CLARFB(3)

🎀 NAME 🎀

CLARFB(3) is the manual page for the LAPACK Library Functions Manual, and the source file is literally:

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

Bestie, that’s the path. Slay. 💅

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

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

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.

💫 Purpose

Okay so the purpose is: 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 whole assignment, and it ate. 💅

🧸 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

Okay so 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 clarfb.f.

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that’s the whole page. Cute sign-off: LAPACK, Version 3.12.0, and the footer path /home/abui...RC/clarfb.f(3). No cap, periodt. 💖✨