DPBCON  -  estimate 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


SYNOPSIS

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

           CHARACTER      UPLO

           INTEGER        INFO, KD, LDAB, N

           DOUBLE         PRECISION ANORM, RCOND

           INTEGER        IWORK( * )

           DOUBLE         PRECISION AB( LDAB, * ), WORK( * )


PURPOSE

       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))).


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) 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    (input) INTEGER
               The leading dimension of the array  AB.   LDAB  >=


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

       RCOND   (output) 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    (workspace) DOUBLE PRECISION 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 ille­
               gal value


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