---
name: "cgtcon.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/cgtcon.f"
---

# cgtcon.f(3)

## NAME

SRC/cgtcon.f

## 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.

Definition at line **139** of file **cgtcon.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.