.TH ZPBCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
ZPBCON - the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
.SH SYNOPSIS
.TP 19
SUBROUTINE ZPBCON(
UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK,
RWORK, INFO )
.TP 19
.ti +4
CHARACTER
UPLO
.TP 19
.ti +4
INTEGER
INFO, KD, LDAB, N
.TP 19
.ti +4
DOUBLE
PRECISION ANORM, RCOND
.TP 19
.ti +4
DOUBLE
PRECISION RWORK( * )
.TP 19
.ti +4
COMPLEX*16
AB( LDAB, * ), WORK( * )
.SH PURPOSE
ZPBCON estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian 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))).
.SH ARGUMENTS
.TP 8
UPLO (input) CHARACTER*1
= \(aqU\(aq: Upper triangular factor stored in AB;
.br
= \(aqL\(aq: Lower triangular factor stored in AB.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = \(aqU\(aq,
or the number of sub-diagonals if UPLO = \(aqL\(aq. KD >= 0.
.TP 8
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 j-th column of U or L is
stored in the j-th column of the array AB as follows:
if UPLO =\(aqU\(aq, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =\(aqL\(aq, AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).
.TP 8
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
.TP 8
ANORM (input) DOUBLE PRECISION
The 1-norm (or infinity-norm) of the Hermitian band matrix A.
.TP 8
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.
.TP 8
WORK (workspace) COMPLEX*16 array, dimension (2*N)
.TP 8
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value