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SSBEV(3F)							     SSBEV(3F)


NAME    [Toc]    [Back]

     SSBEV - compute all the eigenvalues and, optionally, eigenvectors of a
     real symmetric band matrix	A

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, INFO )

	 CHARACTER     JOBZ, UPLO

	 INTEGER       INFO, KD, LDAB, LDZ, N

	 REAL	       AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE    [Toc]    [Back]

     SSBEV computes all	the eigenvalues	and, optionally, eigenvectors of a
     real symmetric band matrix	A.

ARGUMENTS    [Toc]    [Back]

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

     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) REAL 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
	     follows:  if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,jkd)<=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.




									Page 1






SSBEV(3F)							     SSBEV(3F)



     W	     (output) REAL array, dimension (N)
	     If	INFO = 0, the eigenvalues in ascending order.

     Z	     (output) REAL array, dimension (LDZ, N)
	     If	JOBZ = 'V', then if INFO = 0, Z	contains the orthonormal
	     eigenvectors of the matrix	A, with	the i-th column	of Z holding
	     the eigenvector associated	with W(i).  If JOBZ = 'N', then	Z is
	     not referenced.

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

     WORK    (workspace) REAL array, dimension (max(1,3*N-2))

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  if INFO = i,	the algorithm failed to	converge; i offdiagonal
 elements of an intermediate tridiagonal form did not
	     converge to zero.
SSBEV(3F)							     SSBEV(3F)


NAME    [Toc]    [Back]

     SSBEV - compute all the eigenvalues and, optionally, eigenvectors of a
     real symmetric band matrix	A

SYNOPSIS    [Toc]    [Back]

     SUBROUTINE	SSBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, INFO )

	 CHARACTER     JOBZ, UPLO

	 INTEGER       INFO, KD, LDAB, LDZ, N

	 REAL	       AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE    [Toc]    [Back]

     SSBEV computes all	the eigenvalues	and, optionally, eigenvectors of a
     real symmetric band matrix	A.

ARGUMENTS    [Toc]    [Back]

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

     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) REAL 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
	     follows:  if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,jkd)<=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.




									Page 1






SSBEV(3F)							     SSBEV(3F)



     W	     (output) REAL array, dimension (N)
	     If	INFO = 0, the eigenvalues in ascending order.

     Z	     (output) REAL array, dimension (LDZ, N)
	     If	JOBZ = 'V', then if INFO = 0, Z	contains the orthonormal
	     eigenvectors of the matrix	A, with	the i-th column	of Z holding
	     the eigenvector associated	with W(i).  If JOBZ = 'N', then	Z is
	     not referenced.

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

     WORK    (workspace) REAL array, dimension (max(1,3*N-2))

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  if INFO = i,	the algorithm failed to	converge; i offdiagonal
 elements of an intermediate tridiagonal form did not
	     converge to zero.


									PPPPaaaaggggeeee 2222
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