Added global D4 variable holding all group elements and function for …

…getting all symmetries at once.

README.md

@@ -121,7 +121,7 @@ julia> my_alg(m) = ... # some super clever matrix transformation
 
 julia> m = rand(10, 10); # our test matrix
 
-julia> for g in D4
+julia> for g in SquareSymmetries.D4
            @assert inv(g)(my_alg(g(m))) == my_alg(m)
        end 
 ```

src/SquareSymmetries.jl

@@ -1,6 +1,6 @@
 module SquareSymmetries
 
-export unit, rotate90, rotate180, rotate270, flipdiag, flipadiag, flipx, flipy
+export unit, rotate90, rotate180, rotate270, flipdiag, flipadiag, flipx, flipy, symmetries
 
 include("symmetry.jl")
 

src/symmetry.jl

@@ -10,6 +10,11 @@ rotate270(x::AbstractMatrix) = rotl90(x)
 # no base function directly returns this, but we can easily compose it
 flipadiag(x::AbstractMatrix) = rotate180(flipdiag(x))
 
+const D4 = (unit, rotate90, rotate180, rotate270, flipx, flipy, flipdiag, flipadiag)
+
+# convenient function for getting all symmetries of a given matrix at once
+symmetries(x::AbstractMatrix) = map(g -> g(x), D4)
+
 # binary group operation for elements of the symmetry group
 Base.:∘(::typeof(unit), ::typeof(unit)) = unit
 Base.:∘(::typeof(unit), ::typeof(flipx)) = flipx

test/symmetry.jl

@@ -69,26 +69,39 @@ end
     # the '∘' function acts as function composition and group operation at the same time
     # it can be used prevent unneeded computations, e.g., (rotate180 ∘ rotate180)(m) does
     # not actually rotate m twice by 180 degrees but directly returns unit(m)
-    elements = [unit, rotate90, rotate180, rotate270, flipx, flipy, flipdiag, flipadiag]
     m = rand(10, 10)
 
-    for g1 in elements
-        for g2 in elements
+    for g1 in SquareSymmetries.D4
+        for g2 in SquareSymmetries.D4
             @test (g1 ∘ g2)(m) == g1(g2(m))
         end
     end
 end
 
 @testset "Inverse elements" begin
-    elements = [unit, rotate90, rotate180, rotate270, flipx, flipy, flipdiag, flipadiag]
     m = rand(10, 10)
 
     # for all group elements g and all matrices m, g(g^(-1)(m)) = g^(-1)(g(m)) = m
-    for g in elements
+    for g in SquareSymmetries.D4
         @test g(inv(g)(m)) == inv(g)(g(m)) == m
     end
 
-    for g in elements
+    for g in SquareSymmetries.D4
         @test g ∘ inv(g) == inv(g) ∘ g == unit
     end
 end
+
+@testset "Symmetries" begin
+    m = rand(10, 10)
+
+    syms = symmetries(m)
+    @test length(syms) == 8
+    @test syms[1] == unit(m)
+    @test syms[2] == rotate90(m)
+    @test syms[3] == rotate180(m)
+    @test syms[4] == rotate270(m)
+    @test syms[5] == flipx(m)
+    @test syms[6] == flipy(m)
+    @test syms[7] == flipdiag(m)
+    @test syms[8] == flipadiag(m)
+end