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Commit c8c50744 authored by Stephan Hilb's avatar Stephan Hilb
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revert to global dd

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src/DualTVDD.jl
+ 46
− 26
View file @ c8c50744
......@@ -11,16 +11,22 @@ include("projgrad.jl")
using Makie: heatmap
function run()
g = ones(20,20)
#g = [0. 2; 1 0.]
g = rand(10,10)
#g[4:17,4:17] .= 1
#g[:size(g, 1)÷2,:] .= 1
#g = [0. 2; 1 0.]
B = diagm(fill(100, length(g)))
α = 0.1
display(g)
B = 0.1 * rand(length(g), length(g))
B .+= diagm(ones(length(g)))
α = 0.025
display(norm(B))
md = DualTVDD.OpROFModel(g, B, α)
alg = DualTVDD.ChambolleAlgorithm()
ctx = DualTVDD.init(md, alg)
ctx = DualTVDD.init(md, DualTVDD.ChambolleAlgorithm())
ctx2 = DualTVDD.init(md, DualTVDD.ProjGradAlgorithm(λ=1/sqrt(8)/norm(B)))
#scene = vbox(
# heatmap(ctx.s, colorrange=(0,1), colormap=:gray, scale_plot=false, show_axis=false),
......@@ -31,41 +37,51 @@ function run()
#hm = last(scene)
for i in 1:10000
step!(ctx)
step!(ctx2)
#hm[1] = ctx.s
#yield()
#sleep(0.2)
end
display(ctx.p)
display(recover_u!(ctx))
display(copy(ctx.p))
display(copy(recover_u!(ctx)))
println(energy(ctx))
println()
ctx
display(copy(ctx2.p))
display(copy(recover_u!(ctx2)))
println(energy(ctx2))
ctx, ctx2
#hm[1] = ctx.s
#yield()
end
function rundd()
β = 0
f = zeros(2,2)
f[1,:] .= 1
#g = [0. 2; 1 0.]
f = zeros(4,4)
f[1,1] = 1
#f = [0. 2; 1 0.]
#A = diagm(vcat(fill(1, length(f)÷2), fill(1/10, length(f)÷2)))
A = rand(length(f), length(f))
display(A)
println(cond(A))
display(eigen(A))
#A = diagm(fill(1/2, length(f)))
#A = rand(length(f), length(f))
A = 0. * rand(length(f), length(f))
A .+= diagm(ones(length(f)))
#display(A)
B = inv(A'*A + β*I)
println(norm(sqrt(B)))
println(norm(A))
#println(norm(sqrt(B)))
g = similar(f)
vec(g) .= A' * vec(f)
α = .025
α = 1/4
md = DualTVDD.DualTVDDModel(f, A, α, 0., 0.)
alg = DualTVDD.DualTVDDAlgorithm(M=(1,1), overlap=(1,1), σ=1)
alg = DualTVDD.DualTVDDAlgorithm(M=(2,2), overlap=(2,2), σ=1)
ctx = DualTVDD.init(md, alg)
md2 = DualTVDD.OpROFModel(g, B, α)
......@@ -73,11 +89,13 @@ function rundd()
ctx2 = DualTVDD.init(md2, alg2)
for i in 1:1
for i in 1:1000
step!(ctx)
#println(energy(ctx))
end
for i in 1:1000000
for i in 1:10000
step!(ctx2)
#println(energy(ctx2))
end
#scene = heatmap(ctx.s,
......@@ -95,11 +113,11 @@ function rundd()
#hm[1] = ctx.s
#yield()
println("p result")
println("\np result")
display(ctx.p)
display(ctx2.p)
println("u result")
println("\nu result")
display(recover_u!(ctx))
display(recover_u!(ctx2))
......@@ -111,7 +129,7 @@ end
function run3()
f = rand(20,20)
A = rand(length(f), length(f))
A = 0.1*rand(length(f), length(f))
A .+= diagm(ones(length(f)))
g = reshape(A'*vec(f), size(f))
......@@ -160,9 +178,10 @@ function energy(ctx::Union{DualTVDDContext,ProjGradContext})
# v = div(p) + A'*f
map!(kΛ, v, extend(ctx.p, StaticKernels.ExtensionNothing()))
v .+= ctx.g
#display(v)
# |v|_B^2 / 2
u = ctx.B * vec(v)
return sum(u .* vec(v)) / 2
end
......@@ -177,9 +196,10 @@ function energy(ctx::ChambolleContext)
# v = div(p) + g
map!(kΛ, v, extend(ctx.p, StaticKernels.ExtensionNothing()))
v .+= ctx.model.g
#display(v)
# |v|_B^2 / 2
u = ctx.model.B * vec(v)
return sum(u .* vec(v)) / 2
end
......
src/chambolle.jl
+ 1
− 1
View file @ c8c50744
......@@ -16,7 +16,7 @@ using LinearAlgebra
struct ChambolleAlgorithm <: Algorithm
"fixed point inertia parameter"
τ::Float64
function ChambolleAlgorithm(; τ=1/4)
function ChambolleAlgorithm(; τ=1/8)
return new(τ)
end
end
......
src/dualtvdd.jl
+ 32
− 63
View file @ c8c50744
......@@ -34,11 +34,11 @@ function init(md::DualTVDDModel, alg::DualTVDDAlgorithm)
ax = axes(md.f)
# subdomain axes
subax = subaxes(md.f, alg.M, alg.overlap)
subax = subaxes(size(md.f), alg.M, alg.overlap)
# preallocated data for subproblems
subg = [Array{Float64, d}(undef, length.(subax[i])) for i in CartesianIndices(subax)]
subg = [Array{Float64, d}(undef, length.(ax)) for i in CartesianIndices(subax)]
# locally dependent tv parameter
subα = [md.α .* theta.(Ref(ax), Ref(subax[i]), Ref(alg.overlap), CartesianIndices(subax[i]))
subα = [md.α .* theta.(Ref(ax), Ref(subax[i]), Ref(alg.overlap), CartesianIndices(ax))
for i in CartesianIndices(subax)]
# this is the global g, the local gs are getting initialized in step!()
......@@ -53,9 +53,8 @@ function init(md::DualTVDDModel, alg::DualTVDDAlgorithm)
B = diagm(ones(length(md.f))) + md.β * I
# create subproblem contexts
# TODO: extraction of B subparts only makes sense for blockdiagonal B (i.e. A too)
li = LinearIndices(size(md.f))
submds = [OpROFModel(subg[i], B[vec(li[subax[i]...]), vec(li[subax[i]...])], subα[i])
submds = [OpROFModel(subg[i], B, subα[i])
for i in CartesianIndices(subax)]
subalg = ChambolleAlgorithm()
subctx = [init(submds[i], subalg) for i in CartesianIndices(subax)]
......@@ -67,62 +66,32 @@ function init(md::DualTVDDModel, alg::DualTVDDAlgorithm)
end
function step!(ctx::DualTVDDContext)
σ = ctx.algorithm.σ
d = ndims(ctx.p)
ax = axes(ctx.p)
overlap = ctx.algorithm.overlap
li = LinearIndices(size(ctx.model.f))
@inline kfΛ(w) = @inbounds -divergence_global(w)
@inline kfΛ(w) = @inbounds divergence_global(w)
kΛ = Kernel{ntuple(_->-1:1, d)}(kfΛ)
λ = 2*norm(sqrt(ctx.B))^2 # TODO: algorithm parameter
# call run! on each cell (this can be threaded)
for i in eachindex(ctx.subctx)
sax = ctx.subax[i]
ci = CartesianIndices(sax)
for (i, sax) in pairs(ctx.subax)
sg = ctx.subg[i] # julia-bug workaround
# TODO: make p computation local!
# g_i = (A*f - Λ(1-theta_i)p^n)|_{\Omega_i}
# subctx[i].p is used as a buffer
ctx.ptmp .= .-(1 .- theta.(Ref(ax), Ref(sax), Ref(overlap), CartesianIndices(ctx.p))) .* ctx.p
#tmp3 = .-(1 .- theta.(Ref(ax), Ref(sax), Ref(overlap), CartesianIndices(ctx.p)))
#ctx.subctx[i].p .= .-(1 .- theta.(Ref(ax), Ref(sax), Ref(overlap), ci)) .* ctx.p[ctx.subax[i]...]
ctx.subg[i] .= map(kΛ, ctx.ptmp)[sax...]
#map!(kΛ, ctx.subg[i], ctx.subctx[i].p)
ctx.subg[i] .+= ctx.g[sax...]
# set sensible starting value
reset!(ctx.subctx[i])
# precomputed: B/λ * (A'f - Λ(1-θ_i)p^n)
gloc = copy(ctx.subg[i])
# v_0
ctx.ptmp .= theta.(Ref(ax), Ref(sax), Ref(overlap), CartesianIndices(ctx.p)) .* ctx.p
ctx.subctx[i].p .= ctx.ptmp[sax...]
ctx.ptmp .= (1 .- theta.(Ref(ax), Ref(sax), Ref(overlap), CartesianIndices(ctx.p))) .* ctx.p
map!(kΛ, sg, ctx.ptmp)
sg .+= ctx.g
# subcontext B is identity!
subIB = I - ctx.B[vec(li[sax...]), vec(li[sax...])]./λ
subB = ctx.B[vec(li[sax...]), vec(li[sax...])]./λ
for j in 1:10000
subΛp = map(kΛ, ctx.subctx[i].p)
vec(ctx.subg[i]) .= subIB * vec(subΛp) .+ subB * vec(gloc)
for k in 1:1000
step!(ctx.subctx[i])
end
for j in 1:1000
step!(ctx.subctx[i])
end
end
# aggregate (not thread-safe!)
σ = ctx.algorithm.σ
ctx.p .*= 1 - σ
for i in CartesianIndices(ctx.subax)
ctx.p[ctx.subax[i]...] .+= σ .* ctx.subctx[i].p
for (i, sax) in pairs(ctx.subax)
ctx.p .+= σ .* ctx.subctx[i].p
end
end
......@@ -167,8 +136,8 @@ This assumes that subdomains have size at least 2 .* overlap.
theta(ax, sax, overlap, i::CartesianIndex) = prod(theta.(ax, sax, overlap, Tuple(i)))
theta(ax, sax, overlap::Int, i::Int) =
max(0., min(1.,
first(ax) == first(sax) && i < first(ax) + overlap ? 1. : (i - first(sax)) / overlap,
last(ax) == last(sax) && i > last(ax) - overlap ? 1. : (last(sax) - i) / overlap))
first(ax) == first(sax) && i < first(ax) + overlap ? 1. : (i - first(sax) + 1) / (overlap + 1),
last(ax) == last(sax) && i > last(ax) - overlap ? 1. : (last(sax) - i + 1) / (overlap + 1)))
"""
......@@ -177,21 +146,21 @@ theta(ax, sax, overlap::Int, i::Int) =
Determine axes for all subdomains, given per dimension number of domains
`pnum` and overlap `overlap`
"""
function subaxes(domain, pnum, overlap)
overlap = 1 .+ overlap
d = ndims(domain)
tsize = size(domain) .+ (pnum .- 1) .* overlap
psize = tsize .÷ pnum
osize = tsize .- pnum .* psize
overhang(I, j) = I[j] == pnum[j] ? osize[j] : 0
function subaxes(sizes, pnum, overlap)
d = Val(length(sizes))
ax = partition.(sizes, pnum, overlap)
return [ntuple(i -> ax[i][I[i]], d) for I in CartesianIndices(pnum)]
end
indices = Array{NTuple{d, UnitRange{Int}}, d}(undef, pnum)
for I in CartesianIndices(pnum)
indices[I] = ntuple(j -> ((I[j] - 1) * psize[j] - (I[j] - 1) * overlap[j] + 1) :
( I[j] * psize[j] - (I[j] - 1) * overlap[j] + overhang(I, j)), d)
function partition(n, k, o)
part = UnitRange[]
i = 1
while k > 1
s = (n + (k-1)*o) ÷ k
push!(part, i:i+s-1)
i = i + s - o
n -= s - o
k -= 1
end
@assert all(length.(sax) >= 1 .* overlap for sax in indices)
return indices
push!(part, i:i+n-1)
end
src/types.jl
+ 1
− 1
View file @ c8c50744
......@@ -29,7 +29,7 @@ struct DualTVDDModel{U,VV} <: Model
γ::Float64
end
"min_p 1/2 * |div(p) - g|_B^2 + χ_{|p|<=λ}"
"min_p 1/2 * |-div(p) - g|_B^2 + χ_{|p|<=λ}"
struct OpROFModel{U,VV,Λ} <: Model
"given data"
g::U
......
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