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bug fixes in matrix log #32327

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Sep 23, 2019
Merged

bug fixes in matrix log #32327

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fa16d78
bug fixes in matrix log
stevengj Jun 14, 2019
db1cd35
patches to matrix log (#33245)
RalphAS Sep 20, 2019
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50 changes: 21 additions & 29 deletions stdlib/LinearAlgebra/src/triangular.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -2183,32 +2183,14 @@ function log(A0::UpperTriangular{T}) where T<:BlasFloat
end

# Compute accurate superdiagonal of T
p = 1 / 2^s
for k = 1:n-1
Ak = A0[k,k]
Akp1 = A0[k+1,k+1]
Akp = Ak^p
Akp1p = Akp1^p
A[k,k] = Akp
A[k+1,k+1] = Akp1p
if Ak == Akp1
A[k,k+1] = p * A0[k,k+1] * Ak^(p-1)
elseif 2 * abs(Ak) < abs(Akp1) || 2 * abs(Akp1) < abs(Ak)
A[k,k+1] = A0[k,k+1] * (Akp1p - Akp) / (Akp1 - Ak)
else
logAk = log(Ak)
logAkp1 = log(Akp1)
w = atanh((Akp1 - Ak)/(Akp1 + Ak)) + im*pi*ceil((imag(logAkp1-logAk)-pi)/(2*pi))
dd = 2 * exp(p*(logAk+logAkp1)/2) * sinh(p*w) / (Akp1 - Ak)
A[k,k+1] = A0[k,k+1] * dd
end
end
blockpower!(A, A0, 0.5^s)

# Compute accurate diagonal of T
for i = 1:n
a = A0[i,i]
if s == 0
r = a - 1
A[i,i] = a - 1
continue
end
s0 = s
if angle(a) >= pi / 2
Expand Down Expand Up @@ -2245,7 +2227,7 @@ function log(A0::UpperTriangular{T}) where T<:BlasFloat
end

# Scale back
lmul!(2^s, Y)
lmul!(2.0^s, Y)

# Compute accurate diagonal and superdiagonal of log(T)
for k = 1:n-1
Expand All @@ -2257,11 +2239,16 @@ function log(A0::UpperTriangular{T}) where T<:BlasFloat
Y[k+1,k+1] = logAkp1
if Ak == Akp1
Y[k,k+1] = A0[k,k+1] / Ak
elseif 2 * abs(Ak) < abs(Akp1) || 2 * abs(Akp1) < abs(Ak)
elseif 2 * abs(Ak) < abs(Akp1) || 2 * abs(Akp1) < abs(Ak) || iszero(Akp1 + Ak)
Y[k,k+1] = A0[k,k+1] * (logAkp1 - logAk) / (Akp1 - Ak)
else
w = atanh((Akp1 - Ak)/(Akp1 + Ak) + im*pi*(ceil((imag(logAkp1-logAk) - pi)/(2*pi))))
Y[k,k+1] = 2 * A0[k,k+1] * w / (Akp1 - Ak)
z = (Akp1 - Ak)/(Akp1 + Ak)
if abs(z) > 1
Y[k,k+1] = A0[k,k+1] * (logAkp1 - logAk) / (Akp1 - Ak)
else
w = atanh(z) + im * pi * (unw(logAkp1-logAk) - unw(log1p(z)-log1p(-z)))
Y[k,k+1] = 2 * A0[k,k+1] * w / (Akp1 - Ak)
end
end
end

Expand Down Expand Up @@ -2408,14 +2395,19 @@ function blockpower!(A::UpperTriangular, A0::UpperTriangular, p)

if Ak == Akp1
A[k,k+1] = p * A0[k,k+1] * Ak^(p-1)
elseif 2 * abs(Ak) < abs(Akp1) || 2 * abs(Akp1) < abs(Ak)
elseif 2 * abs(Ak) < abs(Akp1) || 2 * abs(Akp1) < abs(Ak) || iszero(Akp1 + Ak)
A[k,k+1] = A0[k,k+1] * (Akp1p - Akp) / (Akp1 - Ak)
else
logAk = log(Ak)
logAkp1 = log(Akp1)
w = atanh((Akp1 - Ak)/(Akp1 + Ak)) + im * pi * unw(logAkp1-logAk)
dd = 2 * exp(p*(logAk+logAkp1)/2) * sinh(p*w) / (Akp1 - Ak);
A[k,k+1] = A0[k,k+1] * dd
z = (Akp1 - Ak)/(Akp1 + Ak)
if abs(z) > 1
A[k,k+1] = A0[k,k+1] * (Akp1p - Akp) / (Akp1 - Ak)
else
w = atanh(z) + im * pi * (unw(logAkp1-logAk) - unw(log1p(z)-log1p(-z)))
dd = 2 * exp(p*(logAk+logAkp1)/2) * sinh(p*w) / (Akp1 - Ak);
A[k,k+1] = A0[k,k+1] * dd
end
end
end
end
Expand Down
15 changes: 15 additions & 0 deletions stdlib/LinearAlgebra/test/dense.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -903,4 +903,19 @@ end
@test adjoint(factorize(adjoint(a))) == factorize(a)
end

@testset "Matrix log issue #32313" begin
for A in ([30 20; -50 -30], [10.0im 0; 0 -10.0im], randn(6,6))
@test exp(log(A)) ≈ A
end
end

@testset "Matrix log PR #33245" begin
# edge case for divided difference
A1 = triu(ones(3,3),1) + diagm([1.0, -2eps()-1im, -eps()+0.75im])
@test exp(log(A1)) ≈ A1
# case where no sqrt is needed (s=0)
A2 = [1.01 0.01 0.01; 0 1.01 0.01; 0 0 1.01]
@test exp(log(A2)) ≈ A2
end

end # module TestDense