Merge pull request #4 from fkastner/nice_linalg

enable and test matrix factorizations

src/NiceLinAlg.jl

@@ -0,0 +1,9 @@
+import LinearAlgebra: Hermitian, Symmetric, UpperTriangular, LowerTriangular
+import LinearAlgebra: cholesky!, _chol!, Cholesky, checkpositivedefinite
+
+
+function cholesky!(A::Union{Hermitian{NiceNumber,S}, Symmetric{NiceNumber,S}} where S, ::Val{false}=Val(false); check::Bool = true)
+    C, info = _chol!(A.data, A.uplo == 'U' ? UpperTriangular : LowerTriangular)
+    check && checkpositivedefinite(info)
+    return Cholesky(C.data, A.uplo, info)
+end

src/NiceNumbers.jl

@@ -6,8 +6,9 @@ import Base: //
 import Base: isless, <, <=, ==, hash
 import Base: one, zero, isinteger, isfinite
 import Base: promote_rule
-import Base: isreal, real, imag, conj, abs
+import Base: isreal, real, imag, conj, abs, abs2
 import LinearAlgebra: norm, norm2
+import Base: copysign
 
 export NiceNumber, nice, @nice
 export isrational
@@ -161,8 +162,10 @@ hash(n::NiceNumber, h::UInt) = hash(n.a, hash(n.coeff, hash(n.radicand, hash(:Ni
 
 conj(n::NiceNumber) = isreal(n) ? n : NiceNumber(n.a, -n.coeff, n.radicand)
 abs(n::NiceNumber) = isreal(n) ? float(n)>0 ? n : -n : sqrt(n*conj(n))
+abs2(n::NiceNumber) = n*conj(n)
 norm(n::NiceNumber) = abs(n)
 norm2(v::AbstractArray{NiceNumber,1}) = sqrt(v'v)
+copysign(n::NiceNumber, m::NiceNumber) = sign(n) == sign(m) ? n : -n
 
 ## macro stuff
 """
@@ -191,4 +194,6 @@ macro nice(code)
     return esc(nice(code))
 end
 
+include("NiceLinAlg.jl")
+
 end # module

test/runtests.jl

@@ -124,4 +124,32 @@ using Test, LinearAlgebra
         @test sprint(io -> show(io, NiceNumber(0, -5, 5))) == "-5⋅√5"
         @test sprint(io -> show(io, NiceNumber(0, 1 // 2, 5))) == "1//2⋅√5"
     end
+
+    @testset "Factorizations" begin
+        @testset "Cholesky" begin
+            @nice L = [2 0 0 0;0 1 0 0;4 6*sqrt(-1) 9 0;0 4 0 2]
+            @test L == cholesky(L*L').L
+        end
+
+        @testset "LU" begin
+            @nice L = [1 0 0;im 1 0; 1/2 -3im 1]
+            @nice U = [1 1 1;0 1 1; 0 0 1]
+            LUL, LUU = lu(L*U, Val(false))
+            @test LUL == L
+            @test LUU == U
+
+            @nice A = [2 2 0;2 2 1; 2 3 5]
+            L, U, p = lu(A, Val(true))
+            @test L == @nice [1 0 0;1 1 0;1 0 1]
+            @test U == @nice [2 2 0;0 1 5;0 0 1]
+            @test p == [1,3,2]
+        end
+
+        @testset "QR" begin
+            @nice A = [4 2;0 3//5;0 -4//5;0 0]
+            Q, R = qr(A)
+            @test Q == @nice [-1 0 0 0;0 -3/5 4/5 0;0 4/5 3/5 0;0 0 0 1]
+            @test R == @nice [-4 -2;0 -1]
+        end
+    end
 end