ZLARFB(3)

✨ NAME ✨

This page lives in the LAPACK Library Functions Manual as ZLARFB(3), with the header path /home/abui...RC/zlarfb.f(3). The NAME line is literally this long path, bestie:

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

No cap, that whole path is the name. 💅

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🌸 SYNOPSIS 🌸

🫶 Functions/Subroutines 🫶

• subroutine ZLARFB (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork) — ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

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🦋 Function/Subroutine Documentation 🦋

subroutine ZLARFB (character side, character trans, character direct,
    character storev, integer m, integer n, integer k, complex*16,
    dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t,
    integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16,
    dimension( ldwork, * ) work, integer ldwork)

ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

🎯 Purpose 🎯

ZLARFB applies a complex block reflector H or its transpose H**H to a complex M-by-N matrix C, from either the left or the right. That's the whole vibe: block reflector, conjugate-transpose, rectangular matrix, left or right. Iconic. ✨

🌈 Parameters 🌈

• SIDE — SIDE is CHARACTER*1
  • = 'L': apply H or H**H from the Left
  • = 'R': apply H or H**H from the Right
• TRANS — TRANS is CHARACTER*1
  • = 'N': apply H (No transpose)
  • = 'C': apply H**H (Conjugate 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 COMPLEX*16 array, dimension
  • (LDV,K) if STOREV = 'C'
  • (LDV,M) if STOREV = 'R' and SIDE = 'L'
  • (LDV,N) if STOREV = 'R' and SIDE = 'R'

See Further Details.

• 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDC,N). On entry, the M-by-N matrix C. On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is COMPLEX*16 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).

Constraint check, bestie: those >= bounds are not suggestions. They are the vibe check for your array dimensions. 💀

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👑 Author 👑

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

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🦋 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.

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 zlarfb.f.

🎀 Author (Doxygen-generated note) 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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source/version: LAPACK Version 3.12.0; footer path: /home/abui...RC/zlarfb.f(3) — no separate date shown in that footer line, periodt. 💖🎀