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