
ZPBCON(l) ) ZPBCON(l)
NAME
ZPBCON  estimate the reciprocal of the condition number (in the 1norm) of a complex Her
mitian positive definite band matrix using the Cholesky factorization A = U**H*U or A =
L*L**H computed by ZPBTRF
SYNOPSIS
SUBROUTINE ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO )
CHARACTER UPLO
INTEGER INFO, KD, LDAB, N
DOUBLE PRECISION ANORM, RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 AB( LDAB, * ), WORK( * )
PURPOSE
ZPBCON estimates the reciprocal of the condition number (in the 1norm) of a complex Her
mitian positive definite band matrix using the Cholesky factorization A = U**H*U or A =
L*L**H computed by ZPBTRF. 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
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub
diagonals if UPLO = 'L'. KD >= 0.
AB (input) COMPLEX*16 array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization A = U**H*U or A =
L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The jth
column of U or L is stored in the jth column of the array AB as follows: if UPLO
='U', AB(kd+1+ij,j) = U(i,j) for max(1,jkd)<=i<=j; if UPLO ='L', AB(1+ij,j)
= L(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
ANORM (input) DOUBLE PRECISION
The 1norm (or infinitynorm) of the Hermitian band 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 1norm 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 ith argument had an illegal value
LAPACK version 3.0 15 June 2000 ZPBCON(l) 
