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.
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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;
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