Mathematica Asked by rami_salazar on March 14, 2021
I have an SDE system which I solve using
proc = ItoProcess[{[DifferentialD]kai1[z] ==
0.0001*I*kai1[z] [DifferentialD]w1[z] +
I*kai1 [z] [DifferentialD]w2[z] -
I*kai3[z] [DifferentialD]w3[z] + kai3[z] [DifferentialD]w4[z] +
kai1[z] [DifferentialD]z,
[DifferentialD]kai2[z] ==
I*kai2[z] [DifferentialD]w1[z] + .1*I*
kai2[z] [DifferentialD]w2[z] -
I*kai4[z] [DifferentialD]w3[z] + kai4[z] [DifferentialD]w4[z] +
kai2[z] [DifferentialD]z,
[DifferentialD]kai3[z] ==
I*kai1[z] [DifferentialD]w1[z] -
I*kai3[z] [DifferentialD]w2[z] +
I*kai1[z] [DifferentialD]w3[z] + kai1[z] [DifferentialD]w4[z] +
kai3[z] [DifferentialD]z,
[DifferentialD]kai4[z] ==
I*kai4[z] [DifferentialD]w1[z] +
I*kai1[z] [DifferentialD]w2[z] -
I*kai3[z] [DifferentialD]w3[z] + kai3[z] [DifferentialD]w4[z] +
kai1[z] [DifferentialD]z}, {kai1[z], kai2[z], kai3[z],
kai4[z]}, {{kai1, kai2, kai3, kai4}, {1, 0, 0, 1}},
z, {w1 [Distributed] WienerProcess[],
w2 [Distributed] WienerProcess[],
w3 [Distributed] WienerProcess[],
w4 [Distributed] WienerProcess[]}]
and then
sol = RandomFunction[proc, {0, 1, 0.01}]
I can then plot the solution via
ListLinePlot[Abs[sol]^2 , PlotRange -> All]
But how can I extract just one of the solutions, ie kai1,2,3,4?
Thanks
Given sol
from your code, I'd do it like this:
data = sol["Path"];
munger[{x_, y_}] := {x, Abs[#]^2} & /@ y
{path1, path2, path3, path4} = Transpose[munger /@ data];
ListLinePlot[{path1, path2, path3, path4}, PlotLegends -> {kai1, kai2, kai3, kai4}]
Correct answer by m_goldberg on March 14, 2021
sol
is TemporalData
so you can extract the data from it
abs = Abs[sol]^2;
data = abs["Paths"][[1, 2 ;;]];
split = Table[{#[[1]], #[[2, i]]} & /@ data, {i, 1, 4}];
split
has 4 elements corresponding to the x, y
values for each function.
ListLinePlot /@ split // GraphicsRow
Answered by Rohit Namjoshi on March 14, 2021
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