 DGTCON(3) estimates 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