```      SUBROUTINE CPPTRF( UPLO, N, AP, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
CHARACTER          UPLO
INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
COMPLEX            AP( * )
*     ..
*
*  Purpose
*  =======
*
*  CPPTRF computes the Cholesky factorization of a complex Hermitian
*  positive definite matrix A stored in packed format.
*
*  The factorization has the form
*     A = U**H * U,  if UPLO = 'U', or
*     A = L  * L**H,  if UPLO = 'L',
*  where U is an upper triangular matrix and L is lower triangular.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  AP      (input/output) COMPLEX array, dimension (N*(N+1)/2)
*          On entry, the upper or lower triangle of the Hermitian matrix
*          A, packed columnwise in a linear array.  The j-th column of A
*          is stored in the array AP as follows:
*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
*          See below for further details.
*
*          On exit, if INFO = 0, the triangular factor U or L from the
*          Cholesky factorization A = U**H*U or A = L*L**H, in the same
*          storage format as A.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  if INFO = i, the leading minor of order i is not
*                positive definite, and the factorization could not be
*                completed.
*
*  Further Details
*  ===============
*
*  The packed storage scheme is illustrated by the following example
*  when N = 4, UPLO = 'U':
*
*  Two-dimensional storage of the Hermitian matrix A:
*
*     a11 a12 a13 a14
*         a22 a23 a24
*             a33 a34     (aij = conjg(aji))
*                 a44
*
*  Packed storage of the upper triangle of A:
*
*  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
*
*  =====================================================================
*
*     .. Parameters ..
REAL               ZERO, ONE
PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
*     ..
*     .. Local Scalars ..
LOGICAL            UPPER
INTEGER            J, JC, JJ
REAL               AJJ
*     ..
*     .. External Functions ..
LOGICAL            LSAME
COMPLEX            CDOTC
EXTERNAL           LSAME, CDOTC
*     ..
*     .. External Subroutines ..
EXTERNAL           CHPR, CSSCAL, CTPSV, XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          REAL, 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
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CPPTRF', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
IF( UPPER ) THEN
*
*        Compute the Cholesky factorization A = U'*U.
*
JJ = 0
DO 10 J = 1, N
JC = JJ + 1
JJ = JJ + J
*
*           Compute elements 1:J-1 of column J.
*
IF( J.GT.1 )
\$         CALL CTPSV( 'Upper', 'Conjugate transpose', 'Non-unit',
\$                     J-1, AP, AP( JC ), 1 )
*
*           Compute U(J,J) and test for non-positive-definiteness.
*
AJJ = REAL( AP( JJ ) ) - CDOTC( J-1, AP( JC ), 1, AP( JC ),
\$            1 )
IF( AJJ.LE.ZERO ) THEN
AP( JJ ) = AJJ
GO TO 30
END IF
AP( JJ ) = SQRT( AJJ )
10    CONTINUE
ELSE
*
*        Compute the Cholesky factorization A = L*L'.
*
JJ = 1
DO 20 J = 1, N
*
*           Compute L(J,J) and test for non-positive-definiteness.
*
AJJ = REAL( AP( JJ ) )
IF( AJJ.LE.ZERO ) THEN
AP( JJ ) = AJJ
GO TO 30
END IF
AJJ = SQRT( AJJ )
AP( JJ ) = AJJ
*
*           Compute elements J+1:N of column J and update the trailing
*           submatrix.
*
IF( J.LT.N ) THEN
CALL CSSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
CALL CHPR( 'Lower', N-J, -ONE, AP( JJ+1 ), 1,
\$                    AP( JJ+N-J+1 ) )
JJ = JJ + N - J + 1
END IF
20    CONTINUE
END IF
GO TO 40
*
30 CONTINUE
INFO = J
*
40 CONTINUE
RETURN
*
*     End of CPPTRF
*
END

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