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Fix for eigen not working properly for 2x2 Hermitian SMatrices #957

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Fix for eigen not working properly for 2x2 Hermitian SMatrices #957

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6670fd2
Update eigen.jl
guberger Sep 4, 2021
f5d94d8
Changes _eigvals for 2x2 Hermitian matrices
guberger Sep 4, 2021
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59 changes: 24 additions & 35 deletions src/eigen.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -31,22 +31,11 @@ end

@inline function _eigvals(::Size{(2,2)}, A::LinearAlgebra.RealHermSymComplexHerm{T}, permute, scale) where {T <: Real}
a = A.data

if A.uplo == 'U'
@inbounds t_half = real(a[1] + a[4])/2
@inbounds d = real(a[1]*a[4] - a[3]'*a[3]) # Should be real

tmp2 = t_half*t_half - d
tmp2 < 0 ? tmp = zero(tmp2) : tmp = sqrt(tmp2) # Numerically stable for identity matrices, etc.
return SVector(t_half - tmp, t_half + tmp)
else
@inbounds t_half = real(a[1] + a[4])/2
@inbounds d = real(a[1]*a[4] - a[2]'*a[2]) # Should be real

tmp2 = t_half*t_half - d
tmp2 < 0 ? tmp = zero(tmp2) : tmp = sqrt(tmp2) # Numerically stable for identity matrices, etc.
return SVector(t_half - tmp, t_half + tmp)
end
@inbounds t_half = (real(a[1]) + real(a[4])) / 2
@inbounds s_half = (real(a[1]) - real(a[4])) / 2
@inbounds tmp2 = A.uplo == 'U' ? s_half^2 + abs2(a[3]) : s_half^2 + abs2(a[2]) # expansion of (tr(A)^2 - 4*det(A)) / 4
tmp = sqrt(tmp2) # normally, tmp > 0 if tmp2 > 0
return SVector(t_half - tmp, t_half + tmp)
end

@inline function _eigvals(::Size{(3,3)}, A::LinearAlgebra.RealHermSymComplexHerm{T}, permute, scale) where {T <: Real}
Expand Down Expand Up @@ -158,20 +147,20 @@ end

@inbounds if A.uplo == 'U'
if !iszero(a[3]) # A is not diagonal
t_half = real(a[1] + a[4]) / 2
d = real(a[1] * a[4] - a[3]' * a[3]) # Should be real

tmp2 = t_half * t_half - d
tmp = tmp2 < 0 ? zero(tmp2) : sqrt(tmp2) # Numerically stable for identity matrices, etc.
t_half = (real(a[1]) + real(a[4])) / 2
s_half = (real(a[1]) - real(a[4])) / 2
tmp2 = s_half^2 + abs2(a[3]) # expansion of (tr(A)^2 - 4*det(A)) / 4
# use abs2 to ensure that it is real and > 0 (not sure about x'x being always > 0 if a[3] ≠ 0)
tmp = sqrt(tmp2) # normally, tmp > 0 if tmp2 > 0
vals = SVector(t_half - tmp, t_half + tmp)

v11 = vals[1] - a[4]
n1 = sqrt(v11' * v11 + a[3]' * a[3])
v11 = s_half - tmp
n1 = sqrt(abs2(v11) + abs2(a[3]))
v11 = v11 / n1
v12 = a[3]' / n1

v21 = vals[2] - a[4]
n2 = sqrt(v21' * v21 + a[3]' * a[3])
v21 = s_half + tmp
n2 = sqrt(abs2(v21) + abs2(a[3]))
v21 = v21 / n2
v22 = a[3]' / n2

Expand All @@ -182,27 +171,27 @@ end
end
else # A.uplo == 'L'
if !iszero(a[2]) # A is not diagonal
t_half = real(a[1] + a[4]) / 2
d = real(a[1] * a[4] - a[2]' * a[2]) # Should be real

tmp2 = t_half * t_half - d
tmp = tmp2 < 0 ? zero(tmp2) : sqrt(tmp2) # Numerically stable for identity matrices, etc.
t_half = (real(a[1]) + real(a[4])) / 2
s_half = (real(a[1]) - real(a[4])) / 2
tmp2 = s_half^2 + abs2(a[2]) # expansion of (tr(A)^2 - 4*det(A)) / 4
# use abs2 to ensure that it is real and > 0 (not sure about x'x being always > 0 if a[3] ≠ 0)
tmp = sqrt(tmp2) # normally, tmp > 0 if tmp2 > 0
vals = SVector(t_half - tmp, t_half + tmp)

v11 = vals[1] - a[4]
n1 = sqrt(v11' * v11 + a[2]' * a[2])
v11 = s_half - tmp
n1 = sqrt(abs2(v11) + abs2(a[3]))
v11 = v11 / n1
v12 = a[2] / n1

v21 = vals[2] - a[4]
n2 = sqrt(v21' * v21 + a[2]' * a[2])
v21 = s_half + tmp
n2 = sqrt(abs2(v21) + abs2(a[3]))
v21 = v21 / n2
v22 = a[2] / n2

vecs = @SMatrix [ v11 v21 ;
v12 v22 ]

return Eigen(vals,vecs)
return Eigen(vals, vecs)
end
end

Expand Down