.TH CGTCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CGTCON - the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF .SH SYNOPSIS .TP 19 SUBROUTINE CGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, WORK, INFO ) .TP 19 .ti +4 CHARACTER NORM .TP 19 .ti +4 INTEGER INFO, N .TP 19 .ti +4 REAL ANORM, RCOND .TP 19 .ti +4 INTEGER IPIV( * ) .TP 19 .ti +4 COMPLEX D( * ), DL( * ), DU( * ), DU2( * ), WORK( * ) .SH 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))). .SH ARGUMENTS .TP 8 NORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: .br = \(aq1\(aq or \(aqO\(aq: 1-norm; .br = \(aqI\(aq: Infinity-norm. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 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. .TP 8 D (input) COMPLEX array, dimension (N) The n diagonal elements of the upper triangular matrix U from the LU factorization of A. .TP 8 DU (input) COMPLEX array, dimension (N-1) The (n-1) elements of the first superdiagonal of U. .TP 8 DU2 (input) COMPLEX array, dimension (N-2) The (n-2) elements of the second superdiagonal of U. .TP 8 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. .TP 8 ANORM (input) REAL If NORM = \(aq1\(aq or \(aqO\(aq, the 1-norm of the original matrix A. If NORM = \(aqI\(aq, the infinity-norm of the original matrix A. .TP 8 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. .TP 8 WORK (workspace) COMPLEX array, dimension (2*N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value