SRC/zungbr.f(3)

NAME
SRC/zungbr.f

SYNOPSIS

  Functions/Subroutines
subroutine zungbr (vect, m, n, k, a, lda, tau, work, lwork, info)
ZUNGBR

Function/Subroutine Documentation

  subroutine zungbr (character vect, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGBR

Purpose:

    !>
    !> ZUNGBR generates one of the complex unitary matrices Q or P**H
    !> 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) 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 ZUNGBR returns the first n
    !> columns of Q, where m >= n >= k;
    !> if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR 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 ZUNGBR 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 ZUNGBR returns P**H as
    !> an N-by-N matrix.
    !>

Parameters
    VECT

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

    M

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

    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).
    !>

    K

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the vectors which define the elementary reflectors,
    !>          as returned by ZGEBRD.
    !>          On exit, the M-by-N matrix Q or P**H.
    !>

    LDA

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

    TAU

    !>          TAU is COMPLEX*16 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 ZGEBRD in its array argument TAUQ or TAUP.
    !>

    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. 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.
    !>

    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 156 of file zungbr.f.

Author

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