This example solves the linear least squares problems for the minimum norm solutions $x_1$ and $x_2$, where $b_j$ is the $j$th column of the matrix $B$, and

The solution is obtained by first obtaining a $QR$ factorization with column pivoting of the matrix $A$, and then the $RZ$ factorization of the leading $k$ by $k$ part of $R$ is computed, where $k$ is the estimated rank of $A$. A tolerance of $0.01$ is used to estimate the rank of $A$ from the upper triangular factor, $R$.

Note that the block size (NB) of $64$ assumed in this example is not realistic for such a small problem, but should be suitable for large problems.