Merge pull request JuliaLang#12095 from JuliaLang/ksh/linalgtests

Fill out linalg tests

Author: kshyatt

base/linalg/eigen.jl

@@ -97,7 +97,7 @@ function eigmin(A::Union{Number, StridedMatrix}; permute::Bool=true, scale::Bool
     iseltype(v,Complex) ? error("DomainError: complex eigenvalues cannot be ordered") : minimum(v)
 end
 
-inv(A::Eigen) = A.vectors/Diagonal(A.values)*A.vectors'
+inv(A::Eigen) = A.vectors * inv(Diagonal(A.values)) / A.vectors
 det(A::Eigen) = prod(A.values)
 
 # Generalized eigenproblem

test/linalg/symmetric.jl

@@ -84,18 +84,23 @@ let n=10
             @test_approx_eq Symmetric(asym)*x+y asym*x+y
         end
 
+        C = zeros(eltya,n,n)
         # mat * mat
         if eltya <: Complex
             @test_approx_eq Hermitian(asym) * a asym * a
             @test_approx_eq a * Hermitian(asym) a * asym
             @test_approx_eq Hermitian(asym) * Hermitian(asym) asym*asym
             @test_throws DimensionMismatch Hermitian(asym) * ones(eltya,n+1)
+            Base.LinAlg.A_mul_B!(C,a,asym)
+            @test_approx_eq C a*asym
         end
         if eltya <: Real && eltya != Int
             @test_approx_eq Symmetric(asym) * Symmetric(asym) asym*asym
             @test_approx_eq Symmetric(asym) * a asym * a
             @test_approx_eq a * Symmetric(asym) a * asym
             @test_throws DimensionMismatch Symmetric(asym) * ones(eltya,n+1)
+            Base.LinAlg.A_mul_B!(C,a,asym)
+            @test_approx_eq C a*asym
         end
 
         # solver
@@ -109,6 +114,21 @@ let n=10
         if eltya <: Real && eltya != Int
             @test_approx_eq inv(Symmetric(asym)) inv(asym)
         end
+
+        # conversion
+        @test Symmetric(asym) == convert(Symmetric,Symmetric(asym))
+        if eltya <: Real && eltya != Int
+            typs = [Float16,Float32,Float64]
+            for typ in typs
+                @test Symmetric(convert(Matrix{typ},asym)) == convert(Symmetric{typ,Matrix{typ}},Symmetric(asym))
+            end
+        end
+        if eltya <: Complex && eltya != Int
+            typs = [Complex64,Complex128]
+            for typ in typs
+                @test Hermitian(convert(Matrix{typ},asym)) == convert(Hermitian{typ,Matrix{typ}},Hermitian(asym))
+            end
+        end
     end
 end
 

test/linalg1.jl

@@ -143,6 +143,12 @@ debug && println("non-symmetric eigen decomposition")
     if eltya != BigFloat && eltyb != BigFloat # Revisit when implemented in julia
         d,v   = eig(a)
         for i in 1:size(a,2) @test_approx_eq a*v[:,i] d[i]*v[:,i] end
+        f = eigfact(a)
+        @test_approx_eq det(a) det(f)
+        @test_approx_eq inv(a) inv(f)
+
+        num_fact = eigfact(one(eltya))
+        @test num_fact.values[1] == one(eltya)
     end
 
 debug && println("symmetric generalized eigenproblem")

test/linalg4.jl

@@ -77,6 +77,10 @@ let a=[1.0:n;]
     for newtype in [Diagonal, Bidiagonal, Tridiagonal, SymTridiagonal]
         @test_throws ArgumentError convert(newtype,A)
     end
+    A = Diagonal(a)
+    for newtype in [UpperTriangular, LowerTriangular]
+        @test full(convert(newtype,A)) == full(A)
+    end
 end
 
 # Binary ops among special types