CXML
        	    
LAPACK version 3.0
cgbbrd(3)

PURPOSE
  CGBBRD - reduce a complex general m-by-n band matrix A to real upper
  bidiagonal form B by a unitary transformation

SYNTAX
  SUBROUTINE CGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, PT,
		     LDPT, C, LDC, WORK, RWORK, INFO )

      CHARACTER	     VECT

      INTEGER	     INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC

      REAL	     D( * ), E( * ), RWORK( * )

      COMPLEX	     AB( LDAB, * ), C( LDC, * ), PT( LDPT, * ), Q( LDQ, * ),
		     WORK( * )

DESCRIPTION
  CGBBRD reduces a complex general m-by-n band matrix A to real upper
  bidiagonal form B by a unitary transformation: Q' * A * P = B.  The routine
  computes B, and optionally forms Q or P', or computes Q'*C for a given
  matrix C.

ARGUMENTS
  VECT	  (input) CHARACTER*1
	  Specifies whether or not the matrices Q and P' are to be formed.  =
	  'N': do not form Q or P';
	  = 'Q': form Q only;
	  = 'P': form P' only;
	  = 'B': form both.

  M	  (input) INTEGER
	  The number of rows of the matrix A.  M >= 0.

  N	  (input) INTEGER
	  The number of columns of the matrix A.  N >= 0.

  NCC	  (input) INTEGER
	  The number of columns of the matrix C.  NCC >= 0.

  KL	  (input) INTEGER
	  The number of subdiagonals of the matrix A. KL >= 0.

  KU	  (input) INTEGER
	  The number of superdiagonals of the matrix A. KU >= 0.

  AB	  (input/output) COMPLEX array, dimension (LDAB,N)
	  On entry, the m-by-n band matrix A, stored in rows 1 to KL+KU+1.
	  The j-th column of A is stored in the j-th column of the array AB
	  as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-
	  ku)<=i<=min(m,j+kl).	On exit, A is overwritten by values generated
	  during the reduction.

  LDAB	  (input) INTEGER
	  The leading dimension of the array A. LDAB >= KL+KU+1.

  D	  (output) REAL array, dimension (min(M,N))
	  The diagonal elements of the bidiagonal matrix B.

  E	  (output) REAL array, dimension (min(M,N)-1)
	  The superdiagonal elements of the bidiagonal matrix B.

  Q	  (output) COMPLEX array, dimension (LDQ,M)
	  If VECT = 'Q' or 'B', the m-by-m unitary matrix Q.  If VECT = 'N'
	  or 'P', the array Q is not referenced.

  LDQ	  (input) INTEGER
	  The leading dimension of the array Q.	 LDQ >= max(1,M) if VECT =
	  'Q' or 'B'; LDQ >= 1 otherwise.

  PT	  (output) COMPLEX array, dimension (LDPT,N)
	  If VECT = 'P' or 'B', the n-by-n unitary matrix P'.  If VECT = 'N'
	  or 'Q', the array PT is not referenced.

  LDPT	  (input) INTEGER
	  The leading dimension of the array PT.  LDPT >= max(1,N) if VECT =
	  'P' or 'B'; LDPT >= 1 otherwise.

  C	  (input/output) COMPLEX array, dimension (LDC,NCC)
	  On entry, an m-by-ncc matrix C.  On exit, C is overwritten by Q'*C.
	  C is not referenced if NCC = 0.

  LDC	  (input) INTEGER
	  The leading dimension of the array C.	 LDC >= max(1,M) if NCC > 0;
	  LDC >= 1 if NCC = 0.

  WORK	  (workspace) COMPLEX array, dimension (max(M,N))

  RWORK	  (workspace) REAL array, dimension (max(M,N))

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