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## sstevx()

subroutine sstevx | ( | character | jobz,
|  | character | range,
|  | integer | n,
|  | real, dimension( * ) | d,
|  | real, dimension( * ) | e,
|  | real | vl,
|  | real | vu,
|  | integer | il,
|  | integer | iu,
|  | real | abstol,
|  | integer | m,
|  | real, dimension( * ) | w,
|  | real, dimension( ldz, * ) | z,
|  | integer | ldz,
|  | real, dimension( * ) | work,
|  | integer, dimension( * ) | iwork,
|  | integer, dimension( * ) | ifail,
|  | integer | info )

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

Download SSTEVX + dependencies [TGZ] [ZIP] [TXT]

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.
      !>

Parameters

  [in]

  JOBZ

      !>          JOBZ is CHARACTER*1
      !>          = 'N':  Compute eigenvalues only;
      !>          = 'V':  Compute eigenvalues and eigenvectors.
      !>

  [in]

  RANGE

      !>          RANGE is 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.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix.  N >= 0.
      !>

  [in,out]

  D

      !>          D is 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.
      !>

  [in,out]

  E

      !>          E is 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.
      !>

  [in]

  VL

      !>          VL is REAL
      !>          If RANGE='V', the lower bound of the interval to
      !>          be searched for eigenvalues. VL < VU.
      !>          Not referenced if RANGE = 'A' or 'I'.
      !>

  [in]

  VU

      !>          VU is REAL
      !>          If RANGE='V', the upper bound of the interval to
      !>          be searched for eigenvalues. VL < VU.
      !>          Not referenced if RANGE = 'A' or 'I'.
      !>

  [in]

  IL

      !>          IL is INTEGER
      !>          If RANGE='I', the index of the
      !>          smallest eigenvalue 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'.
      !>

  [in]

  IU

      !>          IU is INTEGER
      !>          If RANGE='I', the index of the
      !>          largest eigenvalue 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'.
      !>

  [in]

  ABSTOL

      !>          ABSTOL is 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  by Demmel and
      !>          Kahan, LAPACK Working Note #3.
      !>

  [out]

  M

      !>          M is INTEGER
      !>          The total number of eigenvalues found.  0 <= M <= N.
      !>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
      !>

  [out]

  W

      !>          W is REAL array, dimension (N)
      !>          The first M elements contain the selected eigenvalues in
      !>          ascending order.
      !>

  [out]

  Z

      !>          Z is 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.
      !>

  [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 (5*N)
      !>

  [out]

  IWORK

      !>          IWORK is INTEGER array, dimension (5*N)
      !>

  [out]

  IFAIL

      !>          IFAIL is 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.
      !>

  [out]

  INFO

      !>          INFO is 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.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.