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CUNGBR(1)		 LAPACK routine (version 3.2)		     CUNGBR(1)

NAME
       CUNGBR - generates one of the complex unitary matrices Q or P**H deter‐
       mined by CGEBRD when reducing a complex matrix A to bidiagonal form

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

	   CHARACTER	  VECT

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

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

PURPOSE
       CUNGBR generates one of the complex unitary matrices Q or  P**H	deter‐
       mined  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 CUNGBR returns the first n col‐
       umns of Q, where m >= n >= k;
       if  m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR 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 CUNGBR 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 CUNGBR 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 CGEBRD:
	       = '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 CGEBRD.  If VECT = 'P', the number of rows in
	       the original K-by-N matrix reduced by CGEBRD.  K >= 0.

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

       TAU     (input) COMPLEX 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 CGEBRD in  its
	       array argument TAUQ or TAUP.

       WORK    (workspace/output) COMPLEX 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 opti‐
	       mal  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)	 November 2008			     CUNGBR(1)
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