/home/abui.../sgemlqt.f(3)

💅 /home/abui.../sgemlqt.f(3) — Library Functions Manual

okay so bestie, you found the manpage for /home/abui.../sgemlqt.f(3) and we are gonna get you fluent in it. no cap. ✨

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🌸 NAME 🌸

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

like, that's literally the whole file path. the source. the origin story. the main character's birth certificate 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines — this is where the actual ✨content✨ lives:

subroutine SGEMLQT (side, trans, m, n, k, mb, v, ldv, t, ldt, c, ldc,
    work, info)

SGEMLQT — that's her name, say it with your chest 💅

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👑 Function/Subroutine Documentation 👑

subroutine SGEMLQT (character side, character trans, integer m, integer n,
    integer k, integer mb, real, dimension( ldv, * ) v, integer ldv, real,
    dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer
    ldc, real, dimension( * ) work, integer info)

SGEMLQT — she's back and this time with the full type signature. types on types on types 💖

⭐ Purpose ⭐

ok so (and this is the whole vibe, no notes):

!>
!> DGEMLQT 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) = I - V T V**T
!>
!> generated using the compact WY representation as returned by SGELQT.
!>
!> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'.
!>

yes bestie, the docs up top say DGEMLQT even though the routine is SGEMLQT — we do not ask questions, we simply notice it and move on 🙈 (keeping it exactly as written, that's the rule).

so basically: you hand her a matrix C, she slaps Q (or Q**T) on the left or right depending on your choices, and Q itself is a product of K elementary reflectors built with the compact WY representation, courtesy of SGELQT. iconic behavior, honestly 🔥

🌈 Parameters 🌈

SIDE

!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**T from the Left;
!>          = 'R': apply Q or Q**T from the Right.
!>

left or right, pick your fighter. it's giving "which side of the bed do you wake up on" 😭

TRANS

!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Transpose, apply Q**T.
!>

'N' = no transpose, apply Q. 'C' = transpose, apply Q**T. the 'C' is doing so much work here, ngl 🫶

M

!>          M is INTEGER
!>          The number of rows of the matrix C. M >= 0.
!>

rows of C. must be M >= 0. respect the zero-inclusive bound 💜

N

!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>

columns of C. N >= 0. same energy. ⭐

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.
!>

how many elementary reflectors are getting multiplied together to make Q. and pay attention to the bounds, bestie:

• SIDE = 'L' → M >= K >= 0
• SIDE = 'R' → N >= K >= 0

MB

!>          MB is INTEGER
!>          The block size used for the storage of T.  K >= MB >= 1.
!>          This must be the same value of MB used to generate T
!>          in SGELQT.
!>

block size for storing T. the range is K >= MB >= 1 (not zero, one — she has standards 💅). and it must be the exact same MB you used to generate T in SGELQT. mismatch it and you're on your own, fr fr.

V

!>          V is REAL array, dimension
!>                               (LDV,M) if SIDE = 'L',
!>                               (LDV,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
!>          SGELQT in the first K rows of its array argument A.
!>

dimension is (LDV,M) if SIDE = 'L' and (LDV,N) if SIDE = 'R'. the i-th row holds the vector defining H(i), for i = 1,2,...,k, exactly as SGELQT handed it to you in the first K rows of its argument A. handoff queen 🤝

LDV

!>          LDV is INTEGER
!>          The leading dimension of the array V. LDV >= max(1,K).
!>

leading dimension of V. LDV >= max(1,K). write it down, love it, live by it.

T

!>          T is REAL array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by SGELQT, stored as a MB-by-K matrix.
!>

dimension (LDT,K). the upper triangular factors of the block reflectors, straight from SGELQT, stored as an MB-by-K matrix. triangular and thriving 🔺

LDT

!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= MB.
!>

leading dimension of T. LDT >= MB. short and slay 🎀

C

!>          C is REAL array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q.
!>

dimension (LDC,N). on entry: your precious M-by-N matrix C. on exit: overwritten by Q C, Q**T C, C Q**T or C Q. she does not preserve. she transforms 💀 make sure that's what you wanted!

LDC

!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!>

leading dimension of C. LDC >= max(1,M). boundaries are self-care 🌸

WORK

!>          WORK is REAL array. The dimension of
!>          WORK is N*MB if SIDE = 'L', or  M*MB if SIDE = 'R'.
!>

workspace array. size it right: N*MB if SIDE = 'L', or M*MB if SIDE = 'R'. yes, the two spaces after "or" are canon. 🧚

INFO

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

the vibe check 💫

• = 0: successful exit, we ate.
• < 0: if INFO = -i, the i-th argument had an illegal value. somebody passed something cursed and INFO is telling on them.

🫶 Author 🫶

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

four whole institutions collaborated on this. group project that actually worked, unlike yours 😭 (jk jk ily)

Definition at line 151 of file sgemlqt.f. — line 151, mark it, screenshot it, put it on your wall 📌

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. so nobody wrote this page by hand, a robot did it, and honestly? she did great. 💖

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and that's the whole thing bestie — every parameter, every bound, every !> marker, untouched. the facts are sacred, the vibe is free. 🔥

LAPACK — Version 3.12.0 — and the page itself lives at /home/abui.../sgemlqt.f(3). go forth and multiply your reflectors, you absolute icon 👑✨🌈