Make A' lower to postfixapostrophize(A) with default def = Adjoint(A) and clean up fallout.

Author: Sacha0

base/exports.jl

@@ -248,6 +248,7 @@ export
     At_mul_Bt!,
     At_rdiv_B,
     At_rdiv_Bt,
+    postfixapostrophize,
 
 # scalar math
     @evalpoly,

base/linalg/generic.jl

@@ -816,15 +816,18 @@ function inv(A::AbstractMatrix{T}) where T
     ldiv!(factorize(convert(AbstractMatrix{S}, A)), dest)
 end
 
-function pinv(v::AbstractVector{T}, tol::Real=real(zero(T))) where T
-    res = similar(v, typeof(zero(T) / (abs2(one(T)) + abs2(one(T)))))'
+pinv(v::AbstractVector{T}, tol::Real = real(zero(T))) where {T<:Real} = _vectorpinv(Transpose, v, tol)
+pinv(v::AbstractVector{T}, tol::Real = real(zero(T))) where {T<:Complex} = _vectorpinv(Adjoint, v, tol)
+pinv(v::AbstractVector{T}, tol::Real = real(zero(T))) where {T} = _vectorpinv(Adjoint, v, tol)
+function _vectorpinv(dualfn::Tf, v::AbstractVector{Tv}, tol) where {Tv,Tf}
+    res = dualfn(similar(v, typeof(zero(Tv) / (abs2(one(Tv)) + abs2(one(Tv))))))
     den = sum(abs2, v)
     # as tol is the threshold relative to the maximum singular value, for a vector with
     # single singular value σ=√den, σ ≦ tol*σ is equivalent to den=0 ∨ tol≥1
     if iszero(den) || tol >= one(tol)
         fill!(res, zero(eltype(res)))
     else
-        res .= v' ./ den
+        res .= dualfn(v) ./ den
     end
     return res
 end

base/operators.jl

@@ -739,7 +739,8 @@ fldmod1(x::T, y::T) where {T<:Real} = (fld1(x,y), mod1(x,y))
 # efficient version for integers
 fldmod1(x::T, y::T) where {T<:Integer} = (fld1(x,y), mod1(x,y))
 
-# transpose
+# postfix apostophre
+postfixapostrophize(x) = Adjoint(x)
 
 """
     adjoint(A)

src/julia-syntax.scm

@@ -2396,7 +2396,7 @@
                      ,.(apply append rows)))
             `(call (top typed_vcat) ,t ,@a)))))
 
-   '|'|  (lambda (e) (expand-forms `(call adjoint ,(cadr e))))
+   '|'|  (lambda (e) (expand-forms `(call postfixapostrophize ,(cadr e))))
    '|.'| (lambda (e) (begin (deprecation-message (string "The syntax `.'` for transposition is deprecated, "
                                              "and the special lowering of `.'` in multiplication "
                                              "(`*`), left-division (`\\`), and right-division (`/`) "

test/arrayops.jl

@@ -2048,7 +2048,7 @@ end # module AutoRetType
         @test isa(cat((1,2), densearray, densearray), Array)
     end
     @test isa([[1,2,3]'; [1,2,3]'], Matrix{Int})
-    @test isa([[1,2,3]' [1,2,3]'], Transpose{Int, Vector{Int}})
+    @test isa([[1,2,3]' [1,2,3]'], Adjoint{Int, Vector{Int}})
     @test isa([Any[1.0, 2]'; Any[2.0, 2]'], Matrix{Any})
     @test isa([Any[1.0, 2]' Any[2.0, 2]'], Adjoint{Any, Vector{Any}})
     # Test that concatenations of heterogeneous Matrix-Vector pairs yield dense matrices

test/show.jl

@@ -557,7 +557,7 @@ end
 @test replstr(Matrix(1.0I, 10, 10)) == "10×10 Array{Float64,2}:\n 1.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0  1.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0  0.0  1.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0  0.0  0.0  1.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0  0.0  0.0  0.0  1.0  0.0  0.0  0.0  0.0  0.0\n 0.0  0.0  0.0  0.0  0.0  1.0  0.0  0.0  0.0  0.0\n 0.0  0.0  0.0  0.0  0.0  0.0  1.0  0.0  0.0  0.0\n 0.0  0.0  0.0  0.0  0.0  0.0  0.0  1.0  0.0  0.0\n 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  1.0  0.0\n 0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  1.0"
 # an array too long vertically to fit on screen, and too long horizontally:
 @test replstr(collect(1.:100.)) == "100-element Array{Float64,1}:\n   1.0\n   2.0\n   3.0\n   4.0\n   5.0\n   6.0\n   7.0\n   8.0\n   9.0\n  10.0\n   ⋮  \n  92.0\n  93.0\n  94.0\n  95.0\n  96.0\n  97.0\n  98.0\n  99.0\n 100.0"
-@test replstr(collect(1.:100.)') == "1×100 Transpose{Float64,Array{Float64,1}}:\n 1.0  2.0  3.0  4.0  5.0  6.0  7.0  …  95.0  96.0  97.0  98.0  99.0  100.0"
+@test replstr(collect(1.:100.)') == "1×100 Adjoint{Float64,Array{Float64,1}}:\n 1.0  2.0  3.0  4.0  5.0  6.0  7.0  …  95.0  96.0  97.0  98.0  99.0  100.0"
 # too big in both directions to fit on screen:
 @test replstr((1.:100.)*(1:100)') == "100×100 Array{Float64,2}:\n   1.0    2.0    3.0    4.0    5.0    6.0  …    97.0    98.0    99.0    100.0\n   2.0    4.0    6.0    8.0   10.0   12.0      194.0   196.0   198.0    200.0\n   3.0    6.0    9.0   12.0   15.0   18.0      291.0   294.0   297.0    300.0\n   4.0    8.0   12.0   16.0   20.0   24.0      388.0   392.0   396.0    400.0\n   5.0   10.0   15.0   20.0   25.0   30.0      485.0   490.0   495.0    500.0\n   6.0   12.0   18.0   24.0   30.0   36.0  …   582.0   588.0   594.0    600.0\n   7.0   14.0   21.0   28.0   35.0   42.0      679.0   686.0   693.0    700.0\n   8.0   16.0   24.0   32.0   40.0   48.0      776.0   784.0   792.0    800.0\n   9.0   18.0   27.0   36.0   45.0   54.0      873.0   882.0   891.0    900.0\n  10.0   20.0   30.0   40.0   50.0   60.0      970.0   980.0   990.0   1000.0\n   ⋮                                  ⋮    ⋱                                 \n  92.0  184.0  276.0  368.0  460.0  552.0     8924.0  9016.0  9108.0   9200.0\n  93.0  186.0  279.0  372.0  465.0  558.0     9021.0  9114.0  9207.0   9300.0\n  94.0  188.0  282.0  376.0  470.0  564.0     9118.0  9212.0  9306.0   9400.0\n  95.0  190.0  285.0  380.0  475.0  570.0     9215.0  9310.0  9405.0   9500.0\n  96.0  192.0  288.0  384.0  480.0  576.0  …  9312.0  9408.0  9504.0   9600.0\n  97.0  194.0  291.0  388.0  485.0  582.0     9409.0  9506.0  9603.0   9700.0\n  98.0  196.0  294.0  392.0  490.0  588.0     9506.0  9604.0  9702.0   9800.0\n  99.0  198.0  297.0  396.0  495.0  594.0     9603.0  9702.0  9801.0   9900.0\n 100.0  200.0  300.0  400.0  500.0  600.0     9700.0  9800.0  9900.0  10000.0"