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Generalize or restrict a few basic operators #44564

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May 13, 2022
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Generalize or restrict a few basic operators #44564

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a4fda09
Generalize or restrict a few basic operators
dkarrasch Mar 11, 2022
3a23288
fix one int test
dkarrasch Apr 12, 2022
841c83b
add NEWS entry
dkarrasch Apr 13, 2022
9d62ed8
Update NEWS.md
dkarrasch Apr 13, 2022
33d01af
Merge branch 'master' into dk/minus
dkarrasch May 6, 2022
63e66e4
Merge branch 'master' into dk/minus
dkarrasch May 9, 2022
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5 changes: 5 additions & 0 deletions NEWS.md
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Expand Up @@ -14,6 +14,11 @@ Language changes
* New builtins `getglobal(::Module, ::Symbol[, order])` and `setglobal!(::Module, ::Symbol, x[, order])`
for reading from and writing to globals. `getglobal` should now be preferred for accessing globals over
`getfield`. ([#44137])
* A few basic operators have been generalized to more naturally support vector space structures:
`+(x) = x`, unary minus falls back to scalar multiplication with -1, `-(x) = Int8(-1)*x`,
binary minus falls back to addition `-(x, y) = x + (-y)`, and, at the most generic level,
left- and right-division fall back to multiplication with the inverse from left and right,
resp., as stated in the docstring. ([#44564])
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Compiler/Runtime improvements
-----------------------------
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10 changes: 7 additions & 3 deletions base/operators.jl
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Expand Up @@ -525,8 +525,10 @@ julia> identity("Well, what did you expect?")
"""
identity(x) = x

+(x::Number) = x
*(x::Number) = x
+(x) = x
-(x) = Int8(-1)*x
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this seems possibly incorrect for many types (e.g. Unsigned), and less likely for promotion to be defined than negation

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This was the main requested feature in the related issue. This change causes a different error than the one previously expected in the int.jl tests.

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gotcha. As I replied above, I have no context for this change, so I am mostly the wrong person to ask.

-(x, y) = x + (-y)
*(x) = x
(&)(x::Integer) = x
(|)(x::Integer) = x
xor(x::Integer) = x
Expand Down Expand Up @@ -626,7 +628,9 @@ julia> inv(A) * x
-7.0
```
"""
\(x,y) = adjoint(adjoint(y)/adjoint(x))
\(x, y) = inv(x) * y

/(x, y) = x * inv(y)

# Core <<, >>, and >>> take either Int or UInt as second arg. Signed shift
# counts can shift in either direction, and are translated here to unsigned
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3 changes: 2 additions & 1 deletion stdlib/Dates/docs/src/index.md
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Expand Up @@ -206,7 +206,8 @@ ERROR: MethodError: no method matching *(::Date, ::Date)
[...]

julia> dt / dt2
ERROR: MethodError: no method matching /(::Date, ::Date)
ERROR: MethodError: no method matching inv(::Date)
[...]

julia> dt - dt2
4411 days
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2 changes: 2 additions & 0 deletions stdlib/LinearAlgebra/src/adjtrans.jl
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Expand Up @@ -318,6 +318,8 @@ pinv(v::TransposeAbsVec, tol::Real = 0) = pinv(conj(v.parent)).parent

## left-division \
\(u::AdjOrTransAbsVec, v::AdjOrTransAbsVec) = pinv(u) * v
\(u::AdjointAbsVec, y::Number) = adjoint(conj(y) / u.parent)
\(u::TransposeAbsVec, y::Number) = transpose(y / u.parent)


## right-division /
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22 changes: 13 additions & 9 deletions stdlib/LinearAlgebra/test/bidiag.jl
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Expand Up @@ -315,7 +315,7 @@ Random.seed!(1)
typediv=T.uplo == 'U' ? UpperTriangular : Matrix,
typediv2=T.uplo == 'U' ? UpperTriangular : Matrix)
TM = Matrix(T)
@test (T*x)::typemul ≈ TM*x #broken=eltype(x) <: Furlong
@test (T*x)::typemul ≈ TM*x #broken=eltype(x) <: Furlong
@test (x*T)::typemul ≈ x*TM #broken=eltype(x) <: Furlong
@test (x\T)::typediv ≈ x\TM #broken=eltype(T) <: Furlong
@test (T/x)::typediv ≈ TM/x #broken=eltype(T) <: Furlong
Expand All @@ -325,20 +325,24 @@ Random.seed!(1)
end
return nothing
end
A = randn(n,n)
d = randn(n)
dl = randn(n-1)
t = T
for t in (T, #=Furlong.(T)=#), (A, d, dl) in ((A, d, dl), #=(Furlong.(A), Furlong.(d), Furlong.(dl))=#)
if relty <: Integer
A = convert(Matrix{elty}, rand(1:10, n, n))
if (elty <: Complex)
A += im*convert(Matrix{elty}, rand(1:10, n, n))
end
else
A = rand(elty, n, n)
end
for t in (T, #=Furlong.(T)=#), (A, dv, ev) in ((A, dv, ev), #=(Furlong.(A), Furlong.(dv), Furlong.(ev))=#)
_bidiagdivmultest(t, 5, Bidiagonal, Bidiagonal)
_bidiagdivmultest(t, 5I, Bidiagonal, Bidiagonal, t.uplo == 'U' ? UpperTriangular : LowerTriangular)
_bidiagdivmultest(t, Diagonal(d), Bidiagonal, Bidiagonal, t.uplo == 'U' ? UpperTriangular : LowerTriangular)
_bidiagdivmultest(t, Diagonal(dv), Bidiagonal, Bidiagonal, t.uplo == 'U' ? UpperTriangular : LowerTriangular)
_bidiagdivmultest(t, UpperTriangular(A))
_bidiagdivmultest(t, UnitUpperTriangular(A))
_bidiagdivmultest(t, LowerTriangular(A), t.uplo == 'L' ? LowerTriangular : Matrix, t.uplo == 'L' ? LowerTriangular : Matrix, t.uplo == 'L' ? LowerTriangular : Matrix)
_bidiagdivmultest(t, UnitLowerTriangular(A), t.uplo == 'L' ? LowerTriangular : Matrix, t.uplo == 'L' ? LowerTriangular : Matrix, t.uplo == 'L' ? LowerTriangular : Matrix)
_bidiagdivmultest(t, Bidiagonal(d, dl, :U), Matrix, Matrix, Matrix)
_bidiagdivmultest(t, Bidiagonal(d, dl, :L), Matrix, Matrix, Matrix)
_bidiagdivmultest(t, Bidiagonal(dv, ev, :U), Matrix, Matrix, Matrix)
_bidiagdivmultest(t, Bidiagonal(dv, ev, :L), Matrix, Matrix, Matrix)
end
end
end
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2 changes: 1 addition & 1 deletion stdlib/LinearAlgebra/test/dense.jl
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Expand Up @@ -25,7 +25,7 @@ Random.seed!(1234323)
ainv = inv(a)
@test cond(a, 1) == opnorm(a, 1) *opnorm(ainv, 1)
@test cond(a, Inf) == opnorm(a, Inf)*opnorm(ainv, Inf)
@test cond(a[:, 1:5]) == (\)(extrema(svdvals(a[:, 1:5]))...)
@test cond(a[:, 1:5]) == (/)(reverse(extrema(svdvals(a[:, 1:5])))...)
@test_throws ArgumentError cond(a,3)
end
end
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14 changes: 7 additions & 7 deletions stdlib/LinearAlgebra/test/diagonal.jl
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Expand Up @@ -784,8 +784,8 @@ end
U = UpperTriangular(randn(elty, K, K))
L = LowerTriangular(randn(elty, K, K))
D = Diagonal(randn(elty, K))
@test (U / D)::UpperTriangular{elty} == UpperTriangular(Matrix(U) / Matrix(D))
@test (L / D)::LowerTriangular{elty} == LowerTriangular(Matrix(L) / Matrix(D))
@test (U / D)::UpperTriangular{elty} ≈ UpperTriangular(Matrix(U) / Matrix(D)) rtol=2eps(real(elty))
@test (L / D)::LowerTriangular{elty} ≈ LowerTriangular(Matrix(L) / Matrix(D)) rtol=2eps(real(elty))
@test (D \ U)::UpperTriangular{elty} == UpperTriangular(Matrix(D) \ Matrix(U))
@test (D \ L)::LowerTriangular{elty} == LowerTriangular(Matrix(D) \ Matrix(L))
end
Expand All @@ -799,8 +799,8 @@ end
D0 = Diagonal(zeros(elty, K))
@test (D \ S)::Tridiagonal{elty} == Tridiagonal(Matrix(D) \ Matrix(S))
@test (D \ T)::Tridiagonal{elty} == Tridiagonal(Matrix(D) \ Matrix(T))
@test (S / D)::Tridiagonal{elty} == Tridiagonal(Matrix(S) / Matrix(D))
@test (T / D)::Tridiagonal{elty} == Tridiagonal(Matrix(T) / Matrix(D))
@test (S / D)::Tridiagonal{elty} ≈ Tridiagonal(Matrix(S) / Matrix(D)) rtol=2eps(real(elty))
@test (T / D)::Tridiagonal{elty} ≈ Tridiagonal(Matrix(T) / Matrix(D)) rtol=2eps(real(elty))
@test_throws SingularException D0 \ S
@test_throws SingularException D0 \ T
@test_throws SingularException S / D0
Expand Down Expand Up @@ -844,8 +844,8 @@ end
D = Diagonal(rand(1:20, K))
@test (D \ S)::Tridiagonal{Float64} == Tridiagonal(Matrix(D) \ Matrix(S))
@test (D \ T)::Tridiagonal{Float64} == Tridiagonal(Matrix(D) \ Matrix(T))
@test (S / D)::Tridiagonal{Float64} == Tridiagonal(Matrix(S) / Matrix(D))
@test (T / D)::Tridiagonal{Float64} == Tridiagonal(Matrix(T) / Matrix(D))
@test (S / D)::Tridiagonal{Float64} ≈ Tridiagonal(Matrix(S) / Matrix(D)) rtol=2eps()
@test (T / D)::Tridiagonal{Float64} ≈ Tridiagonal(Matrix(T) / Matrix(D)) rtol=2eps()
end

@testset "eigenvalue sorting" begin
Expand Down Expand Up @@ -953,7 +953,7 @@ end
@testset "divisions functionality" for elty in (Int, Float64, ComplexF64)
B = Diagonal(rand(elty,5,5))
x = rand(elty)
@test \(x, B) == /(B, x)
@test \(x, B) ≈ /(B, x) rtol=2eps()
end

@testset "promotion" begin
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9 changes: 2 additions & 7 deletions stdlib/LinearAlgebra/test/generic.jl
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Expand Up @@ -155,8 +155,8 @@ end

@testset "Scaling with rdiv! and ldiv!" begin
@test rdiv!(copy(a), 5.) == a/5
@test ldiv!(5., copy(a)) == a/5
@test ldiv!(zero(a), 5., copy(a)) == a/5
@test ldiv!(5., copy(a)) == 5\a
@test ldiv!(zero(a), 5., copy(a)) == 5\a
end

@testset "Scaling with 3-argument mul!" begin
Expand Down Expand Up @@ -434,17 +434,12 @@ Base.:-(a::ModInt{n}, b::ModInt{n}) where {n} = ModInt{n}(a.k - b.k)
Base.:*(a::ModInt{n}, b::ModInt{n}) where {n} = ModInt{n}(a.k * b.k)
Base.:-(a::ModInt{n}) where {n} = ModInt{n}(-a.k)
Base.inv(a::ModInt{n}) where {n} = ModInt{n}(invmod(a.k, n))
Base.:/(a::ModInt{n}, b::ModInt{n}) where {n} = a*inv(b)

Base.zero(::Type{ModInt{n}}) where {n} = ModInt{n}(0)
Base.zero(::ModInt{n}) where {n} = ModInt{n}(0)
Base.one(::Type{ModInt{n}}) where {n} = ModInt{n}(1)
Base.one(::ModInt{n}) where {n} = ModInt{n}(1)
Base.conj(a::ModInt{n}) where {n} = a
Base.adjoint(a::ModInt{n}) where {n} = ModInt{n}(conj(a))
Base.transpose(a::ModInt{n}) where {n} = a # see Issue 20978
LinearAlgebra.Adjoint(a::ModInt{n}) where {n} = adjoint(a)
LinearAlgebra.Transpose(a::ModInt{n}) where {n} = transpose(a)

@testset "Issue 22042" begin
A = [ModInt{2}(1) ModInt{2}(0); ModInt{2}(1) ModInt{2}(1)]
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4 changes: 2 additions & 2 deletions test/errorshow.jl
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Expand Up @@ -398,8 +398,8 @@ let err_str
@test occursin("MethodError: no method matching +(::$Int, ::Vector{Float64})", err_str)
@test occursin("For element-wise addition, use broadcasting with dot syntax: scalar .+ array", err_str)
err_str = @except_str rand(5) - 1//3 MethodError
@test occursin("MethodError: no method matching -(::Vector{Float64}, ::Rational{$Int})", err_str)
@test occursin("For element-wise subtraction, use broadcasting with dot syntax: array .- scalar", err_str)
@test occursin("MethodError: no method matching +(::Vector{Float64}, ::Rational{$Int})", err_str)
@test occursin("For element-wise addition, use broadcasting with dot syntax: array .+ scalar", err_str)
end


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2 changes: 1 addition & 1 deletion test/int.jl
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Expand Up @@ -123,7 +123,7 @@ end
@test mod(123, UInt8) === 0x7b

primitive type MyBitsType <: Signed 8 end
@test_throws MethodError ~reinterpret(MyBitsType, 0x7b)
@test_throws ErrorException ~reinterpret(MyBitsType, 0x7b)
@test signed(MyBitsType) === MyBitsType

UItypes = Base.BitUnsigned_types
Expand Down