spbt02()

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

[in]	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 !>
[in]	N	!> N is INTEGER !> The number of rows and columns of the matrix A. N >= 0. !>
[in]	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. !>
[in]	NRHS	!> NRHS is INTEGER !> The number of right hand sides. NRHS >= 0. !>
[in]	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. !>
[in]	LDA	!> LDA is INTEGER. !> The leading dimension of the array A. LDA >= max(1,KD+1). !>
[in]	X	!> X is REAL array, dimension (LDX,NRHS) !> The computed solution vectors for the system of linear !> equations. !>
[in]	LDX	!> LDX is INTEGER !> The leading dimension of the array X. LDX >= max(1,N). !>
[in,out]	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. !>
[in]	LDB	!> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !>
[out]	RWORK	!> RWORK is REAL array, dimension (N) !>
[out]	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.

*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            KD, LDA, LDB, LDX, N, NRHS
      REAL               RESID
*     ..
*     .. Array Arguments ..
      REAL               A( LDA, * ), B( LDB, * ), RWORK( * ),
     $                   X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      REAL               ANORM, BNORM, EPS, XNORM
*     ..
*     .. External Functions ..
      REAL               SASUM, SLAMCH, SLANSB
      EXTERNAL           sasum, slamch, slansb
*     ..
*     .. External Subroutines ..
      EXTERNAL           ssbmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0 or NRHS = 0.
*
      IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
         resid = zero
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0.
*
      eps = slamch( 'Epsilon' )
      anorm = slansb( '1', uplo, n, kd, a, lda, rwork )
      IF( anorm.LE.zero ) THEN
         resid = one / eps
         RETURN
      END IF
*
*     Compute  B - A*X
*
      DO 10 j = 1, nrhs
         CALL ssbmv( uplo, n, kd, -one, a, lda, x( 1, j ), 1, one,
     $               b( 1, j ), 1 )
   10 CONTINUE
*
*     Compute the maximum over the number of right hand sides of
*          norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
*
      resid = zero
      DO 20 j = 1, nrhs
         bnorm = sasum( n, b( 1, j ), 1 )
         xnorm = sasum( n, x( 1, j ), 1 )
         IF( xnorm.LE.zero ) THEN
            resid = one / eps
         ELSE
            resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
         END IF
   20 CONTINUE
*
      RETURN
*
*     End of SPBT02
*

Here is the call graph for this function:

Here is the caller graph for this function: