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The step function should have a generic n_steps > 1 implementation and specialized n_steps == 1 implementation #486

@nsiccha

Description

@nsiccha

As in the title and inspired by #485, see e.g.

function step(
lf::DefaultLeapfrog{FT,T},
h::Hamiltonian,
z::P,
n_steps::Int=1;
fwd::Bool=n_steps > 0, # simulate hamiltonian backward when n_steps < 0
full_trajectory::Val{FullTraj}=Val(false),
) where {FT<:AbstractFloat,T<:AbstractScalarOrVec{FT},P<:PhasePoint,FullTraj}
n_steps = abs(n_steps) # to support `n_steps < 0` cases
ϵ = fwd ? step_size(lf) : -step_size(lf)
ϵ = ϵ'
res = FullTraj ? Vector{P}(undef, n_steps) : nothing
(; θ, r) = z
(; value, gradient) = z.ℓπ
for i in 1:n_steps
# Tempering
r = temper(lf, r, (i=i, is_half=true), n_steps)
# Take a half leapfrog step for momentum variable
r = r - ϵ / 2 .* gradient
# Take a full leapfrog step for position variable
∇r = ∂H∂r(h, r)
θ = θ + ϵ .* ∇r
# Take a half leapfrog step for momentum variable
(; value, gradient) = ∂H∂θ(h, θ)
r = r - ϵ / 2 .* gradient
# Tempering
r = temper(lf, r, (i=i, is_half=false), n_steps)
# Create a new phase point by caching the logdensity and gradient
z = phasepoint(h, θ, r; ℓπ=DualValue(value, gradient))
# Update result
if !isnothing(res)
res[i] = z
end
if !isfinite(z)
# Remove undef
if !isnothing(res)
resize!(res, i)
end
break
end
end
return if FullTraj
res
else
z
end
end

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