Double numerical integration of an Experimental data (no function)

Hi all,

I have a rectangular domain ( in x and y) and have 64 points equally distributed data points around this rectangular domain (lets call the data points as A). I have the numerical value of each point on the grid. (sizes: x = 1 x 64, y = 1 x 64, A = 8 x 8)

B = double_integration(A) dx dy.

I tried the already given solution , result = trapz(x,trapz(y,mat,1),2) , but did not get any result. (Error was, LENGTH(X) must equal the length of Y in dim 1.)

Any ideas?

Many thanks

[John D'Errico]

Are the points scattered irregularly around the domain? Or are they on a regular lattice of some sort? Like an 8x8 grid?

[Baris Gungordu]

Yes the data points are arranged as 8 x 8 and I have coordinates in x and y for each point.

Answer 1

[Star Strider]

I would use trapz on each dimension of ‘A’:

int_1 = trapz(A);
Result = trapz(int_1)

[Baris Gungordu]

I tried this, it worked but the result does not look right.

A = reshape(A,64,1);
for i = 1:64
 int1(i,1) = trapz(Y64,A);
end
int2 = trapz(X64,int1);

[Star Strider]

I thought ‘A’ is (8x8), and you want to integrate it.

The trapz function integrates a matrix by integrating the columns, creating a vector. The second trapz call integrates the vector to produce the result of the double integration.

What are your data and what do you want to do with them?

[John D'Errico]

Think of trapz as a single integration, along one axis of the array. You wanted to do a double integration. The first call to trapz will turn the array into a vector of length 8, integrating down the columns of your array by default. Then the second call will integrate the vector, so doing the outer integral.

[Baris Gungordu]

My data is 8x8 but I changed it to 64x1 to make the trapz work.

I want to double integrate my data first respect to x and then with respect to y.

[Star Strider]

The trapz function works very well with matrices. It considers each column of a matrix as individual vectors, and integrates them, creating a vector. The second trapz call integrates the vector. I do not know what ‘x’ and ‘y’ are with respect to ‘A’, but you can easily transpose ‘A’ to integrate with respect to each variable in order, if necessary.