Iterate problem for a complex function and plot it.
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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);
- It contains two variables s1 and s2, I can use contour plot the lines that equal to zero.
- Give a map T, such that s1 -> s1^2+s1*s2^2; s2 -> s1+s1^2*s2+s2;
- 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.
7 个评论
darova
2020-6-12
I don't understand the question. Can you show something? Maybe a picture with explanations?
David Goodmanson
2020-6-13
Hi zohgxian,
do you mean
s1->s1^2+s1*s2^2;
s2->s1+s1^2*s2+s2;
zongxian
2020-6-13
darova
2020-6-14
i still don't understand what are you trying to do with those lines
darova
2020-6-14
Are you asking how to extract data from contour?
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