SPBCON (3lapack)

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 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