Developer Reference for Intel® oneAPI Math Kernel Library for C
Orthogonal Factorizations: ScaLAPACK Computational Routines
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.
Matrix type, factorization |
Factorize without pivoting |
Factorize with pivoting |
Generate matrix Q |
Apply matrix Q |
|---|---|---|---|---|
general matrices, QR factorization |
p?geqrf (Computes the QR factorization of a general m-by-n matrix.) |
p?geqpf (Computes the QR factorization of a general m-by-n matrix with pivoting.) |
p?orgqr (Generates the orthogonal matrix Q of the QR factorization formed by p?geqrf.) p?ungqr (Generates the complex unitary matrix Q of the QR factorization formed by p?geqrf.) |
p?ormqr (Multiplies a general matrix by the orthogonal matrix Q of the QR factorization formed by p?geqrf.) p?unmqr (Multiplies a complex matrix by the unitary matrix Q of the QR factorization formed by p?geqrf.) |
general matrices, RQ factorization |
p?gerqf (Computes the RQ factorization of a general rectangular matrix.) |
p?orgrq (Generates the orthogonal matrix Q of the RQ factorization formed by p?gerqf.) p?ungrq (Generates the unitary matrix Q of the RQ factorization formed by p?gerqf.) |
p?ormrq (Multiplies a general matrix by the orthogonal matrix Q of the RQ factorization formed by p?gerqf.) p?unmrq (Multiplies a general matrix by the unitary matrix Q of the RQ factorization formed by p?gerqf.) |
|
general matrices, LQ factorization |
p?gelqf (Computes the LQ factorization of a general rectangular matrix.) |
p?orglq (Generates the real orthogonal matrix Q of the LQ factorization formed by p?gelqf.) p?unglq (Generates the unitary matrix Q of the LQ factorization formed by p?gelqf.) |
p?ormlq (Multiplies a general matrix by the orthogonal matrix Q of the LQ factorization formed by p?gelqf.) p?unmlq (Multiplies a general matrix by the unitary matrix Q of the LQ factorization formed by p?gelqf.) |
|
general matrices, QL factorization |
p?geqlf (Computes the QL factorization of a general matrix.) |
p?orgql (Generates the orthogonal matrix Q of the QL factorization formed by p?geqlf.) p?ungql (Generates the unitary matrix Q of the QL factorization formed by p?geqlf.) |
p?ormql (Multiplies a general matrix by the orthogonal matrix Q of the QL factorization formed by p?geqlf.) p?unmql (Multiplies a general matrix by the unitary matrix Q of the QL factorization formed by p?geqlf.) |
|
trapezoidal matrices, RZ factorization |
p?tzrzf (Reduces the upper trapezoidal matrix A to upper triangular form.) |
p?ormrz (Multiplies a general matrix by the orthogonal matrix from a reduction to upper triangular form formed by p?tzrzf.) p?unmrz (Multiplies a general matrix by the unitary transformation matrix from a reduction to upper triangular form determined by p?tzrzf.) |
||
pair of matrices, generalized QR factorization |
p?ggqrf (Computes the generalized QR factorization.) |
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pair of matrices, generalized RQ factorization |
p?ggrqf (Computes the generalized RQ factorization.) |