Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  generates  one of the complex unitary matrices Q or P**H determined by ZGEBRD
       when reducing a complex matrix A to bidiagonal form

SYNOPSIS

       SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

           CHARACTER      VECT

           INTEGER        INFO, K, LDA, LWORK, M, N

           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )

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.

ARGUMENTS

        VECT    (input) 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       (input) INTEGER
                The number of rows of the matrix Q or P**H to be returned.
                M >= 0.

        N       (input) 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       (input) 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       (input/output) 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     (input) INTEGER
                The leading dimension of the array A. LDA >= M.

        TAU     (input) 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    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) 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    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value

 LAPACK routine (version 3.2)               April 2011                            ZUNGBR(3lapack)