*> \brief \b CQRT16 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, * RWORK, RESID ) * * .. Scalar Arguments .. * CHARACTER TRANS * INTEGER LDA, LDB, LDX, M, N, NRHS * REAL RESID * .. * .. Array Arguments .. * REAL RWORK( * ) * COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CQRT16 computes the residual for a solution of a system of linear *> equations A*x = b or A'*x = b: *> RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ), *> where EPS is the machine epsilon. *> \endverbatim * * Arguments: * ========== * *> \param[in] TRANS *> \verbatim *> TRANS is CHARACTER*1 *> Specifies the form of the system of equations: *> = 'N': A *x = b *> = 'T': A^T*x = b, where A^T is the transpose of A *> = 'C': A^H*x = b, where A^H is the conjugate transpose of A *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] NRHS *> \verbatim *> NRHS is INTEGER *> The number of columns of B, the matrix of right hand sides. *> NRHS >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension (LDA,N) *> The original M x N matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \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. If TRANS = 'N', *> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M). *> \endverbatim *> *> \param[in,out] B *> \verbatim *> B is COMPLEX 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 - A*X. *> \endverbatim *> *> \param[in] LDB *> \verbatim *> LDB is INTEGER *> The leading dimension of the array B. IF TRANS = 'N', *> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (M) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is REAL *> The maximum over the number of right hand sides of *> norm(B - A*X) / ( max(m,n) * 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 CQRT16( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, $ 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 TRANS INTEGER LDA, LDB, LDX, M, N, NRHS REAL RESID * .. * .. Array Arguments .. REAL RWORK( * ) COMPLEX A( LDA, * ), B( LDB, * ), X( LDX, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CONE PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER J, N1, N2 REAL ANORM, BNORM, EPS, XNORM * .. * .. External Functions .. LOGICAL LSAME REAL CLANGE, SCASUM, SLAMCH EXTERNAL LSAME, CLANGE, SCASUM, SLAMCH * .. * .. External Subroutines .. EXTERNAL CGEMM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Quick exit if M = 0 or N = 0 or NRHS = 0 * IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN RESID = ZERO RETURN END IF * IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN ANORM = CLANGE( 'I', M, N, A, LDA, RWORK ) N1 = N N2 = M ELSE ANORM = CLANGE( '1', M, N, A, LDA, RWORK ) N1 = M N2 = N END IF * EPS = SLAMCH( 'Epsilon' ) * * Compute B - A*X (or B - A'*X ) and store in B. * CALL CGEMM( TRANS, 'No transpose', N1, NRHS, N2, -CONE, A, LDA, X, $ LDX, CONE, B, LDB ) * * Compute the maximum over the number of right hand sides of * norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ) . * RESID = ZERO DO 10 J = 1, NRHS BNORM = SCASUM( N1, B( 1, J ), 1 ) XNORM = SCASUM( N2, X( 1, J ), 1 ) IF( ANORM.EQ.ZERO .AND. BNORM.EQ.ZERO ) THEN RESID = ZERO ELSE IF( ANORM.LE.ZERO .OR. XNORM.LE.ZERO ) THEN RESID = ONE / EPS ELSE RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / $ ( MAX( M, N )*EPS ) ) END IF 10 CONTINUE * RETURN * * End of CQRT16 * END