.TH CLANTB 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CLANTB - 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 triangular band matrix A, with ( k + 1 ) diagonals .SH SYNOPSIS .TP 14 REAL FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK ) .TP 14 .ti +4 CHARACTER DIAG, NORM, UPLO .TP 14 .ti +4 INTEGER K, LDAB, N .TP 14 .ti +4 REAL WORK( * ) .TP 14 .ti +4 COMPLEX AB( LDAB, * ) .SH PURPOSE CLANTB 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 triangular band matrix A, with ( k + 1 ) diagonals. .SH DESCRIPTION CLANTB returns the value .br CLANTB = ( 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 CLANTB as described above. .TP 8 UPLO (input) CHARACTER*1 Specifies whether the matrix A is upper or lower triangular. = \(aqU\(aq: Upper triangular .br = \(aqL\(aq: Lower triangular .TP 8 DIAG (input) CHARACTER*1 Specifies whether or not the matrix A is unit triangular. = \(aqN\(aq: Non-unit triangular .br = \(aqU\(aq: Unit triangular .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. When N = 0, CLANTB is set to zero. .TP 8 K (input) INTEGER The number of super-diagonals of the matrix A if UPLO = \(aqU\(aq, or the number of sub-diagonals of the matrix A if UPLO = \(aqL\(aq. K >= 0. .TP 8 AB (input) COMPLEX array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = \(aqU\(aq, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = \(aqL\(aq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). Note that when DIAG = \(aqU\(aq, the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= K+1. .TP 8 WORK (workspace) REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = \(aqI\(aq; otherwise, WORK is not referenced.