Deprecate scale. Fixes #12945.

NEWS.md

@@ -128,6 +128,8 @@ Deprecated or removed
 
   * `issym` is deprecated in favor of `issymmetric` to match similar functions (`ishermitian`, ...) ([#15192])
 
+  * `scale` is deprecated in favor of either `α*A`, `Diagonal(x)*A`, or `A*Diagonal(x)`. ([#15258])
+
 Julia v0.4.0 Release Notes
 ==========================
 

base/deprecated.jl

@@ -993,3 +993,9 @@ export call
 
 # Changed issym to issymmetric. #15192
 @deprecate issym issymmetric
+
+# 15258
+@deprecate scale(α::Number, A::AbstractArray) α*A
+@deprecate scale(A::AbstractArray, α::Number) A*α
+@deprecate scale(A::AbstractMatrix, x::AbstractVector) A*Diagonal(x)
+@deprecate scale(x::AbstractVector, A::AbstractMatrix) Diagonal(x)*A

base/docs/helpdb/Base.jl

@@ -4382,20 +4382,6 @@ i-th dimension of `A` should be repeated.
 """
 repeat
 
-"""
-    scale(A, b)
-    scale(b, A)
-
-Scale an array `A` by a scalar `b`, returning a new array.
-
-If `A` is a matrix and `b` is a vector, then `scale(A,b)` scales each column `i` of `A` by
-`b[i]` (similar to `A*diagm(b)`), while `scale(b,A)` scales each row `i` of `A` by `b[i]`
-(similar to `diagm(b)*A`), returning a new array.
-
-Note: for large `A`, `scale` can be much faster than `A .* b` or `b .* A`, due to the use of BLAS.
-"""
-scale
-
 """
     ReentrantLock()
 
@@ -6680,12 +6666,11 @@ issetuid
     scale!(A, b)
     scale!(b, A)
 
-Scale an array `A` by a scalar `b`, similar to [`scale`](:func:`scale`) but overwriting `A`
-in-place.
+Scale an array `A` by a scalar `b` overwriting `A` in-place.
 
 If `A` is a matrix and `b` is a vector, then `scale!(A,b)` scales each column `i` of `A` by
-`b[i]` (similar to `A*diagm(b)`), while `scale!(b,A)` scales each row `i` of `A` by `b[i]`
-(similar to `diagm(b)*A`), again operating in-place on `A`.
+`b[i]` (similar to `A*Diagonal(b)`), while `scale!(b,A)` scales each row `i` of `A` by `b[i]`
+(similar to `Diagonal(b)*A`), again operating in-place on `A`.
 
 """
 scale!

base/linalg.jl

@@ -111,7 +111,6 @@ export
     lqfact!,
     lqfact,
     rank,
-    scale,
     scale!,
     schur,
     schurfact!,

base/linalg/dense.jl

@@ -179,7 +179,7 @@ function ^(A::Matrix, p::Number)
     v, X = eig(A)
     any(v.<0) && (v = complex(v))
     Xinv = ishermitian(A) ? X' : inv(X)
-    scale(X, v.^p)*Xinv
+    (X * Diagonal(v.^p)) * Xinv
 end
 
 # Matrix exponential
@@ -483,7 +483,7 @@ function pinv{T}(A::StridedMatrix{T}, tol::Real)
     index       = SVD.S .> tol*maximum(SVD.S)
     Sinv[index] = one(Stype) ./ SVD.S[index]
     Sinv[find(!isfinite(Sinv))] = zero(Stype)
-    return SVD.Vt'scale(Sinv, SVD.U')
+    return SVD.Vt' * (Diagonal(Sinv) * SVD.U')
 end
 function pinv{T}(A::StridedMatrix{T})
     tol = eps(real(float(one(T))))*maximum(size(A))

base/linalg/diagonal.jl

@@ -106,8 +106,10 @@ end
 /{T<:Number}(D::Diagonal, x::T) = Diagonal(D.diag / x)
 *(Da::Diagonal, Db::Diagonal) = Diagonal(Da.diag .* Db.diag)
 *(D::Diagonal, V::AbstractVector) = D.diag .* V
-*(A::AbstractMatrix, D::Diagonal) = scale(A,D.diag)
-*(D::Diagonal, A::AbstractMatrix) = scale(D.diag,A)
+*(A::AbstractMatrix, D::Diagonal) =
+    scale!(similar(A, promote_op(MulFun(), eltype(A), eltype(D.diag))), A, D.diag)
+*(D::Diagonal, A::AbstractMatrix) =
+    scale!(similar(A, promote_op(MulFun(), eltype(A), eltype(D.diag))), D.diag, A)
 
 A_mul_B!(A::Diagonal,B::AbstractMatrix) = scale!(A.diag,B)
 At_mul_B!(A::Diagonal,B::AbstractMatrix)= scale!(A.diag,B)
@@ -181,8 +183,8 @@ function A_ldiv_B!(D::Diagonal, B::StridedVecOrMat)
     end
     return B
 end
-(\)(D::Diagonal, B::AbstractMatrix) = scale(1 ./ D.diag, B)
-(\)(D::Diagonal, b::AbstractVector) = reshape(scale(1 ./ D.diag, reshape(b, length(b), 1)), length(b))
+(\)(D::Diagonal, A::AbstractMatrix) = D.diag .\ A
+(\)(D::Diagonal, b::AbstractVector) = D.diag .\ b
 (\)(Da::Diagonal, Db::Diagonal) = Diagonal(Db.diag ./ Da.diag)
 
 function inv{T}(D::Diagonal{T})

base/linalg/generic.jl

@@ -2,9 +2,6 @@
 
 ## linalg.jl: Some generic Linear Algebra definitions
 
-scale(X::AbstractArray, s::Number) = X*s
-scale(s::Number, X::AbstractArray) = s*X
-
 # For better performance when input and output are the same array
 # See https://github.com/JuliaLang/julia/issues/8415#issuecomment-56608729
 function generic_scale!(X::AbstractArray, s::Number)

base/linalg/matmul.jl

@@ -38,8 +38,6 @@ function scale!(C::AbstractMatrix, b::AbstractVector, A::AbstractMatrix)
     end
     C
 end
-scale(A::AbstractMatrix, b::AbstractVector) = scale!(similar(A, promote_op(MulFun(),eltype(A),eltype(b))), A, b)
-scale(b::AbstractVector, A::AbstractMatrix) = scale!(similar(b, promote_op(MulFun(),eltype(b),eltype(A)), size(A)), b, A)
 
 # Dot products
 

base/sparse.jl

@@ -21,7 +21,7 @@ import Base: @get!, acos, acosd, acot, acotd, acsch, asech, asin, asind, asinh,
     exp, expm1, factorize, find, findmax, findmin, findnz, float, full, getindex,
     hcat, hvcat, imag, indmax, ishermitian, kron, length, log, log1p, max, min,
     maximum, minimum, norm, one, promote_eltype, real, reinterpret, reshape, rot180,
-    rotl90, rotr90, round, scale, scale!, setindex!, similar, size, transpose, tril,
+    rotl90, rotr90, round, scale!, setindex!, similar, size, transpose, tril,
     triu, vcat, vec
 
 import Base.Broadcast: eltype_plus, broadcast_shape

base/sparse/cholmod.jl

@@ -1020,7 +1020,7 @@ function sparse(F::Factor)
     else
         LD = sparse(F[:LD])
         L, d = getLd!(LD)
-        A = scale(L, d)*L'
+        A = (L * Diagonal(d)) * L'
     end
     SparseArrays.sortSparseMatrixCSC!(A)
     p = get_perm(F)

base/sparse/linalg.jl

@@ -826,12 +826,6 @@ end
 scale!(A::SparseMatrixCSC, b::Number) = (scale!(A.nzval, b); A)
 scale!(b::Number, A::SparseMatrixCSC) = (scale!(b, A.nzval); A)
 
-scale{Tv,Ti,T}(A::SparseMatrixCSC{Tv,Ti}, b::Vector{T}) =
-    scale!(similar(A, promote_type(Tv,T)), A, b)
-
-scale{T,Tv,Ti}(b::Vector{T}, A::SparseMatrixCSC{Tv,Ti}) =
-    scale!(similar(A, promote_type(Tv,T)), b, A)
-
 function factorize(A::SparseMatrixCSC)
     m, n = size(A)
     if m == n

base/sparse/sparsevector.jl

@@ -1191,18 +1191,11 @@ scale!(x::AbstractSparseVector, a::Complex) = (scale!(nonzeros(x), a); x)
 scale!(a::Real, x::AbstractSparseVector) = scale!(nonzeros(x), a)
 scale!(a::Complex, x::AbstractSparseVector) = scale!(nonzeros(x), a)
 
-scale(x::AbstractSparseVector, a::Real) =
-    SparseVector(length(x), copy(nonzeroinds(x)), scale(nonzeros(x), a))
-scale(x::AbstractSparseVector, a::Complex) =
-    SparseVector(length(x), copy(nonzeroinds(x)), scale(nonzeros(x), a))
-
-scale(a::Real, x::AbstractSparseVector) = scale(x, a)
-scale(a::Complex, x::AbstractSparseVector) = scale(x, a)
-
-*(x::AbstractSparseVector, a::Number) = scale(x, a)
-*(a::Number, x::AbstractSparseVector) = scale(x, a)
-.*(x::AbstractSparseVector, a::Number) = scale(x, a)
-.*(a::Number, x::AbstractSparseVector) = scale(x, a)
+# *(x::AbstractSparseVector, a::Real) = SparseVector(length(x), copy(nonzeroinds(x)), scale(nonzeros(x), a))
+# *(x::AbstractSparseVector, a::Complex) = SparseVector(length(x), copy(nonzeroinds(x)), scale(nonzeros(x), a))
+# *(a::Number, x::AbstractSparseVector) = xa)
+# .*(x::AbstractSparseVector, a::Number) = scale(x, a)
+# .*(a::Number, x::AbstractSparseVector) = scale(x, a)
 
 
 # dot

doc/stdlib/linalg.rst

@@ -823,25 +823,14 @@ Linear algebra functions in Julia are largely implemented by calling functions f
 
    Construct a diagonal matrix and place ``v`` on the ``k``\ th diagonal.
 
-.. function:: scale(A, b)
-              scale(b, A)
-
-   .. Docstring generated from Julia source
-
-   Scale an array ``A`` by a scalar ``b``\ , returning a new array.
-
-   If ``A`` is a matrix and ``b`` is a vector, then ``scale(A,b)`` scales each column ``i`` of ``A`` by ``b[i]`` (similar to ``A*diagm(b)``\ ), while ``scale(b,A)`` scales each row ``i`` of ``A`` by ``b[i]`` (similar to ``diagm(b)*A``\ ), returning a new array.
-
-   Note: for large ``A``\ , ``scale`` can be much faster than ``A .* b`` or ``b .* A``\ , due to the use of BLAS.
-
 .. function:: scale!(A, b)
               scale!(b, A)
 
    .. Docstring generated from Julia source
 
-   Scale an array ``A`` by a scalar ``b``\ , similar to :func:`scale` but overwriting ``A`` in-place.
+   Scale an array ``A`` by a scalar ``b`` overwriting ``A`` in-place.
 
-   If ``A`` is a matrix and ``b`` is a vector, then ``scale!(A,b)`` scales each column ``i`` of ``A`` by ``b[i]`` (similar to ``A*diagm(b)``\ ), while ``scale!(b,A)`` scales each row ``i`` of ``A`` by ``b[i]`` (similar to ``diagm(b)*A``\ ), again operating in-place on ``A``\ .
+   If ``A`` is a matrix and ``b`` is a vector, then ``scale!(A,b)`` scales each column ``i`` of ``A`` by ``b[i]`` (similar to ``A*Diagonal(b)``\ ), while ``scale!(b,A)`` scales each row ``i`` of ``A`` by ``b[i]`` (similar to ``Diagonal(b)*A``\ ), again operating in-place on ``A``\ .
 
 .. function:: Tridiagonal(dl, d, du)
 

test/blas.jl

@@ -113,7 +113,7 @@ for elty in [Float32, Float64, Complex64, Complex128]
 
         # scal
         α = rand(elty)
-        @test BLAS.scal(n,α,a,1) ≈ scale(α,a)
+        @test BLAS.scal(n,α,a,1) ≈ α * a
 
         # trsv
         A = triu(rand(elty,n,n))

test/linalg/eigen.jl

@@ -50,7 +50,7 @@ debug && println("symmetric generalized eigenproblem")
     asym_sg = asym[1:n1, 1:n1]
     a_sg = a[:,n1+1:n2]
     f = eigfact(asym_sg, a_sg'a_sg)
-    @test_approx_eq asym_sg*f[:vectors] scale(a_sg'a_sg*f[:vectors], f[:values])
+    @test_approx_eq asym_sg*f[:vectors] (a_sg'a_sg*f[:vectors]) * Diagonal(f[:values])
     @test_approx_eq f[:values] eigvals(asym_sg, a_sg'a_sg)
     @test_approx_eq_eps prod(f[:values]) prod(eigvals(asym_sg/(a_sg'a_sg))) 200ε
     @test eigvecs(asym_sg, a_sg'a_sg) == f[:vectors]
@@ -66,7 +66,7 @@ debug && println("Non-symmetric generalized eigenproblem")
     a1_nsg = a[1:n1, 1:n1]
     a2_nsg = a[n1+1:n2, n1+1:n2]
     f = eigfact(a1_nsg, a2_nsg)
-    @test_approx_eq a1_nsg*f[:vectors] scale(a2_nsg*f[:vectors], f[:values])
+    @test_approx_eq a1_nsg*f[:vectors] (a2_nsg*f[:vectors]) * Diagonal(f[:values])
     @test_approx_eq f[:values] eigvals(a1_nsg, a2_nsg)
     @test_approx_eq_eps prod(f[:values]) prod(eigvals(a1_nsg/a2_nsg)) 50000ε
     @test eigvecs(a1_nsg, a2_nsg) == f[:vectors]

test/linalg/generic.jl

@@ -105,26 +105,6 @@ let aa = reshape([1.:6;], (2,3))
             a = sub(aa, 1:2, 1:2)
         end
 
-        # 2-argument version of scale
-        @test scale(a, 5.) == a*5
-        @test scale(5., a) == a*5
-        @test scale([1.; 2.], a) == a.*[1; 2]
-        @test scale([1; 2], a) == a.*[1; 2]
-        @test scale(eye(Int, 2), 0.5) == 0.5*eye(2)
-        @test scale([1; 2], sub(a, :, :)) == a.*[1; 2]
-        @test scale(sub([1; 2], :), a) == a.*[1; 2]
-        @test_throws DimensionMismatch scale(ones(3), a)
-
-        if atype == "Array"
-            @test scale(a, [1.; 2.; 3.]) == a.*[1 2 3]
-            @test scale(a, [1; 2; 3]) == a.*[1 2 3]
-            @test_throws DimensionMismatch scale(a, ones(2))
-        else
-            @test scale(a, [1.; 2.]) == a.*[1 2]
-            @test scale(a, [1; 2]) == a.*[1 2]
-            @test_throws DimensionMismatch scale(a, ones(3))
-        end
-
         # 2-argument version of scale!
         @test scale!(copy(a), 5.) == a*5
         @test scale!(5., copy(a)) == a*5
@@ -168,15 +148,15 @@ end
 
 # scale real matrix by complex type
 @test_throws InexactError scale!([1.0], 2.0im)
-@test isequal(scale([1.0], 2.0im),             Complex{Float64}[2.0im])
-@test isequal(scale(2.0im, [1.0]),             Complex{Float64}[2.0im])
-@test isequal(scale(Float32[1.0], 2.0f0im),    Complex{Float32}[2.0im])
-@test isequal(scale(Float32[1.0], 2.0im),      Complex{Float64}[2.0im])
-@test isequal(scale(Float64[1.0], 2.0f0im),    Complex{Float64}[2.0im])
-@test isequal(scale(Float32[1.0], big(2.0)im), Complex{BigFloat}[2.0im])
-@test isequal(scale(Float64[1.0], big(2.0)im), Complex{BigFloat}[2.0im])
-@test isequal(scale(BigFloat[1.0], 2.0im),     Complex{BigFloat}[2.0im])
-@test isequal(scale(BigFloat[1.0], 2.0f0im),   Complex{BigFloat}[2.0im])
+@test isequal([1.0] * 2.0im,             Complex{Float64}[2.0im])
+@test isequal(2.0im * [1.0],             Complex{Float64}[2.0im])
+@test isequal(Float32[1.0] * 2.0f0im,    Complex{Float32}[2.0im])
+@test isequal(Float32[1.0] * 2.0im,      Complex{Float64}[2.0im])
+@test isequal(Float64[1.0] * 2.0f0im,    Complex{Float64}[2.0im])
+@test isequal(Float32[1.0] * big(2.0)im, Complex{BigFloat}[2.0im])
+@test isequal(Float64[1.0] * big(2.0)im, Complex{BigFloat}[2.0im])
+@test isequal(BigFloat[1.0] * 2.0im,     Complex{BigFloat}[2.0im])
+@test isequal(BigFloat[1.0] * 2.0f0im,   Complex{BigFloat}[2.0im])
 
 # test scale and scale! for non-commutative multiplication
 q = Quaternion([0.44567, 0.755871, 0.882548, 0.423612])

test/linalg/lapack.jl

@@ -16,7 +16,7 @@ let # syevr
         A = convert(Array{elty, 2}, A)
         Asym = A'A
         vals, Z = LAPACK.syevr!('V', copy(Asym))
-        @test_approx_eq Z*scale(vals, Z') Asym
+        @test_approx_eq Z * (Diagonal(vals) * Z') Asym
         @test all(vals .> 0.0)
         @test_approx_eq LAPACK.syevr!('N','V','U',copy(Asym),0.0,1.0,4,5,-1.0)[1] vals[vals .< 1.0]
         @test_approx_eq LAPACK.syevr!('N','I','U',copy(Asym),0.0,1.0,4,5,-1.0)[1] vals[4:5]

test/linalg/svd.jl

@@ -30,7 +30,7 @@ debug && println("\ntype of a: ", eltya, "\n")
 debug && println("singular value decomposition")
     usv = svdfact(a)
     @test usv[:S] === svdvals(usv)
-    @test usv[:U]*scale(usv[:S],usv[:Vt]) ≈ a
+    @test usv[:U] * (Diagonal(usv[:S]) * usv[:Vt]) ≈ a
     @test full(usv) ≈ a
     @test usv[:Vt]' ≈ usv[:V]
     @test_throws KeyError usv[:Z]

test/linalg/triangular.jl

@@ -207,12 +207,6 @@ for elty1 in (Float32, Float64, BigFloat, Complex64, Complex128, Complex{BigFloa
             end
         end
 
-        @test scale(A1,0.5) == 0.5*A1
-        @test scale(0.5,A1) == 0.5*A1
-        @test scale(A1,0.5im) == 0.5im*A1
-        @test scale(0.5im,A1) == 0.5im*A1
-
-
         # Binary operations
         @test A1*0.5 == full(A1)*0.5
         @test 0.5*A1 == 0.5*full(A1)

test/sparsedir/sparse.jl

@@ -228,20 +228,20 @@ sA = sprandn(3, 7, 0.5)
 sC = similar(sA)
 dA = full(sA)
 b = randn(7)
-@test scale(dA, b) == scale(sA, b)
-@test scale(dA, b) == scale!(sC, sA, b)
-@test scale(dA, b) == scale!(copy(sA), b)
+@test dA * Diagonal(b) == sA * Diagonal(b)
+@test dA * Diagonal(b) == scale!(sC, sA, b)
+@test dA * Diagonal(b) == scale!(copy(sA), b)
 b = randn(3)
-@test scale(b, dA) == scale(b, sA)
-@test scale(b, dA) == scale!(sC, b, sA)
-@test scale(b, dA) == scale!(b, copy(sA))
-
-@test scale(dA, 0.5) == scale(sA, 0.5)
-@test scale(dA, 0.5) == scale!(sC, sA, 0.5)
-@test scale(dA, 0.5) == scale!(copy(sA), 0.5)
-@test scale(0.5, dA) == scale(0.5, sA)
-@test scale(0.5, dA) == scale!(sC, sA, 0.5)
-@test scale(0.5, dA) == scale!(0.5, copy(sA))
+@test Diagonal(b) * dA == Diagonal(b) * sA
+@test Diagonal(b) * dA == scale!(sC, b, sA)
+@test Diagonal(b) * dA == scale!(b, copy(sA))
+
+@test dA * 0.5            == sA * 0.5
+@test dA * 0.5            == scale!(sC, sA, 0.5)
+@test dA * 0.5            == scale!(copy(sA), 0.5)
+@test 0.5 * dA            == 0.5 * sA
+@test 0.5 * dA            == scale!(sC, sA, 0.5)
+@test 0.5 * dA            == scale!(0.5, copy(sA))
 @test scale!(sC, 0.5, sA) == scale!(sC, sA, 0.5)
 
 # copy!

test/sparsedir/sparsevector.jl

@@ -580,10 +580,10 @@ let x = sprand(16, 0.5), x2 = sprand(16, 0.4)
 
     # scale
     let sx = SparseVector(x.n, x.nzind, x.nzval * 2.5)
-        @test exact_equal(scale(x, 2.5), sx)
-        @test exact_equal(scale(x, 2.5 + 0.0*im), complex(sx))
-        @test exact_equal(scale(2.5, x), sx)
-        @test exact_equal(scale(2.5 + 0.0*im, x), complex(sx))
+        @test exact_equal(x * 2.5, sx)
+        @test exact_equal(x * (2.5 + 0.0*im), complex(sx))
+        @test exact_equal(2.5 * x, sx)
+        @test exact_equal((2.5 + 0.0*im) * x, complex(sx))
         @test exact_equal(x * 2.5, sx)
         @test exact_equal(2.5 * x, sx)
         @test exact_equal(x .* 2.5, sx)

test/sparsedir/umfpack.jl

@@ -19,7 +19,7 @@ for Tv in (Float64, Complex128)
         lua = lufact(A)
         @test nnz(lua) == 18
         L,U,p,q,Rs = lua[:(:)]
-        @test_approx_eq scale(Rs,A)[p,q] L*U
+        @test_approx_eq (Diagonal(Rs) * A)[p,q] L * U
 
         @test_approx_eq det(lua) det(full(A))
 
@@ -45,15 +45,15 @@ for Ti in Base.SparseArrays.UMFPACK.UMFITypes.types
     Ac = convert(SparseMatrixCSC{Complex128,Ti}, Ac0)
     lua = lufact(Ac)
     L,U,p,q,Rs = lua[:(:)]
-    @test_approx_eq scale(Rs,Ac)[p,q] L*U
+    @test_approx_eq (Diagonal(Rs) * Ac)[p,q] L * U
 end
 
 for elty in (Float64, Complex128)
     for (m, n) in ((10,5), (5, 10))
         A = sparse([1:min(m,n); rand(1:m, 10)], [1:min(m,n); rand(1:n, 10)], elty == Float64 ? randn(min(m, n) + 10) : complex(randn(min(m, n) + 10), randn(min(m, n) + 10)))
         F = lufact(A)
         L, U, p, q, Rs = F[:(:)]
-        @test_approx_eq scale(Rs,A)[p,q] L*U
+        @test_approx_eq (Diagonal(Rs) * A)[p,q] L * U
     end
 end