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Mise à jour globale de Lapack 3.2.2.

    1:       SUBROUTINE DLAQSP( UPLO, N, AP, 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            N
   11:       DOUBLE PRECISION   AMAX, SCOND
   12: *     ..
   13: *     .. Array Arguments ..
   14:       DOUBLE PRECISION   AP( * ), S( * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  DLAQSP 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: *  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
   36: *          On entry, the upper or lower triangle of the symmetric matrix
   37: *          A, packed columnwise in a linear array.  The j-th column of A
   38: *          is stored in the array AP as follows:
   39: *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
   40: *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
   41: *
   42: *          On exit, the equilibrated matrix:  diag(S) * A * diag(S), in
   43: *          the same storage format as A.
   44: *
   45: *  S       (input) DOUBLE PRECISION array, dimension (N)
   46: *          The scale factors for A.
   47: *
   48: *  SCOND   (input) DOUBLE PRECISION
   49: *          Ratio of the smallest S(i) to the largest S(i).
   50: *
   51: *  AMAX    (input) DOUBLE PRECISION
   52: *          Absolute value of largest matrix entry.
   53: *
   54: *  EQUED   (output) CHARACTER*1
   55: *          Specifies whether or not equilibration was done.
   56: *          = 'N':  No equilibration.
   57: *          = 'Y':  Equilibration was done, i.e., A has been replaced by
   58: *                  diag(S) * A * diag(S).
   59: *
   60: *  Internal Parameters
   61: *  ===================
   62: *
   63: *  THRESH is a threshold value used to decide if scaling should be done
   64: *  based on the ratio of the scaling factors.  If SCOND < THRESH,
   65: *  scaling is done.
   66: *
   67: *  LARGE and SMALL are threshold values used to decide if scaling should
   68: *  be done based on the absolute size of the largest matrix element.
   69: *  If AMAX > LARGE or AMAX < SMALL, scaling is done.
   70: *
   71: *  =====================================================================
   72: *
   73: *     .. Parameters ..
   74:       DOUBLE PRECISION   ONE, THRESH
   75:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
   76: *     ..
   77: *     .. Local Scalars ..
   78:       INTEGER            I, J, JC
   79:       DOUBLE PRECISION   CJ, LARGE, SMALL
   80: *     ..
   81: *     .. External Functions ..
   82:       LOGICAL            LSAME
   83:       DOUBLE PRECISION   DLAMCH
   84:       EXTERNAL           LSAME, DLAMCH
   85: *     ..
   86: *     .. Executable Statements ..
   87: *
   88: *     Quick return if possible
   89: *
   90:       IF( N.LE.0 ) THEN
   91:          EQUED = 'N'
   92:          RETURN
   93:       END IF
   94: *
   95: *     Initialize LARGE and SMALL.
   96: *
   97:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
   98:       LARGE = ONE / SMALL
   99: *
  100:       IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
  101: *
  102: *        No equilibration
  103: *
  104:          EQUED = 'N'
  105:       ELSE
  106: *
  107: *        Replace A by diag(S) * A * diag(S).
  108: *
  109:          IF( LSAME( UPLO, 'U' ) ) THEN
  110: *
  111: *           Upper triangle of A is stored.
  112: *
  113:             JC = 1
  114:             DO 20 J = 1, N
  115:                CJ = S( J )
  116:                DO 10 I = 1, J
  117:                   AP( JC+I-1 ) = CJ*S( I )*AP( JC+I-1 )
  118:    10          CONTINUE
  119:                JC = JC + J
  120:    20       CONTINUE
  121:          ELSE
  122: *
  123: *           Lower triangle of A is stored.
  124: *
  125:             JC = 1
  126:             DO 40 J = 1, N
  127:                CJ = S( J )
  128:                DO 30 I = J, N
  129:                   AP( JC+I-J ) = CJ*S( I )*AP( JC+I-J )
  130:    30          CONTINUE
  131:                JC = JC + N - J + 1
  132:    40       CONTINUE
  133:          END IF
  134:          EQUED = 'Y'
  135:       END IF
  136: *
  137:       RETURN
  138: *
  139: *     End of DLAQSP
  140: *
  141:       END