dpotf2.f

          SUBROUTINE DPOTF2( UPLO, N, A, LDA, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, LDA, N
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DPOTF2 computes the Cholesky factorization of a real symmetric
    *  positive definite matrix A.
    *
    *  The factorization has the form
    *     A = U' * U ,  if UPLO = 'U', or
    *     A = L  * L',  if UPLO = 'L',
    *  where U is an upper triangular matrix and L is lower triangular.
    *
    *  This is the unblocked version of the algorithm, calling Level 2 BLAS.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          Specifies whether the upper or lower triangular part of the
    *          symmetric matrix A is stored.
    *          = 'U':  Upper triangular
    *          = 'L':  Lower triangular
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
    *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
    *          n by n upper triangular part of A contains the upper
    *          triangular part of the matrix A, and the strictly lower
    *          triangular part of A is not referenced.  If UPLO = 'L', the
    *          leading n by n lower triangular part of A contains the lower
    *          triangular part of the matrix A, and the strictly upper
    *          triangular part of A is not referenced.
    *
    *          On exit, if INFO = 0, the factor U or L from the Cholesky
    *          factorization A = U'*U  or A = L*L'.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(1,N).
    *
    *  INFO    (output) INTEGER
    *          = 0: successful exit
    *          < 0: if INFO = -k, the k-th argument had an illegal value
    *          > 0: if INFO = k, the leading minor of order k is not
    *               positive definite, and the factorization could not be
    *               completed.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          DOUBLE PRECISION   ONE, ZERO
          PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          INTEGER            J
          DOUBLE PRECISION   AJJ
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          DOUBLE PRECISION   DDOT
          EXTERNAL           LSAME, DDOT
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           DGEMV, DSCAL, XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          UPPER = LSAME( UPLO, 'U' )
          IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
             INFO = -4
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'DPOTF2', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 )
         $   RETURN
    *
          IF( UPPER ) THEN
    *
    *        Compute the Cholesky factorization A = U'*U.
    *
             DO 10 J = 1, N
    *
    *           Compute U(J,J) and test for non-positive-definiteness.
    *
                AJJ = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
                IF( AJJ.LE.ZERO ) THEN
                   A( J, J ) = AJJ
                   GO TO 30
                END IF
                AJJ = SQRT( AJJ )
                A( J, J ) = AJJ
    *
    *           Compute elements J+1:N of row J.
    *
                IF( J.LT.N ) THEN
                   CALL DGEMV( 'Transpose', J-1, N-J, -ONE, A( 1, J+1 ),
         $                     LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
                   CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
                END IF
       10    CONTINUE
          ELSE
    *
    *        Compute the Cholesky factorization A = L*L'.
    *
             DO 20 J = 1, N
    *
    *           Compute L(J,J) and test for non-positive-definiteness.
    *
                AJJ = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
         $            LDA )
                IF( AJJ.LE.ZERO ) THEN
                   A( J, J ) = AJJ
                   GO TO 30
                END IF
                AJJ = SQRT( AJJ )
                A( J, J ) = AJJ
    *
    *           Compute elements J+1:N of column J.
    *
                IF( J.LT.N ) THEN
                   CALL DGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ),
         $                     LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
                   CALL DSCAL( N-J, ONE / AJJ, A( J+1, J ), 1 )
                END IF
       20    CONTINUE
          END IF
          GO TO 40
    *
       30 CONTINUE
          INFO = J
    *
       40 CONTINUE
          RETURN
    *
    *     End of DPOTF2
    *
          END