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Tests for A^p for (secretly) Hermitian and diagonal #23060

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Tests for A^p for (secretly) Hermitian and diagonal #23060

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30 changes: 30 additions & 0 deletions test/linalg/dense.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -596,6 +596,36 @@ end
@test (Ad^0.2)^5 ≈ Ad
@test (Ad^(2/3))*(Ad^(1/3)) ≈ Ad
@test (Ad^im)^(-im) ≈ Ad

#Ah : Hermitian Matrix
Ah = convert(Matrix{elty}, [3 1; 1 3])
if elty <: Base.LinAlg.BlasComplex
Ah += [0 im; -im 0]
end
@test Ah^(1/2) ≈ sqrtm(Ah)
@test Ah^(-1/2) ≈ inv(sqrtm(Ah))
@test Ah^(3/4) ≈ sqrtm(Ah) * sqrtm(sqrtm(Ah))
@test Ah^(-3/4) ≈ inv(Ah) * sqrtm(sqrtm(Ah))
@test Ah^(17/8) ≈ Ah^2 * sqrtm(sqrtm(sqrtm(Ah)))
@test Ah^(-17/8) ≈ inv(Ah^2 * sqrtm(sqrtm(sqrtm(Ah))))
@test (Ah^0.2)^5 ≈ Ah
@test (Ah^(2/3))*(Ah^(1/3)) ≈ Ah
@test (Ah^im)^(-im) ≈ Ah

#ADi : Diagonal Matrix
ADi = convert(Matrix{elty}, [3 0; 0 3])
if elty <: Base.LinAlg.BlasComplex
ADi += [im 0; 0 im]
end
@test ADi^(1/2) ≈ sqrtm(ADi)
@test ADi^(-1/2) ≈ inv(sqrtm(ADi))
@test ADi^(3/4) ≈ sqrtm(ADi) * sqrtm(sqrtm(ADi))
@test ADi^(-3/4) ≈ inv(ADi) * sqrtm(sqrtm(ADi))
@test ADi^(17/8) ≈ ADi^2 * sqrtm(sqrtm(sqrtm(ADi)))
@test ADi^(-17/8) ≈ inv(ADi^2 * sqrtm(sqrtm(sqrtm(ADi))))
@test (ADi^0.2)^5 ≈ ADi
@test (ADi^(2/3))*(ADi^(1/3)) ≈ ADi
@test (ADi^im)^(-im) ≈ ADi
end

@testset "Least squares solutions" begin
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