CODEWITHSUNDEEP
algorithmmatlabmathdiscrete-mathematics
Sagar Masuti
Sagar Masuti

Reputation: 1301

Double integral in matlab with non-uniform grid

I know how to perform the single integral using the trapezoidal rule for non-uniform grid. If my function is f(x,y), then single integral over dx in MATLAB would look like

m1=(sum(diff(x,1,2).*(f(:,1:end-1)+f(:,2:end)),2))/2

Now if I have the function f(x,y,z) how to perform the double integral over dydz using the trapezoidal rule of non-uniform grid in MATLAB ?

Please note its a non-uniform grid.

Upvotes: 0

Views: 1105

Answers (1)

pragmatist1
pragmatist1

Reputation: 919

Using the built in function trapz in MATLAB you can accomplish just that. Here's an example: 

>> x = -3:.1:3;
y = -5:.1:5;
z = -10:0.1:10;
[X,Y,Z] = meshgrid(x,y,z);
F = X.^2 + Y.^2 + Z.^2;
I = trapz(y,trapz(x,F,2));
I = squeeze(I);

What I'm doing is creating a mesh grid of my data points represented by lowercase x,y,z, and evaluating the function, in this case X^2+y^2+Z^2. You would already have alternate data for this. Keep in mind you can always use griddata to re-grid your data uniformly.

I then use trapz twice to integrate the x and y dimension. trapz specifically specifically integrates only over the first matrix dimension that's not equal to 1, allowing me to do this (see documentation here: http://www.mathworks.com/help/matlab/ref/trapz.html).

Finally, I use squeeze on the data to remove all singleton dimensions and return a vector. If I plot the data along the remaining dimension I get: 

>> plot(z,I);

Comparing to my original function, which if integrated analytically between -3 <= x <= 3 and -5 <= y <= 5 I obtain: 680 + 60 z^2. The two are in agreement. plot

Upvotes: 2

Related Questions