DPBCON 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 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))).

UPLO

          UPLO is CHARACTER*1


          = 'U':  Upper triangular factor stored in AB;


          = 'L':  Lower triangular factor stored in AB.

N

          N is INTEGER


          The order of the matrix A.  N >= 0.

KD

          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

          AB is 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 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

          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

ANORM

          ANORM is DOUBLE PRECISION


          The 1-norm (or infinity-norm) of the symmetric band matrix A.

RCOND

          RCOND is 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 1-norm of inv(A) computed in this routine.

WORK

          WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK

          IWORK is INTEGER array, dimension (N)

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011