I have to make a sum over 4 variables. My code is very very slow. I want to know how to speed up this code. This problem is related to but different from one previous problem. Any help or suggestion will be highly appreciated! The code is shown below:
data = Table[ Exp[-((i + j - 20.)/5)^2] Exp[-((i - j)/5)^2], {i, 20}, {j, 20}];
data = Chop[data, 0.00001];
data = data/Sqrt[Sum[(data[[i, j]])^2, {i, 1, 20}, {j, 1, 20}]];
ListDensityPlot[data, InterpolationOrder -> 0, Mesh -> All, PlotRange -> All, ColorFunction -> (Blend[{Hue[2/3], Hue[0]}, #] &)]
c = 3*10^8;
Δ = 0.5;
λ0 = 1500;
CC1[i_, j_, k_, l_, t_] := (data[[i, l]] data[[j,
k]] Cos[π*(c/(λ0 - 10 + i*Δ -
0.5 Δ) +
c/(λ0 - 10 + l*Δ -
0.5 Δ)) t] Cos[π*(c/(λ0 - 10 +
j*Δ - 0.5 Δ) +
c/(λ0 - 10 + k*Δ -
0.5 Δ)) t] +
data[[i, k]] data[[j,
l]] Cos[π*(c/(λ0 - 10 + i*Δ -
0.5 Δ) +
c/(λ0 - 10 + k*Δ -
0.5 Δ)) t] Cos[π*(c/(λ0 - 10 +
j*Δ - 0.5 Δ) +
c/(λ0 - 10 + l*Δ -
0.5 Δ)) t] -
data[[i, j]] data[[k,
l]] Sin[π*(c/(λ0 - 10 + i*Δ -
0.5 Δ) +
c/(λ0 - 10 + j*Δ -
0.5 Δ)) t] Sin[π*(c/(λ0 - 10 +
k*Δ - 0.5 Δ) +
c/(λ0 - 10 + l*Δ -
0.5 Δ)) t])^2;
CC2[t_] := \!\(\*UnderoverscriptBox[\(∑\), \(i = 1\), \(20\)]\(\*UnderoverscriptBox[\(∑\), \(j = 1\), \(20\)]\(\*UnderoverscriptBox[\(∑\), \(k = 1\), \(20\)]\(\*UnderoverscriptBox[\(∑\), \(l = 1\), \(20\)]CC1[i, j, k, l,t]\)\)\)\);
ListPlot[Table[{i, CC2[i*0.001]}, {i, -10, 10, 1}], Joined -> True, Axes -> None, PlotRange -> All, Frame -> True, ImageSize -> {400, 250}]
ListPlot[Table[{i, CC2[i*0.001]}, {i, -10, 10, 0.001}], Joined -> True, Axes -> None, PlotRange -> All, Frame -> True, ImageSize -> {400, 250}]