dstev()

subroutine dstev	(	character	jobz,
		integer	n,
		double precision, dimension( * )	d,
		double precision, dimension( * )	e,
		double precision, dimension( ldz, * )	z,
		integer	ldz,
		double precision, dimension( * )	work,
		integer	info
	)

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

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Purpose:

 DSTEV computes all eigenvalues and, optionally, eigenvectors of a
 real symmetric tridiagonal matrix A.

Parameters

[in]	JOBZ	JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.
[in]	N	N is INTEGER The order of the matrix. N >= 0.
[in,out]	D	D is DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, if INFO = 0, the eigenvalues in ascending order.
[in,out]	E	E is DOUBLE PRECISION array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A, stored in elements 1 to N-1 of E. On exit, the contents of E are destroyed.
[out]	Z	Z is DOUBLE PRECISION 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 D(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 DOUBLE PRECISION array, dimension (max(1,2*N-2)) If JOBZ = 'N', WORK is not referenced.
[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 E did not converge to zero.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 115 of file dstev.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
      INTEGER            INFO, LDZ, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d0, one = 1.0d0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            WANTZ
      INTEGER            IMAX, ISCALE
      DOUBLE PRECISION   BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
     $                   TNRM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, DLANST
      EXTERNAL           lsame, dlamch, dlanst
*     ..
*     .. External Subroutines ..
      EXTERNAL           dscal, dsteqr, dsterf, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          sqrt
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      wantz = lsame( jobz, 'V' )
*
      info = 0
      IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
         info = -1
      ELSE IF( n.LT.0 ) THEN
         info = -2
      ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
         info = -6
      END IF
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DSTEV ', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      IF( n.EQ.1 ) THEN
         IF( wantz )
     $      z( 1, 1 ) = one
         RETURN
      END IF
*
*     Get machine constants.
*
      safmin = dlamch( 'Safe minimum' )
      eps = dlamch( 'Precision' )
      smlnum = safmin / eps
      bignum = one / smlnum
      rmin = sqrt( smlnum )
      rmax = sqrt( bignum )
*
*     Scale matrix to allowable range, if necessary.
*
      iscale = 0
      tnrm = dlanst( 'M', n, d, e )
      IF( tnrm.GT.zero .AND. tnrm.LT.rmin ) THEN
         iscale = 1
         sigma = rmin / tnrm
      ELSE IF( tnrm.GT.rmax ) THEN
         iscale = 1
         sigma = rmax / tnrm
      END IF
      IF( iscale.EQ.1 ) THEN
         CALL dscal( n, sigma, d, 1 )
         CALL dscal( n-1, sigma, e( 1 ), 1 )
      END IF
*
*     For eigenvalues only, call DSTERF.  For eigenvalues and
*     eigenvectors, call DSTEQR.
*
      IF( .NOT.wantz ) THEN
         CALL dsterf( n, d, e, info )
      ELSE
         CALL dsteqr( 'I', n, d, e, z, ldz, work, 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 dscal( imax, one / sigma, d, 1 )
      END IF
*
      RETURN
*
*     End of DSTEV
*

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