DPBCON(3)

NAME
DPBCON - the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF

SYNOPSIS

SUBROUTINE DPBCON(
    UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO )

CHARACTER
    UPLO

INTEGER
    INFO, KD, LDAB, N

DOUBLE
    PRECISION ANORM, RCOND

INTEGER
    IWORK( * )

DOUBLE
    PRECISION AB( LDAB, * ), WORK( * )

PURPOSE
DPBCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite band matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF. 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 subdiagonals if UPLO = 'L'. KD >= 0.

AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
    The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T 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 symmetric 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) DOUBLE PRECISION array, dimension (3*N)

IWORK   (workspace) INTEGER array, dimension (N)

INFO    (output) INTEGER
    = 0: successful exit
    < 0: if INFO = -i, the i-th argument had an illegal value