cla_lin_berr()

subroutine cla_lin_berr	(	integer	N,
		integer	NZ,
		integer	NRHS,
		complex, dimension( n, nrhs )	RES,
		real, dimension( n, nrhs )	AYB,
		real, dimension( nrhs )	BERR
	)

CLA_LIN_BERR computes a component-wise relative backward error.

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Purpose:

    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.

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 array, dimension (N,NRHS) The residual matrix, i.e., the matrix R in the relative backward error formula above.
[in]	AYB	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).
[out]	BERR	BERR is REAL 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.

Date

June 2016

Definition at line 103 of file cla_lin_berr.f.

*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- 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 ..
      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

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