slansb(3P)

NAME

slansb - return 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 symmetric band matrix A, with k super-diagonals

SYNOPSIS

REAL FUNCTION SLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )

CHARACTER NORM, UPLO

INTEGER K, LDAB, N

REAL AB( LDAB, ∗ ), WORK( ∗ )

#include <sunperf.h>

double slansb(char norm, char uplo, int n, int k, float ∗sab, int ldab ) ;

PURPOSE

SLANSB 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 symmetric band matrix A, with k super-diagonals.

DESCRIPTION

SLANSB returns the value

   SLANSB = ( max(abs(A(i,j))), NORM = ’M’ or ’m’
            (
            ( norm1(A),         NORM = ’1’, ’O’ or ’o’
            (
            ( normI(A),         NORM = ’I’ or ’i’
            (
            ( normF(A),         NORM = ’F’, ’f’, ’E’ or ’e’

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 matrix norm.

ARGUMENTS

NORM (input) CHARACTER∗1
Specifies the value to be returned in SLANSB as described above.

UPLO (input) CHARACTER∗1
Specifies whether the upper or lower triangular part of the band matrix A is supplied. = ’U’: Upper triangular part is supplied
= ’L’: Lower triangular part is supplied

N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, SLANSB is set to zero.

K (input) INTEGER
The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0.

AB (input) REAL array, dimension (LDAB,N)
The upper or lower triangle of the symmetric 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 = ’U’, AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = ’L’, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).

LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= K+1.

WORK (workspace) REAL array, dimension (LWORK),
where LWORK >= N when NORM = ’I’ or ’1’ or ’O’; otherwise, WORK is not referenced.