_BANDR(3F)							    _BANDR(3F)

NAME    [Toc]    [Back]

     BANDR, SBANDR   -	EISPACK	routine.  This subroutine reduces a REAL
     SYMMETRIC BAND matrix to a	symmetric tridiagonal matrix using and
     optionally	accumulating orthogonal	similarity transformations.

SYNOPSYS    [Toc]    [Back]

	  subroutine  bandr(nm,	n, mb, a, d, e,	e2, matz, z)
	  integer	   nm, n, mb, z
	  double precision a(nm,mb), d(n), e(n), e2(n),	z(nm,n)
	  logical	   matz

	  subroutine sbandr(nm,	n, mb, a, d, e,	e2, matz, z)
	  integer	   nm, n, mb, z
	  real		   a(nm,mb), d(n), e(n), e2(n),	z(nm,n)
	  logical	   matz

DESCRIPTION    [Toc]    [Back]

     On	INPUT

     NM	must be	set to the row dimension of two-dimensional array parameters
     as	declared in the	calling	program	dimension statement.

     N is the order of the matrix.

     MB	is the (half) band width of the	matrix,	defined	as the number of
     adjacent diagonals, including the principal diagonal, required to specify
     the non-zero portion of the lower triangle	of the matrix.

     A contains	the lower triangle of the symmetric band input matrix stored
     as	an N by	MB array.  Its lowest subdiagonal is stored in the last	N+1-MB
     positions of the first column, its	next subdiagonal in the	last N+2-MB
     positions of the second column, further subdiagonals similarly, and
     finally its principal diagonal in the N positions of the last column.
     Contents of storages not part of the matrix are arbitrary.

     MATZ should be set	to .TRUE. if the transformation	matrix is to be
     accumulated, and to .FALSE. otherwise.  On	OUTPUT

     A has been	destroyed, except for its last two columns which contain a
     copy of the tridiagonal matrix.

     D contains	the diagonal elements of the tridiagonal matrix.

     E contains	the subdiagonal	elements of the	tridiagonal matrix in its last
     N-1 positions.  E(1) is set to zero.

     E2	contains the squares of	the corresponding elements of E. E2 may
     coincide with E if	the squares are	not needed.




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_BANDR(3F)							    _BANDR(3F)



     Z contains	the orthogonal transformation matrix produced in the reduction
     if	MATZ has been set to .TRUE.  Otherwise,	Z is not referenced.
     Questions and comments should be directed to B. S.	Garbow,	Applied
     Mathematics Division, ARGONNE NATIONAL LABORATORY


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