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.
230 lines
6.3 KiB
230 lines
6.3 KiB
2 years ago
|
*> \brief \b CTPT02
|
||
|
|
*
|
||
|
|
* =========== DOCUMENTATION ===========
|
||
|
|
*
|
||
|
|
* Online html documentation available at
|
||
|
|
* http://www.netlib.org/lapack/explore-html/
|
||
|
|
*
|
||
|
|
* Definition:
|
||
|
|
* ===========
|
||
|
|
*
|
||
|
|
* SUBROUTINE CTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
|
||
|
|
* WORK, RWORK, RESID )
|
||
|
|
*
|
||
|
|
* .. Scalar Arguments ..
|
||
|
|
* CHARACTER DIAG, TRANS, UPLO
|
||
|
|
* INTEGER LDB, LDX, N, NRHS
|
||
|
|
* REAL RESID
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
* REAL RWORK( * )
|
||
|
|
* COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
|
||
|
|
* ..
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*> \par Purpose:
|
||
|
|
* =============
|
||
|
|
*>
|
||
|
|
*> \verbatim
|
||
|
|
*>
|
||
|
|
*> CTPT02 computes the residual for the computed solution to a
|
||
|
|
*> triangular system of linear equations op(A)*X = B, when the
|
||
|
|
*> triangular matrix A is stored in packed format. The test ratio is
|
||
|
|
*> the maximum over
|
||
|
|
*> norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
|
||
|
|
*> where op(A) = A, A**T, or A**H, b is the column of B, x is the
|
||
|
|
*> solution vector, 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] AP
|
||
|
|
*> \verbatim
|
||
|
|
*> AP is COMPLEX array, dimension (N*(N+1)/2)
|
||
|
|
*> The upper or lower triangular matrix A, packed columnwise in
|
||
|
|
*> a linear array. The j-th column of A is stored in the array
|
||
|
|
*> AP as follows:
|
||
|
|
*> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
|
||
|
|
*> if UPLO = 'L',
|
||
|
|
*> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=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)*B - 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.
|
||
|
|
*
|
||
|
|
*> \ingroup complex_lin
|
||
|
|
*
|
||
|
|
* =====================================================================
|
||
|
|
SUBROUTINE CTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
|
||
|
|
$ WORK, 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 DIAG, TRANS, UPLO
|
||
|
|
INTEGER LDB, LDX, N, NRHS
|
||
|
|
REAL RESID
|
||
|
|
* ..
|
||
|
|
* .. Array Arguments ..
|
||
|
|
REAL RWORK( * )
|
||
|
|
COMPLEX AP( * ), 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 CLANTP, SCASUM, SLAMCH
|
||
|
|
EXTERNAL LSAME, CLANTP, SCASUM, SLAMCH
|
||
|
|
* ..
|
||
|
|
* .. External Subroutines ..
|
||
|
|
EXTERNAL CAXPY, CCOPY, CTPMV
|
||
|
|
* ..
|
||
|
|
* .. 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 op(A).
|
||
|
|
*
|
||
|
|
IF( LSAME( TRANS, 'N' ) ) THEN
|
||
|
|
ANORM = CLANTP( '1', UPLO, DIAG, N, AP, RWORK )
|
||
|
|
ELSE
|
||
|
|
ANORM = CLANTP( 'I', UPLO, DIAG, N, AP, 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 CTPMV( UPLO, TRANS, DIAG, N, AP, 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 CTPT02
|
||
|
|
*
|
||
|
|
END
|