dpotf2.f

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      SUBROUTINE dpotf2( UPLO, N, A, LDA, INFO )
*
*  -- LAPACK routine (version 3.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     February 29, 1992
*
*     .. 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