# cgtcon.f - Man Page

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine cgtcon (character NORM, integer N, complex, dimension( * ) DL, complex, dimension( * ) D, complex, dimension( * ) DU, complex, dimension( * ) DU2, integer, dimension( * ) IPIV, real ANORM, real RCOND, complex, dimension( * ) WORK, integer INFO)

CGTCON

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))).```
Parameters:

NORM

```          NORM is 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

```          N is INTEGER
The order of the matrix A.  N >= 0.```

DL

```          DL is 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

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

DU

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

DU2

```          DU2 is COMPLEX array, dimension (N-2)
The (n-2) elements of the second superdiagonal of U.```

IPIV

```          IPIV is 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

```          ANORM is 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

```          RCOND is 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

`          WORK is COMPLEX array, dimension (2*N)`

INFO

```          INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value```
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

December 2016

Definition at line 143 of file cgtcon.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgtcon(3) is an alias of cgtcon.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK