LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dstevx()

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

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

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

Purpose:
!>
!> DSTEVX 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
!>          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 DOUBLE PRECISION
!>          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 DOUBLE PRECISION
!>          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*DLAMCH('S'), not zero.
!>          If this routine returns with INFO>0, indicating that some
!>          eigenvectors did not converge, try setting ABSTOL to
!>          2*DLAMCH('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 DOUBLE PRECISION array, dimension (N)
!>          The first M elements contain the selected eigenvalues in
!>          ascending order.
!>
[out]Z
!>          Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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.