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## cungbr()

subroutine cungbr | ( | character | vect,
|  | integer | m,
|  | integer | n,
|  | integer | k,
|  | complex, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex, dimension( * ) | tau,
|  | complex, dimension( * ) | work,
|  | integer | lwork,
|  | integer | info )

CUNGBR

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

Purpose:

      !>
      !> CUNGBR generates one of the complex unitary matrices Q or P**H
      !> 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) or G(i) respectively.
      !>
      !> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
      !> is of order M:
      !> if m >= k, Q = H(1) H(2) . . . H(k) and CUNGBR returns the first n
      !> columns of Q, where m >= n >= k;
      !> if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR returns Q as an
      !> M-by-M matrix.
      !>
      !> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
      !> is of order N:
      !> if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m
      !> rows of P**H, where n >= m >= k;
      !> if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as
      !> an N-by-N matrix.
      !>

Parameters

  [in]

  VECT

      !>          VECT is CHARACTER*1
      !>          Specifies whether the matrix Q or the matrix P**H is
      !>          required, as defined in the transformation applied by CGEBRD:
      !>          = 'Q':  generate Q;
      !>          = 'P':  generate P**H.
      !>

  [in]

  M

      !>          M is INTEGER
      !>          The number of rows of the matrix Q or P**H to be returned.
      !>          M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of columns of the matrix Q or P**H to be returned.
      !>          N >= 0.
      !>          If VECT = 'Q', M >= N >= min(M,K);
      !>          if VECT = 'P', N >= M >= min(N,K).
      !>

  [in]

  K

      !>          K is INTEGER
      !>          If VECT = 'Q', the number of columns in the original M-by-K
      !>          matrix reduced by CGEBRD.
      !>          If VECT = 'P', the number of rows in the original K-by-N
      !>          matrix reduced by CGEBRD.
      !>          K >= 0.
      !>

  [in,out]

  A

      !>          A is COMPLEX array, dimension (LDA,N)
      !>          On entry, the vectors which define the elementary reflectors,
      !>          as returned by CGEBRD.
      !>          On exit, the M-by-N matrix Q or P**H.
      !>

  [in]

  LDA

      !>          LDA is INTEGER
      !>          The leading dimension of the array A. LDA >= M.
      !>

  [in]

  TAU

      !>          TAU is COMPLEX array, dimension
      !>                                (min(M,K)) if VECT = 'Q'
      !>                                (min(N,K)) if VECT = 'P'
      !>          TAU(i) must contain the scalar factor of the elementary
      !>          reflector H(i) or G(i), which determines Q or P**H, as
      !>          returned by CGEBRD in its array argument TAUQ or TAUP.
      !>

  [out]

  WORK

      !>          WORK is COMPLEX 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. LWORK >= max(1,min(M,N)).
      !>          For optimum performance LWORK >= min(M,N)*NB, where NB
      !>          is the optimal blocksize.
      !>
      !>          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.