how to sum different rows within a column

I have 2 columns with 3101 values and i want to add the row 1&2 then row 2&3, 3&4 and so on..

I want to execute this calculation for the entire column with a cummulative sum

p=0.5*(column1(row1+row2))*column2(row2-row1)

the next row should be = 0.5*(column1(row2+row3))*column2(row3-row2) + p

How can I select 2 row values in the same column with the output created in a different column?

Thanks in advance

Answer 1

[Star Strider]

One approach would be to create the third column independently and then concatenate it at the end —

A = randi(9,10,2);
p = 0;
for k = 1:size(A,1)-1
    v(k,:) = (A(k,1)+A(k+1,1))/2 * (A(k+1,2)-A(k,2)) + p;
    p = v(k);
end
A(:,3) = [NaN; v]

A = 10×3

8 1 NaN 3 7 33 8 3 11 3 5 22 3 2 13 1 7 23 4 9 28 1 7 23 3 6 21 6 2 3

.

Answer 2

[Image Analyst]

"to add the row 1&2 then row 2&3, 3&4 and so on.." you can use conv:

kernel = [1;1];
sums = conv(column1, kernel, 'valid');
kernel = [-1; 1];
diffs = conv(column2, kernel, 'valid');

If you want it multiplied by 0.5 and cumulatively summed, you can .....

Well actually I think Star's for loop approach is much simpler to do and understand than my vectorized approach so just go with that.