# cstt22.f - Man Page

TESTING/EIG/cstt22.f

## Synopsis

### Functions/Subroutines

subroutine cstt22 (n, m, kband, ad, ae, sd, se, u, ldu, work, ldwork, rwork, result)
CSTT22

## Function/Subroutine Documentation

### subroutine cstt22 (integer n, integer m, integer kband, real, dimension( * ) ad, real, dimension( * ) ae, real, dimension( * ) sd, real, dimension( * ) se, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( ldwork, * ) work, integer ldwork, real, dimension( * ) rwork, real, dimension( 2 ) result)

CSTT22

Purpose:

``` CSTT22  checks a set of M eigenvalues and eigenvectors,

A U = U S

where A is Hermitian tridiagonal, the columns of U are unitary,
and S is diagonal (if KBAND=0) or Hermitian tridiagonal (if KBAND=1).
Two tests are performed:

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

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

N

```          N is INTEGER
The size of the matrix.  If it is zero, CSTT22 does nothing.
It must be at least zero.```

M

```          M is INTEGER
The number of eigenpairs to check.  If it is zero, CSTT22
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 Hermitian tri-diagonal.```

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

AE

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

SD

```          SD is REAL array, dimension (N)
The diagonal of the (Hermitian tri-) diagonal matrix S.```

SE

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

U

```          U is REAL 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 (LDWORK, M+1)`

LDWORK

```          LDWORK is INTEGER
The leading dimension of WORK.  LDWORK must be at least
max(1,M).```

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 143 of file cstt22.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cstt22(3) is an alias of cstt22.f(3).

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