subroutine zpptri	(	character	UPLO,
		integer	N,
		complex*16, dimension( * )	AP,
		integer	INFO
	)

ZPPTRI

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Purpose:

 ZPPTRI computes the inverse of a complex Hermitian positive definite
 matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
 computed by ZPPTRF.

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 COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, 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 (Hermitian) 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 zpptri.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 ..
      COMPLEX*16         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
      COMPLEX*16         zdotc
      EXTERNAL           lsame, zdotc
*     ..
*     .. External Subroutines ..
      EXTERNAL           xerbla, zdscal, zhpr, ztpmv, ztptri
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble
*     ..
*     .. 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( 'ZPPTRI', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Invert the triangular Cholesky factor U or L.
*
      CALL ztptri( uplo, 'Non-unit', n, ap, info )
      IF( info.GT.0 )
     $   RETURN
      IF( upper ) THEN
*
*        Compute the product inv(U) * inv(U)**H.
*
         jj = 0
         DO 10 j = 1, n
            jc = jj + 1
            jj = jj + j
            IF( j.GT.1 )
     $         CALL zhpr( 'Upper', j-1, one, ap( jc ), 1, ap )
            ajj = ap( jj )
            CALL zdscal( j, ajj, ap( jc ), 1 )
   10    CONTINUE
*
      ELSE
*
*        Compute the product inv(L)**H * inv(L).
*
         jj = 1
         DO 20 j = 1, n
            jjn = jj + n - j + 1
            ap( jj ) = dble( zdotc( n-j+1, ap( jj ), 1, ap( jj ), 1 ) )
            IF( j.LT.n )
     $         CALL ztpmv( 'Lower', 'Conjugate transpose', 'Non-unit',
     $                     n-j, ap( jjn ), ap( jj+1 ), 1 )
            jj = jjn
   20    CONTINUE
      END IF
*
      RETURN
*
*     End of ZPPTRI
*

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