SRS/optim_mixture.jl
Gaspard Jankowiak 11f955d265 remove loops
bug: optimisation yields two identical components
2024-12-20 11:17:09 +01:00

329 lines
8.1 KiB
Julia

module OptimMixture
import GLMakie as GLM
import DelimitedFiles as DF
import BenchmarkTools as BT
import UnicodePlots as UP
import NLopt
import LinearAlgebra: norm, mul!, axpy!, axpby!
import Logging
Logging.global_logger(Logging.ConsoleLogger(stderr, Logging.Info))
const ENERGIES = [2803, 2811, 2819, 2826, 2834, 2842, 2850, 2858, 2866, 2874,
2882, 2890, 2897, 2905, 2913, 2921, 2929, 2937, 2945, 2953,
2961, 2969, 2977, 2985, 2993, 3001, 3009, 3018, 3026, 3034,
3042, 3050]
@kwdef struct Slab{T<:Real}
energy::Int
data::Matrix{T}
end
function load_slabs(; T::Type=Int, width::Int=512, height::Int=512)
slabs = Slab[]
i_min, i_max = typemax(Int), 0
for e in ENERGIES
slab::Slab{T} = Slab{T}(energy=e, data=DF.readdlm("test_sample/HeLa_F-SRS_512x512_$(e)cm-1.txt", ',', T))
push!(slabs, slab)
i_min, i_max = min(i_min, minimum(slab.data)), max(i_max, maximum(slab.data))
end
s = join(size(slabs[1].data), "x")
@info "Loaded $(length(slabs)) $s slabs"
return slabs, i_min, i_max
end
function E_loop(X::Matrix{Float64}, Y::Matrix{Float64})
s = 0
N, M = size(Y)
m = size(X, 2)
for i in 1:N
for j in N+1:N+M
x = 0
for k in 1:m
@inbounds x += X[i, k] * X[j, k]
end
@inbounds s += (x - Y[i, j-N])^2
end
end
return s
end
function E!(X::Matrix{Float64}, Y::Matrix{Float64}, tmp::Matrix{Float64})
N, M = size(Y)
Q!(tmp, X, N)
# roughly 6ms with N = 512*512, M = 32, m = 2
# slighly faster than tmp .= tmp .- Y (7ms)
# slighly faster than tmp .-= Y (7ms)
axpy!(-1.0, Y, tmp)
# roughly 2.5m
# slightly faster than norm2(tmp)
s = sum(x -> x^2, tmp)
return s
end
function test_E(N::Int, M::Int, m::Int; benchmark::Bool=true)
X = rand(N + M, m)
Y = rand(N, M)
tmp = zeros(N, M)
E_from_loop = E_loop(X, Y)
E_from_mul = E!(X, Y, tmp)
@show abs(E_from_mul - E_from_loop)
if benchmark
@info "Running benchmarks..., this may take a while"
show(stdout, "text/plain", BT.@benchmark E_loop($X, $Y))
println()
show(stdout, "text/plain", BT.@benchmark E!($X, $Y, $tmp))
end
end
function Q!(dst::Matrix{Float64}, X::Matrix{Float64}, N::Int)
N_plus_M, _ = size(X)
# roughly 9ms with N = 512*512, M = 32, m = 2
# could be sped up using StrideArray?
mul!(dst, view(X, 1:N, :), view(X, N+1:N_plus_M, :)')
end
function Q_loop!(dst::Matrix{Float64}, X::Matrix{Float64}, N::Int)
N_plus_M, m = size(X)
# roughly 23.5ms with N = 512*512, M = 32, m = 2
for i in 1:N
for j in N+1:N_plus_M
x = 0
for k in 1:m
@inbounds x += X[i, k] * X[j, k]
end
@inbounds dst[i, j-N] = x
end
end
end
function test_Q(N::Int, M::Int, m::Int; benchmark::Bool=true)
X = rand(N + M, m)
Q_from_loop = zeros(N, M)
Q_from_mul = zeros(N, M)
Q!(Q_from_mul, X, N)
Q_loop!(Q_from_loop, X, N)
@show norm(Q_from_mul - Q_from_loop)
if benchmark
@info "Running benchmarks..., this may take a while"
show(stdout, "text/plain", BT.@benchmark Q!($Q_from_mul, $X, $N))
println()
show(stdout, "text/plain", BT.@benchmark Q_loop!($Q_from_loop, $X, $N))
end
end
function DE_loop!(dst::Matrix{Float64}, X::Matrix{Float64}, Y::Matrix{Float64})
dst_W = zeros(size(Y))
DE_loop!!(dst, dst_W, X, Y)
end
function DE!!(dst::Matrix{Float64}, dst_W::Matrix{Float64}, X::Matrix{Float64}, Y::Matrix{Float64})
N_plus_M, m = size(X)
N, M = size(Y)
# dst is the same size as X
# we need storage of size Y
Q!(dst_W, X, N)
# compute W = 2(Q(X) - Y)
axpby!(-2.0, Y, 2.0, dst_W)
mul!(view(dst, 1:N, :), dst_W, view(X, N+1:N_plus_M, :))
mul!(view(dst, N+1:N_plus_M, :), dst_W', view(X, 1:N, :))
end
function DE_loop!!(dst::Matrix{Float64}, dst_W::Matrix{Float64}, X::Matrix{Float64}, Y::Matrix{Float64})
_, m = size(X)
N, M = size(Y)
# dst is the same size as X
# we need storage of size Y
Q_loop!(dst_W, X, N)
# compute W = Q(X) - Y
dst_W .-= Y
for k in 1:m
for i in 1:N
x = 0
for j in 1:M
@inbounds x += dst_W[i, j] * X[N+j, k]
end
@inbounds dst[i, k] = x
end
for j in 1:M
x = 0
for i in 1:N
@inbounds x += dst_W[i, j] * X[i, k]
end
@inbounds dst[N+j, k] = x
end
end
dst .*= 2
end
function check_derivative_E(N::Int, M::Int, m::Int; loop::Bool=false)
X = rand(N + M, m)
Y = rand(N, M)
V = rand(N + M, m) .- 0.5
EX = E_loop(X, Y)
grad_EX = zeros(size(X))
tmp = zeros(size(Y))
if loop
DE_loop!!(grad_EX, tmp, X, Y)
else
DE!!(grad_EX, tmp, X, Y)
end
eps = [10.0^k for k in 1:-1:-12]
errors = zeros(size(eps))
for i in eachindex(eps)
if loop
EX_V_true = E_loop(X + eps[i] * V, Y)
else
EX_V_true = E!(X + eps[i] * V, Y, tmp)
end
EX_V_approx = EX + eps[i] * sum(grad_EX .* V)
# @show EX_V_true
# @show EX_V_approx
errors[i] = abs(EX_V_true - EX_V_approx)
end
# @show eps
# @show errors
foo = UP.lineplot(eps, errors, xscale=:log10, yscale=:log10)
UP.lineplot!(foo, eps, eps)
println(foo)
end
function test_DE(N::Int, M::Int, m::Int; benchmark::Bool=true)
X = rand(N + M, m)
Y = rand(N, M)
tmp_W = zeros(N, M)
∇E_loop = zeros(N + M, m)
∇E = zeros(N + M, m)
DE_loop!!(∇E_loop, tmp_W, X, Y)
DE!!(∇E, tmp_W, X, Y)
@show norm(∇E_loop - ∇E)
if benchmark
@info "Running benchmarks..., this may take a while"
show(stdout, "text/plain", BT.@benchmark DE_loop!!($∇E_loop, $tmp_W, $X, $Y))
println()
show(stdout, "text/plain", BT.@benchmark DE!!($∇E, $tmp_W, $X, $Y))
end
end
function benchmark()
slabs, _, _ = load_slabs(T=Float64)
Y::Matrix{Float64} = hcat([vec(slab.data) for slab in slabs]...)
@show size(Y)
N::Int, M::Int = size(Y)
m::Int = 2
X::Vector{Float64} = fill(0.5, (N + M) * m)
∇E::Vector{Float64} = zeros((N + M) * m)
tmp = zeros(size(Y))
show(stdout, "text/plain", BT.@benchmark DE_loop!!(reshape($∇E, $N + $M, $m), $tmp, reshape($X, $N + $M, $m), reshape($Y, $N, $M)))
println()
show(stdout, "text/plain", BT.@benchmark E_loop(reshape($X, $N + $M, $m), reshape($Y, $N, $M)))
end
function plot_result_mixture_1(X::Vector{Float64}, N::Int, M::Int, m::Int)
X_ = reshape(X, N + M, m)
λ = view(X_, 1:N, :)
s = view(X_, N+1:N+M, :)
@show size(λ)
@show size(s)
fig = GLM.Figure()
axes = map(1:m+1) do i
aspect = if i < m + 1
GLM.DataAspect()
else
nothing
end
GLM.Axis(fig[1, i], aspect=aspect)
end
n = Int(sqrt(N))
# Component density
GLM.image!(axes[1], reshape(view(λ, :, 1), n, n))
GLM.image!(axes[2], reshape(view(λ, :, 2), n, n))
# Spectra
GLM.lines!(axes[3], s[:, 1])
GLM.lines!(axes[3], s[:, 2])
@show norm(λ[:, 1] - λ[:, 2])
@show norm(s[:, 1] - s[:, 2])
display(fig)
end
function optim(algo::Symbol=:LD_MMA)
slabs, _, _ = load_slabs(T=Float64)
Y::Matrix{Float64} = hcat([vec(slab.data) for slab in slabs]...)
@show size(Y)
N::Int, M::Int = size(Y)
m::Int = 2
X::Vector{Float64} = fill(0.5, (N + M) * m)
∇E::Vector{Float64} = zeros((N + M) * m)
tmp = zeros(size(Y))
function objective(X::Vector{Float64}, grad::Vector{Float64})
if length(grad) > 0
DE!!(reshape(grad, N + M, m), tmp, reshape(X, N + M, m), reshape(Y, N, M))
else
@debug "No gradient requested!"
end
# @show "|∇E| = $(norm(grad))"
max_Σ_λ = maximum(sum(view(reshape(X, N + M, m), 1:N, :); dims=2))
value = E!(reshape(X, N + M, m), reshape(Y, N, M), tmp)
@info "E = $value, |∇E| = $(norm(grad)), max_Σ_λ = $max_Σ_λ"
return value
end
opt = NLopt.Opt(algo, (N + M) * m)
NLopt.lower_bounds!(opt, fill(0.0, (N + M) * m))
NLopt.upper_bounds!(opt, vec([fill(1.0, N, m); fill(Inf, M, m)]))
NLopt.min_objective!(opt, objective)
res = NLopt.optimize(opt, X)
return res
end
end # module
res = OptimMixture.optim(:LD_LBFGS);
OptimMixture.plot_result_mixture_1(res[2], 512 * 512, 32, 2)
# OptimMixture.benchmark();
# OptimMixture.test_E(512 * 512, 32, 2)
# OptimMixture.test_DE(512 * 512, 32, 2)
# OptimMixture.test_Q(512 * 512, 32, 2)
# OptimMixture.check_derivative_E(512 * 512, 32, 2)
# OptimMixture.check_derivative_E(512 * 512, 32, 2; loop=true)
# vim: ts=2:sw=2:sts=2