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Mise à jour globale de Lapack 3.2.2.

    1:       SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )
    2: *
    3: *  -- LAPACK 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:       INTEGER            INFO, N
   10:       DOUBLE PRECISION   ANORM, RCOND
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   D( * ), RWORK( * )
   14:       COMPLEX*16         E( * )
   15: *     ..
   16: *
   17: *  Purpose
   18: *  =======
   19: *
   20: *  ZPTCON computes the reciprocal of the condition number (in the
   21: *  1-norm) of a complex Hermitian positive definite tridiagonal matrix
   22: *  using the factorization A = L*D*L**H or A = U**H*D*U computed by
   23: *  ZPTTRF.
   24: *
   25: *  Norm(inv(A)) is computed by a direct method, and the reciprocal of
   26: *  the condition number is computed as
   27: *                   RCOND = 1 / (ANORM * norm(inv(A))).
   28: *
   29: *  Arguments
   30: *  =========
   31: *
   32: *  N       (input) INTEGER
   33: *          The order of the matrix A.  N >= 0.
   34: *
   35: *  D       (input) DOUBLE PRECISION array, dimension (N)
   36: *          The n diagonal elements of the diagonal matrix D from the
   37: *          factorization of A, as computed by ZPTTRF.
   38: *
   39: *  E       (input) COMPLEX*16 array, dimension (N-1)
   40: *          The (n-1) off-diagonal elements of the unit bidiagonal factor
   41: *          U or L from the factorization of A, as computed by ZPTTRF.
   42: *
   43: *  ANORM   (input) DOUBLE PRECISION
   44: *          The 1-norm of the original matrix A.
   45: *
   46: *  RCOND   (output) DOUBLE PRECISION
   47: *          The reciprocal of the condition number of the matrix A,
   48: *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
   49: *          1-norm of inv(A) computed in this routine.
   50: *
   51: *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
   52: *
   53: *  INFO    (output) INTEGER
   54: *          = 0:  successful exit
   55: *          < 0:  if INFO = -i, the i-th argument had an illegal value
   56: *
   57: *  Further Details
   58: *  ===============
   59: *
   60: *  The method used is described in Nicholas J. Higham, "Efficient
   61: *  Algorithms for Computing the Condition Number of a Tridiagonal
   62: *  Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
   63: *
   64: *  =====================================================================
   65: *
   66: *     .. Parameters ..
   67:       DOUBLE PRECISION   ONE, ZERO
   68:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   69: *     ..
   70: *     .. Local Scalars ..
   71:       INTEGER            I, IX
   72:       DOUBLE PRECISION   AINVNM
   73: *     ..
   74: *     .. External Functions ..
   75:       INTEGER            IDAMAX
   76:       EXTERNAL           IDAMAX
   77: *     ..
   78: *     .. External Subroutines ..
   79:       EXTERNAL           XERBLA
   80: *     ..
   81: *     .. Intrinsic Functions ..
   82:       INTRINSIC          ABS
   83: *     ..
   84: *     .. Executable Statements ..
   85: *
   86: *     Test the input arguments.
   87: *
   88:       INFO = 0
   89:       IF( N.LT.0 ) THEN
   90:          INFO = -1
   91:       ELSE IF( ANORM.LT.ZERO ) THEN
   92:          INFO = -4
   93:       END IF
   94:       IF( INFO.NE.0 ) THEN
   95:          CALL XERBLA( 'ZPTCON', -INFO )
   96:          RETURN
   97:       END IF
   98: *
   99: *     Quick return if possible
  100: *
  101:       RCOND = ZERO
  102:       IF( N.EQ.0 ) THEN
  103:          RCOND = ONE
  104:          RETURN
  105:       ELSE IF( ANORM.EQ.ZERO ) THEN
  106:          RETURN
  107:       END IF
  108: *
  109: *     Check that D(1:N) is positive.
  110: *
  111:       DO 10 I = 1, N
  112:          IF( D( I ).LE.ZERO )
  113:      $      RETURN
  114:    10 CONTINUE
  115: *
  116: *     Solve M(A) * x = e, where M(A) = (m(i,j)) is given by
  117: *
  118: *        m(i,j) =  abs(A(i,j)), i = j,
  119: *        m(i,j) = -abs(A(i,j)), i .ne. j,
  120: *
  121: *     and e = [ 1, 1, ..., 1 ]'.  Note M(A) = M(L)*D*M(L)'.
  122: *
  123: *     Solve M(L) * x = e.
  124: *
  125:       RWORK( 1 ) = ONE
  126:       DO 20 I = 2, N
  127:          RWORK( I ) = ONE + RWORK( I-1 )*ABS( E( I-1 ) )
  128:    20 CONTINUE
  129: *
  130: *     Solve D * M(L)' * x = b.
  131: *
  132:       RWORK( N ) = RWORK( N ) / D( N )
  133:       DO 30 I = N - 1, 1, -1
  134:          RWORK( I ) = RWORK( I ) / D( I ) + RWORK( I+1 )*ABS( E( I ) )
  135:    30 CONTINUE
  136: *
  137: *     Compute AINVNM = max(x(i)), 1<=i<=n.
  138: *
  139:       IX = IDAMAX( N, RWORK, 1 )
  140:       AINVNM = ABS( RWORK( IX ) )
  141: *
  142: *     Compute the reciprocal condition number.
  143: *
  144:       IF( AINVNM.NE.ZERO )
  145:      $   RCOND = ( ONE / AINVNM ) / ANORM
  146: *
  147:       RETURN
  148: *
  149: *     End of ZPTCON
  150: *
  151:       END