cpbcon(3)

NAME

CPBCON - estimate the reciprocal of the condition number

(in the 1-norm) of a complex Hermitian positive definite band ma

trix using the Cholesky factorization A = U**H*U or A = L*L**H

computed by CPBTRF

SYNOPSIS

SUBROUTINE  CPBCON(  UPLO,  N, KD, AB, LDAB, ANORM, RCOND,
WORK, RWORK, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, KD, LDAB, N
    REAL           ANORM, RCOND
    REAL           RWORK( * )
    COMPLEX        AB( LDAB, * ), WORK( * )

PURPOSE

CPBCON estimates the reciprocal of the condition number

(in the 1-norm) of a complex Hermitian positive definite band ma

trix using the Cholesky factorization A = U**H*U or A = L*L**H

computed by CPBTRF. 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 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) REAL

The 1-norm (or infinity-norm) of the Hermitian

band matrix A.

RCOND (output) REAL

The reciprocal of the condition number of the ma

trix 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 array, dimension (2*N)

RWORK (workspace) REAL array, dimension (N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille

gal value

LAPACK version 3.0 15 June 2000

CPBCON(3)