SRS/optim_mixture.jl

module OptimMixture

import DelimitedFiles as DF
import BenchmarkTools as BT
import UnicodePlots as UP
import LinearAlgebra: ⋅

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
  energy::Int
  data::Matrix{Int}
end

function load_slabs(width::Int=512, height::Int=512)
  slabs = Slab[]()
  i_min, i_max = typemax(Int), 0
  for e in ENERGIES
    slab = Slab(energy=e, data=DF.readdlm("test_sample/HeLa_F-SRS_512x512_2803cm-1.txt", ',', Int))
    push!(slabs, slab)

    i_min, i_max = min(i_min, minimum(slab.data)), max(i_max, maximum(slab.data))

    return slabs, i_min, i_max
  end
end

function Q_matrix_transpose(X::Matrix{Float64}, Y::Matrix{Float64}, N::Int)
  return sum(abs2, Y - view(X, 1:N, :) * view(X, (N+1):size(X, 1), :)')
end

function Q_matrix_reshape(X::Matrix{Float64}, Y::Matrix{Float64}, N::Int)
  N_plus_M, m = size(X)
  return sum(abs2, Y - view(X, 1:N, :) * reshape(view(X, (N+1):N_plus_M, :), m, N_plus_M - N))
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 Q_loop!(dst::Matrix{Float64}, X::Matrix{Float64}, N::Int)
  N_plus_M, m = size(X)
  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 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 dot_prod_dual_loop(W::Matrix{Float64}, X::Matrix{Float64}, V::Matrix{Float64})
  _, m = size(X)
  N, M = size(W)

  s = 0

  for k in 1:m
    for i in 1:N
      x = 0
      for j in 1:M
        @inbounds x += W[i, j] * X[N+j, k]
      end
      s += x * V[i, k]
    end
    for j in 1:M
      x = 0
      for i in 1:N
        @inbounds x += W[i, j] * X[i, k]
      end
      s += x * V[N+j, k]
    end
  end

  return s
end

function dot_prod_primal_loop(W::Matrix{Float64}, X::Matrix{Float64}, V::Matrix{Float64})
  _, m = size(X)
  N, M = size(W)

  s = 0

  for i in 1:N
    for j in 1:M
      x = 0
      for k in 1:m
        @inbounds x += X[i, k] * V[N+j, k] + X[N+j, k] * V[i, k]

      end
      s += x * W[i, j]
    end
  end

  return s
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 DQ_V_loop!(dst::Matrix{Float64}, X::Matrix{Float64}, V::Matrix{Float64}, N::Int)
  N_plus_M, m = size(X)
  for i in 1:N
    for j in N+1:N_plus_M
      x = 0
      for k in 1:m
        @inbounds x += (V[i, k] * X[j, k] + X[i, k] * V[j, k])
      end
      @inbounds dst[i, j-N] = x
    end
  end
end

function Q_loop_transposed(X::Matrix{Float64}, Y::Matrix{Float64}, N::Int)
  s = 0
  m, N_plus_M = size(X)
  for i in 1:N
    for j in N+1:N_plus_M
      x = 0
      for k in 1:m
        @inbounds x += X[k, i] * X[k, j]
      end
      @inbounds s += (Y[j-N, i] - x)^2
    end
  end
  return s
end

function test_dot_prod(N::Int, M::Int, m::Int)
  X = rand(N + M, m)
  W = rand(N, M)
  V = rand(N + M, m) .- 0.5

  @show dot_prod_primal_loop(W, X, V)
  @show dot_prod_dual_loop(W, X, V)
end

function test_DE(N::Int, M::Int, m::Int)
  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))
  DE_loop!(grad_EX, X, Y)

  eps = [10.0^k for k in 1:-1:-12]
  errors = zeros(size(eps))

  for i in eachindex(eps)
    EX_V_true = E_loop(X + eps[i] * V, Y)
    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_DQ(N::Int, M::Int, m::Int)
  X = rand(N + M, m) * 255
  V = rand(N + M, m)

  QX = zeros(N, M)
  Q_loop!(QX, X, N)

  dst_true = zeros(N, M)
  dst_approx = zeros(N, M)

  eps = [10.0^k for k in 1:-1:-8]
  errors = zeros(size(eps))

  for i in eachindex(eps)
    Q_loop!(dst_true, X + eps[i] * V, N)
    DQ_V_loop!(dst_approx, X, eps[i] * V, N)
    dst_approx .+= QX
    errors[i] = sum(abs, dst_approx - dst_true)
  end

  @show eps
  @show errors

  println(UP.lineplot(eps, errors, xscale=:log10, yscale=:log10))
end

function test(N::Int, M::Int, m::Int)
  Y = rand(N, M) * 255
  X = rand(N + M, m) * 255

  X_pre = copy(X)
  X_pre[N+1:N+M] .= vec(X_pre[N+1:N+M]')

  r_matrix = Q_matrix_transpose(X, Y, N)
  r_loop = Q_loop(X, Y, N)

  @show r_matrix, r_loop, abs(r_matrix - r_loop) / r_loop
end

end # module

# OptimMixture.test(512 * 512, 20, 2)
# OptimMixture.test_DQ(512 * 512, 20, 2)
OptimMixture.test_DE(512 * 512, 20, 2)
# OptimMixture.test_DE(20, 2, 2)
# OptimMixture.test_dot_prod(512^2, 20, 2)

# vim: ts=2:sw=2:sts=2