# sgbt02.f - Man Page

TESTING/LIN/sgbt02.f

## Synopsis

### Functions/Subroutines

subroutine sgbt02 (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)
SGBT02

## Function/Subroutine Documentation

### subroutine sgbt02 (character trans, integer m, integer n, integer kl, integer ku, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real resid)

SGBT02

Purpose:

``` SGBT02 computes the residual for a solution of a banded system of
equations op(A)*X = B:
RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
where op(A) = A or A**T, depending on TRANS, and EPS is the
machine epsilon.
The norm used is the 1-norm.```
Parameters

TRANS

```          TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N':  A    * X = B  (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate transpose = Transpose)```

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix A.  N >= 0.```

KL

```          KL is INTEGER
The number of subdiagonals within the band of A.  KL >= 0.```

KU

```          KU is INTEGER
The number of superdiagonals within the band of A.  KU >= 0.```

NRHS

```          NRHS is INTEGER
The number of columns of B.  NRHS >= 0.```

A

```          A is REAL array, dimension (LDA,N)
The original matrix A in band storage, stored in rows 1 to
KL+KU+1.```

LDA

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,KL+KU+1).```

X

```          X is REAL array, dimension (LDX,NRHS)
The computed solution vectors for the system of linear
equations.```

LDX

```          LDX is INTEGER
The leading dimension of the array X.  If TRANS = 'N',
LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).```

B

```          B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side vectors for the system of
linear equations.
On exit, B is overwritten with the difference B - A*X.```

LDB

```          LDB is INTEGER
The leading dimension of the array B.  IF TRANS = 'N',
LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).```

RWORK

```          RWORK is REAL array, dimension (MAX(1,LRWORK)),
where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK
is not referenced.```

RESID

```          RESID is REAL
The maximum over the number of right hand sides of
norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 147 of file sgbt02.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sgbt02(3) is an alias of sgbt02.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK