# zsptri (l) - Linux Manuals

## NAME

ZSPTRI - computes the inverse of a complex symmetric indefinite 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 indefinite 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. = aqUaq: Upper triangular, form is A = U*D*U**T;
= aqLaq: 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 multipliers 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 = aqUaq, AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; if UPLO = aqLaq, 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.