---
name: "cgtcon"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/cgtcon/3lapack"
---

# cgtcon(3lapack)

estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF

## NAME

CGTCON - estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF

## SYNOPSIS

- SUBROUTINE CGTCON(

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

- CHARACTER

  NORM

- INTEGER

  INFO, N

- REAL

  ANORM, RCOND

- INTEGER

  IPIV( \* )

- COMPLEX

  D( \* ), DL( \* ), DU( \* ), DU2( \* ), WORK( \* )

## 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))).

## 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 array, dimension (N-1)

  The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.

- D (input) COMPLEX array, dimension (N)

  The n diagonal elements of the upper triangular matrix U from the LU factorization of A.

- DU (input) COMPLEX array, dimension (N-1)

  The (n-1) elements of the first superdiagonal of U.

- DU2 (input) COMPLEX 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) 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 (output) 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 (workspace) COMPLEX array, dimension (2\*N)

  - INFO (output) INTEGER

  \= 0:  successful exit\
   \< 0:  if INFO = -i, the i-th argument had an illegal value