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Use safe_sqrt for norms #19

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Use safe_sqrt for norms #19

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ecbd858
Use safe_sqrt for norms
lkdvos Jun 12, 2024
f3c06a8
Compare to absolute eps instead of relative eps
lkdvos Jun 14, 2024
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12 changes: 11 additions & 1 deletion src/OptimKit.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -12,9 +12,19 @@ _add!(vdst, vsrc, α) = LinearAlgebra.axpy!(α, vsrc, vdst)
_precondition(x, g) = g
_finalize!(x, f, g, numiter) = x, f, g

abstract type OptimizationAlgorithm
# print error message and return eps(x) if x is negative
function safe_sqrt(x::Real)
return if x >= 0
sqrt(x)
else
ϵ = eps(typeof(x))
-x < ϵ^(3 / 4) || @error "sqrt of negative number: $x"
ϵ
end
end

abstract type OptimizationAlgorithm
end
const _xlast = Ref{Any}()
const _glast = Ref{Any}()
const _dlast = Ref{Any}()
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6 changes: 3 additions & 3 deletions src/cg.jl
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Expand Up @@ -24,13 +24,13 @@ function optimize(fg, x, alg::ConjugateGradient;
f, g = fg(x)
numfg = 1
innergg = inner(x, g, g)
normgrad = sqrt(innergg)
normgrad = safe_sqrt(innergg)
fhistory = [f]
normgradhistory = [normgrad]

# compute here once to define initial value of α in scale-invariant way
Pg = precondition(x, g)
normPg = sqrt(inner(x, Pg, Pg))
normPg = safe_sqrt(inner(x, Pg, Pg))
α = 1/(normPg) # initial guess: scale invariant
# α = one(normgrad)

Expand Down Expand Up @@ -71,7 +71,7 @@ function optimize(fg, x, alg::ConjugateGradient;
numiter += 1
x, f, g = finalize!(x, f, g, numiter)
innergg = inner(x, g, g)
normgrad = sqrt(innergg)
normgrad = safe_sqrt(innergg)
push!(fhistory, f)
push!(normgradhistory, normgrad)

Expand Down
6 changes: 3 additions & 3 deletions src/gd.jl
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Expand Up @@ -19,13 +19,13 @@ function optimize(fg, x, alg::GradientDescent;
f, g = fg(x)
numfg = 1
innergg = inner(x, g, g)
normgrad = sqrt(innergg)
normgrad = safe_sqrt(innergg)
fhistory = [f]
normgradhistory = [normgrad]

# compute here once to define initial value of α in scale-invariant way
Pg = precondition(x, g)
normPg = sqrt(inner(x, Pg, Pg))
normPg = safe_sqrt(inner(x, Pg, Pg))
α = 1/(normPg) # initial guess: scale invariant

numiter = 0
Expand All @@ -46,7 +46,7 @@ function optimize(fg, x, alg::GradientDescent;
numiter += 1
x, f, g = finalize!(x, f, g, numiter)
innergg = inner(x, g, g)
normgrad = sqrt(innergg)
normgrad = safe_sqrt(innergg)
push!(fhistory, f)
push!(normgradhistory, normgrad)

Expand Down
12 changes: 6 additions & 6 deletions src/lbfgs.jl
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Expand Up @@ -21,7 +21,7 @@ function optimize(fg, x, alg::LBFGS;
f, g = fg(x)
numfg = 1
innergg = inner(x, g, g)
normgrad = sqrt(innergg)
normgrad = safe_sqrt(innergg)
fhistory = [f]
normgradhistory = [normgrad]

Expand All @@ -43,7 +43,7 @@ function optimize(fg, x, alg::LBFGS;
η = scale!(Hg, -1)
else
Pg = precondition(x, deepcopy(g))
normPg = sqrt(inner(x, Pg, Pg))
normPg = safe_sqrt(inner(x, Pg, Pg))
η = scale!(Pg, -1/normPg) # initial guess: scale invariant
end

Expand All @@ -64,7 +64,7 @@ function optimize(fg, x, alg::LBFGS;
numiter += 1
x, f, g = finalize!(x, f, g, numiter)
innergg = inner(x, g, g)
normgrad = sqrt(innergg)
normgrad = safe_sqrt(innergg)
push!(fhistory, f)
push!(normgradhistory, normgrad)

Expand Down Expand Up @@ -95,8 +95,8 @@ function optimize(fg, x, alg::LBFGS;
# define new isometric transport such that, applying it to transported ηprev,
# it returns a vector proportional to ξ but with the norm of ηprev
# still has norm normη because transport is isometric
normη = sqrt(inner(x, ηprev, ηprev))
normξ = sqrt(inner(x, ξ, ξ))
normη = safe_sqrt(inner(x, ηprev, ηprev))
normξ = safe_sqrt(inner(x, ξ, ξ))
β = normη/normξ
if !(inner(x, ξ, ηprev) ≈ normξ * normη) # ξ and η are not parallel
ξ₁ = ηprev
Expand Down Expand Up @@ -131,7 +131,7 @@ function optimize(fg, x, alg::LBFGS;
innerss = inner(x, s, s)

if innersy/innerss > normgrad/10000
norms = sqrt(innerss)
norms = safe_sqrt(innerss)
ρ = innerss/innersy
push!(H, (scale!(s, 1/norms), scale!(y, 1/norms), ρ))
end
Expand Down
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