---
name: "dpbt02.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/dpbt02.f"
---

# dpbt02.f(3)

## NAME

TESTING/LIN/dpbt02.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dpbt02** (uplo, n, kd, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)\
 **DPBT02**

## Function/Subroutine Documentation

### subroutine dpbt02 (character uplo, integer n, integer kd, 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)

**DPBT02**

**Purpose:**

```
!>
!> DPBT02 computes the residual for a solution of a symmetric banded
!> system of equations  A*x = b:
!>    RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
!> where EPS is the machine precision.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the upper or lower triangular part of the
!>          symmetric matrix A is stored:
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*N*

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

*KD*

```
!>          KD is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
!>
```

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of right hand sides. NRHS >= 0.
!>
```

*A*

```
!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          The original symmetric band matrix A.  If UPLO = 'U', the
!>          upper triangular part of A is stored as a band matrix; if
!>          UPLO = 'L', the lower triangular part of A is stored.  The
!>          columns of the appropriate triangle are stored in the columns
!>          of A and the diagonals of the triangle are stored in the rows
!>          of A.  See DPBTRF for further details.
!>
```

*LDA*

```
!>          LDA is INTEGER.
!>          The leading dimension of the array A.  LDA >= max(1,KD+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.   LDX >= max(1,N).
!>
```

*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.  LDB >= max(1,N).
!>
```

*RWORK*

```
!>          RWORK is DOUBLE PRECISION array, dimension (N)
!>
```

*RESID*

```
!>          RESID is DOUBLE PRECISION
!>          The maximum over the number of right hand sides of
!>          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **134** of file **dpbt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.