NAME

ZHPCON - estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF

SYNOPSIS

SUBROUTINE ZHPCON(
UPLO, N, AP, IPIV, ANORM, RCOND, WORK, INFO )

CHARACTER UPLO

INTEGER INFO, N

DOUBLE PRECISION ANORM, RCOND

INTEGER IPIV( ∗ )

COMPLEX∗16 AP( ∗ ), WORK( ∗ )

PURPOSE

ZHPCON estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U∗D∗U∗∗H or A = L∗D∗L∗∗H computed by ZHPTRF. 
 
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM ∗ norm(inv(A))).
 

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) COMPLEX∗16 array, dimension (N∗(N+1)/2)
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.

IPIV    (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D as determined by ZHPTRF.

ANORM   (input) DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND   (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM ∗ AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

WORK    (workspace) COMPLEX∗16 array, dimension (2∗N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

  —  LAPACK version 2.0  —  08 October 1994