194 lines
4.8 KiB
Fortran
194 lines
4.8 KiB
Fortran
*> \brief \b CPTT02
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CPTT02( UPLO, N, NRHS, D, E, X, LDX, B, LDB, RESID )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER LDB, LDX, N, NRHS
|
|
* REAL RESID
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL D( * )
|
|
* COMPLEX B( LDB, * ), E( * ), X( LDX, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CPTT02 computes the residual for the solution to a symmetric
|
|
*> tridiagonal system of equations:
|
|
*> RESID = norm(B - A*X) / (norm(A) * norm(X) * EPS),
|
|
*> where EPS is the machine epsilon.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] UPLO
|
|
*> \verbatim
|
|
*> UPLO is CHARACTER*1
|
|
*> Specifies whether the superdiagonal or the subdiagonal of the
|
|
*> tridiagonal matrix A is stored.
|
|
*> = 'U': E is the superdiagonal of A
|
|
*> = 'L': E is the subdiagonal of A
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The order of the matrix A.
|
|
*> \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] D
|
|
*> \verbatim
|
|
*> D is REAL array, dimension (N)
|
|
*> The n diagonal elements of the tridiagonal matrix A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] E
|
|
*> \verbatim
|
|
*> E is COMPLEX array, dimension (N-1)
|
|
*> The (n-1) subdiagonal elements of the tridiagonal matrix A.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] X
|
|
*> \verbatim
|
|
*> X is COMPLEX array, dimension (LDX,NRHS)
|
|
*> The n by nrhs matrix of 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 array, dimension (LDB,NRHS)
|
|
*> On entry, the n by nrhs matrix of right hand side vectors B.
|
|
*> 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] RESID
|
|
*> \verbatim
|
|
*> RESID is REAL
|
|
*> 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 CPTT02( UPLO, N, NRHS, D, E, X, LDX, B, LDB, 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 LDB, LDX, N, NRHS
|
|
REAL RESID
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL D( * )
|
|
COMPLEX B( LDB, * ), E( * ), X( LDX, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ONE, ZERO
|
|
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER J
|
|
REAL ANORM, BNORM, EPS, XNORM
|
|
* ..
|
|
* .. External Functions ..
|
|
REAL CLANHT, SCASUM, SLAMCH
|
|
EXTERNAL CLANHT, SCASUM, SLAMCH
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC MAX
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CLAPTM
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
* Quick return if possible
|
|
*
|
|
IF( N.LE.0 ) THEN
|
|
RESID = ZERO
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Compute the 1-norm of the tridiagonal matrix A.
|
|
*
|
|
ANORM = CLANHT( '1', N, D, E )
|
|
*
|
|
* Exit with RESID = 1/EPS if ANORM = 0.
|
|
*
|
|
EPS = SLAMCH( 'Epsilon' )
|
|
IF( ANORM.LE.ZERO ) THEN
|
|
RESID = ONE / EPS
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Compute B - A*X.
|
|
*
|
|
CALL CLAPTM( UPLO, N, NRHS, -ONE, D, E, X, LDX, ONE, B, LDB )
|
|
*
|
|
* Compute the maximum over the number of right hand sides of
|
|
* norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
|
|
*
|
|
RESID = ZERO
|
|
DO 10 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
|
|
10 CONTINUE
|
|
*
|
|
RETURN
|
|
*
|
|
* End of CPTT02
|
|
*
|
|
END
|