---
name: "spbt05.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/spbt05.f"
---

# spbt05.f(3)

## NAME

TESTING/LIN/spbt05.f

## SYNOPSIS

### Functions/Subroutines

subroutine **spbt05** (uplo, n, kd, nrhs, ab, ldab, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)\
 **SPBT05**

## Function/Subroutine Documentation

### subroutine spbt05 (character uplo, integer n, integer kd, integer nrhs, real, dimension( ldab, \* ) ab, integer ldab, real, dimension( ldb, \* ) b, integer ldb, real, dimension( ldx, \* ) x, integer ldx, real, dimension( ldxact, \* ) xact, integer ldxact, real, dimension( \* ) ferr, real, dimension( \* ) berr, real, dimension( \* ) reslts)

**SPBT05**

**Purpose:**

```
!>
!> SPBT05 tests the error bounds from iterative refinement for the
!> computed solution to a system of equations A*X = B, where A is a
!> symmetric band matrix.
!>
!> RESLTS(1) = test of the error bound
!>           = norm(X - XACT) / ( norm(X) * FERR )
!>
!> A large value is returned if this ratio is not less than one.
!>
!> RESLTS(2) = residual from the iterative refinement routine
!>           = the maximum of BERR / ( NZ*EPS + (*) ), where
!>             (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
!>             and NZ = max. number of nonzeros in any row of A, plus 1
!>
```

**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 of the matrices X, B, and XACT, and the
!>          order 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 columns of the matrices X, B, and XACT.
!>          NRHS >= 0.
!>
```

*AB*

```
!>          AB is REAL array, dimension (LDAB,N)
!>          The upper or lower triangle of the symmetric band matrix A,
!>          stored in the first KD+1 rows of the array.  The j-th column
!>          of A is stored in the j-th column of the array AB as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
```

*LDAB*

```
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD+1.
!>
```

*B*

```
!>          B is REAL array, dimension (LDB,NRHS)
!>          The right hand side vectors for the system of linear
!>          equations.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>
```

*X*

```
!>          X is REAL array, dimension (LDX,NRHS)
!>          The computed solution vectors.  Each vector is stored as a
!>          column of the matrix X.
!>
```

*LDX*

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

*XACT*

```
!>          XACT is REAL array, dimension (LDX,NRHS)
!>          The exact solution vectors.  Each vector is stored as a
!>          column of the matrix XACT.
!>
```

*LDXACT*

```
!>          LDXACT is INTEGER
!>          The leading dimension of the array XACT.  LDXACT >= max(1,N).
!>
```

*FERR*

```
!>          FERR is REAL array, dimension (NRHS)
!>          The estimated forward error bounds for each solution vector
!>          X.  If XTRUE is the true solution, FERR bounds the magnitude
!>          of the largest entry in (X - XTRUE) divided by the magnitude
!>          of the largest entry in X.
!>
```

*BERR*

```
!>          BERR is REAL array, dimension (NRHS)
!>          The componentwise relative backward error of each solution
!>          vector (i.e., the smallest relative change in any entry of A
!>          or B that makes X an exact solution).
!>
```

*RESLTS*

```
!>          RESLTS is REAL array, dimension (2)
!>          The maximum over the NRHS solution vectors of the ratios:
!>          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
!>          RESLTS(2) = BERR / ( NZ*EPS + (*) )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **169** of file **spbt05.f**.

## Author

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