*> \brief \b CLA_LIN_BERR computes a component-wise relative backward error.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
*
* .. Scalar Arguments ..
* INTEGER N, NZ, NRHS
* ..
* .. Array Arguments ..
* REAL AYB( N, NRHS ), BERR( NRHS )
* COMPLEX RES( N, NRHS )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CLA_LIN_BERR computes componentwise relative backward error from
*> the formula
*> max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
*> where abs(Z) is the componentwise absolute value of the matrix
*> or vector Z.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of linear equations, i.e., the order of the
*> matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NZ
*> \verbatim
*> NZ is INTEGER
*> We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
*> guard against spuriously zero residuals. Default value is N.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrices AYB, RES, and BERR. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] RES
*> \verbatim
*> RES is COMPLEX array, dimension (N,NRHS)
*> The residual matrix, i.e., the matrix R in the relative backward
*> error formula above.
*> \endverbatim
*>
*> \param[in] AYB
*> \verbatim
*> AYB is REAL array, dimension (N, NRHS)
*> The denominator in the relative backward error formula above, i.e.,
*> the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
*> are from iterative refinement (see cla_gerfsx_extended.f).
*> \endverbatim
*>
*> \param[out] BERR
*> \verbatim
*> BERR is REAL array, dimension (NRHS)
*> The componentwise relative backward error from the formula above.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexOTHERcomputational
*
* =====================================================================
SUBROUTINE CLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER N, NZ, NRHS
* ..
* .. Array Arguments ..
REAL AYB( N, NRHS ), BERR( NRHS )
COMPLEX RES( N, NRHS )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
REAL TMP
INTEGER I, J
COMPLEX CDUM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, REAL, AIMAG, MAX
* ..
* .. External Functions ..
EXTERNAL SLAMCH
REAL SLAMCH
REAL SAFE1
* ..
* .. Statement Functions ..
COMPLEX CABS1
* ..
* .. Statement Function Definitions ..
CABS1( CDUM ) = ABS( REAL( CDUM ) ) + ABS( AIMAG( CDUM ) )
* ..
* .. Executable Statements ..
*
* Adding SAFE1 to the numerator guards against spuriously zero
* residuals. A similar safeguard is in the CLA_yyAMV routine used
* to compute AYB.
*
SAFE1 = SLAMCH( 'Safe minimum' )
SAFE1 = (NZ+1)*SAFE1
DO J = 1, NRHS
BERR(J) = 0.0
DO I = 1, N
IF (AYB(I,J) .NE. 0.0) THEN
TMP = (SAFE1 + CABS1(RES(I,J)))/AYB(I,J)
BERR(J) = MAX( BERR(J), TMP )
END IF
*
* If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
* the true residual also must be exactly 0.0.
*
END DO
END DO
END