ZHPTRI - compute the inverse of a complex Hermitian indef
inite 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 indefi
nite 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 mul
tipliers used to obtain the factor U or L as com
puted 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 struc
ture of D as determined by ZHPTRF.
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
gal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singu
lar and its inverse could not be computed.
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