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Mise à jour de Lapack vers la version 3.4.2 et des scripts de compilation
pour rplcas. En particulier, le Makefile.am de giac a été modifié pour ne
compiler que le répertoire src.

    1: *> \brief \b ZLA_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 ZLA_LIN_BERR + dependencies 
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_lin_berr.f"> 
   11: *> [TGZ]</a> 
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_lin_berr.f"> 
   13: *> [ZIP]</a> 
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_lin_berr.f"> 
   15: *> [TXT]</a>
   16: *> \endhtmlonly 
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE ZLA_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: *       COMPLEX*16         RES( N, NRHS )
   29: *       ..
   30: *  
   31: *
   32: *> \par Purpose:
   33: *  =============
   34: *>
   35: *> \verbatim
   36: *>
   37: *>    ZLA_LIN_BERR computes componentwise 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 componentwise 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 zla_gerfsx_extended.f).
   81: *> \endverbatim
   82: *>     
   83: *> \param[out] BERR
   84: *> \verbatim
   85: *>          BERR is COMPLEX*16 array, dimension (NRHS)
   86: *>     The componentwise 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: *> \date September 2012
   98: *
   99: *> \ingroup complex16OTHERcomputational
  100: *
  101: *  =====================================================================
  102:       SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
  103: *
  104: *  -- LAPACK computational routine (version 3.4.2) --
  105: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  106: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  107: *     September 2012
  108: *
  109: *     .. Scalar Arguments ..
  110:       INTEGER            N, NZ, NRHS
  111: *     ..
  112: *     .. Array Arguments ..
  113:       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
  114:       COMPLEX*16         RES( N, NRHS )
  115: *     ..
  116: *
  117: *  =====================================================================
  118: *
  119: *     .. Local Scalars ..
  120:       DOUBLE PRECISION   TMP
  121:       INTEGER            I, J
  122:       COMPLEX*16         CDUM
  123: *     ..
  124: *     .. Intrinsic Functions ..
  125:       INTRINSIC          ABS, REAL, DIMAG, MAX
  126: *     ..
  127: *     .. External Functions ..
  128:       EXTERNAL           DLAMCH
  129:       DOUBLE PRECISION   DLAMCH
  130:       DOUBLE PRECISION   SAFE1
  131: *     ..
  132: *     .. Statement Functions ..
  133:       COMPLEX*16         CABS1
  134: *     ..
  135: *     .. Statement Function Definitions ..
  136:       CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
  137: *     ..
  138: *     .. Executable Statements ..
  139: *
  140: *     Adding SAFE1 to the numerator guards against spuriously zero
  141: *     residuals.  A similar safeguard is in the CLA_yyAMV routine used
  142: *     to compute AYB.
  143: *
  144:       SAFE1 = DLAMCH( 'Safe minimum' )
  145:       SAFE1 = (NZ+1)*SAFE1
  146: 
  147:       DO J = 1, NRHS
  148:          BERR(J) = 0.0D+0
  149:          DO I = 1, N
  150:             IF (AYB(I,J) .NE. 0.0D+0) THEN
  151:                TMP = (SAFE1 + CABS1(RES(I,J)))/AYB(I,J)
  152:                BERR(J) = MAX( BERR(J), TMP )
  153:             END IF
  154: *
  155: *     If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
  156: *     the true residual also must be exactly 0.0.
  157: *
  158:          END DO
  159:       END DO
  160:       END