SLARFB(3)

💅 NAME 💅

okay so bestie, you're on the SLARFB(3) page — the manual name up top is Library Functions Manual, and the page path is /home/abui...RC/slarfb.f(3). The file this page is literally about is:

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

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine SLARFB (side, trans, direct, storev, m, n, k, v, ldv, t, ldt,
    c, ldc, work, ldwork)

SLARFB applies a block reflector or its transpose to a general rectangular matrix. periodt 💅

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🦋 Function/Subroutine Documentation 🦋

here's the full signature, copied exactly so nobody comes for me:

subroutine SLARFB (character side, character trans, character direct,
    character storev, integer m, integer n, integer k, real, dimension( ldv,
    * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real,
    dimension( ldc, * ) c, integer ldc, real, dimension( ldwork, * ) work,
    integer ldwork)

SLARFB applies a block reflector or its transpose to a general rectangular matrix. slay. 🦋

🌈 Purpose 🌈

the whole vibe is this: SLARFB applies a real block reflector H or its transpose H**T to a real m by n matrix C, from either the left or the right. that's the tea ☕

🎀 Parameters 🎀

• SIDE — SIDE is CHARACTER*1.
  • = 'L': apply H or H**T from the Left
  • = 'R': apply H or H**T from the Right
• TRANS — TRANS is CHARACTER*1.
  • = 'N': apply H (No transpose)
  • = 'T': apply H**T (Transpose)
• DIRECT — DIRECT is CHARACTER*1. Indicates how H is formed from a product of elementary reflectors.
  • = 'F': H = H(1) H(2) . . . H(k) (Forward)
  • = 'B': H = H(k) . . . H(2) H(1) (Backward)
• STOREV — STOREV is CHARACTER*1. Indicates how the vectors which define the elementary reflectors are stored:
  • = 'C': Columnwise
  • = 'R': Rowwise
• M — M is INTEGER. The number of rows of the matrix C.
• N — N is INTEGER. The number of columns of the matrix C.
• K — K is INTEGER. The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).
  • If SIDE = 'L', M >= K >= 0;
  • if SIDE = 'R', N >= K >= 0.
• V — V is REAL array, dimension
  • (LDV,K) if STOREV = 'C'
  • (LDV,M) if STOREV = 'R' and SIDE = 'L'
  • (LDV,N) if STOREV = 'R' and SIDE = 'R'

The matrix V. See Further Details. iykyk 👀

• LDV — LDV is INTEGER. The leading dimension of the array V.
  • If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
  • if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
  • if STOREV = 'R', LDV >= K.
• T — T is REAL array, dimension (LDT,K). The triangular k by k matrix T in the representation of the block reflector.
• LDT — LDT is INTEGER. The leading dimension of the array T. LDT >= K.
• C — C is REAL array, dimension (LDC,N).
  • On entry, the m by n matrix C.
  • On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is REAL array, dimension (LDWORK,K).
• LDWORK — LDWORK is INTEGER. The leading dimension of the array WORK.
  • If SIDE = 'L', LDWORK >= max(1,N);
  • if SIDE = 'R', LDWORK >= max(1,M).

👑 Author 👑

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

🔥 Further Details 🔥

The shape of the matrix V and the storage of the vectors which define the H(i) is best illustrated by the following example with n = 5 and k = 3. The elements equal to 1 are not stored; the corresponding array elements are modified but restored on exit. The rest of the array is not used.

and here's the diagram, kept exactly as it appears — Doxygen !> sprinkles and all:

!>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
!>
!>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
!>                   ( v1  1    )                     (     1 v2 v2 v2 )
!>                   ( v1 v2  1 )                     (        1 v3 v3 )
!>                   ( v1 v2 v3 )
!>                   ( v1 v2 v3 )
!>
!>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
!>
!>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
!>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
!>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
!>                   (     1 v3 )
!>                   (        1 )
!>

Definition at line 195 of file slarfb.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie 💖 cute sign-off time: LAPACK Version 3.12.0, page /home/abui...RC/slarfb.f(3) — the footer I got doesn't show a date, so I'm not inventing one, just sending fairy dust 🧚✨🫶