Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Move up the diagonal check in matrix power #23158

Merged
merged 2 commits into from
Aug 7, 2017
Merged
Show file tree
Hide file tree
Changes from all commits
Commits
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
18 changes: 9 additions & 9 deletions base/linalg/dense.jl
Original file line number Diff line number Diff line change
Expand Up @@ -397,6 +397,15 @@ end
function (^)(A::AbstractMatrix{T}, p::Real) where T
n = checksquare(A)

# Quicker return if A is diagonal
if isdiag(A)
retmat = copy(A)
for i in 1:n
retmat[i, i] = retmat[i, i] ^ p
end
return retmat
end

# For integer powers, use power_by_squaring
isinteger(p) && return integerpow(A, p)

Expand All @@ -408,15 +417,6 @@ function (^)(A::AbstractMatrix{T}, p::Real) where T
return (Hermitian(A)^p)
end

# Quicker return if A is diagonal
if isdiag(A)
retmat = copy(A)
for i in 1:n
retmat[i, i] = retmat[i, i] ^ p
end
return retmat
end

# Otherwise, use Schur decomposition
return schurpow(A, p)
end
Expand Down
62 changes: 23 additions & 39 deletions test/linalg/dense.jl
Original file line number Diff line number Diff line change
Expand Up @@ -548,54 +548,38 @@ end
#Aa : only positive real eigenvalues
Aa = convert(Matrix{elty}, [5 4 2 1; 0 1 -1 -1; -1 -1 3 0; 1 1 -1 2])

@test Aa^(1/2) ≈ sqrtm(Aa)
@test Aa^(-1/2) ≈ inv(sqrtm(Aa))
@test Aa^(3/4) ≈ sqrtm(Aa) * sqrtm(sqrtm(Aa))
@test Aa^(-3/4) ≈ inv(Aa) * sqrtm(sqrtm(Aa))
@test Aa^(17/8) ≈ Aa^2 * sqrtm(sqrtm(sqrtm(Aa)))
@test Aa^(-17/8) ≈ inv(Aa^2 * sqrtm(sqrtm(sqrtm(Aa))))
@test (Aa^0.2)^5 ≈ Aa
@test (Aa^(2/3))*(Aa^(1/3)) ≈ Aa
@test (Aa^im)^(-im) ≈ Aa

#Ab : both positive and negative real eigenvalues
Ab = convert(Matrix{elty}, [1 2 3; 4 7 1; 2 1 4])

@test Ab^(1/2) ≈ sqrtm(Ab)
@test Ab^(-1/2) ≈ inv(sqrtm(Ab))
@test Ab^(3/4) ≈ sqrtm(Ab) * sqrtm(sqrtm(Ab))
@test Ab^(-3/4) ≈ inv(Ab) * sqrtm(sqrtm(Ab))
@test Ab^(17/8) ≈ Ab^2 * sqrtm(sqrtm(sqrtm(Ab)))
@test Ab^(-17/8) ≈ inv(Ab^2 * sqrtm(sqrtm(sqrtm(Ab))))
@test (Ab^0.2)^5 ≈ Ab
@test (Ab^(2/3))*(Ab^(1/3)) ≈ Ab
@test (Ab^im)^(-im) ≈ Ab

#Ac : complex eigenvalues
Ac = convert(Matrix{elty}, [5 4 2 1;0 1 -1 -1;-1 -1 3 6;1 1 -1 5])

@test Ac^(1/2) ≈ sqrtm(Ac)
@test Ac^(-1/2) ≈ inv(sqrtm(Ac))
@test Ac^(3/4) ≈ sqrtm(Ac) * sqrtm(sqrtm(Ac))
@test Ac^(-3/4) ≈ inv(Ac) * sqrtm(sqrtm(Ac))
@test Ac^(17/8) ≈ Ac^2 * sqrtm(sqrtm(sqrtm(Ac)))
@test Ac^(-17/8) ≈ inv(Ac^2 * sqrtm(sqrtm(sqrtm(Ac))))
@test (Ac^0.2)^5 ≈ Ac
@test (Ac^(2/3))*(Ac^(1/3)) ≈ Ac
@test (Ac^im)^(-im) ≈ Ac

#Ad : defective Matrix
Ad = convert(Matrix{elty}, [3 1; 0 3])

@test Ad^(1/2) ≈ sqrtm(Ad)
@test Ad^(-1/2) ≈ inv(sqrtm(Ad))
@test Ad^(3/4) ≈ sqrtm(Ad) * sqrtm(sqrtm(Ad))
@test Ad^(-3/4) ≈ inv(Ad) * sqrtm(sqrtm(Ad))
@test Ad^(17/8) ≈ Ad^2 * sqrtm(sqrtm(sqrtm(Ad)))
@test Ad^(-17/8) ≈ inv(Ad^2 * sqrtm(sqrtm(sqrtm(Ad))))
@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

#ADi : Diagonal Matrix
ADi = convert(Matrix{elty}, [3 0; 0 3])
if elty <: Base.LinAlg.BlasComplex
ADi += [im 0; 0 im]
end

for A in (Aa, Ab, Ac, Ad, Ah, ADi)
@test A^(1/2) ≈ sqrtm(A)
@test A^(-1/2) ≈ inv(sqrtm(A))
@test A^(3/4) ≈ sqrtm(A) * sqrtm(sqrtm(A))
@test A^(-3/4) ≈ inv(A) * sqrtm(sqrtm(A))
@test A^(17/8) ≈ A^2 * sqrtm(sqrtm(sqrtm(A)))
@test A^(-17/8) ≈ inv(A^2 * sqrtm(sqrtm(sqrtm(A))))
@test (A^0.2)^5 ≈ A
@test (A^(2/3))*(A^(1/3)) ≈ A
@test (A^im)^(-im) ≈ A
end
end

@testset "Least squares solutions" begin
Expand Down