# zpbcon (l) - Linux Manuals

## NAME

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

## 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 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))).

## ARGUMENTS

UPLO (input) CHARACTER*1
= aqUaq: Upper triangular factor stored in AB;
= aqLaq: 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 = aqUaq, or the number of sub-diagonals if UPLO = aqLaq. 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 j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO =aqUaq, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO =aqLaq, AB(1+i-j,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 1-norm (or infinity-norm) 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 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