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symplectic_perform_step.jl
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symplectic_perform_step.jl
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# http://www.chimica.unipd.it/antonino.polimeno/pubblica/downloads/JChemPhys_101_4062.pdf
function initialize!(integrator, cache::SymplecticEulerConstantCache)
integrator.kshortsize = 2
integrator.k = typeof(integrator.k)(undef, integrator.kshortsize)
# Do the calculation pre
# So that way FSAL interpolation
duprev, uprev = integrator.uprev.x
du, u = integrator.u.x
kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t)
kuprev = integrator.f.f2(duprev, uprev, integrator.p, integrator.t)
@muladd du = duprev + integrator.dt * kdu
ku = integrator.f.f2(du, uprev, integrator.p, integrator.t)
integrator.stats.nf2 += 1
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 2)
integrator.fsalfirst = ArrayPartition((kdu, kuprev))
integrator.fsallast = ArrayPartition((zero(kdu), ku))
end
@muladd function perform_step!(integrator, cache::SymplecticEulerConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
duprev, uprev = integrator.uprev.x
kuprev = integrator.fsalfirst.x[2]
u = uprev + dt * kuprev
# Now actually compute the step
# Do it at the end for interpolations!
kdu = f.f1(duprev, u, p, t)
du = duprev + dt * kdu
ku = f.f2(du, u, p, t)
integrator.stats.nf2 += 1
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
integrator.u = ArrayPartition((du, u))
integrator.fsallast = ArrayPartition((kdu, ku))
integrator.k[1] = integrator.fsalfirst
integrator.k[2] = integrator.fsallast
end
function initialize!(integrator, cache::SymplecticEulerCache)
integrator.kshortsize = 2
resize!(integrator.k, integrator.kshortsize)
integrator.k[1] = integrator.fsalfirst
integrator.k[2] = integrator.fsallast
# Do the calculation pre
# So that way FSAL interpolation
duprev, uprev = integrator.uprev.x
du, u = integrator.u.x
kuprev = integrator.fsalfirst.x[2]
kdu, ku = integrator.fsallast.x
integrator.f.f1(kdu, duprev, uprev, integrator.p, integrator.t)
integrator.f.f2(kuprev, duprev, uprev, integrator.p, integrator.t)
@muladd @.. broadcast=false du=duprev + integrator.dt * kdu
integrator.f.f2(ku, du, uprev, integrator.p, integrator.t)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
integrator.stats.nf2 += 2
end
@muladd function perform_step!(integrator, cache::SymplecticEulerCache, repeat_step = false)
@unpack t, dt, f, p = integrator
duprev, uprev = integrator.uprev.x
du, u = integrator.u.x
kuprev = integrator.fsalfirst.x[2]
kdu, ku = integrator.fsallast.x
@.. broadcast=false u=uprev + dt * kuprev
# Now actually compute the step
# Do it at the end for interpolations!
integrator.stats.nf2 += 1
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
f.f1(kdu, duprev, u, p, t)
@.. broadcast=false du=duprev + dt * kdu
f.f2(ku, du, u, p, t)
end
# some of the algorithms are designed only for the case
# f.f2(p, q, pa, t) = p which is the Newton/Lagrange equations
# If called with different functions (which are possible in the Hamiltonian case)
# an exception is thrown to avoid silently calculate wrong results.
verify_f2(f, p, q, pa, t, ::Any, ::C) where {C <: HamiltonConstantCache} = f(p, q, pa, t)
function verify_f2(f, res, p, q, pa, t, ::Any, ::C) where {C <: HamiltonMutableCache}
f(res, p, q, pa, t)
end
function verify_f2(f, p, q, pa, t, integrator, ::C) where {C <: VelocityVerletConstantCache}
res = f(p, q, pa, t)
res == p ? p : throwex(integrator)
end
function verify_f2(f, res, p, q, pa, t, integrator, ::C) where {C <: VelocityVerletCache}
f(res, p, q, pa, t)
res == p ? res : throwex(integrator)
end
function throwex(integrator)
algn = typeof(integrator.alg)
throw(ArgumentError("Algorithm $algn is not applicable if f2(p, q, t) != p"))
end
# provide the mutable uninitialized objects to keep state and derivative in case of mutable caches
# no such objects are required for constant caches
function alloc_symp_state(integrator)
(integrator.u.x..., integrator.cache.tmp.x...)
end
# load state and derivatives at begin of symplectic iteration steps
function load_symp_state(integrator)
(integrator.uprev.x..., integrator.fsallast.x...)
end
# store state and derivatives at the end of symplectic iteration steps
function store_symp_state!(integrator, ::OrdinaryDiffEqConstantCache, du, u, kdu, ku)
integrator.u = ArrayPartition((du, u))
integrator.fsallast = ArrayPartition((kdu, ku))
integrator.k[1] = integrator.fsalfirst
integrator.k[2] = integrator.fsallast
nothing
end
function store_symp_state!(integrator, ::OrdinaryDiffEqMutableCache, kdu, ku)
copyto!(integrator.k[1].x[1], integrator.k[2].x[1])
copyto!(integrator.k[1].x[2], integrator.k[2].x[2])
copyto!(integrator.k[2].x[2], ku)
copyto!(integrator.k[2].x[1], kdu)
nothing
end
function initialize!(integrator,
cache::C) where {C <:
Union{HamiltonMutableCache, VelocityVerletCache}}
integrator.kshortsize = 2
resize!(integrator.k, integrator.kshortsize)
integrator.k[1] = integrator.fsalfirst
integrator.k[2] = integrator.fsallast
duprev, uprev = integrator.uprev.x
integrator.f.f1(integrator.k[2].x[1], duprev, uprev, integrator.p, integrator.t)
verify_f2(integrator.f.f2, integrator.k[2].x[2], duprev, uprev, integrator.p,
integrator.t, integrator, cache)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
integrator.stats.nf2 += 1
end
function initialize!(integrator,
cache::C) where {
C <:
Union{HamiltonConstantCache, VelocityVerletConstantCache}}
integrator.kshortsize = 2
integrator.k = typeof(integrator.k)(undef, integrator.kshortsize)
duprev, uprev = integrator.uprev.x
kdu = integrator.f.f1(duprev, uprev, integrator.p, integrator.t)
ku = verify_f2(integrator.f.f2, duprev, uprev, integrator.p, integrator.t, integrator,
cache)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
integrator.stats.nf2 += 1
integrator.fsallast = ArrayPartition((kdu, ku))
integrator.k[2] = integrator.fsallast
integrator.fsalfirst = integrator.fsallast
end
@muladd function perform_step!(integrator, cache::VelocityVerletConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
duprev, uprev = load_symp_state(integrator)
# x(t+Δt) = x(t) + v(t)*Δt + 1/2*a(t)*Δt^2
ku = integrator.fsallast.x[1]
dtsq = dt^2
half = cache.half
u = uprev + dt * duprev + dtsq * (half * ku)
kdu = f.f1(duprev, u, p, t + dt)
# v(t+Δt) = v(t) + 1/2*(a(t)+a(t+Δt))*Δt
du = duprev + dt * (half * ku + half * kdu)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 2)
store_symp_state!(integrator, cache, du, u, kdu, du)
end
@muladd function perform_step!(integrator, cache::VelocityVerletCache, repeat_step = false)
@unpack t, dt, f, p = integrator
duprev, uprev = load_symp_state(integrator)
du, u, kdu, ku = alloc_symp_state(integrator)
# x(t+Δt) = x(t) + v(t)*Δt + 1/2*a(t)*Δt^2
ku = integrator.fsallast.x[1]
dtsq = dt^2
half = cache.half
@.. broadcast=false u=uprev + dt * duprev + dtsq * (half * ku)
f.f1(kdu, duprev, u, p, t + dt)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 2)
# v(t+Δt) = v(t) + 1/2*(a(t)+a(t+Δt))*Δt
@.. broadcast=false du=duprev + dt * (half * ku + half * kdu)
store_symp_state!(integrator, cache, kdu, du)
end
@muladd function perform_step!(integrator, cache::Symplectic2ConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, b1, b2 = cache
duprev, uprev, _, kuprev = load_symp_state(integrator)
# update position
u = uprev + dt * b1 * kuprev
# update velocity
kdu = f.f1(duprev, u, p, t)
du = duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b2 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a2 * kdu
kdu = f.f1(du, u, p, tnew)
ku = f.f2(du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 3)
integrator.stats.nf2 += 2
store_symp_state!(integrator, cache, du, u, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic2Cache, repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, b1, b2 = cache.tab
duprev, uprev, _, kuprev = load_symp_state(integrator)
du, u, kdu, ku = alloc_symp_state(integrator)
# update position
@.. broadcast=false u=uprev + dt * b1 * kuprev
# update velocity
f.f1(kdu, duprev, u, p, t)
@.. broadcast=false du=duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b2 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a2 * kdu
f.f1(kdu, du, u, p, tnew)
f.f2(ku, du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 3)
integrator.stats.nf2 += 2
store_symp_state!(integrator, cache, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic3ConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, b1, b2, b3 = cache
duprev, uprev, _, kuprev = load_symp_state(integrator)
# update position
u = uprev + dt * b1 * kuprev
# update velocity
kdu = f.f1(duprev, u, p, integrator.t)
du = duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b2 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b3 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a3 * kdu
kdu = f.f1(du, u, p, tnew)
ku = f.f2(du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 4)
integrator.stats.nf2 += 3
store_symp_state!(integrator, cache, du, u, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic3Cache, repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, b1, b2, b3 = cache.tab
duprev, uprev, _, kuprev = load_symp_state(integrator)
du, u, kdu, ku = alloc_symp_state(integrator)
# update position
@.. broadcast=false u=uprev + dt * b1 * kuprev
# update velocity
f.f1(kdu, duprev, u, p, integrator.t)
@.. broadcast=false du=duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b2 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b3 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a3 * kdu
f.f1(kdu, du, u, p, tnew)
f.f2(ku, du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 4)
integrator.stats.nf2 += 3
store_symp_state!(integrator, cache, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic4ConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, b1, b2, b3, b4 = cache
duprev, uprev, _, kuprev = load_symp_state(integrator)
# update position
u = uprev + dt * b1 * kuprev
# update velocity
kdu = f.f1(duprev, u, p, t)
du = duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b2 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b3 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b4 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a4 * kdu
kdu = f.f1(du, u, p, tnew)
ku = f.f2(du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 5)
integrator.stats.nf2 += 4
store_symp_state!(integrator, cache, du, u, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic4Cache, repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, b1, b2, b3, b4 = cache.tab
duprev, uprev, _, kuprev = load_symp_state(integrator)
du, u, kdu, ku = alloc_symp_state(integrator)
# update position
@.. broadcast=false u=uprev + dt * b1 * kuprev
# update velocity
f.f1(kdu, duprev, u, p, t)
@.. broadcast=false du=duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b2 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b3 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b4 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a4 * kdu
f.f1(kdu, du, u, p, tnew)
f.f2(ku, du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 5)
integrator.stats.nf2 += 4
store_symp_state!(integrator, cache, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic45ConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
alg = unwrap_alg(integrator, false)
@unpack a1, a2, a3, a4, a5, b1, b2, b3, b4, b5 = cache
duprev, uprev, _, kuprev = load_symp_state(integrator)
# update position
u = uprev + dt * b1 * kuprev
# update velocity
kdu = f.f1(duprev, u, p, t)
du = duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b2 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b3 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b4 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b5 * ku
kdu = f.f1(du, u, p, tnew)
if alg isa McAte42
du = du + dt * a5 * kdu
kdu = f.f1(du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
end
ku = f.f2(du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 5)
integrator.stats.nf2 += 5
store_symp_state!(integrator, cache, du, u, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic45Cache, repeat_step = false)
@unpack t, dt, f, p = integrator
alg = unwrap_alg(integrator, false)
@unpack a1, a2, a3, a4, a5, b1, b2, b3, b4, b5 = cache.tab
duprev, uprev, _, kuprev = load_symp_state(integrator)
du, u, kdu, ku = alloc_symp_state(integrator)
# update position
@.. broadcast=false u=uprev + dt * b1 * kuprev
# update velocity
f.f1(kdu, duprev, u, p, t)
@.. broadcast=false du=duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b2 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b3 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b4 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b5 * ku
f.f1(kdu, du, u, p, tnew)
if alg isa McAte42
@.. broadcast=false du=du + dt * a5 * kdu
f.f1(kdu, du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 1)
end
f.f2(ku, du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 5)
integrator.stats.nf2 += 5
store_symp_state!(integrator, cache, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic5ConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6 = cache
duprev, uprev, _, kuprev = load_symp_state(integrator)
# update position
u = uprev + dt * b1 * kuprev
# update velocity
kdu = f.f1(duprev, u, p, integrator.t)
du = duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b2 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b3 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b4 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b5 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a5 * kdu
tnew = tnew + a5 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b6 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a6 * kdu
kdu = f.f1(du, u, p, tnew)
ku = f.f2(du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 7)
integrator.stats.nf2 += 6
store_symp_state!(integrator, cache, du, u, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic5Cache, repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, a5, a6, b1, b2, b3, b4, b5, b6 = cache.tab
duprev, uprev, _, kuprev = load_symp_state(integrator)
du, u, kdu, ku = alloc_symp_state(integrator)
# update position
@.. broadcast=false u=uprev + dt * b1 * kuprev
# update velocity
f.f1(kdu, duprev, u, p, integrator.t)
@.. broadcast=false du=duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b2 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b3 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b4 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b5 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a5 * kdu
tnew = tnew + a5 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b6 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a6 * kdu
f.f1(kdu, du, u, p, tnew)
f.f2(ku, du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 7)
integrator.stats.nf2 += 6
store_symp_state!(integrator, cache, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic6ConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, a5, a6, a7, a8, b1, b2, b3, b4, b5, b6, b7, b8 = cache
duprev, uprev, _, kuprev = load_symp_state(integrator)
# update position
u = uprev + dt * b1 * kuprev
# update velocity
kdu = f.f1(duprev, u, p, integrator.t)
du = duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b2 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b3 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b4 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b5 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a5 * kdu
tnew = tnew + a5 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b6 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a6 * kdu
tnew = tnew + a6 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b7 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a7 * kdu
tnew = tnew + a7 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b8 * ku
kdu = f.f1(du, u, p, tnew)
# @.. broadcast=false du = du + dt*a8*kdu
ku = f.f2(du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 8)
integrator.stats.nf2 += 8
store_symp_state!(integrator, cache, du, u, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic6Cache, repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, a5, a6, a7, a8, b1, b2, b3, b4, b5, b6, b7, b8 = cache.tab
duprev, uprev, _, kuprev = load_symp_state(integrator)
du, u, kdu, ku = alloc_symp_state(integrator)
# update position
@.. broadcast=false u=uprev + dt * b1 * kuprev
# update velocity
f.f1(kdu, duprev, u, p, integrator.t)
@.. broadcast=false du=duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b2 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b3 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b4 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b5 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a5 * kdu
tnew = tnew + a5 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b6 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a6 * kdu
tnew = tnew + a6 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b7 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a7 * kdu
tnew = tnew + a7 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b8 * ku
f.f1(kdu, du, u, p, tnew)
# @.. broadcast=false du = du + dt*a8*kdu
f.f2(ku, du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 8)
integrator.stats.nf2 += 8
store_symp_state!(integrator, cache, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic62ConstantCache,
repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10 = cache
duprev, uprev, _, kuprev = load_symp_state(integrator)
# update position
u = uprev + dt * b1 * kuprev
# update velocity
kdu = f.f1(duprev, u, p, integrator.t)
du = duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b2 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b3 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b4 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b5 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a5 * kdu
tnew = tnew + a5 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b6 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a6 * kdu
tnew = tnew + a6 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b7 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a7 * kdu
tnew = tnew + a7 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b8 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a8 * kdu
tnew = tnew + a8 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b9 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a9 * kdu
tnew = tnew + a9 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b10 * ku
kdu = f.f1(du, u, p, tnew)
# @.. broadcast=false du = du + dt*a10*kdu
ku = f.f2(du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 10)
integrator.stats.nf2 += 10
store_symp_state!(integrator, cache, du, u, kdu, ku)
end
@muladd function perform_step!(integrator, cache::Symplectic62Cache, repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10 = cache.tab
duprev, uprev, _, kuprev = load_symp_state(integrator)
du, u, kdu, ku = alloc_symp_state(integrator)
# update position
@.. broadcast=false u=uprev + dt * b1 * kuprev
# update velocity
f.f1(kdu, duprev, u, p, integrator.t)
@.. broadcast=false du=duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b2 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b3 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b4 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b5 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a5 * kdu
tnew = tnew + a5 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b6 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a6 * kdu
tnew = tnew + a6 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b7 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a7 * kdu
tnew = tnew + a7 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b8 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a8 * kdu
tnew = tnew + a8 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b9 * ku
f.f1(kdu, du, u, p, tnew)
@.. broadcast=false du=du + dt * a9 * kdu
tnew = tnew + a9 * dt
f.f2(ku, du, u, p, tnew)
@.. broadcast=false u=u + dt * b10 * ku
f.f1(kdu, du, u, p, tnew)
# @.. broadcast=false du = du + dt*a10*kdu
f.f2(ku, du, u, p, tnew)
OrdinaryDiffEqCore.increment_nf!(integrator.stats, 10)
integrator.stats.nf2 += 10
store_symp_state!(integrator, cache, kdu, ku)
end
@muladd function perform_step!(integrator, cache::McAte8ConstantCache, repeat_step = false)
@unpack t, dt, f, p = integrator
@unpack a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14, a15, a16,
b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12, b13, b14, b15, b16 = cache
duprev, uprev, _, kuprev = load_symp_state(integrator)
# update position
u = uprev + dt * b1 * kuprev
# update velocity
kdu = f.f1(duprev, u, p, integrator.t)
du = duprev + dt * a1 * kdu
# update position & velocity
tnew = t + a1 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b2 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a2 * kdu
# update position & velocity
tnew = tnew + a2 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b3 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a3 * kdu
# update position & velocity
tnew = tnew + a3 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b4 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a4 * kdu
# update position & velocity
tnew = tnew + a4 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b5 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a5 * kdu
tnew = tnew + a5 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b6 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a6 * kdu
tnew = tnew + a6 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b7 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a7 * kdu
tnew = tnew + a7 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b8 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a8 * kdu
tnew = tnew + a8 * dt
ku = f.f2(du, u, p, tnew)
u = u + dt * b9 * ku
kdu = f.f1(du, u, p, tnew)
du = du + dt * a9 * kdu