SRC/zunmbr.f(3)

🦋 SRC/zunmbr.f(3) — Library Functions Manual 💅

🌸 NAME 🌸

SRC/zunmbr.f

That’s the page name, bestie — iconic little LAPACK subroutine page energy ✨

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine zunmbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc,
    work, lwork, info)
ZUNMBR

💅 Function/Subroutine Documentation 💅

subroutine zunmbr (character vect, character side, character trans, integer
    m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda,
    complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c,
    integer ldc, complex*16, dimension( * ) work, integer lwork, integer
    info)
ZUNMBR

💖 Purpose 💖

okay so here’s the tea ☕ — if VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H

and if VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C with:

                SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      P * C          C * P
TRANS = 'C':      P**H * C       C * P**H

Here Q and P**H are the unitary matrices determined by ZGEBRD when reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) and G(i) respectively. No cap, that’s literally the setup 💅

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order of the unitary matrix Q or P**H that is applied.

If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:

• if nq >= k, Q = H(1) H(2) . . . H(k);
• if nq < k, Q = H(1) H(2) . . . H(nq-1).

If VECT = 'P', A is assumed to have been a K-by-NQ matrix:

• if k < nq, P = G(1) G(2) . . . G(k);
• if k >= nq, P = G(1) G(2) . . . G(nq-1).

🎀 Parameters 🎀

one bullet per parameter because we are organized and cute like that 🫶

• VECT — VECT is CHARACTER*1
  • = 'Q': apply Q or Q**H;
  • = 'P': apply P or P**H.
• SIDE — SIDE is CHARACTER*1
  • = 'L': apply Q, QH, P or PH from the Left;
  • = 'R': apply Q, QH, P or PH from the Right.
• TRANS — TRANS is CHARACTER*1
  • = 'N': No transpose, apply Q or P;
  • = 'C': Conjugate transpose, apply QH or PH.
• M — M is INTEGER — the number of rows of the matrix C. M >= 0, periodt.
• N — N is INTEGER — the number of columns of the matrix C. N >= 0, slay.
• K — K is INTEGER — if VECT = 'Q', the number of columns in the original matrix reduced by ZGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by ZGEBRD. K >= 0.
• A — A is COMPLEX*16 array, dimension

(LDA,min(nq,K)) if VECT = 'Q'
(LDA,nq)        if VECT = 'P'

The vectors which define the elementary reflectors H(i) and G(i), whose products determine the matrices Q and P, as returned by ZGEBRD.

• LDA — LDA is INTEGER — the leading dimension of the array A. If VECT = 'Q', LDA >= max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
• TAU — TAU is COMPLEX*16 array, dimension (min(nq,K)) — TAU(i) must contain the scalar factor of the elementary reflector H(i) or G(i) which determines Q or P, as returned by ZGEBRD in the array argument TAUQ or TAUP.
• C — C is COMPLEX*16 array, dimension (LDC,N) — on entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or C*P**H.
• LDC — LDC is INTEGER — the leading dimension of the array C. LDC >= max(1,M).
• WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) — on exit, if INFO = 0, WORK(1) returns the optimal LWORK.
• LWORK — LWORK is INTEGER — the dimension of the array WORK. If SIDE = 'L', LWORK >= max(1,N); if SIDE = 'R', LWORK >= max(1,M); if N = 0 or M = 0, LWORK >= 1. For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the optimal blocksize. (NB = 0 if M = 0 or N = 0.)

If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🌸 Author 🌸

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

📌 Definition at line 194 of file zunmbr.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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cute sign-off, bestie: source/version is LAPACK Version 3.12.0, page is SRC/zunmbr.f(3), and the footer didn’t give me a date, so I’m not inventing one — periodt 💖✨