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Take samples at distances proportional to speed. Refresh proportional to speed. #112

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Take samples at distances proportional to speed. Refresh proportional to speed. #112

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5e8b239
Use findmin
mschauer Jun 20, 2022
c79d701
Move function
mschauer Jun 20, 2022
f61abfd
Use non-equidistant sample scheme
mschauer Jun 20, 2022
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112 changes: 65 additions & 47 deletions src/not_fact_samplers.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -29,15 +29,12 @@ end
function ab(x, θ, C::LocalBound, ∇ϕx::AbstractVector, v, B::BouncyParticle)
(C.c + dot(θ, ∇ϕx), v, 2sqrt(length(θ))/C.c/norm(θ, 2))
end
function ab(x, θ, C::LocalBound, vdϕ::Number, v, B::BouncyParticle)
@assert vdϕ isa Number
(C.c + vdϕ, v, 2sqrt(length(θ))/C.c/norm(θ, 2))
end


function ab(x, θ, C::GlobalBound, ∇ϕx, v, B::Boomerang)
(sqrt(normsq(θ) + normsq((x - B.μ)))*C.c, 0.0, Inf)
end
ab(x, θ, c, Flow) = ab(x, θ, GlobalBound(c), nothing, nothing, Flow)
ab(x, θ, c, flow) = ab(x, θ, GlobalBound(c), nothing, nothing, flow)

function event(t, x, θ, Z::Union{BouncyParticle,Boomerang})
t, copy(x), copy(θ), nothing
Expand Down Expand Up @@ -150,34 +147,55 @@ function pdmp(∇ϕ!, t0, x0, θ0, T, c::Bound, Flow::Union{BouncyParticle, Boom
end


##################################
################################## ##################################
function ab(t, x, θ, C::LocalBound, vdϕ::Number, v, B::BouncyParticle)
@assert vdϕ isa Number
(C.c + vdϕ, v, t + 2sqrt(length(θ))/C.c/norm(θ, 2))
end

function pdmp_inner!(rng, dϕ::F1, ∇ϕ!::F2, ∇ϕx, t, x, θ, c::Bound, abc, (t′, renew), τref, (acc, num),
Flow::BouncyParticle, args...; subsample=false, oscn=false, factor=1.5, adapt=false) where {F1, F2}
function next_event1(rng, u::Tuple, abc, flow)
t, x, v, V = u
a, b, Δ = abc
τ = t + poisson_time(a, b, rand(rng))
τrefresh = t + waiting_time_ref(rng, flow)/V
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Refreshment at intensity corresponding to speed

when, what = findmin((τ, Δ, τrefresh))
return when, (:bounce, :expire, :refresh)[what]
end

function pdmp_inner!(rng, dϕ::F1, ∇ϕ!::F2, ∇ϕx, t, x, θ, V, c::Bound, abc, (t′, action), Δrec, (acc, num),
flow::BouncyParticle, args...; subsample=false, oscn=false, factor=1.5, adapt=false) where {F1, F2}
while true
if τref < t′
t, _ = move_forward!(τref - t, t, x, θ, Flow)
refresh!(rng, θ, Flow)
if t + Δrec/V <= t′ # record! (large speed, more records)
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Take samples of the particle position at deterministic time intervals (to reduce sampling error), but measure time proportional to speed (large speed, more samples taken)

t, _ = move_forward!(V\Δrec, t, x, θ, flow)
Δrec = 1/flow.λref
return t, V, (acc, num), c, abc, (t′, action), Δrec
end
Δrec = Δrec - (t′ - t)*V # coming closer to rec
@assert Δrec > 0.0
if action == :refresh
@assert Δrec >= 0
t, _ = move_forward!(t′ - t, t, x, θ, flow)
refresh!(rng, θ, flow)
V = norm(θ, 2)
θdϕ, v = dϕ(t, x, θ, args...)
#∇ϕx = grad_correct!(∇ϕx, x, Flow)
l = λ(θdϕ, Flow)
τref = t + waiting_time_ref(rng, Flow)
abc = ab(x, θ, c, θdϕ, v, Flow)
t′, renew = next_time(t, abc, rand(rng))
return t, (acc, num), c, abc, (t′, renew), τref
elseif renew
#∇ϕx = grad_correct!(∇ϕx, x, flow)
l = λ(θdϕ, flow)
abc = ab(t, x, θ, c, θdϕ, v, flow)
t′, action = next_event1(rng, (t, x, θ, V), abc, flow)
#return t, V, (acc, num), c, abc, (t′, action), Δrec
elseif action == :expire
τ = t′ - t
t, _ = move_forward!(τ, t, x, θ, Flow)
t, _ = move_forward!(τ, t, x, θ, flow)
θdϕ, v = dϕ(t, x, θ, args...)
#∇ϕx = grad_correct!(∇ϕx, x, Flow)
abc = ab(x, θ, c, θdϕ, v, Flow)
t′, renew = next_time(t, abc, rand(rng))
else
#∇ϕx = grad_correct!(∇ϕx, x, flow)
abc = ab(t, x, θ, c, θdϕ, v, flow)
t′, action = next_event1(rng, (t, x, θ, V), abc, flow)
else # action == :reflect
τ = t′ - t
t, _ = move_forward!(τ, t, x, θ, Flow)
t, _ = move_forward!(τ, t, x, θ, flow)
θdϕ, v = dϕ(t, x, θ, args...)
#∇ϕx = grad_correct!(∇ϕx, x, Flow)
l, lb = λ(θdϕ, Flow), pos(abc[1] + abc[2]*τ)
#∇ϕx = grad_correct!(∇ϕx, x, flow)
l, lb = λ(θdϕ, flow), pos(abc[1] + abc[2]*τ)
num += 1
if rand(rng)*lb <= l
acc += 1
Expand All @@ -191,25 +209,25 @@ function pdmp_inner!(rng, dϕ::F1, ∇ϕ!::F2, ∇ϕx, t, x, θ, c::Bound, abc,
#error("subsampling needs to be seeded by time")
end
if oscn
@assert Flow.L == I
oscn!(rng, θ, ∇ϕx, Flow.ρ; normalize=false)
@assert flow.L == I
oscn!(rng, θ, ∇ϕx, flow.ρ; normalize=false)
else
reflect!(∇ϕx, x, θ, Flow)
reflect!(∇ϕx, x, θ, flow)
end
θdϕ, v = dϕ(t, x, θ, args...)
#∇ϕx = grad_correct!(∇ϕx, x, Flow)
abc = ab(x, θ, c, θdϕ, v, Flow)
t′, renew = next_time(t, abc, rand(rng))
!subsample && return t, (acc, num), c, abc, (t′, renew), τref
#∇ϕx = grad_correct!(∇ϕx, x, flow)
abc = ab(t, x, θ, c, θdϕ, v, flow)
t′, action = next_event1(rng, (t, x, θ, V), abc, flow)
#!subsample && return t, V, (acc, num), c, abc, (t′, action), Δrec
else
abc = ab(x, θ, c, θdϕ, v, Flow)
t′, renew = next_time(t, abc, rand(rng))
abc = ab(t, x, θ, c, θdϕ, v, flow)
t′, action = next_event1(rng, (t, x, θ, V), abc, flow)
end
end
end
end
"""
pdmp(dϕ, ∇ϕ!, t0, x0, θ0, T, c::Bound, Flow::BouncyParticle, args...; oscn=false, adapt=false, subsample=false, progress=false, progress_stops = 20, islocal = false, seed=Seed(), factor=2.0)
pdmp(dϕ, ∇ϕ!, t0, x0, θ0, T, c::Bound, flow::BouncyParticle, args...; oscn=false, adapt=false, subsample=false, progress=false, progress_stops = 20, islocal = false, seed=Seed(), factor=2.0)

The first directional derivative `dϕ[1]` tells me if I move up or down the potential. The second directional derivative `dϕ[2]` tells me how fast the first changes. The gradient `∇ϕ!` tells me the surface I want to reflect on.

Expand Down Expand Up @@ -256,31 +274,31 @@ The remaining arguments:
t, x = ZigZagBoomerang.sep(trace)

"""
function pdmp(dϕ, ∇ϕ!, t0, x0, θ0, T, c::Bound, Flow::BouncyParticle, args...; oscn=false, adapt=false, subsample=false, progress=false, progress_stops = 20, islocal = false, seed=Seed(), factor=2.0)
function pdmp(dϕ, ∇ϕ!, t0, x0, θ0, T, c::Bound, flow::BouncyParticle, args...; oscn=false, adapt=false, subsample=false, progress=false, progress_stops = 20, islocal = false, seed=Seed(), factor=2.0)
t, x, θ, ∇ϕx = t0, copy(x0), copy(θ0), copy(θ0)
V = norm(θ, 2)
rng = Rng(seed)
Ξ = Trace(t0, x0, θ0, Flow)
τref = waiting_time_ref(rng, Flow)
Ξ = Trace(t0, x0, θ0, flow)
θdϕ, v = dϕ(t, x, θ, args...)
#@assert v2 ≈ v
#@assert θdϕ ≈ dot(∇ϕx, θ)

#∇ϕx = grad_correct!(∇ϕx, x, Flow)
#∇ϕx = grad_correct!(∇ϕx, x, flow)
num = acc = 0
#l = 0.0
abc = ab(x, θ, c, θdϕ, v, Flow)
abc = ab(t, x, θ, c, θdϕ, v, flow)
if progress
prg = Progress(progress_stops, 1)
else
prg = missing
end
stops = ismissing(prg) ? 0 : max(prg.n - 1, 0) # allow one stop for cleanup
tstop = T/stops

t′, renew = next_time(t, abc, rand(rng))
Δrec = 1/flow.λref
t′, action = next_event1(rng, (t, x, θ, V), abc, flow)
while t < T
t, (acc, num), c, abc, (t′, renew), τref = pdmp_inner!(rng, dϕ, ∇ϕ!, ∇ϕx, t, x, θ, c, abc, (t′, renew), τref, (acc, num), Flow, args...; oscn=oscn, subsample=subsample, factor=factor, adapt=adapt)
push!(Ξ, event(t, x, θ, Flow))
t, V, (acc, num), c, abc, (t′, action), Δrec = pdmp_inner!(rng, dϕ, ∇ϕ!, ∇ϕx, t, x, θ, V, c, abc, (t′, action), Δrec, (acc, num), flow, args...; oscn=oscn, subsample=subsample, factor=factor, adapt=adapt)
push!(Ξ, event(t, x, θ, flow))

if t > tstop
tstop += T/stops
Expand All @@ -299,5 +317,5 @@ struct Wrapper{F}
end
(F::Wrapper)(y, t, x, θ, args...) = F.f(y, x, args...), nothing

pdmp(∇ϕ!, t0, x0, θ0, T, c, Flow::Union{BouncyParticle, Boomerang}, args...; nargs...) =
pdmp(Wrapper(∇ϕ!), t0, x0, θ0, T, GlobalBound(c), Flow, args...; nargs...)
pdmp(∇ϕ!, t0, x0, θ0, T, c, flow::Union{BouncyParticle, Boomerang}, args...; nargs...) =
pdmp(Wrapper(∇ϕ!), t0, x0, θ0, T, GlobalBound(c), flow, args...; nargs...)
23 changes: 11 additions & 12 deletions src/notfactiter.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -58,31 +58,30 @@ end

function iterate(FS::NotFactSampler{<:Any, <:Tuple})
t0, (x0, θ0) = FS.u0
Flow = FS.F
flow = FS.F
n = length(x0)
t, x, θ, ∇ϕx = t0, copy(x0), copy(θ0), copy(θ0)
V = norm(θ, 2)
c = FS.c
rng = FS.rng
τref = waiting_time_ref(rng, Flow)

Δrec = 1/flow.λref

dϕ, ∇ϕ! = FS.∇ϕ![1], FS.∇ϕ![2]
θdϕ, v = dϕ(t, x, θ, FS.args...)
num = acc = 0
abc = ab(x, θ, c, θdϕ, v, Flow)

t′, renew = next_time(t, abc, rand(rng))
iterate(FS, ((t => (x, θ)), ∇ϕx, (acc, num), c, abc, (t′, renew), τref))
abc = ab(t, x, θ, c, θdϕ, v, flow)
t′, action = next_event1(rng, (t, x, θ, V), abc, flow)
iterate(FS, ((t => (x, θ, V)), ∇ϕx, (acc, num), c, abc, (t′, action), Δrec))
end
using Test


function iterate(FS::NotFactSampler{<:Any, <:Tuple}, (u, ∇ϕx, (acc, num), c, abc, (t′, renew), τref))
t, (x, θ) = u
function iterate(FS::NotFactSampler{<:Any, <:Tuple}, (u, ∇ϕx, (acc, num), c, abc, (t′, action), Δrec))
t, (x, θ, V) = u
dϕ, ∇ϕ! = FS.∇ϕ![1], FS.∇ϕ![2]
t, (acc, num), c, abc, (t′, renew), τref = pdmp_inner!(FS.rng, dϕ, ∇ϕ!, ∇ϕx, t, x, θ, c, abc, (t′, renew), τref, (acc, num), FS.F, FS.args...; FS.kargs...)
t, V, (acc, num), c, abc, (t′, action), Δrec = pdmp_inner!(FS.rng, dϕ, ∇ϕ!, ∇ϕx, t, x, θ, V, c, abc, (t′, action), Δrec, (acc, num), FS.F, FS.args...; FS.kargs...)

ev = rawevent(t, x, θ, FS.F)
u = t => (x, θ)
return ev, (u, ∇ϕx, (acc, num), c, abc, (t′, renew), τref)
u = t => (x, θ, V)
return ev, (u, ∇ϕx, (acc, num), c, abc, (t′, action), Δrec)
end