# sstech.f - Man Page

TESTING/EIG/sstech.f

## Synopsis

### Functions/Subroutines

subroutine sstech (n, a, b, eig, tol, work, info)
SSTECH

## Function/Subroutine Documentation

### subroutine sstech (integer n, real, dimension( * ) a, real, dimension( * ) b, real, dimension( * ) eig, real tol, real, dimension( * ) work, integer info)

SSTECH

Purpose:

```    Let T be the tridiagonal matrix with diagonal entries A(1) ,...,
A(N) and offdiagonal entries B(1) ,..., B(N-1)).  SSTECH 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
SSTECT).  Here EPS = TOL*MACHEPS*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

N

```          N is INTEGER
The dimension of the tridiagonal matrix T.```

A

```          A is REAL array, dimension (N)
The diagonal entries of the tridiagonal matrix T.```

B

```          B is REAL array, dimension (N-1)
The offdiagonal entries of the tridiagonal matrix T.```

EIG

```          EIG is REAL array, dimension (N)
The purported eigenvalues to be checked.```

TOL

```          TOL is REAL
Error tolerance for checking, a multiple of the
machine precision.```

WORK

`          WORK is REAL array, dimension (N)`

INFO

```          INFO is INTEGER
0  if the eigenvalues are all correct (to within
1 +- TOL*MACHEPS*MAXEIG)
>0 if the interval containing the INFO-th eigenvalue
contains the incorrect number of eigenvalues.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 100 of file sstech.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sstech(3) is an alias of sstech.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK