# How to know dimensions to give in trapz function

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J K on 11 Jul 2019
Commented: Rena Berman on 19 Sep 2019
Hi,
Let's say I have a matrix (see below). How do I know what number to put in the dimension variable? Matlab just gives some odd explanation without telling how to determine the dimension. Could someone please help to understand how to get the value for dim?
[Kx, W, Ky] = meshgrid(kx, w, ky);
for j = 1:9;
functione = exp(-((W-w_o).^2)/deltaW.^2).*exp(-(Kx.^2+Ky.^2)/(deltaK.^2)).*exp(1i.*sqrt((W/c).^2-(Kx.^2+Ky.^2)).*z(j));
normw = trapz(functione.^2,dim)*dw
normkx = trapz(functione.^2,dim)*dkx
normky = trapz(functione.^2,dim)*dky

It is up to you along which dimension you want it to integrate
Rena Berman on 19 Sep 2019

let's say you have a column vector x and you calculate y according to y = ax^2
now if a is a vector, you will get a matrix y:
x = linspace(0,10,5)';
a = [1 10 100];
y = a.*(x.^2)
y =
1.0e+04 *
0 0 0
0.0006 0.0063 0.0625
0.0025 0.0250 0.2500
0.0056 0.0563 0.5625
0.0100 0.1000 1.0000
This y matrix represents 3 possible column vectors ax^2 with different parameter value
Now to integrate correctoly, you should integrate along the first dimension (same dimension as the x column vector)
dim = 1;
A = trapz(x,y,dim)
A =
1.0e+04 *
0.0344 0.3438 3.4375

It all depends on the data, matrices can have many dimensions...
J K on 12 Jul 2019
I understand it all now. Thank you so much for your extensive answers!