How to compute diagonal entries of a matrix of inner products (gram matrix) in a vectorized way?

Question

Brando Miranda 2016-4-5

1
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/277357-how-to-compute-diagonal-entries-of-a-matrix-of-inner-products-gram-matrix-in-a-vectorized-way

编辑： Brando Miranda 2016-5-2

I am interested in computing only the diagonals of a matrix of inner products between vectors (Gram matrix). Say that we have the Dx1 vectors t_i stacked in matrix as follows t = [t_1, ..., t_k, ..., t_K]. I want to computed only the diagonal as in:

inner_product = t_i' * t_i

One obvious way to do it is to do:

Gram = t' * t

and then extract the diagonal entries Gram(i,i) but it seems that matlab is doing a lot of unnecessary computation (computing the off diagonals) and I wanted to avoid this using vectorized code. One can obviously also implemented this with a for loop and iterate through the matrix, however, since I have large vectors and I have the resources to store the data in GPUs, it seems silly to me do such a for loop when I can just take advantage of vectorized code.

Is it possible to compute only the diagonal entries of the gram matrix using vectorized code?