.TH ZGBCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZGBCON - the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, .SH SYNOPSIS .TP 19 SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO ) .TP 19 .ti +4 CHARACTER NORM .TP 19 .ti +4 INTEGER INFO, KL, KU, LDAB, N .TP 19 .ti +4 DOUBLE PRECISION ANORM, RCOND .TP 19 .ti +4 INTEGER IPIV( * ) .TP 19 .ti +4 DOUBLE PRECISION RWORK( * ) .TP 19 .ti +4 COMPLEX*16 AB( LDAB, * ), WORK( * ) .SH PURPOSE ZGBCON estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGBTRF. .br An estimate is obtained for norm(inv(A)), and 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 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KL (input) INTEGER The number of subdiagonals within the band of A. KL >= 0. .TP 8 KU (input) INTEGER The number of superdiagonals within the band of A. KU >= 0. .TP 8 AB (input) COMPLEX*16 array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by ZGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1. .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). .TP 8 ANORM (input) DOUBLE PRECISION 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) DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). .TP 8 WORK (workspace) COMPLEX*16 array, dimension (2*N) .TP 8 RWORK (workspace) DOUBLE PRECISION array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value