subroutine dpptri	(	character	UPLO,
		integer	N,
		double precision, dimension( * )	AP,
		integer	INFO
	)

DPPTRI

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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.

Parameters

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangular factor is stored in AP; = 'L': Lower triangular factor is stored in AP.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in,out]	AP	AP is 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.
[out]	INFO	INFO is 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.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

November 2011

Definition at line 95 of file dpptri.f.

*
*  -- LAPACK computational routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      CHARACTER          uplo
      INTEGER            info, n
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   ap( * )
*     ..
*
*  =====================================================================
*
*     .. 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)**T.
*
         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)**T * 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
*

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