[WIP] Lanes's time complexity

using Plots

# Independent variables and parameters

Ns = [1; 1000:1000:10000] # Time steps

Ms = [512, 4096, 32768] # No. of atoms

Ps = [2^i for i in 0:8] # No. of processors

s = 0.05 # Serial code proportion

L = 60 # No. of configurations

I = 60 # No. of bispectrum components

UQ_subit = 100 # No. of UQ subiterations

UQ_runs = 100 # No. of UQ runs

UQ_prop = 0.1

STD_AD = 1.0

Enzyme = 0.25

# Time complexities. TODO: define time complexities

DFT(M, P) = M * (s + (1-s) / P)

SNAP_FITTING(M, P) = (L * M * I + L) / P + 2 * (L - (I + 2) / 3) * (I + 2)^2 / P

MD(M, P) = 3 * M * (s + (1-s) / P)

UQ(M, P, AD) = UQ_runs * M * AD / P

Lane1(N, M, P, AD) = N * UQ_subit * (DFT(M, P) + MD(M, P) + UQ(M, P, AD)) 

Lane3(N, M, P, AD) = N * UQ_prop  * (DFT(M, P) + SNAP_FITTING(M, P, AD)) +

                     N * UQ_subit * (MD(M, P)  + UQ(M, P, AD))

# twojmax = 6

# J = twojmax / 2.0

# ncoeff = round(Int, (J + 1) * (J + 2) * (( J + (1.5)) / 3. ) + 1)

# numTypes = 2

# A_cols = numTypes * ncoeff

# no_atomic_conf = 62

# A_rows(M) = no_atomic_conf * (1 + 3 * M + 3 * 3 * M)

# # https://www.stat.cmu.edu/~ryantibs/convexopt-S15/scribes/09-num-lin-alg-scribed.pdf

# SNAP_SYSTEM_DEF(M, P, AD) = 

# QR_SOL(M, P, AD) = 2 * (A_cols - A_rows(M) / 3) * A_rows(M)^2

# SNAP_FITTING(M, P, AD) = SNAP_SYSTEM_DEF(M, P, AD) + QR_SOL(M, P, AD)

# SNAP_FORCES(M, P, AD) = 3 * AD(M) + 3 * M * ncoeff * numTypes 

# Lane1(N, M, P, AD) = N * (DFT_FORCES(M, P) + MD(M, P) + UQ(M, P, AD)) 

# Lane2(N, M, P, AD) = N * (SNAP_FORCES(M, P, AD) + MD(M, P) + UQ(M, P, AD))

# Lane3(N, M, P, AD) = SNAP_FITTING(M, P, AD) + N * (SNAP_FORCES(M, P, AD) + MD(M, P) + UQ(M, P, AD))

# Plot time complexity

plot()

styles = [:solid, :dash, :dot]

P = 1

for i in 1:length(Ms)

  local M = Ms[i]

  plot!(Ns, Lane1.(Ns, M, P, STD_AD), yaxis=:log, color="black",

        line=styles[i], linewidth=2.5, label = "$M atoms")

  plot!(Ns, Lane1.(Ns, M, P, Enzyme), yaxis=:log, color="red",

        line=styles[i], linewidth=2.5, label = "$M atoms")

end

plot!(  legend=:outerright, legendfontsize=10, 

        xtickfontsize=12, ytickfontsize=12,

        xguidefontsize=12, yguidefontsize=12, dpi=600)

ylabel!("Time complexity")

xlabel!("No. of time steps")

#savefig("Lane1_time_complexity_serial_prop_$s.png")

# Plot time complexity difference

plot()

styles = [:solid, :dash, :dot]

N = Ns[end]

P = 1

diff = Lane1.(N, Ms, P, STD_AD) .- Lane1.(N, Ms, P, Enzyme)

plot!(diff, yaxis=:log, color="red", falpha=0.5, linewidth=2.5, st=:bar,

      xticks=(1:length(Ms), Ms), label = "$N time steps", m=5)

plot!(  legend=:topleft, legendfontsize=12, 

        xtickfontsize=12, ytickfontsize=12,

        xguidefontsize=12, yguidefontsize=12, dpi=600)

ylabel!("Time complexity")

xlabel!("No. of atoms")

#savefig("Lane1_time_complexity_diff_serial_prop_$s.png")

# Plot speedup

styles = [:solid, :dash, :dot]

N = Ns[end]

M = Ms[end]

t_serial = Lane1(N, M, 1, STD_AD)

plot(Ps, t_serial ./ Lane1.(N, M, Ps, STD_AD), color="black",

     line=styles[1], linewidth=2.5, label = "Standard AD")

t_serial = Lane1(N, M, 1, Enzyme)

plot!(Ps, t_serial ./ Lane1.(N, M, Ps, Enzyme), color="red",

      line=styles[2], linewidth=2.5, label = "Enzyme")

plot!(  legend=:bottomright, legendfontsize=12, 

        xtickfontsize=12, ytickfontsize=12,

        xguidefontsize=12, yguidefontsize=12, dpi=600)

ylabel!("Theoretical speedup")

xlabel!("No. of processors")

#savefig("Lane1_speedup.png")