ssbev()

subroutine ssbev	(	character	jobz,
		character	uplo,
		integer	n,
		integer	kd,
		real, dimension( ldab, * )	ab,
		integer	ldab,
		real, dimension( * )	w,
		real, dimension( ldz, * )	z,
		integer	ldz,
		real, dimension( * )	work,
		integer	info
	)

SSBEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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Purpose:

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

Parameters

[in]	JOBZ	JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.
[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	KD	KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.
[in,out]	AB	AB is 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,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.
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD + 1.
[out]	W	W is REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.
[out]	Z	Z is 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.
[in]	LDZ	LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).
[out]	WORK	WORK is REAL array, dimension (max(1,3*N-2))
[out]	INFO	INFO is 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 off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 144 of file ssbev.f.

*
*  -- LAPACK driver routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, KD, LDAB, LDZ, N
*     ..
*     .. Array Arguments ..
      REAL               AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e0, one = 1.0e0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LOWER, WANTZ
      INTEGER            IINFO, IMAX, INDE, INDWRK, ISCALE
      REAL               ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
     $                   SMLNUM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLAMCH, SLANSB
      EXTERNAL           lsame, slamch, slansb
*     ..
*     .. External Subroutines ..
      EXTERNAL           slascl, ssbtrd, sscal, ssteqr, ssterf, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          sqrt
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      wantz = lsame( jobz, 'V' )
      lower = lsame( uplo, 'L' )
*
      info = 0
      IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
         info = -1
      ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
         info = -2
      ELSE IF( n.LT.0 ) THEN
         info = -3
      ELSE IF( kd.LT.0 ) THEN
         info = -4
      ELSE IF( ldab.LT.kd+1 ) THEN
         info = -6
      ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
         info = -9
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SSBEV ', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      IF( n.EQ.1 ) THEN
         IF( lower ) THEN
            w( 1 ) = ab( 1, 1 )
         ELSE
            w( 1 ) = ab( kd+1, 1 )
         END IF
         IF( wantz )
     $      z( 1, 1 ) = one
         RETURN
      END IF
*
*     Get machine constants.
*
      safmin = slamch( 'Safe minimum' )
      eps = slamch( 'Precision' )
      smlnum = safmin / eps
      bignum = one / smlnum
      rmin = sqrt( smlnum )
      rmax = sqrt( bignum )
*
*     Scale matrix to allowable range, if necessary.
*
      anrm = slansb( 'M', uplo, n, kd, ab, ldab, work )
      iscale = 0
      IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
         iscale = 1
         sigma = rmin / anrm
      ELSE IF( anrm.GT.rmax ) THEN
         iscale = 1
         sigma = rmax / anrm
      END IF
      IF( iscale.EQ.1 ) THEN
         IF( lower ) THEN
            CALL slascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
         ELSE
            CALL slascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
         END IF
      END IF
*
*     Call SSBTRD to reduce symmetric band matrix to tridiagonal form.
*
      inde = 1
      indwrk = inde + n
      CALL ssbtrd( jobz, uplo, n, kd, ab, ldab, w, work( inde ), z, ldz,
     $             work( indwrk ), iinfo )
*
*     For eigenvalues only, call SSTERF.  For eigenvectors, call SSTEQR.
*
      IF( .NOT.wantz ) THEN
         CALL ssterf( n, w, work( inde ), info )
      ELSE
         CALL ssteqr( jobz, n, w, work( inde ), z, ldz, work( indwrk ),
     $                info )
      END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
      IF( iscale.EQ.1 ) THEN
         IF( info.EQ.0 ) THEN
            imax = n
         ELSE
            imax = info - 1
         END IF
         CALL sscal( imax, one / sigma, w, 1 )
      END IF
*
      RETURN
*
*     End of SSBEV
*

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