Iterate problem for a complex function and plot it.

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.

[darova]

I don't understand the question. Can you show something? Maybe a picture with explanations?

[David Goodmanson]

Hi zohgxian,

do you mean

s1->s1^2+s1*s2^2;
s2->s1+s1^2*s2+s2;  

[zongxian]

I have add example codes, and change the error, @darova, @David Goodmanson.

[darova]

i still don't understand what are you trying to do with those lines

[zongxian]

@darova, every points on these lines will iterate one times (apply map T).

[darova]

Are you asking how to extract data from contour?

[zongxian]

if we can extract data that will be a good way. Then I can apply map T on these data. @darova

Answer 1

[darova]

To extract data from contour use get

[C,h] = contour(...);
xdata = get(h,'xdata');

[zongxian]

You gave me some inspiration, and then I iterated through the points I got. Thank you.