# cgtcon.f man page

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.

**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