244 lines
6.9 KiB
Fortran
244 lines
6.9 KiB
Fortran
*> \brief \b CTRT02
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
|
|
* LDB, WORK, RWORK, RESID )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER DIAG, TRANS, UPLO
|
|
* INTEGER LDA, LDB, LDX, N, NRHS
|
|
* REAL RESID
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* REAL RWORK( * )
|
|
* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
|
|
* $ X( LDX, * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CTRT02 computes the residual for the computed solution to a
|
|
*> triangular system of linear equations A*x = b, A**T *x = b,
|
|
*> or A**H *x = b. Here A is a triangular matrix, A**T is the transpose
|
|
*> of A, A**H is the conjugate transpose of A, and x and b are N by NRHS
|
|
*> matrices. The test ratio is the maximum over the number of right
|
|
*> hand sides of
|
|
*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
|
|
*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] UPLO
|
|
*> \verbatim
|
|
*> UPLO is CHARACTER*1
|
|
*> Specifies whether the matrix A is upper or lower triangular.
|
|
*> = 'U': Upper triangular
|
|
*> = 'L': Lower triangular
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] TRANS
|
|
*> \verbatim
|
|
*> TRANS is CHARACTER*1
|
|
*> Specifies the operation applied to A.
|
|
*> = 'N': A *x = b (No transpose)
|
|
*> = 'T': A**T *x = b (Transpose)
|
|
*> = 'C': A**H *x = b (Conjugate transpose)
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] DIAG
|
|
*> \verbatim
|
|
*> DIAG is CHARACTER*1
|
|
*> Specifies whether or not the matrix A is unit triangular.
|
|
*> = 'N': Non-unit triangular
|
|
*> = 'U': Unit triangular
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> 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 X and B. NRHS >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] A
|
|
*> \verbatim
|
|
*> A is COMPLEX array, dimension (LDA,N)
|
|
*> The triangular matrix A. If UPLO = 'U', the leading n by n
|
|
*> upper triangular part of the array A contains the upper
|
|
*> triangular matrix, and the strictly lower triangular part of
|
|
*> A is not referenced. If UPLO = 'L', the leading n by n lower
|
|
*> triangular part of the array A contains the lower triangular
|
|
*> matrix, and the strictly upper triangular part of A is not
|
|
*> referenced. If DIAG = 'U', the diagonal elements of A are
|
|
*> also not referenced and are assumed to be 1.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDA
|
|
*> \verbatim
|
|
*> LDA is INTEGER
|
|
*> The leading dimension of the array A. LDA >= max(1,N).
|
|
*> \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] B
|
|
*> \verbatim
|
|
*> B is COMPLEX array, dimension (LDB,NRHS)
|
|
*> The right hand side vectors for the system of linear
|
|
*> equations.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] LDB
|
|
*> \verbatim
|
|
*> LDB is INTEGER
|
|
*> The leading dimension of the array B. LDB >= max(1,N).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] WORK
|
|
*> \verbatim
|
|
*> WORK is COMPLEX array, dimension (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(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
|
|
*> \endverbatim
|
|
*
|
|
* Authors:
|
|
* ========
|
|
*
|
|
*> \author Univ. of Tennessee
|
|
*> \author Univ. of California Berkeley
|
|
*> \author Univ. of Colorado Denver
|
|
*> \author NAG Ltd.
|
|
*
|
|
*> \date December 2016
|
|
*
|
|
*> \ingroup complex_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE CTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
|
|
$ LDB, WORK, RWORK, RESID )
|
|
*
|
|
* -- 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 DIAG, TRANS, UPLO
|
|
INTEGER LDA, LDB, LDX, N, NRHS
|
|
REAL RESID
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL RWORK( * )
|
|
COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
|
|
$ X( LDX, * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
REAL ZERO, ONE
|
|
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER J
|
|
REAL ANORM, BNORM, EPS, XNORM
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
REAL CLANTR, SCASUM, SLAMCH
|
|
EXTERNAL LSAME, CLANTR, SCASUM, SLAMCH
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CAXPY, CCOPY, CTRMV
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC CMPLX, 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
|
|
*
|
|
* Compute the 1-norm of A or A**H.
|
|
*
|
|
IF( LSAME( TRANS, 'N' ) ) THEN
|
|
ANORM = CLANTR( '1', UPLO, DIAG, N, N, A, LDA, RWORK )
|
|
ELSE
|
|
ANORM = CLANTR( 'I', UPLO, DIAG, N, N, A, LDA, RWORK )
|
|
END IF
|
|
*
|
|
* Exit with RESID = 1/EPS if ANORM = 0.
|
|
*
|
|
EPS = SLAMCH( 'Epsilon' )
|
|
IF( ANORM.LE.ZERO ) THEN
|
|
RESID = ONE / EPS
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Compute the maximum over the number of right hand sides of
|
|
* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
|
|
*
|
|
RESID = ZERO
|
|
DO 10 J = 1, NRHS
|
|
CALL CCOPY( N, X( 1, J ), 1, WORK, 1 )
|
|
CALL CTRMV( UPLO, TRANS, DIAG, N, A, LDA, WORK, 1 )
|
|
CALL CAXPY( N, CMPLX( -ONE ), B( 1, J ), 1, WORK, 1 )
|
|
BNORM = SCASUM( N, WORK, 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 CTRT02
|
|
*
|
|
END
|