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217 lines
5.8 KiB
217 lines
5.8 KiB
2 years ago
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*> \brief \b ZPBT02
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
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* RWORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER KD, LDA, LDB, LDX, N, NRHS
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* DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZPBT02 computes the residual for a solution of a Hermitian banded
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*> system of equations A*x = b:
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*> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
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*> where EPS is the machine precision.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> Hermitian matrix A is stored:
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows and columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] KD
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*> \verbatim
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*> KD is INTEGER
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*> The number of super-diagonals of the matrix A if UPLO = 'U',
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*> or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> The original Hermitian band matrix A. If UPLO = 'U', the
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*> upper triangular part of A is stored as a band matrix; if
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*> UPLO = 'L', the lower triangular part of A is stored. The
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*> columns of the appropriate triangle are stored in the columns
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*> of A and the diagonals of the triangle are stored in the rows
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*> of A. See ZPBTRF for further details.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER.
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*> The leading dimension of the array A. LDA >= max(1,KD+1).
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*> \endverbatim
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*>
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*> \param[in] X
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*> \verbatim
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*> X is COMPLEX*16 array, dimension (LDX,NRHS)
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*> The computed solution vectors for the system of linear
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*> equations.
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*> \endverbatim
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*>
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*> \param[in] LDX
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*> \verbatim
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*> LDX is INTEGER
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*> The leading dimension of the array X. LDX >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in,out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (LDB,NRHS)
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*> On entry, the right hand side vectors for the system of
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*> linear equations.
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*> On exit, B is overwritten with the difference B - A*X.
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the array B. LDB >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is DOUBLE PRECISION
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*> The maximum over the number of right hand sides of
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*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
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$ RWORK, RESID )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER KD, LDA, LDB, LDX, N, NRHS
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DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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COMPLEX*16 CONE
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PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER J
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DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH, DZASUM, ZLANHB
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EXTERNAL DLAMCH, DZASUM, ZLANHB
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* ..
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* .. External Subroutines ..
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EXTERNAL ZHBMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0 or NRHS = 0.
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*
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IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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* Exit with RESID = 1/EPS if ANORM = 0.
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*
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EPS = DLAMCH( 'Epsilon' )
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ANORM = ZLANHB( '1', UPLO, N, KD, A, LDA, RWORK )
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IF( ANORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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RETURN
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END IF
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*
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* Compute B - A*X
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*
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DO 10 J = 1, NRHS
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CALL ZHBMV( UPLO, N, KD, -CONE, A, LDA, X( 1, J ), 1, CONE,
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$ B( 1, J ), 1 )
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10 CONTINUE
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*
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* Compute the maximum over the number of right hand sides of
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* norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
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*
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RESID = ZERO
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DO 20 J = 1, NRHS
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BNORM = DZASUM( N, B( 1, J ), 1 )
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XNORM = DZASUM( N, X( 1, J ), 1 )
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IF( XNORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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ELSE
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RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
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END IF
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20 CONTINUE
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*
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RETURN
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*
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* End of ZPBT02
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*
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END
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