154 lines
4.3 KiB
Fortran
154 lines
4.3 KiB
Fortran
*> \brief \b SLA_LIN_BERR computes a component-wise relative backward error.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download SLA_LIN_BERR + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_lin_berr.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sla_lin_berr.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_lin_berr.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
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*
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* .. Scalar Arguments ..
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* INTEGER N, NZ, NRHS
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* ..
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* .. Array Arguments ..
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* REAL AYB( N, NRHS ), BERR( NRHS )
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* REAL RES( N, NRHS )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SLA_LIN_BERR computes componentwise relative backward error from
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*> the formula
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*> max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
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*> where abs(Z) is the componentwise absolute value of the matrix
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*> or vector Z.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of linear equations, i.e., the order of the
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*> matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] NZ
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*> \verbatim
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*> NZ is INTEGER
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*> We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
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*> guard against spuriously zero residuals. Default value is N.
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*> \endverbatim
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*>
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*> \param[in] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides, i.e., the number of columns
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*> of the matrices AYB, RES, and BERR. NRHS >= 0.
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*> \endverbatim
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*>
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*> \param[in] RES
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*> \verbatim
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*> RES is REAL array, dimension (N,NRHS)
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*> The residual matrix, i.e., the matrix R in the relative backward
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*> error formula above.
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*> \endverbatim
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*>
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*> \param[in] AYB
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*> \verbatim
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*> AYB is REAL array, dimension (N, NRHS)
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*> The denominator in the relative backward error formula above, i.e.,
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*> the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
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*> are from iterative refinement (see sla_gerfsx_extended.f).
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*> \endverbatim
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*>
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*> \param[out] BERR
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*> \verbatim
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*> BERR is REAL array, dimension (NRHS)
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*> The componentwise relative backward error from the formula above.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup realOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE SLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
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*
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* -- LAPACK computational routine (version 3.7.0) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* December 2016
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*
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* .. Scalar Arguments ..
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INTEGER N, NZ, NRHS
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* ..
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* .. Array Arguments ..
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REAL AYB( N, NRHS ), BERR( NRHS )
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REAL RES( N, NRHS )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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REAL TMP
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INTEGER I, J
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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* ..
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* .. External Functions ..
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EXTERNAL SLAMCH
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REAL SLAMCH
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REAL SAFE1
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* ..
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* .. Executable Statements ..
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*
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* Adding SAFE1 to the numerator guards against spuriously zero
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* residuals. A similar safeguard is in the SLA_yyAMV routine used
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* to compute AYB.
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*
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SAFE1 = SLAMCH( 'Safe minimum' )
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SAFE1 = (NZ+1)*SAFE1
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DO J = 1, NRHS
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BERR(J) = 0.0
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DO I = 1, N
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IF (AYB(I,J) .NE. 0.0) THEN
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TMP = (SAFE1+ABS(RES(I,J)))/AYB(I,J)
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BERR(J) = MAX( BERR(J), TMP )
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END IF
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*
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* If AYB is exactly 0.0 (and if computed by SLA_yyAMV), then we know
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* the true residual also must be exactly 0.0.
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*
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END DO
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END DO
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END
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