.TH CTBCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CTBCON - the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm .SH SYNOPSIS .TP 19 SUBROUTINE CTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, RWORK, INFO ) .TP 19 .ti +4 CHARACTER DIAG, NORM, UPLO .TP 19 .ti +4 INTEGER INFO, KD, LDAB, N .TP 19 .ti +4 REAL RCOND .TP 19 .ti +4 REAL RWORK( * ) .TP 19 .ti +4 COMPLEX AB( LDAB, * ), WORK( * ) .SH PURPOSE CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as .br RCOND = 1 / ( norm(A) * norm(inv(A)) ). .br .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 UPLO (input) CHARACTER*1 .br = \(aqU\(aq: A is upper triangular; .br = \(aqL\(aq: A is lower triangular. .TP 8 DIAG (input) CHARACTER*1 .br = \(aqN\(aq: A is non-unit triangular; .br = \(aqU\(aq: A is unit triangular. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KD (input) INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. .TP 8 AB (input) COMPLEX array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = \(aqU\(aq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = \(aqL\(aq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = \(aqU\(aq, the diagonal elements of A are not referenced and are assumed to be 1. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. .TP 8 RCOND (output) REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). .TP 8 WORK (workspace) COMPLEX array, dimension (2*N) .TP 8 RWORK (workspace) REAL array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value