# spbt02.f - Man Page

TESTING/LIN/spbt02.f

## Synopsis

### Functions/Subroutines

subroutine **spbt02** (uplo, n, kd, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)**SPBT02**

## Function/Subroutine Documentation

### subroutine spbt02 (character uplo, integer n, integer kd, 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)

**SPBT02**

**Purpose:**

SPBT02 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 REAL 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 SPBTRF for further details.

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

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

*RWORK*RWORK is REAL array, dimension (N)

*RESID*RESID is REAL 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 **spbt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page spbt02(3) is an alias of spbt02.f(3).

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