Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  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 CPTTRF

```

#### SYNOPSIS

```       SUBROUTINE CPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )

INTEGER        INFO, N

REAL           ANORM, RCOND

REAL           D( * ), RWORK( * )

COMPLEX        E( * )

```

#### PURPOSE

```       CPTCON  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 CPTTRF.
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) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by CPTTRF.

E       (input) COMPLEX 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 CPTTRF.

ANORM   (input) REAL
The 1-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 the
1-norm of inv(A) computed in this routine.

RWORK   (workspace) REAL array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

```

#### FURTHERDETAILS

```        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.

LAPACK routine (version 3.3.1)             April 2011                            CPTCON(3lapack)
```