1SLANTB(1)           LAPACK auxiliary routine (version 3.2)           SLANTB(1)
2
3
4

NAME

6       SLANTB  -  returns the value of the one norm, or the Frobenius norm, or
7       the infinity norm, or the element of largest absolute value of an n  by
8       n triangular band matrix A, with ( k + 1 ) diagonals
9

SYNOPSIS

11       REAL FUNCTION SLANTB( NORM, UPLO, DIAG, N, K, AB, LDAB, WORK )
12
13           CHARACTER DIAG, NORM, UPLO
14
15           INTEGER   K, LDAB, N
16
17           REAL      AB( LDAB, * ), WORK( * )
18

PURPOSE

20       SLANTB   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 triangular band matrix A,  with ( k + 1 ) diagonals.
23

DESCRIPTION

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

ARGUMENTS

40       NORM    (input) CHARACTER*1
41               Specifies the value to  be  returned  in  SLANTB  as  described
42               above.
43
44       UPLO    (input) CHARACTER*1
45               Specifies whether the matrix A is upper or lower triangular.  =
46               'U':  Upper triangular
47               = 'L':  Lower triangular
48
49       DIAG    (input) CHARACTER*1
50               Specifies whether or not the matrix A is  unit  triangular.   =
51               'N':  Non-unit triangular
52               = 'U':  Unit triangular
53
54       N       (input) INTEGER
55               The  order of the matrix A.  N >= 0.  When N = 0, SLANTB is set
56               to zero.
57
58       K       (input) INTEGER
59               The number of super-diagonals of the matrix A if UPLO = 'U', or
60               the  number  of sub-diagonals of the matrix A if UPLO = 'L'.  K
61               >= 0.
62
63       AB      (input) REAL array, dimension (LDAB,N)
64               The upper or lower triangular band  matrix  A,  stored  in  the
65               first k+1 rows of AB.  The j-th column of A is stored in the j-
66               th column of the array AB as follows: if UPLO = 'U',  AB(k+1+i-
67               j,j)  = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
68               = A(i,j) for j<=i<=min(n,j+k).  Note that when DIAG = 'U',  the
69               elements of the array AB corresponding to the diagonal elements
70               of the matrix A are not referenced, but are assumed to be one.
71
72       LDAB    (input) INTEGER
73               The leading dimension of the array AB.  LDAB >= K+1.
74
75       WORK    (workspace) REAL array, dimension (MAX(1,LWORK)),
76               where LWORK >= N when NORM = 'I'; otherwise, WORK is not refer‐
77               enced.
78
79
80
81 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLANTB(1)