.TH SLANGB 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) "
.SH NAME
SLANGB - 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
SLANGB( 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
AB( LDAB, * ), WORK( * )
.SH PURPOSE
SLANGB 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
SLANGB returns the value
.br
SLANGB = ( 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 SLANGB as described
above.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, SLANGB 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) REAL 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.