zhpcon(l) - Linux man page

Name

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

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