.TH CLANGB 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CLANGB - the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals .SH SYNOPSIS .TP 14 REAL FUNCTION CLANGB( NORM, N, KL, KU, AB, LDAB, WORK ) .TP 14 .ti +4 CHARACTER NORM .TP 14 .ti +4 INTEGER KL, KU, LDAB, N .TP 14 .ti +4 REAL WORK( * ) .TP 14 .ti +4 COMPLEX AB( LDAB, * ) .SH PURPOSE CLANGB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals. .SH DESCRIPTION CLANGB returns the value .br CLANGB = ( max(abs(A(i,j))), NORM = \(aqM\(aq or \(aqm\(aq .br ( .br ( norm1(A), NORM = \(aq1\(aq, \(aqO\(aq or \(aqo\(aq .br ( .br ( normI(A), NORM = \(aqI\(aq or \(aqi\(aq .br ( .br ( normF(A), NORM = \(aqF\(aq, \(aqf\(aq, \(aqE\(aq or \(aqe\(aq where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. .SH ARGUMENTS .TP 8 NORM (input) CHARACTER*1 Specifies the value to be returned in CLANGB as described above. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, CLANGB is set to zero. .TP 8 KL (input) INTEGER The number of sub-diagonals of the matrix A. KL >= 0. .TP 8 KU (input) INTEGER The number of super-diagonals of the matrix A. KU >= 0. .TP 8 AB (input) COMPLEX array, dimension (LDAB,N) The band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl). .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. .TP 8 WORK (workspace) REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = \(aqI\(aq; otherwise, WORK is not referenced.