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spbcon

 NAME
      SPBCON - 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 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 fac-
              torization 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
              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) com-
              puted 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