# cstt21.f - Man Page

TESTING/EIG/cstt21.f

## Synopsis

### Functions/Subroutines

subroutine cstt21 (n, kband, ad, ae, sd, se, u, ldu, work, rwork, result)
CSTT21

## Function/Subroutine Documentation

### subroutine cstt21 (integer n, integer kband, real, dimension( * ) ad, real, dimension( * ) ae, real, dimension( * ) sd, real, dimension( * ) se, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( * ) work, real, dimension( * ) rwork, real, dimension( 2 ) result)

CSTT21

Purpose:

``` CSTT21  checks a decomposition of the form

A = U S U**H

where **H means conjugate transpose, A is real symmetric tridiagonal,
U is unitary, and S is real and diagonal (if KBAND=0) or symmetric
tridiagonal (if KBAND=1).  Two tests are performed:

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

RESULT(2) = | I - U U**H | / ( n ulp )```
Parameters

N

```          N is INTEGER
The size of the matrix.  If it is zero, CSTT21 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 REAL array, dimension (N)
The diagonal of the original (unfactored) matrix A.  A is
assumed to be real symmetric tridiagonal.```

AE

```          AE is REAL 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 REAL array, dimension (N)
The diagonal of the real (symmetric tri-) diagonal matrix S.```

SE

```          SE is REAL 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 COMPLEX array, dimension (LDU, N)
The unitary matrix in the decomposition.```

LDU

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

WORK

`          WORK is COMPLEX array, dimension (N**2)`

RWORK

`          RWORK is REAL array, dimension (N)`

RESULT

```          RESULT is REAL 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

Univ. of Colorado Denver

NAG Ltd.

Definition at line 131 of file cstt21.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cstt21(3) is an alias of cstt21.f(3).

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