NAME¶

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

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.