redhat man page for zungbr

ZUNGBR(l)								 )								 ZUNGBR(l)

NAME
       ZUNGBR - generate 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 (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 version 3.0						   15 June 2000 							 ZUNGBR(l)