ZPPCON(1) LAPACK routine (version 3.2) ZPPCON(1)NAME
ZPPCON - estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite packed matrix using
the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF
SYNOPSIS
SUBROUTINE ZPPCON( UPLO, N, AP, ANORM, RCOND, WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, N
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 AP( * ), WORK( * )
PURPOSE
ZPPCON estimates the reciprocal of the condition number (in the 1-norm)
of a complex Hermitian positive definite packed matrix using the
Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF. An
estimate is obtained for norm(inv(A)), and the reciprocal of the condi‐
tion number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
ARGUMENTS
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization A
= U**H*U or A = L*L**H, packed columnwise in a linear array.
The j-th column of U or L is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j; if UPLO
= 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
ANORM (input) DOUBLE PRECISION
The 1-norm (or infinity-norm) of the Hermitian matrix A.
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, com‐
puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
mate of the 1-norm of inv(A) computed in this routine.
WORK (workspace) COMPLEX*16 array, dimension (2*N)
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK routine (version 3.2) November 2008 ZPPCON(1)
