DGTCON (3lapack)

estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF

SYNOPSIS

  SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK,
                     IWORK, INFO )

      CHARACTER      NORM

      INTEGER        INFO, N

      DOUBLE         PRECISION ANORM, RCOND

      INTEGER        IPIV( * ), IWORK( * )

      DOUBLE         PRECISION D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )

PURPOSE

  DGTCON estimates the reciprocal of the condition number of a real
  tridiagonal matrix A using the LU factorization as computed by DGTTRF.

  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

  NORM    (input) CHARACTER*1
          Specifies whether the 1-norm condition number or the infinity-norm
          condition number is required:
          = '1' or 'O':  1-norm;
          = 'I':         Infinity-norm.

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

  DL      (input) DOUBLE PRECISION array, dimension (N-1)
          The (n-1) multipliers that define the matrix L from the LU
          factorization of A as computed by DGTTRF.

  D       (input) DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the upper triangular matrix U from the
          LU factorization of A.

  DU      (input) DOUBLE PRECISION array, dimension (N-1)
          The (n-1) elements of the first superdiagonal of U.

  DU2     (input) DOUBLE PRECISION array, dimension (N-2)
          The (n-2) elements of the second superdiagonal of U.

  IPIV    (input) INTEGER array, dimension (N)
          The pivot indices; for 1 <= i <= n, row i of the matrix was
          interchanged with row IPIV(i).  IPIV(i) will always be either i or
          i+1; IPIV(i) = i indicates a row interchange was not required.

  ANORM   (input) DOUBLE PRECISION
          If NORM = '1' or 'O', the 1-norm of the original matrix A.  If NORM
          = 'I', the infinity-norm of the original 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 (2*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