SRC/slarfb.f(3)

💅 SRC/slarfb.f

okay so bestie, this is a LAPACK manpage for slarfb and it's genuinely iconic — it's the girl that applies your block reflector (or its transpose) to a general rectangular matrix. fr fr, she does the heavy lifting so you don't have to. let's get into it 🎀

---

✨ 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. that's the whole vibe. 💅

---

🌸 FUNCTION/SUBROUTINE DOCUMENTATION 🌸

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. yes ma'am 💖

🦋 PURPOSE 🦋

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.

like, she takes your C and she transforms it. main character energy only. ✨

🌈 PARAMETERS 🌈

• SIDE — SIDE is CHARACTER*1, and it's literally just "which side tho":
  • = 'L': apply H or H**T from the Left
  • = 'R': apply H or H**T from the Right
• TRANS — TRANS is CHARACTER*1, the transpose vibe check:
  • = 'N': apply H (No transpose)
  • = 'T': apply H**T (Transpose)
• DIRECT — DIRECT is CHARACTER*1, and it explains 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, which tells you how the vectors that define the elementary reflectors are stored:
  • = 'C': Columnwise
  • = 'R': Rowwise
• M — M is INTEGER, aka the number of rows of the matrix C. 🍓
• N — N is INTEGER, aka 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). the constraints are NOT optional, bestie:
  • 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 below, it's worth it, the diagrams eat 💅

• 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). it's the triangular k by k matrix T in the representation of the block reflector. she's triangular, she's iconic, she's doing her best. 👑
• LDT — LDT is INTEGER, the leading dimension of the array T. and LDT >= K. no exceptions, periodt.
• 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. yeah she gets fully replaced, hope you didn't need the original 😭
• LDC — LDC is INTEGER, the leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is REAL array, dimension (LDWORK,K). her little workspace moment 🧚
• 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.

the whole squad showed up, we love a collab ✨

---

💜 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 triangular part of V (including its diagonal) is not referenced.

ok so this next bit is the part where the diagrams are genuinely the best thing on the page — look at her go:

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 )

⚠️ reminder bestie: the triangular part of V (including its diagonal) is not referenced. don't come for her, she's just not looking at it. 💀

---

📍 Definition

Definition at line 194 of file slarfb.f.

---

💫 AUTHOR 💫

Generated automatically by Doxygen for LAPACK from the source code. she was born this way, no cap 🦋

---

and that's the page! this whole thing is from LAPACK Version 3.12.0 for SRC/slarfb.f(3) — slay, go call your reflectors responsibly. 💖✨🎀