    C = cholesky(B, RowMaximum(), check=false)
     cholstring = sprint((t, s) -> show(t, "text/plain", s), C)
     rankstring = "$(C.uplo) factor with rank $(rank(C)):"
     factorstring = sprint((t, s) -> show(t, "text/plain", s), C.uplo == 'U' ? C.U : C.L)
@@ -444,10 +444,10 @@ end
 end
 
 @testset "destructuring for Cholesky[Pivoted]" begin
-    for val in (true, false)
+    for val in (NoPivot(), RowMaximum())
         A = rand(8, 8)
         B = A'A
-        C = cholesky(B, Val(val), check=false)
+        C = cholesky(B, val, check=false)
         l, u = C
         @test l == C.L
         @test u == C.U
@@ -507,7 +507,7 @@ end
          2048 1920 2940 1008 2240 2740;
          4470 4200 6410 2240 4875 6015;
          5490 5140 7903 2740 6015 7370]
-    B = cholesky(A, Val(true), check=false)
+    B = cholesky(A, RowMaximum(), check=false)
     @test det(B)  ==  0.0
     @test det(B)  ≈  det(A) atol=eps()
     @test logdet(B)  ==  -Inf

stdlib/LinearAlgebra/test/factorization.jl

@@ -6,7 +6,7 @@ using Test, LinearAlgebra
 @testset "equality for factorizations - $f" for f in Any[
     bunchkaufman,
     cholesky,
-    x -> cholesky(x, Val(true)),
+    x -> cholesky(x, RowMaximum()),
     eigen,
     hessenberg,
     lq,
@@ -45,7 +45,7 @@ end
 @testset "size for factorizations - $f" for f in Any[
     bunchkaufman,
     cholesky,
-    x -> cholesky(x, Val(true)),
+    x -> cholesky(x, RowMaximum()),
     hessenberg,
     lq,
     lu,