Routines for the computation and efficient updating of the QR factorization of a matrix.

This group provides routines for modifying the original matrix via rank-1 updates, row/column insertions, deletions, or shifts, and updating the corresponding orthogonal matrix Q and upper trapezoidal matrix R without recomputing the entire decomposition from scratch. It supports both full and economized QR factorizations and relies on Givens rotations for maintaining the triangular structure of the R matrix.