1DLANSB(1)           LAPACK auxiliary routine (version 3.1)           DLANSB(1)
2
3
4

NAME

6       DLANSB  -  the  value  of  the  one norm, or the Frobenius norm, or the
7       infinity norm, or the element of largest absolute value of an  n  by  n
8       symmetric band matrix A, with k super-diagonals
9

SYNOPSIS

11       DOUBLE PRECISION FUNCTION DLANSB( NORM, UPLO, N, K, AB, LDAB, WORK )
12
13           CHARACTER    NORM, UPLO
14
15           INTEGER      K, LDAB, N
16
17           DOUBLE       PRECISION AB( LDAB, * ), WORK( * )
18

PURPOSE

20       DLANSB   returns  the value of the one norm,  or the Frobenius norm, or
21       the  infinity norm,  or the element of  largest absolute value  of an n
22       by n symmetric band matrix A,  with k super-diagonals.
23
24

DESCRIPTION

26       DLANSB returns the value
27
28          DLANSB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
29                   (
30                   ( norm1(A),         NORM = '1', 'O' or 'o'
31                   (
32                   ( normI(A),         NORM = 'I' or 'i'
33                   (
34                   ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
35
36       where   norm1   denotes the  one norm of a matrix (maximum column sum),
37       normI  denotes the  infinity norm  of a matrix  (maximum row  sum)  and
38       normF   denotes  the  Frobenius norm of a matrix (square root of sum of
39       squares).  Note that  max(abs(A(i,j)))   is  not  a  consistent  matrix
40       norm.
41
42

ARGUMENTS

44       NORM    (input) CHARACTER*1
45               Specifies  the  value  to  be  returned  in DLANSB as described
46               above.
47
48       UPLO    (input) CHARACTER*1
49               Specifies whether the upper or lower  triangular  part  of  the
50               band  matrix  A  is supplied.  = 'U':  Upper triangular part is
51               supplied
52               = 'L':  Lower triangular part is supplied
53
54       N       (input) INTEGER
55               The order of the matrix A.  N >= 0.  When N = 0, DLANSB is  set
56               to zero.
57
58       K       (input) INTEGER
59               The  number  of  super-diagonals  or  sub-diagonals of the band
60               matrix A.  K >= 0.
61
62       AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
63               The upper or lower triangle of the  symmetric  band  matrix  A,
64               stored  in  the  first K+1 rows of AB.  The j-th column of A is
65               stored in the j-th column of the array AB as follows: if UPLO =
66               'U',  AB(k+1+i-j,j)  =  A(i,j)  for max(1,j-k)<=i<=j; if UPLO =
67               'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
68
69       LDAB    (input) INTEGER
70               The leading dimension of the array AB.  LDAB >= K+1.
71
72       WORK    (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
73               where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK
74               is not referenced.
75
76
77
78 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLANSB(1)