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LAPACK-3

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LAPACK-3: estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as

```NAME
LAPACK-3  -  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 factorization 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,
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*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)     March 2011                       LAPACK-3(3)
```

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