LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ dstech()

subroutine dstech ( integer  N,
double precision, dimension( * )  A,
double precision, dimension( * )  B,
double precision, dimension( * )  EIG,
double precision  TOL,
double precision, dimension( * )  WORK,
integer  INFO 
)

DSTECH

Purpose:
    Let T be the tridiagonal matrix with diagonal entries A(1) ,...,
    A(N) and offdiagonal entries B(1) ,..., B(N-1)).  DSTECH checks to
    see if EIG(1) ,..., EIG(N) are indeed accurate eigenvalues of T.
    It does this by expanding each EIG(I) into an interval
    [SVD(I) - EPS, SVD(I) + EPS], merging overlapping intervals if
    any, and using Sturm sequences to count and verify whether each
    resulting interval has the correct number of eigenvalues (using
    DSTECT).  Here EPS = TOL*MAZHEPS*MAXEIG, where MACHEPS is the
    machine precision and MAXEIG is the absolute value of the largest
    eigenvalue. If each interval contains the correct number of
    eigenvalues, INFO = 0 is returned, otherwise INFO is the index of
    the first eigenvalue in the first bad interval.
Parameters
[in]N
          N is INTEGER
          The dimension of the tridiagonal matrix T.
[in]A
          A is DOUBLE PRECISION array, dimension (N)
          The diagonal entries of the tridiagonal matrix T.
[in]B
          B is DOUBLE PRECISION array, dimension (N-1)
          The offdiagonal entries of the tridiagonal matrix T.
[in]EIG
          EIG is DOUBLE PRECISION array, dimension (N)
          The purported eigenvalues to be checked.
[in]TOL
          TOL is DOUBLE PRECISION
          Error tolerance for checking, a multiple of the
          machine precision.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (N)
[out]INFO
          INFO is INTEGER
          0  if the eigenvalues are all correct (to within
             1 +- TOL*MAZHEPS*MAXEIG)
          >0 if the interval containing the INFO-th eigenvalue
             contains the incorrect number of eigenvalues.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.