I have a generated a data set of a function $\alpha(\lambda_2,\varepsilon):\mathbb{R}_+ \times (0,1) \mapsto (0,1)$. I used mathematica to generate a list by varying $\lambda_2$ and $\varepsilon$; $\varepsilon$ is very small, and $\lambda$ is in between 0.5 and 1.0.
{Nλ1, Nμ1, Nμ2, NCN} = {0., 1., 1., 7060};
Clear[Tableϵ, Tableλ, Tableαϵλ];
Tableϵ = Table[10^-m, {m, 3, 15, 1/3}];
Tableλ = Table[m, {m, 0.5, 1.0, 1/20}];
Tableαϵλ = {};
For[j = 1, j <= Length[Tableλ], j++, {
lastkϵ = NCN - 1;
For[i = 1, i <= Length[Tableϵ], i++, {
With[{Nλ2 = Tableλ[[j]], ϵ = Tableϵ[[i]]}, {
For[k = lastkϵ, k > Nλ2 NCN, k--, {
If[ε[Nλ1, Nλ2, Nμ1, Nμ2, k/NCN, NCN] < ϵ && Nλ2 < k/NCN < 2 Nλ2, {
AppendTo[Tableαϵλ, {ϵ, Nλ2, N[k/NCN]}],
Break[]
}];
}]
}];
lastkϵ = k;
}];
}];
Now, I'd like to generate some nice plots. In fact, I wanted to see the curves of $\alpha \approx k/NCN$ as a function of $\varepsilon$ using $\lambda_2$ as series (eventually excluding some to look nicer.
My question is, how do I break this data set into series that I can filter for some plots?
Thank you in advance.
Δ1[λ1_, λ2_, μ1_, μ2_, c0_ ] := 1/4 + (μ2/(λ1 + λ2) (c0 μ1 - λ1 - λ2 )/( 2 μ1 - μ2));
Sp1[λ1_, λ2_, μ1_, μ2_, c0_ ] := 1/2 + Sqrt[Δ1[λ1, λ2, μ1, μ2, c0]]; Sp2[λ1_, λ2_, μ1_, μ2_, c0_ ] := 1/2 - Sqrt[Δ1[λ1, λ2, μ1, μ2, c0]];
Δ2[λ1_, λ2_, μ1_, μ2_, c0_ ] := (2 λ1 μ1 + 2 λ2 μ1 - λ1 μ2 - λ2 μ2)^2 - 3 (2 λ2 μ1 - λ2 μ2) (-2 λ1 μ1 - 2 λ2 μ1 + λ1 μ2 + λ2 μ2); Δ3[λ1_, λ2_, μ1_, μ2_, c0_ ] := 2 (2 λ1 μ1 + 2 λ2 μ1 - λ1 μ2 - λ2 μ2)^3 - 9 (2 λ2 μ1 - λ2 μ2) (2 λ1 μ1 + 2 λ2 μ1 - λ1 μ2 - λ2 μ2) (-2 λ1 μ1 - 2 λ2 μ1 + λ1 μ2 + λ2 μ2) + 27 (2 λ2 μ1 - λ2 μ2)^2 (λ1 μ2 + λ2 μ2 - c0 μ1 μ2);
Sq1[λ1_, λ2_, μ1_, μ2_, c0_ ] := -1/(3 λ2) (λ1 + λ2 + 2 Sqrt[Δ2[λ1, λ2, μ1, μ2, c0]] Cos[1/3 ArcTan[Sqrt[4 Δ2[λ1, λ2, μ1, μ2, c0]^3/Δ3[λ1, λ2, μ1, μ2, c0]^2 - 1]] + (2 π )/3]);
Sq2[λ1_, λ2_, μ1_, μ2_, c0_ ] := -1/(3 λ2) (λ1 + λ2 + 2 Sqrt[Δ2[λ1, λ2, μ1, μ2, c0]] Cos[1/3 ArcTan[Sqrt[4 Δ2[λ1, λ2, μ1, μ2, c0]^3/Δ3[λ1, λ2, μ1, μ2, c0]^2 - 1]] + (4 π )/3]);
Sq3[λ1_, λ2_, μ1_, μ2_, c0_ ] := -1/(3 λ2) (λ1 + λ2 + 2 Sqrt[Δ2[λ1, λ2, μ1, μ2, c0]] Cos[1/3 ArcTan[Sqrt[4 Δ2[λ1, λ2, μ1, μ2, c0]^3/Δ3[λ1, λ2, μ1, μ2, c0]^2 - 1]]]);
F[λ1_, λ2_, μ1_, μ2_, c0_, n_] := 1 - (2 λ2 μ1 + λ1 μ2 - c0 μ1 μ2 )/(λ2 (2 μ1 - μ2)) ( 1 - Sq3[λ1, λ2, μ1, μ2, c0]/Sp1[λ1, λ2, μ1, μ2, c0] )/(1 - Sq3[λ1, λ2, μ1, μ2, c0]) Sp1[λ1, λ2, μ1, μ2, c0]^-n
ε[λ1_, λ2_, μ1_, μ2_, c0_, CN_] := Chop[(2 λ2 μ1 + λ1 μ2 - c0 μ1 μ2)/(λ2 (2 μ1 - μ2)) (1 - Sq3[λ1, λ2, μ1, μ2, c0]/Sp1[λ1, λ2, μ1, μ2, c0])/(1 - Sq3[λ1, λ2, μ1, μ2, c0]) Sp1[λ1, λ2, μ1, μ2, c0]^Round[-CN (1 - c0)] ]
πminus[λ1_, λ2_, μ1_, μ2_, c0_] := (c0 - (λ1 + λ2)/μ1)/(λ2 (2/μ2 - 1/μ1))
Select
to pull out what you want from the list though. $\endgroup$ – george2079 Mar 22 '16 at 13:55