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# zhetri

```
NAME
ZHETRI - compute the inverse of a complex Hermitian indefin-
ite 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 indefin-
ite 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 multi-
pliers 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 triangu-
lar 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 refer-
enced.

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.
```