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*> \brief \b ZGTT02
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
* RESID )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER LDB, LDX, N, NRHS
* DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
* COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
* $ X( LDX, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGTT02 computes the residual for the solution to a tridiagonal
*> system of equations:
*> RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS),
*> where EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER
*> Specifies the form of the residual.
*> = 'N': B - A * X (No transpose)
*> = 'T': B - A**T * X (Transpose)
*> = 'C': B - A**H * X (Conjugate transpose)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGTER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrices B and X. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] DL
*> \verbatim
*> DL is COMPLEX*16 array, dimension (N-1)
*> The (n-1) sub-diagonal elements of A.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is COMPLEX*16 array, dimension (N)
*> The diagonal elements of A.
*> \endverbatim
*>
*> \param[in] DU
*> \verbatim
*> DU is COMPLEX*16 array, dimension (N-1)
*> The (n-1) super-diagonal elements of A.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is COMPLEX*16 array, dimension (LDX,NRHS)
*> The computed solution vectors X.
*> \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*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 - op(A)*X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(B - op(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.
*
*> \date November 2011
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB,
$ RESID )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER LDB, LDX, N, NRHS
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
$ X( LDX, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER J
DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, DZASUM, ZLANGT
EXTERNAL LSAME, DLAMCH, DZASUM, ZLANGT
* ..
* .. External Subroutines ..
EXTERNAL ZLAGTM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0 or NRHS = 0
*
RESID = ZERO
IF( N.LE.0 .OR. NRHS.EQ.0 )
$ RETURN
*
* Compute the maximum over the number of right hand sides of
* norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ).
*
IF( LSAME( TRANS, 'N' ) ) THEN
ANORM = ZLANGT( '1', N, DL, D, DU )
ELSE
ANORM = ZLANGT( 'I', N, DL, D, DU )
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = DLAMCH( 'Epsilon' )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute B - op(A)*X.
*
CALL ZLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B,
$ LDB )
*
DO 10 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
10 CONTINUE
*
RETURN
*
* End of ZGTT02
*
END
|
