CUNMBR(3)

💅 CUNMBR(3) 💅

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

Okay bestie, welcome to the CUNMBR(3) page from the Library Functions Manual — this is the file it documents, fr.

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

CUNMBR

💖 Function/Subroutine Documentation 💖

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

CUNMBR

🌈 Purpose 🌈

If VECT = 'Q', CUNMBR 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

If VECT = 'P', CUNMBR 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 CGEBRD 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.

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 🍓

• 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.
• N — N is INTEGER; the number of columns of the matrix C. N >= 0.
• K — K is INTEGER; if VECT = 'Q', the number of columns in the original matrix reduced by CGEBRD. If VECT = 'P', the number of rows in the original matrix reduced by CGEBRD. K >= 0.
• A — A is COMPLEX 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 CGEBRD.

• 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 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 CGEBRD in the array argument TAUQ or TAUP.
• C — C is COMPLEX 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 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 195 of file cunmbr.f.

👑 Author 👑

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