SORMQL(3)

💅 SORMQL(3) 💅

Okay bestie, quick vibe check: this page comes from the Library Functions Manual, and the header title is /home/abui...RC/sormql.f(3). We’re folding that in right here so you don’t have to stare at a raw header line. Now let’s get into the LAPACK of it all. ✨

---

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sormql.f

That’s the source-file path this page is about — no cap. 🫶

---

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

       subroutine SORMQL (side, trans, m, n, k, a, lda, tau, c, ldc, work,
           lwork, info)
           SORMQL

---

💖 Function/Subroutine Documentation 💖

   subroutine SORMQL (character side, character trans, integer m, integer n,
       integer k, real, dimension( lda, * ) a, integer lda, real, dimension( *
       ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * )
       work, integer lwork, integer info)
       SORMQL

The name tag is literally SORMQL. Iconic, honestly. 👑

🎀 Purpose 🎀

SORMQL’s whole main-character move is overwriting the general real M-by-N matrix C with one of these four combos, depending on SIDE and TRANS:

!>
!> SORMQL overwrites the general real M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'T':      Q**T * C       C * Q**T
!>
!> where Q is a real orthogonal matrix defined as the product of k
!> elementary reflectors
!>
!>       Q = H(k) . . . H(2) H(1)
!>
!> as returned by SGEQLF. Q is of order M if SIDE = 'L' and of order N
!> if SIDE = 'R'.
!>

So yes: Q is a real orthogonal matrix built as the product of k elementary reflectors, and it comes back from SGEQLF. Q is of order M if SIDE = 'L', and of order N if SIDE = 'R'. Periodt. 🌈

🌈 Parameters 🌈

• SIDE — SIDE is CHARACTER*1. = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. Pick your side, bestie.
• TRANS — TRANS is CHARACTER*1. = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
• M — M is INTEGER. The number of rows of the matrix C. M >= 0.
• N — N is INTEGER. The number of columns of the matrix C. N >= 0.
• K — K is INTEGER. The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0.
• A — A is REAL array, dimension (LDA,K). The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQLF in the last k columns of its array argument A.
• LDA — LDA is INTEGER. The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N).
• TAU — TAU is REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQLF.
• C — C is REAL array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER. The dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M). For good performance, LWORK should generally be larger.

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. Iconic workspace-query behavior, honestly. 💅

• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

🧚 Author 🧚

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 166 of file sormql.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

---

Final footer sign-off, bestie: LAPACK, Version 3.12.0, and /home/abui...RC/sormql.f(3). That’s the whole footer flex. Mwah. 💋✨