Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3  -  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 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 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 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 subdiagonals 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 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 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 1-norm 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 i-th argument had an illegal value

LAPACK routine (version 3.3.1)             April 2011                            SPBCON(3lapack)