# cgtcon.f man page

cgtcon.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine cgtcon (characterNORM, integerN, complex, dimension( * )DL, complex, dimension( * )D, complex, dimension( * )DU, complex, dimension( * )DU2, integer, dimension( * )IPIV, realANORM, realRCOND, complex, dimension( * )WORK, integerINFO)

**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:**

September 2012

Definition at line 141 of file cgtcon.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

cgtcon(3) is an alias of cgtcon.f(3).