SPBCON(3f)               LAPACK routine (version 3.1)               SPBCON(3f)



NAME
       SPBCON - 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 3.1)    November 2006                      SPBCON(3f)
