*> \brief \b ZTPT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, * WORK, RWORK, RESID ) * * .. Scalar Arguments .. * CHARACTER DIAG, TRANS, UPLO * INTEGER LDB, LDX, N, NRHS * DOUBLE PRECISION RESID * .. * .. Array Arguments .. * DOUBLE PRECISION RWORK( * ) * COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZTPT02 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, when the triangular matrix A is stored in packed format. *> Here A**T denotes the transpose of A, A**H denotes 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 *> 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] AP *> \verbatim *> AP is COMPLEX*16 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*16 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*16 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*16 array, dimension (N) *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is DOUBLE PRECISION *> 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. * *> \ingroup complex16_lin * * ===================================================================== SUBROUTINE ZTPT02( 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 DOUBLE PRECISION RESID * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ) COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER J DOUBLE PRECISION ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DZASUM, ZLANTP EXTERNAL LSAME, DLAMCH, DZASUM, ZLANTP * .. * .. External Subroutines .. EXTERNAL ZAXPY, ZCOPY, ZTPMV * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX, 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 = ZLANTP( '1', UPLO, DIAG, N, AP, RWORK ) ELSE ANORM = ZLANTP( 'I', UPLO, DIAG, N, AP, RWORK ) 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 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 ZCOPY( N, X( 1, J ), 1, WORK, 1 ) CALL ZTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 ) CALL ZAXPY( N, DCMPLX( -ONE ), B( 1, J ), 1, WORK, 1 ) BNORM = DZASUM( N, WORK, 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 ZTPT02 * END