# Iterate problem for a complex function and plot it.

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zongxian on 11 Jun 2020
Commented: zongxian on 14 Jun 2020
Now I have a complex function, for example
1.8633 - 0.00576465 s1^3 + s1^2 (0.160853 - 0.050155 s2) - 1.20076 s2 + 0.161107 s2^2 - 0.00576465 s2^3 + s1 (-1.1984 + 0.631511 s2 - 0.050155 s2^2);
1. It contains two variables s1 and s2, I can use contour plot the lines that equal to zero.
2. Give a map T, such that s1 -> s1^2+s1*s2^2; s2 -> s1+s1^2*s2+s2;
3. After the map, repeat the contour plot for the new function.
Matlab codes:
S1=0:0.01:10;
S2=0:0.01:10;
[s1,s2] = meshgrid(S1,S2);
Z=1.8633 - 0.00576465 .* s1.^3 + s1.^2 .* (0.160853 - 0.050155 .* s2) - 1.20076 .* s2 + 0.161107 .* s2.^2 - 0.00576465 .* s2.^3 + s1 .* (-1.1984 + 0.631511 .* s2 - 0.050155 .* s2.^2);
contour(s1,s2,Z,[0,0]) This figure is Contour when the equation equal to zero, then I want all the points on these lines will iterate by a rule (as above 2).
My question is how to plot it more convenient, my way is solve the funciton first (solve s1), then I can get s1 equal a formula, then do the iterate separately, and plot (s1, s2), but it will be difficult, because there are some solution for s1 at the same time, so I want to know is there any other method do it.
% Since it's a cubic function, there are three solutions,
s1 = f1(s2)
s1 = f2(s2)
s1 = f3(s2)
% Apply the mapping to the three formulas
(news1,news2) = T[s1, f1(s2)]
....(another two are same as this one)
% Then use plot(news1, news2) get new lines which apply the mapping
% But the solution is complicated， so is there any convenient way.

zongxian on 14 Jun 2020
@darova, every points on these lines will iterate one times (apply map T).
darova on 14 Jun 2020
Are you asking how to extract data from contour?
zongxian on 14 Jun 2020
if we can extract data that will be a good way. Then I can apply map T on these data. @darova

darova on 14 Jun 2020
To extract data from contour use get
[C,h] = contour(...);
xdata = get(h,'xdata');

#### 1 Comment

zongxian on 14 Jun 2020
You gave me some inspiration, and then I iterated through the points I got. Thank you.