zla_lin_berr.f

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*> \brief \b ZLA_LIN_BERR computes a component-wise relative backward error.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
* 
*       .. Scalar Arguments ..
*       INTEGER            N, NZ, NRHS
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
*       COMPLEX*16         RES( N, NRHS )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*>    ZLA_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*16 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 DOUBLE PRECISION 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 zla_gerfsx_extended.f).
*> \endverbatim
*>     
*> \param[out] BERR
*> \verbatim
*>          BERR is DOUBLE PRECISION 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. 
*
*> \date June 2016
*
*> \ingroup complex16OTHERcomputational
*
*  =====================================================================
      SUBROUTINE zla_lin_berr ( N, NZ, NRHS, RES, AYB, BERR )
*
*  -- LAPACK computational routine (version 3.6.1) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..
      INTEGER            N, NZ, NRHS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   AYB( n, nrhs ), BERR( nrhs )
      COMPLEX*16         RES( n, nrhs )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      DOUBLE PRECISION   TMP
      INTEGER            I, J
      COMPLEX*16         CDUM
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, REAL, DIMAG, MAX
*     ..
*     .. External Functions ..
      EXTERNAL           dlamch
      DOUBLE PRECISION   DLAMCH
      DOUBLE PRECISION   SAFE1
*     ..
*     .. Statement Functions ..
      COMPLEX*16         CABS1
*     ..
*     .. Statement Function Definitions ..
      cabs1( cdum ) = abs( dble( cdum ) ) + abs( dimag( 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 = dlamch( 'Safe minimum' )
      safe1 = (nz+1)*safe1

      DO j = 1, nrhs
         berr(j) = 0.0d+0
         DO i = 1, n
            IF (ayb(i,j) .NE. 0.0d+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