ZHPTRI (3lapack)

compute the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF

SYNOPSIS

  SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO )

      CHARACTER      UPLO

      INTEGER        INFO, N

      INTEGER        IPIV( * )

      COMPLEX*16     AP( * ), WORK( * )

PURPOSE

  ZHPTRI computes the inverse of a complex Hermitian indefinite matrix A in
  packed storage using the factorization A = U*D*U**H or A = L*D*L**H
  computed by ZHPTRF.

ARGUMENTS

  UPLO    (input) CHARACTER*1
          Specifies whether the details of the factorization are stored as an
          upper or lower triangular matrix.  = 'U':  Upper triangular, form
          is A = U*D*U**H;
          = 'L':  Lower triangular, form is A = L*D*L**H.

  N       (input) INTEGER
          The order of the matrix A.  N >= 0.

  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
          On entry, the block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by ZHPTRF, stored as a packed
          triangular matrix.

          On exit, if INFO = 0, the (Hermitian) inverse of the original
          matrix, stored as a packed triangular matrix. The j-th column of
          inv(A) is stored in the array AP as follows: if UPLO = 'U', AP(i +
          (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-
          1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.

  IPIV    (input) INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D as
          determined by ZHPTRF.

  WORK    (workspace) COMPLEX*16 array, dimension (N)

  INFO    (output) INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
          inverse could not be computed.