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    1: *> \brief \b DLA_LIN_BERR computes a component-wise relative backward error.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DLA_LIN_BERR + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_lin_berr.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_lin_berr.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_lin_berr.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DLA_LIN_BERR( N, NZ, NRHS, RES, AYB, BERR )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       INTEGER            N, NZ, NRHS
   25: *       ..
   26: *       .. Array Arguments ..
   27: *       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
   28: *       DOUBLE PRECISION   RES( N, NRHS )
   29: *       ..
   30: *
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *>    DLA_LIN_BERR computes component-wise relative backward error from
   38: *>    the formula
   39: *>        max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
   40: *>    where abs(Z) is the component-wise absolute value of the matrix
   41: *>    or vector Z.
   42: *> \endverbatim
   43: *
   44: *  Arguments:
   45: *  ==========
   46: *
   47: *> \param[in] N
   48: *> \verbatim
   49: *>          N is INTEGER
   50: *>     The number of linear equations, i.e., the order of the
   51: *>     matrix A.  N >= 0.
   52: *> \endverbatim
   53: *>
   54: *> \param[in] NZ
   55: *> \verbatim
   56: *>          NZ is INTEGER
   57: *>     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
   58: *>     guard against spuriously zero residuals. Default value is N.
   59: *> \endverbatim
   60: *>
   61: *> \param[in] NRHS
   62: *> \verbatim
   63: *>          NRHS is INTEGER
   64: *>     The number of right hand sides, i.e., the number of columns
   65: *>     of the matrices AYB, RES, and BERR.  NRHS >= 0.
   66: *> \endverbatim
   67: *>
   68: *> \param[in] RES
   69: *> \verbatim
   70: *>          RES is DOUBLE PRECISION array, dimension (N,NRHS)
   71: *>     The residual matrix, i.e., the matrix R in the relative backward
   72: *>     error formula above.
   73: *> \endverbatim
   74: *>
   75: *> \param[in] AYB
   76: *> \verbatim
   77: *>          AYB is DOUBLE PRECISION array, dimension (N, NRHS)
   78: *>     The denominator in the relative backward error formula above, i.e.,
   79: *>     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
   80: *>     are from iterative refinement (see dla_gerfsx_extended.f).
   81: *> \endverbatim
   82: *>
   83: *> \param[out] BERR
   84: *> \verbatim
   85: *>          BERR is DOUBLE PRECISION array, dimension (NRHS)
   86: *>     The component-wise relative backward error from the formula above.
   87: *> \endverbatim
   88: *
   89: *  Authors:
   90: *  ========
   91: *
   92: *> \author Univ. of Tennessee
   93: *> \author Univ. of California Berkeley
   94: *> \author Univ. of Colorado Denver
   95: *> \author NAG Ltd.
   96: *
   97: *> \ingroup doubleOTHERcomputational
   98: *
   99: *  =====================================================================
  100:       SUBROUTINE DLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
  101: *
  102: *  -- LAPACK computational routine --
  103: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  104: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  105: *
  106: *     .. Scalar Arguments ..
  107:       INTEGER            N, NZ, NRHS
  108: *     ..
  109: *     .. Array Arguments ..
  110:       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
  111:       DOUBLE PRECISION   RES( N, NRHS )
  112: *     ..
  113: *
  114: *  =====================================================================
  115: *
  116: *     .. Local Scalars ..
  117:       DOUBLE PRECISION   TMP
  118:       INTEGER            I, J
  119: *     ..
  120: *     .. Intrinsic Functions ..
  121:       INTRINSIC          ABS, MAX
  122: *     ..
  123: *     .. External Functions ..
  124:       EXTERNAL           DLAMCH
  125:       DOUBLE PRECISION   DLAMCH
  126:       DOUBLE PRECISION   SAFE1
  127: *     ..
  128: *     .. Executable Statements ..
  129: *
  130: *     Adding SAFE1 to the numerator guards against spuriously zero
  131: *     residuals.  A similar safeguard is in the SLA_yyAMV routine used
  132: *     to compute AYB.
  133: *
  134:       SAFE1 = DLAMCH( 'Safe minimum' )
  135:       SAFE1 = (NZ+1)*SAFE1
  136: 
  137:       DO J = 1, NRHS
  138:          BERR(J) = 0.0D+0
  139:          DO I = 1, N
  140:             IF (AYB(I,J) .NE. 0.0D+0) THEN
  141:                TMP = (SAFE1+ABS(RES(I,J)))/AYB(I,J)
  142:                BERR(J) = MAX( BERR(J), TMP )
  143:             END IF
  144: *
  145: *     If AYB is exactly 0.0 (and if computed by SLA_yyAMV), then we know
  146: *     the true residual also must be exactly 0.0.
  147: *
  148:          END DO
  149:       END DO
  150: *
  151: *     End of DLA_LIN_BERR
  152: *
  153:       END