def calculate$\_$S$($X$,$ n$,$ m$)$:

$\text{'}\text{'}\text{'}$

function calculate$\_$S$($X$)$

Computes the S matrix.

Syntax:

S$=$calculate$\_$S$($X$)$

Input:

X: nxd data matrix with n vectors $($rows$)$ of dimensionality d

n: number of rows in X

m: output number of columns in S

Output:

Matrix S of size nxm

S$[$i$,$j$]$ is the inner$-$product between vectors X$[$i$,$:$]$ and X$[$i$,$:$]$

$\text{'}\text{'}\text{'}$

#assert n $==$ X$.$shape$[0]$