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DGBBRD(1)		 LAPACK routine (version 3.2)		     DGBBRD(1)

NAME
       DGBBRD  - reduces a real general m-by-n band matrix A to upper bidiago‐
       nal form B by an orthogonal transformation

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

	   CHARACTER	  VECT

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

	   DOUBLE	  PRECISION  AB(  LDAB, * ), C( LDC, * ), D( * ), E( *
			  ), PT( LDPT, * ), Q( LDQ, * ), WORK( * )

PURPOSE
       DGBBRD reduces a real general m-by-n band matrix A to upper  bidiagonal
       form  B	by  an orthogonal 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) DOUBLE PRECISION 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 gen‐
	       erated during the reduction.

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

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

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

       Q       (output) DOUBLE PRECISION array, dimension (LDQ,M)
	       If VECT = 'Q' or 'B', the m-by-m orthogonal 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) DOUBLE PRECISION array, dimension (LDPT,N)
	       If VECT = 'P' or 'B', the n-by-n orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (2*max(M,N))

       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			     DGBBRD(1)
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