Question

I’m having a weird result with Matlab’s trapz function. I have two variables, zptest and omega, both of which are positive, 3000x2x1 arrays.

When I plot zptest vs omega (plot(zptest(:,1,1),omega(:,1,1)) the curve is clearly positive and should give a positive result when integrating. This is not the case, however, as shown below:

trapz(zptest(:,1,1),omega(:,1,1))

ans =

-0.049999940237341

just to prove that both omega and zptest are positive:

find(omega(:,1,1) < 0)

ans =

Empty matrix: 0-by-1

find(zptest(:,1,1) < 0)

ans =

Empty matrix: 0-by-1

I know I’m not giving any context to what I’m actually doing but this seems like a context independent problem. Does anyone have any idea what’s going on?

Answer 1

Try re-ordering x in ascending order (and y-values accordingly):

x_order = x(end:-1:1); %fliplr
y_order = y(end:-1:1); %fliplr
trapz(x_order, y_order)

In trapz(x,y) differentiation of x is applied through diff(x,1,1), i.e. [x(2:n,:) - x(1:n-1,:)]. If your x is descending this will give negative dx. It doesn’t matter if it is positive or negative. However, in plot the curve will appear positive-definite (you don’t actually see the order of points, just pairs from two vectors on a plane).

Example (compare the following):

x = [-1 -0.5 0]; y = 0.5-x; 
figure; plot(x,y); hold on; plot(-x, y,'r')
trapz(x, y)
trapz(-x, y)
figure; plot(x, y); hold on; plot(fliplr(-x), fliplr(y),'r')
trapz(fliplr(-x), fliplr(y))