NAME

       zungbr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zungbr (VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)
           ZUNGBR

Function/Subroutine Documentation

   subroutine zungbr (characterVECT, integerM, integerN, integerK, complex*16, dimension( lda, *
       )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK,
       integerLWORK, integerINFO)
       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.

       Date:
           April 2012

       Definition at line 158 of file zungbr.f.

Author

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