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## zunmbr()

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

Download ZUNMBR + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> 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
      !>
      !> 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.
      !>
      !> 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

  [in]

  VECT

      !>          VECT is CHARACTER*1
      !>          = 'Q': apply Q or Q**H;
      !>          = 'P': apply P or P**H.
      !>

  [in]

  SIDE

      !>          SIDE is CHARACTER*1
      !>          = 'L': apply Q, Q**H, P or P**H from the Left;
      !>          = 'R': apply Q, Q**H, P or P**H from the Right.
      !>

  [in]

  TRANS

      !>          TRANS is CHARACTER*1
      !>          = 'N':  No transpose, apply Q or P;
      !>          = 'C':  Conjugate transpose, apply Q**H or P**H.
      !>

  [in]

  M

      !>          M is INTEGER
      !>          The number of rows of the matrix C. M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of columns of the matrix C. N >= 0.
      !>

  [in]

  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.
      !>

  [in]

  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.
      !>

  [in]

  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)).
      !>

  [in]

  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.
      !>

  [in,out]

  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.
      !>

  [in]

  LDC

      !>          LDC is INTEGER
      !>          The leading dimension of the array C. LDC >= max(1,M).
      !>

  [out]

  WORK

      !>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
      !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
      !>

  [in]

  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.
      !>

  [out]

  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.