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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes the inverse of a complex Hermitian indefinite matrix A in packed storage using the factorization A = U*D*U**H

```NAME
LAPACK-3  -  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

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.

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
```