ZPBCON(3f)

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

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
    = '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 j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', 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