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test_waterlily.jl
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test_waterlily.jl
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using TunedSmoother,BenchmarkTools,Plots,DataStructures
using TunedSmoother: p₀
# Generate WaterLily simulation data
data = create_waterlily()
# Optimize the psuedo-inverse functions
begin # this block takes around 30 minutes. the next block has the results
smooth! = pseudo!
scaleloss = zeros(Float32,6,length(data))
scaleloss[1,:] .= [loss(test;p=zeros(Float32,5),smooth!) for (name,test) ∈ data]
scaleloss[2,:] .= [loss(test;p=p₀,smooth!) for (name,test) ∈ data]
opt = OrderedDict(name=>p₀ for name ∈ keys(data))
for scale ∈ 1:4
@show scale
scaledata = scale==4 ? data : create_waterlily(p=scale+2,cases=keys(data))
opt = OrderedDict(name=>fit(train,opt[name]) for (name,train) ∈ scaledata)
scaleloss[scale+2,:] .= [loss(test;p=opt[name],smooth!) for (name,test) ∈ data]
end
end
begin # output from the block above
opt = OrderedDict(
circle => [-0.00727588, -0.102282, -0.0178857, 0.760556, -0.586334, 1.78245, 1.14314, 0.167734],
TGV => [-0.0617478, 0.00940791, 0.00780108, 0.391629, -0.260235, -1.16419, -0.5565, -0.0615989],
donut => [-0.134641, -0.0313802, 0.00234106, 0.286056, -0.159517, -0.021158, -0.213197, -0.0317727],
wing => [-0.229121, -0.253223, -0.042952, 0.782714, -0.604938, -0.00708945, 0.0287928, 0.00663962],
shark => [-0.279771, -0.281626, -0.0476559, 0.821296, -0.649919, -0.00109436, 0.055443, 0.00988565])
scaleloss= [-0.46811 -0.63303 -0.64559 -0.52364 -0.58142
-1.75374 -1.52343 -1.48713 -1.37156 -1.45274
-1.7893 -1.69872 -1.63804 -1.42732 -1.46177
-1.81289 -1.73545 -1.64428 -1.42765 -1.48817
-1.80914 -1.73749 -1.65463 -1.43041 -1.49582
-1.82367 -1.73825 -1.65887 -1.4328 -1.50249]
end
# plot loss across examples and scales
begin
using StatsPlots,CategoricalArrays
cats = ["Jacobi","transfer","⅛","¼","½","1"]
ctg = CategoricalArray(repeat(cats,inner=length(data)))
levels!(ctg,cats)
groupedbar(scaleloss', size = (500,400),
group=ctg, legend=:outerbottomright, palette=:Greens_6,
yaxis=("log₁₀ residual reduction",:flip),
xaxis=("cases",(1:length(data),keys(data))),)
end
savefig("scaleloss.pdf")
begin
scaledata = create_waterlily(p=4)
scaledata[wing] = filter(d->itcount(d,GS!)<32,scaledata[wing])
opt2 = OrderedDict(name=>fit(train,p₀;it=2) for (name,train) ∈ scaledata)
end
begin
opt2 = OrderedDict(
circle => [0.143873, 0.114321, 0.0243589, -0.166979, -0.211476],
TGV => [-0.445295, -0.175371, -0.0100856, -0.147759, 0.0],
donut => [0.121331, 0.0259214, 0.00808, -0.149346, -0.0750463],
wing => [0.0259344, -0.123088, -0.0268142, -0.174569, -0.542905],
shark => [0.0673015, -0.104415, -0.024194, -0.182964, -0.298915]
)
# c = [avecount(test,pseudo!;p=opt2[name]) for (name,test) ∈ data]
c = [2.0 2.11 2.99 5.99 6.9]
end
# time a single Vcycle
begin
temp!(st;kw...) = mg!(st;inner=2,mxiter=1,kw...)
jacobi_time = @belapsed temp!(st;smooth! = Jacobi!) setup=(st=state($data[shark][1]...)) #
gauss_time = @belapsed temp!(st;smooth! = GS!) setup=(st=state($data[shark][1]...)) #
sor_time = @belapsed temp!(st;smooth! = SOR!) setup=(st=state($data[shark][1]...)) #
pseudo_time = @belapsed temp!(st) setup=(st=state($data[shark][1]...)) #
gauss_time /= jacobi_time
sor_time /= jacobi_time
pseudo_time /= jacobi_time
end
# Count the number of cycles needed
crosscount = [[avecount(d,GS!) for (_,d) ∈ data]'.*gauss_time
[avecount(d,SOR!) for (_,d) ∈ data]'.*sor_time
[avecount(d,pseudo!) for (_,d) ∈ data]'.*pseudo_time
[avecount(d,pseudo!;p=opt2[name]) for (name,d) ∈ data]'.*pseudo_time]
crosscount = [ 7.0 7.56 10.5 18.585 20.825
6.4 9.632 9.632 17.92 20.128
2.74 4.11 4.1511 8.7954 10.1106
2.74 2.8907 4.0963 8.2063 9.453
]
begin
using StatsPlots,CategoricalArrays
n = length(data)
cats = ["Gauss-Sidel","SOR","Ã⁻¹ transfer","Ã⁻¹ tuned-¼"]
colors = repeat([palette(:default)[2],palette(:default)[4],:lightgreen,palette(:default)[3]],inner=n)
ctg = CategoricalArray(repeat(cats,inner=n))
levels!(ctg,cats)
groupedbar(crosscount',size=(400,400),
group=ctg, legend=:topleft,c=colors,
yaxis=("relative time"),
xaxis=("cases",(1:length(data),keys(data))),)
end
savefig("crosscount.pdf")
# plot best pseudo-inverse functions across examples
begin
using Plots
p₀ = Float32[-0.104447, -0.00238399, 0.00841367, -0.158046, -0.115103]
pmodels(p) = (D->1+p[1]+D*(p[2]+D*p[3]),L->L*(p[4]*(L-2)+p[5]*(L-1)))
a,_ = pmodels(p₀)
plot(-6:0.1:0,a,label="transfer",size=(400,400),
xaxis=("aᵢᵢ"),yaxis=("fᵢᵢ"),legend=:bottomleft)
for (name,p) in opt2
x = name ∈ (TGV,donut) ? (-6:0.1:0) : (-4:0.1:0)
a,_ = pmodels(p)
plot!(x,a,label=name)
end
display(plot!(-6:0,i->1,label="jacobi",c=:grey))
savefig("diag_fun.png")
x = 0:0.02:1
_,a = pmodels(p₀)
plot(x,a,label="transfer",size=(400,400),
xaxis=("aᵢⱼ"),yaxis=("fᵢⱼ"),legend=:bottomright)
for (name,p) in opt2
_,a = pmodels(p)
plot!(x,a,label=name)
end
display(plot!(x,i->0,label="jacobi",c=:grey))
savefig("lower_fun.png")
end
begin
using GeometricMultigrid: Vcycle!
for (name,h) in ((circle,160),(wing,300),(shark,160))
# for (name,h) in ((TGV,300),)
# for (name,h) in ((donut,160),)
smooth! = pseudo!
# st = state(data[name][25]...;smooth!)
st = state(data[name][end]...;smooth!)
x = copy(st.x.data)
x .-= st.x[1]
x[st.A.D .> -1.5] .= NaN
r = copy(st.r)
f(x) = @. log10(clamp(abs(x),1e-6,Inf64))
Vcycle!(st;smooth!)
plot(heatmap(x[st.x.R]',legend=false,clims=(-1,1)),
heatmap(f(r.data[st.x.R]'),legend=false,c=:Reds,clims=(-6,-1)),
heatmap(f(st.r.data[st.x.R]'),legend=false,c=:Reds,clims=(-6,-1)),
# plot(heatmap(x[st.x.R[:,:,end÷4]]',legend=false,clims=(-1,1)),
# plot(heatmap(x[st.x.R[:,:,end÷4]]',legend=false),
# heatmap(f(r.data[st.x.R[:,:,end÷4]]'),legend=false,c=:Reds,clims=(-6,-1)),
# heatmap(f(st.r.data[st.x.R[:,:,end÷4]]'),legend=false,c=:Reds,clims=(-6,-1)),
layout = (1,3),size=(900,h),axis=nothing)
savefig(string(name)*"triple.png")
end
end
begin
name = shark
anim = @animate for d in data[name]
st = state(d...)
x = copy(st.x.data)
x .-= st.x[1]
x[st.A.D .> -1.5] .= NaN
r = copy(st.r)
f(x) = @. log10(clamp(abs(x),1e-6,Inf64))
plot(heatmap(x[st.x.R]', legend=false, c=:bluesreds, clims=(-1,1)),
heatmap(f(r.data[st.x.R]'), legend=false, c=:Reds, clims=(-6,-1)),
layout=(1,2), size=(1000,250), axis=nothing)
end
gif(anim,string(name)*".gif")
end