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Mise à jour de lapack vers la version 3.3.0.

    1:       SUBROUTINE DPOTF2( UPLO, N, A, LDA, 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:       CHARACTER          UPLO
   10:       INTEGER            INFO, LDA, N
   11: *     ..
   12: *     .. Array Arguments ..
   13:       DOUBLE PRECISION   A( LDA, * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  DPOTF2 computes the Cholesky factorization of a real symmetric
   20: *  positive definite matrix A.
   21: *
   22: *  The factorization has the form
   23: *     A = U' * U ,  if UPLO = 'U', or
   24: *     A = L  * L',  if UPLO = 'L',
   25: *  where U is an upper triangular matrix and L is lower triangular.
   26: *
   27: *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
   28: *
   29: *  Arguments
   30: *  =========
   31: *
   32: *  UPLO    (input) CHARACTER*1
   33: *          Specifies whether the upper or lower triangular part of the
   34: *          symmetric matrix A is stored.
   35: *          = 'U':  Upper triangular
   36: *          = 'L':  Lower triangular
   37: *
   38: *  N       (input) INTEGER
   39: *          The order of the matrix A.  N >= 0.
   40: *
   41: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
   42: *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
   43: *          n by n upper triangular part of A contains the upper
   44: *          triangular part of the matrix A, and the strictly lower
   45: *          triangular part of A is not referenced.  If UPLO = 'L', the
   46: *          leading n by n lower triangular part of A contains the lower
   47: *          triangular part of the matrix A, and the strictly upper
   48: *          triangular part of A is not referenced.
   49: *
   50: *          On exit, if INFO = 0, the factor U or L from the Cholesky
   51: *          factorization A = U'*U  or A = L*L'.
   52: *
   53: *  LDA     (input) INTEGER
   54: *          The leading dimension of the array A.  LDA >= max(1,N).
   55: *
   56: *  INFO    (output) INTEGER
   57: *          = 0: successful exit
   58: *          < 0: if INFO = -k, the k-th argument had an illegal value
   59: *          > 0: if INFO = k, the leading minor of order k is not
   60: *               positive definite, and the factorization could not be
   61: *               completed.
   62: *
   63: *  =====================================================================
   64: *
   65: *     .. Parameters ..
   66:       DOUBLE PRECISION   ONE, ZERO
   67:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
   68: *     ..
   69: *     .. Local Scalars ..
   70:       LOGICAL            UPPER
   71:       INTEGER            J
   72:       DOUBLE PRECISION   AJJ
   73: *     ..
   74: *     .. External Functions ..
   75:       LOGICAL            LSAME, DISNAN
   76:       DOUBLE PRECISION   DDOT
   77:       EXTERNAL           LSAME, DDOT, DISNAN
   78: *     ..
   79: *     .. External Subroutines ..
   80:       EXTERNAL           DGEMV, DSCAL, XERBLA
   81: *     ..
   82: *     .. Intrinsic Functions ..
   83:       INTRINSIC          MAX, SQRT
   84: *     ..
   85: *     .. Executable Statements ..
   86: *
   87: *     Test the input parameters.
   88: *
   89:       INFO = 0
   90:       UPPER = LSAME( UPLO, 'U' )
   91:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
   92:          INFO = -1
   93:       ELSE IF( N.LT.0 ) THEN
   94:          INFO = -2
   95:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
   96:          INFO = -4
   97:       END IF
   98:       IF( INFO.NE.0 ) THEN
   99:          CALL XERBLA( 'DPOTF2', -INFO )
  100:          RETURN
  101:       END IF
  102: *
  103: *     Quick return if possible
  104: *
  105:       IF( N.EQ.0 )
  106:      $   RETURN
  107: *
  108:       IF( UPPER ) THEN
  109: *
  110: *        Compute the Cholesky factorization A = U'*U.
  111: *
  112:          DO 10 J = 1, N
  113: *
  114: *           Compute U(J,J) and test for non-positive-definiteness.
  115: *
  116:             AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
  117:             IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
  118:                A( J, J ) = AJJ
  119:                GO TO 30
  120:             END IF
  121:             AJJ = SQRT( AJJ )
  122:             A( J, J ) = AJJ
  123: *
  124: *           Compute elements J+1:N of row J.
  125: *
  126:             IF( J.LT.N ) THEN
  127:                CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
  128:      $                     LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
  129:                CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
  130:             END IF
  131:    10    CONTINUE
  132:       ELSE
  133: *
  134: *        Compute the Cholesky factorization A = L*L'.
  135: *
  136:          DO 20 J = 1, N
  137: *
  138: *           Compute L(J,J) and test for non-positive-definiteness.
  139: *
  140:             AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
  141:      $            LDA )
  142:             IF( AJJ.LE.ZERO.OR.DISNAN( AJJ ) ) THEN
  143:                A( J, J ) = AJJ
  144:                GO TO 30
  145:             END IF
  146:             AJJ = SQRT( AJJ )
  147:             A( J, J ) = AJJ
  148: *
  149: *           Compute elements J+1:N of column J.
  150: *
  151:             IF( J.LT.N ) THEN
  152:                CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
  153:      $                     LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
  154:                CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
  155:             END IF
  156:    20    CONTINUE
  157:       END IF
  158:       GO TO 40
  159: *
  160:    30 CONTINUE
  161:       INFO = J
  162: *
  163:    40 CONTINUE
  164:       RETURN
  165: *
  166: *     End of DPOTF2
  167: *
  168:       END