SORGRQ(3)

🦋 sorgrq.f(3) — or like, the glow-up guide to SORGRQ 🦋

okay bestie, welcome to the Library Functions Manual entry for

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

yes that's the whole path, no I'm not abbreviating it, it's literally the NAME section and we respect the source file's full government name ✨

---

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine SORGRQ (m, n, k, a, lda, tau, work, lwork, info)
    SORGRQ

that's it. that's the icon. the main character of this manpage, no cap 💅

---

🎀 Function/Subroutine Documentation 🎀

subroutine SORGRQ (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SORGRQ

⭐ Purpose ⭐

ok so this is the whole point of the routine, pay attention 🫶

!>
!> SORGRQ generates an M-by-N real matrix Q with orthonormal rows,
!> which is defined as the last M rows of a product of K elementary
!> reflectors of order N
!>
!>       Q  =  H(1) H(2) . . . H(k)
!>
!> as returned by SGERQF.
!>

short version: it builds you the matrix Q, M-by-N, real, with orthonormal rows — and Q is literally the last M rows of the product of K elementary reflectors of order N, i.e.

Q  =  H(1) H(2) . . . H(k)

all that coming at you fresh from SGERQF. slay. it's giving "handed down by the oracle" 🧚

💜 Parameters 💜

• M — M is INTEGER. it's the number of rows of the matrix Q. the rule is M >= 0. that's it, that's the whole vibe check.
• N — N is INTEGER. the number of columns of the matrix Q. constraint: N >= M. so like, no squishing it the other way, periodt.
• K — K is INTEGER. the number of elementary reflectors whose product defines the matrix Q. constraint: M >= K >= 0. keep it in range bestie 🔥
• A — A is REAL array, dimension (LDA,N).
  • on entry: the (m-k+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.
  • on exit: the M-by-N matrix Q. boom, glow-up complete 💖
• LDA — LDA is INTEGER. the first dimension of the array A. constraint: LDA >= max(1,M). don't skip this one, it WILL notice 🙈
• TAU — TAU is REAL array, dimension (K). TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGERQF. it's the little sparkle that makes the reflector work ✨
• WORK — WORK is REAL array, dimension (MAX(1,LWORK)). on exit, if INFO = 0, then WORK(1) returns the optimal LWORK. it's like a receipt for the ideal workspace size 🧾
• LWORK — LWORK is INTEGER. the dimension of the array WORK, with LWORK >= max(1,M).
  • for optimum performance, LWORK >= M*NB, where NB is the optimal blocksize. go bigger, live your best life 🌈
  • 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. it's a lil peek, not a full send 👀
• INFO — INFO is INTEGER.
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument has an illegal value 💀 (yes, negative INFO means someone passed a bad argument, go find out which one)

fr fr, the LWORK = -1 query mode is not an error. don't panic-text me about it. it's literally documented behaviour. 🫶

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 127 of file sorgrq.f. iconic. line 127 specifically. we love a precise citation 🎀

---

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. the robots made this one, be nice to them 🤖💕

---

and that's the whole page bestie — every parameter, every constraint, every default, nothing skipped, nothing invented. iykyk 💅

LAPACK — Version 3.12.0 — /home/abui...RC/sorgrq.f(3) ... mwah, that's the sign-off, go forth and orthogonalise your rows 🦋✨🍓