I want to do a 1D integral of some 2D data

Suppose I have a function which is defined as some numerical data which is equally spaced and I wish to compute:

How would I go about it? I thought I would start something akin to:

x=linspace(-3,3,200),y=linspace(-3,3,200);

[X,Y]=meshgrid(x,y);

Z=0.5*(X.^2+Y.^2);

%This creates a plottable surface, then I tried something like:

g=trapz(Z,y,2);

but it threw up an error. Any suggestions?

Answer 1

[Wan Ji]

trapz function has been wrongly used, trapz(x_array, F(x,y)) is with . So you should do following

x=linspace(-3,3,200);
y=linspace(-3,3,100);
[X,Y]=meshgrid(x,y);
Z=0.5*(X.^2+Y.^2);
%This creates a plottable surface, then I tried something like:
g=trapz(y,Z);
plot(x,g,'r*')
hold on
g2 = 0.5*(x.^2*6 + 1/3*(3^3+3^3));
plot(x,g2, 'b--')
legend('trapz','exact')

[Matthew Hunt]

That's precisely what I was looking for, thank you.

Answer 2

[Walter Roberson]

g=trapz(y,Z,2);

... but be careful about which dimension is x and which dimension is y. In MATLAB, rows correspond to y and columns correspond to x, and rows is the first dimension...