Contents


NAME

     zungbr - generate one of the complex unitary matrices  Q  or
     P**H  determined  by CGEBRD when reducing a complex matrix A
     to bidiagonal form

SYNOPSIS

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

     CHARACTER * 1 VECT
     DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
     INTEGER M, N, K, LDA, LWORK, INFO

     SUBROUTINE ZUNGBR_64(VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO)

     CHARACTER * 1 VECT
     DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
     INTEGER*8 M, N, K, LDA, LWORK, INFO

  F95 INTERFACE
     SUBROUTINE UNGBR(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
            [INFO])

     CHARACTER(LEN=1) :: VECT
     COMPLEX(8), DIMENSION(:) :: TAU, WORK
     COMPLEX(8), DIMENSION(:,:) :: A
     INTEGER :: M, N, K, LDA, LWORK, INFO

     SUBROUTINE UNGBR_64(VECT, M, [N], K, A, [LDA], TAU, [WORK], [LWORK],
            [INFO])

     CHARACTER(LEN=1) :: VECT
     COMPLEX(8), DIMENSION(:) :: TAU, WORK
     COMPLEX(8), DIMENSION(:,:) :: A
     INTEGER(8) :: M, N, K, LDA, LWORK, INFO

  C INTERFACE
     #include <sunperf.h>

     void zungbr(char vect, int m, int n,  int  k,  doublecomplex
               *a, int lda, doublecomplex *tau, int *info);

     void zungbr_64(char vect, long m, long n, long k, doublecom-
               plex   *a,  long  lda,  doublecomplex  *tau,  long
               *info);

PURPOSE

     zungbr 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 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)
               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.

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

     N (input) 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) If VECT = 'Q', the number of columns in the origi-
               nal  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.

     A (input/output)
               On entry, the vectors which define the  elementary
               reflectors,  as  returned by CGEBRD.  On exit, the
               M-by-N matrix Q or P**H.
     LDA (input)
               The leading dimension of the array A. LDA >= M.

     TAU (input)
               (min(M,K)) if VECT = 'Q' (min(N,K)) if VECT =  'P'
               TAU(i)  must contain the scalar factor of the ele-
               mentary reflector H(i) or G(i), which determines Q
               or  P**H, as returned by CGEBRD in its array argu-
               ment TAUQ or TAUP.

     WORK (workspace)
               On exit, if INFO = 0, WORK(1) returns the  optimal
               LWORK.

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