SRC/clarfb.f(3)

SRC/clarfb.f(3) 🦋

okay bestie, this page lives in the Library Functions Manual and it’s giving “LAPACK subroutine that makes block reflectors move.” 💖 We’re talking about clarfb, and yes, every parameter gets its moment.

🌸 NAME

SRC/clarfb.f

✨ SYNOPSIS ✨

Functions/Subroutines

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

clarfb — CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. 🫶

🧚 Function/Subroutine Documentation

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

CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix. No cap, that’s the whole mood. 💅

🎯 Purpose

okay so the actual assignment: CLARFB 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 tea. 😭✨

🔧 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 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 COMPLEX 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 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 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. iykyk ✨

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 clarfb.f.

👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole page, bestie! footer vibes: LAPACK Version 3.12.0, source page SRC/clarfb.f(3) — mwah 💋✨