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Première mise à jour de lapack et blas.

    1: *> \brief \b DLAS2 computes singular values of a 2-by-2 triangular matrix.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DLAS2 + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlas2.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlas2.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlas2.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
   22: *
   23: *       .. Scalar Arguments ..
   24: *       DOUBLE PRECISION   F, G, H, SSMAX, SSMIN
   25: *       ..
   26: *
   27: *
   28: *> \par Purpose:
   29: *  =============
   30: *>
   31: *> \verbatim
   32: *>
   33: *> DLAS2  computes the singular values of the 2-by-2 matrix
   34: *>    [  F   G  ]
   35: *>    [  0   H  ].
   36: *> On return, SSMIN is the smaller singular value and SSMAX is the
   37: *> larger singular value.
   38: *> \endverbatim
   39: *
   40: *  Arguments:
   41: *  ==========
   42: *
   43: *> \param[in] F
   44: *> \verbatim
   45: *>          F is DOUBLE PRECISION
   46: *>          The (1,1) element of the 2-by-2 matrix.
   47: *> \endverbatim
   48: *>
   49: *> \param[in] G
   50: *> \verbatim
   51: *>          G is DOUBLE PRECISION
   52: *>          The (1,2) element of the 2-by-2 matrix.
   53: *> \endverbatim
   54: *>
   55: *> \param[in] H
   56: *> \verbatim
   57: *>          H is DOUBLE PRECISION
   58: *>          The (2,2) element of the 2-by-2 matrix.
   59: *> \endverbatim
   60: *>
   61: *> \param[out] SSMIN
   62: *> \verbatim
   63: *>          SSMIN is DOUBLE PRECISION
   64: *>          The smaller singular value.
   65: *> \endverbatim
   66: *>
   67: *> \param[out] SSMAX
   68: *> \verbatim
   69: *>          SSMAX is DOUBLE PRECISION
   70: *>          The larger singular value.
   71: *> \endverbatim
   72: *
   73: *  Authors:
   74: *  ========
   75: *
   76: *> \author Univ. of Tennessee
   77: *> \author Univ. of California Berkeley
   78: *> \author Univ. of Colorado Denver
   79: *> \author NAG Ltd.
   80: *
   81: *> \ingroup OTHERauxiliary
   82: *
   83: *> \par Further Details:
   84: *  =====================
   85: *>
   86: *> \verbatim
   87: *>
   88: *>  Barring over/underflow, all output quantities are correct to within
   89: *>  a few units in the last place (ulps), even in the absence of a guard
   90: *>  digit in addition/subtraction.
   91: *>
   92: *>  In IEEE arithmetic, the code works correctly if one matrix element is
   93: *>  infinite.
   94: *>
   95: *>  Overflow will not occur unless the largest singular value itself
   96: *>  overflows, or is within a few ulps of overflow. (On machines with
   97: *>  partial overflow, like the Cray, overflow may occur if the largest
   98: *>  singular value is within a factor of 2 of overflow.)
   99: *>
  100: *>  Underflow is harmless if underflow is gradual. Otherwise, results
  101: *>  may correspond to a matrix modified by perturbations of size near
  102: *>  the underflow threshold.
  103: *> \endverbatim
  104: *>
  105: *  =====================================================================
  106:       SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )
  107: *
  108: *  -- LAPACK auxiliary routine --
  109: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  110: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  111: *
  112: *     .. Scalar Arguments ..
  113:       DOUBLE PRECISION   F, G, H, SSMAX, SSMIN
  114: *     ..
  115: *
  116: *  ====================================================================
  117: *
  118: *     .. Parameters ..
  119:       DOUBLE PRECISION   ZERO
  120:       PARAMETER          ( ZERO = 0.0D0 )
  121:       DOUBLE PRECISION   ONE
  122:       PARAMETER          ( ONE = 1.0D0 )
  123:       DOUBLE PRECISION   TWO
  124:       PARAMETER          ( TWO = 2.0D0 )
  125: *     ..
  126: *     .. Local Scalars ..
  127:       DOUBLE PRECISION   AS, AT, AU, C, FA, FHMN, FHMX, GA, HA
  128: *     ..
  129: *     .. Intrinsic Functions ..
  130:       INTRINSIC          ABS, MAX, MIN, SQRT
  131: *     ..
  132: *     .. Executable Statements ..
  133: *
  134:       FA = ABS( F )
  135:       GA = ABS( G )
  136:       HA = ABS( H )
  137:       FHMN = MIN( FA, HA )
  138:       FHMX = MAX( FA, HA )
  139:       IF( FHMN.EQ.ZERO ) THEN
  140:          SSMIN = ZERO
  141:          IF( FHMX.EQ.ZERO ) THEN
  142:             SSMAX = GA
  143:          ELSE
  144:             SSMAX = MAX( FHMX, GA )*SQRT( ONE+
  145:      $              ( MIN( FHMX, GA ) / MAX( FHMX, GA ) )**2 )
  146:          END IF
  147:       ELSE
  148:          IF( GA.LT.FHMX ) THEN
  149:             AS = ONE + FHMN / FHMX
  150:             AT = ( FHMX-FHMN ) / FHMX
  151:             AU = ( GA / FHMX )**2
  152:             C = TWO / ( SQRT( AS*AS+AU )+SQRT( AT*AT+AU ) )
  153:             SSMIN = FHMN*C
  154:             SSMAX = FHMX / C
  155:          ELSE
  156:             AU = FHMX / GA
  157:             IF( AU.EQ.ZERO ) THEN
  158: *
  159: *              Avoid possible harmful underflow if exponent range
  160: *              asymmetric (true SSMIN may not underflow even if
  161: *              AU underflows)
  162: *
  163:                SSMIN = ( FHMN*FHMX ) / GA
  164:                SSMAX = GA
  165:             ELSE
  166:                AS = ONE + FHMN / FHMX
  167:                AT = ( FHMX-FHMN ) / FHMX
  168:                C = ONE / ( SQRT( ONE+( AS*AU )**2 )+
  169:      $             SQRT( ONE+( AT*AU )**2 ) )
  170:                SSMIN = ( FHMN*C )*AU
  171:                SSMIN = SSMIN + SSMIN
  172:                SSMAX = GA / ( C+C )
  173:             END IF
  174:          END IF
  175:       END IF
  176:       RETURN
  177: *
  178: *     End of DLAS2
  179: *
  180:       END