You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
217 lines
5.8 KiB
217 lines
5.8 KiB
2 years ago
|
*> \brief \b CPBT02
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE CPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
|
||
|
|
* RWORK, RESID )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* CHARACTER UPLO
|
||
|
|
* INTEGER KD, LDA, LDB, LDX, N, NRHS
|
||
|
|
* REAL RESID
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* REAL RWORK( * )
|
||
|
|
* COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> CPBT02 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.
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Arguments:
|
||
|
|
* ==========
|
||
|
|
*
|
||
|
|
*> \param[in] UPLO
|
||
|
|
*> \verbatim
|
||
|
|
*> 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
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] N
|
||
|
|
*> \verbatim
|
||
|
|
*> N is INTEGER
|
||
|
|
*> The number of rows and columns of the matrix A. N >= 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] KD
|
||
|
|
*> \verbatim
|
||
|
|
*> 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.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] NRHS
|
||
|
|
*> \verbatim
|
||
|
|
*> NRHS is INTEGER
|
||
|
|
*> The number of right hand sides. NRHS >= 0.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] A
|
||
|
|
*> \verbatim
|
||
|
|
*> A is COMPLEX 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 CPBTRF for further details.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDA
|
||
|
|
*> \verbatim
|
||
|
|
*> LDA is INTEGER.
|
||
|
|
*> The leading dimension of the array A. LDA >= max(1,KD+1).
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] X
|
||
|
|
*> \verbatim
|
||
|
|
*> X is COMPLEX array, dimension (LDX,NRHS)
|
||
|
|
*> The computed solution vectors for the system of linear
|
||
|
|
*> equations.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDX
|
||
|
|
*> \verbatim
|
||
|
|
*> LDX is INTEGER
|
||
|
|
*> The leading dimension of the array X. LDX >= max(1,N).
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in,out] B
|
||
|
|
*> \verbatim
|
||
|
|
*> B is COMPLEX 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.
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[in] LDB
|
||
|
|
*> \verbatim
|
||
|
|
*> LDB is INTEGER
|
||
|
|
*> The leading dimension of the array B. LDB >= max(1,N).
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] RWORK
|
||
|
|
*> \verbatim
|
||
|
|
*> RWORK is REAL array, dimension (N)
|
||
|
|
*> \endverbatim
|
||
|
|
*>
|
||
|
|
*> \param[out] RESID
|
||
|
|
*> \verbatim
|
||
|
|
*> RESID is REAL
|
||
|
|
*> The maximum over the number of right hand sides of
|
||
|
|
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
|
||
|
|
*> \endverbatim
|
||
|
|
*
|
||
|
|
* Authors:
|
||
|
|
* ========
|
||
|
|
*
|
||
|
|
*> \author Univ. of Tennessee
|
||
|
|
*> \author Univ. of California Berkeley
|
||
|
|
*> \author Univ. of Colorado Denver
|
||
|
|
*> \author NAG Ltd.
|
||
|
|
*
|
||
|
|
*> \ingroup complex_lin
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE CPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
|
||
|
|
$ RWORK, RESID )
|
||
|
|
*
|
||
|
|
* -- 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 RWORK( * )
|
||
|
|
COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
*
|
||
|
|
* .. Parameters ..
|
||
|
|
REAL ZERO, ONE
|
||
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
|
||
|
|
COMPLEX CONE
|
||
|
|
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
|
||
|
|
* ..
|
||
|
|
* .. Local Scalars ..
|
||
|
|
INTEGER J
|
||
|
|
REAL ANORM, BNORM, EPS, XNORM
|
||
|
|
* ..
|
||
|
|
* .. External Functions ..
|
||
|
|
REAL CLANHB, SCASUM, SLAMCH
|
||
|
|
EXTERNAL CLANHB, SCASUM, SLAMCH
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL CHBMV
|
||
|
|
* ..
|
||
|
|
* .. 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 = CLANHB( '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 CHBMV( 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 = SCASUM( N, B( 1, J ), 1 )
|
||
|
|
XNORM = SCASUM( 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 CPBT02
|
||
|
|
*
|
||
|
|
END
|