SPBCON(3)      LAPACK routine of NEC Numeric Library Collection      SPBCON(3)



NAME
       SPBCON

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



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)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangular factor stored in AB;
                     = 'L':  Lower triangular factor stored in AB.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           KD        (input)
                     KD is INTEGER
                     The number of superdiagonals of the matrix A if UPLO = 'U',
                     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

           AB        (input)
                     AB is 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)
                     LDAB is INTEGER
                     The leading dimension of the array AB.  LDAB >= KD+1.

           ANORM     (input)
                     ANORM is REAL
                     The 1-norm (or infinity-norm) of the symmetric band matrix A.

           RCOND     (output)
                     RCOND is 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      (output)
                     WORK is REAL array, dimension (3*N)

           IWORK     (output)
                     IWORK is INTEGER array, dimension (N)

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



LAPACK routine                  31 October 2017                      SPBCON(3)