Asked by Pauline
on 22 Apr 2013

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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Answer by Teja Muppirala
on 23 Apr 2013

Accepted answer

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;

Answer by Cedric Wannaz
on 23 Apr 2013

Edited by Cedric Wannaz
on 23 Apr 2013

**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)

Walter Roberson
on 23 Apr 2013

Cedric Wannaz
on 23 Apr 2013

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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## 3 Comments

## Cedric Wannaz (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/73160#comment_144883

I am not sure to fully understand your question.. you get a vector

xand you want to print elementsx(i-1)for allisuch asx(i)equals 1?## Pauline (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/73160#comment_144885

Hi, Cedric. Not quite, perhaps my edit to the question would help clarify my problem?

## Walter Roberson (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/73160#comment_144894

Saying x(:,1) and x(:,2) would make the question clearer.