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Mise à jour de lapack vers la version 3.3.0.

    1:       SUBROUTINE DLAQSY( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )
    2: *
    3: *  -- LAPACK auxiliary routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       CHARACTER          EQUED, UPLO
   10:       INTEGER            LDA, N
   11:       DOUBLE PRECISION   AMAX, SCOND
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   A( LDA, * ), S( * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  DLAQSY equilibrates a symmetric matrix A using the scaling factors
   21: *  in the vector S.
   22: *
   23: *  Arguments
   24: *  =========
   25: *
   26: *  UPLO    (input) CHARACTER*1
   27: *          Specifies whether the upper or lower triangular part of the
   28: *          symmetric matrix A is stored.
   29: *          = 'U':  Upper triangular
   30: *          = 'L':  Lower triangular
   31: *
   32: *  N       (input) INTEGER
   33: *          The order of the matrix A.  N >= 0.
   34: *
   35: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
   36: *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
   37: *          n by n upper triangular part of A contains the upper
   38: *          triangular part of the matrix A, and the strictly lower
   39: *          triangular part of A is not referenced.  If UPLO = 'L', the
   40: *          leading n by n lower triangular part of A contains the lower
   41: *          triangular part of the matrix A, and the strictly upper
   42: *          triangular part of A is not referenced.
   43: *
   44: *          On exit, if EQUED = 'Y', the equilibrated matrix:
   45: *          diag(S) * A * diag(S).
   46: *
   47: *  LDA     (input) INTEGER
   48: *          The leading dimension of the array A.  LDA >= max(N,1).
   49: *
   50: *  S       (input) DOUBLE PRECISION array, dimension (N)
   51: *          The scale factors for A.
   52: *
   53: *  SCOND   (input) DOUBLE PRECISION
   54: *          Ratio of the smallest S(i) to the largest S(i).
   55: *
   56: *  AMAX    (input) DOUBLE PRECISION
   57: *          Absolute value of largest matrix entry.
   58: *
   59: *  EQUED   (output) CHARACTER*1
   60: *          Specifies whether or not equilibration was done.
   61: *          = 'N':  No equilibration.
   62: *          = 'Y':  Equilibration was done, i.e., A has been replaced by
   63: *                  diag(S) * A * diag(S).
   64: *
   65: *  Internal Parameters
   66: *  ===================
   67: *
   68: *  THRESH is a threshold value used to decide if scaling should be done
   69: *  based on the ratio of the scaling factors.  If SCOND < THRESH,
   70: *  scaling is done.
   71: *
   72: *  LARGE and SMALL are threshold values used to decide if scaling should
   73: *  be done based on the absolute size of the largest matrix element.
   74: *  If AMAX > LARGE or AMAX < SMALL, scaling is done.
   75: *
   76: *  =====================================================================
   77: *
   78: *     .. Parameters ..
   79:       DOUBLE PRECISION   ONE, THRESH
   80:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
   81: *     ..
   82: *     .. Local Scalars ..
   83:       INTEGER            I, J
   84:       DOUBLE PRECISION   CJ, LARGE, SMALL
   85: *     ..
   86: *     .. External Functions ..
   87:       LOGICAL            LSAME
   88:       DOUBLE PRECISION   DLAMCH
   89:       EXTERNAL           LSAME, DLAMCH
   90: *     ..
   91: *     .. Executable Statements ..
   92: *
   93: *     Quick return if possible
   94: *
   95:       IF( N.LE.0 ) THEN
   96:          EQUED = 'N'
   97:          RETURN
   98:       END IF
   99: *
  100: *     Initialize LARGE and SMALL.
  101: *
  102:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
  103:       LARGE = ONE / SMALL
  104: *
  105:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
  106: *
  107: *        No equilibration
  108: *
  109:          EQUED = 'N'
  110:       ELSE
  111: *
  112: *        Replace A by diag(S) * A * diag(S).
  113: *
  114:          IF( LSAME( UPLO, 'U' ) ) THEN
  115: *
  116: *           Upper triangle of A is stored.
  117: *
  118:             DO 20 J = 1, N
  119:                CJ = S( J )
  120:                DO 10 I = 1, J
  121:                   A( I, J ) = CJ*S( I )*A( I, J )
  122:    10          CONTINUE
  123:    20       CONTINUE
  124:          ELSE
  125: *
  126: *           Lower triangle of A is stored.
  127: *
  128:             DO 40 J = 1, N
  129:                CJ = S( J )
  130:                DO 30 I = J, N
  131:                   A( I, J ) = CJ*S( I )*A( I, J )
  132:    30          CONTINUE
  133:    40       CONTINUE
  134:          END IF
  135:          EQUED = 'Y'
  136:       END IF
  137: *
  138:       RETURN
  139: *
  140: *     End of DLAQSY
  141: *
  142:       END