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slight optimization of exp, sqrt, ^ for positive semidefinite output #1359

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Merged
merged 5 commits into from
May 16, 2025
Merged

slight optimization of exp, sqrt, ^ for positive semidefinite output #1359

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aaa32c2
optimization of exp, sqrt, ^
araujoms May 13, 2025
786d49f
use rmul!
araujoms May 13, 2025
8958055
make it work for immutable types
araujoms May 13, 2025
634f7a5
Update src/symmetric.jl
araujoms May 15, 2025
dcbf39e
type stability
araujoms May 15, 2025
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21 changes: 18 additions & 3 deletions src/symmetric.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -833,6 +833,12 @@ function svdvals!(A::RealHermSymComplexHerm)
return sort!(vals, rev = true)
end

#computes U * Diagonal(abs2.(v)) * U', destroying U
function _psd_spectral_product!(v, U)
rmul!(U, Diagonal(v))
return U * U'
end

# Matrix functions
^(A::SymSymTri{<:Complex}, p::Integer) = sympow(A, p)
^(A::SelfAdjoint, p::Integer) = sympow(A, p)
Expand All @@ -848,7 +854,8 @@ function ^(A::SelfAdjoint, p::Real)
isinteger(p) && return integerpow(A, p)
F = eigen(A)
if all(λ -> λ ≥ 0, F.values)
retmat = (F.vectors * Diagonal((F.values).^p)) * F.vectors'
map!(λ -> λ^0.5p, F.values)
retmat = _psd_spectral_product!(F.values, F.vectors)
return wrappertype(A)(retmat)
else
retmat = (F.vectors * Diagonal(complex.(F.values).^p)) * F.vectors'
Expand All @@ -860,7 +867,7 @@ function ^(A::SymSymTri{<:Complex}, p::Real)
return Symmetric(schurpow(A, p))
end

for func in (:exp, :cos, :sin, :tan, :cosh, :sinh, :tanh, :atan, :asinh, :atanh, :cbrt)
for func in (:cos, :sin, :tan, :cosh, :sinh, :tanh, :atan, :asinh, :atanh, :cbrt)
@eval begin
function ($func)(A::SelfAdjoint)
F = eigen(A)
Expand All @@ -870,6 +877,13 @@ for func in (:exp, :cos, :sin, :tan, :cosh, :sinh, :tanh, :atan, :asinh, :atanh,
end
end

function exp(A::SelfAdjoint)
F = eigen(A)
map!(λ -> exp(0.5λ), F.values)
retmat = _psd_spectral_product!(F.values, F.vectors)
return wrappertype(A)(retmat)
end

function cis(A::SelfAdjoint)
F = eigen(A)
retmat = F.vectors .* cis.(F.values') * F.vectors'
Expand Down Expand Up @@ -929,7 +943,8 @@ function sqrt(A::SelfAdjoint; rtol = eps(real(float(eltype(A)))) * size(A, 1))
F = eigen(A)
λ₀ = -maximum(abs, F.values) * rtol # treat λ ≥ λ₀ as "zero" eigenvalues up to roundoff
if all(λ -> λ ≥ λ₀, F.values)
retmat = (F.vectors * Diagonal(sqrt.(max.(0, F.values)))) * F.vectors'
map!(λ -> λ < 0 ? zero(λ) : fourthroot(λ), F.values)
retmat = _psd_spectral_product!(F.values, F.vectors)
return wrappertype(A)(retmat)
else
retmat = (F.vectors * Diagonal(sqrt.(complex.(F.values)))) * F.vectors'
Expand Down