# Orthogonal Factorizations

This section describes the ScaLAPACK routines for the QR (RQ) and LQ (QL) factorization of matrices. Routines for the RZ factorization as well as for generalized QR and RQ factorizations are also included. For the mathematical definition of the factorizations, see the respective LAPACK sections or refer to [SLUG].

Table “Computational Routines for Orthogonal Factorizations” lists ScaLAPACK routines that perform orthogonal factorization of matrices.

Computational Routines for Orthogonal Factorizations
Matrix type, factorization | Factorize without pivoting | Factorize with pivoting | Generate matrix Q | Apply matrix Q
--- | --- | --- | --- | ---
general matrices, QR factorization | p?geqrf | p?geqpf | p?orgqr p?ungqr | p?ormqr p?unmqr
general matrices, RQ factorization | p?gerqf |  | p?orgrq p?ungrq | p?ormrq p?unmrq
general matrices, LQ factorization | p?gelqf |  | p?orglq p?unglq | p?ormlq p?unmlq
general matrices, QL factorization | p?geqlf |  | p?orgql p?ungql | p?ormql p?unmql
trapezoidal matrices, RZ factorization | p?tzrzf |  |  | p?ormrz p?unmrz
pair of matrices, generalized QR factorization | p?ggqrf |  |  |
pair of matrices, generalized RQ factorization | p?ggrqf |  |  |