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DSBEVX(3F)							    DSBEVX(3F)

NAME
     DSBEVX - compute selected eigenvalues and, optionally, eigenvectors of a
     real symmetric band matrix A

SYNOPSIS
     SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL, VU,
			IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO
			)

	 CHARACTER	JOBZ, RANGE, UPLO

	 INTEGER	IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N

	 DOUBLE		PRECISION ABSTOL, VL, VU

	 INTEGER	IFAIL( * ), IWORK( * )

	 DOUBLE		PRECISION AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( *
			), Z( LDZ, * )

PURPOSE
     DSBEVX computes selected eigenvalues and, optionally, eigenvectors of a
     real symmetric band matrix A.  Eigenvalues and eigenvectors can be
     selected by specifying either a range of values or a range of indices for
     the desired eigenvalues.

ARGUMENTS
     JOBZ    (input) CHARACTER*1
	     = 'N':  Compute eigenvalues only;
	     = 'V':  Compute eigenvalues and eigenvectors.

     RANGE   (input) CHARACTER*1
	     = 'A': all eigenvalues will be found;
	     = 'V': all eigenvalues in the half-open interval (VL,VU] will be
	     found; = 'I': the IL-th through IU-th eigenvalues will be found.

     UPLO    (input) CHARACTER*1
	     = 'U':  Upper triangle of A is stored;
	     = 'L':  Lower triangle of A is stored.

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

     KD	     (input) INTEGER
	     The number of superdiagonals of the matrix A if UPLO = 'U', or
	     the number of subdiagonals if UPLO = 'L'.	KD >= 0.

     AB	     (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
	     On entry, the upper or lower triangle of the symmetric band
	     matrix A, stored in the first KD+1 rows of the array.  The j-th
	     column of A is stored in the j-th column of the array AB as

									Page 1

DSBEVX(3F)							    DSBEVX(3F)

	     follows:  if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
	     kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
	     j<=i<=min(n,j+kd).

	     On exit, AB is overwritten by values generated during the
	     reduction to tridiagonal form.  If UPLO = 'U', the first
	     superdiagonal and the diagonal of the tridiagonal matrix T are
	     returned in rows KD and KD+1 of AB, and if UPLO = 'L', the
	     diagonal and first subdiagonal of T are returned in the first two
	     rows of AB.

     LDAB    (input) INTEGER
	     The leading dimension of the array AB.  LDAB >= KD + 1.

     Q	     (output) DOUBLE PRECISION array, dimension (LDQ, N)
	     If JOBZ = 'V', the N-by-N orthogonal matrix used in the reduction
	     to tridiagonal form.  If JOBZ = 'N', the array Q is not
	     referenced.

     LDQ     (input) INTEGER
	     The leading dimension of the array Q.  If JOBZ = 'V', then LDQ >=
	     max(1,N).

     VL	     (input) DOUBLE PRECISION
	     VU	     (input) DOUBLE PRECISION If RANGE='V', the lower and
	     upper bounds of the interval to be searched for eigenvalues. VL <
	     VU.  Not referenced if RANGE = 'A' or 'I'.

     IL	     (input) INTEGER
	     IU	     (input) INTEGER If RANGE='I', the indices (in ascending
	     order) of the smallest and largest eigenvalues to be returned.  1
	     <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.  Not
	     referenced if RANGE = 'A' or 'V'.

     ABSTOL  (input) DOUBLE PRECISION
	     The absolute error tolerance for the eigenvalues.	An approximate
	     eigenvalue is accepted as converged when it is determined to lie
	     in an interval [a,b] of width less than or equal to

	     ABSTOL + EPS *   max( |a|,|b| ) ,

	     where EPS is the machine precision.  If ABSTOL is less than or
	     equal to zero, then  EPS*|T|  will be used in its place, where
	     |T| is the 1-norm of the tridiagonal matrix obtained by reducing
	     AB to tridiagonal form.

	     Eigenvalues will be computed most accurately when ABSTOL is set
	     to twice the underflow threshold 2*DLAMCH('S'), not zero.	If
	     this routine returns with INFO>0, indicating that some
	     eigenvectors did not converge, try setting ABSTOL to
	     2*DLAMCH('S').

									Page 2

DSBEVX(3F)							    DSBEVX(3F)

	     See "Computing Small Singular Values of Bidiagonal Matrices with
	     Guaranteed High Relative Accuracy," by Demmel and Kahan, LAPACK
	     Working Note #3.

     M	     (output) INTEGER
	     The total number of eigenvalues found.  0 <= M <= N.  If RANGE =
	     'A', M = N, and if RANGE = 'I', M = IU-IL+1.

     W	     (output) DOUBLE PRECISION array, dimension (N)
	     The first M elements contain the selected eigenvalues in
	     ascending order.

     Z	     (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
	     If JOBZ = 'V', then if INFO = 0, the first M columns of Z contain
	     the orthonormal eigenvectors of the matrix A corresponding to the
	     selected eigenvalues, with the i-th column of Z holding the
	     eigenvector associated with W(i).	If an eigenvector fails to
	     converge, then that column of Z contains the latest approximation
	     to the eigenvector, and the index of the eigenvector is returned
	     in IFAIL.	If JOBZ = 'N', then Z is not referenced.  Note: the
	     user must ensure that at least max(1,M) columns are supplied in
	     the array Z; if RANGE = 'V', the exact value of M is not known in
	     advance and an upper bound must be used.

     LDZ     (input) INTEGER
	     The leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
	     'V', LDZ >= max(1,N).

     WORK    (workspace) DOUBLE PRECISION array, dimension (7*N)

     IWORK   (workspace) INTEGER array, dimension (5*N)

     IFAIL   (output) INTEGER array, dimension (N)
	     If JOBZ = 'V', then if INFO = 0, the first M elements of IFAIL
	     are zero.	If INFO > 0, then IFAIL contains the indices of the
	     eigenvectors that failed to converge.  If JOBZ = 'N', then IFAIL
	     is not referenced.

     INFO    (output) INTEGER
	     = 0:  successful exit.
	     < 0:  if INFO = -i, the i-th argument had an illegal value.
	     > 0:  if INFO = i, then i eigenvectors failed to converge.	 Their
	     indices are stored in array IFAIL.

									Page 3

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