ZGTCON(1) LAPACK routine (version 3.2) ZGTCON(1)NAME
ZGTCON - estimates the reciprocal of the condition number of a complex
tridiagonal matrix A using the LU factorization as computed by ZGTTRF
SYNOPSIS
SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK,
INFO )
CHARACTER NORM
INTEGER INFO, N
DOUBLE PRECISION ANORM, RCOND
INTEGER IPIV( * )
COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
PURPOSE
ZGTCON estimates the reciprocal of the condition number of a complex
tridiagonal matrix A using the LU factorization as computed by ZGTTRF.
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*16 array, dimension (N-1)
The (n-1) multipliers that define the matrix L from the LU fac‐
torization of A as computed by ZGTTRF.
D (input) COMPLEX*16 array, dimension (N)
The n diagonal elements of the upper triangular matrix U from
the LU factorization of A.
DU (input) COMPLEX*16 array, dimension (N-1)
The (n-1) elements of the first superdiagonal of U.
DU2 (input) COMPLEX*16 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, com‐
puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
mate of the 1-norm of inv(A) computed in this routine.
WORK (workspace) COMPLEX*16 array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
LAPACK routine (version 3.2) November 2008 ZGTCON(1)
