SRC/zlarfb.f(3)

🌸 NAME 🌸

SRC/zlarfb.f — okay so this is the SRC/zlarfb.f(3) page from the Library Functions Manual, bestie. It's giving “one file, one very specific Fortran subroutine,” and honestly? Iconic. ✨

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine zlarfb — ZLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

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

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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: 🎯

Okay so here's the main-character assignment: 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. 💅

💅 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).

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

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.

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 194 of file zlarfb.f.

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🌈 Author 🌈

This page itself was generated automatically by Doxygen for LAPACK from the source code. The autogenerated credit is literally: Generated automatically by Doxygen for LAPACK from the source code. 💫

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okay bestie, that's the whole SRC/zlarfb.f(3) page. Footer vibe: LAPACK, Version 3.12.0, and SRC/zlarfb.f(3) — mwah 💋✨