```      SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
\$                   M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
*
*  -- LAPACK driver routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          JOBZ, RANGE
INTEGER            IL, INFO, IU, LDZ, M, N
REAL               ABSTOL, VL, VU
*     ..
*     .. Array Arguments ..
INTEGER            IFAIL( * ), IWORK( * )
REAL               D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  SSTEVX computes selected eigenvalues and, optionally, eigenvectors
*  of a real symmetric tridiagonal 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.
*
*  N       (input) INTEGER
*          The order of the matrix.  N >= 0.
*
*  D       (input/output) REAL array, dimension (N)
*          On entry, the n diagonal elements of the tridiagonal matrix
*          A.
*          On exit, D may be multiplied by a constant factor chosen
*          to avoid over/underflow in computing the eigenvalues.
*
*  E       (input/output) REAL array, dimension (max(1,N-1))
*          On entry, the (n-1) subdiagonal elements of the tridiagonal
*          matrix A in elements 1 to N-1 of E.
*          On exit, E may be multiplied by a constant factor chosen
*          to avoid over/underflow in computing the eigenvalues.
*
*  VL      (input) REAL
*  VU      (input) REAL
*          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) REAL
*          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.
*
*          Eigenvalues will be computed most accurately when ABSTOL is
*          set to twice the underflow threshold 2*SLAMCH('S'), not zero.
*          If this routine returns with INFO>0, indicating that some
*          eigenvectors did not converge, try setting ABSTOL to
*          2*SLAMCH('S').
*
*          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) REAL array, dimension (N)
*          The first M elements contain the selected eigenvalues in
*          ascending order.
*
*  Z       (output) REAL 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 (INFO > 0), 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) REAL array, dimension (5*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.
*
*  =====================================================================
*
*     .. Parameters ..
REAL               ZERO, ONE
PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
*     ..
*     .. Local Scalars ..
LOGICAL            ALLEIG, INDEIG, TEST, VALEIG, WANTZ
CHARACTER          ORDER
INTEGER            I, IMAX, INDIBL, INDISP, INDIWO, INDWRK,
\$                   ISCALE, ITMP1, J, JJ, NSPLIT
REAL               BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
\$                   TMP1, TNRM, VLL, VUU
*     ..
*     .. External Functions ..
LOGICAL            LSAME
REAL               SLAMCH, SLANST
EXTERNAL           LSAME, SLAMCH, SLANST
*     ..
*     .. External Subroutines ..
EXTERNAL           SCOPY, SSCAL, SSTEBZ, SSTEIN, SSTEQR, SSTERF,
\$                   SSWAP, XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          MAX, MIN, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
ALLEIG = LSAME( RANGE, 'A' )
VALEIG = LSAME( RANGE, 'V' )
INDEIG = LSAME( RANGE, 'I' )
*
INFO = 0
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE
IF( VALEIG ) THEN
IF( N.GT.0 .AND. VU.LE.VL )
\$         INFO = -7
ELSE IF( INDEIG ) THEN
IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
INFO = -9
END IF
END IF
END IF
IF( INFO.EQ.0 ) THEN
IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
\$      INFO = -14
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SSTEVX', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
M = 0
IF( N.EQ.0 )
\$   RETURN
*
IF( N.EQ.1 ) THEN
IF( ALLEIG .OR. INDEIG ) THEN
M = 1
W( 1 ) = D( 1 )
ELSE
IF( VL.LT.D( 1 ) .AND. VU.GE.D( 1 ) ) THEN
M = 1
W( 1 ) = D( 1 )
END IF
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 = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
*
*     Scale matrix to allowable range, if necessary.
*
ISCALE = 0
IF ( VALEIG ) THEN
VLL = VL
VUU = VU
ELSE
VLL = ZERO
VUU = ZERO
ENDIF
TNRM = SLANST( '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 SSCAL( N, SIGMA, D, 1 )
CALL SSCAL( N-1, SIGMA, E( 1 ), 1 )
IF( VALEIG ) THEN
VLL = VL*SIGMA
VUU = VU*SIGMA
END IF
END IF
*
*     If all eigenvalues are desired and ABSTOL is less than zero, then
*     call SSTERF or SSTEQR.  If this fails for some eigenvalue, then
*     try SSTEBZ.
*
TEST = .FALSE.
IF( INDEIG ) THEN
IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
TEST = .TRUE.
END IF
END IF
IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
CALL SCOPY( N, D, 1, W, 1 )
CALL SCOPY( N-1, E( 1 ), 1, WORK( 1 ), 1 )
INDWRK = N + 1
IF( .NOT.WANTZ ) THEN
CALL SSTERF( N, W, WORK, INFO )
ELSE
CALL SSTEQR( 'I', N, W, WORK, Z, LDZ, WORK( INDWRK ), INFO )
IF( INFO.EQ.0 ) THEN
DO 10 I = 1, N
IFAIL( I ) = 0
10          CONTINUE
END IF
END IF
IF( INFO.EQ.0 ) THEN
M = N
GO TO 20
END IF
INFO = 0
END IF
*
*     Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN.
*
IF( WANTZ ) THEN
ORDER = 'B'
ELSE
ORDER = 'E'
END IF
INDWRK = 1
INDIBL = 1
INDISP = INDIBL + N
INDIWO = INDISP + N
CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E, M,
\$             NSPLIT, W, IWORK( INDIBL ), IWORK( INDISP ),
\$             WORK( INDWRK ), IWORK( INDIWO ), INFO )
*
IF( WANTZ ) THEN
CALL SSTEIN( N, D, E, M, W, IWORK( INDIBL ), IWORK( INDISP ),
\$                Z, LDZ, WORK( INDWRK ), IWORK( INDIWO ), IFAIL,
\$                INFO )
END IF
*
*     If matrix was scaled, then rescale eigenvalues appropriately.
*
20 CONTINUE
IF( ISCALE.EQ.1 ) THEN
IF( INFO.EQ.0 ) THEN
IMAX = M
ELSE
IMAX = INFO - 1
END IF
CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
END IF
*
*     If eigenvalues are not in order, then sort them, along with
*     eigenvectors.
*
IF( WANTZ ) THEN
DO 40 J = 1, M - 1
I = 0
TMP1 = W( J )
DO 30 JJ = J + 1, M
IF( W( JJ ).LT.TMP1 ) THEN
I = JJ
TMP1 = W( JJ )
END IF
30       CONTINUE
*
IF( I.NE.0 ) THEN
ITMP1 = IWORK( INDIBL+I-1 )
W( I ) = W( J )
IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
W( J ) = TMP1
IWORK( INDIBL+J-1 ) = ITMP1
CALL SSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
IF( INFO.NE.0 ) THEN
ITMP1 = IFAIL( I )
IFAIL( I ) = IFAIL( J )
IFAIL( J ) = ITMP1
END IF
END IF
40    CONTINUE
END IF
*
RETURN
*
*     End of SSTEVX
*
END

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