NAME

zhptri - compute 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 )

void zhptri(char uplo, long int n, doublecomplex ∗zap, long int ∗ipivot, long int ∗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.

Sun, Inc.  —  Last change: 20 Sep 1996