
SPBCON(l) ) SPBCON(l)
NAME
SPBCON  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 SPBTRF
SYNOPSIS
SUBROUTINE SPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, IWORK, INFO )
CHARACTER UPLO
INTEGER INFO, KD, LDAB, N
REAL ANORM, RCOND
INTEGER IWORK( * )
REAL AB( LDAB, * ), WORK( * )
PURPOSE
SPBCON 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 SPBTRF. 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) REAL 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) REAL
The 1norm (or infinitynorm) of the symmetric band matrix A.
RCOND (output) REAL
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) REAL 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 SPBCON(l) 
