# dsbt21.f - Man Page

TESTING/EIG/dsbt21.f

## Synopsis

### Functions/Subroutines

subroutine dsbt21 (uplo, n, ka, ks, a, lda, d, e, u, ldu, work, result)
DSBT21

## Function/Subroutine Documentation

### subroutine dsbt21 (character uplo, integer n, integer ka, integer ks, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) work, double precision, dimension( 2 ) result)

DSBT21

Purpose:

``` DSBT21  generally checks a decomposition of the form

A = U S U**T

where **T means transpose, A is symmetric banded, U is
orthogonal, and S is diagonal (if KS=0) or symmetric
tridiagonal (if KS=1).

Specifically:

RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
RESULT(2) = | I - U U**T | / ( n ulp )```
Parameters

UPLO

```          UPLO is CHARACTER
If UPLO='U', the upper triangle of A and V will be used and
the (strictly) lower triangle will not be referenced.
If UPLO='L', the lower triangle of A and V will be used and
the (strictly) upper triangle will not be referenced.```

N

```          N is INTEGER
The size of the matrix.  If it is zero, DSBT21 does nothing.
It must be at least zero.```

KA

```          KA is INTEGER
The bandwidth of the matrix A.  It must be at least zero.  If
it is larger than N-1, then max( 0, N-1 ) will be used.```

KS

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

A

```          A is DOUBLE PRECISION array, dimension (LDA, N)
The original (unfactored) matrix.  It is assumed to be
symmetric, and only the upper (UPLO='U') or only the lower
(UPLO='L') will be referenced.```

LDA

```          LDA is INTEGER
The leading dimension of A.  It must be at least 1
and at least min( KA, N-1 ).```

D

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

E

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

U

```          U is DOUBLE PRECISION array, dimension (LDU, N)
The orthogonal matrix in the decomposition, expressed as a
dense matrix (i.e., not as a product of Householder
transformations, Givens transformations, etc.)```

LDU

```          LDU is INTEGER
The leading dimension of U.  LDU must be at least N and
at least 1.```

WORK

`          WORK is DOUBLE PRECISION array, dimension (N**2+N)`

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.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 145 of file dsbt21.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dsbt21(3) is an alias of dsbt21.f(3).

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