DLARFB(3)

🎀 NAME

okay so this page is DLARFB(3) from the Library Functions Manual, and the source-file path is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlarfb.f. The header/footer also shows the truncated path /home/abui...RC/dlarfb.f(3) — yes bestie, same page energy, just abbreviated 💅.

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✨ SYNOPSIS

Functions/Subroutines

• subroutine DLARFB (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork) — DLARFB applies a block reflector or its transpose to a general rectangular matrix. Iconic behavior, no cap.

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

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💖 Function/Subroutine Documentation

subroutine DLARFB

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

DLARFB applies a block reflector or its transpose to a general rectangular matrix. Literally the main character of this page 👑.

Purpose

DLARFB 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.

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. It 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. It 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 a DOUBLE PRECISION 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 👀.
• 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 a DOUBLE PRECISION 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 a DOUBLE PRECISION 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 a DOUBLE PRECISION 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.

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 dlarfb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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bye bestie 🫶 — footer says LAPACK Version 3.12.0, and the source/version path vibe is /home/abui...RC/dlarfb.f(3). The original footer didn’t show a date field, so no invented date here, periodt 💜.