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*> \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
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