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Improved support for flow integrators

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This commit is contained in:
Alberto Ramos 2021-11-03 11:49:35 +01:00
parent 410a6d7b25
commit d19b3a1132
8 changed files with 154 additions and 66 deletions
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180
src/YM/YMflow.jl
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@ -9,6 +9,68 @@
### created: Sat Sep 25 08:37:14 2021
###
struct FlowIntr{N,T}
r::T
e0::NTuple{N,T}
e1::NTuple{N,T}
add_zth::Bool
c0::T
eps::T
tol::T
eps_ini::T
max_eps::T
sft_fac::T
end
# pre-defined integrators
wfl_euler(::Type{T}, eps::T, tol::T) where T = FlowIntr{0,T}(one(T),(),(),false,one(T),eps,tol,one(T)/200,one(T)/10,9/10)
zfl_euler(::Type{T}, eps::T, tol::T) where T = FlowIntr{0,T}(one(T),(),(),true, (one(T)*5)/3,eps,tol,one(T)/200,one(T)/10,9/10)
wfl_rk2(::Type{T}, eps::T, tol::T) where T = FlowIntr{1,T}(one(T)/2,(-one(T)/2,),(one(T),),false,one(T),eps,tol,one(T)/200,one(T)/10,9/10)
zfl_rk2(::Type{T}, eps::T, tol::T) where T = FlowIntr{1,T}(one(T)/2,(-one(T)/2,),(one(T),),true, (one(T)*5)/3,eps,tol,one(T)/200,one(T)/10,9/10)
wfl_rk3(::Type{T}, eps::T, tol::T) where T = FlowIntr{2,T}(one(T)/4,(-17/36,-one(T)),(8/9,3/4),false,one(T),eps,tol,one(T)/200,one(T)/10,9/10)
zfl_rk3(::Type{T}, eps::T, tol::T) where T = FlowIntr{2,T}(one(T)/4,(-17/36,-one(T)),(8/9,3/4),true, (one(T)*5)/3,eps,tol,one(T)/200,one(T)/10,9/10)
function Base.show(io::IO, int::FlowIntr{N,T}) where {N,T}
if (abs(int.c0-1) < 1.0E-10)
println(io, "WILSON flow integrator")
elseif (abs(int.c0-5/3) < 1.0E-10) && int.add_zth
println(io, "ZEUTHEN flow integrator")
elseif (abs(int.c0-5/3) < 1.0E-10) && !int.add_zth
println(io, "SYMANZIK flow integrator")
else
println(io, "CUSTOM flow integrator")
if int.add_zth
println(io, " - ", int.c0, " (with zeuthen term)")
else
println(io, " - ", int.c0)
end
end
if N == 0
println(io, " * Euler schem3")
elseif N == 1
println(io, " * One stage scheme. Coefficients3")
println(io, " stg 1: ", int.e0[1], " ", int.e1[1])
elseif N == 2
println(io, " * Two stage scheme. Coefficients:")
println(io, " stg 1: ", int.e0[1], " ", int.e1[1])
println(io, " stg 2: ", int.e0[2], " ", int.e1[2])
end
println(io, " * Fixed step size parameters: eps = ", int.eps)
println(io, " * Adaptive step size parameters: tol = ", int.tol)
println(io, " - max eps: ", int.max_eps)
println(io, " - initial eps: ", int.eps_ini)
println(io, " - safety scale: ", int.sft_fac)
return nothing
end
"""
function add_zth_term(ymws::YMworkspace, U, lp)
@ -73,69 +135,82 @@ function krnl_add_zth!(frc, frc2::AbstractArray{TA}, U::AbstractArray{TG}, lp::S
return nothing
end
function flw_euler(U, ns, eps, c0, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace; add_zth=false)
@timeit "Integrating flow equations (Euler)" begin
function flw(U, int::FlowIntr{NI,T}, ns::Int64, eps, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) where {NI,T}
@timeit "Integrating flow equations" begin
for i in 1:ns
force_gauge(ymws, U, c0, 1, gp, lp)
if add_zth
add_zth_term(ymws::YMworkspace, U, lp)
end
U .= expm.(U, ymws.frc1, 2*eps)
end
end
return nothing
end
function flw_rk3(U, ns, eps, c0, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace; add_zth=false)
@timeit "Integrating flow equations (RK3)" begin
for i in 1:ns
e0 = eps/2
force_gauge(ymws, U, c0, 1, gp, lp)
if add_zth
force_gauge(ymws, U, int.c0, 1, gp, lp)
if int.add_zth
add_zth_term(ymws::YMworkspace, U, lp)
end
ymws.mom .= ymws.frc1
U .= expm.(U, ymws.mom, e0)
e0 = -34*eps/36
e1 = 16*eps/9
force_gauge(ymws, U, c0, 1, gp, lp)
if add_zth
add_zth_term(ymws::YMworkspace, U, lp)
U .= expm.(U, ymws.mom, 2*eps*int.r)
for k in 1:NI
force_gauge(ymws, U, int.c0, 1, gp, lp)
if int.add_zth
add_zth_term(ymws::YMworkspace, U, lp)
end
ymws.mom .= int.e0[k].*ymws.mom .+ int.e1[k].*ymws.frc1
U .= expm.(U, ymws.mom, 2*eps)
end
ymws.mom .= e0.*ymws.mom .+ e1.*ymws.frc1
U .= expm.(U, ymws.mom)
e1 = 6*eps/4
force_gauge(ymws, U, c0, 1, gp, lp)
if add_zth
add_zth_term(ymws::YMworkspace, U, lp)
end
ymws.mom .= e1.*ymws.frc1 .- ymws.mom
U .= expm.(U, ymws.mom)
end
end
return nothing
end
flw(U, int::FlowIntr{NI,T}, ns::Int64, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) where {NI,T} = flw(U, int, ns, int.eps, gp, lp, ymws)
##
# Adaptive step size integrators
##
wfl_euler(U, ns, eps, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) = flw_euler(U, ns, eps, 1, gp, lp, ymws)
zfl_euler(U, ns, eps, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) = flw_euler(U, ns, eps, 5.0/3.0, gp, lp, ymws, add_zth=true)
wfl_rk3(U, ns, eps, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) = flw_rk3(U, ns, eps, 1, gp, lp, ymws)
zfl_rk3(U, ns, eps, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) = flw_rk3(U, ns, eps, 5.0/3.0, gp, lp, ymws, add_zth=true)
function flw_adapt(U, int::FlowIntr{NI,T}, tend::T, epsini::T, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) where {NI,T}
eps = int.eps_ini
dt = tend
nstp = 0
while true
ns = convert(Int64, floor(dt/eps))
if ns > 10
flw(U, int, 9, eps, gp, lp, ymws)
ymws.U1 .= U
flw(U, int, 2, eps/2, gp, lp, ymws)
flw(ymws.U1, int, 1, eps, gp, lp, ymws)
dt = dt - 10*eps
nstp = nstp + 10
# adjust step size
ymws.U1 .= ymws.U1 ./ U
maxd = CUDA.mapreduce(dev_one, max, ymws.U1, init=zero(tend))
eps = min(int.max_eps, 2*eps, int.sft_fac*eps*(int.tol/maxd)^(one(tend)/3))
else
flw(U, int, ns, eps, gp, lp, ymws)
dt = dt - ns*eps
flw(U, int, 1, dt, gp, lp, ymws)
dt = zero(tend)
nstp = nstp + ns + 1
end
if dt == zero(tend)
break
end
end
return nstp, eps
end
flw_adapt(U, int::FlowIntr{NI,T}, tend::T, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace) where {NI,T} = flw_adapt(U, int, tend, int.eps_ini, gp, lp, ymws)
##
# Observables
##
"""
function Eoft_plaq([Eslc,] U, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)
@ -151,7 +226,7 @@ function Eoft_plaq(Eslc, U, gp::GaugeParm{T}, lp::SpaceParm{N,M,B,D}, ymws::YMwo
tp = ntuple(i->i, N-1)
V3 = prod(lp.iL[1:end-1])
fill!(Eslc,zero(T))
Etmp = zeros(T,lp.iL[end])
for ipl in 1:M
@ -159,8 +234,8 @@ function Eoft_plaq(Eslc, U, gp::GaugeParm{T}, lp::SpaceParm{N,M,B,D}, ymws::YMwo
CUDA.@sync begin
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_plaq_pln!(ymws.cm, U, gp.Ubnd, ztw[ipl], ipl, lp)
end
Etmp .= (gp.ng .- reshape(Array(CUDA.mapreduce(real, +, ymws.cm;dims=tp)),lp.iL[end])/V3 )
Etmp .= (gp.ng .- reshape(Array(CUDA.mapreduce(real, +, ymws.cm;dims=tp)),lp.iL[end]) ./ V3 )
if ipl < N
for it in 2:lp.iL[end]
Eslc[it,ipl] = Etmp[it] + Etmp[it-1]
@ -201,7 +276,7 @@ function krnl_plaq_pln!(plx, U::AbstractArray{T}, Ubnd::T, ztw, ipl, lp::SpacePa
end
I = point_coord((b,r), lp)
plx[I] = ztw*tr(U[b,1,r]*gt / (U[b,2,r]*U[bu2,id1,ru2]))
plx[I] = ztw*tr(U[b,id1,r]*gt / (U[b,id2,r]*U[bu2,id1,ru2]))
return nothing
end
@ -219,22 +294,23 @@ function Qtop(Qslc, U, gp::GaugeParm, lp::SpaceParm{4,M,B,D}, ymws::YMworkspace)
ztw = ztwist(gp, lp)
tp = (1,2,3)
fill!(ymws.rm, zero(eltype(ymws.rm)))
CUDA.@sync begin
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_field_tensor!(ymws.frc1, ymws.frc2, U, gp.Ubnd, 1,6, ztw[1], ztw[5], lp)
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_field_tensor!(ymws.frc1, ymws.frc2, U, gp.Ubnd, 1,6, ztw[1], ztw[6], lp)
end
CUDA.@sync begin
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_add_qd!(ymws.rm, -, ymws.frc1, ymws.frc2, U, lp)
end
CUDA.@sync begin
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_field_tensor!(ymws.frc1, ymws.frc2, U, gp.Ubnd, 2,5, ztw[2], ztw[4], lp)
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_field_tensor!(ymws.frc1, ymws.frc2, U, gp.Ubnd, 2,5, ztw[2], ztw[5], lp)
end
CUDA.@sync begin
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_add_qd!(ymws.rm, +, ymws.frc1, ymws.frc2, U, lp)
end
CUDA.@sync begin
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_field_tensor!(ymws.frc1, ymws.frc2, U, gp.Ubnd, 3,4, ztw[3], ztw[6], lp)
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_field_tensor!(ymws.frc1, ymws.frc2, U, gp.Ubnd, 3,4, ztw[3], ztw[4], lp)
end
CUDA.@sync begin
CUDA.@cuda threads=lp.bsz blocks=lp.rsz krnl_add_qd!(ymws.rm, -, ymws.frc1, ymws.frc2, U, lp)