.TH ZHPTRI 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZHPTRI - 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 .SH SYNOPSIS .TP 19 SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, N .TP 19 .ti +4 INTEGER IPIV( * ) .TP 19 .ti +4 COMPLEX*16 AP( * ), WORK( * ) .SH 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. .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = \(aqU\(aq: Upper triangular, form is A = U*D*U**H; .br = \(aqL\(aq: Lower triangular, form is A = L*D*L**H. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 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 = \(aqU\(aq, AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; if UPLO = \(aqL\(aq, AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n. .TP 8 IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHPTRF. .TP 8 WORK (workspace) COMPLEX*16 array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value .br > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its inverse could not be computed.