In this section a simple example is presented to illustrate the basic use of the continuer.
This example generates a curve in the
-plane
such that
. So if the user specifies a point reasonably close to this curve we
get the unit circle. The defining function is
![]() |
(97) |
curve.m | |
1 | function out = curve |
2 | % |
3 | % Curve file of circle |
4 | % |
5 | |
6 | out{1} = @curve_func; |
7 | out{2} = @defaultprocessor; |
8 | out{3} = @options; |
9 | out{4} = []; %@jacobian; |
10 | out{5} = []; %@hessians; |
11 | out{6} = []; %@testf; |
12 | out{7} = []; %@userf; |
13 | out{8} = []; %@process; |
14 | out{9} = []; %@singmat; |
15 | out{10} = []; %@locate; |
16 | out{11} = []; %@init; |
17 | out{12} = []; %@done; |
18 | out{13} = @adapt; |
19 | function f = curve_func(arg) |
20 | x = arg; |
21 | f = x(1)^2+x(2)^2-1; |
22 | |
23 | function varargout = defaultprocessor(varargin) |
24 | if nargin > 2 |
25 | s = varargin{3}; |
26 | varargout{3} = s; |
27 | end |
28 | % no special data |
29 | varargout{2} = []; |
30 | % all done succesfully |
31 | varargout{1} = 0; |
32 | |
33 | function option = options |
34 | option = contset; |
35 |
|
36 | function [res,x,v] = adapt(x,v) |
37 | res=[]; |
38 | |
curve.m |
>> init; >> [x,v,s]=cont(@curve,[1;0]); first point found tangent vector to first point found Closed curve detected at step 70 elapsed time = 0.1 secs npoints curve = 70
The generated curve is plotted in Figure 32 with the command:
>> cpl(x,v,s)In this case x has dimension 2, so a 2D-plot is drawn with the first component of x (value of the state variable