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

NAME

6       CLANHB  -  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       hermitian band matrix A, with k super-diagonals
9

SYNOPSIS

11       REAL FUNCTION CLANHB( NORM, UPLO, N, K, AB, LDAB, WORK )
12
13           CHARACTER NORM, UPLO
14
15           INTEGER   K, LDAB, N
16
17           REAL      WORK( * )
18
19           COMPLEX   AB( LDAB, * )
20

PURPOSE

22       CLANHB   returns  the value of the one norm,  or the Frobenius norm, or
23       the  infinity norm,  or the element of  largest absolute value  of an n
24       by n hermitian band matrix A,  with k super-diagonals.
25
26

DESCRIPTION

28       CLANHB returns the value
29
30          CLANHB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
31                   (
32                   ( norm1(A),         NORM = '1', 'O' or 'o'
33                   (
34                   ( normI(A),         NORM = 'I' or 'i'
35                   (
36                   ( normF(A),         NORM = 'F', 'f', 'E' or 'e'
37
38       where   norm1   denotes the  one norm of a matrix (maximum column sum),
39       normI  denotes the  infinity norm  of a matrix  (maximum row  sum)  and
40       normF   denotes  the  Frobenius norm of a matrix (square root of sum of
41       squares).  Note that  max(abs(A(i,j)))   is  not  a  consistent  matrix
42       norm.
43
44

ARGUMENTS

46       NORM    (input) CHARACTER*1
47               Specifies  the  value  to  be  returned  in CLANHB as described
48               above.
49
50       UPLO    (input) CHARACTER*1
51               Specifies whether the upper or lower  triangular  part  of  the
52               band matrix A is supplied.  = 'U':  Upper triangular
53               = 'L':  Lower triangular
54
55       N       (input) INTEGER
56               The  order of the matrix A.  N >= 0.  When N = 0, CLANHB is set
57               to zero.
58
59       K       (input) INTEGER
60               The number of super-diagonals  or  sub-diagonals  of  the  band
61               matrix A.  K >= 0.
62
63       AB      (input) COMPLEX array, dimension (LDAB,N)
64               The  upper  or  lower  triangle of the hermitian band matrix A,
65               stored in the first K+1 rows of AB.  The j-th column  of  A  is
66               stored in the j-th column of the array AB as follows: if UPLO =
67               'U', AB(k+1+i-j,j) = A(i,j) for  max(1,j-k)<=i<=j;  if  UPLO  =
68               'L',  AB(1+i-j,j)    =  A(i,j) for j<=i<=min(n,j+k).  Note that
69               the imaginary parts of the diagonal elements need  not  be  set
70               and are assumed to be zero.
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' or '1' or 'O'; otherwise, WORK
77               is not referenced.
78
79
80
81 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       CLANHB(1)
Impressum