dstev.f

          SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ
          INTEGER            INFO, LDZ, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DSTEV computes all eigenvalues and, optionally, eigenvectors of a
    *  real symmetric tridiagonal matrix A.
    *
    *  Arguments
    *  =========
    *
    *  JOBZ    (input) CHARACTER*1
    *          = 'N':  Compute eigenvalues only;
    *          = 'V':  Compute eigenvalues and eigenvectors.
    *
    *  N       (input) INTEGER
    *          The order of the matrix.  N >= 0.
    *
    *  D       (input/output) 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.
    *
    *  E       (input/output) 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.
    *
    *  Z       (output) 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.
    *
    *  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 (max(1,2*N-2))
    *          If JOBZ = 'N', WORK 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, the algorithm failed to converge; i
    *                off-diagonal elements of E did not converge to zero.
    *
    *  =====================================================================
    *
    *     .. 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
    *
          END