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Specialize norm-related functions for Diagonal #1457

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Specialize norm-related functions for Diagonal #1457

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3261d84
Specialize norm-related functions for Diagonal
jishnub Sep 20, 2025
ba8b30a
Move iteration to within `_generic_normp`
jishnub Sep 20, 2025
5635f3a
Fix generic norm for negative p and add tests
jishnub Sep 20, 2025
f582bfb
Merge generic_normp methods
jishnub Sep 20, 2025
5b56ab6
Optional second argument in `norm` for p=2
jishnub Sep 20, 2025
b83fcba
Move functions next to opnorm
jishnub Sep 20, 2025
e74bdb4
fix `normMinusInf` for 1x1 matrices
jishnub Sep 23, 2025
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17 changes: 17 additions & 0 deletions src/diagonal.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -1111,6 +1111,23 @@ end
/(u::AdjointAbsVec, D::Diagonal) = (D' \ u')'
/(u::TransposeAbsVec, D::Diagonal) = transpose(transpose(D) \ transpose(u))

# norm
function generic_normMinusInf(D::Diagonal)
norm_diag = norm(D.diag, -Inf)
return size(D,1) > 1 ? min(norm_diag, zero(norm_diag)) : norm_diag
end
generic_normInf(D::Diagonal) = norm(D.diag, Inf)
generic_norm1(D::Diagonal) = norm(D.diag, 1)
generic_norm2(D::Diagonal) = norm(D.diag)
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)

_opnorm1(A::Diagonal) = maximum(norm(x) for x in A.diag)
_opnormInf(A::Diagonal) = maximum(norm(x) for x in A.diag)
_opnorm12Inf(A::Diagonal, p) = maximum(opnorm(x, p) for x in A.diag)
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13 changes: 13 additions & 0 deletions test/diagonal.jl
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Expand Up @@ -1576,4 +1576,17 @@ end
@test D == D2
end

@testset "norm" begin
D = Diagonal(float.(1:3))
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@stevengj stevengj Sep 23, 2025 •
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Maybe

for D in ( Diagonal(1:3), Diagonal(1:1), Diagonal(1:0) )

to test the 1x1 and 0x0 cases?

Also, skip the float conversion to make sure the result is floating-point, maybe add a ::Float64 assert to the result

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