---
name: "dgbt02.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dgbt02.f"
---

# dgbt02.f(3)

## NAME

TESTING/LIN/dgbt02.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dgbt02** (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)\
 **DGBT02**

## Function/Subroutine Documentation

### subroutine dgbt02 (character trans, integer m, integer n, integer kl, integer ku, integer nrhs, double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldx, \* ) x, integer ldx, double precision, dimension( ldb, \* ) b, integer ldb, double precision, dimension( \* ) rwork, double precision resid)

**DGBT02**

**Purpose:**

```
!>
!> DGBT02 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (MAX(1,LRWORK)),
!>          where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK
!>          is not referenced.
!>
```

*RESID*

```
!>          RESID is DOUBLE PRECISION
!>          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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **147** of file **dgbt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.