
DPBCON(l) ) DPBCON(l)
NAME
DPBCON  estimate the reciprocal of the condition number (in the 1norm) of a real symmet
ric 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 1norm) of a real symmet
ric 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 sub
diagonals 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 jth
column of U or L is stored in the jth column of the array AB as follows: if UPLO
='U', AB(kd+1+ij,j) = U(i,j) for max(1,jkd)<=i<=j; if UPLO ='L', AB(1+ij,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 1norm (or infinitynorm) 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 1norm 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 ith argument had an illegal value
LAPACK version 3.0 15 June 2000 DPBCON(l) 
