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Mise à jour globale de Lapack 3.2.2.

    1:       SUBROUTINE DPOEQUB( N, A, LDA, S, SCOND, AMAX, INFO )
    2: *
    3: *     -- LAPACK routine (version 3.2)                                 --
    4: *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
    5: *     -- Jason Riedy of Univ. of California Berkeley.                 --
    6: *     -- November 2008                                                --
    7: *
    8: *     -- LAPACK is a software package provided by Univ. of Tennessee, --
    9: *     -- Univ. of California Berkeley and NAG Ltd.                    --
   10: *
   11:       IMPLICIT NONE
   12: *     ..
   13: *     .. Scalar Arguments ..
   14:       INTEGER            INFO, LDA, N
   15:       DOUBLE PRECISION   AMAX, SCOND
   16: *     ..
   17: *     .. Array Arguments ..
   18:       DOUBLE PRECISION   A( LDA, * ), S( * )
   19: *     ..
   20: *
   21: *  Purpose
   22: *  =======
   23: *
   24: *  DPOEQU computes row and column scalings intended to equilibrate a
   25: *  symmetric positive definite matrix A and reduce its condition number
   26: *  (with respect to the two-norm).  S contains the scale factors,
   27: *  S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with
   28: *  elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal.  This
   29: *  choice of S puts the condition number of B within a factor N of the
   30: *  smallest possible condition number over all possible diagonal
   31: *  scalings.
   32: *
   33: *  Arguments
   34: *  =========
   35: *
   36: *  N       (input) INTEGER
   37: *          The order of the matrix A.  N >= 0.
   38: *
   39: *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
   40: *          The N-by-N symmetric positive definite matrix whose scaling
   41: *          factors are to be computed.  Only the diagonal elements of A
   42: *          are referenced.
   43: *
   44: *  LDA     (input) INTEGER
   45: *          The leading dimension of the array A.  LDA >= max(1,N).
   46: *
   47: *  S       (output) DOUBLE PRECISION array, dimension (N)
   48: *          If INFO = 0, S contains the scale factors for A.
   49: *
   50: *  SCOND   (output) DOUBLE PRECISION
   51: *          If INFO = 0, S contains the ratio of the smallest S(i) to
   52: *          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
   53: *          large nor too small, it is not worth scaling by S.
   54: *
   55: *  AMAX    (output) DOUBLE PRECISION
   56: *          Absolute value of largest matrix element.  If AMAX is very
   57: *          close to overflow or very close to underflow, the matrix
   58: *          should be scaled.
   59: *
   60: *  INFO    (output) INTEGER
   61: *          = 0:  successful exit
   62: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   63: *          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
   64: *
   65: *  =====================================================================
   66: *
   67: *     .. Parameters ..
   68:       DOUBLE PRECISION   ZERO, ONE
   69:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
   70: *     ..
   71: *     .. Local Scalars ..
   72:       INTEGER            I
   73:       DOUBLE PRECISION   SMIN, BASE, TMP
   74: *     ..
   75: *     .. External Functions ..
   76:       DOUBLE PRECISION   DLAMCH
   77:       EXTERNAL           DLAMCH
   78: *     ..
   79: *     .. External Subroutines ..
   80:       EXTERNAL           XERBLA
   81: *     ..
   82: *     .. Intrinsic Functions ..
   83:       INTRINSIC          MAX, MIN, SQRT, LOG, INT
   84: *     ..
   85: *     .. Executable Statements ..
   86: *
   87: *     Test the input parameters.
   88: *
   89: *     Positive definite only performs 1 pass of equilibration.
   90: *
   91:       INFO = 0
   92:       IF( N.LT.0 ) THEN
   93:          INFO = -1
   94:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
   95:          INFO = -3
   96:       END IF
   97:       IF( INFO.NE.0 ) THEN
   98:          CALL XERBLA( 'DPOEQUB', -INFO )
   99:          RETURN
  100:       END IF
  101: *
  102: *     Quick return if possible.
  103: *
  104:       IF( N.EQ.0 ) THEN
  105:          SCOND = ONE
  106:          AMAX = ZERO
  107:          RETURN
  108:       END IF
  109: 
  110:       BASE = DLAMCH( 'B' )
  111:       TMP = -0.5D+0 / LOG ( BASE )
  112: *
  113: *     Find the minimum and maximum diagonal elements.
  114: *
  115:       S( 1 ) = A( 1, 1 )
  116:       SMIN = S( 1 )
  117:       AMAX = S( 1 )
  118:       DO 10 I = 2, N
  119:          S( I ) = A( I, I )
  120:          SMIN = MIN( SMIN, S( I ) )
  121:          AMAX = MAX( AMAX, S( I ) )
  122:    10 CONTINUE
  123: *
  124:       IF( SMIN.LE.ZERO ) THEN
  125: *
  126: *        Find the first non-positive diagonal element and return.
  127: *
  128:          DO 20 I = 1, N
  129:             IF( S( I ).LE.ZERO ) THEN
  130:                INFO = I
  131:                RETURN
  132:             END IF
  133:    20    CONTINUE
  134:       ELSE
  135: *
  136: *        Set the scale factors to the reciprocals
  137: *        of the diagonal elements.
  138: *
  139:          DO 30 I = 1, N
  140:             S( I ) = BASE ** INT( TMP * LOG( S( I ) ) )
  141:    30    CONTINUE
  142: *
  143: *        Compute SCOND = min(S(I)) / max(S(I)).
  144: *
  145:          SCOND = SQRT( SMIN ) / SQRT( AMAX )
  146:       END IF
  147: *
  148:       RETURN
  149: *
  150: *     End of DPOEQUB
  151: *
  152:       END