cpptri()

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

CPPTRI

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Purpose:

 CPPTRI 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 CPPTRF.

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 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

December 2016

Definition at line 95 of file cpptri.f.

*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, N
*     ..
*     .. Array Arguments ..
      COMPLEX            AP( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE
      parameter( one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            UPPER
      INTEGER            J, JC, JJ, JJN
      REAL               AJJ
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      COMPLEX            CDOTC
      EXTERNAL           lsame, cdotc
*     ..
*     .. External Subroutines ..
      EXTERNAL           chpr, csscal, ctpmv, ctptri, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          real
*     ..
*     .. 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( 'CPPTRI', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Invert the triangular Cholesky factor U or L.
*
      CALL ctptri( 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 chpr( 'Upper', j-1, one, ap( jc ), 1, ap )
            ajj = ap( jj )
            CALL csscal( 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 ) = real( cdotc( n-j+1, ap( jj ), 1, ap( jj ), 1 ) )
            IF( j.LT.n )
     $         CALL ctpmv( 'Lower', 'Conjugate transpose', 'Non-unit',
     $                     n-j, ap( jjn ), ap( jj+1 ), 1 )
            jj = jjn
   20    CONTINUE
      END IF
*
      RETURN
*
*     End of CPPTRI
*

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