ZHETRI (3lapack)

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

SYNOPSIS

  SUBROUTINE ZHETRI( UPLO, N, A, LDA, IPIV, WORK, INFO )

      CHARACTER      UPLO

      INTEGER        INFO, LDA, N

      INTEGER        IPIV( * )

      COMPLEX*16     A( LDA, * ), WORK( * )

PURPOSE

  ZHETRI computes the inverse of a complex Hermitian indefinite matrix A
  using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF.

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.

  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
          On entry, the block diagonal matrix D and the multipliers used to
          obtain the factor U or L as computed by ZHETRF.

          On exit, if INFO = 0, the (Hermitian) inverse of the original
          matrix.  If UPLO = 'U', the upper triangular part of the inverse is
          formed and the part of A below the diagonal is not referenced; if
          UPLO = 'L' the lower triangular part of the inverse is formed and
          the part of A above the diagonal is not referenced.

  LDA     (input) INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

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

  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.