NAME

CGTCON - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF

SYNOPSIS

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

CHARACTER NORM

INTEGER INFO, N

REAL ANORM, RCOND

INTEGER IPIV( ∗ )

COMPLEX D( ∗ ), DL( ∗ ), DU( ∗ ), DU2( ∗ ), WORK( ∗ )

PURPOSE

CGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF. 
 
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) COMPLEX array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.

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

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

DU2     (input) COMPLEX 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) REAL
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) 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) COMPLEX array, dimension (2∗N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

  —  LAPACK version 2.0  —  08 October 1994