Enhance generic methods for transpose and transpose!

docs/src/matrix.md

@@ -76,7 +76,8 @@ scalar_matrix(R::Ring, n::Int, a::RingElement)
 diagonal_matrix(::RingElement, ::Int, ::Int)
 zero(::MatElem{T}, ::Ring) where T <: RingElement
 one(::MatElem{T}) where T <: RingElement
-transpose(::MatrixElem{T}) where T <: RingElement
+transpose(::MatElem)
+transpose!(::MatElem)
 tr(::MatElem{T}) where T <: RingElement
 det{T <: RingElem}(::MatElem{T})
 rank{T <: RingElem}(::MatElem{T})

ext/TestExt/Rings-conformance-tests.jl

@@ -721,10 +721,26 @@ function test_MatSpace_interface(S::MatSpace; reps = 20)
 
             t = transpose(a)
             @test t isa ST
+            @test base_ring(t) == base_ring(a)
             @test nrows(t) == ncols(S)
             @test ncols(t) == nrows(S)
             @test transpose(t) == a
             @test a == A
+
+            if nrows(S) == ncols(S)
+              # in-place transpose! only supported for square matrices
+              t = transpose!(deepcopy(a))
+              @test t isa ST
+              @test base_ring(t) == base_ring(a)
+              @test t == transpose(a)
+            end
+
+            z = zero_matrix(R, ncols(a), nrows(a))
+            t = transpose!(z, a)
+            @test t isa ST
+            @test base_ring(t) == base_ring(a)
+            @test t == transpose(a)
+            @test a == A
          end
       end
 

src/Matrix.jl

@@ -1457,21 +1457,18 @@ end
 
 
 @doc raw"""
-    transpose(x::MatrixElem{T}) where T <: NCRingElement
+    transpose(x::MatElem)
+    transpose(x::MatRingElem)
 
-Return the transpose of the given matrix.
+Return the transpose of `x`.
 
 # Examples
 
 ```jldoctest
 julia> R, t = polynomial_ring(QQ, :t)
 (Univariate polynomial ring in t over rationals, t)
 
-julia> S = matrix_space(R, 3, 3)
-Matrix space of 3 rows and 3 columns
-  over univariate polynomial ring in t over rationals
-
-julia> A = S([t + 1 t R(1); t^2 t t; R(-2) t + 2 t^2 + t + 1])
+julia> A = matrix(R, [t + 1 t R(1); t^2 t t; R(-2) t + 2 t^2 + t + 1])
 [t + 1       t             1]
 [  t^2       t             t]
 [   -2   t + 2   t^2 + t + 1]
@@ -1483,9 +1480,42 @@ julia> B = transpose(A)
 
 ```
 """
-transpose(x::MatrixElem{T}) where T <: NCRingElement
+function transpose(x::MatElem)
+  z = similar(base_ring(x), ncols(x), nrows(x))
+  return transpose!(z, x)
+end
+
+transpose(x::MatRingElem) = transpose(matrix(x))
+
+@doc raw"""
+    transpose!(x::MatElem)
+    transpose!(x::MatRingElem)
+    transpose!(z::T, x::T) where T <: MatElem
+    transpose!(z::T, x::T) where T <: MatRingElem
+
+Return the transpose of `x`, possibly modifying the object `z` in the process.
+Aliasing is permitted.
+
+The unary version only is supported if `x` is a square matrix.
+"""
+function transpose!(x::MatElem)
+  @req is_square(x) "Matrix must be a square matrix"
+  return transpose!(x, x)
+end
 
-transpose!(A::MatrixElem) = transpose(A)
+function transpose!(z::T, x::T) where T <: MatElem
+  if z === x
+    n = nrows(x)
+    for i in 1:n, j in i+1:n
+      x[i, j], x[j, i] = x[j, i], x[i, j]
+    end
+  else
+    for i in 1:nrows(x), j in 1:ncols(x)
+      z[j, i] = x[i, j]
+    end
+  end
+  return z
+end
 
 ###############################################################################
 #

src/exports.jl

@@ -586,6 +586,8 @@ export total_degree
 export total_ring_of_fractions
 export tr
 export trailing_coefficient
+export transpose
+export transpose!
 export truncate
 export typed_hcat
 export typed_hvcat

src/generic/GenericTypes.jl

@@ -1169,12 +1169,14 @@ end
 struct MatRingElem{T <: NCRingElement} <: AbstractAlgebra.MatRingElem{T}
    data::MatElem{T}
 
-  function MatRingElem(A::MatElem{TT}) where TT <: NCRingElement
+  function MatRingElem{TT}(A::MatElem{TT}) where TT <: NCRingElement
     nrows(A) == ncols(A) || error("Matrix must be square")
     return new{TT}(A)
    end
 end
 
+MatRingElem(A::MatElem{TT}) where TT <: NCRingElement = MatRingElem{TT}(A)
+
 function MatRingElem(R::NCRing, n::Int, A::Vector{T}) where T <: NCRingElement
    t = matrix(R, n, n, A)
    return MatRingElem(t)

src/generic/MatRing.jl

@@ -54,9 +54,9 @@ Base.isassigned(a::MatRingElem, i, j) = isassigned(matrix(a), i, j)
 #
 ###############################################################################
 
-function transpose(x::MatRingElem)
-   return MatRingElem(transpose(matrix(x)))
-end
+transpose(x::MatRingElem) = MatRingElem(transpose(matrix(x)))
+transpose!(x::MatRingElem) = MatRingElem(transpose!(matrix(x)))
+transpose!(z::T, x::T) where T <: MatRingElem = MatRingElem(transpose!(matrix(z), matrix(x)))
 
 ###############################################################################
 #

test/generic/Matrix-test.jl

@@ -4454,6 +4454,15 @@ end
   c = mul!(c, a, QQ(2))
   @test c == a * QQ(2)
 
+  # test 2-arg transpose! with destination != source
   b = transpose(a)
-  @test AbstractAlgebra.transpose!(a) == b
+  c = zero_matrix(QQ, 3, 2)
+  @test AbstractAlgebra.transpose!(c, a) == b
+
+  # test 2-arg transpose! with destination == source
+  x = QQ[1 2; 3 4]
+  @test AbstractAlgebra.transpose!(x, x) == QQ[1 3; 2 4]
+
+  # in-place transpose of non-square matrix does not work
+  @test_throws ArgumentError AbstractAlgebra.transpose!(a)
 end