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

# zptcon(3lapack)

computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L\*D\*L\*\*H or A = U\*\*H\*D\*U computed by ZPTTRF

## NAME

ZPTCON - computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L\*D\*L\*\*H or A = U\*\*H\*D\*U computed by ZPTTRF

## SYNOPSIS

- SUBROUTINE ZPTCON(

  N, D, E, ANORM, RCOND, RWORK, INFO )

- INTEGER

  INFO, N

- DOUBLE

  PRECISION ANORM, RCOND

- DOUBLE

  PRECISION D( \* ), RWORK( \* )

- COMPLEX\*16

  E( \* )

## PURPOSE

ZPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L\*D\*L\*\*H or A = U\*\*H\*D\*U computed by ZPTTRF. Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as\
\
                  RCOND = 1 / (ANORM \* norm(inv(A))).\

## ARGUMENTS

- N (input) INTEGER

  The order of the matrix A.  N \>= 0.

- D (input) DOUBLE PRECISION array, dimension (N)

  The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by ZPTTRF.

- E (input) COMPLEX\*16 array, dimension (N-1)

  The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by ZPTTRF.

- ANORM (input) DOUBLE PRECISION

  The 1-norm of the original matrix A.

- RCOND (output) DOUBLE PRECISION

  The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM \* AINVNM), where AINVNM is the 1-norm of inv(A) computed in this routine.

- RWORK (workspace) DOUBLE PRECISION array, dimension (N)

  - INFO (output) INTEGER

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

## FURTHER DETAILS

The method used is described in Nicholas J. Higham, "Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.