```      SUBROUTINE DPPTRI( 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 ..
DOUBLE PRECISION   AP( * )
*     ..
*
*  Purpose
*  =======
*
*  DPPTRI computes the inverse of a real symmetric positive definite
*  matrix A using the Cholesky factorization A = U**T*U or A = L*L**T
*  computed by DPPTRF.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangular factor is stored in AP;
*          = 'L':  Lower triangular factor is stored in AP.
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
*          On entry, the triangular factor U or L from the Cholesky
*          factorization A = U**T*U or A = L*L**T, packed columnwise as
*          a linear array.  The j-th column of U or L is stored in the
*          array AP as follows:
*          if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
*          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
*
*          On exit, the upper or lower triangle of the (symmetric)
*          inverse of A, overwriting the input factor U or L.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*          > 0:  if INFO = i, the (i,i) element of the factor U or L is
*                zero, and the inverse could not be computed.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   ONE
PARAMETER          ( ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
LOGICAL            UPPER
INTEGER            J, JC, JJ, JJN
DOUBLE PRECISION   AJJ
*     ..
*     .. External Functions ..
LOGICAL            LSAME
DOUBLE PRECISION   DDOT
EXTERNAL           LSAME, DDOT
*     ..
*     .. External Subroutines ..
EXTERNAL           DSCAL, DSPR, DTPMV, DTPTRI, XERBLA
*     ..
*     .. 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( 'DPPTRI', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 )
\$   RETURN
*
*     Invert the triangular Cholesky factor U or L.
*
CALL DTPTRI( UPLO, 'Non-unit', N, AP, INFO )
IF( INFO.GT.0 )
\$   RETURN
*
IF( UPPER ) THEN
*
*        Compute the product inv(U) * inv(U)'.
*
JJ = 0
DO 10 J = 1, N
JC = JJ + 1
JJ = JJ + J
IF( J.GT.1 )
\$         CALL DSPR( 'Upper', J-1, ONE, AP( JC ), 1, AP )
AJJ = AP( JJ )
CALL DSCAL( J, AJJ, AP( JC ), 1 )
10    CONTINUE
*
ELSE
*
*        Compute the product inv(L)' * inv(L).
*
JJ = 1
DO 20 J = 1, N
JJN = JJ + N - J + 1
AP( JJ ) = DDOT( N-J+1, AP( JJ ), 1, AP( JJ ), 1 )
IF( J.LT.N )
\$         CALL DTPMV( 'Lower', 'Transpose', 'Non-unit', N-J,
\$                     AP( JJN ), AP( JJ+1 ), 1 )
JJ = JJN
20    CONTINUE
END IF
*
RETURN
*
*     End of DPPTRI
*
END

```