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## 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

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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)

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