zla_lin_berr()

subroutine zla_lin_berr	(	integer	n,
		integer	nz,
		integer	nrhs,
		complex*16, dimension( n, nrhs )	res,
		double precision, dimension( n, nrhs )	ayb,
		double precision, dimension( nrhs )	berr
	)

ZLA_LIN_BERR computes a component-wise relative backward error.

Download ZLA_LIN_BERR + dependencies [TGZ] [ZIP] [TXT]

Purpose:

    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.

Parameters

[in]	N	N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	NZ	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.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrices AYB, RES, and BERR. NRHS >= 0.
[in]	RES	RES is COMPLEX*16 array, dimension (N,NRHS) The residual matrix, i.e., the matrix R in the relative backward error formula above.
[in]	AYB	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).
[out]	BERR	BERR is DOUBLE PRECISION array, dimension (NRHS) The componentwise relative backward error from the formula above.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 100 of file zla_lin_berr.f.

*
*  -- 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 ..
      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 of ZLA_LIN_BERR
*

Here is the call graph for this function:

Here is the caller graph for this function: