Values of intersection points of plot. Print results.

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Pauline
Pauline 2013-4-22
Suppose I have a code that numerically integrates a set of ODEs, where my dependent variable is t and the vector of variables is x. I wish to print and plot values of x(1) for whenever x(2)=1. How might I achieve that? Some sort of "If" function?
In other words, graphically speaking, I can plot x(1) against x(2) and draw a vertical line at x(2)=1 and I want to know the x(1) values at the intersections of the plot and the vertical line.
Thanks.
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Pauline
Pauline 2013-4-23
Hi, Cedric. Not quite, perhaps my edit to the question would help clarify my problem?
Walter Roberson
Walter Roberson 2013-4-23
Saying x(:,1) and x(:,2) would make the question clearer.

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采纳的回答

Teja Muppirala
Teja Muppirala 2013-4-23
If your x is the output of an ODE solver, then it might not hit x2 = 1 exactly and you will need to interpolate.
You could use a line intersection finder from the file exchange or the Mapping Toolbox's POLYXPOLY function, or you could kind of do it manually:
% Just making some test data
A = [-0.1 -2; 2 -0.2];
F = @(t,x) A*x;
[T,X] = ode45(F,[0 10],[5; 2]);
plot(X(:,2),X(:,1)); xlabel('X(2)'),ylabel('X(1)');
hold on;
x2 = X(:,2); % Get the second state
x2goal = 1; % Position of vertical line
% Find zero crossings by changes in sign
E = x2-x2goal; % Find when E == 0
dE = diff(sign(E));
t = find(abs(dE)==2);
t = [t + E(t)./(E(t)-E(t+1)); find(E==0)]; %Linear Interpolation
t = sort(t); %Not necessary
crossings = interp1(X(:,1),t)
% Plot the result
plot(x2goal,crossings,'r.','markersize',16)
grid on;

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Cedric
Cedric 2013-4-23
编辑：Cedric 2013-4-23
EDIT: this answer is wrong, I answered too quickly without paying attention to the fact that your x is the output of an ODE solver. Please jump directly to Teja's answer.
Ok, then you can proceed as follows:
id = x(:,2) == 1 ;
x(id,1) % This will provide you with all x(:,1) that
% correspond to a x(:,2) equal to 1.
id is a vector of logicals (outcome of the test of equality on x(:,2)), that we use for indexing x(:,1). If you want to have the positions numerically, you can use
find(id)
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Cedric
Cedric 2013-4-23
编辑：Cedric 2013-4-23
Ah yes, if x gets out of an ODE solver, Walter's comment and Teja's answer are really important; I should have thought a little further.
EDIT: and my answer is even wrong if you don't interpolate, because it is absolutely not trivial to quantify how far from 1 points that are from each side of 1 can be. Setting a large tolerance would be wrong too as it could lead to taking points that are not around any 1 crossing.

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