How convolution with 'same' parameter select the first item?

In the example of 'same' shape,

u = [-1 2 3 -2 0 1 2];
v = [2 4 -1 1];
w = conv(u,v,'same')

w =

    15     5    -9     7     6     7    -1

The full convolution is [-2 0 15 5 -9 7 6 7 -1 2]. Why start from the 3rd item 15? Not 2nd item 0?

Answer 1

[Image Analyst]

The full convolution has more numbers because the window can "go off" the edge of the data. Do you understand that part? If so, the answer should be obvious. Where do you think the 15 should go? Remember there are no negative indexes or zero indexes.