zpbt02()

subroutine zpbt02	(	character	UPLO,
		integer	N,
		integer	KD,
		integer	NRHS,
		complex*16, dimension( lda, * )	A,
		integer	LDA,
		complex*16, dimension( ldx, * )	X,
		integer	LDX,
		complex*16, dimension( ldb, * )	B,
		integer	LDB,
		double precision, dimension( * )	RWORK,
		double precision	RESID
	)

ZPBT02

Purpose:

 ZPBT02 computes the residual for a solution of a Hermitian 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 Hermitian 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 COMPLEX*16 array, dimension (LDA,N) The original Hermitian 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 ZPBTRF for further details.
[in]	LDA	LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
[in]	X	X is COMPLEX*16 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 COMPLEX*16 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 DOUBLE PRECISION array, dimension (N)
[out]	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.

Date

December 2016

Definition at line 138 of file zpbt02.f.

*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            KD, LDA, LDB, LDX, N, NRHS
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), X( LDX, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      COMPLEX*16         CONE
      parameter( cone = ( 1.0d+0, 0.0d+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DZASUM, ZLANHB
      EXTERNAL           dlamch, dzasum, zlanhb
*     ..
*     .. External Subroutines ..
      EXTERNAL           zhbmv
*     ..
*     .. 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 = dlamch( 'Epsilon' )
      anorm = zlanhb( '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 zhbmv( uplo, n, kd, -cone, a, lda, x( 1, j ), 1, cone,
     $               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 = dzasum( n, b( 1, j ), 1 )
         xnorm = dzasum( 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 ZPBT02
*

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