SORMRQ(3)

💅 NAME 💅

okay bestie, welcome to the Library Functions Manual page for SORMRQ 🦋. the exact path this page is filed under is /home/abui...RC/sormrq.f(3) — yes, that's the whole NAME section, and it's giving "my full government name is a filesystem path" 💀.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

here's the signature, no cap:

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

🦋 Function/Subroutine Documentation 🦋

the full signature is literally:

subroutine SORMRQ (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)
    SORMRQ

🌸 Purpose 🌸

SORMRQ overwrites the general real M-by-N matrix C with the stuff in this exact matrix block:

!>
!> SORMRQ 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(1) H(2) . . . H(k)
!>
!> as returned by SGERQF. Q is of order M if SIDE = 'L' and of order N
!> if SIDE = 'R'.
!>

so basically: SIDE = 'L' means apply from the left, SIDE = 'R' means apply from the right; TRANS = 'N' means no transpose and apply Q, TRANS = 'T' means transpose and apply Q**T. Q is the real orthogonal matrix made from the product of k elementary reflectors, exactly as SGERQF returns it. Q has order M when SIDE = 'L', and order N when SIDE = 'R'. 💖

🎀 Parameters 🎀

• SIDE — CHARACTER*1. = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right.
• TRANS — CHARACTER*1. = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T.
• M — INTEGER. The number of rows of the matrix C. M >= 0.
• N — INTEGER. The number of columns of the matrix C. N >= 0.
• K — 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 — REAL array, dimension (LDA,M) if SIDE = 'L', or (LDA,N) if SIDE = 'R'. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGERQF in the last k rows of its array argument A.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,K).
• TAU — REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGERQF.
• C — 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 — INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — REAL array, dimension (MAX(1,LWORK)). On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — 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.

• INFO — 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 sormrq.f. ⭐

yep, that's where it lives, bestie. 🫶

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

---

okay that's the whole page, bestie. footer sign-off energy: LAPACK Version 3.12.0 and /home/abui...RC/sormrq.f(3) — that's the version/source line this page gives us, and no extra date is printed on this one. byeee 🫶✨