Function to compute matmul(transpose(A),A)?

[Beliavsky]

Stdlib has corr and cov functions that compute the correlation and covariance matrices of the columns of an array. Computing the correlation matrix of the columns of array A, assuming that the elements of each column have been shifted by the column mean, involves calculating

matmul(transpose(A),A)

Could this be added as a function? If this can be computed efficiently, the programmer can calculate the correlation matrix using computed or a priori means and variances, as I described in Give stats functions optional mean arguments?

BLAS does have dgemm to multiply matrices, either of which may be transposed, but does it optimize the special but common case that the two matrices are the same?

[ivan-pi]

I just tested this with the Linnea tool, which recommends two algorithms:

• Algorithm 1: use the BLAS level 3 routine dsyrk to calculate one half of the resulting symmetric matrix, then copy the other half
• Algorithm 2: use the BLAS level 3 routine dgemm

Unfortunately, the tool only supports Julia output.