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# zsptri

```
NAME
ZSPTRI - compute the inverse of a complex symmetric indefin-
ite matrix A in packed storage using the factorization A =
U*D*U**T or A = L*D*L**T computed by ZSPTRF

SYNOPSIS
SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO )

CHARACTER      UPLO

INTEGER        INFO, N

INTEGER        IPIV( * )

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

PURPOSE
ZSPTRI computes the inverse of a complex symmetric indefin-
ite matrix A in packed storage using the factorization A =
U*D*U**T or A = L*D*L**T computed by ZSPTRF.

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**T;
= 'L':  Lower triangular, form is A = L*D*L**T.

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 multi-
pliers used to obtain the factor U or L as computed
by ZSPTRF, stored as a packed triangular matrix.

On exit, if INFO = 0, the (symmetric) 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 ZSPTRF.

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.
```