Fix generic norm for negative p and add tests

Author: jishnub

src/diagonal.jl

@@ -1249,11 +1249,17 @@ end
 
 # norm
 function generic_normMinusInf(D::Diagonal)
-    norm_diag = generic_normMinusInf(D.diag)
+    norm_diag = norm(D.diag, -Inf)
     min(norm_diag, zero(norm_diag))
 end
-generic_normInf(D::Diagonal) = generic_normInf(D.diag)
-generic_norm1(D::Diagonal) = generic_norm1(D.diag)
-_generic_norm2(D::Diagonal, maxabs) = _generic_norm2(D.diag, maxabs)
-_generic_normp(D::Diagonal, p, maxabs) = _generic_normp(D.diag, p, maxabs)
+generic_normInf(D::Diagonal) = norm(D.diag, Inf)
+generic_norm1(D::Diagonal) = norm(D.diag, 1)
+generic_norm2(D::Diagonal) = norm(D.diag, 2)
+function generic_normp(D::Diagonal, p)
+    v = norm(D.diag, p)
+    if size(D,1) > 1 && p < 0
+        v = norm(zero(v), p)
+    end
+    return v
+end
 norm_x_minus_y(D1::Diagonal, D2::Diagonal) = norm_x_minus_y(D1.diag, D2.diag)

src/generic.jl

@@ -575,11 +575,8 @@ norm_sqr(x::Union{T,Complex{T},Rational{T}}) where {T<:Integer} = abs2(float(x))
 function generic_norm2(x)
     maxabs = normInf(x)
     (ismissing(maxabs) || iszero(maxabs) || isinf(maxabs)) && return maxabs
-    return _generic_norm2(x, maxabs)
-end
-
-function _generic_norm2(x, maxabs::T) where {T}
     (v, s) = iterate(x)::Tuple
+    T = typeof(maxabs)
     if isfinite(length(x)*maxabs*maxabs) && !iszero(maxabs*maxabs) # Scaling not necessary
         sum::promote_type(Float64, T) = norm_sqr(v)
         for v in Iterators.rest(x, s)

test/diagonal.jl

@@ -1576,4 +1576,17 @@ end
     @test D == D2
 end
 
+@testset "norm" begin
+    D = Diagonal(float.(1:3))
+    A = Array(D)
+    @testset for p in -2:2
+        p == 0 && continue
+        @test norm(D, p) ≈ sum(abs.(D).^p)^(1/p)
+        @test norm(D, p) ≈ norm(A, p)
+    end
+    @test norm(D, Inf) ≈ norm(A, Inf)
+    @test norm(D, -Inf) ≈ norm(A, -Inf)
+    @test norm(D, 0) ≈ norm(A, 0)
+end
+
 end # module TestDiagonal