# dstt21.f - Man Page

TESTING/EIG/dstt21.f

## Synopsis

### Functions/Subroutines

subroutine dstt21 (n, kband, ad, ae, sd, se, u, ldu, work, result)
DSTT21

## Function/Subroutine Documentation

### subroutine dstt21 (integer n, integer kband, double precision, dimension( * ) ad, double precision, dimension( * ) ae, double precision, dimension( * ) sd, double precision, dimension( * ) se, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) work, double precision, dimension( 2 ) result)

DSTT21

Purpose:

``` DSTT21 checks a decomposition of the form

A = U S U'

where ' means transpose, A is symmetric tridiagonal, U is orthogonal,
and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1).
Two tests are performed:

RESULT(1) = | A - U S U' | / ( |A| n ulp )

RESULT(2) = | I - UU' | / ( n ulp )```
Parameters

N

```          N is INTEGER
The size of the matrix.  If it is zero, DSTT21 does nothing.
It must be at least zero.```

KBAND

```          KBAND is INTEGER
The bandwidth of the matrix S.  It may only be zero or one.
If zero, then S is diagonal, and SE is not referenced.  If
one, then S is symmetric tri-diagonal.```

```          AD is DOUBLE PRECISION array, dimension (N)
The diagonal of the original (unfactored) matrix A.  A is
assumed to be symmetric tridiagonal.```

AE

```          AE is DOUBLE PRECISION array, dimension (N-1)
The off-diagonal of the original (unfactored) matrix A.  A
is assumed to be symmetric tridiagonal.  AE(1) is the (1,2)
and (2,1) element, AE(2) is the (2,3) and (3,2) element, etc.```

SD

```          SD is DOUBLE PRECISION array, dimension (N)
The diagonal of the (symmetric tri-) diagonal matrix S.```

SE

```          SE is DOUBLE PRECISION array, dimension (N-1)
The off-diagonal of the (symmetric tri-) diagonal matrix S.
Not referenced if KBSND=0.  If KBAND=1, then AE(1) is the
(1,2) and (2,1) element, SE(2) is the (2,3) and (3,2)
element, etc.```

U

```          U is DOUBLE PRECISION array, dimension (LDU, N)
The orthogonal matrix in the decomposition.```

LDU

```          LDU is INTEGER
The leading dimension of U.  LDU must be at least N.```

WORK

`          WORK is DOUBLE PRECISION array, dimension (N*(N+1))`

RESULT

```          RESULT is DOUBLE PRECISION array, dimension (2)
The values computed by the two tests described above.  The
values are currently limited to 1/ulp, to avoid overflow.
RESULT(1) is always modified.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 125 of file dstt21.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dstt21(3) is an alias of dstt21.f(3).

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